[1st Edition] 9780444634047, 9780444634054

Table of contents :
Content:
CopyrightPage iv
Introduction to the SeriesPage v
ContributorsPages xiii-xv
Editors' IntroductionPages xvii-xxJohn Piggott, Alan Woodland
AcknowledgmentsPage xxi
Chapter 1 - The Global Demography of Aging: Facts, Explanations, FuturePages 3-56D.E. Bloom, D.L. Luca
Chapter 2 - Macroeconomics, Aging, and GrowthPages 59-118R. Lee
Chapter 3 - Migration and the Demographic ShiftPages 119-177A. Zaiceva, K.F. Zimmermann
Chapter 4 - Global Demographic Trends: Consumption, Saving, and International Capital FlowsPages 179-235O. Attanasio, A. Bonfatti, S. Kitao, G. Weber
Chapter 5 - Insurance Markets for the ElderlyPages 237-309H. Fang
Chapter 6 - Intergenerational Risk SharingPages 311-380R. Beetsma, W. Romp
Chapter 7 - The Political Economy of Population AgingPages 381-444G. Casamatta, L. Batté
Chapter 8 - Retirement Incentives and Labor SupplyPages 457-566R. Blundell, E. French, G. Tetlow
Chapter 9 - Investing and Portfolio Allocation for RetirementPages 567-608B. Kaschützke, R. Maurer
Chapter 10 - Conflict and Cooperation Within the Family, and Between the State and the Family, in the Provision of Old-Age SecurityPages 609-660A. Cigno
Chapter 11 - Complex Decision Making: The Roles of Cognitive Limitations, Cognitive Decline, and AgingPages 661-709M.P. Keane, S. Thorp
Chapter 12 - Taxation, Pensions, and Demographic ChangePages 713-780A. Woodland
Chapter 13 - Social Security and Public InsurancePages 781-863A. Börsch-Supan, K. Härtl, D.N. Leite
Chapter 14 - Workplace-Linked Pensions for an Aging DemographicPages 865-904O.S. Mitchell, J. Piggott
Chapter 15 - Poverty and AgingPages 905-950J. Marchand, T. Smeeding
Chapter 16 - Health and Long-Term CarePages 951-989E.C. Norton
Chapter 17 - The HRS Around the World SurveysPages 993-1018L.I. Dobrescu, J.P. Smith
IndexPages I-1-I-22

Citation preview

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INTRODUCTION TO THE SERIES

The aim of the Handbooks in Economics series is to produce Handbooks for various branches of economics, each of which is a definitive source, reference, and teaching supplement for use by professional researchers and advanced graduate students. Each Handbook provides self-contained surveys of the current state of a branch of economics in the form of chapters prepared by leading specialists on various aspects of this branch of economics. These surveys summarize not only received results but also newer developments, from recent journal articles and discussion papers. Some original material is also included, but the main goal is to provide comprehensive and accessible surveys. The Handbooks are intended to provide not only useful reference volumes for professional collections but also possible supplementary readings for advanced courses for graduate students in economics. Kenneth J. Arrow and Michael D. Intriligator

v

CONTRIBUTORS

O. Attanasio University College London; Centre for Economic Policy Research (CEPR); Institute for Fiscal Studies (IFS), London, United Kingdom; National Bureau of Economic Research (NBER), Cambridge, MA, United States L. Batt
e Toulouse School of Economics (GREMAQ-CNRS and Centre for Economic Policy Research (CEPR)), Toulouse, France R. Beetsma Amsterdam School of Economics, University of Amsterdam, Amsterdam, The Netherlands; Network for Studies on Pensions, Aging and Retirement (Netspar), The Netherlands; Centre for Economic Policy Research (CEPR), London, United Kingdom; Center for Economic Studies and the Ifo Institute (CESifo), M€ unich, Germany D.E. Bloom Harvard T.H. Chan School of Public Health, Boston, MA, United States R. Blundell University College London and Institute for Fiscal Studies (IFS), London, United Kingdom A. Bonfatti University of Padua, Padua, Italy A. B€ orsch-Supan Munich Center for the Economics of Aging (MEA) at the Max Planck Institute for Social Law and Social Policy (MPISOC); Technical University of Munich, M€ unchen, Germany; National Bureau of Economic Research (NBER), Cambridge, MA, United States G. Casamatta Toulouse School of Economics (GREMAQ-CNRS and Centre for Economic Policy Research (CEPR)), Toulouse, France A. Cigno University of Florence, Firenze, Italy L.I. Dobrescu School of Economics and ARC Centre of Excellence in Population Ageing Research (CEPAR), University of New South Wales, Sydney, NSW, Australia H. Fang University of Pennsylvania, Philadelphia, PA; National Bureau of Economic Research (NBER), Cambridge, MA, United States; ARC Centre of Excellence in Population Ageing Research (CEPAR), University of New South Wales, Sydney, NSW, Australia E. French University College London and Institute for Fiscal Studies (IFS), London, United Kingdom K. H€artl Munich Center for the Economics of Aging (MEA) at the Max Planck Institute for Social Law and Social Policy (MPISOC), M€ unchen, Germany xiii

xiv

Contributors

B. Kasch€ utzke House of Finance, Goethe University Frankfurt, Frankfurt am Main, Germany M.P. Keane University of Oxford, Oxford, United Kingdom; School of Economics and the ARC Centre of Excellence in Population Ageing Research (CEPAR), University of New South Wales, Sydney, NSW, Australia S. Kitao Keio University, Tokyo, Japan R. Lee University of California, Berkeley, CA, United States D.N. Leite Munich Center for the Economics of Aging (MEA) at the Max Planck Institute for Social Law and Social Policy (MPISOC), M€ unchen, Germany; Center for Economics and Finance at University of Porto (CEF-UP), Porto, Portugal D.L. Luca Mathematica Policy Research, Cambridge, MA, United States J. Marchand University of Alberta, Edmonton, AB, Canada R. Maurer House of Finance, Goethe University Frankfurt, Frankfurt am Main, Germany O.S. Mitchell The Wharton School of the University of Pennsylvania, Philadelphia, PA, United States E.C. Norton University of Michigan and National Bureau of Economic Research (NBER), Ann Arbor, MI, United States J. Piggott ARC Centre of Excellence in Population Ageing Research (CEPAR), University of New South Wales, Sydney, NSW, Australia W. Romp Amsterdam School of Economics, University of Amsterdam, Amsterdam, The Netherlands T. Smeeding Robert M. La Follette School of Public Affairs, University of Wisconsin-Madison, Madison, WI, United States J.P. Smith RAND Corporation, Santa Monica, CA, United States G. Tetlow University College London and Institute for Fiscal Studies (IFS), London, United Kingdom S. Thorp The University of Sydney, Sydney, NSW, Australia

Contributors

G. Weber Centre for Economic Policy Research (CEPR); Institute for Fiscal Studies (IFS), London, United Kingdom; University of Padua, Padua, Italy A. Woodland School of Economics; ARC Centre of Excellence in Population Ageing Research (CEPAR), The University of New South Wales, Sydney, NSW, Australia A. Zaiceva University of Modena and Reggio Emilia, Modena, Italy; Institute for the Study of Labor (IZA), Bonn, Germany K.F. Zimmermann Harvard University, Cambridge, MA, United States; The United Nations University – Maastricht Economic and Social Research Institute on Innovation and Technology (UNU-MERIT), Maastricht, The Netherlands; Bonn University, Bonn, Germany

xv

EDITORS’ INTRODUCTION

Population aging is exerting unprecedented pressures on long-established social norms and policy institutions globally. Sustained falls in fertility and increasing life expectancy are raising deep questions about intergenerational exchange and equity and policy formulation, and will drive global movements in labor, capital, and trade in unknown ways over coming decades. Households are facing unfamiliar and complex yet critical life choices. Employers face the challenge of adapting to an older workforce. And governments under fiscal stress are retreating from the provision of retirement income and health care, raising new challenges for policy design and delivery and opportunities for the private sector in meeting the resource needs of older generations. The United Nations has described the phenomenon as pervasive (it is a global trend); unprecedented (never before has the world witnessed such a change); enduring (it is a change that is likely to be permanent); and profound (it affects all of us in our everyday lives). Managing these forces is a formidable task, requiring new knowledge and an evidence base that is still in the early stages of development. The need for an intensive and cuttingedge research effort related to demographic aging is documented in the international literature. General calls appear in, for example, the World Health Organization (2015) and the National Academy of Sciences (2012). The National Academies have also identified cognitive aging as a specific area of research need (Blazer et al., 2015). Population aging may be thought of as encompassing two related but distinct phenomena. First is the aging of the baby boomers. Second is the impact of population dynamics and evolving changes in demographic structure, nationally, regionally, and globally, comprising both national and regional shifts in fertility, along with the associated management of intergenerational relationships. The first of these is generally given more attention, because the challenges are very direct. In particular, retirement and retirement financing, health and aging, and aged care are all important priorities, requiring changes in policy formulation, business practice, and family behavior, all of which need to be informed by research. However, the longer-term influences of shifting population dynamics are also very important. The impact of generational imbalance on intergenerational solidarity, on taxation policy, on the structure of the labor force, and on intragenerational inequality and old age poverty are all topics requiring research to fully understand their contours and importance. Similarly, the implications of global population dynamics for trade, migration, and capital flows may be far-reaching, but have been little researched. This Handbook, in two volumes, aims to contribute to the accumulating knowledge base around population aging by bringing together some of the world’s leading

xvii

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Editors’ introduction

economists to provide perspectives from their field to understand the issue. Its objective is to gather into one place as much accumulated knowledge and insight as possible on the economic causes and consequences of demographic change, along with analyses of the policy responses that have emerged. The hope is that this will provide a base to inform and inspire future research in the field. It can be read either as a whole or as a source of expert knowledge on a specific topic. Volume 1A begins by documenting and explaining theories about demographic change, and then highlights macroeconomic and market adjustments. The underlying motivation here is to provide up-to-date syntheses of current economic thinking on the broad causes and consequences of population aging. Volume 1B drills down to analyze household behavior and policy response. Intergenerational transfers, of time, money, and other resources, are primarily transacted through family and government, so it is natural that these institutions receive emphasis. A concluding chapter describes the data infrastructure which has been built around older cohorts over the last quarter century, and which will provide an important basis for future empirical research in the field. Volume 1A opens with an account of the current state of empirical knowledge and theoretical structures to explain the phenomenon of population aging (Part I). This thorough overview provides the backdrop for much of the analysis to follow. It is important, when viewing population aging from a developed country perspective, to appreciate that data reliability varies widely across jurisdictions. Population data are regarded as highly reliable in the developed world, but in undeveloped and emerging economies, this is not always so. To give just one example, Indonesia, the world’s fourth most populous nation, is still struggling to determine how its demography is unfolding (McDonald, 2014). It is therefore important to begin the volume with what is known and what we understand about the demography of population aging. Part II examines both macroeconomic and specific market analyses to explore what we know about the overall economic impacts of population aging. It includes chapters devoted to macroeconomic and global analysis. They deal both with adjustments within a country, and with the interactions between regions with different demographic dynamics. These operate through various mechanisms, including capital and labor flows. A separate chapter is devoted to the links between migration and aging. This part also includes chapters analyzing the functioning of the insurance market in the face of an aging demographic, intergenerational risk-sharing, and the political economy of aging. Volume 1B begins with a group of chapters (Part III) designed to show how population aging impacts household decisions and behavior. These impacts can be direct, for example, through the influence of smaller families and longer life spans, and indirect, through fiscal adjustments that change the nature of household decision-making. Chapters cover labor market interaction and the retirement decision, perhaps the most important of these decisions, financial choices, and issues within the family. A striking feature of policy reform in the face of an aging demographic is that households

Editors’ introduction

and families are increasingly confronting complex choices that are unfamiliar. Part III concludes with a chapter on complex choices, cognition, and confusion. Part IV brings a policy perspective to demographic change. Chapters in this part cover the major areas of policy that are impacted by an aging demographic—taxation, health and long-term care, retirement incomes, and inequality. The taxation chapter begins by analyzing the fiscal implications of demographic change. It then discusses design issues, such as age-dependent taxation and the role of capital income taxation in an aging economy. Two chapters deal with retirement incomes, divided into a treatment of government-provided social security programs, and employer-based pensions, which are supported and regulated by policy structures. Workplace pensions are seen as having an important role in the future, as publicly provided retirement incomes face increasing fiscal stress. These are followed by a chapter focused on aging and poverty. Part IV concludes with a chapter on health and long-term care, which emphasizes this latter topic, now at the frontier of policy toward an aging demographic in many countries. Finally, a concluding chapter (Part V) reviews an important social science research infrastructure development—the establishment of multidisciplinary and nationally representative surveys of older cohorts over the last 30 years, and which now cover about two-thirds of the world’s population. These surveys, which are to a considerable extent harmonized between countries, generate an enormous potential for future research. Inevitably, in an enterprise of this kind, there are gaps. Important among these is a treatment of methodologies regarding mortality and morbidity projections. Official projections have over a long period of time systematically underestimated life-expectancy increase (Antolin, 2007, Table 3), with important consequences for estimates of future costs of social security. Research by academic actuaries and statistical demographers is shedding new light on approaches to these projections, which are crucial in arriving at well-informed household decisions and government policies in the future. Similarly, morbidity trends, and the important question of whether morbidity is expanding or compressing (relatively and absolutely) as life expectancy increases, remain unsettled in many countries. Neither does the Handbook explicitly cover infrastructure development, in particular housing. The role of housing in the context of population aging, both as a stream of services, which needs to adapt to an aging demographic as physical abilities and household structures change with age, and as a capital asset that can act as a stock of precautionary savings in later life, is clearly worthy of analysis. Housing also plays an important role in intergenerational transfers and consequently in influencing the intragenerational wealth distribution among younger cohorts, an important social development. Finally, the relationship between technology and population aging has not been much explored. For example, the role of research and development in reducing mature age mortality rates through improved health technology, especially for those living in developed countries, has been essential in increasing life expectancy at mature ages over the last

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Editors’ introduction

several decades. There are doubtless many other examples of how population aging and technical development might be related. Many other topics could have been reviewed. But we hope that those we have identified, and the contributors’ excellent analyses, will serve as a useful base for moving research on the economics of population aging forward. JOHN PIGGOTT ALAN WOODLAND

REFERENCES Antolin, P., 2007. Longevity risk and private pensions. In: OECD Working Paper on Insurance and Private Pensions. No. 3. Available at SSRN, http://ssrn.com/abstract¼962028 orhttp://dx.doi.org/10.2139/ ssrn.962028. Blazer, D.G., Yaffe, K., Liverman, C.T. (Eds.), 2015. Cognitive Aging: Progress in Understanding and Opportunities for Action. National Academies Press, Washington, D.C. McDonald, P., 2014. The demography of Indonesia in comparative perspective. Bull. Indones. Econ. Stud. 50 (1), 29–52. National Academy of Sciences, 2012. Aging and the Macroeconomy: Long-Term Implications of an Older Population. National Academy of Sciences, Washington, D.C. World Health Organization (WHO), 2015. World Report on Ageing and Health.

ACKNOWLEDGMENTS

We are deeply grateful to the contributors of this volume for their hard work on these chapters, and for the care they have taken in responding to our editorial requests. As editors, we followed a rigorous process of external review, with two external reviews sought, and in almost all cases delivered, for each chapter. This process, while time consuming, led to substantially improved chapters, and we would like to thank the reviewers for their insights. As many authors explicitly acknowledge, this process led to substantial improvements. This volume also benefited immensely from a workshop held in the Department of Global Health and Population, Harvard University, in October 2013. We are grateful to David Bloom for hosting the workshop and to the Harvard University Australian Studies Committee for support. The project has been supported throughout by the ARC Centre of Excellence in Population Ageing Research (CEPAR) (ARC Grant No. CE110001029).

xxi

CHAPTER 1

The Global Demography of Aging: Facts, Explanations, Future D.E. Bloom*, D.L. Luca† *

Harvard T.H. Chan School of Public Health, Boston, MA, United States Mathematica Policy Research, Cambridge, MA, United States

†

Contents 1. Introduction 2. Population Aging 2.1 Trends and Projections 2.2 Reliability of Population Projections 3. The Demographic Transition and Population Aging 3.1 The Historic Demographic Transition 3.2 The Ongoing Demographic Transition in Developing Countries 4. The Demographic Determinants of Population Aging 4.1 Decline in Fertility 4.1.1 4.1.2 4.1.3 4.1.4

Theoretical Framework Developed Countries Developing Countries The Future of Fertility

4.2 Increase in Life Expectancy 4.2.1 Developed Countries 4.2.2 Developing Countries 4.2.3 The Future of Mortality

4.3 Migration as a Determinant of the Age Structure 5. The Nature of Aging 5.1 The Rise of Noncommunicable Diseases 5.1.1 The Prevalence and Economic Costs of Dementia 5.1.2 The Risk Factors of NCDs and Policy Implications

5.2 The Question of Compression or Expansion of Morbidity 5.3 Living Arrangements for the Elderly 5.3.1 Developed Countries 5.3.2 Developing Countries

6. Open Research Questions 7. Concluding Remarks Acknowledgments References

Handbook of the Economics of Population Aging, Volume 1A ISSN 2212-0076, http://dx.doi.org/10.1016/bs.hespa.2016.06.002

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© 2016 Elsevier B.V. All rights reserved.

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Handbook of the Economics of Population Aging

Abstract Population aging is the 21st century's dominant demographic phenomenon. Declining fertility, increasing longevity, and the progression of large-sized cohorts to the older ages are causing elder shares to rise throughout the world. The phenomenon of population aging, which is unprecedented in human history, brings with it sweeping changes in population needs and capacities, with potentially significant implications for employment, savings, consumption, economic growth, asset values, and fiscal balance. This chapter provides a broad overview of the global demography of aging. It reviews patterns, trends, and projections involving various indicators of population aging and their demographic antecedents and sequelae. The chapter also reviews theories economists use to explain the behavioral changes driving the most prominent demographic shifts. Finally, it discusses the changing nature of aging, the future of longevity, and associated policy implications, highlighting some key research issues that require further examination.

Keywords Population aging, Economic demography, Longevity

JEL Classification Codes J11 (Demographic Trends, Macroeconomic Effects, and Forecasts), J14 (Economics of the Elderly), N30 (Economic History—Labor and Consumers, Demography, Education, Health, Welfare, Income, Wealth, Religion, and Philanthropy—General, International, or Comparative)

1. INTRODUCTION The world is experiencing a sea change in its population age structure. People are living longer lives, and the share of older people in the total population is expanding rapidly. Between 2005 and 2050, the proportion of the population aged 60 and older will increase in every country in the world. The number of centenarians worldwide will more than double by 2030, with nearly 3.4 million centenarians alive by 2050. Population aging has many societal and policy implications. The demographic shift threatens to lower labor force participation and savings rates, increase health expenditures, and strain pension and health schemes. The rising prevalence of noncommunicable diseases disproportionately burdens the elderly, and whether the additional years resulting from increased longevity will be characterized by ill health is unclear. Living arrangements for the elderly must be considered, and many are concerned that reduced labor force participation and savings and strains on pension and healthcare systems will slow economic growth. However, demographic change has historically spurred behavioral adjustments, and technological and institutional innovations may yet mitigate the effects of population aging. Examples of such innovations include modified retirement policies, womenfriendly work policies, changes in healthcare systems, increased educational investments in people, and more private savings, among others.

The Global Demography of Aging

This chapter has two main objectives. First, it provides an overview of demographic change in the world today, including differences and similarities over time, geographical region, and stage of development. Variations in fertility and life expectancy (including healthy life expectancy improvement) are central here. Second, it introduces economists’ attempts to explain the changes in behavior, especially in reproductive behavior, that have generated these population dynamics. We begin by presenting key facts and trends regarding past and projected future population aging in Section 2. The data and figures presented will serve as anchors for the analyses in this and subsequent chapters in this volume. Section 3 reviews the history of the demographic transition and its interaction with population aging. Section 4 reviews the economic literature on different hypotheses and their supporting evidence explaining recent decades’ decline in fertility and increase in life expectancy. We also discuss different views on the future of fertility and longevity and the role of migration as a determinant of the population age structure. Section 5 discusses how aging is changing in terms of the types of illnesses the elderly face and the effects on living arrangements. Section 6 discusses several open research questions followed by some concluding remarks.

2. POPULATION AGING 2.1 Trends and Projections This section documents some salient facts and trends in population aging. Overall, major changes have occurred in the world’s age and population structure over the last half-century, with the increase in population shares at advanced ages being a prominent feature. Fig. 1 depicts population pyramids from 1950 to 2010 and projections until 2100 (United Nations, Department of Economic and Social Affairs, Population Division, 2015).a As is evident, the pyramid shape representative in 1950 and 1980 is giving way to a more dome or beehive-like shape, as the population at younger ages shrinks over time. The youth bulge seen in the earlier snapshots, combined with declining fertility and increasing life expectancy, is causing the proportion of the elderly in the population to increase. The elderly population is poised to increase dramatically both in size and share of total population in the first half of the century and is projected to continue to increase, albeit at a slower speed, toward the end of the century. As a whole, the world’s population has grown quickly in the last half-century, more than doubling from around 2.5 billion in 1950 to more than 7 billion today. It is projected a

The projections displayed in Fig. 1 are based on the United Nations’ (UN) medium-fertility scenario. If fertility rates in the coming decades are lower than the “medium scenario” estimate, the share of elderly in the population will rise even further.

5

Fig. 1 World population by age group, 1950–2100. Source: UN, World Population Prospects, 2015.

The Global Demography of Aging

to reach more than 9 billion by 2050 and 11 billion by 2100. Population growth at younger ages (0–14) has flattened out over the last few decades. The size and share of the working-age population (15–59) have grown steadily since 1950, but its growth has been fueled mostly by developing countries. In more developed countries, the population share of 15–59 year olds has been somewhat level and is in fact projected to decrease to around 50% by 2100. In contrast, the 60+ and 80 + age groups are growing rapidly both in absolute numbers and as a share of the total population, and both figures are higher now than at any time in history. The number of people aged 60+ increased from 200 million in 1950 to around 760 million today. By 2020, this number is projected to rise to 1 billion, by 2050 to 2 billion, and by 2100 to 3 billion. The number of people aged 80 +, or the “oldest old,” grew markedly from 14 million in 1950 to around 108 million today and will be over 900 million by 2100 if current projections prevail. Because the oldest old tend to have higher rates of severe chronic health problems that are costly in terms of both dollar amounts and time, the rapid growth of this cohort has important implications for individuals, families, and governments. Older age cohorts, moreover, are beginning to account for a substantial proportion of the total population, as Fig. 2 shows. Indeed, people aged 60+ are expected to constitute a greater population share in all countries between 2000 and 2050. While the phenomenon of population aging is taking place throughout the world, considerable heterogeneity exists across nations and among regions.b Most developed countries already have large elderly cohorts, with 20% of the population aged 60 +. This proportion will rise to more than 30% in the next four decades. Among developed countries, Japan currently has the largest proportion of people (30%) aged 60+. This distinction is expected to hold in 2050, when the figure will reach 44%. In the developing world, only 10% of the population is currently aged 60+, but this will soon change. By 2050, this proportion is expected to more than double. While the aging transition has occurred over at least a century in developed countries, developing countries are projected to reach nearly similar levels of population aging by the middle of this century. We now focus on the elderly population in the world’s two population superpowers (China and India) and the largest population developing country populations in Latin America (Brazil), and Africa (Nigeria). Fig. 3 shows the expected growth of the elderly population in these countries, which had elderly population shares ranging from 5% to b

In presenting figures and tables, we follow the United Nations’ classification of regions based on their recent economic development status: more developed or less developed. The less developed regions include all the countries of Africa, Asia (excluding Japan), and Latin America and the Caribbean, and Melanesia, Micronesia, and Polynesia. The more developed regions comprise Australia/New Zealand, Europe, Northern America, and Japan (United Nations Statistics Division, 2014). We refer to countries belonging to the group of more developed regions as “developed countries” and countries in the group of less developed regions as “developing countries.”

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Handbook of the Economics of Population Aging

45 40 35 Share of population (%)

8

30 25 20 15 10 5 0 1950

1960

1970

1980 World

1990

2000

2010

2020

2030

More developed regions

2040

2050

2060

2070

2080

2090

2100

Less developed regions

Fig. 2 Population share of those aged 60 and over, by level of development, 1950–2100.

7% in 1950. In all four countries, population aging will be a major demographic trend between now and 2100, but the extent will vary substantially. We pay particular attention to China and India because of their sheer size; their combined population accounts for 40% of the world’s total population. Population aging in these two countries has been rapid and will continue in the first half of the next century. By 2050, the 60+ age group is projected to constitute 20% of India’s population and 36% of China’s, totaling more than 750 million people. By 2100, these numbers will be 34% and 40% for India and China respectively. The pace of aging will be especially rapid in China, where the absolute number of the population aged 60 + grew by 67% between 2000 and 2015 and is projected to more than triple to close to 400 million by the end of this century. The projected combined elderly population of these two countries will be close to 1 billion by 2100. Brazil represents a swiftly developing South American country, where the large and rapid decline in fertility and increase in longevity of the past several decades will propel its elderly population to more than triple from less than 20 million in 2010 to close to 70 million in 2050. Nigeria provides a valuable counterpoint from the sub-Saharan African region, where the HIV/AIDS epidemic has played a large role in shaping the demographic structure. As a consequence, Nigeria’s elderly population has grown much more slowly over the last half-century. The share of the 60+ population essentially remained flat between 1950 and 2015 at roughly 5%, although it is projected to more than double by the end of the century. This contrast is especially stark when compared with other developing countries of a similar size.

China

India

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40

30

25

20

15

134.8 million

10

35

Share of population (%)

Share of population (%)

566.3 million

397.9 million

35

5

30

25

20

15

171.5 million 10

5

0

0 1950 1960 1970 1980 1990 2000 2010 2020 2030 2040 2050 2060 2070 2080 2090 2100 60+

1950 1960 1970 1980 1990 2000 2010 2020 2030 2040 2050 2060 2070 2080 2090 2100

80+

60+

Brazil

Nigeria

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40

35

35

77.8 million

30

25

20

30.3 million

15

10

5

Share of population (%)

Share of population (%)

80+

30

25

20

115.2 million 15

10

12.4 million

5

0

0 1950 1960 1970 1980 1990 2000 2010 2020 2030 2040 2050 2060 2070 2080 2090 2100 60+

80+

1950 1960 1970 1980 1990 2000 2010 2020 2030 2040 2050 2060 2070 2080 2090 2100 60+

80+

Fig. 3 Population share of those aged 60 and over, and those aged 80 and over in China, India, Brazil, and Nigeria, 1950–2100.

Handbook of the Economics of Population Aging

55 50 45 40 Old dependency ratio

10

35 30 25 20 15 10 5 0 1950

1960

1970

1980 World

1990

2000

2010

2020

2030

More developed regions

2040

2050

2060

2070

2080

2090

2100

Less developed regions

Fig. 4 Old-age dependency ratio (in percent), by level of development, 1950–2100.

Fig. 4 depicts the old-age dependency ratio (OADR), which measures the ratio of persons aged 65+ per 100 working-age persons (15–64). This metric, which we express in percent terms, helps gauge the pressure on the productive population to support the elderly and is hence an important indicator for governments and policymakers. For all countries, the old-age dependency ratio is currently at 12.6%, meaning there is roughly one elderly person for every eight working-age persons. This ratio is projected to increase to close to 40% by the end of the century. In developed countries, the OADR is currently at approximately 25% and is expected to increase to 50% by 2100. There is approximately one elderly person for every 10 working-age persons in developing countries currently, but this ratio will increase to closer to 1 for 3 by 2100. Changes in the sex composition of the population will accompany population aging. Overall, more male than female babies are born, but male mortality rates are higher than female mortality rates at all stages of life. While biology can explain part of this difference, differential behavior and risk factors play larger roles (Rogers et al., 2010; Seifarth et al., 2012). The resulting predominance of women among the elderly has been a longstanding and widely recognized phenomenon. However, this predominance is now diminishing with health improvements at all ages and medical advances in treating cardiovascular disease (which is concentrated among men). Fig. 5 depicts the UN’s population estimates and the forecast of the male to female ratio for the 60 + population from 1950 to 2100. Among the elderly, females will continue to outnumber males, in both developed and developing countries, although the sex ratio of the elderly in developed regions has increased rapidly since the mid-1980s. In developing regions, the sex ratio of the elderly has increased slightly since 1965 and is projected to remain roughly level or to increase

The Global Demography of Aging

100 95 90

Males/100 females

85 80 75 70 65 60 55 50 1950

1960

1970

1980 World

1990

2000

2010

2020

2030

More developed regions

2040

2050

2060

2070

2080

2090

2100

Less developed regions

Fig. 5 Change in M/F ratio, 60 + population, by level of development, 1950–2100.

slightly. Gender imbalance at older ages has policy implications in terms of living arrangements and the financial security of widows, especially in developing countries amid changing norms for the care of the elderly. We discuss some of these issues in Section 5.3.

2.2 Reliability of Population Projections The data used in this chapter comprise mainly population data and projections from the United Nations (UN). In addition to the UN estimates, many governments also produce population estimates for their own countries. Several other agencies, including the US Census Bureau and the World Bank, produce global estimates as well. These population projections are important tools for government policymakers and private planners to gauge future demand for various resources and to allocate funds. Demographic forecasts have heightened awareness of population aging, and increasing concern over adequate funding of pensions and health care systems have led to landmark reforms in these arenas throughout the world. So a peripheral, but important, question is how accurate are population projections? We focus on the UN population estimates as they are the most widely used. The first thing to note is that UN population projections are not static. They change every 2 years to reflect new data from censuses, demographic surveys, vital and population registers, and various other sources.c In instances when a large amount of new census data become available, updated fertility and mortality data can lead to significant revisions in the c

For a detailed review of the methodology, the UN uses to calculate its population estimates, refer to Lutz and Samir (2010) and Bongaarts (2009).

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estimates of future population size. Table 1 shows that the projections for the 60+ and 80 + populations in absolute numbers and in shares of total population have changed significantly, even in recent years. The greatest percent change occurred for the population aged 80 + by 2050 between the 1994 and 2010 forecasts. The UN estimate of the size of this age group has risen by 20% or more since 1994, for the world and across both developed and less developed regions, highlighting the magnitude to which estimates can change within a somewhat short period of time. While the accuracy of current population projections cannot be assessed, the success of previous projections can be compared with historical or current population figures. Since the 1950s, the UN has provided 12 estimates for the global population in year 2000. Only one of these projections was off by more than 4%. Errors in projections have also decreased over time (National Research Council, 2000). However, projections for individual countries and specific age groups have had much more varied levels of success.d In particular, producing accurate projections for developing countries and for the youngest and oldest age groups has been challenging for several reasons. First, data for developing countries are somewhat limited and unreliable, and errors in baseline estimates play a dominant role in projection accuracy, especially in shorter forecast horizons (National Research Council, 2000). Second, many developing countries are still undergoing demographic transition, which means fertility and mortality are both still high and changing rapidly, leading to more room for projection error (Lutz et al., 2008). Relatedly, UN assumptions about future trends in fertility and mortality rely mainly on empirical regularities in past trends in countries that have already completed the demographic transition; whether these assumptions are appropriate for developing countries that are still undergoing demographic transitions is not clear (Bongaarts, 2009). Projections for intermediate age groups between 15 and 64 have in general been fairly precise, with error not exceeding 2%. Population projections for the very young and very old, however, have historically been too high and too low, respectively. Projections of total fertility has been too high, leading to upward bias in population projections for the very young. And as mortality improvements continue to be larger than forecasted for most of the world (exceptions are sub-Saharan Africa and the former Soviet Union), the projected population of the 80+ has been consistently underestimated. While almost all demographers agree that the proportion of the 80+ population will increase significantly over the next century, the magnitude of the increase is uncertain as future trends in old-age mortality continue to be highly debated (see Section 4.2 for a discussion of the future of longevity). Further, because UN population estimates do not incorporate different mortality scenarios, the uncertainty of the elderly population is likely understated. d

Projections of world population tend to be more accurate than individual country projections because country errors tend to cancel out in aggregate and because world population projections are not subject to migration errors.

Table 1 Change in UN forecast of 2050 elderly population, 1994–2010 Total 60 + 80 + 60 + Share (population, billions)

Forecast year

80 + Share (%)

World

1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 % Change % Change % Change % Change

94–00 00–06 06–12 94–12

9.83 9.37 8.91 9.32 8.92 9.08 9.19 9.15 9.30 9.55
5.2
1.4 3.9
2.8

1.97 1.94 1.97 1.96 1.91 1.97 2.01 2 2.03 2.02
0.5 2.6 0.5 2.5

0.33 0.32 0.37 0.38 0.38 0.39 0.4 0.4 0.4 0.39 15.2 5.3
2.5 18.2

20.04 20.70 22.11 21.03 21.41 21.70 21.87 21.86 21.83 21.15 4.94 4.00
3.29 5.54

3.36 3.42 4.15 4.08 4.26 4.30 4.35 4.37 4.30 4.08 21.45 6.75
6.18 21.65

8.63 8.20 7.75 8.14 7.70 7.84 7.95 7.88 7.99 8.25
5.7
2.3 3.8
4.4

1.61 1.58 1.59 1.57 1.51 1.57 1.6 1.6 1.63 1.6
2.5 1.9 0
0.6

0.24 0.23 0.27 0.27 0.26 0.28 0.28 0.27 0.28 0.27 12.5 3.7
3.6 12.5

18.66 19.27 20.52 19.29 19.61 20.03 20.13 20.30 20.40 19.39 3.39 4.35
3.64 3.96

2.78 2.80 3.48 3.32 3.38 3.57 3.52 3.43 3.50 3.27 19.27 6.18
7.08 17.68

1.21 1.16 1.16 1.18 1.22 1.24 1.25 1.28 1.31 1.30
2.5 5.9 4 7.4

0.36 0.36 0.38 0.4 0.39 0.4 0.41 0.42 0.42 0.42 11.1 2.5 2.4 16.7

0.09 0.09 0.1 0.11 0.11 0.12 0.12 0.12 0.12 0.12 22.2 9.1 0 33.3

29.75 31.03 32.76 33.90 31.97 32.26 32.80 32.81 32.06 32.31 13.94
3.24
1.50 8.59

7.44 7.76 8.62 9.32 9.02 9.68 9.60 9.38 9.16 9.23 25.33 2.98
3.85 24.10

Less developed regions

1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 % Change % Change % Change % Change

94–00 00–06 06–12 94–12

More developed regions

1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 % Change % Change % Change % Change

94–00 00–06 06–12 94–12

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Finally, net migration also tends to be poorly projected, affecting estimates of the size of the working-age population (as migrants tend to be young adults) and the old-age dependency ratio, but for most countries the flow of migration has been slow enough to avoid a major impact on population estimates. The assumptions used in making population estimates have changed since 2010. For example, prior to the 2010 revision, the assumption was that the total fertility rate (TFR) in countries adjusting from high to low fertility will eventually approach a fertility floor of 1.85, regardless of their current position in the transition. Similarly, for countries already below replacement fertility levels, the assumption was that fertility would recover at a uniform pace that would converge to the fertility floor of 1.85 children per woman. The new approach does not adopt a set fertility floor and assumes that the projected pace of the decline depends on the country’s current level of fertility, country-specific historical trends, and past trends of other countries that have already undergone fertility transitions (United Nations Statistics Division, 2014). As demographers become more proficient in predicting broad fertility and mortality trends—the key determinants of future population size—population estimates will also become more accurate. Regardless, because population projections still rely primarily on past trends and the implicit assumption that the conditions currently influencing fertility, mortality, and migration will persist in the future, population projection data carry substantial uncertainty and should be interpreted with caution. While policymakers frequently use population projections, little is known about how uncertainties in these estimates are dealt with. A survey conducted by the European Commission among policy experts who use demographic data found that they tend to ignore the issue of uncertainty even though they were aware of it. In theory, policymakers have several methodological options, as discussed in Lee and Tuljapurkar (2000). The standard method is to use high-, medium-, and low-probability scenarios, although demographers tend to eschew this approach because of its strong assumptions. Beyond methodological issues, how much, if at all, the alternatives affect policy decisions is unclear. Lack of agreement and knowledge on how to tackle uncertainty in practice seems to be a barrier (Ahn et al., 2005). Future research calls for more studies to understand the impact of past errors on policy adoption and to provide a framework for approaching and incorporating uncertainty in policy planning.

3. THE DEMOGRAPHIC TRANSITION AND POPULATION AGING The age structure of the population changes as a natural consequence of the demographic transition, which we briefly overview in this section. The demographic transition comprises three stages. The starting point occurs in a Malthusian world where both mortality and fertility are high and population growth is near zero, as high death rates offset high birth rates. Then, in the first stage of the demographic

The Global Demography of Aging

transition—when mortality begins to decline while fertility remains high—mortality declines most at the youngest ages, causing the proportion of children in the population to increase. Mortality decline thus initially renders populations younger rather than older in a phase that can persist for decades. Second, fertility begins to decline, such that the population growth rate also declines (but remains positive). This second stage may last 40 or 50 years. As fertility declines, the working-age population grows faster than the population as a whole, reducing the total dependency ratio. In the third stage, mortality and fertility both reach low equilibrium levels, and the overall population stops growing and sometimes declines. In this third stage, increasing longevity leads to a rapid rise in the elderly population while low fertility slows the growth of the working-age population. After completion of all three stages of the transition, population growth returns to near zero as fertility and mortality stabilize at low levels. The entire transition typically takes more than a century to complete and results in a much larger population size. The demographic transition is projected to be complete in all countries by 2100 (Lee, 2003). Although the stages of the demographic transition are the same, the experience of developed nations is distinct from that of the developing world in its timing, determinants, and economic considerations. We therefore separate our following discussion by level of development.

3.1 The Historic Demographic Transition We now briefly review the historic demographic transition of the developed world. In Western Europe, the first stage of the demographic transition—mortality decline—began around 1800. Population growth in Europe was slow and uneven for centuries, averaging 0.3% per year before 1700 (Lee, 2003). In perhaps the most widely studied case, mortality decline in England started around the middle of the eighteenth century. By 1820, life expectancy at birth in England reached 41 years, an increase of 6 years from the previous century, and remained stable for the next 50 years through the Industrial Revolution. Mortality continued to fall more rapidly after 1870, so that life expectancy had risen to 50 years by the early twentieth century and continued to climb until reaching around 80 years today (Cutler et al., 2006). With some variations in timing, other developed countries experienced similar transitions. Although considerable debate remains, the fall in mortality has been attributed primarily to three broad reasons. First is the improvement in living standards as a byproduct of economic development as reflected in measures such as higher caloric intake and better access to health care and medicine (Fogel, 1997; Preston, 1975). The second explanation relates to the role of targeted social policy measures, such as the development of public health infrastructures such as water sanitation and vaccination programs (Preston, 1975; Cutler et al., 2006). Finally, education appears to have played an important role in the

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diffusion of knowledge on good health practices and the increasing acceptance of the germ theory of disease (Lleras-Muney, 2005). Fogel (1997) argues that nearly all mortality reduction between the late eighteenth century and the late nineteenth century can be attributed to improved nutrition (via increased income). As agricultural yields improved during the eighteenth century, the caloric intake of the average individual and adult height increased significantly as mortality declined. However, while income growth and caloric availability likely played an important role, the timing of economic growth and the onset of the modern mortality decline did not align consistently (Easterlin, 2004). Further, as Preston notes in his seminal 1975 article, life expectancy has been increasing over time even holding income fixed, and proposes instead that public health measures could explain more of the historical mortality decline. Similarly, Cutler et al. (2006) argue that the cross-country differences in health stem from institutional ability to implement known technologies and adopt new ideas about personal health, rather than from variations in income. Consistent with this hypothesis, Murtin (2013) finds that schooling, rather than income per capita, is the primary determinant of the mortality transition using aggregate panel data. Lleras-Muney (2005) exploits compulsory schooling law changes in the United States to account for schooling and finds that education is indeed linked to lower mortality. Of course, these theories are not necessarily mutually exclusive, making precise accounting difficult. But overall, most of the decline in mortality can be attributed to better health technology, higher wealth, and improved education, with varying degrees of importance depending on the time and context. We revisit this topic in Section 4.2, where we discuss in greater depth the specific reasons behind more recent increases in life expectancy. Population growth is the next stage of the transition, as mortality falls and fertility remains high. The modern expansion of human population began around 1800, rising from around 1 billion to 2.5 billion by 1950. Then fertility begins to fall following the decline in mortality and subsequent population growth. Most presently developed nations began their fertility transitions in the late nineteenth or early twentieth centuries, with a median fertility decline of about 40% from 1870 to 1930 (Coale and Treadway, 1986). The causes of fertility decline remain hotly debated, but neoclassical economics emphasizes the gradual evolution in the demand for children (Becker, 1981; Galor and Weil, 2000). This explanation highlights the rising opportunity cost of childbearing stemming from factors including increases in female labor force participation and wages, the returns to schooling, and demand for child quality. Other factors that affect the supply of children, such as availability of and advancement in contraceptive technology, also have been shown to have significant impacts on fertility, but are unlikely to be dominant forces. We discuss these and other theories and their respective merits in Section 4.1.2. In the final stage of the transition, mortality and fertility fall to long-run low levels and population growth returns to zero or even falls below zero. Most developed countries

The Global Demography of Aging

have now reached this final stage of their transition. Many Western European countries, such as Spain, Italy, and Germany, currently have birth rates below the population replacement rate of 2.1 births per woman. Some countries, including Russia and Japan, face significant population declines because birth rates and net migration rates have fallen below crude death rates. Because the demographic transition occurred earlier in developed countries, the phenomenon of population aging also began earlier there. The 60+ population share was already at 12% in 1950 (higher than the current share in less developed regions), has doubled to approximately 24% today, and is projected to continue to rise at a similar pace until the middle of this century, when population aging is expected to slow.

3.2 The Ongoing Demographic Transition in Developing Countries Although separated by roughly a century, the demographic transition in developing countries mirrors that in developed nations, but at a much more rapid pace. The limited available pretransitional data from India and Taiwan indicate that TFRs were typically six or higher, and life expectancy was highly variable and averaged in the low 20s (Preston, 1975). While many developing countries did not begin the mortality transition until sometime in the twentieth century, life expectancy gains were quite rapid once their transitions commenced. In China and India, life expectancies have risen by nearly 30 years since 1950. In African countries overall—where economic progress has been slower— life expectancy rose by more than 13 years from the 1950s to 1980s, before stalling in the face of the HIV/AIDS epidemic. For most developing countries, the second stage of the demographic transition— fertility decline—typically began in the post-World War II period or later (Lee, 2003). Fertility transitions in East Asia were particularly early and rapid, while those in South Asia and Latin America have been slower (Casterline, 2001). Below replacement rates are observed not only in the developed world, but also in various emerging countries including Brazil, Taiwan, Korea, and China. We delve into the reasons for fertility and mortality declines in developing countries in the past few decades in Sections 4.1 and 4.2. From 1950 to 1990, fertility and mortality rates declined roughly in tandem, although the birth rate was still around twice as large as the mortality rate, leading to a large population boom in developing countries. Whereas the population growth rate in Europe has not exceeded 1% and exceeded 1.5% only briefly in the United States in the modern era, population growth in developing countries reached historically unprecedented rates, attaining a peak of 2.5% in the 1960s. Population growth in developing countries has since slowed as fertility continues to decline. As the youth bulge progresses through the age structure, combined with sustained low levels of fertility and rising longevity, many developing countries are now beginning to witness rapid population aging. While today’s proportions of older people typically are

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higher in more developed countries, the most rapid increases in older populations are occurring in the less developed world. Whereas the elderly population share took more than a century to double in developed countries such as France, countries such as China and Brazil are expected to achieve the same in around a quarter of the time (Kinsella and Gist, 1995). Between 2015 and 2050, the 60 + population in less developed countries is projected to increase by 177% as compared with an increase of 41% in more developed countries.

4. THE DEMOGRAPHIC DETERMINANTS OF POPULATION AGING As described in the previous section, the interplay of declining fertility and increasing longevity within the demographic transition is the root cause of population aging. However, how these factors affect aging and their implications are different. A fertility decline reduces the numbers of the very young, which translates into smaller cohort sizes of the young and working age population as time goes on and low birth rates continue. Holding longevity constant, lower fertility implies higher OADR and may impose higher resource costs on the population. However, an increase in life expectancy raises the average age of the population and the share of elderly population by increasing the numbers of surviving older people. If rising longevity due to reductions in old-age mortality is associated with improved health and productivity of the elderly, then the economic pressures of population aging may be less severe. Of these two forces, fertility decline has played a larger role in population aging (Weil, 1997; United Nations, Department of Economic and Social Affairs, Population Division, 2001). Weil (1997) shows that at least two-thirds of the increase in the US elderly population is due to fertility decline. Bloom et al. (2010b) show that the fertility decline had a much larger impact on the age structure in 1960–2005 using a sample of Asian countries, even in China where life expectancy increased by 31 years (approximately 70%) in the same period. Migration also plays a role in determining the age structure of open economies. Immigrants tend to be young and of working age, so to the extent that population aging is viewed as a problem to be solved, changes in immigration policy have been touted as a possible solution to ameliorate its effects. However, as we will discuss shortly in Section 4.3, the flow of immigrants necessary to ease the pressures of population aging is unfeasibly large.

4.1 Decline in Fertility Fertility decline has been the most important demographic driver of population aging (United Nations, Department of Economic and Social Affairs, Population Division, 2001). Fig. 6 depicts the TFR, defined as the average number of children that a woman would bear over her lifetime, in the world, in more developed regions, and in less developed regions from 1950 to 2010 and projected until 2100. Globally, TFR has fallen from five

The Global Demography of Aging

Number of children per woman

8

6

4

2

0 1950

1960

1970

1980 World

1990

2000

2010

2020

2030

2040

More developed regions

2050

2060

2070

2080

2090

2100

Less developed regions

Fig. 6 Total fertility rate, by level of development, 1950–2100.

children per women in 1950 to roughly 2.5 today and is forecasted to fall even further in the next few decades. From 2005 to 2010, 50 countries (out of 202) had TFRs of 4.0 or higher. The fertility rate is projected to fall to roughly 2.2 by 2045–50 even among currently developing countries, and only one country (Niger) is expected to have a TFR higher than 4.0. Current projections show fertility rates across more developed and less developed regions further converging, with TFR at 1.88 and 2 for developed and developing regions by the end of this century, respectively. Fig. 1 shows the impact of falling fertility, demonstrating the shrinking base of the population pyramid as the shares of 0–14 year olds worldwide declines and the correspondingly widening top of the pyramid as the population of elderly people grow in both absolute numbers and percent of total population. This section highlights recent trends in fertility and some leading explanations for the trends within the economic literature. We begin by presenting a basic theoretical model proposed by Becker (1960) in Section 4.1.1, which has been used as the primary framework in economics to understand fertility. We then provide several explanations with supporting evidence for the continuing fertility decline in the developed world in the post-WWII era in Section 4.1.2. We move on to discuss the fertility transition in the developing world in Section 4.1.3, where the bulk of the fertility decline occurred in the last half-century as many countries began the second phase of their demographic transitions. The economic literature on fertility is expansive, and we limit the discussion herein to how fertility is related to aging and to the post-WII modern era.e e

For further discussion of the historical aspects of the fertility transition, Guinnane (2011) provides an excellent review.

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4.1.1 Theoretical Framework We begin with the basic Becker framework to explain the demand for children (Becker, 1960, 1991/1981), as it has become the canonical model in economics for understanding fertility. In the simplest model, the number of children is treated analogously to other consumer (normal) goods in a basic neoclassical two-good utility (U) maximization framework. Parents choose the number of children (n) and goods (Z) to maximize U ¼ U ðn, Z Þ, subject to a budget constraint (π c n + π z Z ¼ I), where the cost of child rearing and indirect opportunity costs determine the price of children (π c), and π z is the unit cost of goods (Z). The cost of child rearing comprises direct and indirect costs. Examples of direct costs include clothing, education, and food. Indirect costs include opportunity costs, such as foregone earnings of women who take time off from the labor market to care for their children. In this framework, the usual first-order conditions determine the optimal quantities of n and Z, where the demand for children depends on the relative price of π c/π z. Simple comparative statics then implies that an increase in the relative price of children would reduce the demand for children (and increase the demand for other commodities), holding real income constant. An increase in pure income would raise the demand for children, but if the higher income reflects an increase in wages, then the substitution effect may dominate the income effect, so that the number of children demanded is reduced. Becker then augments this simple model by including the quality of children as a variable, as denoted by expenditures on children. The household thus seeks to maximize a utility function comprising the quantity of children (n), the quality of children (q), and the quantities of all other goods (Z). Both quality and quantity of children are normal goods, and the household budget constraint is now (π c qn + π z z ¼ I), where π c is the constant cost of a unit of quality, and q the total quality of each child. It
can be shown that income elasticities of demand for n, q, and Z must satisfy α εn + εq + ð1
αÞεZ ¼ 1, where α is the share of family income devoted to children, and εn, εq and εz are income elasticities with respect to n, q, and z, respectively. If children are normal goods, then total expenditures on children will increase with income (εn + εq > 0Þ. However, if εq is large enough, it is possible that εn < 0: In other words, higher income is expected to be associated with a greater demand for children. However, greater demand for children may be offset at least in part by greater resource endowments per child (ie, increased quality of children) rather than by an increase in the number of children. Becker and Lewis (1973) present a more generalized version of the Becker (1960) model. The authors introduce fixed costs of n and q, such that the budget constraint is now π n n + π q q + nqπ c + π z z ¼ I, where π n and π q are the fixed costs of each child and the unit of quality, respectively. The shadow price of an additional child, pn, then becomes π n + π c q, and the shadow price of an additional unit of quality, pq, is π q + π c n. Hence, pn is an increasing function of q and pq is an increasing function of n. Because the household chooses n and q, the shadow prices are endogenous.

The Global Demography of Aging

The important takeaway from the model is that quantity and quality are closely related, because the shadow price of quality depends on quantity and the shadow price of quantity depends on quality. As an example, if π q decreases due to an increase in education subsidies, then the fall in pq induces an increase in quality. This in turn induces an increase in pn and thus a somewhat large decrease in quantity. Of course, Becker was not the first to suggest that economic costs and benefits affect the fertility decision. For example, Notestein (1953) attributed the fertility transition to several broad social and economic changes, including urbanization leading to changes in the economic benefits and costs of children and the emergence of new economic roles for women that are incompatible with childbearing—all ideas that can be formalized within the Becker model. Most existing economic frameworks build upon or can be largely reconciled with Becker’s seminal model, including much of Becker’s later work (Becker and Tomes, 1976; Barro and Becker, 1989), Easterlin (1975), Willis (1973), Michael and Willis (1976), among others.f In addition, most existing fertility theories in economics and other fields can be traced to the basic tenet of the Becker model, ie, that the demand for children has a downward-facing slope like any normal good and as the “price” of children increases, fertility will decline. The empirical evidence (some of which we will discuss below) is overall consistent with the model’s main prediction: as the price of children increases (or decreases), the quantity demanded, or fertility, decreases (or increases). As such, we believe that the Becker model is the most useful and parsimonious framework to have in mind when examining fertility trends. 4.1.2 Developed Countries As noted in Section 3.1, the bulk of the fertility decline in developed regions began in the late nineteenth or early twentieth centuries as they experienced their demographic transitions. By 1950, TFRs in the developed world had already fallen to 2.8 and declined further to 1.7 by 2010. The demographic transition in the developed world is more or less complete (Bongaarts, 2009). The completion of the demographic transition has left fertility rates in most developed countries at below replacement levels. In some countries in Europe and Asia, fertility rates fell to the “lowest low”—defined as fewer than 1.3 children per woman—in the 1990s (Kohler et al., 2002). As a result, several countries such as Japan now face population declines. Distinct variation in fertility trends also exist across industrialized nations. For example, North America has had higher fertility than Western Europe (1.89 vs 1.66 children per woman), and projections f

This is not to say that significant differences do not occur among these models or that no detractors of the Becker model exist. In particular, the earlier work by Easterlin and Becker differed in their assumptions of preference formations, although the basic ideas behind the two schools of thought remain similar and complementary. In particular, rather than assuming homogeneous preferences, Easterlin suggests that attitudes toward both children and other goods and services vary depending on the individual. See Sanderson (1976) for a more detailed discussion.

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suggest that this divergence between the two principal regions of the North will persist into the near future. For developed countries in the last stage of their demographic transitions, the most significant dynamic change in the modern era is the aging demographic associated with the “baby boom.” The United States and other developed countries experienced baby booms in the decade following World War II, when birth rates increased dramatically for two decades and led to a sharp and transitory deviation from the long-term trend of declining fertility, followed by the baby bust, which returned birth rates to preboom (or lower) levels. By the 1970s, fertility had fallen to replacement or even below replacement levels in most developed countries. As the baby boom cohorts continue to approach retirement age, they will account for much of the oncoming aging population in developed regions. After a slight slowdown in population aging in the past two decades, driven by low fertility in the 1930s, population aging will accelerate rapidly in the next few decades due to the graying of the baby boom cohorts (Fig. 2). In the United States, the baby boomers began turning 65 in 2011 and are now driving growth at the older ages of the population. There were approximately 76.4 million baby boomers in 2012, representing close to one-quarter of the entire US population. By 2029, when all the baby boomers will reach retirement age, more than 20% of the total US population will be over the age of 65. Just as this generation had an impact on the educational system and the labor market during their school-age and economically productive years, the boomers’ retirement and savings choices will have significant implications for the labor market and pension spending across developed nations. However, although the size of the baby boomers’ cohorts will decline through mortality, this shift toward an increasingly older population is expected to persist, although much less rapidly, due to the longer-term trends in declining fertility.

4.1.2.1 The Cost of Children

Most reasons cited for the decline in fertility in the developed world pertain to the “price” of children. The challenge in empirical identification is then to find exogenous variation in the proxies for said price. The price of children may refer to the direct costs (childcare, costs of schooling) and indirect costs, namely the opportunity cost of time needed for childbearing and childrearing mostly on the mother’s part. As wages for women increased in the postwar era, more women were drawn into the labor force. Within the Becker framework, the intuition is that the substitution effect of increasing women’s relative wages dominates the income effect, such that women work more and reduce their fertility. The rise in women’s wages could also induce a quantity– quality tradeoff that would further imply fewer children. As the unified growth theory (which employs the Beckerian quantity–quality framework) emphasizes, technological change may have decreased the comparative advantage of males in physically intensive

The Global Demography of Aging

tasks, raised the demand for female labor, and therefore increased the opportunity cost of fertility (Galor and Weil, 1996). Because fertility and labor supply are likely jointly determined, the challenge in empirical identification is then to find exogenous variation in the proxies for the “price” of children. Using data from Sweden, Schultz (1985) finds that exogenous increases in women’s relative wages can explain a quarter of the decline in fertility from 1860 to 1910. Butz and Ward (1979) suggest that the rise in male wages in the postwar period, which increased household income, followed by a sharp increase in female wages (which increases the cost of children assuming women are the primary caretakers) can help explain the baby boom and bust in the United States. More recently, Jensen (2012) finds that young women in rural India with more labor market opportunities were significantly less likely to get married and have children. Somewhat surprisingly, although the rise of female wages and labor force participation has been credited extensively as a major reason for the fall in fertility (Becker, 1960; Galor and Weil, 1996; Schultz, 2001), little systematic research has been done to identify the causal rather than correlative impact of female wages and labor market structure on fertility.g The price of children has also been examined via the lens of direct cash allowances for families with children, parental leave benefits, availability of childcare facilities, and related pronatalist polices. In the Becker model, these policies may result in a reduction in the cost of children (eg, public subsidy) or as an increase in income (eg, transfer payments), which should imply an increase in the demand for children (either in quantity or quality). Overall, fertility behavior seems to respond to targeted financial incentives such as child subsidies, but not welfare benefits (Buttner and Lutz, 1990; Cohen et al., 2007; Milligan, 2005; Gauthier, 2007).h Results examining the impact of family-friendly work policies are mixed, and the estimates, when positive, are typically small (Gauthier, 2007). As governments and private organizations become more attuned to the needs of working parents, more research needs to be conducted on how alternative policies such as expanding paternal leave benefits or flexible work schedules may affect fertility. Recent studies on paternity leave have found that increasing paternity leave increases fertility slightly (Feyrer et al., 2008), but does not change the traditional household division of labor (Cools et al., 2015). Studies focusing on the direct costs of childrearing in terms of childcare prices and availability have also yielded mixed results (Gauthier, 2007). For example, M€ ork et al. g

h

However, the reverse relationship of the impact of fertility on female labor supply has been examined more thoroughly. These papers attempt to isolate the causality of child quantity through various natural experiments, such as the exogenous event of twinning (Rosenzweig and Wolpin, 1980) or by exploiting parental preferences for a mixed sibling sex composition (Angrist and Evans, 1998), and typically find that more children lead to lower female labor supply, with some heterogeneous effects by education and age. Studies using macrolevel data have generally concluded the impact of government policies is most likely on the timing of births rather than completed fertility (Gauthier, 2007).

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(2013) examine the impact of Swedish childcare reform, which effectively reduced user fee costs. The authors find that fertility increased by approximately 10% among childless couples. However, Schlosser (2005) examines the introduction of free public preschool in Israel on Arab mothers’ labor supply and fertility and finds no effect on fertility but a positive effect on labor supply. In yet another study, Furtado and Hock (2010) demonstrate that lower wages in the childcare sector due to low-skill immigration are associated with higher fertility among highly educated women in the United States. Bauernschuster et al. (forthcoming) find evidence that a substantial expansion of public childcare for children under three in Germany increased birth rates, suggesting that policy may be effective in reversing low fertility. Because lower childcare costs represent a pure reduction in the cost of having children for women already in the labor force, effects on fertility may also be observed in certain contexts where rates of female labor force participation are already high.i

4.1.2.2 The Role of Education

Several theoretical models, including the unified growth theory proposed by Galor and Weil (1999, 2000) and Galor and Moav (2002), emphasize the idea that increasing demand for human capital is a driving force behind the decline in fertility. The empirical evidence is consistent with the theory: education and fertility are consistently negatively correlated in both macro- and micro-level data (Strauss and Thomas, 1995; Martin, 1995). Murtin (2013) finds average years of primary schooling to be the most dominant long-run determinant of the fertility transition, rather than income standards or child mortality. How might education affect fertility? First, the increasing returns to education, which can be interpreted as lowering the cost of quality, lead parents to substitute child quantity for child quality (Becker et al., 1990). Second, the increasing quantity and quality of schooling of women, especially in higher education after WWII, may have increased female wages and labor market opportunities, hence increasing the cost of childbearing (as we touched on in Section 4.1.3.1). Third, education may affect a woman’s fertility and child-investment choices by improving a woman’s knowledge of contraceptive technologies and healthy pregnancy behaviors (eg, limiting smoking or drinking). Overall, fairly strong evidence shows that education affects fertility. Rosenzweig and Schultz (1989) demonstrate that a woman’s education explains the ability to use contraception effectively. Currie and Moretti (2003) evaluate a woman’s educational attainment using the availability of colleges in her county and show that higher maternal i

A reduction in childcare costs tends to have confounding effects, and the net effect on fertility is difficult to determine. On one hand, it represents a reduction in direct costs of childrearing, potentially leading to higher fertility. On the other hand, it may also increase female labor supply by encouraging mothers to enter paid work and thus reduce fertility.

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education improves child health outcomes and reduces parity. Monstad et al. (2008) use a similar natural experiment in Norway to show that more schooling leads to a postponement in childbirth, but not in completed fertility. One exception to these results are McCrary and Royer (2011), who use age-at-school-entry policies as identification and find that increasing schooling does not affect the probability of motherhood or age at first birth. One possible explanation to explain the difference in results is that education affects fertility nonlinearly and also at different stages of the transition and economic development. While education clearly seems to play an important role in determining fertility, the extent to which the increasing returns to schooling and rise in women in higher education can explain the postwar fertility trends and contribute to the aging phenomenon in developed regions deserves more investigation. 4.1.2.3 The Accessibility of Birth Control

The role of fertility regulation in explaining fertility has also been intensely debated. While demographers have historically emphasized contraceptive technology in the decline in fertility, economists have been more skeptical. For example, Westoff and Ryder (1977) attribute the decrease in fertility to a “contraceptive revolution” that began with the invention of the birth control pill (the pill). In contrast, Becker (1991/1981) argues that major changes in fertility were caused by shifts in the demand for children, and improvements in birth control methods were mainly an induced response to decreased demand for children rather than a cause of the decreased demand. Other economists have also pointed out that historical fertility transitions in the nineteenth and early twentieth centuries occurred without the advancement of new contraceptive technologies (Guinnane, 2011; Lee, 2003). Nonetheless, recent research suggests that access to birth control technology contributed to the decline in fertility in the modern era. In particular, the pill and legalized abortion—both of which arguably allow women to control their fertility more directly relative to other methods such as condoms and coitus interruptus (withdrawal)—seem to have played significant roles. Bailey (2010) uses state and time variation in legal access to birth control (“Comstock” laws) in the United States and finds that as much as 40% of the total change in the marital fertility rate from 1955 to 1965 could be attributed to the advent of the pill. Further, Bailey (2006, 2013) and Goldin and Katz (2002) find that the pill significantly altered labor market and fertility decisions and even relative wages for women in the United States. Similar, but more suggestive, evidence exists for Europe (Murphy, 1993). Legalized abortion also appears to have been a contributing factor to declining fertility. Levine et al. (1999) use state and time variation to find that legalization of abortion led to a 5–8% decline in birth rates, with a larger decline among teens and nonwhite women. Access to legalized abortion may also have affected fertility indirectly, via increased schooling investments among cohorts who were exposed to abortion reforms (Angrist

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and Evans, 1999). Nonetheless, unclear is to what extent the results from these studies, which have mostly been set in the West, can be extrapolated to currently developing countries, as the legalization of oral contraception and abortion in the West coincided with various concurrent forces, including increased demand for women’s work, improvements in the quality of education for women, lessened discrimination against women, and shifting norms about the role of women. That said, studies using panel aggregate data and other settings outside the developed world also support that abortion affects fertility. For example, using a cross-country panel analysis, Bloom et al. (2009) find that removing legal restrictions on abortion significantly reduces fertility and increases a woman’s labor supply. Pop-Eleches (2006) finds that an abortion ban in Romania in 1966 led to a doubling of birth rates. 4.1.2.4 The Baby Boom and Bust

As the baby boom cohorts approach retirement age, they will increase the rate of population aging in developed regions. The causes of the baby booms and subsequent busts in the Western world are hotly contested. The puzzle in part stems from the concurrence of rising fertility with increasing urbanization, educational attainment, and women’s labor force participation—trends typically associated with declining fertility and counter to the standard Becker framework. Perhaps the most well-known economic theory to explain the baby boom and bust is Easterlin (1961). Easterlin theorizes that couples choose to have children based on a ratio of potential earning power and the desire to obtain material objects. The economic stability of the country and the way that people are raised to value material objects determine this ratio. The “relative income” theory explains the baby boom by suggesting that the late 1940s and the 1950s brought low desires to have material objects because of the Great Depression and World War II. Plentiful employment opportunities after the war gave rise to a high relative income, which encouraged high fertility. The next generation had a greater desire for material objects; however, an economic slowdown in the United States resulted in fewer job opportunities. This combination resulted in lower fertility rates, or the baby bust. An important implication of Easterlin’s hypothesis is that the cohort size should be negatively correlated with fertility rates, but the empirical support for this notion has been mixed (see Macunovich, 1998, for a review). Critics of the Easterlin model have emphasized the faulty prediction of the model that the United States should experience another baby boom in the 1990s. In reality, fertility rates did not change markedly in the 1990s. Other intriguing theories have been proposed to explain baby booms. Greenwood et al. (2005) suggest a new and specific price-based explanation for the baby boom. In an overlapping generation’s framework, they argue that a burst in the productivity of household technology in post-World War II United States led to a reduction in the shadow price of childbearing. These so-called engines of liberation, such as microwaves, dishwashers, and other innovations, lowered the cost of having children and led to a

The Global Demography of Aging

pronounced rise in fertility between 1940 and 1960. However, Bailey and Collins (2011) do not find any support for this hypothesis. They find similar baby booms and busts in populations without such innovations, including the Amish, who use modern technology less than other US households. Further, they find that county-level appliance ownership and electrification negatively predict changes in fertility, suggesting that advances in household technology are not responsible for the US baby boom. Butz and Ward (1979) provide an empirical framework in the spirit of Becker that emphasizes the distinction between male and female earnings. Their analysis suggests that the baby boom of the 1950s can be explained as a response to rising male income, whereas the subsequent baby bust was primarily due to the increases in female wages and income. Assuming that the husband’s time is not an important input in the child production function and that children are normal goods, an increase in the husband’s market wage shifts the household budget out and leads to a higher demand for children. In contrast, an increase in women’s wage increases the price of children because it increases the opportunity cost of childrearing (and bearing). While not without detractors (see for example Macunovich, 1995), Butz and Ward’s article has become one of the canonical articles on US fertility due to its simplicity and conformity with the Becker framework. Their article was published in 1979, so an updated analysis using newer and longer time series data, and perhaps using data from other developed countries, would be very useful in understanding fertility in more recent decades. 4.1.3 Developing Countries The experience of population growth and fertility has been markedly different in developing regions, where many countries are still experiencing their demographic transitions. Less data on developing countries’ mortality and fertility in their pretransitional periods are available, but from what we know TFRs were typically at six or higher and life expectancy was highly variable and averaged in the low 20s (Bhat, 1989). However, once the fertility transition began in developing regions, the pace of fertility decline that has occurred was remarkably rapid: TFR fell from 6.0 to 2.7 in 1965–70 and 2010–15, after staying at around six children per woman since 1950. Recent evidence from Asian countries suggests that some developing countries may be on a trajectory toward even lower long-run fertility than high-income countries. Korea, Singapore, and Hong Kong all have estimated TFRs close to 1.0 in 2010, compared with values ranging from 3.5 to 6.0 children per woman in 1970. Latin America has undergone a less dramatic decline, where TFR remains above replacement at 2.15, although exceptions exist, such as Brazil, where TFR is now at 1.82. Sub-Saharan Africa provides a contrasting example, where TFR remains high at 5.1 children per woman. Baby booms and busts also occur in developing countries, but more as a consequence of changes in fertility associated with ongoing demographic transitions, where dropping fertility rates tend to follow rapid declines in infant and child mortality. The lag between

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falling mortality and fertility created a “baby boom” generation, which was larger than the cohorts that preceded and followed it. This change in age structure has important implications for economic growth: an initial surge in young dependents soon translates into an increase in the proportion of the working-age population. This phenomenon is known as the “demographic dividend” (Bloom et al., 2002). Because labor supply and savings are higher among working-age adults, economic growth increases dramatically as a baby boom generation moves through the age structure. The eventual aging of these baby boom cohorts, which are affected by increasing longevity over time, will play a large role in driving rapid population aging in the coming decades. As developing nations reach the end of their demographic transitions, the equilibrium phenomena of lower fertility and higher life expectancy will continue to increase the proportion of older people in the population. Many of the reasons for declining fertility in developing countries apply to the earlier decline in developed regions. The following sections discuss several reasons that are more distinct to the experience of developing countries in recent decades. 4.1.3.1 The Decline in Child Mortality

A decline in fertility often follows falling child mortality. Many countries experienced this during their demographic transitions, including England and Sweden in the nineteenth century and India and other developing countries more recently. Declining child mortality has therefore often been proposed as an important determinant for the decline in fertility, although what the standard fertility framework would predict as a result of a decline in child mortality is unclear. On one hand, lower child mortality could be interpreted as a reduction in the cost of children because it reduces the number of births needed to produce a surviving child. This would imply a resulting increase in fertility. On the other hand, when mortality is stochastic and parents want to avoid the result of few (or zero) surviving children, a precautionary demand for children, or “child hoarding,” results (Neher, 1971; Nugent, 1985). Sah (1991) and Kalemli-Ozcan (2003) suggest that when hoarding is taken into account, declining child mortality can have a strong negative impact on fertility. A decline in child mortality may also induce a quality–quantity interaction. For example, parents might substitute efforts to prevent child death with expenditures on other aspects of quality, because the rate of return on such expenditures would increase. If total parental expenditures increased, the effective price of quantity could increase and the demand for surviving children would decrease (Becker, 1960). However, a decline in child mortality also reduces the price of child quantity, which tends to stimulate fertility, particularly if the precautionary demand for children is modest (Galor, 2012). The evidence supporting the causal effect of child mortality on fertility is mixed. Using panel data from 118 countries, Angeles (2010) shows that a fall in lagged child mortality of one standard deviation is associated with a decline in TFR of 1.13 children per

The Global Demography of Aging

woman. However, using a large panel of countries, Murtin (2013) finds that education, rather than child mortality or economic growth, has been the main socioeconomic determinant of the decline in fertility since 1879. The difficulty in identifying the causal impact of child mortality is that it is often associated with drops in adult mortality and survival, which may in turn affect parental demand for children. Decline in adult mortality may also play a role by extending the time horizon over which returns to human capital investments can be reaped, which may encourage investment in child quality and simultaneously lower fertility. Further, child mortality and fertility may be endogenously determined. A growing literature indicates that education affects both child health and fertility (Breierova and Duflo, 2004; Chou et al., 2010; Osili and Long, 2008). A less discussed issue is the impact of declining child morbidity, which could be viewed as a reduction in the cost of child “quality.” Per the Becker framework, this would then induce a fall in child quantity. Bleakley and Lange (2009) find that large-scale hookworm eradication in the US South in the early twentieth century not only improved the health and human capital outcomes of the affected children, but also decreased fertility in the treatment areas relative to control areas. Overall, however, the evidence is insufficient to conclude that the decline in child mortality is a major determinant for the fall in fertility, and more research is needed.

4.1.3.2 Anticipated Future Support from Children

Old-age security is frequently cited as a rationale for childbearing among traditional societies. Per this argument, anticipated future support from children is an important component of the fertility decision. Hence, child hoarding and replacement effects may be especially strong in developing countries where child mortality is somewhat high and limited credit markets and societal institutions for old-age support exist (Caldwell, 1976; Nugent, 1985). The empirical evidence supporting this hypothesis is surprisingly scarce. A few studies argue and provide evidence that fertility in developing countries has declined due to a lessened need for old-age support from children as a result of development and modernization. Using cross-country data, Entwisle and Winegarden (1984) show that fertility varies inversely with the level and breadth of publicly provided old-age support. In rural Mexico, Nugent and Gillaspy (1983) find some evidence of fertility reduction when farmers were given access to a government-backed pension program.j More research is certainly needed to understand whether the gradual shift away from family-based old-age support in developed countries will also occur in developing countries and how much the growing availability of substitutes for old-age security affects the decline j

The issue of endogeneity is ever present. Pension programs are also likely introduced as a consequence of lower fertility and higher demand for government-financed old-age support.

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in the demand for children. We return to a related issue on the living arrangements for the elderly in Section 5.3. 4.1.3.3 Contraceptives and Family Planning Programs

One major difference between the fertility transitions in developed and developing regions is the introduction of contraceptives and family planning programs. Family planning programs were highly popular from the 1970s to the mid-1990s, but fell out of vogue by the 2000s (Bongaarts et al., 2012). Such policies can range from more coercive interventions, eg, China’s one-child policy, to providing contraceptive information and services, such as the Family Planning and Health Services Project in the Matlab region of Bangladesh.k How much the availability of modern contraceptives and family planning policies played a role in the fertility decline in developing countries is yet another topic of heated discourse. Supporters argue that family planning policies and the availability of modern contraceptive technology, coupled with an “unmet need” for birth control, has contributed significantly to the fertility transition, accounting for more than 40% of the decline during 1960–65 to 1985–90 (Bongaarts, 1997). Detractors contend that programs that are either coercive or simply lower the cost of contraception have limited success in altering fertility preferences, but most agree that more comprehensive, educational campaigns can be effective (Pritchett, 1994; Simmons, 1996; van Ginneken and Razzaque, 2003). The empirical evidence of the aggregate impact of family planning policies is mixed. Boulier (1986) uses cross-national data to show that the expansion of family planning programs from 1965 to 1975 resulted in significant fertility decline. However, both Schultz (1994) and Tsui (2001) find that family planning efforts have only a small effect on TFRs. Studies of specific programs have yielded more insight. The Bangladesh MATLAB program, an experimental maternal, child health, and family planning program, suggests that treated villages experienced fertility declines of 17% and that the decline in fertility persisted for nearly two decades (Joshi and Schultz, 2013). However, because MATLAB introduced other community health services as well (such as immunizations), disentangling the impact on fertility of family-planning aspects of the program from these other services is difficult. A similar quasi-experimental program that took place in Ghana in 1993 led to comparable reductions in fertility rates (Debpuur et al., 2002). Colombia’s large-scale Profamilia family planning program is estimated to have led to 9–12% of the total decline in fertility during the period of interest (Miller, 2010). Jones (2011) exploits arguably exogenous shocks in contraceptive availability in Ghana resulting from cuts in US funding to show that a reduction in supply leads to an increase in realized fertility of 10%. An interesting experimental study conducted k

China ended its one-child policy in November 2015, and how much fertility will increase, if at all, remains to be seen. Available from: http://www.nytimes.com/2015/10/30/world/asia/china-end-one-childpolicy.html?_r¼0.

The Global Demography of Aging

in Zambia found that women who were given access to contraceptives with their husbands had lower contraceptive use and more births than women who were given access to contraceptives alone, suggesting that intrahousehold tensions regarding fertility may be an important factor when determining contraceptive uptake (Ashraf et al., 2014). Overall, these studies show that contraceptive accessibility and family planning programs do matter, but are unlikely to be a major contributor to the rapid decline in fertility observed in most developing countries. 4.1.3.4 Education

The role of education has arguably played an even more important role in the fertility decline in developing regions. As governments and international organizations such as the World Bank and the UN have continued to emphasize education as a primary driver of economic growth, the quantity of schooling in many developing regions has increased considerably. As Murtin (2013) has found using aggregate data, education, rather than income growth or the fall in child mortality, is the most robust explanatory factor of fertility. In Section 4.1.3.2, we discussed the mechanisms through which education may reduce fertility and some of the supporting evidence from developed regions. The evidence from micro studies set in developing countries also supports this hypothesis. Duflo et al. (2015) conducted a large randomized evaluation in western Kenya to show that education subsidies reduced teen pregnancy. Chicoine (2012) exploits a policy change in Kenya that lengthened primary school by 1 year to find similar results—the reform led to more schooling, delay in marriage, and reduced fertility. Breierova and Duflo (2004) use a large school construction program in Indonesia to estimate the causal impact of education on fertility and find that schooling leads to lower fertility. 4.1.3.5 The Impact of Social Media

A recent strand of economic research has focused on how other factors have altered preferences toward smaller family sizes. Social media, for example, appears to have played a role in shaping preferences. La Ferrara et al. (2012) show that exposure to soap operas featuring families that are much smaller than reality have led to a decline in the number of births by around 10%. Similarly, Jensen and Oster (2009) find that the introduction of cable television leads to an improvement in the status of women and lower likelihood of pregnancy. While the digital divide between high- and low-income countries remains large, Internet use and information technology services continue to grow rapidly in many developing countries (Chinn and Fairlie, 2010), and examining how access to such other forms of information affect fertility preferences and health behaviors will be interesting. 4.1.4 The Future of Fertility In the coming years, the rate of fertility will be a crucial determinant of the structure of the future aging population—yet another subject of debate. Fig. 6 shows the projection

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of TFR (medium variant) to 2100, which depicts fertility leveling after 2050 for less developed regions. For more developed regions, fertility appears to converge to what appears to be a long-run equilibrium of slightly below replacement level. This projection is consistent with one view that the pace of fertility decline will slow but continue as developing countries approach the end of the fertility transition, that fertility near the replacement level will prevail in the long run, and that some variation across countries will occur depending on socioeconomic conditions (see Bongaarts, 2002, for a discussion). Morgan (2003) argues that despite ideological and structural changes to society, biological dispositions will still compel families to have two children. However, with TFR going below replacement levels in many countries (as of 2010–15, 170 out of 233 countries have below replacement TFR), much skepticism exists regarding its recovery to above 2.1 (Lesthaeghe and Willems, 1999). Kohler et al. (2006) argue that the lowest-low fertility that has been concentrated in parts of Europe and Asia will spread to other parts of the world. They also predict that lowest-low fertility will continue for several decades, although they anticipate a slight reversal as seen in some European Union (EU) countries such as Italy and Spain. Lowest-low fertility has dramatic implications for the population: combined with sustained low mortality, persistent TFR levels at or below 1.3 imply a reduction of the annual number of births by 50% and a halving of the population size in less than 45 years (Kohler et al., 2006). Prevailing below replacement fertility also has compounding effects on population decline in the sense that shrinking cohorts imply declining numbers of potential parents. However, recent signs of recovery have been seen in cohort fertility in many regions of the world, even in regions with where lowest-low fertility has been observed (Myrskyl€a et al., 2013). Because no compelling theory of reproductive behavior exists in low-fertility societies, much of the predictions about future fertility remain unfortunately speculative. Certainly, past predictions about current fertility have not held up to scrutiny. Further, while the economic research in recent years has been successful in identifying causal determinants of fertility, the most rigorous research occurs at the micro level and is context specific, so that the degree of external validity is unclear. As we have reviewed, the empirical evidence is also often mixed depending on the setting. Further, impacts on fertility have often been economically small. Many unanswered puzzles remain at the macro level as well—for example, why does the United States have higher fertility than both Canada and the EU when the United States does not have subsidized daycare and has one of the least generous parental leave policies? Finally, whether governments should design policy to directly intervene in individual fertility choices remains controversial, although many examples of such population policies exist (both to increase and to decrease fertility). Also unclear is whether governments should aim to increase population in countries with below replacement fertility; after all, population control was the goal for neo-Malthusians and remains so for many

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governments today in developing countries. Nonetheless, policies such as helping women reconcile tensions between work and family life may be valuable to society in other aspects with the additional “benefit” of increasing fertility.

4.2 Increase in Life Expectancy The second key factor behind population aging is increasing life expectancy. As Fig. 7 shows, global life expectancy increased from 47 years in 1950 to over 65 today and is projected to reach 83 years by 2100. Both developed and developing countries are seeing rises in life expectancy—developed regions witnessed an increase of more than 10 years since 1950–55 to 78.3 in 2010–15, whereas developing regions experienced a remarkably rapid increase exceeding 20 years over the same period, from 41.5 to 68.8. In particular, countries in East Asia have had the most dramatic gains. The increase in life expectancy is responsible for a significant portion of the increase in population aging, although its role has not been as large as the fertility decline. Bloom et al. (2010a) calculate one-fifth of the projected rise in India’s 60 + population between 2000 and 2050 is attributable to rising life expectancy during that period. An analogous exercise for China shows that increasing life expectancy is responsible for one-seventh of the rise in China’s elderly population. The convergence in life expectancy between more and less developed regions, however, has stalled for two reasons. First, the HIV/AIDS epidemic and armed conflicts have led to decreased life expectancy in some African countries over the last few decades. Second, the collapse of the Soviet Union led male life expectancy in Russia and Eastern Europe to fall dramatically in the 1990s, so much so that a 10-year life expectancy 90

Life expectancy at birth (years)

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Fig. 7 Life expectancy, by level of development, 1950–2100.

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gap now exists between men and women in Russia. Nonetheless, the gap in life expectancy at birth between developed and currently developing regions is projected to shrink to approximately 7 years by 2100. Combined with the decline in fertility, the rise in life expectancy will result in a sharp increase in the population share of the elderly. In Section 3, we discussed several reasons for the historical decrease in mortality in the nineteenth and early twentieth century, including economic growth, public health interventions, and medical innovations, including antibiotics and sulfa drugs and success in reducing communicable diseases (Cutler et al., 2006; Cutler and Miller, 2005; Jayachandran et al., 2010; Sickles and Taubman, 1993; Wolpin, 1997). These reductions mainly occurred in early and middle life. We now turn our attention to increases in longevity in the last half-century. 4.2.1 Developed Countries Unlike the earlier decline during the nineteenth and early twentieth centuries, the decline in mortality in the latter half of the twentieth century has been concentrated in late life. Increase in longevity in recent decades in the developed world is mostly attributed to advances in medical technology, especially those that led to reductions in cardiovascular disease mortality (Cutler et al., 2006). In the United States, cardiovascular disease mortality has declined by more than 50% since 1960, and cardiovascular disease mortality reductions account for 70% of the 7-year increase in life expectancy between 1960 and 2000. The development of bypass surgery in the 1960s, angioplasty in the 1970s, and new medications to treat hypertension have all contributed to the reduction in cardiovascular disease mortality (Cutler and Kadiyala, 2001). In addition to advances in medical technology, the decline in smoking is widely acknowledged as a major factor in reducing cardiovascular disease (Cutler and Meara, 2004). US smoking rates have halved since the US Surgeon General’s landmark 1964 report on the harms of smoking (United States Public Health Service, Office of the Surgeon General, 1964). The existing research has shown that higher taxes dramatic reduction in smoking has sparked a large body of literature examining the impact of different smoking cessation policies, and the research suggests that cigarette taxes, smoking bans, and comprehensive advertising bans can be effective in lowering smoking consumption (Blecher, 2008; Chaloupka and Warner, 2000; Evans et al., 1999; Saffer and Chaloupka, 2000). Continuing declines in infant mortality, mainly due to improved neonatal medical care for low birth-weight babies, account for an additional 19% of the increase in life expectancy since 1960 in the United States (Cutler and Meara, 2004). In sum, improvements in medical technology and the reduction in smoking are responsible for the bulk of the increase in life expectancy. Other contributing factors include continual declines in infant mortality; reduced mortality from external causes, primarily motor vehicle accidents; reduced mortality from pneumonia and influenza; and a slight decrease in cancer mortality. While we use the United States as a case study,

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improved medical technology and reduced smoking led to a similar decline in adult mortality in other developed countries (Cutler et al., 2006). 4.2.2 Developing Countries Life expectancy is lower in developing countries (Fig. 7), but has been on a rapid upward trajectory. For many developing countries, life expectancy increased more than 20 years in just a few decades from 1960 to 2000. In India and China, life expectancies have risen by nearly 30 years since 1950. In sub-Saharan African countries, life expectancy rose by 13 years from 1950 to 1990, before stagnating in part due to the HIV/AIDS epidemic. The decrease in mortality in developing countries post-World War II occurred fairly rapidly: adult mortality fell from approximately 300 to 100 deaths under age 50 per 1000 alive at age 15. In developed countries, the number fell only from 102 to 62. Child mortality declined even more in less-developed regions, from 247 deaths under age 5 per 1000 live births in 1950 to 65 in 2010, which likely played the most important role in increasing life expectancy in developing countries (Soares, 2007). However, a large gap in child mortality remains between developed and developing countries; 99% of global child deaths occur in developing countries. Overall, mortality reductions in developing countries in the modern era took place across the entire age distribution, with significant improvements in the survival of both children and adults (Soares, 2007). The determinants of mortality in low-income countries also differ significantly from those in high-income countries. In the latter, the current leading causes of deaths are noncommunicable diseases (NCDs) such as cancer and cardiovascular diseases, while in the former infectious diseases still play a dominant role in deaths, although the incidence of NCDs is also growing rapidly in low-income countries.l Modern-era mortality reductions experienced by developing regions are similar to those developed regions experienced in the beginning of the twentieth century (Becker et al., 2005). Specifically, life expectancy has increased mainly through a decline in influenzarelated disease (eg, pneumonia), infectious diseases, and diarrheal diseases (Palloni and Wyrick, 1981; Preston, 1980; Soares, 2007). The existing evidence suggests public health infrastructure, including the development of water supply, sewerage, and immunization, can explain roughly 50% of the mortality decline in developing countries since WWII (Preston et al., 1981). Much of the mortality decline appears to have occurred independently of improvements in income and nutrition, especially where health programs have become less reliant on countries’ economic conditions but more dependent on the concerns of the developed world or international organizations (Heuveline, 2001; Preston, 1980; Soares, 2007). Increases in educational attainment, and in particular, women’s education also appear to have played important roles (Cutler et al., 2006; Preston, 1980; Soares, 2007). Numerous l

In Section 5.1, we return to the changing nature of aging.

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studies using microdata have demonstrated that female schooling has strong explanatory power of child mortality (see Soares, 2007 and Fuchs et al., 2010, for a review). Growing causal evidence that exploits natural experiments in school expansions and compulsory schooling laws on child mortality also highlights the negative impact of schooling (Breierova and Duflo, 2004; Chou et al., 2010; Lleras-Muney, 2005). Relatedly, the diffusion of knowledge such as the germ theory and simple changes in health behavior appear to have significantly reduced mortality rates (Preston, 1996). Mortality declined rapidly in less-developed regions, in part because the earlier development of modern medical technologies and public health measures in currently highincome countries enabled somewhat quick diffusion to the rest of the world (Cutler et al., 2006). At the same time, much more can clearly be done from a policy perspective to further reduce mortality in developing countries. Due to lack of financial incentives, pharmaceutical research on diseases that affect low-income countries, such as malaria and tuberculosis, is limited. Because of high costs, antiretroviral therapy only reaches a small percent of the millions of HIV/AIDS-infected patients in sub-Saharan Africa (Kremer, 2002). 4.2.3 The Future of Mortality As with fertility, the views regarding the trajectory and nature of mortality over the coming decades range widely. Oeppen and Vaupel (2002) suggest that, based on the average life expectancy gain of 2.4 years per decade, record life expectancy could reach 97.5 years by the middle of this century and 109 by 2100. More tempered estimates suggest average life expectancy will approach 90 years by the end of the twenty-first century (Lee and Carter, 1992; Tuljapurkar et al., 2000). While most scholars believe that advances in medical technology and public health improvements will continue to drive down mortality rates at all ages, there is considerable dissent on the speed and magnitude of these trends, as well as the role of biology on these trends (Carnes and Olshansky, 2007). More pessimistic scholars suggest that achieving further life expectancy gains may become increasingly difficult as human longevity approaches its biological limit of about 85 years (Fries, 1980; Olshansky et al., 2001). They also argue that past life expectancy improvements in the first half of the twentieth century were largely driven by reductions in infectious disease mortality among children and young adults in the first half of the 20th century, and it would be unlikely to see the same large reductions among the current major causes of death, such as heart disease and cancer (Bongaarts, 2006). In fact, Olshansky et al. (2005) argue that with growing obesity rates in the United States, we may expect to see life expectancy decline by close to a year in the first half of this century.

4.3 Migration as a Determinant of the Age Structure Finally, we discuss migration as a factor to explain changes in the population age structure. According to some analyses, international migration is now the dominant

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determinant of the size, rate of change, and composition of populations in developed countries. This holds true especially in Europe, where fertility is persistently low compared with the United States, Canada, and Australia. Within the 15 original European Union countries, the net demographic effect of international migration in recent years has been to add between 1.4 and 1.9 million persons per year to the total population, and net immigration far outpaces the rate of natural increase (the excess of births over deaths) (Coleman, 2008). Further, migrants tend to be of prime working age and hence boost the labor force population of the receiving country (Zlotnik, 2012). Not only do migrants directly affect the age structure and labor force of the host country, but their differential fertility or mortality also compounds these effects. For example, immigrants may increase fertility in the recipient country because they tend to have average higher fertility (Blau, 1992; Coleman, 1994). The TFR of many countries in Western Europe has been elevated by 0.1 or more due to the higher average fertility of immigrants, although substantial variation in fertility rates exists among immigrants from different origin countries. Immigrants from Pakistan, Bangladesh, Turkey, Morocco, Tunisia, and countries in sub-Saharan Africa have higher fertility than their European counterparts and have contributed to elevating total fertility in recipient countries. From 2001 to 2006, TFR in England and Wales increased from 1.63 to 1.86, and births from 594,634 to 669,601. Sixty-four percent of that increase is attributable to births to immigrant mothers (Coleman, 2008). As the children of immigrants move through the age structure, they will reduce the proportion of elderly in the population, ceteris paribus. As the later chapter on migration will further discuss, accurate migration data remain scarce even for developed countries, and hence the impact of immigration on the age structure is difficult to quantify. Policymakers have touted immigration as the panacea to population aging in the face of low fertility in developed countries—with certain caveats. While immigrants tend to be younger, immigrants also age, so the immigration flow required to maintain the age structure increases progressively over time. Coleman (2008) simulates the old-age dependency ratio based on several migration scenarios and shows that even with aggressive projections of “replacement migration,” the potential support ratio continues to decline. A similar United Nations, Department of Economic and Social Affairs, Population Division (2001) study attempts to quantify the migrant flow required to maintain 1995 support ratios for several countries, and these simulations indicate that very large net migration flows are necessary. For example, in the case of the United Kingdom, an average annual net inflow of 1.2 million migrants would be required to maintain the support ratio at the present level of 4.15 until 2050. (The average annual number of net migrants in the United Kingdom from 2008 to 2012 was 201,000.) An inflow of such magnitude would hardly be sustainable, as this would imply that the United Kingdom’s population would reach 100 million by 2030, 200 million by 2070, 300 million by 2090, and so on (Shaw, 2001).

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We can also look to the past to investigate the long-run equilibrium effects of migration. LeBras (1991) analyzes the demographic impact of postwar migration in several OECD countries. By simulating a counterfactual population projected from 1946 with the assumption of zero migration, the author compares the projected with the actual realized population structure in the early 1980s. He finds that international migration did indeed reduce population aging in the sense that the actual median age is lower than the projected median age. However, the reduction is small (less than 1 year), and the proportion of the population over age 65 was reduced by less than 1% over the study period, during which substantial net migration gains occurred (LeBras, 1991). In turn, international migration has exacerbated population decline and hastened population aging for origin countries. This is because migration is selective of prime working-age individuals, leaving origin countries with smaller populations and higher dependency burdens (Zlotnik, 2012). Several countries in Eastern Europe have experienced negative net emigration, including Latvia, Lithuania, Bulgaria, Romania, Poland, and Slovakia. Such patterns can reverse quickly, however. For example, Russia lost 110,000 people to net emigration in 2003, but by 2007 net immigration had risen to 241,000, much of it from Central Asia (Coleman, 2008). The overall evidence suggests that migration has not been a major driver of population aging, nor it is a sufficient “cure” for revitalizing aging societies with low fertility rates. Although international migration has generally contributed to reducing population aging in host countries, the effect is small even when migration flows are large, and the estimated net migration flows needed to sustain current support ratios are unrealistically large. The final trend we note is “out-migration,” which refers to movement away from particular regions or cities within countries, a familiar pattern in both developed and developing countries. Rural to urban migration in developing countries is particularly marked. We discuss the impact of out-migration on living arrangements of the elderly in Section 5.3.

5. THE NATURE OF AGING As people live longer, considerable debate concerns the quality of life in later years. Can we expect additional years to be characterized by both physical and mental health, or will they be characterized by disabling chronic illnesses? Who do the elderly live with, and who supports them financially and physically? This section describes the changing nature of aging and some potential implications for research and policy.

5.1 The Rise of Noncommunicable Diseases As discussed in Section 3, infectious diseases were the dominant cause of death for much of human history. As mortality has fallen sharply over time, the global disease landscape

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has also shifted dramatically. For example, the top three causes of death in 1900 in the United States were influenza, tuberculosis, and gastrointestinal infections, while heart disease, cancer, and noninfectious airway diseases were the top three in 2010 (Jones et al., 2012). In particular, the prevalence of chronic conditions—known as noncommunicable diseases (NCDs)—has risen at an alarming rate during the past two decades in both developed and developing countries. NCDs and aging are intrinsically linked: age is a well-established risk factor for NCDs, and the burden of NCDs lies primarily with the elderly because NCDs are generally long lasting and slow growing. NCDs include a wide range of chronic conditions, but the four most prominent NCDs (as measured by their contribution to disability adjusted life years, or DALYs) are cardiovascular disease, cancer, chronic respiratory diseases, and diabetes. The World Health Organization (WHO) estimates that these four NCDs alone were responsible for the deaths of more than 31 million people worldwide in 2010 (Alwan, 2011). Dementia, which is characterized by progressive cognitive decline that interferes with independent functioning, is another chronic disease of aging. While NCDs have typically been viewed as “diseases of affluence,” roughly 80% of all NCD deaths now occur in low- and middleincome countries, and NCDs are the largest cause of death in most developing regions, excluding Africa (Alwan, 2011). As populations age, annual NCD deaths are projected to rise substantially, reaching 52 million by 2030. Annual cardiovascular disease mortality is projected to increase by 6 million and annual cancer deaths by 4 million. In contrast, annual deaths from infectious diseases are projected to decline by 7 million over the next 20 years (Alwan, 2011). Comorbidities are also increasing; many of the most common NCDs frequently occur simultaneously with other conditions, and growing numbers of people have more than one condition, especially if they smoke. In the United States, an estimated 85% of all health care is used by people with at least one chronic condition, and two-thirds of all Medicare spending is on people with five or more chronic conditions (Benjamin, 2010). 5.1.1 The Prevalence and Economic Costs of Dementia Although not one of the four best-established NCDs, we devote a subsection to dementia because of its rising prevalence and severely disabling nature—the disability weight for dementia was estimated to be higher than for all health conditions except spinal cord injury and terminal cancer (WHO, 2003). The potential costs of dementia are also huge, both in terms of direct medical and care costs, as conditions associated with dementia are typically progressive and irreversible, as well as indirect costs such as lost productivity of family carers, as care of dementia patients can be extremely time intensive. Understanding the risk factors and prevalence of dementia is therefore a high priority for policymakers, but data challenges abound—primarily the paucity of quality data and the uncertainty in ascertaining dementia. Recent credible estimates place the prevalence of dementia at

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around 14% for the US 70+ population using data from the Health and Retirement Survey (Hurd et al., 2013; Plassman et al., 2007). Estimates of the prevalence of Alzheimer’s disease range from 4.3% among the 75+ population in 1997 (Brookmeyer et al., 1998) to 9.7% among the 70+ in 2002 (Plassman et al., 2007). Prevalence estimates of European dementia are typically slightly lower, ranging from 6% to 9% among the elderly (Lobo et al., 1999; Ott et al., 1995). Projections suggest that the prevalence of Alzheimer’s will more than triple in the next few decades in the United States (Brookmeyer et al., 1998; Hebert et al., 2003). Global estimates remain speculative—some of these estimates rely mainly on expert opinions—but they suggest that the prevalence in developing regions is currently lower but will grow rapidly in the next several decades, tripling for some Asian countries including India and China. With growing prevalence come increasing concerns about the burgeoning costs of dementia. Estimates of the total monetary cost of dementia range from $150 billion to more than $215 billion, which is comparable to the financial burden of heart disease (the current most costly disease in the United States), and these estimates are projected to roughly triple by 2050 (Alzheimer’s Association, 2010; Hurd et al., 2013). The monetary cost per adult is projected to increase by approximately 80% by 2040 (Hurd et al., 2013). However, such projections typically derive age-specific incidence rates from community-level studies and apply those rates to population projections to predict future prevalence rates assuming that prevalence rates are static, which may not be realistic. Advances in care and medical technologies may alter the costs of dementia. Also not clear is whether the prevalence of dementia has increased solely because of population aging per se, or whether prevalence among the elderly population has also grown over time, and, if so, why. Regardless, the impact of dementia will clearly be felt more forcefully in coming decades as the population share of the elderly continues to rise. We will return briefly to the impact of dementia on the household in Section 5.3. 5.1.2 The Risk Factors of NCDs and Policy Implications The increasing prevalence of NCDs suggests a clear need for new approaches to prevent and treat such conditions. From a public finance perspective, the growing prevalence of NCDs accompanying population aging may lead to much larger health costs. Moreover, because of the changing demographic structure, any increased health costs may need to be financed by a relatively smaller working-age population. Hence, curbing the growth of NCDs has become a major concern for health policymakers. Considerable scope for intervention exists. Although nonmodifiable conditions such as genetic makeup, age, and sex determine some risk factors, individuals can avoid NCDs and improve health outcomes in concrete ways (Bloom and Shannon, 2014). For example, the key underlying causes of death globally from NCDs are high blood pressure, tobacco use, high blood glucose, physical inactivity, and overweight/obesity—all conditions that are at least partially rectifiable or avoidable.

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The prevalence of these modifiable risk factors varies by region, gender, age, and income level (Alwan, 2011). For example, the disease consequence of smoking occurs disproportionately among the elderly, because they tend to have been smokers for a long time. While the benefits of smoking cessation are proportionately less among the elderly and may manifest more slowly than among younger smokers, cessation remains the most effective way of altering smoking-induced disease risks at all ages, including those over the age of 60 years (Burns, 2000). Overweight/obesity is more prevalent in high-income countries, where more than half of all adults are overweight and just over one-fifth are obese. However, overweight/ obesity has recently started to affect lower-income countries: the increase in prevalence from 1980 to 2008 was twice that of the corresponding increase in upper-middle and high-income countries (Finucane et al., 2011). In fact, Mexico has the highest rate of obesity in the world with a 32.8% adult obesity rate, just overtaking the United States at 31.8% (United Nations, Food and Agriculture Organization, 2013). Although obesity is less of a problem among today’s elderly than among adults and children, obesity prevalence is growing progressively among older age groups in some countries, including the United States (Arterburn et al., 2004). And as the current overweight cohorts age, obesity will become a much more dominant problem among the elderly. In terms of potential policy recommendations, regular physical activity, limited tobacco use, and healthy diet are obviously needed changes. In particular, physical activity is important for the elderly not only for its direct cardiovascular health benefits, but also for its associated lower risks of cognitive impairment, Alzheimer’s disease, and dementia of any type (Laurin et al., 2001). Smoking in high-income countries has decreased dramatically due to both government regulation (such as curbing smoking in public spaces, imposing cigarette taxes, and launching extensive media campaigns), and believing that similar results can be achieved in developing countries is not unreasonable. Promoting exercise and healthy eating in both children and adults remains a major challenge worldwide. In the United States and United Kingdom, experiments with “nudging”—the use of behavioral economics to steer people towards more desirable decisions by presenting choices in different ways—have shown mixed success, eg, front-of-package labeling or calorie posting designed to help consumers make healthier food choices (Bollinger et al., 2010; Downs et al., 2009). The impact of more controversial efforts such as the “soda ban” (banning of soft drinks in cups larger than 0.5 l) in New York City have yet to be fully evaluated. Systematic research, perhaps via randomized-control trials, is needed to understand which interventions are most effective.

5.2 The Question of Compression or Expansion of Morbidity As life expectancy and the epidemic of NCDs continue to rise, how do health and quality of life of the elderly change as people get older? If people live longer, but the additional

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years lived are spent in disability or ill health, then the impact of population aging on medical spending will be substantially more severe. A related key question concerns at what stage of life morbidity sets in. The notion of “compression of morbidity,” in which morbidity is thought to condense in the years near the end of life, has remained a source of debate since Fries first introduced it in 1980. Fries suggested that the same forces that led to the decrease in mortality would also result in a postponement of disease and disability, so that ill health would be compressed into a shorter period of time prior to death. Other scholars, such as Gruenberg (1977), posit the opposite, where reduced mortality will lead to a pandemic of chronic diseases and an expansion of morbidity. Manton (1982) proposes a dynamic equilibrium where the prevalence of disability would increase as mortality falls, but the severity of disability would decline, resulting in indeterminate impacts on disability-free and disabled life expectancies. The empirical evidence supporting these theories is mixed. Crimmins and Beltra´nSa´nchez (2010) argue that the evidence supporting the compression thesis is limited. For example, the incidence of a first heart attack has remained somewhat stable between the 1960s and 1990s and the incidence of some of the most common cancers has been increasing until recently. Cai and Lubitz (2007) find increases in the active life expectancy and decreases in life expectancy with severe disability using US data between 1992 and 2002. Crimmins et al. (1994) also find increases in the length of disability-free life, but no change in the length of disabled life when comparing the 1984 and 1994 cohorts of the Longitudinal Studies of Aging. Based on data from the Medicare Current Beneficiary Survey (MCBS), which covers a representative sample of the entire US elderly population in 1991–2009, recent work by Cutler et al. (2013) suggests that significant evidence exists for the compression of morbidity. As the MCBS is linked to time of death data, one advantage of this study is that the authors can define precise measures of disability-free and disabled life expectancies (whereas past studies have not been able to link health to an individual’s life stage). The authors find that for a typical person aged 65, life expectancy increased by 0.7 years between 1992 and 2005. Disability-free life expectancy increased by 1.6 years, and disabled life expectancy fell by 0.9 years. Overall, this evidence suggests that while the prevalence of diseases is indeed increasing among the elderly, the impact of such diseases on the individual has been reduced, being both less lethal and less disabling, and the period of life where ill health becomes disabling has been compressed toward the end of life. Consistent with this, the US labor force participation rate of people 65 years and older has continued to increase since 1985. While many other contributing factors likely exist, this phenomenon suggests that the elderly are able to remain productive participants of the workforce. However, open questions remain about whether this trend of compression has continued beyond 2005, whether compression of morbidity is occurring in other countries, and what are the reasons that explain the apparent variations between countries.

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5.3 Living Arrangements for the Elderly How will population aging affect household structure and living arrangements, and how do these trends differ between high- and low-income countries, by gender, and between urban and rural areas? Understanding these living arrangements is important from a policy perspective, as they are important determinants of the well-being and social and financial position of the elderly and the social support networks available to them. 5.3.1 Developed Countries We first review the evidence from developed countries. Using US Census data, Ruggles (2007) reports that intergenerational coresidence has declined dramatically since the mid19th century. Almost 70% of persons aged 65 or older resided with their adult children in the mid-1850s, but by the end of the twentieth century, fewer than 15% did so. These changes are attributable to several factors, including the establishment of the Social Security program, the decline of agricultural inheritance, and the rising income of the older generation (Engelhardt et al., 2005; Ruggles, 2007). Other frequently cited reasons for the decline of the joint family household include urbanization, industrialization, and demographic changes, although the data do not necessarily support these views (Costa, 1997; Ruggles, 2007). Other high-income countries generally mirror the US trends: a declining proportion of elderly persons live with their children, and older people spend substantially fewer years living in old-age coresidence. In Europe, more and more elderly choose to live independently for as long as possible, even after the death of a spouse. Coresidence is significantly less common among divorced men than among divorced women. A low-income situation in a family, among either children or older persons, increases the probability that parents and adult children will coreside (de Jong Gierveld et al., 2001). Overall, the literature suggests that privacy is a normal good for the elderly in developed countries and that increased living independence is desired (Costa, 1997, 1999; de Jong Gierveld et al., 2001; Engelhardt et al., 2005; Ruggles, 2007). Even as joint households are diminishing, children remain an important source of support for older people who live alone, providing care, social companionship, and housekeeping assistance. This informal, private-sector support still prevails across more developed countries, despite the availability of institutional care and other social services. Surveys in developed countries demonstrate that adult children tend to be more supportive, either through time or money, of parents living alone than of parents who are still together (de Jong Gierveld et al., 2001). At the same time, the idea of institutionalization as a “last resort” appears to be fading, and an increasing number of older persons have opted for residential care (Oldman and Quilgars, 1999). A notable trend in both the United States and Europe is the rise of unmarried cohabitation following divorce or bereavement. According to US Census figures, cohabitation figures for people over

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65 have tripled in the past decade, jumping from 193,000 in 2000 to 575,000 in 2010. Similarly, in Europe, cohabitation among the elderly is becoming increasingly common and accepted (de Jong Gierveld, 2004). As discussed in Section 5.1, the rise of population aging also brings the growing prevalence of NCDs, some of which, such as dementia, require time-intensive care. In the United States, unpaid caregivers, many of whom live in the same household and are typically family members, still provide most of the care of such debilitating disease. Caring for a person with Alzheimer’s or another dementia can often be very difficult, and the impacts on the caregiver range from lost earnings to emotional stress. Many people with dementia also receive paid services at home or in other settings such as adult day centers and assisted living facilities over the course of their illness (Alzheimer’s Association, 2010). At the same time, given the high average cost of these paid services, most households cannot afford them on a long-term basis unless they have Medicaid coverage or private long-term care insurance. Hence, the necessity of family caregiving of dementia patients may lead to an increase in intergenerational coresidence. 5.3.2 Developing Countries The experience of aging is substantially different in developing countries. Few developing countries offer formal pension plans for residents, especially those in rural areas, and few people are able to accumulate sufficient assets or savings to support themselves in old age. According to national surveys, less than 11% of the elderly have a pension of any sort in India (Uppal and Sarma, 2007). Further, saving is difficult or impossible for many because earnings are low. Hence, the elderly in developing countries typically rely on extended family for support in their old age (Hashimoto et al., 1992). At the same time, the factors that led to the devolution of the joint household in developed countries beginning a century ago are now affecting the developing world at a much faster rate. These changes, including the rise of nonagricultural employment, reductions in fertility, rural to urban migration, and changing societal mores, all have profound implications for the support and care of the elderly. For example, rising off-farm employment and increased mobility among working-age children implies that their elderly parents often live alone. The decline in fertility has left the elderly with fewer children to provide support, and, as migration fragments families, the elderly will have to work more and longer. In India, where old-age income support is limited, labor force participation remains close to 40% among the elderly and is even higher among the rural elderly (Uppal and Sarma, 2007). Similarly, in China a large proportion of the elderly continue to work in the formal labor force, and those who have withdrawn from the formal sector contribute to the informal sector through activities such as caring for their grandchildren and doing household chores (Pang et al., 2004). The family remains the dominant social institution for the support and care of the elderly in most of the developing world. In China, multigeneration family households

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are still one of the main living arrangements for the elderly, especially in rural areas (Pang et al., 2004). However, the trends may be changing. Data from the China Household Income Project and Census show that an increasing number of elderly persons, especially those in urban areas, are more likely to live with their spouses than in intergenerational joint households with their children (Meng and Luo, 2008). A recent RAND study uses the data from the China Health and Retirement Longitudinal Study (CHARLS) to show that while many Chinese elderly live alone or only with a spouse, most have a child living nearby to guarantee care when needed (Lei et al., 2011). In addition to the tremendous fertility decline (in part due to the family-planning policies that began in the early 1970s), scholars have attributed the declining joint household in urban China to an increased availability of pensions and the housing reform beginning in the 1990s, which increased housing availability and enabled elders to live alone (Meng and Luo, 2008; Palmer and Deng, 2008; Zeng and Wang, 2003). Similar trends in living arrangements have been observed in other developing countries. In India, while coresidence in a joint household remains predominate, the share of older Indians living with only a spouse or alone has doubled since the early 1990s, and the share of older Indians living with their children declined by about 7 percentage points during the same period (Kumar et al., 2011). Living patterns in Latin America are similar to those in Asia, although the regional average for coresidence with adult children is substantially higher in Asia. Another notable difference in Latin America is that the gender ratio of coresident children is near 1.0, whereas most countries in Asia and Africa exhibit son preference (Bongaarts and Zimmer, 2002). In African countries, the HIV/AIDS epidemic has affected family structure and living arrangements of the elderly. Many older people have lost the support of their children and are forced to care for young grandchildren. Using the Demographic and Health Surveys, Kautz et al. (2010) find that an increase in annual AIDS mortality of 1 death per 1000 people was associated with a 1.5% increase in the proportion of older individuals living alone and a 0.4% increase in the number of older individuals living in missing generation households. Not yet clear is whether the elderly in developing countries prefer to live independently or with family, or whether these preferences will shift over time. As previously mentioned, most prior studies of the effects of income on living arrangements in the developed world concur that individuals do have preferences over living arrangements and that because additional income increases the incidence of independent living, this is the preferred living state (eg, see Costa, 1999). Surveys focusing on the elderly will play increasingly important roles in understanding the living arrangements and well-being of the elderly. Institutionalization is still a somewhat new concept, and data on institutional care in developing countries are scarce. In China, where such facilities have traditionally been very limited, only an estimated 2% of the elderly are in institutional care (Gu et al., 2007), although institutional care is now expanding rapidly (Feng et al., 2012).

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A 2006 survey of 101 privately run care homes in Bueno Aires, Argentina, demonstrates that close to 40% of nursing homes are unregulated. Conditions even in the regulated homes are concerning, with most residents claiming a poor quality of life (Redondo and Lloyd-Sherlock, 2010). As population aging continues at a rapid pace, policymakers clearly need to pay increasing attention to the institutional care industry as it inevitably expands. Other challenges are particular to the developing world. First, higher female life expectancy becomes a problem in developing countries where literacy and financial independence for women are low (Chen and Volpe, 1998). Second, although fertility in rural areas tends to be higher than in urban areas, aging problems will be more serious in rural areas because of continuing rural to urban migration of mostly young people. In China, the rural–urban exodus has been deemed the largest flow of internal migration in history (Zhang and Song, 2003). A large share of the elderly lives in rural areas, where necessary institutional support and services are more difficult to obtain. Policymakers should thus pay special attention to elderly widows and those in rural areas. The topic of who cares for the elderly will also be of increasing importance to policymakers in the developing world, as the prevalence of NCDs such as dementia that require timeintensive care continues to grow and the potential pool of family caregivers diminishes due to changing social norms, migration, conflict, and HIV/AIDS.

6. OPEN RESEARCH QUESTIONS We end with a collection of open research questions that have emerged throughout the chapter. Two demographic forces—fertility decline and increased life expectancy—drive population aging. While the demographic components of population aging are well established, the reasons for the changes in them that have led to populating aging remain actively debated. Numerous questions on the topic of fertility remain open. First, more research on the causal effect of the increasing returns to education on fertility behavior, in particular the rise of women in higher education and female wages, would be welcome. Much room exists for research to be conducted on how alternative policies such as expanding paternal leave benefits or flexible work schedules may affect fertility. Whether private organizations or the state should undertake these policies is also a relevant question. And even though the decline of child mortality has been frequently hailed as a reason for the fall in fertility, the causal relationship between the two factors is surprisingly poorly documented. Similarly, old-age support from children is a frequently cited motivation for having children, but the empirical evidence for the hypothesis is lacking. Better understanding the demand for children will both provide more insight on where fertility is heading and help shape policy. A consensus does not exist on the future of fertility and longevity. While some scholars predict that fertility will stabilize at replacement rate, other scholars remain

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doubtful given that TFR has fallen far below replacement in many countries. Whether we will see an end to the rise in longevity is another subject of debate. The difficulty in predicting fertility and longevity is reflected in population projections, which tend to overestimate populations at very young ages and underestimate populations at very old ages. While economists have generally left the task of population forecasting to demographers, the new era of machine learning presents exciting opportunities for economists to use big data to analyze and forecast population dynamics, such as fertility trends and migration patterns. The shift to NCDs, including dementia, suggest that health and pension policies need to be tailored to factor in the long-lasting, costly nature of these diseases. At the same time, certain risk factors causing NCDs are preventable and manageable, including smoking and obesity, and more systematic research on innovative strategies to modify such behaviors is welcome. Relatedly, more investigation on whether a compression or expansion of morbidity occurs at old age, which will help shed light on the economic productivity and health care costs of the growing elderly population, is needed. Where do the elderly live and who cares for them? Are they happy and economically secure? How do living arrangements and sources of financial support compare across countries? To understand the well-being, economic security, and preferences of the elderly, data on the elderly are needed. The lack of such data presents a stumbling block for researchers and policymakers, especially in developing countries. An exciting development in this arena is the growing Health and Retirement Survey family, which comprises harmonized longitudinal panel surveys that focus on the elderly population. Of particular note are the Longitudinal Aging Study in India (LASI), which is in pilot stage, and the Chinese Health and Retirement Longitudinal Survey (CHARLS), which began in 2011. These two surveys will provide a more complete picture of the rapidly growing elderly population in the two most populous countries in the world. Related surveys include the Japanese Study of Aging and Retirement (JSTAR), the English Longitudinal Study of Aging (ELSA), and the impending Health and Aging in Africa: Longitudinal Studies of INDEPTH communities (HAALSI). These efforts will enable researchers to gain a more complete picture of the dynamic character of the aging process and the health, social support, and economic security of the growing elderly population.

7. CONCLUDING REMARKS While population aging certainly poses new challenges, doomsday scenarios about irreparable economic strain are likely overstated. The demographic shift of population aging has the potential to inspire behavioral adjustments and technological and institutional innovations to considerably offset its possible negative results. Mitigating the negative consequences of population aging will involve some combination of increased labor supply from women, immigrants, and older people; investment in education and training at

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all ages; increased rates of savings during the working years; slower growth of benefits; and faster growth of tax contributions to finance government transfers to older people. Some of these policy shifts have already began to take place: many EU countries have opted to raise the retirement age over the next few decades and have enacted partial privatizations of their pension systems in recent years. Governments and private organizations alike have adopted other strategies to encourage savings, such as pension (or 401 K) auto-enrollment. Several developing countries are considering adopting or expanding pension and health programs for the elderly (Kinsella and Velkoff, 2001). China established a contributory pension system in 1997, which covered more than 280 million urban workers and 460 million rural workers by the end of 2012 (Pozen, 2013). However, challenges abound in designing and implementing pension systems in developing countries, including poor financial literacy and public budget constraints (Bloom and McKinnon, 2013). Even in developing countries that have implemented pension programs, such as several countries in Latin America, low participation rates remain a problem (Auerbach et al., 2007). The exact mix of interventions should be tailored to country contexts and will determine the distribution of costs between current and future cohorts of the elderly. Importantly, the sooner these policy and institutional reforms are considered and implemented, the smoother the transition to a grayer population will be. Although demographic change has historically posed significant challenges and will continue to do so, demography is not destiny. The adaptations that human society and individuals can make in the face of such changes are equally impactful and key to transforming challenges of an aging population into opportunities for change and growth.

ACKNOWLEDGMENTS The authors gratefully acknowledge funding from the National Institute on Aging (grant no. 1 P30 AG024409-12).

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Palmer, E., Deng, Q., 2008. What has economic transition meant for the well-being of the elderly in China. In: Gustafsson, B.A., Li, S., Sicular, T. (Eds.), Inequality and Public Policy in China. Cambridge University Press, Cambridge, pp. 182–203. Pang, L., de Brauw, A., Rozelle, S., 2004. Working until you drop: the elderly of rural China. China J. 52, 73–94. Plassman, B.L., Langa, K.M., Fisher, G.G., Heeringa, S.G., Weir, D.R., Ofstedal, M.B., et al. 2007. Prevalence of dementia in the United States: the aging, demographics, and memory study. Neuroepidemiology 29 (1–2), 125–132. Pop-Eleches, C., 2006. The impact of an abortion ban on socioeconomic outcomes of children: evidence from Romania. J. Polit. Econ. 114 (4), 744–773. Pozen, R.C., 2013. Tackling the Chinese pension system. (Paulson Institute Policy Memorandum). Retrieved from: http://www.tandemsites.com/paulson/website/wp-content/uploads/2015/04/ China-Pensions_Pozen_English_FINAL.pdf. Preston, S.H., 1975. The changing relation between mortality and level of economic development. Popul. Stud. J. Demogr. 29 (2), 231–248. Preston, S.H., 1980. Causes and consequences of mortality declines in less developed countries during the twentieth century. In: Easterlin, E. (Ed.), Population and Economic Change in Developing Countries. University of Chicago Press, Chicago, IL, pp. 289–360. Preston, S.H., 1996. Population studies of mortality. Popul. Stud. J. Demogr. 50 (3), 525–536. Preston, S.H., Haines, M.R., Pamuk, E., 1981. Effects of industrialization and urbanization on mortality in developed countries. pp. 233–254. http://www.popline.org/node/388274. Pritchett, L.H., 1994. Desired fertility and the impact of population policies. Popul. Dev. Rev. 20 (1), 1–55. Redondo, N., Lloyd-Sherlock, P., 2010. Institutional care for older people in developing countries: repressing rights or promoting autonomy? The case of Buenos Aires, Argentina. J. Popul. Ageing 2 (1), 41–56. Rogers, R.G., Everett, B.G., Saint Onge, J.M., Krueger, P.M., 2010. Social, behavioral, and biological factors, and sex differences in mortality. Demography 47 (3), 555–578. Rosenzweig, M., Schultz, T.P., 1989. Schooling, information and nonmarket productivity: contraceptive use and its effectiveness. Int. Econ. Rev. 30 (2), 457–477. Rosenzweig, M.R., Wolpin, K.I., 1980. Testing the quantity-quality fertility model: the use of twins as a natural experiment. Econometrica 48 (1), 227–240. Ruggles, S., 2007. The decline of intergenerational coresidence in the United States, 1850 to 2000. Am. Sociol. Rev. 72 (6), 964–989. Saffer, H., Chaloupka, F., 2000. The effect of tobacco advertising bans on tobacco consumption. J. Health Econ. 19 (6), 1117–1137. Sah, R.K., 1991. The effects of child mortality changes on fertility choice and parental welfare. J. Polit. Econ. 99 (3), 582–606. Sanderson, W.C., 1976. On two schools of the economics of fertility. Popul. Dev. Rev. 2 (3/4), 469–477. Schlosser, A., 2005. Public Preschool and the Labor Supply of Arab Mothers: Evidence from a Natural Experiment. The Hebrew University of Jerusalem, Jerusalem. Mimeograph. Schultz, T.P., 1985. Changing world prices, women’s wages, and the fertility transition: Sweden, 1860–1910. J. Polit. Econ. 93 (6), 1126–1154. Schultz, T.P., 1994. Human capital, family planning, and their effects on population growth. Am. Econ. Rev. 84 (2), 255–260. Schultz, T.P., 2001. The fertility transition: economic explanations. Economic Growth Center Discussion Paper No. 833. Seifarth, J.E., McGowan, C.L., Milne, K.J., 2012. Sex and life expectancy. Gend. Med. 9 (6), 390–401. Shaw, C., 2001. United Kingdom population trends in the 21st century. Popul. Trends 103 (1), 37–46. Sickles, R.C., Taubman, P., 1993. Mortality and morbidity among adults and the elderly. In: Rosenzweig, M.R., Stark, O. (Eds.), Handbook of Population and Family Economics. Elsevier, Amsterdam, pp. 559–643.

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Simmons, R., 1996. Women’s lives in transition: a qualitative analysis of the fertility decline in Bangladesh. Stud. Fam. Plann. 27 (5), 251–268. Soares, R.R., 2007. On the determinants of mortality reductions in the developing world. Popul. Dev. Rev. 33 (2), 247–287. Strauss, J., Thomas, D., 1995. Human resources: empirical modeling of household and family decisions. In: Behrman, J., Srinivasan, T.N. (Eds.), Handbook of Development Economics, Vol. 3A. Elsevier. Amsterdam, pp. 1883–2023. Tsui, A.O., 2001. Population policies, family planning programs, and fertility: the record. Popul. Dev. Rev. 27 (Suppl.), 184–204. Tuljapurkar, S., Li, N., Boe, C., 2000. A universal pattern of mortality decline in the G7 countries. Nature 405 (6788), 789–792. United Nations, Department of Economic and Social Affairs, Population Division, 2001. World Population Ageing: 1950-2050. Retrieved from: http://www.un.org/esa/population/publications/ worldageing19502050/pdf/8chapteri.pdf. United Nations, Department of Economic and Social Affairs, Population Division, 2015. World Population Prospects: The 2015 Revision. UNDESA, New York United Nations, Food and Agriculture Organization, 2013. The State of Food and Agriculture 2013. FAO, Rome. United Nations Statistics Division, 2014. Composition of Macro Geographical (continental) Regions, Geographical Sub-Regions, and Selected Economic and Other Groupings. Retrieved from: http://unstats. un.org/unsd/methods/m49/m49regin.htm. United States Public Health Service, Office of the Surgeon General, 1964. Smoking and Health: Report of the Advisory Committee to the Surgeon General of the Public Health Service. Public Health Service Publication No. 1103. Retrieved from: http://profiles.nlm.nih.gov/NN/B/B/M/Q/. Uppal, S., Sarma, S., 2007. Ageing, health, and labor market activity: the case of India. World Health Popul. 9 (4), 79–97. van Ginneken, J., Razzaque, A., 2003. Supply and demand factors in the fertility decline in Matlab, Bangladesh in 1977–1999. Eur. J. Popul. 19 (1), 29–45. Weil, D.N., 1997. The economics of population aging. In: Rosenzweig, M.R., Stark, O. (Eds.), Handbook of Population and Family Economics. Elsevier, Amsterdam, pp. 967–1014. Westoff, C.F., Ryder, N.B., 1977. The pill and the IUD. In: The Contraceptive Revolution. Princeton University Press, Princeton, NJ, pp. 31–48. Willis, R.J., 1973. A new approach to the economic theory of fertility behavior. J. Polit. Econ. 81 (2, Pt. II), S14–S64. Wolpin, K.I., 1997. Determinants and consequences of the mortality and health of infants and children. In: Rosenzweig, M.R., Stark, O. (Eds.), Handbook of Population and Family Economics. Elsevier, Amsterdam, pp. 483–557. World Health Organization (WHO), 2003. World Health Report 2003—Shaping the Future. WHO, Geneva. Zeng, Y., Wang, Z., 2003. Dynamics of family and elderly living arrangements in China: new lessons learned from the 2000 census. China Rev. 3 (2), 95–119. Zhang, K.H., Song, S., 2003. Rural-urban migration and urbanization in China: evidence from time-series and cross-section analyses. China Econ. Rev. 14 (4), 386–400. Zlotnik, H., 2012. International migration and population ageing. In: Beard, J.R., Biggs, S., Bloom, D.E., Fried, L.P., Hogan, P., Kalache, A., Jay Olshansky, S. (Eds.), Global Population Ageing: Peril or Promise. World Economic Forum, Geneva, pp. 97–102.

CHAPTER 2

Macroeconomics, Aging, and Growth R. Lee University of California, Berkeley, CA, United States

Contents 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12.

Introduction Population Aging Population Aging, Dependency, and Redistribution of Income Across Generations Reallocation Systems The Changing Age Pattern of Consumption Population Aging and Economic Growth in Comparative Steady States The Golden Rule Case International Comparisons of Support Systems for Elderly Population Aging and Capital Market Equilibrium with Transfers Secular Stagnation Dynamic Analysis of Population Aging Special Topics on Population Aging, Saving, and Capital Intensification 12.1 Population Aging and Saving: Will Saving Rates Decline? 12.2 The Role of PAYGO Transfers, Public and Private, Implicit Debt, Asset Accumulation, and Capital Intensity 12.3 Public Sector Transfers 12.4 Open and Closed Economies in an Aging World 12.5 Will Population Aging Cause an Asset Price Meltdown? 12.6 How Much Population Aging Is Optimal? 13. Population Aging and Human Capital Intensification 14. Aging and Productivity Growth 14.1 Age and Productivity of Workers 14.2 Endogenous Growth and Population Aging 15. Political Economy of Population Aging and the Public Sector 16. Policy Issues 17. Research Directions 17.1 Fertility, Mortality, and Possibly Health Status 17.2 Intergenerational Transfers 17.3 Age at Retirement 17.4 Global Perspective 17.5 Technological Progress and Endogenous Growth 18. Conclusions Acknowledgments References

Handbook of the Economics of Population Aging, Volume 1A ISSN 2212-0076, http://dx.doi.org/10.1016/bs.hespa.2016.05.002

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Abstract Inevitable population aging and slower population growth will affect the economies of all nations in ways influenced by cultural values, institutional arrangements, and economic incentives. One outcome will be a tendency toward increased capital intensity, higher wages, and lower returns on capital, a tendency partially offset when the elderly are supported by public or private transfers rather than assets, and when economies are open, in which case aging will lead to increased flows of capital and labor. Rising human capital investment per child accompanies the falling fertility that drives population aging, and partially offsets slower labor force growth. Research to date finds little effect on technological progress or labor productivity. National differences in labor supply at older ages, per capita consumption of the elderly relative to younger ages, strength of public pension and health care systems, and health and vitality of the elderly all condition the impact of population aging on the economy. Policy responses include increasing the size of the labor force, mainly by raising the retirement age; reducing benefits and/or raising taxes for public transfer programs for the elderly, with concern for deadweight loss and the fair distribution of costs across socioeconomic classes; investing more in children to increase the quality and productivity of the future labor force; and public programs that promote fertility by facilitating market work for women with children.

Keywords Population aging, Macroeconomic, Demographic transition, Consequences, Human capital, Economic growth, Support ratio, Demand for wealth, Capital

JEL Classification Codes J14, J11, J18, E20, E24, H51, H55

1. INTRODUCTION As low fertility and longer life lead to increased numbers of elderly relative to younger adults, there is increasing concern about possible macroeconomic consequences. These consequences unfold on the time scale of demographic change, which is to say not from quarter-to-quarter or year-to-year, but rather decade-to-decade. Will rising old age dependency reduce consumption per capita? Will there be a deepening of capital, and if so, will rates of return drop, leading to an “asset price meltdown”? Or will capital instead flow to the younger developing countries, so that rates of return in developed countries fall less? Might the quality of more highly educated labor effectively substitute for quantity? Will an older labor force be less productive and will innovation and technological progress slow down? Longer-working elderly crowd out employment of the young? Has population aging already brought secular stagnation to the rich nations of the world, underlying the anemic recovery from the Great Recession and condemning their economies to recurring asset price bubbles? This chapter discusses these and related points. Samuelson (1958, 1975a) was one of the first economists to focus attention on the broader issues surrounding population growth rates, old age dependency, capital deepening, and the central role of intergenerational transfers in shaping the relations among these. A landmark paper by Cutler et al. (1990) framed and analyzed the macroeconomic

Macroeconomics, Aging, and Growth

issues in greater detail with more demographically realistic models. Weil (1997) is an excellent handbook chapter on the economics of aging and Howitt and Weil (2008) is an excellent Palgrave article on the topic. If individuals lived independent lives in isolation they would not care about the ages of others—the age distribution of the population would be irrelevant to them. However, human generations overlap so economic interactions among them can and do occur, both through markets and through nonmarket intergenerational transfers, both private and public. To quote Howitt and Weil’s (2008) Palgrave article, “Population aging has economic effects whenever some economic interaction (the sale of a good or service, the provision of a government benefit, and so on) brings together people whose participation is a function of their age … Old-age pensions, child rearing, and the combining of old people’s capital with young people’s labor are all cases where a change in the relative numbers on either side of the equation will have important effects.” Similarly, Sheiner et al. (2007, 16) in their primer on the macroeconomics of population aging tell us that “If generations were not linked, then, by definition, the consumption choices of one generation and the generation’s size would not affect the consumption possibilities of subsequent generations. But intergenerational linkages are important. Such linkages include not only transfer programs and bequests but also, in a closed economy, connections through saving and the return to capital.” This chapter will focus on these interactions with particular emphasis on public and private intergenerational transfers and on capital. I will begin with a brief discussion of population aging. Next I consider economic dependency and the economic life cycle, followed by a consideration of how resources are reallocated from those in working ages to the young and old who consume more than they produce. I will then consider the special case of economies and populations in steady state, and develop the analytically simple but enlightening case of comparative golden rule steady states and equilibrium in the capital market. With that background, we will turn to more dynamic models of nonsteady state. After this, we will consider a number of important special topics including the productivity of an aging labor force, innovation, and intensification of human capital, followed by a concluding discussion.

2. POPULATION AGING It is natural to think of population aging in terms of longer life, calling for adjustments in life cycle planning to accommodate the longer expected time horizon. However, in populations closed to migration, the evolution of the age distribution depends on fertility, mortality, and the initial population age distribution. Mortality decline and longer life do tend to make the population older, since on average individuals in each generation live longer. However, lower mortality also makes a population grow faster, so that younger generations are larger at birth than older ones, which tends to make the population younger. In low mortality countries, the net outcome from mortality decline is population

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aging, but in high mortality countries mortality decline can make populations younger, as it did for developing countries after WWII. Fertility decline, however, leads unambiguously to population aging, because it slows population growth. Life cycle adjustments to longer life can help to meet the economic challenges of population aging, but these adjustments do not address what is often the greater challenge of aging arising from low fertility and slow or negative population growth. The process by which populations move from initially high fertility and mortality with young age distributions to low fertility and mortality with old age distributions is called the demographic transition (Lee, 2003). This transition, starting with declining mortality, can take around two centuries to unfold. Most countries in the world have started the process, and most have advanced from mortality decline to fertility decline, and are aging due to both. For each country, its own changing population age distribution poses economic problems but may also present important advantages. There are profound differences between countries and regions of the world in the stage of the transition that has been reached and the age distribution that results. These demographic differences may lead to differences in factor prices that yield at least transitory economic opportunities to be realized through international flows of trade, capital, and labor. It will be useful to look more closely at the demographic drivers, starting with mortality decline which leads to longer lives and later deaths. When mortality decline means that an actual individual lives longer, it is clear ex post that time has been added at the end of that individual’s life. However, ex ante people are exposed to the risk of death at every age starting from birth, and deaths occur at all ages. Survival is a matter of probabilities. Based on these probabilities, we can describe the distribution of expected person-years lived at each age for a new birth or for a synthetic cross-sectional cohort. The sum across all ages of these expected person-years lived is life expectancy at birth, either actual, for a generation, or synthetic, for a particular year or period. When mortality declines, the expected person-years lived at each age rises, and the sum of the increases is the increased years of life expectancy. These increases are not distributed evenly across age (see Lee, 1994; Eggleston and Fuchs, 2012). When mortality declines from a high level, most of the gains in person-years lived occur in childhood. When mortality declines from a low level as in the rich industrial nations today, most of the gains occur above age 65. The more mortality declines, the more the possibilities for improvement at younger ages are used up, and the more subsequent gains must occur at older ages. The reproductive age of females is bounded at 45 or so. When survival from birth to age 45 approaches unity, further mortality declines have no effect on the number of births and raise the population growth rate only through increased numbers at the older ages without affecting the steady-state growth rate. The discussion so far has been based on chronological age, age measured in calendar years. Changes in age distribution are of interest for two reasons. The first is that physiological state varies with age: children are largely incapable of providing for themselves

Macroeconomics, Aging, and Growth

and have poor judgment; older people have lower health, strength, energy levels, abilities to learn, flexibility, and cognitive capacities compared to prime age adults. At the same time, knowledge, skill, judgment, and wisdom increase with age. Consequently, productive efficiency at first rises with age and then later declines and the disutility of labor rises (Skirbekk, 2008). The second reason is that chronological boundaries are often embedded in public policies, most notably at age 65 which has become an almost official threshold for becoming elderly in many countries. However, over the past century or so the physiological state of health and vigor associated with any particular age has been improving, or put differently, age-specific rates of disability and ill health at any older age have been declining. For the earlier part of the 20th century, this has been shown for the United States by Fogel (2004) and collaborators. For the years since the early 1980s, Freedman et al. (2013) have demonstrated a similar but more rapid decline. Although this decline appears to have stopped since 2000 in the United States, the health status of the elderly at any given age is much improved relative to earlier decades, as reflected in statements such as “70 is the new 60” (National Research Council, 2012, Chapter 4). If we redefine “aging” based on physiological status rather than chronological age, then the extent of population aging projected from today through 2050 is much reduced in all industrial nations (Sanderson and Scherbov, 2010). Projected improvements in health and functional status offset the increase in elderly projected on the basis of chronological age. In particular, the fraction of expected adult years lived in good health out of all expected adult years remains roughly constant. We reach similar conclusions when defining old age by distance from death, that is, by remaining life expectancy, so that the threshold automatically rises as life expectancy increases. This approach is consistent with the finding that health costs depend much more on time until death than on chronological age. Based on the improving functional status measures reported in Sanderson and Scherbov, chronological population “aging” should pose no fundamental economic problem. However, to the extent that both public institutions and popular culture have enshrined age 65 as the appropriate age for retirement, a problem is created. The greatest challenge in the coming decades may be to adjust our institutions and cultural perceptions as rapidly as populations experience chronological aging. In any event, chronological population aging is inevitable, since with longer life fertility cannot remain above replacement level in a finite world. Countries differ greatly in their position in the transition, with some late-starting populations still extremely young and others far older. However, no country is yet near to its long-term level of population aging given its current birth and death rates. Based on the United Nations medium projections, for example, every country in the world will experience at least a doubling of the ratio of those over 65 to those ages 20–64, the old age dependency ratio (OADR). Even Japan, the oldest sizable country in the world, is projected to go from an OADR of 0.38 in 2010 to 0.76 in 2050 (United Nations Population Division, 2011).

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As economies become increasingly open with globalization, global aging rather than national aging will govern capital intensity and factor prices in an economy. Differences in the timing and degree of population aging may shape international flows of capital, trade, and labor (B€ orsch-Supan et al., 2006). While aging is currently most advanced in the rich industrial nations (other than the United States), many developing nations including Brazil and China have experienced very rapid fertility decline and will age exceptionally rapidly in coming decades. Population aging is coming. How will it affect the macroeconomy?

3. POPULATION AGING, DEPENDENCY, AND REDISTRIBUTION OF INCOME ACROSS GENERATIONS Because the biological capacities and needs of individuals vary with age, and also for cultural, institutional, and behavioral reasons, labor income and consumption vary with age over the life cycle. Labor income depends on labor force participation rates, efficiency per hour of work, and hours worked per participant. Here it will be useful to focus on the age profile of labor income itself, drawing on estimates from the National Transfer Accounts (NTA) project (Lee and Mason, 2011; United Nations Population Division, 2013; d’Albis and Moosa, 2015; www.ntaccounts.org). In NTA, the age profile of labor income is defined as the average across all individuals at a given age, whether working or not, of before-tax wages and salaries including fringe benefits, plus labor’s share of self-employment income, and unpaid family labor (assumed to be two-thirds, with the remaining third going to assets). The age profile of consumption includes an average across all individuals at a given age of an imputed portion of household consumption expenditure for the household in which each individual lives (including health and education), plus in-kind public sector transfers (mainly health care, long-term care, and education) to each individual. Imputation is done in proportion to equivalent adult consumer (EAC) weights that increase linearly from 0.5 at ages 0–4 to 1.0 at age 20, except for private expenditures on health and education which are estimated separately. These age profiles are cross-sectional estimates based on standard surveys. Longitudinal age profiles would reflect similar age patterns superimposed on a growth-induced upward trend. Fig. 1 shows the resulting age profiles of labor income and consumption. For comparison across countries, these have been standardized by dividing both labor income and consumption at each age by the average level of labor income across ages 30–49 for each country. The figure shows the average of these ratios for five rich industrial nations and five lower income countries. The shapes are broadly similar. Consumption greatly exceeds labor income at younger ages and older ages, and ages between earn a substantial surplus. Consumption is also funded out of asset income of various kinds we will consider later. There are important differences between the rich and poor countries. Labor income

Macroeconomics, Aging, and Growth

Fig. 1 Labor income and consumption age profiles from NTA averaged for six low income and six high income countries. Notes: For comparability, each age profile is divided by the average level of labor income in the country for ages 30–49, before averaging across countries. Labor income is an average across males and females including zero values, based on pretax wages and salaries plus employer-provided benefits, plus two-thirds of self-employment income (the other third is allocated to assets), and includes unpaid household labor as reported in surveys, allocated to household members with reported unpaid labor. Consumption is household consumption expenditure on health and education allocated to recipients of these, plus other consumption allocated in proportion to weights that are 0.5 for age 0–4 and then rise linearly to 1.0 at age 20. It also includes public in-kind transfers such as public education, publicly provided health care, and publicly provided long-term care, allocated to recipient.

begins at younger ages in lower income countries, although high youth unemployment in some African countries pulls down the average. Labor income peaks later in the rich countries and then declines much more rapidly, in part due to the availability and incentive structures of public pensions. Beyond age 65 or so labor income is very low. In the lower income countries the decline in labor income begins earlier but is much more gradual, and labor income remains substantial even in the 80s. There is interesting regional and national variation in these patterns (Lee and Mason, 2011, Chapters 5 and 6). Consumption per child is distinctly higher in the richer nations reflecting heavier investment in human capital, particularly education (recall that public and private expenditures on education are included in this measure of consumption, as described earlier). The figure also shows a very important difference at adult ages. In lower income countries, consumption is relatively flat across ages, with younger adults and the elderly consuming similar amounts. In the rich countries, however, the pattern is very different: consumption rises throughout the older ages, particularly above age 80. This pattern is not universal among the richer nations, but is particularly pronounced in the United

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States, Sweden, Finland, Germany, the United Kingdom, and Japan. At older ages it reflects the growing importance of public expenditure on health care, and above 80 on long-term care as well. Population aging increases the share of people at the older ages where consumption greatly exceeds labor income, and to varying degrees may reduce the share of people at the younger dependent ages. The net effect of changing population age distribution on overall dependency is measured by the “support ratio.” The support ratio is sometimes measured as the share of the population in the working ages, say 20–64 or 15–60, divided by the total population. Cutler et al. (1990) introduced a different approach, using data for the United States to calculate the base period age profile of labor income and of consumption, which were used to calculate the support ratio by weighting the changing population age distributions. This is the approach we take here, calculating the support ratio as the population-weighted sum across ages of labor income divided by the populationweighted sum of consumption, using base period NTA age profiles. Let y be the average product of labor, L and C be the population-weighted sums of labor income and consumption, respectively, and s be the share of output saved. Then consumption per EAC, an age-standardized measure of consumption per capita, is given by c ¼ (L/C)(1  s)y. That is, other things equal (we will relax this assumption later), consumption per EAC varies in proportion to the support ratio, L/C, and proportional variations in the support ratio will correspond to proportional variations in consumption per EAC (Cutler et al., 1990). If y is trending upward with productivity growth, the support ratio still locates consumption relative to this trend. The age profiles for some base year can be combined with population projections to form hypothetical projections of the support ratio. Of course, we expect both the consumption and labor income age profiles to change in the future, for example, if the retirement age rises or public transfers to the elderly are reduced. The projected support ratio is just an analytic tool to capture the pure demographic consequences, but it is in no way a forecast; that would require more comprehensive procedures and serve a different purpose. Fig. 2 shows projections of support ratios based on NTA data and the United Nations Population Division (2011) population projections from 1960 to 2060. Population aging begins earliest in Japan, around 1970, and progresses rapidly starting around 1990, reaching its deepest point around 2060. Spain’s aging starts later but is even more rapid. The United States has only modest aging, with rate of decline of the support ratio only half that of Japan and Spain. In China, starting around 1970, we see a very rapid increase in the support ratio due to its rapid fertility decline, which has the initial effect of reducing child dependency and raising the share of the population in the labor force, generating what is called the “demographic dividend.” In this case, the dividend (calculated as the rate of increase in the support ratio) adds 0.8% annually to the growth rate of c (over 1974–2012, on average). Starting just after 2012, however, fertility decline has slowed labor force growth enough that the elderly population begins to predominate, bringing

Macroeconomics, Aging, and Growth

Fig. 2 Support ratios for selected countries based on UN projections and NTA age profiles, indexed to 1.0 in 2010. Notes: Support ratios for selected countries based on United Nations Population Division (2011) projections and NTA age profiles like those shown in Fig. 1 (see notes in Fig. 1). The support ratio is the ratio of effective labor to effective consumers, where effective labor is the sum of the population age distribution times the baseline age profile of labor income, and effective consumers are defined similarly. The support ratios are all standardized to 1.0 in 2010 to facilitate visual comparison of changes. The inset annualized rate of change is given as a percent, eg, 0.11 indicates 0.11% per year increase.

an end to the dividend phase, and initiating population aging so that between 2012 and 2050, 0.4% will be subtracted from the growth rate of c. India has a number of decades before its dividend phase ends and population aging begins, with the whole process slowed by the gradualness of its fertility decline. Finally, in Nigeria fertility decline has barely begun, and it will experience a modest dividend over many decades. These contrasts between the dividend phase and population aging phase are important, but they would be swamped by productivity growth rates of recent decades in China or India. The support ratio and its changes here reflect all sectors of the economy. If we instead focus on the fiscal support ratio for the public sector (based on age profiles of taxes paid and benefits received), or even more if we focus on specific public transfer programs for the elderly such as pensions or health care, then the effects of population aging can look very much larger. It is important to realize that they refer to only a fraction of the economy. For some purposes, the fiscal support ratio may be informative because it could be viewed as reflecting external costs and benefits of fertility, while private transfers correspond to private costs of childbearing which may be taken into account when individuals choose their fertility.

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The support ratio is widely used as a simple and intuitive measure of the effect of the changing population age distribution on per capita consumption, but let us take a deeper look at it. The interpretation of the support ratio given above begins with the identity Y ¼ Ly, where L is labor and y is average output per worker. In the standard model with constant returns to scale and capital and labor the only factors of production, average output is given by y ¼ f(k) where k is capital per worker. If we now add one worker to the population the identity Y ¼ Ly suggests that Y will rise by y to (L + 1)y. But if this worker brings only labor and no capital, then k will fall and Y will rise by the marginal product of labor, not by its average product, y. If instead we add an elderly nonworker to the population then we are led to expect that output will not rise at all and will now be shared by one more consumer causing consumption per capita to drop. But if this elder is like the average old person in the United States, he/she will own a substantial amount of capital accumulated during the working years, and this will raise K so that Y will rise by the marginal product of capital times the elder’s capital holding, or by the elder’s capital income. Continuing this line of thought we might consider that the worker would also come with some modest amount of capital in addition to pure labor, but less than k. This discussion suggests that the support ratio may overstate the advantage of having more workers and overstate the cost of having more elderly. An alternative measure is what Lee and Mason (2013) call the “general support ratio” or GSR. It reflects the extent to which individuals and governments have actually prepared for population aging by accumulating assets in advance. It has the same denominator as the standard support ratio, that is, effective consumers. The numerator includes effective labor as in the standard support ratio, but it also includes the effective amount of asset income used to pay for consumption, that is the population-weighted sum of asset income less saving at each age. This numerator at each age equals the amount of consumption that is paid for out of net transfers, both public and private. If T is the sum of population-weighted net transfers and C is effective consumers, then T/C ¼ 1  GSR, where T/C is aggregate net transfers as a share of aggregate consumption. In a closed population this will be 0 in the base period, because transfers given and received must cancel and add up to 0, and for the same reason the GSR will be unity in the base period. However, as the population age distribution changes while we hold all the relevant age profiles fixed (for consumption, labor income, asset income, and saving) T/C will move away from 0 indicating changes in the extent to which transfers would have to increase or decline to maintain balance, and the GSR will move away from unity indicating changes in the true level of dependency. Lee and Mason (2013) use NTA data to show that in countries like Sweden, Finland, and Slovenia, where older people rely virtually 100% on public transfers to fund their consumption, there is no difference between the standard support ratio and the GSR as the populations age. However, in countries like the United States or Mexico, where older people rely heavily on asset income to fund their consumption, and rely much less

Macroeconomics, Aging, and Growth

on public transfers, the GSR declines much less than the standard ratio, by only 40% as much in the case of the United States, for example. The GSR also indicates a later end to the first demographic dividend as countries move through the demographic transition and a larger dividend.

4. REALLOCATION SYSTEMS We saw, not surprisingly, that the young and the old in all countries consume much more than the labor income they generate. How do they do this? What is the nature of their claims on a portion of current output? There are three basic systems that support consumption in excess of labor income for young and old: private transfers, public transfers, and asset income. Asset income is used to fund consumption to the extent that it is not saved. In NTA, asset income minus saving at each age—that is, the portion used to fund consumption—is referred to somewhat awkwardly as “asset-based reallocation.” Children’s consumption is largely provided by parental expenditures for child rearing, that is private transfers, and human capital investment (which I will consider to be part of consumption for the moment) is paid for by a mixture of public and private transfers. Consumption by the elderly in excess of their labor income is funded by a mixture of public transfers, private transfers, and asset-based reallocations. The excess labor income of the prime working years goes for taxes, private transfers, and saving. A seminal article by Cox (1987) asked whether transfers are motivated by altruism or by exchange, where elders might make inter vivos transfers or bequests in exchange for care and attention from a child, attention that has no close market substitute. (The Cox terminology is different than in this chapter, since “Transfer” as I use it here cannot involve a quid pro quo by definition. This difference is purely semantic. We can certainly ask whether a given intergenerational payment is made for altruistic reasons or as part of an exchange.) The Cox question is important for understanding the consequences of public transfers, among other things. For example, Barro (1974) showed that if generations are altruistically linked by intergenerational transfers from young to old or from old to young, then in the simplest case changes in private intergenerational transfers would simply offset changes in public intergenerational transfers such as a new public pension system.a The argument is that the altruistic intergenerational linkage, even if only between parents and children, would through recursion mean that families effectively have infinite horizons. In this case, new government bonds or new tax and transfer programs do not change family wealth over the infinite horizon and therefore do not change the amount that the current generation would want to consume relative to its descendants so long as all families are at interior solutions for optimal bequests rather than at a

Barro’s result requires the assumption that parental altruism is strong enough to be operative and that markets are perfect so that receipt of an inheritance does not change lifetime production opportunities.

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Fig. 3 How the gap between consumption and labor income at each age is made up in the United States (NTA data): Components are net public transfers received; net private transfers received; and asset income minus savings. Notes: The figure shows the cumulative sum of the three components when all are the same sign, otherwise the components of different sign must be added. The sum equals consumption minus labor income at each age as shown in Fig. 1. Private transfers include interhousehold transfers as reported in surveys and intrahousehold transfers which are calculated as the difference between consumption (see notes in Fig. 1) and income from labor income and assets. Asset-based reallocations are the difference between asset income and saving at each age.

a corner. It follows that, in theory, government bonds or taxes and transfers would have no effect on consumption of different generations, and private intergenerational transfers would simply offset public transfers. The relation of public transfers to private ones is also discussed in Chapter 10 by Cigno (this volume), and Arrondel and Masson (2006) review the empirical evidence on this topic. Fig. 3 illustrates these patterns for the United States. In childhood, private transfers fund most of ordinary consumption (food, housing, clothes, and recreation) while public transfers largely fund education. In addition, children receive transfers of public services such as national defense, roads, police, and research that are allocated equally on a per capita basis by NTA. Prime age adults pay taxes and make private transfers to their children. They also consume increasing amounts of asset income although some of it is saved (saving is not shown in this figure). After age 65 or so transfers received from the public sector outweigh taxes paid, and public transfers contribute substantially to old age consumption. The main source of funds for old age consumption in the United States, however, is assets. In NTA data saving by the elderly remains positive at all ages in most countries, but much asset income is nonetheless consumed. Older people in most

Macroeconomics, Aging, and Growth

countries continue to make net transfers to younger family members rather than receiving net support from them on average above age 65, although at older ages above 75, it is common for the elderly to receive net transfers from their families. East Asia and Thailand are exceptions, where net private transfers to the elderly can be quite important starting at earlier ages. Returning to the prime adult years in the United States, we see that there is no age at which even young adults are saving more than the asset income they receive. From where do these assets that are generating asset income come, if not from savings? It appears that they come from end-of-life bequests that are not yet measured by NTA. Although most such bequests are surely received at later adult ages given current mortality patterns, enough may be received at younger ages to account for this outcome, an outcome which is quite common in NTA countries.

5. THE CHANGING AGE PATTERN OF CONSUMPTION Among the many important messages in Samuelson’s (1958) classic paper on the consumption loan economy was this: the lifetime consumption and welfare for individuals in a society with a given level of per capita consumption can vary greatly depending on how that consumption is distributed by age and generation. For example, suppose a population with two overlapping generations (OLG) (age groups) is doubling each generation so that the younger age group is always twice the size of the older one, and income at each age is constant over time and derives entirely from labor. Gaps between consumption and labor income are made up by transfers. Consider two different lifetime consumption patterns, A and B. In A members of the younger generation always consume twice as much as the older generation whereas in B the reverse is true, and they consume half as much as the older generation. In A lifetime consumption (the unweighted sum) will be 20% less than in B because in A, the larger age group also has the higher per capita consumption. In a different regime of population decline and aging scenario A could instead yield higher lifetime consumption than B.b A social planner would maximize lifetime welfare by choosing the lifetime consumption pattern that an optimizing individual would choose if faced with an interest rate equal to the population growth rate plus the rate of productivity growth. In an aging society with slow or negative population growth this interest rate will be lower and perhaps negative, and for standard intertemporal utility functions the longitudinal age profile of consumption would also flatten, rising more slowly with age and time. In contrast, the b

Consider a given period (subscript suppressed) which has some level of output, all of which is consumed; A call the aggregate amount C. Let cA Y be the amount consumed by each young individual in case A, and cO be A A consumed by each old person. By assumption cY ¼ 2cO . If NO is the number NY is the number of
A  of old and A A ¼ 5NO cO . Solving for + NO cO young, with NY ¼ 2NO , then the social budget constraint is C ¼ 2NY 2cO A A A cA and c , and summing, we find c + c ¼ ð 3=5 Þ ð C=N Þ. The same calculation for case B yields 0 O Y O Y B cO + cYB ¼ ð3=4ÞðC=N0 Þ. It follows that lifetime consumption (undiscounted) is 20% less in case A than B.

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market equilibrium rate of interest in Samuelson’s economy (with three adult age groups) was strongly negative, inducing young people to borrow and consume at a high rate, while older people consumed very little. Consequently, lifetime welfare was very low relative to the social planner optimum. In the real world, age patterns of consumption are determined in part by individual decisions, but also by unpredictable changes in government pension programs and in-kind transfers of health care, long-term care, and education. It is also well established in behavioral economics that individuals are not good long-term planners, which is particularly relevant for retirement planning. Consumption by children is largely driven by their parents’ decisions. For these reasons, we should not expect age trajectories of consumption to conform closely to predictions of life cycle saving models. In fact, age patterns of consumption have changed a great deal in recent decades in the rich nations. Fig. 1 showed the difference between the cross-sectional age profiles of consumption in the lower income countries and the rich countries. In NTA, the lower income age pattern holds on average all the way through the third income quartile of countries, including countries like Taiwan and South Korea. Fig. 4 shows how the cross-sectional age profile of consumption has changed in the United States, comparing 1960, 1981, and 2011. In 1960, total consumption declined substantially after age 60. In 1981 it rises across all ages rather than declining. And by 2011, it rises very strongly across

Fig. 4 How the cross-sectional consumption age profile has tilted toward older ages over the past 50 years in the United States (NTA). Notes: Consumption has been divided by average labor income at ages 30–49 in each year, and the vertical axis units give this ratio. In 2011, the age detail is no longer available to make a full set of age profiles to age 90+ because survey data are truncated at 85 +. The figure shows the composition of consumption in each year with components labeled in 2011. Each component sums to the corresponding item in the national accounts when weighted by population by age in that year. Public other is items that are not agetargeted such as national defense, roads, and medical research. These items are given the average per capita value at each age. Updated from Lee, R., Donehower, G., Miller, T., 2011. The changing shape of the economic lifecycle in the United States, 1970 to 2003. Chapter 15 in R. Lee and A. Mason (eds.), Population Aging and the Generational Economy: A Global Perspective. Edward Elgar.

Macroeconomics, Aging, and Growth

the whole range of ages and accelerates after age 85 (this cannot be seen for 2011 because age details were truncated at 85+, but the acceleration is clear in 2007 and other earlier years). Inspection of the components of consumption suggests that much of this increase is due to increasing public provision of health care including long-term care. In the United States, public coverage of health care for those 65 and over (Medicare) began in 1967, and similarly for long-term care for those meeting an asset test (Medicaid). Inspection also shows that private expenditures at older ages increased greatly, with a sharp drop in 2011 at age 65 when Medicare becomes available. But total private consumption has also risen at older ages, and it seems likely that this reflects the increased generosity of public pension benefits (Social Security). The ratio of consumption at age 80 to consumption at age 20 doubled between 1960 and 2007, from 0.83 to 1.67. This tilt toward older ages in the cross-sectional age distribution of consumption in the United States is opposite to what Samuelson’s social planner would choose in the face of declining population growth rates and projected population aging. At the same time, we note that the health care component of consumption has special features since health and survival are preconditions for enjoying standard consumption.

6. POPULATION AGING AND ECONOMIC GROWTH IN COMPARATIVE STEADY STATES The support ratios we discussed earlier indicate the consequences of shifting levels of dependency in the economy resulting from changing population age distributions. However, that discussion implicitly focused on labor as the sole productive factor, whereas capital is also important, as reflected in the discussion of the GSR. In this and following sections, we will broaden the framework to include both labor and capital in a neoclassical growth model. Even without behavioral heterogeneity by age, the same slower population growth that produces population aging also raises the capital intensity and per capita income of the economy, assuming that saving rates remain constant. If we allow heterogeneity across age and assume that life cycle saving prevails then we would expect older populations to have higher proportions of dissavers and therefore have lower aggregate saving rates. But we would also expect that the lower fertility and longer life that lead to population aging would lead individuals to save more to provide for a longer life in retirement and to save more because with lower fertility they would expect to consume more in retirement, and therefore would plan to save more when younger. The net effect on saving rates is not clear (Tobin, 1967; Lee et al., 2000; Sanchez-Romero, 2013, and for a different view, Deaton and Paxson, 1994). However, it is clear that the elderly would hold more assets than the young, and as their share in the population rises, assets per worker, and per capita in the population would also rise. Depending on whether assets are invested domestically or abroad, and whether they are held as equities or bonds, population aging could raise domestic capital

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intensity, labor productivity, wages, and per capita incomes. The notion that an older person who pays for her consumption out of her own asset income is “dependent” on workers can also be questioned. Samuelson (1975a) pointed out that when populations grow more rapidly, there will be less capital per worker (for a given saving rate), tending to reduce per capita output and consumption. At the same time, more rapid population growth will mean fewer old people per worker, and therefore a lower old age dependency cost, which would tend to raise per capita consumption. He suggested that consumption would be maximized at some intermediate population growth rate. Deardorff (1976) showed that on Samuelson’s assumptions the optimum would be at plus or minus an infinite growth rate, and Samuelson agreed but showed that his result would still follow given more realistic assumptions (Samuelson, 1976). We will discuss these issues starting with capital dilution and then turning to the population age distribution. In the standard Solow (1956) model with homogeneous population and a constant saving rate, it is well known that for a given saving rate, when the population growth rate slows then capital per worker rises, and consequently wages and per capita income rise while interest rates fall (Solow, 1956). In this model, the golden rule saving rate (which maximizes steady-state per capita consumption) is lower when the population growth rate is lower, but at the same time the capital/labor ratio, wages, and per capita income are higher and interest rates are lower. Across golden rule steady states, proportional changes in per capita consumption c are given by: d lnc=dn ¼ k=c. If the ratio of capital to consumption is four, for example, per capita consumption would be 4% lower in a golden rule steady state with population growth rate 1% per year higher. Slower population growth permits capital deepening even with lower saving rates. Individuals in this Solow model are homogeneous in all respects except age, although the fact that each individual is born at a particular time and therefore has a particular age hardly matters, since individuals of all ages behave identically. The average age in a stable population growing at n > 0 would be 1/n, which rises as the growth rate falls (for n  0, the average age is infinite). Individuals also have finite lives with life expectancy at birth given by 1/d, where d is the proportion of the population dying each year. Now let us move beyond age heterogeneity in this trivial sense to the realistic case in which economic behavior varies with age. We will see that the important features of the Solow model discussed earlier are preserved once behavioral age heterogeneity is introduced. However, for simplicity we will begin by adding age-related behavior in a consumption loan model with no capital, as in Samuelson (1958). We will assume that there is no capital or durable good. Labor is the only source of income. Let y(x) be labor income at age x, and c(x) be consumption at age x, with both assumed constant over time for simplicity. Let N(x,t) be the population age x at time t.

Macroeconomics, Aging, and Growth

Aggregate output in year t, Y(t), is given by total labor income, and aggregate consumption is given similarly: ðω

N ðx, tÞyðxÞdx ¼ Y ðt Þ

0

ðω

(1) N ðx, tÞc ðxÞdx ¼ C ðt Þ

0

Consider a demographic steady state in which every age group grows at the same rate n and the proportional age distribution of the population is fixed. Demographers refer to this as a stable population. The number of births is B(t) ¼ B(0)ent. Assume that the population is closed to migration. Let l(x) be the proportion of births that survive from birth to age x, which is assumed constant over time. In this case, the proportion of the population at age x is: N ðx, tÞ enx l ðxÞ ¼ benx l ðxÞ ¼ ðω N ðt Þ na e l ðaÞda

(2)

0

where b is the crude birth rate, B(t)/N(t). Substituting from (2) into (1) and assuming that Y(t) ¼ C(t) as must be true in an economy with no durable good and no waste: ðω 0

enx lðxÞc ðxÞdx ¼

ðω

enx l ðxÞyðxÞdx

(3)

0

This equation describes a cross-sectional budget constraint that is sometimes called the social budget constraint. Note, however, that you could also view this as an individual life cycle budget constraint that says the survival-weighted present value of consumption at birth equals the survival-weighted present value of labor income, with discounting at the rate of population growth n. Now differentiate both sides of the social budget constraint with respect to the population growth rate n while holding survivorship, l(x), constant. Since mortality is held constant, the changes in n must reflect differences in fertility. In order for the identity C ¼ Y to continue to hold when n changes, the age profiles of consumption, or labor income, or both, must change. For simplicity, suppose that it is consumption that changes. To represent these changes in a particularly simple way, suppose that consumption by age varies proportionately with a multiplicative factor of β which is 1.0 for the initial value of n. Let γ(x) be the baseline age schedule of consumption such that c(x) ¼ βγ(x). Note that dc(x)/dn ¼ (dβ/dn)γ(x).

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dY dC ¼ dn dn ðω ðω ðω @c ðxÞ nx nx dx  xe l ðxÞyðxÞdx ¼  xe l ðxÞc ðxÞdx + enx l ðxÞ @n 0 0 0 ðω ðω ð @β ω nx nx nx e l ðxÞγ ðxÞdx  xe l ðxÞyðxÞdx ¼  xe l ðxÞc ðxÞdx + (4) @n 0 0 0 ðω ðω xenx l ðxÞc ðxÞdx xenx l ðxÞyðxÞdx @β 0 0  ¼ C Y @n @β Ac  A y ¼ @n On the left side of the last equation, we have the average age of consuming in the population less the average age of producing, in the cross-section.c On the right, we have the proportional change in consumption at each age and overall in the population crosssection, for a change in the population growth rate across steady states. This result tells us that when the population growth rate rises (and therefore the population age distribution becomes younger) consumption must adjust so that the budget balance identity C ¼ Y continues to hold. If Ac > Ay then the left side is positive and age-specific consumption will rise. The reason is that people on average produce at younger ages than they consume, so having a greater proportion of younger people relaxes the social budget constraint and permits higher consumption at every age. We can drop the artificial simplifying assumption about β, and the assumption that labor supply is constant, and instead get a result that constrains the weighted sum of variations in y(x) and in c(x) over the life cycle, while permitting adjustment to take the form of an increase in the retirement age, for example, or a reduction in specifically old age consumption. If Ac  Ay ¼ 4 years, then an increase in the population growth rate by 0.01 (1% per year) would permit an increase in consumption of 4% at every age. Suppose that people work from age 20 to age 65, and then survive to age 80 when all die, and that the population growth rate is 0. Suppose they consume the same amount c at every age, and earn the same amount y at every age that they work. Then the average age of consumption is 40 and the average age of earning is (20 + 65)/2 ¼ 42.5. In this example, Ac  Ay ¼ 2.5, and higher fertility and more rapid population growth require a reduction in consumption at every age. If Ac > Ay then the same logic says that age-specific consumption must be reduced to balance the social budget constraint in an older population. Later, we will see that many rich countries have Ac > Ay and would benefit from more rapid population c

More precisely, this is the age at which the average unit of output is consumed minus the age at which the average unit of output is produced.

Macroeconomics, Aging, and Growth

growth (at least so far as age distribution is concerned) while almost all nonrich countries have Ac < Ay and would benefit from slower population growth.

7. THE GOLDEN RULE CASE We now want to analyze economies with population age distributions and with capital. There are various ways we could proceed. One approach is to analyze the way that population aging affects the decisions of a social planner in a Ramsey–Cass–Koopmans (Koopmans, 1967) model with a population of immortal individuals. This setup also applies to a population of dynastic altruistic household heads, who through the altruistic linkage of generations, effectively act like infinitely long-lived individuals. In this general approach, the optimal trajectories of saving, consumption, capital accumulation, and economic growth are determined independent of the population age distribution, and then output each period is distributed through transfers to achieve the maximum welfare according to the criterion chosen. Thus, there is a two-stage optimization in which first the trajectories of saving and capital are optimized and second consumption is allocated across ages and generations to maximize the welfare function (Calvo and Obstfeld, 1988; Samuelson, 1975b). There are two drawbacks to using this setup to explore the consequences of population aging. First, the dynastic altruistic assumption is extreme and assumes away most of the interesting consequences of population aging. Second, in the standard setup in which the Planner optimizes the integral over time of population-weighted utility, the Planner maintains the same capital–labor ratio regardless of the population growth rate (or age structure) determined solely by the rate of (intergenerational) time preference in the welfare function (Calvo and Obstfeld, 1988; Cutler et al., 1990), so capital deepening does not occur in an aging population and the entire response takes the form of variation in the aggregate savings rate. For these reasons, this version of the Ramsey model does not seem appealing, although the interested reader can find a useful empirical application to the United States in Cutler et al. (1990). If instead the planner maximizes the integral of unweighted per capita consumption, however, then the marginal product of capital is set equal to the population growth rate plus the social discount rate. If the social discount rate is zero, then the economy converges to the “golden rule” path, which chooses the saving rate to maximize per capita consumption. In this case, with slower population growth (and consequent aging), the optimal saving rate is reduced and capital intensity rises. For me, this is a plausible and appealing outcome. However, with this per capita objective function, the Planner would seek to raise consumption by small generations and reduce it for large generations during the approach to steady state, to take advantage of the generational differences in cost of achieving higher utility, and that is unappealing.

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Turning now to the second stage of the optimization, often and perhaps typically (based on my own simulations) the optimal or actual pattern of consumption by age would require massive downward intergenerational transfers of capital, which could take place either as bequests at death or alternatively as inter vivos transfers, to maintain the optimal capital intensity. Thus transfers are a key component of the age structured Ramsey model, although they are seldom discussed. Another approach is to assume nonaltruistic individuals with finite lives as in Diamond (1965). Although the assumption of zero altruism may seem extreme, there are mechanical ways to build in parental investments in offspring. However, the Diamond model, like many OLG models, has only two adult age groups, and this has been shown by d’Albis (2007) to be too limiting, since for example it imposes an exogenous limit to the ages of positive saving. This implies a monotonic negative relationship between the rate of population growth and the capital intensity and per capita income of the economy, whereas d’Albis shows that with a continuous age distribution the relationship should be nonmonotonic, with a population growth rate which maximizes per capita income. Later, I will follow Arthur and McNicoll (1978) in adding a continuous population age distribution to a Solow growth model, and take the shapes of the age profiles of consumption and labor income to be as observed in various actual populations, rather than to assume that they are chosen optimally by the actors. I will assume that saving and capital intensity are consistent with golden rule, without specifying how golden rule is brought about. The golden rule growth path is the steady state that maximizes consumption per capita, and so it assumes that every generation has the same per capita consumption (absent technological progress, purely for simplicity). When the population growth rate changes then both the saving rate and the capital–labor ratio change, while the steadystate assumption avoids the problem of treating small and large generations asymmetrically—but also gives no guidance outside of steady state. Despite these restrictive features, the golden rule case is useful for several reasons: it is very tractable analytically with a flexible and realistic population age distribution; it incorporates many of the core effects of population aging including the key role of intergenerational transfers; and it is neutral with respect to institutions and behavior and in that sense reveals the fundamental and general consequences of population aging. In a comment on Samuelson (1975a), Arthur and McNicoll (1978) build into the Solow model a population with continuous age distribution. They consider the effect of a small difference in the population growth rate across golden rule steady states, deriving the following elegant result: @β k ¼ Ac  Ay  @n c

(5)

where k is the capital–labor ratio, β has the same meaning as in Eq. (4), that is indexes the level of lifetime consumption, and c is ordinary per capita consumption, C/N. In other

Macroeconomics, Aging, and Growth

words, the effect of slower population growth and population aging across golden rule steady states is a simple sum of the beneficial capital deepening effect and a possibly deleterious dependency effect. Samuelson (1958, 1975a,b) considered the costs of old age dependency but not of child dependency. Arthur and McNicoll’s (1978) result takes both into account. Based on data from the NTA project and a few other sources, average ages of consumption and labor income have been calculated for a large number of countries at different levels of income and in different regions of world. Fig. 5 charts these data as arrows with the head at the average age of consumption and the tail at the average age of earning labor income. The length of the arrow is Ac  Ay with an arrow pointing to the right indicating a positive difference and to the left a negative one. The countries are organized by geographic region, and the regions go from the lowest per capita income at the bottom to the highest at the top. Countries within regions are ranked in the same way. In the bottom panel are found two hunter–gatherer communities, and Kenya, the lone African country. All the arrows point downward (leftward) outside of Europe and the United States except for Japan, indicating that the average age of consumption is less than that of earning labor income. In these countries, higher fertility and more rapid population growth lead unambiguously to lower golden rule consumption. The Samuelson tradeoff does not occur. These countries would benefit from lower fertility. In Japan and in six European countries (Hungary, Slovenia, Austria, Italy, UK, and Germany), however, the arrows have reversed direction and point to the right, indicating that consumption occurs at an older age than labor income. In these, the Samuelson tradeoff occurs, but given how short the arrows are the capital dilution effect dominates and the overall effect of faster growth is negative—despite the perception by governments that fertility is too low. The average ages and the direction of the arrows depend both on the ages of consumption and of labor income across the individual life cycle and on the age distribution of the population itself. In particular, because labor income is fairly symmetric around its average age, and low at both young and old ages, population aging has relatively little effect on its average age. Consumption, however, is lower in childhood, and in the rich countries is tilted toward older ages. The mean age of consumption is strongly affected by population aging. Consequently, countries with lower fertility and slower population growth tend to have Ac > Ay . Population aging has a powerful effect, although such factors as age at retirement and publicly provided health care matter as well (Mason and Lee, 2013). Arthur–McNicoll’s Eq. (5) tells a straightforward story about the Samuelson (1975a) tradeoff between dependency and capital dilution in the golden rule case. And yet one might expect that the result would depend on the extent to which individuals provide for their own old age through life cycle saving vs relying on intergenerational transfers from younger family members or the public sector. The equation appears to abstract entirely

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Life cycle wealth 0.29 −1.77 0.78 −0.61 1.72 −0.25 1.60 0.00 0.84 0.24 0.09 −1.98 0.55 −3.47 −2.62 −1.74 −3.17 −2.49 −3.20 −4.94 −2.57 −3.21 −3.40 −3.42 −2.77 −2.66 −4.17 −2.67 −4.93 −5.14 −3.55 −4.06 −4.40 −6.32 −3.11 −3.02 −4.62 −5.40

United States and EUROPE United States Austria Sweden Germany Finland United Kingdom Spain Italy Slovenia Hungary EAST ASIA Japan Taiwan South Korea China LATIN AMERICA Argentina Chile Mexico Uruguay Costa Rica Brazil Peru Colombia Jamaica SOUTHEAST ASIA Thailand Indonesia Philippines India AFRICA South Africa Nigeria Senegal Kenya Ache, etc. !Kung

25

30

35 40 Average age

45

Fig. 5 The direction of redistribution of income across age in selected populations. The head of the arrow points to the average age of consumption and the tail is at the average age of earning labor income. The length of the arrow is Ac  Ay . An arrow pointing to the right indicating a positive difference with income redistributed from young to old, and to the left a negative one.

from such institutional and behavioral factors, and this was also true of the original Arthur–McNicoll formulation. However, further development of the model with age distribution permits us to introduce transfers and saving/asset accumulation as alternative ways to smooth consumption relative to labor income. Earlier, I asserted that aggregate

Macroeconomics, Aging, and Growth

consumption must equal aggregate labor income, but I said nothing about how the young and the old managed to fund their consumption in excess of their labor income at those ages. Now we will look at these arrangements in more detail in a model that includes capital. Consider the budget for an individual at age x. The difference between consumption and labor income at that age must be made up by net transfers received (transfers received minus transfers made to other ages) and by asset income received minus saving: c ðxÞ  yl ðxÞ ¼ ½τ + ðxÞ  τ ðxÞ + ½nkðxÞ  sðxÞ

(6)

The first bracketed quantity on the RHS is net transfers received. It can be decomposed into public and private components. The second bracketed quantity can be decomposed into public asset income minus public savings and the private equivalent. I will refer to this bracketed quantity as “asset-based reallocation.” Under the golden rule assumption with no technological progress, the return to capital is n, the population growth rate. We can interpret k here as assets rather than capital, and take it to include negative values (debt) as well as positive, and the whole bracketed quantity therefore to include public and private borrowing and lending as well as saving and dissaving. It will be useful to define transfer wealth held by an individual at age x, T(x), as the survival-weighted present value (discounted at n) of expected transfers to be received in the future minus transfers to be made. This transfer wealth concept is well known in the context of Pay As You Go public pensions, but it can be applied to all kinds of transfers, including transfers from older to younger such as public education. We can then calculate the aggregate transfer wealth T for the whole population as the population-weighted sum across all ages of T(x). The flows of transfers at any given time t must sum to 0 across individuals in a closed economy, since every dollar of transfer given is exactly offset by the dollar of transfer received. However, the aggregate stock of transfer wealth T can be positive, negative, or zero. To see this, consider a pure Pay As You Go pension system. Every adult has paid into the system ever since reaching the age of labor force entry, so adults of every generation, young or old, expect to receive more in the future than they expect to pay in the future, and therefore at every age the pension wealth is positive. Therefore, the aggregate transfer wealth T held through this pension system is positive.d We can take this analysis a step farther. Willis (1988) showed that aggregate transfer wealth T in a golden rule economy is given by:

d

Every steady-state system of transfers pays a rate of return equal to the population growth rate plus the productivity growth rate. If transfer wealth is calculated using a discount rate r > n then the pension wealth will typically be negative at some ages, but that does not happen in golden rule conditions when the discount rate equals the population growth rate plus productivity growth rate.

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T ¼ τ + ½Aτ +  Aτ 

(7)

Here τ + is the annual gross flow of transfers made in the population (which is identically equal to the flow of transfers received in a closed population), and the quantity in brackets is the average age of receiving transfers minus the average age of making transfers in the population. When the preponderance of transfers goes from parents to the children they are rearing, then the average age of receiving transfers will be much lower than that of making transfers, and T < 0. When the preponderance of transfers goes from working age adults to the elderly, then T > 0. It will also be useful to define life cycle wealth of an individual at age x, W(x), as the survival-weighted present value (discounted at n) of expected future consumption minus expected future labor income. This is the amount of wealth that the individual would have to hold in order to be able to consume the expected amount at each age given expected future earnings. Then aggregate life cycle wealth W is the population-weighted sum of W(x). Willis (1988) (see also Lee, 1994a,b; Bommier and Lee, 2003) showed that:
 W ¼ c Ac  Ay (8) where c is ordinary per capita income. In Fig. 5, the column to the right indicates the life cycle wealth W as given by (8), which is the area of each arrow. The thickness of the arrow indicates c relative to per capita income, so the area is life cycle wealth as a multiple of per capita income (under golden rule steady-state conditions). This life cycle wealth can be held in two forms, as capital or as transfer wealth. For example, a 50 year old expects to be able to consume more in old age than she earns, by combining a public pension with retirement savings (Willis, 1988; Lee, 1994a,b; Bommier and Lee, 2003; Lee and Mason, 2011, Chapter 2). W ¼T +K

(9)

Debt and credit do not enter into this equation because in a closed economy they must cancel (when government debt is allocated to tax payers). Substituting from (7) and (8) into (9) and rearranging, we find that:
 T ¼ Ac  Ay  k=c (10) Referring back to (5), we have the striking result from Willis (1988) that: @β T ¼ (11) @n c That is, across golden rule steady states, the change in age-specific consumption is proportional to the ratio of aggregate transfer wealth to per capita consumption. T may be positive, negative, or zero, depending on context. In societies with aging populations that make heavy pension and health care transfers to the elderly, T will be positive and this result tells us that higher fertility and more rapid population growth will be beneficial.

Macroeconomics, Aging, and Growth

In low income societies with high fertility and young populations, T will be negative and this result tells us that lower fertility and slower growth will be beneficial. Now consider an economy in which either there are no transfers whatsoever, or upward and downward transfers are perfectly balanced so that Aτ + ¼ Aτ and T ¼ 0. Since by assumption this economy is golden rule, there must be very substantial life cycle wealth held in the form of capital in order for the elderly to be able to consume more than they earn. In this case, we see from (11) that a small difference in the population growth rate due to different fertility would have no effect at all on age-specific consumption, since the derivative is zero. The increase in the consumption needs of the elderly would be exactly offset by the increase in life cycle asset holdings arising from life cycle savings. The population growth rate for which the derivative is zero is the one that maximizes life cycle consumption (the second derivative condition is met). It follows that in golden rule economies, population aging due to low fertility is a problem only to the extent that the economy relies on asymmetric transfers to redistribute income to the elderly. When the elderly provide for their own retirements by relying on their earlier life cycle savings, population aging has no adverse effect. The obvious question, then, is to what extent do economies in fact rely on asymmetric transfer systems? We draw on NTA data to assess the sign and size of T. NTA finds that average private transfers are invariably downward, from older to younger. Even in those countries in which there is substantial familial support of the elderly, as in East Asia, it is dominated by familial child rearing transfers (see Lee and Mason, 2011, Chapter 4). However, net public transfers go from old to young in some countries, but from young to old in others (Lee and Mason, 2011, Chapter 4). Fig. 6 plots arrows for total transfers, that is, public and private combined, in the same format as Fig. 5. The head of each arrow is at the average age of receiving transfers and the tail at the average age of making transfers in various populations. The figure plots the arrows based on 2010 population data and then it plots the arrows that would result if the current age profiles of transfers remained unchanged while the population age distributions changed as projected to 2050 by the United Nations Population Division (2011). The current arrows almost all point to the left, indicating net transfers flowing from older to younger ages, except for a few European countries. However, the projections to 2050 indicate that more countries would shift to upward transfers, and the regional average arrows for Europe and the United States and for East Asia would both point to the right, indicating upward transfers. Taking these results at face value, they suggest that today almost all countries would benefit from having somewhat older age distributions (Lee and Mason et al., 2014), but by 2050 many would benefit from having younger age distributions. However, there are a number of problems with this interpretation. First, none of these countries is on a golden rule growth path; second, there is every reason to expect the age profiles of consumption, labor income, and transfers themselves to change in both rich and nonrich countries; and third, none of these populations is stable now. Assessment of the

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Current wealth

2050 wealth

United States and EUROPE

−1.73

−0.44

United States

−4.25

−3.05

Austria

0.90

2.95

Sweden

−0.82

0.22

Germany

−0.33

1.96

Spain

−1.50

−0.07

Slovenia

−0.22

2.11

Hungary

1.03

3.13

EAST ASIA

−3.29

−0.09

Japan

−1.41

1.04

South Korea

−5.01

−0.85

China

−2.60

−0.10

LATIN AMERICA

−4.97

−0.99

Argentina

−4.26

1.55

Chile

−4.80

−0.18

Mexico

−7.12

−3.37

Costa Rica

−4.35

0.10

Brazil

−4.97

1.27

Peru

−5.90

−2.52

SOUTHEAST ASIA

−5.39

−2.76

Thailand

−4.25

−0.71

Philippines

−6.96

−4.76

India

−4.65

−2.71

South Africa

−5.82

−4.23

25

30

35

40 45 Average age

50

55

60

Fig. 6 The direction of transfers, private plus public, across age in selected populations. The head of the arrow points to the average age of receiving a transfer and the tail is at the average age of making a transfer. The length of the arrow is At +  At . An arrow pointing to the right indicates transfers flowing upward from young to old, and to the left a downward transfer.

consequences of ongoing population aging in the 21st century requires dynamic simulations of more complex models. Nonetheless, these simple golden rule steady-state models, and the empirical estimates of transfer flows, provide some helpful insights. In particular, the macroeconomic impacts of population aging depend on: (1) the age pattern of consumption in relation to labor income over the life cycle; (2) the extent to which the gap between consumption and labor income is made up through transfers rather than by drawing on assets accumulated through earlier saving, and the extent to which these transfers are asymmetric with age; and (3) population aging raises the capital intensity of the economy and affects wages, profits, and interest rates accordingly.

Macroeconomics, Aging, and Growth

So far we have considered only population aging that arises from low fertility and slow or negative population growth. Some part of population aging is due to declining mortality, however. The same model setup can be used to analyze the effect of mortality decline as in Lee (1994a) and Lee and Tuljapurkar (1997). In general, mortality decline raises the population growth rate and thereby has all the effects just analyzed for fertility change. However, in countries where mortality is already low, the effect on population growth rates of further decline is negligible. The important effect arises from the interaction of increased person-years lived at each age in the life cycle with the age profiles of consumption and labor income. It is particularly important to note that in early years of mortality decline, starting from high mortality, most of the person years gained occur in childhood and during the working years. However, as mortality declines and life expectancy rises, the share of the person years gained above age 65 rises. By the time life expectancy reaches 70 or 75, further mortality reductions lead to person years gained that are mostly at older ages. In the United States and other high income countries, 75% of the gains in life over the last 25 years have accrued to ages 65 and over and in most rich industrial nations years of labor force participation have declined as a share of life expectancy since 1980 (Eggleston and Fuchs, 2012).

8. INTERNATIONAL COMPARISONS OF SUPPORT SYSTEMS FOR ELDERLY While Fig. 6 showed the general direction of total transfers, whether toward older or younger members of the population, it is also useful to see more institutional detail. National economies vary a great deal in how consumption by older people is funded. For starters, in some countries the elderly continue to work to a substantial degree while in others they earn very little labor income. In NTA data, we find that labor income at older ages is particularly low where either public or private transfers are an important source of old age support, as in Europe, Latin America, and East Asia. Where asset income is more important older people tend to continue to work, as in the United States, Mexico, and parts of South and Southeast Asia. Fig. 7 focuses on how the gap between consumption and labor income in old age is funded, which makes it possible to use a triangle graph in which the shares of funding from asset income, private transfers, and public transfers sum to 1.0. Each point in the figure represents one country, identified by the two letter code of the United Nations. Each vertex refers to a single funding source, as labeled. A point located at a vertex indicates that in that country, funding for the elder gap comes entirely from that source. Positions along the line connecting two vertices indicate a mixture of funding from those two sources, with zero from the third. Points located inside the triangle have funding from all three sources. Points outside the triangle to the right have negative funding from family

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Fig. 7 How the gap between consumption and labor income for people 65+ is funded in different countries, by public transfers, by private transfers, or by asset income. The shares add to 1.0.

transfers, which is to say that older people on net make transfers to younger, rather than the reverse. Six countries are located on or near the public transfers vertex, indicating 100% funding from that source: Austria, Slovenia, Hungary, and Sweden, but also Argentina and Brazil (Brazil’s position indicates that public transfers equal the gap between consumption and labor income, but that additional funds from asset income are used to make large private transfers to younger family members). In another group of countries, public transfers fund two-thirds of the gap: Germany, Uruguay, Spain, Costa Rica, and Chile, with China and Japan close by. In nearly two-thirds of the countries shown the elderly rely very heavily on public transfers. It is striking that reliance on private familial transfers is so rare. No countries are near the private transfer vertex. Four countries in East and Southeast Asia (China, South Korea, Taiwan, and Thailand) rely one-sixth to one half on private transfers, as does Jamaica. Japan, interestingly, is not among them. In eight countries, the elderly rely at least 50% on asset income to fund the gap: the United States, Mexico, Jamaica, Uruguay, Great Britain, Philippines, Thailand, and India. The fact that the elderly in relatively few countries rely much on asset income in their old age does not necessarily mean they do not own assets. It is possible that they own substantial assets but that they save all the asset income rather than using it to fund consumption. In this case they will leave very substantial bequests, intentionally or not, when they die.

Macroeconomics, Aging, and Growth

These measures of flows do not correspond exactly to the variables in Eqs. (9) and (11) but they nonetheless are suggestive in that regard. In general, the greater the reliance of the elderly on asset income, the less the impact of population aging on consumption across the life cycle.

9. POPULATION AGING AND CAPITAL MARKET EQUILIBRIUM WITH TRANSFERS Consider an hypothetical economy with pure life cycle saving (for consumption smoothing alone, with no altruistic motives toward children or parents, and no precautionary motive), in the extreme case in which individuals must borrow at some interest rate to fund their consumption starting at birth, and then continue to save and dissave over their lifetimes to achieve their desired consumption trajectory in the complete absence of public or private transfers, with perfect annuitization, and with zero saving for any other purpose. Producers in this economy have a demand for capital that depends on the interest rate at which funds can be borrowed. The economy reaches equilibrium with some interest rate and some amount of capital, where the amount that individuals want to invest is just equal to the amount that producers want to borrow. In this economy and population, the capital held for life cycle smoothing purposes would be different than the golden rule amount, except by unlikely accident. Suppose that capital is less than golden rule. If the age trajectories of consumption and labor income remain the same, but we now introduce downward transfers from older to younger, for example in the realistic form of parents bearing the costs of rearing their children, then we can see from (9) that as transfer wealth declines, capital would increase. The desire to make downward intergenerational transfers, including both inter vivos transfers and end-of-life bequests, generates a demand for wealth beyond life cycle saving. This point was made forcefully by Kotlikoff and Summers (1981, 1988) in a series of articles suggesting that the desire to make intergenerational transfers is a more important source of demand for capital than is the desire to smooth consumption over the life cycle as in the life cycle saving hypothesis (Modigliani, 1988). There is some hypothetical level of downward transfers that would make T sufficiently negative that K would be raised to the golden rule level. In a golden rule steady state of this sort with T < 0, population aging due to lower fertility and slower population growth would raise lifetime consumption (see Eq. 11 and Arthur and McNicoll, 1978). This case is illustrated in Fig. 8 (based on Willis, 1988; see also, Eggertsson and Mehrotra, 2014, 7) which shows the discount rate on the vertical axis, including the golden rule rate where r ¼ n, and shows on the horizontal axis the corresponding demand for life cycle wealth by individuals, W, and its components transfer wealth T and capital K, expressed on a per capita basis. The extent to which this demand for wealth by households exceeds transfer wealth T is the supply of investment funds for the production

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At D, pure life cycle demand for K less than golden rule. If augmented by desire to make downward transfers capital rises, reaching golden rule at B.

At B the pure life cycle demand for K is coincidentally exactly right for golden rule

WA(r,ñ)

Rate of return, r

WB(r,ñ) WC(r,ñ)

D r=n=ñ golden rule

B

A T0 C

At E, pure life cycle demand for K above golden rule, dynamically inefficient with r < n. Greater efficiency with upward transfers T > 0, eventually reaching golden rule at B.

E Producers’ demand for K = K(r, ñ)

Demand and supply for wealth W, capital K, and transfer wealth T

Fig. 8 Equilibrium in the capital market and the roles of the aggregate demand for wealth (WA) and aggregate transfer wealth (T), illustrated for three different demands for wealth schedules. The population growth rate n is fixed at ñ. Notes: The heavy line is the demand for capital by producers, equating r to the marginal product of capital. The life cycle demand for wealth by households (for purposes of achieving planned life cycle consumption given planned life cycle labor earnings) is shown for three different cases. In case E, when r ¼ ñ it just happens to equal exactly the producers’ demand for capital at r ¼ ñ with transfer wealth T ¼ 0, and therefore corresponds to the golden rule case. In case A, the life cycle demand for wealth when r ¼ ñ is less than the golden rule amount, perhaps because people plan to work longer in old age or to consume less in old age. In this case, only if people make substantial transfers to the young either privately, eg, through bequests, or publicly, eg, through a large publicly owned capital stock to which new births automatically gain a share, can golden rule be achieved. In case B, the life cycle demand for wealth at r ¼ ñ is greater than the golden rule level, perhaps because people plan to retire very early and to consume more in old age than in youth. In this case to achieve golden rule it would be necessary to satisfy a part of the demand for life cycle wealth through upward transfers such as familial support of the elderly or a Pay As You Go public pension system. D marks a possible nongolden rule steady-state equilibrium for case A with transfer wealth less negative so that r > ñ. Other institutional arrangements leading to other values of T would generate different nongolden rule steady-state equilibria (elaborated from Willis, 1988).

sector. The amount of investment funds demanded by the production sector is plotted as the heavy black line which is lower when the interest rate is high and conversely. The intersection of the demand and supply of capital curves locates the equilibrium interest rate and the equilibrium values of W, T, and K. The golden rule equilibrium without transfers occurs when the demand for wealth is given by WB, which intersects the

Macroeconomics, Aging, and Growth

producers’ demand for capital at interest r ¼ n. In this case, T ¼ 0, and small changes in the population growth rate and aging in the neighborhood of n will have no effect on life cycle consumption (evaluated at the initial interest rate r ¼ n). Given labor supply by age and intertemporal consumption preferences, this corresponds to a sort of double optimum for both the capital–labor ratio and the desired level of capital holdings to achieve consumption smoothing. The situation described in the paragraph earlier occurs when the demand for wealth curve lies to the left of WB, here shown as WA, which intersects the demand for capital curve at an interest rate above the golden rule rate n. However, with a sufficiently strong desire to make downward transfers to children T will be sufficiently negative so that the overall demand for wealth can lead to the golden rule outcome. In this case, population aging (a reduction in n) will raise age-standardized consumption across golden rule steady states as indicated by Eq. (11). Now suppose that the pure life cycle demand for capital would exceed the golden rule amount, as some have feared might be the case in aging populations. This leads to the so-called dynamically inefficient outcome with r < n, where the rate of return on capital is less than the rate of economic growth and less than could be earned through a program of upward transfers such as PAYGO public pensions. All transfer systems earn a rate of return of n in steady state (assuming no productivity growth). This situation is illustrated by the demand for wealth curve WC in Fig. 8, lying to the right of WB, with equilibrium at E. In this case, by introducing a system of upward transfers such as public pensions, public health care, or national debt, or private transfers to support the elderly, T can be raised to a positive value which would displace enough capital to reach the golden rule steady state with r ¼ n. In this case, life cycle consumption could be raised by making the population younger through increasing fertility, since T > 0 (see Eq. 11). A number of these theoretical and empirical themes are drawn together in Table 1 which shows results for the golden rule case (for those economies that have capital) under particular assumptions made in the literature. The first case with both capital and transfers, covered in the first four rows of the table, has already been discussed. The next row assumes T ¼ 0. In this case, as we have seen, population aging has no effect on age adjusted consumption. But this case is entirely unrealistic, since it does not even allow for parental expenditures for rearing children, or else assumes perfect symmetry of transfers. In the next row, we have the case when there is no demand for life cycle wealth, so W ¼ 0. This would be true, for example, in the standard Solow growth model in which individuals are homogeneous other than in age. Since labor and consumption are the same at all ages, there is no demand for life cycle wealth. With W ¼ 0 we have K ¼ T. That is, all saving must be motivated by the desire to transfer capital to the new members of the population. For this reason, a slight increase in the age of the population (reduction in n) will raise golden rule consumption with an elasticity of –k/c, as we know it does from earlier discussion.

89

Table 1 The effect of slower population growth and population aging on lifetime consumption across golden rule steady states under different assumptions about presence of capital (K) and aggregate transfer wealth (T) which can be positive or negative Proportional effect on lifetime Constraints on system for consumption of a small decrease in reallocating income across ages through capital or transfers population growth rate, population aging Other comments on this case

General case: W¼T+K

T/c With T > 0, population aging and slower growth are costly

T>0

>0

T n. Suppose that life cycle saving is an important source of the private demand for holdings of capital, so that the demand for capital is positive at all ages, but rises until the age at retirement and then soon after declines as the older individual spends down her capital to pay for consumption. Older people hold more capital than younger in this case. As the population ages, the demand schedule for capital (like

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WA(r,n˜ ) in Fig. 8) will shift to the right, and the equilibrium amount of capital will rise while the rate of return falls. Numerical simulations for a number of countries are shown in Lee and Mason (2010a). To put this in very concrete terms, an older population with a prefunded pension system or private retirement accounts will demand more assets than a younger one. In a closed economy with a balanced budget, this demand for assets will translate into a demand for capital. It is possible that deep population aging, such as is projected for many low fertility nations by 2050, could push an economy from a situation like A today (in the absence of transfers) to a situation like C in three or four decades. In the absence of old age support by public or familial transfers, population aging should lead to capital intensification.

12.3 Public Sector Transfers In most countries and in all rich industrial nations consumption by the elderly is funded by a mixture of public and private transfers rather than solely by asset income, as shown earlier in Fig. 7. However, transfers are also made downward to children. Fig. 6 showed that around 2010, almost all countries have net downward transfers when public and private are combined. These countries are likely to be found somewhat to the right of A in Fig. 8, with downward transfers generating a demand for capital in addition to the life cycle saving demand. However, projected population aging between now and 2050 will lead to a reversal of the net direction of transfers, assuming the current age profiles of transfers are unchanged in shape. By 2050, if there are no adjustments in the shape of the public and private transfer age profiles, net transfers will be upward, and economies would tend to have less capital than otherwise, because upward transfers substitute for life cycle savings and asset holdings. If we restrict our attention just to public transfers (see Lee and Mason, 2011, figure 4.6), we find that among the rich industrial nations all have net upward public transfers flows except for the United States which has a relatively young population and relatively low public pension benefits. It has been well established that public transfer programs in many rich nations will be seriously unbalanced as populations age over the next few decades unless benefits for the elderly are cut sufficiently and/or taxes to pay for these benefits are raised sufficiently (later retirement is viewed here as a reduction in benefits and an increase in taxes). If such adjustments are not made, then the public sector will dissave and government debt will rise. Rising government debt is a form of upward transfer from future generations to current ones, and substitutes for current private saving and asset accumulation for life cycle purposes. Government borrowing will compete with efforts by producers to borrow for investment in capital and lead to lower capital intensity. I suggested earlier that population aging would raise the capital intensity of economies. But it is possible that the reverse will happen if governments fail to make

Macroeconomics, Aging, and Growth

appropriate adjustments in their transfer programs for the elderly, and if growing public debt displaces private capital. For this reason, any conclusions about aging and capital intensification must be conditional on assumptions about the response of the public sector to the need for reform in pensions, health care, and long-term care (National Research Council, 2012, Chapter 7).

12.4 Open and Closed Economies in an Aging World Many of the conclusions reached above hold only in a closed economy. In an open economy that is not too large, interest rates, wage rates, and therefore capital intensity are all set on international markets. It is arguable that even the United States should be viewed as open and not too large in this context. In the polar case of a small, open economy, population aging would not affect domestic capital intensity. Population aging would lead to an increase in domestic asset intensity (an increased ratio of assets to labor income) but assets would be held substantially in the form of investments in foreign capital or foreign debt. In this case, domestic population aging would raise asset holdings and asset income, and the share of asset income in national income would rise, but rates of return to capital would not fall and wages would not rise. These would continue to be set on international markets. The bigger picture is that the whole world is aging, or will be soon, so global population aging will affect factor returns in international markets. For example, the median age of the population in rich developed nations is projected by the United Nations Population Division (2011) to rise from 39 years in 2010 to 48 years in 2050, and in the rest of the world from 27 in 2010 to 37 in 2050. The global OADR (OADR ¼ population  65 divided by population 20–64) is projected to rise from 0.134 in 2010 to 0.283 in 2050, more than doubling. If each country’s population is weighted by its projected per capita income for each future year, then the global weighted average OADR is projected to rise from 0.195 in 2010 to 0.378 in 2050, nearly doubling (National Research Council, 2012). That is the big picture, but of course, the timing and pace of population aging vary from country to country and from region to region. The currently rich industrial nations experienced earlier demographic transitions and in many cases also deeper fertility declines, and their populations are older now and will be aging rapidly between now and 2050. Japan experienced an early, rapid, and deep fertility decline, but other East Asian countries were not far behind including China, and they also will age rapidly between now and 2050. The same is true of some countries in Latin American, the Middle East, and North Africa. Much of the developing world including India, however, is moving more slowly through the demographic transition and aging will come to it later and more slowly. These differences in population age distribution combined with differences in economic growth create important opportunities and incentives for

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international capital flows as simulated by B€ orsch-Supan et al. (2006). Williamson and Higgins (1997), in a cross-national empirical study, found that indeed population age distribution influenced international capital flows. For some countries, the international context will ameliorate the impact of population aging. For example, aging European economies, if closed, would experience capital deepening with falling rates of return, and rising wages. However, the rest of the world is younger and these European economies, by exporting some of their savings, can reduce the decline in rates of return and reduce the rise in wages (B€ orsch-Supan et al., 2006). The United States is considerably younger than Europe, and Kruger and Ludwig (2007) find that openness reduces the rate of return to capital and raises wages rather than the reverse, because the United States is younger than most other OECD countries and through openness they effectively import population aging. To a greater degree, this will be true of many developing countries. For Europe, openness means that older people who hold assets benefit through higher income while younger people with fewer assets but more labor lose through lower wages. While the reasoning just given seems straightforward, multiregional OLG models with actual and projected demographic change show more subtle effects that can be counter intuitive (B€ orsch-Supan et al., 2006). The expected effects do occur initially, but after a few decades these effects wear off and are replaced by weakened or reversed effects in some cases. Using an international OLG model, Fehr et al. (2008) find that in developed nations as a region, even a large increase in fertility or mortality would not have much effect until 2070, due to the momentum of demographic change.

12.5 Will Population Aging Cause an Asset Price Meltdown? Older people often rely to some degree on funded retirement plans, whether their own or through an employer’s pension. The ability of such plans to deliver income for retirees depends on the rate of return on assets. This lends urgency to the question whether population aging will lead to an “asset price meltdown,” a topic that has been the subject of an academic literature (Poterba, 2001, 2005; Brooks, 2006; Kruger and Ludwig, 2007; Geanakoplos et al., 2004; Abel, 2001, 2003; B€ orsch-Supan, 2006) accompanied by more strongly voiced concerns in the popular press. It is suggested that a decline in rates of return or meltdown might occur for two reasons. First, population aging is expected to lead to capital intensification with a resulting decline in the return to capital (Arnott and Chaves, 2011; Liu and Spiegel, 2011), as capital–labor ratios rise, as discussed earlier. Second, a subtler argument is that older people are more risk averse and prefer an investment portfolio with a higher proportion of bonds. As a baby boom moves into old age its members will sell off their equities in order to buy bonds, reducing the price of equities, and raising the price of bonds. There could be a similar effect on houses and housing prices as older people sell their homes and move into smaller rental units.

Macroeconomics, Aging, and Growth

Abel (2001, 2003) makes a somewhat different argument for the case of aging baby booms as opposed to secular population aging. The basic idea is that baby booms will raise the price of capital due to the adjustment costs to achieve more rapid investment, and that rational investors will realize that the price of capital will decline after the baby boom passes. He emphasizes the importance of considering the supply conditions for capital as well as the demand for investment opportunities. Population aging can be foreseen decades in advance, so if participants in asset markets are forward looking, it is unlikely that slowly moving population aging would lead to a sudden decline in asset prices or to a dramatic meltdown. There have been many empirical studies of the relation between demographic change and asset price movements, reviewed in National Research Council (2012), Chapter 8. The results of these studies have been mixed, and when analysis is modeled in the international open economy context, the studies tend to find at best small effects of population aging (B€ orschSupan et al., 2006; Ludwig et al., 2012). Open international contexts dilute and counteract the effects of population aging. It is also important to keep in mind, however, that the return on capital will be influenced by the trend in labor supply as well, which like capital will be strongly influenced by international flows, that is by labor migration. Furthermore, it is not only the quantity of labor in relation to capital that matters. It is also the amount of human capital per worker. This will be discussed later in Section 13 on human capital intensification.

12.6 How Much Population Aging Is Optimal? From Arthur and McNicoll’s (1978) result given in (5) we have the effect on consumption of a slight change in the population growth rate, where consumption is measured as the height of the consumption age profile. We have age profiles of labor income and consumption for different countries. If we assume an elasticity of output with respect to capital of 1/3 under constant returns to scale, depreciation at 0.05, and productivity growth at 0.02, we can find the population growth rate and age structure that maximize the height of the consumption profile. In fact, this has been done in Lee and Mason et al. (2014) and Hock and Weil (2012). Results vary by country. In general, however, a slightly negative steady-state population growth rate is “optimal” in this sense, and the associated fertility rates are around 1.6 births per woman. This calculation is based solely on the simple neoclassical growth rate with age distribution and fixed age shapes of consumption and labor income. Nonetheless, the result is striking. Taking the capital costs of population growth into account changes the outcome. Without including these capital costs, the maximizing growth rate would be close to 0. If we focused only on the age profiles of tax payers and recipients of public transfers, then substantially more rapid growth and higher fertility would be desirable. One might be uncomfortable with the idea that a negative population growth rate could be sustained and be optimal. However, it is completely standard to work with

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steady states in which population growth and productivity growth are both greater than zero. The long-run problems posed by that scenario are vastly greater than those caused by mildly negative population growth.

13. POPULATION AGING AND HUMAN CAPITAL INTENSIFICATION There are good reasons to expect that population aging will be accompanied by increased investment in the human capital of children so that the quality of the workforce will rise, and a reduction in the relative quantity of labor will be offset to some degree by an increase in its quality. Such an increase in labor quality would have several relevant effects. First, it would raise labor income and therefore tend to reduce capital intensification measured by the ratio of capital to number of workers. This would reduce any decline in the rate of return to assets as populations aged. Second, it would raise the earnings and incomes of more recent generations relative to older ones, and thereby ease the problems of pay-as-you-go (PAYGO) pension systems in which benefits are determined by wages at retirement and are not indexed to wage levels in subsequent years (the U.S. Social Security system is of this sort, for example). In such systems growth in wages per worker is just as helpful for fiscal balance as growth in number of workers. Third, it would raise the level of per capita income. The main cause of population aging is low fertility. In the well-known quantity– quality tradeoff theory of fertility (Becker and Lewis, 1973; Willis, 1974), couples seek to maximize their utility which depends on their own consumption and also on the number of children they have and on the average quality of those children. They face a budget constraint in which number of children is multiplied times the quality of children because this product is total spending on children. For simplicity assume that a couple first decides on the share of income they will devote to children, and then given that amount, decides how to allocate this amount between quantity and quality subject to the constraint. In this case, variations in tastes or prices or incomes across otherwise similar couples would lead to a negative relation between quantity and quality with an elasticity of approximately 1. The theory suggests that income elasticity for quality is substantially higher than for quantity, so that when incomes rise over time in a country, couples choose to have fewer children and to invest proportionately more in each child. A version of this theory might also be applied to public education to suggest increasing spending per child in countries in which fertility is falling. Fig. 9 presents NTA data on human capital spending per child relative to fertility. Human capital spending is defined as the sum over ages 3–26 of per capita spending at each age (a synthetic cohort measure), combining both public and private spending, plus a similar sum for public and private health care spending from age 0 to 17. For comparative purposes, this measure for a country is divided by that country’s average labor income across ages 30–49. Fertility is measured as the TFR in the 5 years before the base year of the survey used for the NTA

Macroeconomics, Aging, and Growth

Fig. 9 Human capital investment by fertility across countries based on NTA and United Nations fertility. Notes: Human capital spending is public and private spending on education and health by year of age summed from age 3 to 26 for education and 0 to 17 for health. Fertility is the TFR in the 5 years preceding the NTA base year.

estimates. The data are plotted on a log–log scale with each point corresponding to a country, distinguished by region. There is a moderately strong negative relationship with a slope of 0.7. For present purposes, the direction of causality does not matter, whether from fertility to human capital, from human capital to fertility, or from economic development to both. The point is that lower fertility is associated with higher investment per child. In high fertility countries about 1–2 years of labor income is invested in human capital per child, whereas in a country with fertility near 1.0, 5, or 6 years of labor income are invested in each child. A similar or stronger relationship is observed over time within countries (Lee and Mason, 2010b, 2011). As it happens, this relationship is largely due to variations in public education rather than in private expenditures, although within the Asia Region, it holds also for private expenditures on education. Lee and Mason (2010b) also develop an OLG model incorporating these estimates as well as estimates of returns to human capital in the literature and conclude that the substitution of quality of workers for quantity of workers could greatly reduce the old age dependency costs of population aging. Another reason to expect human capital investment to rise as populations age is that capital intensification reduces returns to capital and raises returns to labor and to human capital. This creates an incentive to shift investment from physical capital to human capital. Ludwig et al. (2012) and Ludwig and Vogel (2009) develop OLG models

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incorporating this insight which are applied to the United States and to a set of countries, and they find that increased human capital investment substantially offsets the effect on wages and rates of return of population aging. Becker and Murphy (1988) provide an elegant theory of the interrelation of human capital investment, public education, public transfers to the elderly (pensions and health care), and capital accumulation. A different approach to a similar set of issues takes fertility and longevity as exogenous and models the investment in human capital as a matter of individual optimization over the life cycle. Heijdra and Reijnders (2012) exemplify this approach. In an OLG model with these features, they find that an increase in longevity accompanied by a postponement in the depreciation of human capital leads to an increase in both physical capital and human capital, with the human capital increase larger so that wages (per efficiency unit of labor) fall and the rate of return to capital rises, reversing the usual result, and illustrating the importance of taking human capital into account in this context. Cervellati and Sunde (2013) show that so long as mortality declines within the working ages, it raises the incentives for investment in human capital.

14. AGING AND PRODUCTIVITY GROWTH There are two very different issues to consider here. One is that population aging means aging of the labor force which may reduce its efficiency, dynamism, and ability to adopt new technology and its willingness to take risks. The other is that the very machinery generating technological progress may move more slowly in an aging population. We will begin by considering the aging labor force.

14.1 Age and Productivity of Workers As the population ages, there will also be a shift toward older ages in the labor force even if labor supply by age of individuals remains the same. This shift will be strengthened if the age at retirement rises with longer life, as appears very likely. The projected aging of the labor force raises two basic questions. First, are older workers less productive than younger ones, and if so will this lead to slower productivity growth, at least during a transitional stage? And second, will an older population be less creative and innovative than a younger one, leading to slower technological progress and productivity growth? It is tempting to look to the age profile of average real wages to show us how labor productivity varies with age. There are serious difficulties with this approach. First, older people who continue to work may be selected for health, strength, and vitality and therefore not be representative of older people in general or those older people who might be induced to supply more labor. Second, seniority and rules against age discrimination may influence the wages paid to older workers beyond what their productivity might warrant. Third, cross-sectional data will show effects of generation as well as age. Difficulties like

Macroeconomics, Aging, and Growth

these have led some analysts to study direct measures of ability by age, for example performance in athletic events or in chess (Fair, 2008; Skirbekk, 2004) or cognitive ability (Skirbekk et al., 2012). Pekkarinen and Uusitalo (2012) use piece rates for Finnish blue collar workers and fund that hourly productivity rises up to age 40 and then remains constant. A thoughtful review of this literature is given in National Research Council (2012), Chapter 6. Based on its survey of the literature and its own calculations, it concludes that “there is likely to be a negligible effect of the age composition of the labor force on aggregate productivity over the next two decades” (p. 120) while cautioning that the evidence is very fragile.

14.2 Endogenous Growth and Population Aging It is arguable that the mechanisms and consequences considered so far—support ratios, capital intensity, and human capital intensity—are all just one-time adjustments that do not alter the trajectory of economic growth. Even a small effect of an aging labor force and slower population growth on the pace of technological change would come to dominate all other influences. Will an aging labor force be less innovative and slow technological progress? For changes in long-term economic growth rates we need to turn to endogenous growth models. There are many examples of these, which are briefly reviewed in Jones (2002) and Prettner (2013). In Jones’ model, growth is driven by “the discovery of new ideas throughout the world” (p. 221) and because new ideas come from people, perhaps engaged in formal research and development efforts, population size has an effect and therefore “long-run per capita growth is ultimately tied to world population growth” (p. 224). In this view, then, the slowing population growth that causes population aging will also reduce the rate of technological progress. Jones emphasizes, however, that it is population growth in those countries that are at the technological frontier that matters, and surely these would include the rich developed nations but increasingly also developing nations like China and newly industrialized nations like Taiwan and South Korea. This perspective suggests that as population growth rates fall and populations age, technological progress will slow. A contrary view, drawing on the relation of human capital investment to fertility levels, is that slowing population growth will go hand in hand with increasing human capital intensity, and this might prove more important than raw population numbers in generating new ideas and progress. Many analyses in this literature abstract from age and treat population as homogeneous. Prettner (2013), in a useful paper, introduces fertility, mortality, and population age distribution into models of endogenous technological progress (dependent on population size) and semiendogenous (dependent on population growth rates, as in Jones above) that previously had homogeneous individuals. In his analysis lower fertility does impede progress but longer life favors it by reducing discount rates and encouraging

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investment in human capital, and it is the balance of these effects that matters. Although the two modeling approaches yield different implications of aging for economic growth, he concludes that current demographic changes featuring declines in both mortality and fertility will not necessarily slow technological progress or economic growth, and could indeed make them more rapid. Population aging might also affect the direction of technological progress, for example by influencing its factor bias. Slower labor force growth and capital intensification could incentivize labor saving technological change, for example. Population aging also changes the composition of demand, tilting it toward health care services, and incentivizing research and development in this area. Additionally, it raises the demand for workers in elder care, including elder care in the home. In Japan we see advances in the use of specialized robots to substitute for elder care workers in the home. Because the public sector is heavily involved in provision or funding of long-term care, it might play a special role in this area. Research on the way that population aging affects the direction of research and development, and technological change, is very limited. Another set of issues arises around the political influence of the elderly on the process of innovation. Lancia and Prarolo (2012) use an OLG model with children, workers, and retirees to analyze the interests of each in the costly adoption of existing new technologies. They find that as longevity increases and the population ages, even though individuals respond by investing more in human capital, the growing share of elderly tends to oppose the adoption of new technologies through the political process, and a slowdown in innovation and growth is one possible outcome. More prosaically, it is worth noting that population aging, and more generally changing population age distributions, have a mechanical effect on measured aggregate unemployment rates and on employment rates. For example, Horn and Heap (1999) calculated age-standardized unemployment rates for the United States over the period 1980–97, and found that it varied relative to the standard BLS measure from 0.3% less to 0.5% more over this 17-year period. Perhaps this should not be surprising, because the passage of the baby boom through the population age distribution was a major event. Nonetheless, it is worth noting that the young have higher unemployment rates than older workers, and so population aging will affect the standard measure and should be taken into account. Similarly, and probably more important, employment rates vary by age. For example, Fujita (2014) notes that the aggregate participation rate declined from 2000 to 2013 by more than 4 percentage points, and that an important share of this drop was due to the aging of the baby boom, particularly starting in 2010. Hotchkiss (2009) finds that changing population age distribution accounts for much of the variation in the aggregate participation rate since 1950, and holding age-specific participation rates fixed at 2008 levels, would predict a decline of 2.4 percentage points from 2008 to 2020—mainly reflecting the retirement of the baby boom generations. Changes in population age distribution can have an important impact on these aggregate measures which

Macroeconomics, Aging, and Growth

in turn have important roles in policy discussions, and failing to take their role into account can lead to erroneous interpretations.

15. POLITICAL ECONOMY OF POPULATION AGING AND THE PUBLIC SECTOR There are two leading questions in the political economy of population aging. One is how public spending on human capital investment will be affected. The other is how public transfers to the elderly will be affected. The first question is complicated by the quantity–quality issues surrounding fertility and human capital investment, as discussed earlier. But an additional factor is how longer lives and the growing proportion of elderly voters will affect spending on education. This is related to the second question, since increased public spending on transfers to the elderly could crowd out public investment in children. From an empirical perspective, Gruber and Wise (2002) report how changes in the share of elderly are associated with public spending on the elderly in OECD countries from 1980 to 1995, in a setup with country and period fixed effects. They found that a 1% increase in the share of the elderly was accompanied by only a 0.47% increase in transfers to the elderly as a share of GDP, so that per capita transfers to the elderly were reduced by population aging, while aggregate transfers to the elderly were increased. At the same time, there was no increase in total transfers, because transfers to other age groups, including children, were reduced. In sum, as the population ages, per capita transfers to individuals at each age, including the elderly, are reduced, even though aggregate transfers to the elderly are increased. This analysis suggests that population aging leads to less human capital investment than otherwise. In a different paper, de Mello et al. (2016) analyze survey results from 34 countries in Europe and Central Asia, finding that older people are more likely to support increased public spending on pensions and less likely to support it for education. Another literature focuses on theoretical aspects of the political economy of aging. Razin et al. (2002) develop a two age group OLG model with different skills classes of labor and different ability levels. The voting population forms coalitions around spending on public intra- and intergenerational transfers. The elderly would like to raise transfer spending, since they are major beneficiaries, while many working age voters would rather reduce public spending on transfers because they stand to lose. They show that population aging would actually lead to reduced payroll taxes and reduced transfers unless population ages to the point where the median voter is old—a highly unlikely prospect. Gradstein and Kaganovich (2004) consider the effect of longer life on public spending on education. They develop a two age group OLG model in which younger adults want to invest more in the human capital of the young, because they are concerned about future productivity growth which will affect rates of return earned by their savings over

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a retirement period that will be longer due to increased longevity. The already old and retired, however, would rather spend less on human capital investment, and with longer life there share in the population rises. They find that the interests of the younger adults will dominate, favoring increased spending on human capital, even though the crosssectional relationship of aging and educational spending across local areas could be the opposite as is sometimes found. A much-cited paper by Becker and Murphy (1988) presents a coherent theory in which public education arises to remedy inefficiencies and institutional failures in familial investment in human capital, and public pensions arise to repay the wind-fall losses suffered by the initial generations who pay taxes for public education but received none themselves. Bommier et al. (2010) explore this theory empirically in the case of the United States.

16. POLICY ISSUES Population aging is inevitable in a world with rising life expectancy, because fertility must decline. Some parts of the world (Europe, North America, East Asia, parts of Latin America) are farther through the demographic transition with lower or negative growth rates and early population aging. Possibly these countries can reduce the impact of population aging through increased immigration, but this is doubtful because immigrants themselves become old and in the long run tend to make receiving countries older (Goldstein, 2009). Nor are pronatalist policies likely to have a major impact on fertility. Because net upward public transfers are pervasive, population aging will be costly and will require adjustments which could take various forms (Weil, 1997; Elmendorf and Sheiner, 2000; Sheiner et al., 2007). These include raising labor supply by delaying retirement or increasing labor force participation of women; raising saving rates; raising taxes; and reducing government benefits. For illustrative calculations of tradeoffs among these options, see Sheiner et al. (2007) for the case of the United States. In each case, adjustments can be made earlier or later, with corresponding differences in generational impacts, but they will have to be made. These adjustments will have to be greater in countries with greater population aging in coming decades such as Japan, Spain, or Germany, and in countries with more generous public transfers to the elderly, as in Sweden, Austria, or Brazil. In countries with less projected population aging and less generous transfers to the elderly, such as the United States or Mexico, the needed adjustments will be smaller. To get an idea of the magnitude of the fiscal consequences of population aging, assume that public benefit profiles (pensions, education, health care, and long-term care) keep the same shape as they have around 2010, but shift upward with projected productivity growth. Project GDP forward based on population projections and productivity growth. We can then project the percentage point increase in government spending on these programs as a share of GDP. Such projections are not intended to give a realistic

Macroeconomics, Aging, and Growth

picture of the future, because they assume no adjustments to program benefits and adjustments will surely occur, even if by economic collapse. Mason et al. (2015, figs. 3 and 4) report such projections of the fiscal consequences of population aging, from 2015 to 2065 based on NTA data. For the United States, the projected increase in government spending due to population aging would be a relatively modest 8.5 percentage points of GDP. For Brazil it would be 14 percentage points. For Japan, 16 and for Germany 18 percentage points. These are very large increases, and for some countries they will come on top of already very high shares of government spending out of GDP. These increases indicate a growing dependency burden that will lead to reductions in consumption below what it would otherwise be. But a more serious concern may be the distortions to economic behavior that would result from the increased taxes needed to support such big increases. The distortions might take many forms. Large increases in payroll taxes would distort incentives for supplying labor, perhaps leading to declining labor supply at all ages. It has been well established that the incentives built into many public pension plans have a strong effect on retirement behavior (Gruber and Wise, 1999). Higher payroll taxes would also reduce private returns to human capital and might lead young adults and their parents to invest less in their education, reducing productivity growth, and perhaps reducing technical progress as well. Some have suggested that higher payroll taxes, by reducing after tax incomes, might lead to reductions in fertility which would in turn increase population aging and reduce the tax base. Paying for the increased costs of these transfers for the elderly through other kinds of taxes, such as a tax on capital, would lead to other kinds of problems and distortions, as discussed by Razin et al. (2002). Such concerns suggest that government should not simply raise taxes to cover the rising cost of benefits for the elderly. There are alternatives for policy. One is to facilitate and incentivize the postponement of retirement by older workers. This means removing mandatory retirement laws, barring employment discrimination against older people, removing early retirement incentives from public and private pension programs, and encouraging employers to offer part-time work. Longer work life is a natural response to longer and healthier life, however, it cannot be expected to solve all the economic problems of population aging, some of which arise from low fertility rather than from longer life. Another policy option is to maintain the current PAYGO program structure for a portion of benefits, but to introduce private accounts for additional costs. Alternatively, PAYGO programs may be restructured to mimic defined contribution private accounts, as in the Notional Defined Contribution pension program introduced by Sweden and subsequently adopted by other countries. The incentive structures in such programs may avoid some of the distortions in ordinary public pension programs. On a more optimistic note, Dolls et al. (2015) use a microsimulation model including a partial equilibrium treatment of the labor market, to analyze the labor market, and fiscal response to projected demographic change in 27 European countries, and to assess the impact of 5 year increases in the statutory retirement age. Their microsimulation

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approach enables them to take into account population heterogeneity including by educational attainment, and they also incorporate both a demand side response of wage rates to declining labor supply, and the supply side response of labor to rising wage rates. They find that taking into account labor market responses eliminates more than half of the adverse fiscal consequences. When a policy response of increased retirement age (parallel to increased life expectancy) is taken into account, again with wage responses, the adverse fiscal impact of aging is completely removed, on average.

17. RESEARCH DIRECTIONS There are many questions of interest to be explored. Here are a few. • Could increased investment in human capital, public or private, offset the decline in the number of workers relative to elderly? Would the possibility of such substitution of quality for quantity be exhausted after a generation or two or could it be a long-term solution? This would involve a mixture of empirical analysis and theoretical analysis. • To what extent could international capital flows reduce capital intensification and declining rates of return in aging economies? How would consumption, savings, bequests, and intergenerational equity be affected? • What would be the consequences of a transition from an unfunded to a funded public pension program or system of private accounts as in Chile? How would asset holdings, saving, consumption, and bequests be affected? How would intergenerational equity be affected? • Similarly, what would be the consequences of a transition from familial support of the elderly to a public transfer system or a public or private funded system? How would saving and asset holdings be affected? How would human capital investment be affected? How would intergenerational equity be affected? • How does the transition to lower fertility and to very low fertility (eg, one birth per woman) affect lifetime consumption, saving, asset holdings, bequests, and intergenerational equity in systems of familial or public support of the elderly? • To what extent could postponed retirement offset the increase in dependency and decline in the support ratio across the demographic transition? Would postponed retirement lead to lower saving rates? • Would there be important advantages for lower income developing countries in instituting private retirement accounts or funded public pensions early in the transition before aging begins to appear? Might population aging then raise capital intensity and promote economic growth? Questions of this sort could be investigated using models for simulation, optimization, or other kinds of analysis. Here are some suggestions for the kinds of models that might be useful.

Macroeconomics, Aging, and Growth

17.1 Fertility, Mortality, and Possibly Health Status There are two sources of population aging: rising life expectancy and low or falling fertility. Some macroeconomic impacts of population aging depend on its source. It is important to consider both sources, and this is possible only if both are in the model. Often in OLG models mortality is omitted entirely. Except for the few countries that still have high mortality, mortality during the first 50 years of life is no longer very important, so the key is to include mortality in the transition from working life into retirement, or from early retirement to later retirement. Adult mortality rises exponentially at about 10% per year of age, doubling roughly every 7 years, so including this age variation and including mortality at older ages are important. Another key question is whether improving longevity is accompanied by improving health. If so, this alters the consequences, since the problems of population aging are then more institutional and behavioral than fundamental, in the sense that the proportion of expected life spent in need of care and unable to work may remain unchanged. Trends in health status are particularly important if the age at retirement is made endogenous. Heijdra and Reijnders (2012) demonstrate the importance of these points by analyzing several different demographic/health scenarios, each leading to a different conclusion. My personal view is that trajectories of fertility, mortality, and health should be taken as exogenous. While theories are available to relate these to individual choices, they have little predictive power and their use might obscure the workings of some betterunderstood mechanisms.

17.2 Intergenerational Transfers Between the public sector and household sector 55% of GDP is transferred across age groups, mostly to children or the elderly (Lee and Donehower, 2011, 185). Within the household, lower fertility may reduce the total costs of transfers to children, but it also is associated with greater investments in the human capital of each child. Public sector transfers to the elderly may substitute for saving during the working years or may enable asset preservation and increased end-of-life bequests by the elderly. Intergenerational transfers play a central role in investment in human and physical capital, and for this and other reasons are centrally important for the consequences of population aging. It is not clear how best to model bequests. Sometimes they are assumed away by assuming complete annuitization of wealth, and sometimes they are made simply accidental by assuming annuitization is not available. With fewer children per decedent, and with retreat from defined benefit pensions in the United States, bequests may become more important in relation to the macroeconomy. In my view, patterns of intergenerational transfers should be taken as given rather than treated as endogenous, until more progress has been made in understanding the relevant individual behavior and political economy. But including transfers is important, and

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saving and investment decisions can be modeled as if individuals took the transfer context as given when planning for risk buffering and life cycle consumption smoothing.

17.3 Age at Retirement Retirement age is obviously important, and it has been shown to respond to pension incentives, policy incentives, and other changes in the economy. This suggests that for some purposes it should be endogenous, and for other purposes it should be taken as a policy variable.

17.4 Global Perspective Population aging is coming all over the world, but with uneven timing. Treating an economy as closed would capture some important implications of population aging while missing the consequences of demographic change elsewhere. It would exaggerate capital intensification and falling rates of return on capital in the older rich countries, by ignoring the possibilities of investing abroad. It would understate capital intensification in a country like the United States with moderate aging, but with open financial markets. Treating an aging economy as financially open would minimize the effects on its factor prices, while maximizing the changes in assets and asset income. Both perspectives are useful.

17.5 Technological Progress and Endogenous Growth Even a very small difference in the rate of technical progress will dominate age distribution effects in the long run. For models based on population size it is not clear that population aging would be relevant. However, for models such as Jones’ in which the rate of technological progress is driven by the population growth rate, aging economies will have slower progress even if aging is not the root cause.

18. CONCLUSIONS Population aging is inevitable and will affect the macroeconomies of all nations. However, because cultural values and institutional arrangements differ from place to place, the consequences of aging will likewise differ. In some countries, the elderly continue to work productively into old age, in others they withdraw early from the labor force, or perhaps are unproductive relative to younger workers. In some countries, the elderly are supported by transfers from their families, in others by transfers from the public sector. In still others, they rely more heavily on income from assets accumulated earlier in life. In some countries, the elderly consume far more than younger adults, while in others they consume about the same as younger adults. For all these reasons, the elderly depend to varying degrees on transfers from the younger population, and consequently population aging has larger or smaller macroeconomic impacts.

Macroeconomics, Aging, and Growth

There are a number of widely held assertions about these impacts, but these are not always true. a. Population aging raises dependency and reduces support ratios. This assertion is true but yet may be misleading. Elderly people are not dependent unless they rely on transfers from the working age population. Even if elderly people do little work, they may not be highly dependent on transfers. They may instead use asset income to fund their consumption. In this case dependency ratios and support ratios may be misleading. Having more elderly may mean having more asset income. At the same time, we have seen that consumption by the elderly has risen faster than at other adult ages in recent decades in many rich industrial nations. There are great differences among nations in how the consumption of the elderly is funded. b. Population aging will mean lower consumption than otherwise. Not necessarily. Population aging is due mainly to low fertility which is accompanied by increased human capital investment per child leading to a more productive labor force. Quality substitutes for quantity in the labor force. Also, population aging may be accompanied by capital intensification that offsets some of the increased dependency. Furthermore, as life lengthens and health improves at older ages, labor supply may increase, for example through rising age at retirement. International trade and international capital flows may effectively export population aging to younger countries, reducing its consequences. c. Population aging leads to capital deepening, with rising wages and falling rates of return. Not necessarily. This will not be true for an open economy. It will not be true if there are important public transfers to the elderly and the government runs up national debt in the face of population aging rather than balancing the budget (National Research Council, 2012). And it would not be true along an optimal growth trajectory if a social planner’s objective function weighted per capita utility by the size of the population (Cutler et al., 1990). However, it is true in the golden rule case discussed earlier, and in that case fertility below replacement, population decline, and the population aging it brings, appear to be beneficial. d. Population aging brings an aging labor force which is less productive and less innovative. Not necessarily. Simple calculations based on age-specific earnings suggest that population aging will have only a tiny effect on average labor force productivity (“negligible” according to National Research Council, 2012, Chapter 6), and a study finds that mixed teams including older workers make fewer major errors than young teams. As for creativity, innovation and technological progress, the National Research Council (2012) concluded that “While age is an important determinant of invention and innovation, it explains very little about actual performance across societies. Other factors, such as education, support institutions, economic and social rewards, and religious institutions, tend to dominate the actual distribution of scientific output.” It is also true that technological advances are a global public good, and aging in a given country would have little effect on the technologies available to it for adoption.

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Population aging will pose difficult problems in societies that rely heavily on public or private transfers to the elderly. In other countries where aging will be less profound, or the elderly rely more on continuing work and on asset income and less on public or private transfers, the problems will be muted. Increased investment in human capital, adjustment of taxes and benefits in the face of population aging, and facilitation of postponed retirement, will go a long way to soften the impact of population aging.

ACKNOWLEDGMENTS Research for this chapter was funded by grants from the National Institutes of Health, NIA R37 AG025247 and R24AG045055. The content is solely the responsibility of the author and does not necessarily represent the official views of the National Institutes of Health. I am very grateful for the helpful comments and suggestions I received from two anonymous referees and from Hippolyte d’Albis, which led to many improvements. I am also grateful to Gretchen Donehower, Andrew Mason, and all the country research teams in the NTA project for the use of their data. These researchers are identified and more detailed information is given in the NTA website: www.ntaccounts.org.

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CHAPTER 3

Migration and the Demographic Shift A. Zaiceva*,†, K.F. Zimmermann{,§,¶ *

University of Modena and Reggio Emilia, Modena, Italy Institute for the Study of Labor (IZA), Bonn, Germany { Harvard University, Cambridge, MA, United States § The United Nations University – Maastricht Economic and Social Research Institute on Innovation and Technology (UNU-MERIT), Maastricht, The Netherlands ¶ Bonn University, Bonn, Germany †

Contents 1. Introduction 2. Trends in Population Aging and International Migration 3. Age and Migration: Supply-and-Demand Framework 3.1 Theoretical Determinants of Migration: Supply-Push and Demand-Pull Factors 3.2 Age and Migration: Empirical Studies with Individual Data 3.3 Age and Migration: Empirical Studies with Aggregate Data 3.4 Changing Migration Patterns: Mobility of the Elderly and Demand for Eldercare 4. Aging and Migration: Implications for Labor Markets, Public Budgets, and Political Economy 4.1 Aging, Migration, and Labor Markets 4.2 Aging, Migration, and Public Budgets 4.3 Aging, Migration, Welfare, and Political Economy Aspects 4.4 Aging and Individual Attitudes Toward Immigrants 5. Migration, Aging, and Health 6. Conclusions Acknowledgments References

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Abstract This chapter investigates the two-way relationship between population aging and international migration. After documenting the trends for both, we review the supply-push and demand-pull determinants of migration, focusing particularly on the role of age and aging. We subsequently analyze the implications of migration in the context of aging for labor markets, as well as for health and public budgets, including in the context of political economy. Although immigration is sometimes suggested as a solution for the aging problem, the existing academic literature from different fields is more cautious about its role and potential. While some suggest that large-scale, selective immigration might contribute to alleviating demographic pressures, in general, researchers conclude that migration alone is not likely to play a significant role.

Keywords Aging, Migration, Demographic pressures, Elderly migration, Attitudes toward migration, Political economy of immigration

Handbook of the Economics of Population Aging, Volume 1A ISSN 2212-0076, http://dx.doi.org/10.1016/bs.hespa.2016.08.002

© 2016 Elsevier B.V. All rights reserved.

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JEL Classification Codes F22, F66, J11, J14, J61, O15

1. INTRODUCTION The demographic shift to low mortality and low fertility, as well as its implied population aging and shrinking working-age population, is one of the most important challenges for many countries to achieve a prosperous future. The expected changes threaten the functionality of labor markets, the sustainability of pension and healthcare systems, and public budgets. Therefore, methods and policies for alleviating aging challenges have been gaining greater importance for researchers and policymakers. Immigration into aging developed countries is sometimes suggested as a “solution” for the aging “challenges,” assuming that the inflow of young working-age individuals would have a “rejuvenating effect” on the receiving country’s population. Immigration has become the main source of population growth in many developed countries, and its importance will increase in the future as a native population ages and declines due to death. Immigrants are young and also usually have greater fertility than natives. For example, in the United States, immigrants and their descendants accounted for 51% of the increase in the US population over 1960–2005, and they are projected to contribute as much as 82% of the total increase in the US population over 2005–2050 (Pew Research Center, 2014). Its importance is even larger in Europe, where both natural increase in population and immigration are smaller. On the other hand, immigration remains one of the most controversial issues on the policy agenda. Fueled by a large inflow of migrants in 2014–2016, many of them war refugees, which has been labeled a “refugee crisis,” migration has become a major concern in several European countries. Given these trends, can immigration compensate for declining and aging populations? Can it alleviate the burden on public budgets and healthcare systems that many countries will face or are already facing? These are the questions that we deal with in this chapter. In demography, the size and structure of a population is influenced by fertility, mortality, and migration. Unlike fertility and mortality, migration affects two populations: the one in the country or region of origin and the one in the destination (McDonald, 2016). Mechanically, in-migration (immigration) increases the size of the receiving country’s population, while outmigration (emigration) decreases it. Then positive net migration (the difference between immigrants and emigrants) affects population size in the same way as a natural increase (the difference between births and deaths); zero net migration may still affect the composition of the population (McDonald, 2016). Migrants contribute to the population size of the receiving (and sending) country, also via fertility. Finally, as migrants are typically young, both immigration and emigration between countries affect each country’s age distribution. Overall, there is a two-way relation between the demographic structure and migration: a country’s demographic structure affects migration, and migration affects a country’s demographic structure.

Migration and the Demographic Shift

Fargues (2011a) surveys relevant demographic studies, arguing that there is a gap in the theory relating migration and demography (see also Coleman, 2006).a He presents a systematic analysis of a two-way interaction between the demographic transition (specifically about one of its components, decreased fertility) and international migration. On the one hand, international migrants from developing countries may reduce fertility in their home countries by bringing home the norms and values of the receiving, more developed countries (Fargues, 2011a; Beine et al., 2013). On the other hand, reduced fertility and delayed family formation may lead to increased migration of single individuals. This two-way relation between the demographic structure of sending and receiving countries and migration is behind the economic and labor market impacts and implications surveyed in this chapter.b The chapter attempts to cover both low- and middle-income countries that are typically migrant-sending, as well as developed, migrant-receiving countries. Although population aging is common for most countries in the world, it is most acute in the developed countries, particularly in Europe. Therefore, we will pay more attention to a discussion of the interaction between migration and aging, as well as their implications and impacts for these countries. Nevertheless, where feasible, we also refer to developing countries, which will experience increased aging in the future or are already aging. Besides the direct demographic effects of contributing to population growth and shifting the age distribution toward a younger age, immigration may lead to increased fertility in the receiving countries, at least temporarily.c Migrants typically have a higher average fertility than natives, at least at the beginning of their time in the host country, but fertility declines in the next generation. Aging developed countries need migrants for a

b

c

In the author’s words: “While many empirical studies have highlighted the reciprocal implications of demographic growth and migration, theory is largely silent: international migration theory does not put much emphasis on demography and demographic theory simply ignores international migration” (Fargues, 2011a, pp. 588–589). To avoid overlap with other chapters in this volume, we have not covered topics that are already discussed extensively there and have focused exclusively on the interaction between aging and migration. We also do not aim to survey here broad literature on the macro- and micro-determinants and effects of migration, but rather focus strictly on aging and its interaction with migration when discussing the determinants and impacts. Some demographers have labeled the phenomenon of low fertility and high immigration as the “Third Demographic Transition.” (The First Demographic Transition is the shift from high levels of fertility and mortality to low levels, while the Second Demographic Transition describes a change in living arrangements and sexual behavior, including childbearing.) The Third Demographic Transition is suggested to be responsible for major changes in the ethnic composition of the receiving countries’ population (Coleman, 2006). However, the projections behind these scenarios are highly disputable, as they are based on current migration and fertility trends (Fargues, 2014). Moreover, ethnic and national identities are important and even may be beneficial, while immigrants may culturally and economically assimilate into or integrate with the receiving countries (see, for example, Constant et al., 2009, 2012; Constant and Zimmermann, 2008, 2013a,b for studies of ethnic identities and immigrant integration).

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another reason: The increasing share of older residents stimulates higher demand for healthcare and care services in general, and migrants fill the available vacancies in these countries. Taking into account the declining size of the working-age population, particularly in Europe, as well as the facts that migrants are young, migration is a selected process, and migrants are likely to integrate and contribute to the receiving country’s labor markets and public budgets, pro-immigration policies become relevant (see also Fargues, 2014). However, research also suggests that caution is needed when evaluating the overall contribution of immigration for several reasons. First, the increase in immigration needed to compensate for the declining native working-age population would need to be unrealistically large. Second, immigration policies would have to be highly selective, aiming at attracting young and high-skilled migrants, which may exacerbate the skills shortages or demographic problems in the sending countries. Third, the successful implementation of pro-immigration policies is difficult and crucially depends on public attitudes toward immigration. The current East–West divide in Europe regarding refugee quotas illustrates this well. Fourth, there also may be convergence over time in migrant and native demographic and labor market behavior, including fertility and retirement decisions. Finally, migrants themselves also age in the destination countries when they stay there after retirement, which generates continued demand for old-age social security and eldercare. Overall, migration is just one of many channels to consider when analyzing the effects of aging. This chapter reviews the existing economic research that brings together population aging and migration and identifies gaps in the literature and avenues for future research. Section 2 begins by documenting trends in aging and international migration. Section 3 first puts age and migration into a supply-push and demand-pull framework by reviewing studies on migration determinants, with a particular focus on age and aging issues, and then discusses the mobility of the elderly and demand for eldercare. Section 4 considers migratory implications in the context of aging in labor markets and on public budgets, including in a political economy context. Section 5 discusses migrant health and aging, and Section 6 concludes by presenting implications for policy and suggestions for future research.

2. TRENDS IN POPULATION AGING AND INTERNATIONAL MIGRATION The number of persons aged 60 years or over is projected to grow from 810 million in 2012 to more than 2 billion by 2050, with the number of older persons due to surpass children for the first time in history (United Nations, 2012). The old-age support ratio, which measures how many people there are of working age (20–64 years old) relative to the number of retirement-age people (65 +), is higher in less-developed countries than more-developed regions and is projected to decline further in the latter

Migration and the Demographic Shift

by 2050. By contrast, the old-age dependency ratio, which is the ratio between elderly persons (65 +) and the number of persons of working age (generally 15–64) in the EU27, is projected to double by 2050 (European Commission, 2012). The aging problem is particularly acute in Europe and Japan, and less so in the United States, where both fertility and immigration are higher. In Italy, for example, the total fertility rate has declined to an unprecedented 1.2 children per woman over 1995–2000 and averaged 1.4 children per woman over 2010–2015 (UN Population Division), while the share of pensioners is already over 70 per 100 workers (Bloom and SousaPoza, 2013). An increasing proportion of older-age population relative to the working-age population represents a challenge for labor markets, welfare, and healthcare systems. Immigration may seem to be a solution to this challenge since immigrants contribute to filling the gaps in working-age population. Owing to the low fertility rate in most developed regions, net migration has become the main factor of population growth in such countries [see Fig. 1 for the statistics for the current 28 members of the European Union (EU)]. If these trends persist, net migration will solely account for the entire population growth in the developed world by 2050. However, as discussed later in this chapter, many scholars doubt that immigration alone can constitute a feasible solution for the aging challenge. Analyzing and measuring migration is not an easy task. Counting international migrants is challenging, and making cross-country comparisons is even more complicated

EU28

3,000,000

1,000,000 0

1960

1970

1980

1990

2000

2010

Year Total population change Natural change of population Net migration plus statistical adjustment

Fig. 1 Population change in 28 EU countries, 1960–2010. Source: Eurostat, Population Statistics.

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due to poor data quality and different definitions. Purely mechanically, it is important to distinguish between flows and stocks since the latter accounts for outflows and refers to net migration (inflows minus outflows). Migration statistics in some countries include those born in other countries (so-called foreign-born), while others define migrants according to their citizenship or nationality (so-called foreign nationals), while still others report both separately. Immigrants may take citizenship of the receiving country or retain the citizenship of several countries. Moreover, children of migrants, the so-called second generation (who also are often called “people with a migration background”) constitute an additional challenge. Finally, it is fundamental to differentiate between temporary and permanent migration. These two types of migration may have different implications for labor markets and public budgets; for example, temporary migrants typically are not eligible for public pensions. In addition, migrants have various motives to move, which results in different types of migration (ie, work-related, family reunification, seeking refugee or asylum, retiring, or being on holiday). For example, labor migrants constitute an important share among all migrants in the United Kingdom, whereas the majority of migrants in the United States fall in the category of family reunification, while humanitarian migration represents an important part in Canada, the Netherlands, Norway, and the United Kingdom (OECD, 2007). The current refugee flows into Europe have boosted the importance of this type of migration in the EU countries. Generally speaking, the official statistics usually reflect only legal migration,d and often only permanent migration is considered when evaluating its impacts, even though much of today’s migration is temporary or circular. Despite these measurement problems, it is estimated that the total number of international migrants has increased in recent decades, reaching 232 million persons in 2013; this is an increase of 57 million persons compared to 2000 (or from 2.8% of the world’s population to 3.2%), 48% of whom are females (United Nations, 2013a,b). At the same time, the number of those over 65 years old among all international migrants has reached 26 million, or 11.1%, ranging from 13% of all international migrants in the developed regions to 8% in the developing ones; Europe and Oceania report the highest shares: 14% and 15%, respectively (United Nations, 2013a,b). The majority of international migrants move from less- to more-developed countries, with their distribution by age suggesting that, relative to the overall population, the largest shares are among the working age (see Figs. 2A and B). Fig. 2B also shows that in Canada and Australia (as well as New Zealand), the proportions of those over 65 are close to those of working age, and these countries (together with Switzerland) represent regions with the largest shares of migrants over 65 in the overall population. This reflects historical migration patterns d

It is estimated that illegal migration adds 10%–15% to the foreign-born stock in Organisation of Economic Cooperation and Development (OECD) countries (Hatton and Williamson, 2002).

Migration and the Demographic Shift

A 30.0 25.0 Developed regions, total

20.0

Europe 15.0 Northern America 10.0 Oceania 5.0 0.0 0–19

20–64

65+

B 40.0 35.0 Germany 30.0

Italy

25.0

UK

20.0

US Japan

15.0

Australia 10.0

Canada

5.0

Switzerland

0.0 0–19

20–64

65+

Fig. 2 Migrants across age. (A) International migrants as a percentage of the population by age, 2013. (B) International migrants as a percentage of the population by age for selected countries, 2013. United Nations, Department of Economic and Social Affairs, Population Division (2013). The Age and Sex of Migrants 2013 Wallchart (United Nations Publication, Sales No. 12.XIII.2).

and earlier migrations, as well as smaller shares of native elderly in these countries. In proportion to the total world population, international migrants over 65 represent 4.5% overall (while those aged 20–64 comprise 4.1%), constituting 8.5% in the developed regions and 2.1% in the developing regions (13.7% and 2.0%, respectively) (United Nations, 2013a,b). Several events in recent history have contributed to the increase in immigration and refugees and asylum seekers, such as the fall of the Berlin Wall and dissolution of the Soviet bloc; wars in the former Yugoslavia, and most recently in Iraq and Syria; the

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recent EU eastern enlargements; as well as changes in migration and legalization policies, including initiatives to attract skilled migrants.e Although the 2008 economic downturn has slowed economic migration to both the United States and Europe, refugee migration has instead increased due to rising conflicts and wars. Among the developed countries, the United States is the major migrant-receiving country in absolute terms, followed by Germany, which remains the main destination country within the European Union. Table 1 shows the top 10 immigration and

Table 1 Top 10 immigration and emigration countries Top 10 immigration countries

1 2 3 4 5 6 7 8 9 10

2000

2013

United States Russian Federation Germany India France Canada Ukraine Saudi Arabia United Kingdom Australia

United States Russian Federation Germany Saudi Arabia United Arab Emirates United Kingdom France Canada Australia Spain

Top 10 emigration countries

1 2 3 4 5 6 7 8 9 10

2000

2013

Russian Federation Mexico India Ukraine Bangladesh China Afghanistan United Kingdom Pakistan Kazakhstan

India Mexico Russian Federation China Bangladesh Pakistan Ukraine Philippines United Kingdom Afghanistan

Notes: International migrant stock at mid-year by sex and by major area, region, country or area, 1990–2013. Total migrant stock at mid-year by major area, region, country, or area of destination, 1990–2013. Trends in International Migrant Stock: The 2013 Revision. UN Population Division.

e

For a discussion of historical migration trends in Europe and implications of the eastern enlargements, see Zaiceva and Zimmermann (2008) and Kahanec et al. (2010), among others; for a discussion of high-skilled migration policies in Europe, see Kahanec and Zimmermann (2011).

Migration and the Demographic Shift

emigration countries in 2000 and 2013 based on statistics from the United Nations (UN). As this table shows, the largest immigrant stocks were in the United States, Russia, and Germany in both years, while India, Mexico, and Russia constituted the top sending countries. Regarding the rest of the immigrant-receiving countries, India and Ukraine were within the top 10 receiving countries in 2000 (probably also reflecting return migration), but not in 2013; United Arab Emirates and Spain joined the list in 2013. On the other hand, Kazakhstan was within the top 10 sending countries in 2000, but not in 2013, while the Philippines emerged among the top senders in 2013. In developing and middle-income countries, outmigration contributes to alleviating excess labor supply. Demographic booms, a rapid growth in the cohort of young individuals resulting in greater competition for resources and in the labor market, together with poor national economic performance, are among significant determinants of outmigration. However, many developing countries are also starting to age, owing to declining fertility, increasing life expectancy, and the emigration of typically young individuals. Consequently, these countries face a potential decline in their workingage population in the near future. For example, due to aging and its one-child policies, China is predicted to shift from a large positive natural increase over 1960–2010 to a substantial negative natural increase, combined with negative net migration, over 2010–2060 (Bruni, 2012). Over 1982–2005, the mean provincial age in China rose by approximately 30% (from just under 21 to nearly 27 years old), while the share of the population aged 15–29 has been declining constantly since 1990 (Bodvarsson et al., 2014). Other countries, such as Russia, have experienced low fertility and high mortality rates, accompanied by positive net migration, while several new EU member states (Romania, Bulgaria, Latvia, and Lithuania) are likely to face serious demographic and economic challenges, accompanied by both low fertility and high outmigration.f In order to forecast future population trends, demographic projections make various assumptions regarding migration. In contrast to birth and death, which are more straightforward to predict, migration represents the most problematic component of population projections (Coleman, 2008; European Commission, 2012).g Accordingly, despite the potential importance of increasing immigration, it is highly unlikely to offset the large f

g

For an analysis of recent return migration trends and potential further outmigration in the new EU member states, see Zaiceva and Zimmermann (2016). For example, it was estimated that an annual net migration of even 2.2 million persons would not be enough to compensate for a population declining by 3.4 million in the more developed regions by 2050 (United Nations, 2006; Table 7). Europe will be hit particularly strongly, with a natural increase amounting to
3.2 million with net immigration of 0.7 million by 2050, while in North America, population growth will be positive (0.4 million persons) and net immigration is likely to be larger (1.3 million) by 2050. Contrarily, in less-developed regions, net immigration will remain negative in 2050, while there will be a natural increase reaching 37 million persons, most of which will happen in Africa and, to a lesser degree, Asia.

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declining working-age population due to the demographic shift. For example, according to earlier forecasts, net migration to Europe would need to increase fourfold to keep the size of the working age population constant (United Nations, 2006). However, caution is needed when interpreting these numbers since these projections are subject to great uncertainty and criticism, including a “replacement migration” scenario suggested by the United Nations in 2001h (see, for example, Bruni, 2012; Fargues and McCormick, 2013; and the references therein for a critical discussion of UN migration projections and suggested alternative scenarios; Coleman, 2008, for a study of demographic effects of migration in Europe; and Zlotnik, 2012, for demographic impacts of migration on aging). Overall, despite predictions that Europe will lose some of its population by 2050 if no immigration takes place, and its neighbors in the Middle East and North and sub-Saharan Africa will have the fastest-growing populations, demographers conclude that immigration alone will not suffice. Moreover, since migrants also age in the receiving countries, permanent replacement migration would “initiate a spiral,” with more and more migrants needed to offset aging in the future (Fargues, 2011b, p. 16). Figs. 3 and 4 illustrate this. In the no-migration scenario, the overall population in the EU27 is projected to decline by 11% by 2050 (Fig. 3A), with the total labor force A

B Total

Total

65+ 45+ 20–65 Below 45

0–20 −50%

0%

50%

Continue precrisis migration

100% No migration

−20% −15% −10%

−5%

0%

5%

10%

No migration

Fig. 3 Expected relative change in population and labor force by age, EU27. (A) Total population, 2010–2050. (B) Labor force, 2010–2025. Data are from Fargues, P., 2011b. International Migration and Europe’s Demographic Challenge. Research Report/Background Paper. EU-US Immigration Systems 2011/09. Migration Policy Centre, Robert Schuman Centre for Advanced Studies, European University Institute, Florence, Table 2, p. 5; Fargues, P., McCormick, A., 2013. Aging of skills and complementary immigration in the EU, 2010–2025. Working Paper RSCAS 2013/81, Migration Policy Centre, Robert Schuman Centre for Advanced Studies, European University Institute, Florence, Table 1, p. 4.

h

According to the UN report, “replacement migration refers to the international migration that would be needed to offset declines in the size of population, the declines in the population of working age, as well as to offset the overall ageing of a population” (p. 1)

Migration and the Demographic Shift

20,000

15,000

10,000

5000

0

−5000 2025

2050

Fig. 4 Projected number of migrants aged 20–65 needed to maintain the size of the working-age population at 2010 level (thousands). Notes: The number of migrants required is calculated as the difference between population aged 20–65 in 2010 and population aged 20–65 according to Eurostat projection in the no-migration scenario in a respective year. Data are from Fargues, P., 2011b. International migration and Europe’s demographic challenge. Research Report/Background Paper. EU-US Immigration Systems 2011/09. Migration Policy Centre, Robert Schuman Centre for Advanced Studies, European University Institute, Florence, Table 4, p. 14.

declining by more than 7% by 2025 (Fig. 3B). Also, the working-age population, particularly those under 45 years old, is estimated to decline in all EU member states, leading to a so-called aging of skills (Fargues and McCormick, 2013). If migration trends continue at their precrisis levels (Fig. 3A), the overall population will increase by a modest 3% by 2050; however, this increase is entirely due to the increase in the oldest age group, while the population aged 20–65 will decrease despite immigration (although the decline will be smaller than in the no-migration scenario). Can immigration fill the gap in the native labor force? If immigration is permanent and migrants do not return, they will age in the receiving country, and thus more and more immigration of the young will be needed in the future. In 2000, assuming the same fertility of migrants as of natives, the United Nations calculated an unrealistically large “replacement migration” needed to maintain the share of population aged 15–64 to that aged 65+ over the period 2000–2050 (United Nations, 2001). More recently, Fargues (2011b) shows that temporary migrants may partially contribute to easing the population decline in the receiving countries and also calculates the number of “temporary migrants” required in the EU27 (defined as those who would return to their country of origin). It should be noted, however, that if these migrants return after retirement, they may still be

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eligible for pensions in the receiving countries, thus still affecting the social security systems. Fig. 4 shows the hypothetical number of such temporary migrants that would be needed in order to maintain the size of the working-age population in the EU member states at the 2010 level, calculated in the counterfactual scenario of no migration (neither immigration nor emigration). Several facts are worth mentioning. First, the highest number of migrants will be required in fast-aging countries such as Germany, Italy, Spain, the United Kingdom, and Poland. Second, in several new member states, the demographic decline is likely to be more pronounced due to continuing emigration, so even larger numbers of immigrants will be needed for these countries. Finally, these figures illustrate that the required numbers are quite high, amounting to the total of more than 84 million immigrants in the EU27 by 2050. For example, according to these calculations, an additional 18.5 million temporary migrants aged 20–65 would need to enter Germany between 2010 and 2050, compared with the total stock of 10.7 million foreign-born residing in the country in 2011 (OECD SOPEMI, 2013). Table 2 illustrates the aging and immigration situation in OECD countries and provides age and skills distributions for both native and foreign-born population that set the stage for subsequent discussions throughout this chapter. Countries are ranked according to the old dependency ratio from most to least aging: aging is most acute in Japan, Germany, and Italy, while the “youngest” countries are Mexico, Turkey, and Chile. Such traditional immigration countries as Australia, New Zealand, Canada, and the United States are at the lower end of the old-age dependency ratio distribution. Regarding the age distribution between natives and immigrants, in all countries (apart from Estonia, Hungary, Israel, Mexico, Poland, and Slovak Republic), the share of working-age immigrants (25–64) is larger than the corresponding share for natives. Meanwhile, the share of those older than 65 is significantly lower among immigrants than among natives (with the notable exceptions of Australia, Canada, the Czech Republic, Estonia, Hungary, Israel, Mexico, Poland, Slovak Republic, and Turkey, where this share is higher; and France, where the two shares are almost equal). These patterns suggest, first, the importance of labor migration and, second, differing historical migration patterns in countries such as Australia, Israel, or the new EU members, resulting in larger proportions of older migrants. Regarding education, several interesting facts emerge. First, in many northern and western European countries, the United States, and several new EU members (ie, the Czech Republic, Poland, Slovakia, and Slovenia) the shares of low-skilled immigrants are higher than the corresponding shares for natives. This reflects the importance of labor demand factors and certain immigration policies (such as European guest worker agreements adopted in the 1960s or family reunification policies). On the other hand, in the majority of countries, the share of migrants with tertiary education is higher than that of natives. Overall, these facts point to a selective nature of migration and the importance of migration policies and historical migration patterns.

Table 2 Aging, immigrant share, and characteristics of immigrant and native populations in OECD countries, 2010/11 Education, share of

Japan Germany Italy Greece Portugal Sweden Austria Finland France Belgium Denmark Estonia Spain Switzerland Hungary United Kingdom Slovenia Netherlands Norway Czech Rep. Luxembourg Australia

Share of persons aged between 25 and 64

Old dependency ratio, 2010

Share of foreign born

Natives

Immigr.

Natives

Immigr.

Natives

Immigr.

Natives

Immigr.

Natives

Immigr.

36.07 31.81 30.41 28.71 28.47 28.08 26.11 26.08 26.02 26 25.34 25.17 24.94 24.78 24.28 24.08

1.1 14.6 10.3 13.1 9.0 15.6 18.0 4.9 13.0 16.1 10.5 17.8 12.9 29.4 4.3 14.2

62.0 60.8 72.3 62.4 63.5 59.9 71.6 63.6 63.3 70.7 63.1 65.6 66.5 69.5 67.0 62.6

74.5 76.5 83.5 77.6 79.4 72.7 79.9 78.4 70.9 78.6 74.9 58.2 77.8 82.1 63.5 73.6

26.8 25.7 14.5 25.0 23.9 23.4 12.0 21.8 20.4 12.1 21.8 16.9 22.0 12.4 19.7 21.2

6.6 14.2 3.0 8.0 7.1 15.3 8.2 5.5 20.5 10.1 8.6 40.0 7.1 8.6 26.9 12.4

17.4 18.8 51.0 45.4 71.6 24.9 23.6 32.1 35.6 34.4 33.8 21.3 55.5 18.4 31.1 38.5

11.4 38.8 47.6 41.2 47.8 27.0 33.2 51.1 47.5 43.9 32.7 18.2 46.6 30.9 23.4 29.1

50.4 58.1 36.9 34.7 15.4 50.4 60.9 39.8 40.8 36.5 41.2 48.7 18.4 54.1 51.5 34.8

53.6 41.6 41.3 41.5 29.7 44.0 48.3 27.1 28.9 29.1 37.8 42.3 29.8 37.8 49.1 24.3

32.2 23.1 12.1 19.9 13.0 24.7 15.5 28.1 23.6 29.1 25.0 30.0 26.1 27.5 17.3 26.7

35.0 19.6 11.1 17.4 22.5 29.0 18.5 21.8 23.6 27.0 29.5 39.5 23.6 31.3 27.5 46.6

23.87 23.04 22.61 20.94 20.41 20.03

12.5 11.4 12.8 7.6 44.6 30.4

66.2 65.0 63.4 67.4 59.7 64.9

77.9 80.8 79.0 69.5 79.4 69.6

19.8 19.6 20.4 18.3 21.9 15.7

15.2 9.8 6.3 20.2 10.7 20.2

27.6 35.4 29.2 18.4 33.7 28.5

40.3 40.1 35.0 29.0 39.7 22.2

54.0 38.9 43.1 67.3 47.7 44.7

49.0 33.8 30.2 51.7 29.7 38.5

18.5 25.8 27.7 14.3 18.6 26.8

10.6 26.0 34.8 19.3 30.6 39.4

Share of persons aged 65 +

Low

Medium

High

Continued

Table 2 Aging, immigrant share, and characteristics of immigrant and native populations in OECD countries, 2010/11—cont’d Education, share of

United States Poland Canada New Zealand Iceland Ireland Slovak Rep. Israel Chile Turkey Mexico

Share of persons aged between 25 and 64

Old dependency ratio, 2010

Share of foreign born

Natives

Immigr.

Natives

Immigr.

Natives

Immigr.

Natives

Immigr.

Natives

Immigr.

19.49

16.6

64.4

75.0

16.8

12.7

16.7

32.1

52.1

37.5

31.2

30.3

19.14 18.46 18.38

1.8 24.7 33.3

69.0 66.6 63.3

20.0 70.0 67.3

15.1 15.5 18.3

75.3 20.3 17.3

23.8 20.9 59.5

37.8 17.7 30.2

57.8 38.4 14.7

44.4 30.2 32.2

18.4 40.7 25.8

17.9 52.1 37.6

18.15 17.33 16.28 15.88 13.14 10.34 8.97

10.0 19.0 3.0 31.8 1.6 1.4 0.5

73.0 66.9 68.8 68.4 62.4 71.8 64.4

77.1 79.1 66.1 60.7 71.2 77.9 57.3

8.6 17.1 14.5 5.1 14.4 4.8 9.2

3.7 5.4 28.2 32.0 5.7 11.3 10.3

39.8 38.0 46.8 24.3 28.4 71.9 71.3

36.5 19.6 50.5 23.1 10.6 49.6 41.9

34.7 35.4 36.3 42.8 48.5 17.9 19.1

34.4 41.2 31.1 31.5 52.9 31.0 31.0

25.5 26.6 16.9 32.9 23.2 10.2 9.5

29.1 39.2 18.4 45.4 36.5 19.4 27.0

Share of persons aged 65 +

Low

Medium

High

Notes: “Immigrants” refer to foreign-born. Shares exclude persons with unknown age, education, and duration of stay. “High education” refers to tertiary education, “medium education” to upper secondary, and “low education” to less than upper secondary. Population in all columns, apart from column 1, includes individuals aged 15 +. Arslan, C., Dumont, J.-C., Kone, Z., Moullan, Y., Ozden, C., Parsons, C., Xenogiani, T., 2014. A new profile of migrants in the aftermath of the recent economic crisis. OECD Social, Employment and Migration Working Papers, No. 160. OECD Publishing, Tables 4 and 5; OECD, 2013. International Migration Outlook: SOPEMI 2013, and statistical database (OECD Statistics).

Migration and the Demographic Shift

In the context of this chapter, a natural question arises: Is there a potential correlation between the receiving country’s age structure, particularly its aging and immigrants’ ages, skills, and occupations? Fig. 5 suggests that there is indeed such a relation. For the graphs in this figure, we have employed the OECD Database on Immigrants in OECD and Non-OECD Countries (DIOC) datasets for 2005/2006 and 2010/2011.i The graphs suggest a significant positive correlation between the share of natives older than 65 years in the receiving countries and the share of working-age immigrants (those between 25 and 64 years old), as well as with the share of low-educated migrants in both 2005/2006 and 2010/2011. On the other hand, there is a significant negative relation between the proportion of older natives and the share of immigrants with tertiary education in both years. Finally, there is a statistically significant positive correlation between the share of elderly natives and immigrants in lower-skilled occupations. There might be multiple channels behind these relations, and the rest of this chapter attempts to shed more light on these. The next section explores the relation between age, aging, and migration by reviewing the factors behind the migration decision, with a particular focus on age. In turn, the subsequent sections discuss the labor market, welfare, political economy, fiscal, and health implications of migration in the context of aging, as well as the role of migration in alleviating aging challenges.

3. AGE AND MIGRATION: SUPPLY-AND-DEMAND FRAMEWORK We begin the analysis of the two-way interaction between aging and migration with a discussion of the causality running from age to migration. Age constitutes one of the most important determinants of a move, so it is likely that demographic aging will affect migration.

3.1 Theoretical Determinants of Migration: Supply-Push and Demand-Pull Factors Prior to considering how aging interferes with the migration decision, it is instructive to first briefly discuss the factors affecting the individual choice to migrate (for surveys, see, among others, Massey et al., 1993; Ghatak et al., 1996; Greenwood, 1997 for internal migration; Bauer and Zimmermann, 1999; Borjas, 1999a; Bodvarsson and Van den Berg, 2009). For the more recent treatment of the migration decision, including a dynamic intertemporal model, see Kennan and Walker (2013); for a recent discussion of migration and ethnicity, see Constant and Zimmermann (2013b)). It is important to emphasize that the purpose of this section is not to provide a comprehensive review i

At this time, occupations were available only for the 2005/2006 dataset. The 2010/2011 figures in the graphs are slightly different from those in Table 2, since in the original publication on which this table is based, individuals with missing age, education, and duration of stay were excluded, while we exclude missing observations only from the calculation of the specific shares.

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0.25

0.25 JPN DEUITA GRC PRT SWE ESP FIN BEL DNK GBR SVN LUX NOR FRA NLD CZE

0.2

HUN

0.15 EST POL

JPN

PRT SWE GBR HUN CZE

0.15

NZL

LVA

ISL IRL USA RUS CAN AUS CHL BGR

SVK

0.1

ITA

DEU GRC

0.2

EST LVA RUS

CHE

CAN

BGR CHL

NZLISL IRL USA POL CHE AUS

0.1

AUT

ESP FIN BEL DNK SVN LUX NOR FRA NLD

SVK

AUT

LTU MLT ROU CYP

LTU

MLT

ROU CYP

MEX

MEX

0.05

ISR

0.2

0.4

0.05

TUR

0.6

0.8

1

ISR

0

TUR

0.2

Share of migrants, work. age

0.4

0.6

0.8

Share of migrants with low. educ.

0.25

0.25 JPN ITA

0.2

JPN

DEU GRC

ITA

PRT BEL FIN GBR

0.2

SWE

ESP

PRT

LUX NOR FRA

SVN HUN

NLD

NZL

CZE

0.15

EST

GBR NOR

ISL

LVA RUS CHL

0.1

POL SVK

LVA RUS

USA

NZL IRL CHE CHL BGR

BGR

0.1

AUT MLT

DNK HUNLUX FRA NLD

SVN

CZE ISL IRLPOL USA CHE AUS

CAN SVK

SWE

ESP FIN BEL

DNK

0.15

EST CAN

AUS

AUT

LTU

ROU CYP

MLT

MEX

LTU

CYP

ROU

MEX

0.05

0.05

ISR TUR

0.1

DEU GRC

0.2

0.3

0.4

0.5

ISR

TUR

0.1

0.6

0.2

0.3

0.4

0.5

Share of migrants with tert. educ.

Share of migrants with sec. educ.

0.25

DEU ITA SWE PRT

BEL LUX

0.2

CHE FRA FIN

GBR

DNK

ESP AUT

NLD USA

0.15

NZL AUS

0.1

IRL CAN

CHL

MEX

0.05 0.4

0.5

0.6

0.7

0.8

Share of migr., low skilled occ.

Fig. 5 Elderly and immigrants by age and skills in OECD countries. Notes: “Low” education refers to no education, completed primary, and uncompleted secondary education (ISCED 0/1/2); “secondary” education refers to completed secondary education (ISCED 3/4); and “tertiary” education refers to completed tertiary education (ISCED 5/6). “Low-skilled occupations” refer to the following low and medium skill occupations: service workers and shop and market sales, skilled agricultural and fishery workers, crafts and related trade workers, plant and machine operators and assemblers, elementary occupations (ISCO 5–9). For the United States, these occupations are based on the US Census Bureau occupation codes and include occupations ranging from healthcare support occupations to transportation and material moving occupations (USA_11–USA_22; military-specific group is excluded). For Mexico, these occupations are based on the Mexican classification of occupations and include occupations ranging from industrial workers, artisans, and helpers to agricultural workers (MEX_5–MEX_11). The last graph with the share of migrants in lowskilled occupations refers to 2005/2006, while other graphs—to 2010/2011. The correlations are in general stronger for 2005/2006 for the then OECD members. DIOC dataset 2005/2006 and 2010/2011.

Migration and the Demographic Shift

of the studies on the determinants of migration, but rather to focus on several selected works that consider age, aging, population structure by age, and related demographic variables as determinants. Wages and employment differentials between sending and receiving countries are usually considered among the main push and pull factors of migration. The simple neoclassical migration model postulates that the decision to move depends on the wage differences between the two regions, which are extended to include the expected rather than the actual wage differential and the probability of finding employment in the destination (Harris and Todaro, 1970). Hence, at the aggregate level, differences in earnings, unemployment rates, costs of living, public goods, and public transfers are important determinants of a move. The microeconomic approach emphasizes that migration is an investment in human capital, underlying the importance of the expected returns and costs of migration (Sjaastad, 1962). As in any investment decision, an individual calculates the present discounted value of the expected lifetime earnings stream (ie, the returns to human capital) in sending and receiving regions, and migrates only if the returns minus the migration costs are higher in the destination. Age plays an important role since the older the individual, the smaller the probability to move, which reflects the smaller expected lifetime gain from moving for older people (as discussed next). Furthermore, the decision to move is also affected by the costs of moving, including not only the monetary costs such as travel expenses and foregone earnings, but also psychological costs arising from separation from family and friends. Skills are also important, given that moving costs are lower for more skilled individuals, reflecting lower job search costs as well as human capital transferability. Moreover, a greater geographical distance between the sending and receiving regions will deter migration, reflecting higher migration costs, as well as less or lower-quality information about more distant labor markets (although nowadays, the relevance of geographical distance is declining due to technology). A vast empirical literature with aggregate-level data estimates so-called gravity-type models, where geographical distance between countries is included in the regressions as a proxy for migration costs. In addition, more recent studies highlight the importance of linguistic, cultural, or genetic distance (for a recent study, see Adsera and Pytlikova, 2015; and the references therein). Migrant networks in the destination region, or diasporas, constitute another relevant factor in the migration decision (Massey, 1990).j Moving costs are reduced substantially when there are migrants from the same sending country already residing in a particular j

See McKenzie and Rapoport (2010) for a study on migrant networks and their role in migrants’ selfselection; Beine et al. (2011a,b) and Pedersen et al. (2008) for recent econometric tests with macro data; Beine et al. (2011c) for a literature review on the impact of migrant networks and relevant methodological issues; and Plaza (2013) for the diaspora literature, among other studies.

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destination country since they can provide information about the labor market, housing, and other host-country conditions. Family considerations are also important, and some migrants may not necessarily gain from migration as tied-movers, while migration probability decreases with family size (Sandell, 1977; Mincer, 1978). From another perspective, migration can be a risk-sharing strategy of a household that chooses to send some of its members abroad to diversify risks to its income from asymmetric shocks. Additionally, migration may occur in order to improve the income situation of a household relative to other households, in a so-called relative deprivation approach (Stark and Taylor, 1991). Finally, migrants may be positively or negatively selected with respect to skills, although intermediate selection also may be the case (see, among others, Borjas, 1987; Chiswick, 1999; Chiquiar and Hanson, 2005; McKenzie and Rapoport, 2010). In order to better understand how age affects the migration decision, let us further rely on a human capital framework and consider a sending country s and a receiving country r with respective wages ws and wr. Assume that an individual decides at age 20 whether to migrate by comparing the wages that these countries offer. Assuming a retirement age of 65, the present value of her expected lifetime earnings in two locations can be written as PV ðw s Þ ¼

65 X

65 X was war r andPV ð w Þ ¼ a
20 a
20 a¼20 ð1 + d Þ a¼20 ð1 + d Þ

where d is the discount rate and a is the individual’s age. Further assuming that the migration costs C, the individual will move if the returns, minus the moving costs, are larger in a potential destination than those in the country of origin: PV ðwr Þ
C > PV ðws Þ A straightforward implication of the human capital theory is that younger individuals will have a higher probability of migrating due to the greater time horizon over which to reap the returns to this investment. Furthermore, the moving costs, which include not only monetary costs but also the psychic costs of separation from family and friends or information search costs, might be higher for older individuals. Thus, the supply of migrants will be larger at younger ages. Drawing on Borjas (1987), Chiswick (2000), Hatton (2005), and Clark et al. (2007), the migration equation can be expressed as follows. Assume that an individual i with skills si is deciding between remaining in source country s and obtaining wage ws(si) or moving to a receiving country r and earning wage wr(si). The move involves costs that can be individual specific, such as the psychic cost of separation from family and friends (zi), as well as costs that are common for all individuals, such as ticket fares (c). The probability of an individual moving to country r will depend on the net gain from migration:

Migration and the Demographic Shift

where

ProbðM ¼ 1Þ ¼ Prob ðV > 0Þ, V ¼ wr ðsi Þ
ws ðsi Þ
zi
c

Assuming that wages and costs are normally distributed with means μs, μr, and μz, and summing over all individuals, the emigration rate from the source country to the destination country can be expressed as follows:  
μr + μs + μz + c M ¼1
Φ σV This equation implies that, for a given skill level, the emigration rate will be higher with a higher mean wage rate in the receiving country, a lower mean wage rate in the sending country, or lower mean individual-specific migration costs and fixed migration costs. This equation can be further extended by adding policy variables such as quotas or skill-specific selective migration policy parameters (Clark et al., 2007; Mayda, 2010; Ortega and Peri, 2013).

3.2 Age and Migration: Empirical Studies with Individual Data Numerous empirical studies have estimated the individual migration decision, consistently concluding that age has a negative impact on migration probability (see, among others, Bauer and Zimmermann, 1999, for a review; Zaiceva and Zimmermann, 2008). Table 3 reviews some selected studies and presents the signs of the estimated coefficients on the age variable. Despite different countries and time periods for which estimates have been carried out, as well as different econometric methods, the studies presented in this table overwhelmingly show that age affects the decision to move negatively. When nonlinearly entered into the migration equation, it has an inverted U-shaped profile, with the maximum migration likelihood manifesting at younger ages, mostly at 20 or 30 years old. A host of studies examine the determinants of migration intentions rather than the actual migration decision. However, it has to be kept in mind that such intentions do not necessarily transform into actual actions.k These studies arrive at similar conclusions regarding migration determinants as those that employ actual migration data. In particular, younger individuals are found to be more likely to intend to move abroad, consistent with the human capital theory of migration. Our own analysis of the individual determinants of migration in Europe confirms that older individuals are less likely to move. In the European context, Zaiceva and k

Although several studies find that intentions are correlated with a subsequent move, other researchers claim a substantial forecast error exists (see, for instance, a recent study by van den Berg and Weynandt, 2013, for the case of return migration).

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Zimmermann (2008) analyze intentions to move abroad for individuals from both new and old EU member states before and after the 2004 EU enlargement; the results show that age has a similarly strong negative effect in both regions. The analysis of the actual migration decision using the EU Labor Force Survey data for 10 new EU member states across 2009 and 2010 is in line with these findings. As shown in Table 4, the probability to work in another country decreases with age and is lowest for the most elderly individuals. Table 3 Selected studies with age as individual determinant of migration

Study

International Massey and Brown (2011) Stark and Taylor (1991) Vadean and Piracha (2009) Interregional Bodvarsson et al. (2014)

Liebig and Sousa-Poza (2006) Hunt (2006)

Country

Age

Age squared

From Mexico to the United States and Canada From Mexico to the United States From Albania

United States: + Canada: 0

United States:
Canada:



China

LPM: Age 15–19: + Age 19–30: +/0 Age 30–65:



15–19 years

Age 18–21: + Age 22–25: + Age 26–29: + Age 30–35: + Age 36–45: 0 (Ref: age 46–53) Age 16–22: + Age 23–29: + Age 40–49:
Age 50 +:
(Ref: 30–39) +

18–21 years

Switzerland East–West Germany

B€ oheim and Taylor (2002)

Great Britain

Agesa (2001)

Kenya: rural-tourban Mexico United States

Stark and Taylor (1991) Hunt and Kau (1985)

Age of maximum migration probability

+

Around 30 years 20–30 years

Permanent:
Return:
Circular:


+


23–29 years




20–30 years

Notes: Signs of estimated coefficients on age are reported. “+” stands for significant positive, “
” for significant negative, and “0” for the insignificantly different from zero coefficient.

Migration and the Demographic Shift

Of course, it also reflects the lowest likelihood of work for these individuals in general, and the results remain unchanged when controlled for the labor force status of an individual in column 2. In addition, the probability of working abroad is highest at 20–29 years of age, in line with the aforementioned studies using individual data.

3.3 Age and Migration: Empirical Studies with Aggregate Data At the aggregate level, demographic factors, particularly the size of the young cohort, are among the key “fundamentals that drive world migration” (Hatton and Williamson, 2002, 2003; Clark et al., 2004). As the authors note, it may affect emigration directly by raising the share of young in the overall population, thus increasing the proportion of individuals with a higher propensity to move, as well as indirectly via labor market effects. Such generational crowding, or being born into a large cohort, increases competition in the labor market and thus acts as a push factor for emigration. Therefore, the age structure in sending countries reflects an important determinant of migration, and emigration is expected to be larger from countries with population distributions skewed toward younger ages. Similarly, the relative proportion of the young population in the receiving countries also may influence immigration into these countries as a pull factor via demand-side effects. As noted previously, migration is a forward-looking investment decision, and the present value of migrating is determined by the difference between the discounted income streams in the destination and source countries and the discounted migration costs. This net gain from migration will depend on the remaining working period of individual i, with larger gains the longer this period is. In other words, the younger the potential migrant, the larger the net gain from migrating, and thus the higher the probability of moving. Hence, migration will be affected by the share of young individuals in the source country: the larger it is, the higher emigration will be for a given wage differential, minus costs (Clark et al., 2002). In addition, high fertility (and thus a high supply of young labor) Table 4 Age as a determinant of labor migration from 10 new EU member states (1)

Age 15–19 Age 20–29 Age 40–49 Age 50–59 Age 60 + Observations

0.0010 (0.0007) 0.0024*** (0.0002)
0.0009*** (0.0002)
0.0030*** (0.0002)
0.0049*** (0.0002) 1,113,447

(2)

0.0006 (0.0007) 0.0019*** (0.0002)
0.0010*** (0.0002)
0.0030*** (0.0002)
0.0048*** (0.0002) 1,113,442

Notes: Marginal effects from probit regressions. The dependent variable is equal to one if an individual works in a country different from his/her home country. Robust standard errors are in parentheses.***Significant at 1%. The 10 new EU member states are Bulgaria, Czech Republic, Estonia, Hungary, Latvia, Lithuania, Poland, Romania, Slovakia, and Slovenia. The sample includes individuals older than 14 years old and excludes those in military service. The reference category is age 30–39. Other regressors include gender, marital status, number of children, education, year, and country dummies in column 1, as well as labor market status 1 year before the survey in column 2. EU Labor Force survey 2009 and 2010.

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and generational crowding, combined with low local labor demand, also stimulate emigration. On the contrary, declining fertility and demographic shifts in the source country will affect the share of young individuals entering the labor market and likely diminish the emigration rate. Indeed, the increase in Mexico’s population relative to the United States has been an important factor affecting Mexican emigration. Population changes were a result of differences in the timing of demographic transitions in these countries: In the United States, fertility rates began to fall in the late 1950s, compared to after the 1980s in the case of Mexico (Hanson and McIntosh, 2010). As the Mexican fertility rate is converging to the US level, Hanson and McIntosh (2009) suggest that future emigration from Mexico will decline significantly, with the expected emigration rate for labor market entrants in 2030 to be only one-third of the level it was in 2000; this is assuming constant labor demand and leaving aside network effects that may attract migrants even with slowing population growth (Hanson and McIntosh, 2010). Table 5 reports the signs on demographic cohort variables from several selected studies. Regarding the share of the young population in the source country, researchers often find that it significantly and positively influences migration (see Table 5). On the other hand, Clark et al. (2007) find that the demographic variable is not statistically significant in their regression for emigration to the United States from 81 countries when using within or between estimators. Hatton and Williamson (2003) report elasticities of emigration out of Africa that are, as they note, comparable to those found in their earlier study for the late 19th-century European (especially Irish) emigration. In particular, an approach instrumenting the share of young adults by the proportion of the population aged 10–14, implemented 5 years earlier, suggests that a rise in the share of the African young adult population by 5 percentage points increases net outmigration by 1.3 per thousand. Consistent with these emigration findings, the share of young adults in the receiving countries is negatively correlated with immigration; the magnitude of the effect implies that a decrease in the receiving country’s young adult share by 5 percentage points would increase the net immigration rate by 0.9 per thousand of the population (Hatton and Williamson, 2002). There is also a similar effect when including a younger cohort into the analysis (as in Hatton and Williamson, 2011), indicating that an increase of 1 percentage point in the cohort aged 0–14 years in the source country would increase emigration to the United States by around 3%. Notably, projecting migration into the future until 2030 suggests that migration pressure from the developing world to the United States will not increase and that the composition of future US immigrants will shift from Hispanic to more African. Decomposing this overall effect, the authors show that the demographic variable has the largest negative impact on future migration for Latin America, Asia, the Middle East, and North Africa, offsetting the positive impact of the income gap and leading to the overall negative effect. On the contrary, the demographic pressures are of a much smaller magnitude in sub-

Table 5 Selected studies with share of young cohort as macro determinant of migration Study Country Dependent variable

Clark et al. (2007) Hatton and Williamson (2003) Hatton and Williamson (2002)

Hatton and Williamson (2009) Hatton and Williamson (2011) Mayda (2010)

Belot and Ederveen (2012)

Bertocchi and Strozzi (2008) Hanson and McIntosh (2010)

Hanson and McIntosh (2012)

To the United States from 81 countries, 1971–1998 To the United States from 21 African countries, 1977–1995 From 12 European countries, 1860–1913; To the United States from 81 countries, 1971–1998; United States to 80 countries, 1970–2000 To the United States from 62 countries, 1970–2000 To the United States from 62 countries, 1970/74–2000/04 To 14 OECD countries from multiple origin countries, 1980–1995 Between 22 OECD countries, 1990–2003 To the EU15 and Israel from 88 countries 14 European countries, 1870–1910 From Mexico to the United States, 1960–2000

To the United States, Canada, United Kingdom, Spain from 25 Latin American countries, 1980–2005

Gross emigration rate Net emigration rate Gross emigration rate Gross emigration rate Net immigration rate

Gross emigration rate Gross emigration rate Gross emigration rate (inflows), multiplied by 100,000 Total inflows Immigration rate (inflows) Gross immigration rate Net migration rate as difference in the size of birth cohort between 10 years in Mexican states Net migration rate as difference in the size of birth cohort

Demographic variable

Sign

Origin countries’ share of population aged 15–29 Origin countries’ share of population aged 15–29 Lagged origin country birth rate Origin countries’ share of population aged 15–29 Share of population aged 15–29 in the receiving countries

0 + + +


Lagged origin countries’ share of population aged 0–14 Lagged origin countries’ share of population aged 0–14 Origin countries’ share of population aged 15–29

0/+

Origin countries’ share of population aged 20–39 Origin countries’ share of population aged 15–29 Share of population aged 15–29 in country Size of a Mexican state birth cohort relative to the number of US high school dropouts in that birth cohort Birth rates in the country of origin’s cohort (birth cohort size) relative to that of destination Age cohort dummies (16–22, 23–34, 35–40)

0

+ 0/+

0/+
+

Rel. birth cohort size: United States: + United Kingdom:
Canada, Spain: 0 Pooled: + Highest at ages 23–34

Notes: Signs of estimated coefficients on demographic variables are reported. “+” stands for significant positive, “
” for significant negative, “0” for the insignificantly different from zero coefficient.

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Saharan Africa, with dominating relative income and education gaps as well as strong network effects, thus leading to an overall large positive impact on future emigration. Hanson and McIntosh (2010, 2012) employ another approach. The authors measure net bilateral migration rates by year and age cohorts using data on immigrant stocks from destination country censuses divided by the size of the respective birth cohorts from the origin country. Identifying how shocks to young cohorts affect migration over their working lives accounts for dynamic life-cycle effects. This approach allows for examining international migration over a long time span, which exploits country-of-origin variation in birth rates (labor supply). However, this comes at the expense of ignoring self-selection issues, given that it requires aggregating across-skill levels. Hanson and McIntosh (2012) show that a 10% increase in the relative size of the origin birth cohort leads to an increase of 0.36 percentage points in the net migration rate to the United States over the course of 10 years; this is similar to the number found using Mexican data (Hanson and McIntosh, 2010), where cross-state, cross-time variation in the timing of the demographic transition was used for identification. In other words, the 52% decrease in total fertility rates that occurred in Mexico between 1978 and 2002, in itself, would cause the fraction of Mexican birth cohorts migrating to the United States each decade to drop by almost 2 percentage points. These results are in line with Hatton and Williamson (2011), which predict a future decline in Latin American and Caribbean immigration to the United States over the next two decades, along with an increasing share of immigrants from sub-Saharan Africa. Our own estimates of immigration to Germany from 212 countries serve as an example showing that the share of young population in the country of origin has a positive effect only before the 2008 crisis and for more advanced economies (see Table 6). In the case of immigration to Germany from the rest of the world, the impact of

Table 6 Young cohort size as a determinant of migration to Germany, 2000–2011 United States, Canada, Japan, Israel, Australia, New Zealand, European EU28 Economic Area (EEA) Other countries

Share of population aged 15–29 Observations

Pre-2008

Post-2008

Pre-2008

Post-2008

Pre-2008

Post-2008

17.57*** (6.417)


20.82*** (6.421)

11.18** (3.500)


11.75* (6.251)


2.36 (4.913)


5.08 (6.651)

206

108

72

36

354

174

Notes: Estimates from panel fixed-effects models are reported. Robust standard errors are in parentheses. *Significant at 10%; **significant at 5%; ***significant at 1%. Dependent variable is log gross migration to Germany, divided by the source country population. Other regressors include source country GDP per capita and its square, unemployment rate, and year dummies. Immigration flows are from the OECD International Migration database, GDP per capita, purchasing power parity (PPP) (constant 2005 international dollars), unemployment rate, and population are from the World Bank World Development Indicators database.

Migration and the Demographic Shift

demographic structure in the sending countries is not statistically significant, a finding consistent with that of Clark et al. (2007). What are the implications of the demographic aging in light of the aforementioned findings? First, the human capital model implies that the net migration benefits are lower and the moving costs are higher for older workers. These are due to the shorter time horizon for reaping the returns on the migration investment, as well as the higher costs of job search, learning, and the physical move; larger social capital; and more origin- or firmspecific human capital. Second, although fertility remains higher in many developing regions than in developed ones, it is also declining in many migrant-sending countries. Hence, a demographic shift to lower fertility and aging population in the source countries may lead to a decreasing overall supply of migrant labor. The overall conclusion from the aforementioned studies is that a population’s demographic structure is an important determinant of migration and that younger cohorts are generally more likely to move. Generational crowding acts as a push factor via its direct impact on migration probability and its indirect effects on labor markets. Demographic transitions shape current migration patterns and are likely to influence the future nature of migration. In the United States, the composition of migrants is shifting and is predicted to shift further from fewer Mexicans to more Africans or Asians, with an important part of this change attributable to demographic factors. In general, population aging in many migrant-sending countries is likely to lead to a fall in the average migration rate, as older workers are in general less likely to move. Older individuals may face higher costs of moving in terms of weaker health and psychic costs of separating from family and friends. In addition, there may be certain institutional restrictions on the mobility of the elderly related to pension transferability or access to healthcare in the new locations.l Finally, aging may have an additional spillover effect: the mobility of workers of all ages may decrease, as demonstrated in a recent study (Karahan and Rhee, 2014). These authors develop a model suggesting that with an increase in the share of older workers with higher moving costs, it is more profitable for firms to hire more of these workers, as older workers accept lower wages. This in turn reduces both in-migration and outmigration in this state. The authors show that 60% of the decline in the US interstate migration is due to population aging, while almost 80% of it is attributable to this indirect effect of aging. On the other hand, however, there may also be an increase in elderly migration as the large baby-boom generation reaches retirement age, due to increased life expectancy and better health. Moreover, migration of care workers may become relatively more important due to the increasing share of the elderly in many countries. Finally, return migration l

As an extreme case, in China, there are restrictions on mobility stemming from Hukou, a household’s registration, which excludes the elderly from a priority group for granting a new registration, which is required for accessing free medical care in a new destination (Bodvarsson et al., 2014).

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is also likely to happen more frequently after retirement. The next subsection sheds more light on these issues.

3.4 Changing Migration Patterns: Mobility of the Elderly and Demand for Eldercare Currently, the share of international migrants aged 65 + is around 8.5% of the elderly population in all developed regions, ranging from around 8% in Europe to more than 27% in Oceania (see Figs. 2A and B). Among 27 million of all international migrants aged 65 or over, 70% live in developed countries, with Europe hosting the largest number of older international migrants—11.9 million, or 44% of all older migrants (United Nations, 2010). Among the overall migrant population, the share of older migrants has declined somewhat (from 12% to 11%) between 1990 and 2013 (United Nations, 2013a,b). The share of population aged 65 and over will increase in the future, which may also lead to the elderly having increased mobility. Indeed, after a declining migration probability from the age of 30 onward (as discussed in the previous section), research shows that there might be another migration peak around retirement age. Constant and Massey (2003), analyzing 14 years of longitudinal data on immigrants in Germany, establish that the probability of return migration is larger closer to retirement and that return is also determined by social attachments in Germany and in origin countries. Cobb-Clark and Stillman (2013) derive a theoretical model in which the probability of return migration is maximized at retirement and, consistently with their model, estimate a negative relationship between immigrants’ retirement status and the return migration rate of their fellow countrymen, suggesting that immigrants from countries with higher return migration rates are less likely to be observed as retired in Australia compared to immigrants from countries with lower return migration rates. Yahirun (2009) similarly shows that male migrants in Germany are more likely to return when aged 62–74 than when aged 51–55. Both studies define return migration as migration abroad given respondents’ older age. In addition, among elderly men who are naturalized German citizens, those with vocational education and employed full time, having German-born children, being homeowners, and receiving subsidized housing are less likely to move abroad, whereas those who are married and receive unemployment benefits are more likely to return (emigrate) (Yahirun, 2009). Factors affecting migration of the elderly differ from the conventional push and pull factors that drive migration for work-related reasons, such as wages and unemployment differentials (see Section 2).m Better climate and other environmental amenities, low costs of living, accessible and affordable healthcare, low taxes, good service infrastructure, and m

For a recent review of the existing sociological and economic studies, see, for example, Sander et al. (2010). Jones (2008) discusses migration of the elderly and analyzes its factors and related migration of care specialists in Asian countries; he concludes that both retirement migration and migration of care workers are likely to increase with aging.

Migration and the Demographic Shift

proximity to family and friends are among the main macro-level pull factors of retirement migration; meanwhile, higher-level education, greater wealth, and higher income are related to a higher likelihood of retirement migration at the individual level ( Jones, 2008; Sander et al., 2010). Dimou and Schaffar (2014), however, do not find a significant impact of medical care, consumption facilities, or cultural amenities on elderly migration within France, while the impact of real estate prices is ambiguous. Elderly migration may also be a response to a reduced income after retirement as a strategy of saving on housing and other consumption costs by moving to less expensive (often nonurban) areas. Employing the European Community Household Panel, Tatsiramos (2006) shows that homeowners above the age of 50 are less likely to move compared to renters, and that older homeowners mostly move to smaller dwellings. Moreover, having a mortgage, retirement, death of a spouse, and excessive housing costs are positively correlated with a move in central and northern European countries, but not in southern ones. However, geographic mobility of the “oldest old” in need of care may also be toward the larger cities so that they can be closer to relatives working there or to eldercare providers (Sander et al., 2010). Immigration policies also matter. Family unification migration in the United States has turned out to be an important phenomenon in the context of aging. Tienda (2013) shows that as a result of the 1965 Amendments to the Immigration and Nationality Act, there was an increase in late-age immigration for migrants from all regions. Indeed, if in the beginning of the 1980s, the share of children (0–16 years old) outnumbered the elderly migrants (50 and older) by more than double, these shares became roughly equal after 2005 (around 17%). The share of late-age immigrants from Asia increased from around 14% to almost 20% over the same period, constituting the largest share among migrants and suggesting that having sponsoring parents is significantly more common for Asians than for other immigrants (see also Jasso and Rosenzweig, 1989). On the other hand, countries might seek to attract retirement migrants, who may bring their funds and savings to the destination, while explicit policies may be adopted in order to reach this goal, such as specific retirement visas used in some Asian countries such as the Philippines, Thailand, Indonesia, and Malaysia (Jones, 2008). Finally, healthcare and eldercare workers may also move in response to an increased demand for such services. Indeed, health professionals, particularly physicians, are overrepresented among the immigrant population in most OECD countries, and the international migration of these professionals is aimed at overcoming short-term or area-specific (i.e., often in rural or remote areas) shortages in both developed and developing countries (see Grignon et al., 2013 for a recent review of studies on the determinants and impacts of the migration of health professionals). Population aging is likely to increase migration of healthcare workers in the longer term, although it is likely to change the composition of these migrants from, for example, pediatricians toward more ophthalmologists or chronic disease specialists and even more so toward low-skilled healthcare providers (Grignon et al., 2013). Examples of such policies include Canada’s

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formal “live-in caregiver program,” which was initially designed for childcare workers, yet is increasingly also being used for eldercare workers (Grignon et al., 2013), as well as Italy’s reliance on formal and informal eldercare providers, called badanti. Moreover, immigration of these workers, apart from satisfying the demand for such labor, may have other effects. Immigration of foreign domestic workers, by providing childcare and eldercare services to a household, increases employment of native women, in particular those with young children and elderly parents, as well as with the highest opportunity cost of time (Cortes and Pan, 2013; Cortes and Tessada, 2011; Farre et al., 2011). Particularly relevant for this survey, Farre et al. (2011) show that recent large waves of female immigration to Spain made household services, particularly eldercare, more affordable, which led skilled native women to stay in the workforce longer and to retire later when having elderly dependents in the household. Thus, apart from the direct effect of population aging and increasing demand for such workers, the indirect effect may arise when increased participation of native high-skilled women may offset negative fiscal impacts of aging (see Section 4 for a discussion of fiscal impacts). In conclusion, age plays an important role in the migration decision, and population aging is likely to shape migration patterns. The demographic shift in many migrantsending countries is likely to prompt a fall in the average supply of migrant labor, as older workers are generally less mobile. However, on the other hand, there may be an increase in the relative importance of elderly migration, including return and retirement migration, due to aging and better health. An increased demand for eldercare workers is another likely implication of population aging and may lead to an even higher mobility of healthcare and eldercare providers. In this context, policies regarding pension portability and access to healthcare abroad become crucial. Pensions are usually granted independent of where the person lives, and in most cases, they can be taken to new destinations, implying a continuous strain on the pensioner’s country’s public budget and suggesting that the residence choice may not be as important. Migrating to a new destination, however, matters for a pensioner’s consumption choice since she will consume goods and services, including healthcare and long-term care, in the destination country. Finally, migrating to countries with lower healthcare costs may become an important strategy at older ages.

4. AGING AND MIGRATION: IMPLICATIONS FOR LABOR MARKETS, PUBLIC BUDGETS, AND POLITICAL ECONOMY Population aging is often viewed as a threat to the sustainability of pay-as-you-go pension systems when the number of taxpayers decreases while the number of those who draw from the social security system increases. Immigration of young labor is sometimes suggested as a means to relieve the strain on public budgets. However, the contribution of immigrants to alleviating the fiscal burden depends on their labor market

Migration and the Demographic Shift

participation and effects, skill level, and their remaining working life span in the host country and lifetime net payments into public budgets. We commence this section by briefly reviewing the effects of migration for labor markets in the context of population aging; subsequently, we discuss the role of migration through studying the fiscal impact of aging on public expenditures and finally proceed to discuss political economy considerations.

4.1 Aging, Migration, and Labor Markets The labor market performance of migrants has profound implications for a country’s public expenditures, particularly for alleviating the burden of aging. In 2013, the foreign-born worker unemployment rate amounted on average to 13% in the OECD countries relative to 9% for natives, with employment rates being 64% and 66%, respectively (OECD Statistics). However, there is great variation by country and gender. For example, in Germany, the unemployment rate for 8.9% (5.2%) for migrant (native) men and 8.3% (4.5%) for migrant (native) women. There are also differences in labor force participation. While for all OECD countries, the labor force participation rates equaled 73% for both migrants and natives in 2013, again there is variation between genders. In Germany, the participation rate of migrant men is slightly higher than that of natives (83.2% and 81.8%), while for women there is a substantial gap between migrants and natives (64.3% and 73.8%, respectively). Migrants usually enter the host country’s labor market with lower wages and higher unemployment rates than natives, but over time, their wages and employment rates may catch up to those of natives. Gender and cultural aspects are also relevant, as labor force participation rates of female migrants may remain lower than that of men and native women, which consequently has fiscal implications.n The labor market impacts of immigration generally depend on migrants’ skills and selection patterns, as well as on whether immigrants and natives are substitutes or complements. In a simple model, and in the absence of other adjustment mechanisms, those who are substitutes with migrants lose in terms of wages and employment (for example, in the case of low-skilled migrants, low-skilled natives, or earlier immigrants), while those whom migrants complement will gain.o Typically, immigrants are more likely to be complements to older native workers who have more destination country– and firm-specific human capital. Since an increase in the age of the active population and increased cohort of older workers may adversely affect labor market outcomes and productivity (Zimmermann, 1991; Winkelmann and Zimmermann, 1993; Bloom and Sousa-Poza, 2013), immigration n

o

Starting with the seminal papers of Chiswick (1978) and Borjas (1985), numerous papers have investigated the assimilation of immigrants in host countries’ labor markets. For the impact of gender and culture on female immigrants’ labor force participation, see, among others, Antecol (2000). Numerous studies have examined the impact of immigration on natives’ wages and employment, typically finding a small effect if any (for one such survey, see Dustmann et al., 2008).

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may have a rejuvenating effect. Zimmermann (1991) and Winkelmann and Zimmermann (1993) are among the few earlier economic studies to have analyzed the implications of aging for labor markets, namely on unemployment and mobility. Although not directly considering migration in the model, Zimmermann (1991) suggests that the relatively high immigration of Eastern Germans would not substantially change the aging issue in the West, highlighting a positive impact of relative cohort size and age on unemployment in the short run, with no evidence of higher unemployment in the long run. An increase in the age of the active population might also reduce labor mobility, increase unemployment, and adversely affect productivity, thus generating efficiency losses (Winkelmann and Zimmermann, 1993). Furthermore, it is also likely to lead to a mismatch between labor demand and supply due to the reduced mobility of older workers, as well as their inappropriate skills or unwillingness to accept wage cuts. Consequently, immigration might contribute to easing the problems of aging, given that immigrants are more mobile than natives due to positive selection and their job-to-job changes are found to be unrelated to age. However, the authors also find that while being less frequently unemployed than natives at the early stages of their working lives, immigrants are more frequently unemployed in later stages. This suggests that even if migration occurs on a larger scale and might ease the problems of aging via reduced average age of the working population and increased flexibility and mobility, it also may incur a cost in terms of more frequent unemployment in later stages of the life cycle. Since immigrants themselves also age, they might adjust their behavior, including job mobility and labor supply, to that of natives. On the other hand, however, immigrants’ assimilation into the receiving country’s labor market could result in a lower probability of unemployment for migrants who have spent more years in the host country. Furthermore, a recent study by Borjas (2011) finds that the employment rate of native men in the United States falls much faster than that of immigrants as retirement approaches, due to the 10-year window during which an immigrant needs to work in the United States to qualify for social security benefits. Once this 10-year rule is satisfied, the probability of being employed also falls substantially for older immigrants. Moreover, the sizable cohort effect, which suggests the declining relative employment propensity across successive immigrant cohorts of arrival, mirrors the decline in earnings and overall cohort quality documented in the earlier literature (Borjas, 1985).p

p

The effects of population aging on labor markets and its implications for public policy are extensively disorsch-Supan (2008) discusses the implicussed in B€ orsch-Supan (2003), using Germany as an example; B€ cations for labor, products, and capital markets. The author suggests that in addition to increased taxes and contributions, labor productivity will need to increase; hence he calls for ever more efficient education and training to accelerate human capital formation. In addition, the demand for goods will shift toward more services and products for older individuals; in turn, this implies important changes in the employment structure across different sectors of the economy and would require a substantial increase in labor mobility.

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In the aggregate, researchers conclude that migration is not likely to play a significant role when analyzing the effects of aging, and the effects of population aging on economic growth are also likely to be modest (Bloom and Canning, 2004; Bloom et al., 2010, 2011),q although there may be some more pronounced effects on labor markets. Generational crowding may influence relative wages and labor supply, but life-cycle behavior is also likely to change, with these behavioral effects (longer working life, higher productivity and labor force participation, higher savings, and investment in human capital) counteracting the potential negative consequences of aging (Bloom and Sousa-Poza, 2013). The benefits of such a “demographic dividend” crucially depend on proper policies, including those concerning migration, fertility, more flexible pension arrangements, or relevant labor market policies that encourage labor force participation. Even if older individuals might be less productive than their younger counterparts, changes in the behavior of individuals and firms, as well as relevant policies, will counterbalance the declining working-age population and shifting age structure (Bloom and SousaPoza, 2013).

4.2 Aging, Migration, and Public Budgets The fiscal impact of immigration, along with its impact on the labor market, are among the most acute and debated issues; they become particularly important in the context of aging. Numerous papers have investigated immigrants’ contributions to public budgets and their welfare dependency. Some have explicitly focused on aging and whether immigration can alleviate the demographic burden (see, for example, B€ orsch-Supan, 1994; Felderer, 1994 for early contributions). In general, the role of social security benefits in attracting immigrants and the effect of immigration on public budgets depend on immigrants’ attachment to the labor market and on their welfare consumption. The impact varies across countries, studies, and gender. While some studies document the existence of a “welfare magnet” (Borjas, 1999a,b), others find that essentially, social security benefits play no role in attracting immigrants, even within the European Union, which has generous social security systems, although some report immigrants relying more on welfare in Northern European countries (see, among others, Barrett and McCarthy, 2008; Bratsberg et al., 2010, 2014; Dustmann et al., 2010; Kerr and Kerr, 2011; Giulietti et al., 2012; Dustmann and Frattini, 2013; Giulietti and Wahba, 2013). Moreover, despite some evidence that low-skilled migrants are net beneficiaries of the welfare state (Borjas and Trejo, 1991; Borjas, 1999a), even if migrants consume public goods such as healthcare and education, young and high-skilled migrants are usually considered net contributors to social security systems. In this context, the immigration of young labor migrants is suggested to alleviate the fiscal burden resulting from aging. Overall, net fiscal effects of migration depend on both migrant self-selection q

The impacts of aging on growth are discussed in Chapter 2 by Lee (this volume).

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and selective immigration policies, and this selection mechanism, together with early labor market integration, increase the chances of migrants making a positive net fiscal contribution (Hinte, 2014). A recent study provides a comprehensive review of the impacts of immigration on the public finances, incorporating both the impacts of immigration on fiscal balance in a static setting, the effects of immigration in a dynamic framework through its effects on relative population size of different generations as well as related decision-making and political economy aspects (Preston, 2014); see also Rowthorn (2008) for an earlier survey of fiscal impacts of immigration. Migration and capital mobility have been typically ignored in earlier analysis of the demographic transition in developed countries, which has mainly employed closedeconomy models (Fehr et al., 2004). Both partial and general equilibrium frameworks nowadays are employed to understand the impacts on public budgets. The need to incorporate dynamic aspects into the analysis is acknowledged in the literature, in particular, when evaluating the consequences of population ageing. One area of the research literature uses the generational accounting approach to calculate the fiscal consequences of immigration. Generational accounting is a dynamic framework allowing for calculating the net discounted contribution for both immigrants and natives over their lifetimes, as well as for future generations. This methodology calculates the present value of taxes paid and transfers received over the life span of a representative individual in generational accounts. The current and future generational accounts are compared with future government consumption and initial net debt: the fiscal policy is not sustainable if the former is smaller than the latter. Incorporating immigration into a generational accounting framework, Auerbach and Oreopoulos (1999) show that immigration to the United States reduces the fiscal burden for natives when the entire fiscal balance is shifted to future generations, although the gain is quite small while Auerbach and Oreopoulos (2000) emphasize the importance of skill composition of migrants. Bonin et al. (2000) find a somewhat larger impact for Germany—namely, that increased immigration may help to decrease the fiscal burden for future generations, who would face a tax reduction. There is a larger positive impact with both more skilled immigration and migrants’ integration into the labor market. These positive fiscal effects occur for two reasons: first, younger migrants are net contributors to public budgets, even after taking into account their additional government consumption; and second, there is a larger future native-born cohort. As argued in Bonin et al. (2000), a larger effect for Germany compared to the United States is due to more pronounced aging and a smaller share of foreigners residing in Germany. However, also in this case, even huge immigration flows would alleviate the fiscal pressures of aging only partially. A positive net fiscal contribution of migrants for Germany, including over the lifetime, is also reported in Zimmermann and Hinte (2005) and Hinte and Zimmermann (2014). Unsurprisingly, net tax contributions are the highest during the period of active

Migration and the Demographic Shift

labor market participation. Moreover, older migrants, although being net receivers of transfer payments, are much less of a burden to public funds than natives of the same age group. The migrant population also has a more favorable demographic structure, with migrants on average being younger than natives and approximately two-thirds belonging to age groups that are net contributors to public funds according to the generational balances. In contrast, in Denmark, the fiscal impact is only marginally positive for migrants within the age range 35–65, while it is negative for all migrants (Hinte and Zimmermann, 2014; Zimmermann and Hinte, 2005). Important differences are found between West European and non-West European migrants: while the former’s fiscal impact is similar to that of natives, the latter exhibit negative effects across all ages, both in the short run and over the lifetime. These results for Denmark may be attributable to a relatively larger share of refugees among migrants and their poorer labor market integration. Immigrants are found to positively contribute also to the Italian welfare system throughout their working lives, which results in only partially alleviating the fiscal burden on future generations, and the impact is larger when migrants remain permanently in the country (Moscarola, 2003). Positive and significant impact of immigration on intertemporal public finance is found for Spain as well (Collado et al., 2004). When calculating the net gain of immigrants, it is important to account for the costs and eventual contributions of their children. In their calculations for the United States, Lee and Miller (1997) were the first to recognize and correct the problem inherent in earlier studies using the immigrant household approach: such studies ignored the fact that immigrant children born in the United States were included in calculations of costs (ie, as they were present in a household), but were dropped once they left a household, thus excluding their future tax contributions. The authors also find that the long-term fiscal impacts of immigrants depend on their educational level, age, and time spent in the United States, with higher educated and young migrants generating substantial net fiscal premia (see also Lee and Miller, 2000, for a revision). Consistent with the generational accounting framework, the authors also advocate for a selective immigration policy. Storesletten (2000) employs a dynamic general equilibrium, overlapping generations model and considers the age and skill composition of immigrants in the United States. The author shows that if immigration predominantly involves young, legal, and high-skilled individuals who pay taxes, the net fiscal effects are likely to be large and positive, even when accounting for future retirement costs, as well as for family migration with children. However, even without accounting for family and taking the most feasible age range of immigrants (25–49 years old), it would require an 11-fold increase in high-skilled immigration compared to current numbers to offset the aging effects. In addition, return migration reduces the discounted contribution of high-skilled immigrants under 50 years old. Fehr et al. (2004) are also less enthusiastic regarding the role of immigration in alleviating the aging burden. They develop a three-region (ie, United States, Japan, Europe)

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dynamic, overlapping generations general equilibrium model, introducing immigration and capital mobility into it. Their model is similar to Storesletten’s (2000), albeit with some important extensions, and the conclusions are similar: namely, that the impact of immigration on alleviating the fiscal burden due to aging in the United States is negligible, but that increasing the number of high-skilled immigrants can be beneficial. The net effect of immigration is negligible due to other offsetting factors, such as lower native wages due to immigration and thus lower taxes, as well as immigrants’ consumption of public goods and social welfare. Moreover, improving future public budgets would require huge increases in high-skilled immigrants, all of whom would have to come from the developing world, thus exacerbating brain-drain problems. The positive net fiscal gain of immigration is smaller in the case of a European welfare state, such as Sweden, having a large public sector and generous social security benefits. Storesletten (2003) employs an overlapping generations model and follows Lee and Miller (1997) to compute the net public gain for a new immigrant, including the costs and contributions of future children. He finds a net gain from immigration of young individuals for public budgets, while the immigration of those younger than 10 and older than 50 implies net costs, as does the immigration of an average migrant, as was the case for the United States. These results depend crucially on the migrants’ expected labor market participation. The larger gain for the United States is due to better labor market performance; in particular, the immigrant employment rate is comparable to that of US natives, whereas in Sweden, it is substantially lower for immigrants than for natives. In addition, the immigrant-native wage gap is larger in Sweden than in the United States, which has implications for taxes and redistribution policies, which are more generous in Sweden. However, it should be acknowledged that such partial equilibrium models with fixed behavior may underestimate the cost of immigration.r Finally, a recent study by Docquier and Marchiori (2012) evaluates the macroeconomic and fiscal impacts of migration in the context of demographic aging not only for the receiving but also for the sending countries in a unified framework. The authors analyze migration from the Middle East and Northern African (MENA) countries to the EU15. They employ a multiple-region, dynamic, overlapping generations, general equilibrium model that features high- and low-skilled individuals and assumes permanent migration, equal fertility of migrants and natives, as well as the same educational attainment of immigrant and native children. Their analysis shows that, for the European Union, increased migration would alleviate the fiscal and economic pressures of aging. However, selecting immigrants leads only to a moderate reduction in tax rates due to the contemporaneous general equilibrium effects of immigration on wages and skill r

Indeed, for example, analyzing the impact of low-skilled immigration in a general equilibrium framework, Canova and Ravn (2000) show that although price effects are small, immigration is associated with tax increases that are required to finance the increased pressure on the welfare system (also see Borjas, 1994).

Migration and the Demographic Shift

premium, as well as on interest rates. Nevertheless, selecting skilled migrants has a strong positive impact on income per capita. Regarding sending countries, increased emigration, especially of the highly skilled, has a strong detrimental impact on tax rates and income per capita, amplifying the economic and fiscal burden of aging in these countries. Moreover, a brain-waste scenario, in which high-skilled migrants are employed in lowskilled occupations in the receiving countries, delivers the worst results for both regions. The negative effects of the brain drain on sending countries are mitigated if there are various positive diaspora externalities (for example, increased trade or investments between the regions) or ex-ante opportunity for enhanced human capital (the so-called brain-gain scenario), and in particular, in the case of increased incentives to invest in human capital in the origin that lead to the overall increase in the home country’s educational attainment. The authors emphasize that due to future aging problems in MENA countries, such selective migration policies should be temporary. Thus, the overall conclusion from these studies is that immigration alone cannot entirely sustain fiscal systems, although selective immigration policies combined with proper pension and fiscal reforms may contribute to alleviating some of the burden for future generations.

4.3 Aging, Migration, Welfare, and Political Economy Aspects The impact of migration on welfare depends on, among other things, the political migration regime in the receiving country, which is adopted as a result of voting. In a recent paper, Razin and Wahba (2015) show that accounting for the migration policy regime is crucial for testing the welfare magnet hypothesis. They find evidence for this hypothesis in the free migration regime, showing that the generosity of the welfare state changes the skill composition of migrants to more unskilled as they are net beneficiaries of the system. In the restricted migration regime, native voters vote for skilled migrants in order to mitigate the fiscal burden. In this section, we continue a discussion of the interaction between migration and aging and their implications for welfare by focusing on the political economy aspects.s s

As in the rest of this chapter, we do not attempt to provide a comprehensive review of the literature on the political economy effects of immigration or the implications of aging for welfare in this section; rather, we focus on selected studies that are, in one aspect or another, strictly related to the interaction between migration and aging. Much of the discussion on the political economy of migration and welfare can be found in Razin et al. (2011) and Razin and Sadka (2014a,b). Two earlier papers by these authors examined the political economy of the welfare state with migration and the welfare state with population aging. Razin et al. (2002) show that low-skilled immigration could lead to lower taxes and less redistribution than in the case with no immigration, even if migrants belong to a pro-transfer coalition. They also find empirical support for this hypothesis. Razin et al. (2002), in a theoretical political economy model, show that population aging could reduce the welfare state’s size and negative relation between the dependency ratio and labor taxes and social security transfers. The subsequent discussion in the field questioned these findings, including the assumption that the payments by the median worker had no influence on the benefits that she would receive after retirement.

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From a political economy perspective, the older the median voter, the more important pension spending (and thus higher payroll taxes) and public goods for the elderly (such as eldercare and healthcare) become on the political agenda. Thus, population aging and an increasing demand for and decreasing supply of social security transfers implied by it will influence the political economy debate on immigration and voting in favor of or against immigration policies (Razin and Sand, 2007). In the political economy models, older voters would prefer higher social security transfers and more generous welfare in general and would vote for more (young) labor migrants, especially high-skilled ones, who would help finance these transfers via taxes. The young would prefer paying lower taxes (and thus having lower social security benefits financed by these taxes) and may vote for having fewer migrants, which may reduce their wages more. In addition, migrants may vote, and when allowed to vote for fiscal policy, migrant voters may change the political balance between the young and the old in both labor-receiving and laborsending countries (Tosun, 2009). Razin and Sadka (1999, 2000) show that migration is Pareto-improving in a dynamic, two-period, overlapping generations model with a pay-as-you-go pension system and savings. They show that both current low- and high-income natives, as well as young and old natives, benefit from (or at least are not harmed by) low-skilled immigration. The equilibrium is pro-migration even in the case of unskilled migrants who are net beneficiaries of welfare; there is no necessary burden of such migration on future generations, given that the current elderly’s gain also may spread to future generations. In other words, in an everlasting world, the fiscal burden of low-skilled migration may be shifted forward indefinitely. Hence, all generations would vote in favor of migration. This model was criticized on various grounds, including by the authors themselves. For example, the model assumes that migrants and natives have the same population growth rate, as well as preferences, and that the skills of migrants’ offspring are similarly distributed to those of natives. Indeed, relaxing these assumptions and instead assuming the higher immigrant fertility (compared to natives) and natives being more skilled than migrant offspring (ie, immigrants’ children have less human capital than natives), Krieger (2004) shows that the results are no longer unambiguous. In his model, there is a positive externality on the domestic retirees due to higher total contributions, and an ambiguous one for domestic workers and future generations, which depends on whether the positive fertility effect or the negative skill effect dominates. If the positive fertility effect dominates, labor supply and contributions would both increase now as well as in the next period, and thus not only current retirees would gain, but the current young and future generations would as well. On the other hand, if the negative skills effect dominates, the immigration impact on pension benefits would be negative since an average immigrant’s child would contribute less to the pension system than the average native, while both groups would receive the same benefits. The political economy implications

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subsequently suggest that retirees will always vote in favor of unlimited immigration, while young workers in the initial period will be pro-immigration only if the positive fertility effect offsets the negative skills effect (keeping wages constant).t Even when wages fall, there may be a welfare gain from a positive effect on future pensions, which would offset the negative impact on wages if immigrants’ fertility rates or skill levels are sufficiently high, calling for selective migration policies, which aligns with the studies described in the previous section (see also Krieger, 2003 for an analysis of different pension regimes). Several other studies show that immigration may not be beneficial for public finance and could decrease welfare. Leers et al. (2004) introduce heterogeneous labor, but abstract from capital. Allowing for general equilibrium effects of aging and migration on wages and incorporating mobile and nonmobile labor, the authors suggest that if immigrants constitute a substantial share of mobile labor and if immigrants’ fertility declines less than that of natives, mobile labor may become redundant, leading to a decrease in its wages, which incentivizes emigration. In addition, higher pay-as-yougo taxes induced by aging create additional incentives for the young to emigrate. They also demonstrate that if public pensions are endogenous (ie, if aging leads the elderly to lobby successfully for higher taxes), it may take several generations before a steady state is reached and the initial migration flow may be opposite to the steady-state migration.u Calahorrano and Lorz’s (2011) overlapping generations model captures the gradual shift in the political weight toward the old generation. The shift is a result of population aging—in other words, a decline in population growth. The authors show that a decline in the growth rate of the native population has an expansionary effect on immigration, which may offset the initial decline in population growth. In a more recent study endogenizing fiscal and migration policies, Razin and Sadka (2014a) analyze how current fiscal and migration policies will affect the age distribution, and thus the coalitions and outcomes of voting processes in the future. Assuming that firstgeneration migrants have higher fertility than natives but the second generation is fully integrated (and thus has the same fertility and other characteristics), they show in their model that the state of the economy will depend on the share of native high-skilled young t

u

In practice, the younger generation often votes pro-migration, whereas the older members of the society opt against. A recent example of this is the pro-Brexit vote in the United Kingdom. This typically has to do with differences in preferences (more openness of the younger generation), greater fears of older people, or differences in the expectations about the contributions of migrants to the future of the country through productivity and innovations. See also Section 4.4. Kemnitz (2003, 2008) introduces unemployment into the analysis. Kemnitz (2003) shows that low-skilled immigration increases the unemployment rate and harms low-skilled natives. Although immigration is beneficial to natives’ general welfare overall, this gain can be attenuated by the expansion of the pension system. In Kemnitz’s (2008) model, immigration benefits retirees and improves the pension system only if total employment declines, because with inelastic labor demand, any increase in employment reduces the wages used to finance pensions. See also a review of related studies in Aslanyan (2014).

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in the population. When this share is low, the preferred policy is a moderately generous welfare state with a large but not extreme inflow of high-skilled migrants (a so-called center-group policy). Increasing the share of native high-skilled young, the policy would change to a more generous welfare state and larger inflow of high-skilled migrants (the left-group policy), until this group becomes sufficiently large, in which case the group’s preferred policy (the right-group policy) would be implemented with nongenerous welfare and limited high-skilled migration. It also raises strategic concerns among currently young voters about the possible future decreases in their pension benefits, as the number of next-generation young, including high-skilled migrants, increases, making the high-skilled a majority in the future, and those people would vote for low benefits. This model thus suggests important implications for population aging and population growth rates: the higher rate of population growth and the younger population shifts the preferred policy more to the right (ie, to a less generous welfare state and more controlled migration). Employing a similar model, Razin and Sadka (2014b) show that even the inflow of low-skilled migrants may be beneficial to the old, despite their net fiscal burden on public budgets over the life cycle. Low-skilled migrants impose a net fiscal burden by contributing less in taxes than the discounted future benefits that they receive. However, in this model, this burden is postponed indefinitely since the pay-as-you-go social security system lives indefinitely.v,w Aslanyan (2014) extends the model, challenging the idea that unskilled immigration may sustain the pension system at all. He shows that unskilled immigration not only reduces general welfare, but may even decrease pension benefits. This effect is due to a lower level of capital available postimmigration, since immigrants will have children that are not matched by any savings. As a result of such capital dilution, postmigration v

As is acknowledged by the authors, if the system is terminated at some period, that period’s young would lose since there will be no one to finance their old-age benefits in the next period when they will become old. And the larger migration is, the larger the total loss would be, since there would be more young due to migration in the next period and reflecting the net fiscal burden in the initial period. w In earlier work, Razin and Sand (2007) suggest the following strategic implications. Since the young prefer low taxes and the older generation prefers high taxes that generate higher social security contributions, when both immigration and social security policies are determined endogenously by a majority voting process, the older the native-born population, the more likely it is that the immigration policy will be liberalized to sustain a social security system. If there is an open immigration policy, there will be more young workers in the next period who pay taxes, and thus pension benefits increase. However, too many young immigrants would mean that the median decisive voter in the next period is also young and will vote for no taxes. Thus, a threshold level of immigration is necessary, such that the young voter would choose immigration quotas in order to strategically switch the next period voter from young to old. Such a “demographic switching” strategy means that the young voter would admit only a limited number of immigrants in order to change the decisive voter’s identity from young to old in the next period (due to a negative native population growth rate and positive immigrant population growth rate) to maximize the next period’s pension benefits. The older voter would vote for maximum immigration, which (combined with higher immigrant fertility) would lead to a young decisive voter in the next period. See also Razin and Sand (2009).

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welfare decreases and even gains in pension benefits from migration are offset by the losses in wages. In particular, for the initial young population, the welfare gains are the highest when immigrants are unskilled, while the initial retired population gain from immigration and the gain increases with the migrant’s skill level. Applying data to this model, its political economy implications suggest that immigration policies are based on public finance considerations or that gerontocracy prevails—that is, the current old population defines immigration policy and would cause welfare losses for the current young and for future generations. Increasing the proportion of active, elderly electorate may significantly influence the political balance of public spending by voting for policies that benefit the old (eg, pensions, healthcare) at the expense of those benefiting the young (eg, education). A strand of the literature investigates the political economy of education spending and an existence of intergenerational conflict; that is, whether there is a negative relation between the share of elderly people and spending on education (see, for example, Poterba, 1997; Harris et al., 2001; Tosun, 2015). Studies arrive at mixed conclusions depending on the aggregation level of the data employed. Tosun (2015) argues that introducing immigration into this model is important. Tosun et al. (2012) use the US intercounty migration rate of the elderly rather than the share of the retiree population and account for reverse causality, endogeneity of the migration variable, and spatial interdependence; they find the negative relation between retiree immigration and spending on education, thus confirming the existence of the intergenerational conflict. This relation is strongest for the age group 75–85 and becomes positive and significant for the 85+ age group. The authors’ suggested explanations for these differences include heterogeneity in the elderly’s preferences, as well as the oldest group possibly having grandchildren who may influence their behavior and voting preferences.x x

Tosun (2009) develops an overlapping generations model with international labor mobility, aging population, and fiscal spending on both education and social security and examines how migration shapes the demographic structure and voting preferences over fiscal policy. With immigration, the age distribution within the population would then shift toward the young and young migrant workers would vote for the education tax, leading to higher education spending, higher human capital, and larger growth in the receiving region. The sending region would lose its young labor but may still enjoy capital and income growth. The model also suggests that restricting migrant workers’ political participation in the destination produces inferior growth results. Regarding another aspect, natives’ preferences toward public or private education are analyzed using a political economy setup in Coen-Pirani (2011) for the United States and Tanaka et al. (2014) for Spain. In these models, the quality of public education is endogenously determined by voting and immigration affects voters’ preferences over public education (also see a recent review of this latter literature in Ortega and Tanaka, 2015). Finally, related to the literature surveyed in this section on the political economy of redistribution, a recent paper by Ortega (2010) investigates the political economy of income redistribution in the presence of immigration. In his model, voters’ preferences are influenced by their own and their children’s expected skills rather than by age balance, and immigration policy may be used strategically in his model by the unskilled natives in order to ensure political support for redistribution in the future. Also, see an earlier contribution in Ortega (2005) and the references in both studies.

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4.4 Aging and Individual Attitudes Toward Immigrants Despite potential positive effects and its potential contribution to alleviating the aging challenges, liberalizing immigration is difficult, given that voters and their attitudes determine the policies of democratic societies. An aging population, in turn, implies that the age distribution of the median voter is shifted toward the older generation. Would older individuals vote for or against immigration? This section continues the political economy theme and discusses individual attitudes toward immigrants in the context of aging. The theoretical arguments outlined so far in this chapter suggest that older individuals might be more in favor of (labor) migration. This is because they benefit both from the additional contributions of migrants to public budgets and pensions and the complementarity between young migrants and older natives who, in contrast to young natives, would not face a wage decrease and are likely to also benefit as capital owners. However, the relation with age is more complicated. For example, individuals may care about the future political balance and behave strategically when choosing current immigration levels. Empirical studies on the determinants of attitudes toward immigration often find a negative, or hump-shaped, relationship with age (see, for example, Dustmann and Preston, 2007; Facchini and Mayda, 2009, 2012; Calahorrano, 2013). Bauer et al. (2000) find a positive correlation for both favorable and unfavorable attitudes. For a recent review, see Calahorrano (2013). This suggests that even if increased immigration could partially relieve the negative impacts of aging, liberalizing immigration might be further complicated by the aging process per se, since the older electorate may be more or less in favor of it. The impact of age on individual preferences toward immigration may be confounded by the cohort effect, as the negative correlation with age may reflect either a growing aversion to immigration over one’s life cycle or the fact that older cohorts of individuals are less in favor of immigration. Using panel data for Germany over 1999–2010, Calahorrano (2013) finds that immigration is more of a concern among older rather than younger individuals; however, relative to other areas of worry, immigration is of relatively greater concern at young ages and becomes less prominent over the life cycle. Regarding cohort effects, older cohorts were found to be more concerned about immigration than younger generations. A study by Ivlevs (2012) incorporates macro-level demographic aging factors into an analysis of attitudes toward immigration. It tests the cross-sectional correlation between local fertility rates and preferences for immigrants in Latvia, a new EU member in which population aging and a declining labor force (due to both emigration and dramatically declined births during the 1990s) are among the most important issues emerging on the policy agenda. In line with predictions from theoretical political economy models, the elderly and those living in municipalities with low birth rates were found to support immigration more, with this effect being stronger among the older population and females. Individual opinions on whether immigration is an effective solution to the population aging problem in 27 EU countries are positively related to education, urban residence, the absence of children, as well as gross domestic product (GDP) per capita, while the correlation with the share of foreigners is negative (Ceobanu and Koropeckyj-Cox,

Migration and the Demographic Shift

Need to work

Contribute to taxes EU10 + 2 EU15

Legal contribute to taxes

Help solve aging 0

10

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60

Fig. 6 Attitudes toward immigrants in Europe, 2009. Notes: Proportion of respondents replying “tend to agree” in response to the corresponding questions, weighted by sample weights provided for the EU15 and new EU members (EU10 + 2); only includes natives. Authors’ calculations from the Eurobarometer 71.3 dataset.

2013). No significant correlation was found for the share of population over 65, the fertility rate, or the population growth rate. To provide an illustration, we use the 2009 Eurobarometer dataset, which contains similar questions regarding the role of migrants in alleviating the aging burden. In addition, the survey comprises other relevant questions on future pensions and sustainability of European social security systems. Fig. 6 plots different domains of the attitudes toward immigrants—namely, labor demand (“we need immigrants to work in certain sectors of our economy”), fiscal and welfare (“[legal] immigrants contribute more in taxes than they benefit from health and welfare services”), and aging (“the arrival of immigrants in Europe can be effective in solving the problem of Europe’s ageing population”). The figure indicates that the proportion of individuals who agree that immigrants can alleviate the aging problem is below 40% in both the old EU15 and new EU member states. In the old EU15 countries, this number is substantially lower than the one indicating the labor demand side (more than 50%) and is higher than the one reflecting perceptions regarding immigrants’ fiscal contributions: only slightly more than 20% (30%) of respondents agree that immigrants’ (legal immigrants’) net contribution to public budgets is positive. Countries with the largest proportion of respondents perceiving immigration as a solution to the aging problem are Spain, Sweden, and Finland, while the new EU member states constitute the least optimistic group in this aspect. Moreover, there is a negative correlation between the attitudes toward immigration as a solution to aging and opinions that the welfare system will be too expensive in 2030 (Fig. 7A). Contrarily, there is a positive correlation with the proportion of individuals who are confident about their future pensions (Fig. 7B). To summarize this section, the demographic shift brings about changes and challenges for both labor markets and public budgets, while the role of migration per se in alleviating

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A 0.6

0.4

0.2

0 0.5

0.6 0.7 0.8 Welfare system too expensive in 2030

0.9

0.4 0.6 Confident about future pension

0.8

B 0.6

0.4

0.2

0 0.2

Fig. 7 Individual opinions about sustainability of the future welfare system, confidence in their own pensions, and immigration alleviating the aging problem in Europe, 2009. Authors’ calculations from the Eurobarometer 71.3 dataset.

these challenges is likely to be not large and not sustainable. Overall, the literature is skeptical about the contribution of migration, although properly designed selective migration policies, combined with major fiscal reforms, are suggested to ease the fiscal pressures associated with aging. From a political economy perspective, although the elderly

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may theoretically prefer more labor migrants who would pay taxes and pension contributions, the situation may be more complex in actuality.

5. MIGRATION, AGING, AND HEALTH The increasing number of immigrants who age in receiving countries suggests the importance of better understanding their health outcomes and demand for healthcare services. An aging immigrant population may impose an additional strain for healthcare systems. There is indeed some evidence suggesting that immigrants may constitute a burden for countries’ healthcare, participating more often than natives in healthcare programs such as Medicaid (Borjas and Hilton, 1996), or relying more on employer-sponsored health insurance in the case of welfare cutbacks (Borjas, 2003). On the other hand, more recent studies for the United Kingdom and Germany find no significant differences between immigrants and natives in their use of hospital and general practitioner services (Wadsworth, 2012). There is also evidence that (both legal and undocumented) migrants’ healthcare consumption is positively affected by their social networks and by the presence of doctors who speak their language (Deri, 2005; Devillanova, 2008), both of which might be even more important at older ages. A substantial body of research across different fields examines the health outcomes of immigrants. The main fact documented in this literature is that, at the time of entry, immigrants are on average healthier than the native population, but that this health advantage dissipates with time in the destination country and is often absent for the second generation.y Among the suggested explanations in the literature for the existence of such a “healthy immigrant effect” are positive selection on health for migrants (due to both self-selection and selective health-screening policies in the destination country), negative selection on health for return migrants (outmigration of less healthy migrants back to their countries of origin, a so-called salmon bias), and cultural norms and behavior, including the positive impact of migrant networks and neighborhoods. In addition, data problems exist, particularly undercounting deaths or emigration of migrants and problems with disease diagnoses for migrants due to, for example, their less frequent medical visits, at least upon arrival. For the United States, researchers consistently document that health outcomes of Hispanic (particularly Mexican) immigrants are superior or similar to that of white natives, despite their disadvantageous socioeconomic situation, a phenomenon referred to as the “Hispanic paradox” (for a review of the literature, see Markides and Eschbach, 2011; y

However, such a “healthy immigrant effect” is not necessarily relevant for all migrant categories. For example, refugees and humanitarian migrants may have worse health upon arrival than the native-born population. Moreover, not all studies find an existing healthy immigrant effect. Finally, there is also significant heterogeneity across immigrant source countries and ethnicities, conveying that not all immigrant groups necessarily enjoy a health advantage.

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Markides and Gerst, 2011). In contrast, African-American death rates are higher than those of whites at all ages, except 85 and over. Moreover, the life expectancy of immigrants is reported to be longer than that of US natives, with Asian-Pacific Islander and Hispanic immigrants enjoying the highest life expectancy. However, despite lower mortality, several studies report that Hispanic and other immigrants have poorer self-reported health than non-Hispanic whites, as well as increased prevalence of morbidity, disability, diabetes, hypertension, and heart diseases among elderly immigrants. These findings attribute the latter, among others, to increased life expectancy but also to better diagnosis and management of chronic diseases (Jasso et al., 2004; Markides and Gerst, 2011; and references therein). Thus, despite immigrants arriving with better health, by old age, they (or at least most of the Hispanic minorities) seem to experience more health problems than the native population, even accompanied by lower mortality and higher life expectancy (Jasso et al., 2004; Markides and Gerst, 2011). Caution, however, is needed when interpreting these trends. First, tabulated from a cross section of data, the deterioration of health status across years may reflect the cohort’s declining health quality rather than assimilation or aging effects. Second, a proper counterfactual (that is, migrants’ health status had they never migrated) is never observed (Jasso et al., 2004). Selectivity in immigration and outmigration is important, and it is crucial that self-selection, including health, is quite different at young and older ages. Health is part of an individual’s human capital and affects his or her decision to move in a number of ways (Jasso et al., 2004). Since health is positively correlated with labor supply and earnings, healthier individuals will experience a larger gain from migration and hence have a higher probability to move. In addition, the larger the moving costs (eg, distance), the more pronounced a positive selection on health will be. Also, at older ages, labor market motives for migration are less important. Indeed, while migration is primarily for work at younger ages and wage and employment differentials are the main factors, migration at older ages may be driven by quite different motives, such as the presence of amenities or lower living costs, as well as the availability of healthcare services or relatives who could care for seniors in the case of poor health (see Section 3).z

z

Consistent with the positive health selection, Jasso et al. (2004) report descriptive evidence of a longer life expectancy at age 5 for Asian and Latino immigrants to the United States than for those who stay in their countries of origin. However, this advantage in life expectancy falls starting at age 65, remaining only slightly higher for immigrants, while disappearing for Hispanic elderly in the second generation. In line with this, Halliday and Kimmitt (2008) analyze internal migration in the United States from 1984 to 1993 and find that while deteriorating health reduces mobility for men below age 60, for older men, mobility is higher with both good and bad health (relative to average health). For women, rather than their own health, it is the health of the spouse that matters, with elderly women being more likely to move with a healthy spouse.

Migration and the Demographic Shift

Regarding selective return migration, the evidence is more mixed. Some studies find evidence for the existence of a negative selection on health for Hispanic emigrants (for example, Palloni and Arias, 2004). Abraı´do-Lanza et al. (1999) find a mortality advantage for Cuban migrants who could not freely return home, as well as for Puerto Ricans whose deaths in Puerto Rico are recorded in US national statistics, thus casting doubt on the existence of a salmon bias. Turra and Elo (2008) directly test the unhealthy return migration of migrants aged 65 and over by comparing the mortality of foreign-born and native emigrants from the United States to that of immigrants and natives in the United States. The authors find evidence for the salmon bias hypothesis for Hispanics; namely, that mortality is higher among foreign-born social security beneficiaries living abroad than among their counterparts residing in the United States, and the effect is larger among recent emigrants. In addition, they also find an existing salmon bias for other nonHispanic white immigrants. Despite the existence of unhealthy elderly outmigration, the authors conclude that it is too small to explain a significant part of the Hispanic mortality advantage. Furthermore, salmon bias due to emigration is partially offset by higher mortality of return migrants to the United States. Alternative explanations of superior Hispanic health include protective networks, cultural norms, and neighborhoods (see Markides and Eschbach, 2011 and the references therein). Economic strain earlier in the life cycle was also suggested to negatively affect health later in life, and thus be attributable to the declining health status of immigrants in old age (Wakabayashi, 2009). Adapting a host country’s unhealthy behavior and eating habits is obviously also important. Fenelon (2012) suggests that smoking behavior explains an important (though incomplete) part of the Hispanic life expectancy advantage, which is diminished for those born in the United States who smoke more heavily, converging to US natives.aa Antecol and Bedard (2006) analyze the unhealthy assimilation of migrants in the United States, employing the cross-sectional National Health Interview Survey from 1989 to 1996. The authors control for a large array of factors, attempting to account for cohort effects as well. They find that immigrant women, although entering the United States with a body mass index (BMI) around 2 percentage points lower than that of native-born women, converge completely to American BMIs within the first decade of residence in the United States, while the corresponding numbers for men suggest BMIs 5 percentage points lower upon arrival and closing one-third of the gap after 15 years of residence. Moreover, the results for females were driven largely by Hispanic female immigrants, while black immigrants did not converge to their native-born counterparts. In addition, Hispanic and white immigrants, but not black, were also found to converge to their respective US-born counterparts in self-reported health status, unfavorable health conditions, and activity limitations. aa

Heavier smoking in the United States may be due to an income effect (ie, higher incomes in the United States).

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The existence of a significant health advantage for new immigrants and subsequent convergence to the health of natives is also documented for Australia, Canada, Germany, and the United Kingdom (see, among others, Gee et al., 2004; Chiswick et al., 2006; Kennedy et al., 2006; Biddle et al., 2007; Sander, 2008; Giuntella and Mazzonna, 2014; and the references therein). An interesting channel of health convergence has been suggested in a recent study for Germany. The authors show that convergence in health is faster among those working in more physically demanding jobs. Moreover, immigrants are also found to affect positively the health of natives, particularly blue-collar workers, by improving their working conditions and reducing the average workload as they select themselves into less healthy occupations that carry more of a physical burden (Giuntella and Mazzonna, 2014). Notably, the situation may differ regarding older immigrants. Available studies report a nonsignificant health gap, or even a health disadvantage, faced by older or aging migrants relative to their native counterparts in terms of both physical and mental health. Using Canadian cross-sectional data, the healthy immigrant effect was not relevant for recent migrants over 65 years old; rather the opposite was true: These migrants (or at least men) had worse health on average (both self-reported and objective) than the native-born population (Gee et al., 2004; Kobayashi and Prus, 2012). In addition, old-age migrants who immigrated 10 or more years ago were more similar to natives in terms of their health status. No significant health differences (neither subjective nor objective) were documented between Canadian immigrants and native-born aged 55 years and older when not disaggregating by the length of stay or migrant origin and migration status (Newbold and Filice, 2006).ab Overall, given that middle-aged or older immigrants constitute over half of the foreign-born adult population in Canada (Gee et al., 2004), these results suggest important implications for that country’s healthcare policies. In general, these studies did not distinguish between different countries of origin, nor did they account for the cohort effects. Recently, the absence of a healthy immigrant effect for immigrants aged 65 and older was confirmed using several cross sections and controlling for cohorts of arrival in Canada (Desch^enes, 2012). Important differences by source region were also found, with European-born seniors being significantly more likely to have a non-life-threatening chronic condition and poor self-assessed health than their Canadian-born counterparts; in addition, older Asian migrants were more likely to have an activity limitation, but less likely to have a chronic condition (Desch^enes, 2012). Employing the 2004 wave of the Survey of Health Aging and Retirement in Europe (SHARE), Lanari and Bussini (2012) report findings from eight important immigrantreceiving Western and Northern European countries (Austria, Belgium, Denmark, ab

One exception was related to the Health Utilities Index, which is an objective measure of health status that shows older immigrants experiencing a lower health index, ceteris paribus.

Migration and the Demographic Shift

France, Germany, Sweden, Switzerland, and the Netherlands). The results indicate that among seniors aged 50 years and older, most immigrant groups are more likely to have worse self-reported health and to suffer from depression than native-born. Also, the perception of health is found to worsen with the length of stay (although a nonlinear pattern was also found). The highest odds of poor health relative to natives were reported for older Eastern European migrants residing in Germany, France, and Sweden, while depression was particularly likely again for Eastern Europeans living in France and Sweden, as well as for Africans living in the Netherlands and France. Using the same dataset, Ladin and Reinhold (2013) also suggest that aging immigrants face increased odds of depression, but this comes despite a physical health advantage.ac Constant et al. (2014) use the same data and document an advantage in subjective health upon arrival for older migrants in Europe, relative to both natives and previous migrant cohorts, as well as a subsequence convergence to natives. Finally, a recent study with SHARE data argues that selective policies matter, as older immigrants to Europe are on average healthier than natives upon arrival, while in Israel, which does not restrict immigration of Jewish people, older immigrants are less healthy than natives, and this health disadvantage disappears only after 20 years of residence in the country (Constant et al., 2015). Our tabulations for Germany (see Table 7) are generally in line with these studies. While the proportions of those reporting bad or poor health and those diagnosed with Table 7 Health of natives and immigrants in German Socio-Economic Panel (GSOEP), 2011 Age Natives YSM 0–10 YSM 11–20 YSM >20 Bad or Poor Health

15–30 31–40 41–60 > 60

0.055 0.093 0.180 0.282

0.034 0.072 0.314 0.438*

0.061 0.070 0.227 0.383

0.028 0.068 0.237 0.308

0.031 0.145 0.353 0.471*

0.000 0.108 0.227 0.524

0.070 0.120 0.313 0.578

Diagnosed Severe Illness

15–30 31–40 41–60 > 60

0.069 0.138 0.344 0.635

Notes: Sample means are reported. “YSM” ¼ years since migration. *The number of observations within this specific group is less than 30. “Bad or Poor Health” refers to the self-reported health status and is equal to 1 if an individual describes his or her current health as “bad” or “poor.” “Diagnosed severe illness” is equal to 1 if a doctor has ever diagnosed an individual to have at least one of the following illnesses: stroke, blood pressure problems, diabetes, cancer, psychiatric problems, arthritis, or a heart condition.

ac

Higher depression rates were also documented for older Mexican-American immigrants (Gerst et al., 2010).

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severe illness are lower among recent migrants than natives at younger ages, the situation is reversed in the case of self-reported health for those over 60, and even for those over 40. This proportion is lower for seniors who stay in Germany for more than 10 years, converging with the level of natives. Interestingly, the share of immigrants aged 60 and older diagnosed with a severe illness is lower for both recent migrants and those who stay longer than 10 years than it is for natives. A final observation worth mentioning is that migration itself, being a stressful event, may adversely affect health, especially in the long run when migrants age. Johnson and Taylor (2012) focus on the effect of migration at young ages on mortality at older ages by investigating long-distance moves within the United States from three US states (Montana, North Dakota, and South Dakota). Instrumenting migration by being born close to a railroad, the authors find that, given survival until age 65, migration reduces the probability of living to age 75 by 16% relative to nonmigrants. Employing data from the Irish Longitudinal Study on Ageing, Barrett and Mosca (2012a,b,c) find that older Irish returnees are more likely to suffer from alcohol problems and social isolation. They also acknowledge a migration endogeneity problem and attempt to correct for it using an instrumental variables approach. Another recent study suggests the existence of a negative causal effect of migration on health outcomes. Gibson et al. (2013) exploit a natural experiment setting comparing successful and unsuccessful lottery applicants for migration from Tonga to New Zealand, which allows them to experimentally estimate a counterfactual outcome for migrants had they stayed. The authors find no evidence of a “healthy migrant effect,” and posited that migration causes significant and persistent increases in blood pressure and incidence of hypertension, which, in turn, is the major risk factor of premature mortality. Migration was also found to increase stress and sodium consumption. In sharp contrast, employing the same natural experiment setting, migration was found to improve the overall mental health for Tongan migrants in the short run (Stillman et al., 2009). This finding is in contrast to the view that migration, as a stressful event, may have negative consequences for mental health, as may a potential hardship or discrimination in the receiving country. The results may be attributable to the fact that the study examined a specific migrant group (although the authors show that Tongan migrants are similar in many characteristics to an average migrant worker from a developing country), focused on a relatively young population (aged 15–48), and looked at only the very short-run effect (roughly 1 year after migrating), while negative effects for mental health may manifest themselves later in life. In sum, despite the overall healthy immigrant effect documented in the literature, the health outcomes for older migrants are less unambiguous. Some recent available studies suggest the absence of such an effect. In some cases, newly arrived senior immigrants have even worse health statuses than their native-born counterparts, which highlights the importance of different motives for migration later in life (see Section 3, earlier in this chapter). In addition, aging migrants may experience a health disadvantage due to such

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factors as assimilation to less healthy habits and diets. Finally, migration itself may cause a negative impact on health. Negative selection on health for older return migrants is also possible. Finally, there is evidence from welfare states such as the United Kingdom and Germany suggesting that migrants do not disproportionally use more hospital and general practitioner services. The net effect depends on the scale of aging migrants in the receiving countries, the magnitude of later-life migration and return migration, and migrant selection on health status. This in turn has important implications for healthcare and migration policies.

6. CONCLUSIONS The demographic shift to low fertility and low mortality and implied population aging represents one of the most important challenges in modern times. In this chapter, we have discussed how the interaction between international migration and population aging could affect labor markets, the political economy, as well as fiscal and healthcare systems in order to explain implications for future immigration policy and public budgets. Demographic transitions currently shape migration patterns and will likely continue to influence the nature of migration in the future. A population’s demographic structure is a prominent migration determinant since younger cohorts are generally more mobile. Moreover, generational crowding in sending countries acts as a push factor via its direct impact on migration probability and its indirect effects via labor markets. In general, population aging in many migrant-sending countries is likely to lead to a fall in the average migration rate, given that older workers are generally less likely to move. However, migration of the elderly, including return migration after retirement, may gain more importance. Moreover, the migration of health specialists and eldercare workers may increase due to the increasing share of the old-age population in many countries. Regarding the implications of immigration for labor markets and public budgets in the context of aging, existing research suggests that its role is likely to be limited. In order to contribute sustainably to pension systems and to ease the demographic burden, migration as we currently know it would have to increase by unrealistically large numbers. It would still be necessary to employ selective immigration and to execute labor market and pension system reforms like an increase in the retirement age and increasing weekly working hours; and to deal with the substantial and ongoing rise in life expectancy, and the fact that also migrants age and their fertility rates tend to adjust to the level of natives. Immigration is mainly a tool to moderate adjustment pressures of demographic change in the short run. Even if migration occurred on a larger scale and reduced the average age of the working population, as well as increased flexibility and mobility, it may also incur costs in terms of more frequent unemployment at later life-cycle stages, or pension costs as migrants’ retirement decisions may converge to those of natives.

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The net effect of immigration for public budgets could also be smaller due to other offsetting factors; for example, native wages due to immigration could be lower and thus reduce tax payments, as well as immigrants’ consumption of public goods and potential use of social welfare. That this does not play a substantial role currently in general does not rule out its potential role in the future. In addition, improving future public budgets may require huge increases in high-skilled immigration. If permanent, these immigrants would have to come from the developing world, and hence possibly create brain-drain challenges. Nevertheless, migrants, due to their more favorable demographic structure and if properly integrated in the labor market, may ease the strain on public budgets arising because of aging and thus be net contributors rather than net recipients of transfers. This crucially depends on migrants’ selectivity, as well as on selective immigration policies and relevant labor market integration policies. From a political economy perspective, even if a large number of migrants would be willing to enter, it is not easily achievable politically. Political economy models suggest that the aging median voter implies more preferences for pension spending, and thus higher payroll taxes and voting in favor of more labor migration. In practice, however, individual attitudes toward immigration are often found to be negatively correlated with age or to follow a hump-shaped profile, suggesting a more complicated relationship between age and preferences for immigration. Nevertheless, there is also some evidence that natives, and particularly the elderly, living in municipalities with low birth rates are more in favor of immigration. Last but not least, important implications for healthcare policies arise, along with the sustainability of healthcare systems. Young migrants may be positively selected on health, which is not necessarily true for older migrants. Moreover, selective immigration policies play a role in shaping migrants’ health status. Although the interplay between migration and aging has gained some attention, it remains a controversial topic with substantial room for further research. On the supply side, the population age structure has been incorporated as a demographic determinant into migration decision models; nonetheless, further evidence is needed for more countries, including the impact for migrant-sending regions, as well as those of elderly migration and return migration. On the demand side, we must gain a better understanding of labor market needs and immigration effects in the context of an aging population and a shrinking working-age population. Do migrants complement native elderly workers? What are the redistributive effects of immigration in an aging society? Are elderly migrants similar to natives in terms of labor market and retirement behavior? Are elderly migrants more likely to return to their origin country after retirement? What are interregional and international mobility patterns of elderly migrants and the implied changes in the demand for goods and services in the destination and sending regions? What are the implications of higher demand for and increasing mobility of healthcare and eldercare specialists? From a political economy perspective, are aging societies more

Migration and the Demographic Shift

pro-immigrant? What are the impacts for healthcare systems in the receiving (and sending) countries as an increasing number of natives (and migrants) age? Studies concerning these topics are crucial to grasp a better understanding of the interaction between migration and aging, as well as its implications for policies. Overall, in terms of policy implications, immigration is sometimes suggested as a solution to the aging challenge. However, the existing literature is more cautious regarding its actual role and potential. Although selective immigration policies have been argued to possibly contribute to alleviate demographic pressures in the short run, it is unlikely that immigration will increase to the extent that would be needed in the long run. Moreover, the immigration of young and high-skilled immigrants from less-developed countries could exacerbate skill shortages and demographic challenges in those origin countries. It would be important to combine selective migration and labor market integration polices with structural reform policies. Such policies would include proper fiscal and pension reforms, policies aimed at increasing fertility or labor force productivity, as well as those aimed at increasing the labor force participation of marginal groups, such as women and the elderly (see, among others, Bloom and Sousa-Poza, 2013). However, these issues face substantial political resistance. Finally, some authors suggest that temporary and circular migration may constitute a better policy option in dealing with the developed world’s demographic transition and other short-term adjustment pressures. It should be noted, however, that return migration may also decrease the discounted fiscal contribution of high-skilled, middle-aged immigrants (Storesletten, 2000). Nevertheless, temporary or circular migration is an example of a triple-win situation in which both receiving and sending countries, as well as migrants, could benefit, given properly designed pension transferability and other relevant policies, and which may have a rejuvenating effect on aging societies (Bodvarsson and Van den Berg, 2009; Constant et al., 2013; Fargues, 2014).

ACKNOWLEDGMENTS We would like to thank the editors, two anonymous referees; participants of a handbook workshop at Harvard University, as well as Alan Barrett, Deborah Cobb-Clark, Timothy Hatton, Ron Lee, Konstantinos Tatsiramos, and Mehmet Tosun, for very useful comments and suggestions; Simone Sch€ uller for technical assistance with the GSOEP data; and Victoria Finn for editorial support on earlier drafts of this chapter.

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Razin, A., Sadka, E., 1999. Migration and pension with international capital mobility. J. Public Econ. 74 (1), 141–150. Razin, A., Sadka, E., 2000. Unskilled migration: a burden or a boon for the welfare state? Scand. J. Econ. 102 (3), 463–479. Razin, A., Sadka, E., 2014a. Aging and migration: the US and the EU. In: Migration States and Welfare States. Why Is America Different from Europe? Palgrave Macmillan US, New York (Chapter 10). Razin, A., Sadka, E., 2014b. Is the net fiscal burden a proper predictor of the political attitude towards migration? In: Razin, A, Sadka, E. (Eds.), Migration States and Welfare States. Why Is America Different from Europe? Palgrave Macmillan US, New York (Chapter 11). Razin, A., Sand, E., 2007. The role of immigration in sustaining the social security system: a political economy approach. CEPR Discussion Paper No. 6302. Razin, A., Sand, E., 2009. Migration-regime liberalization and social security: political-economy effect. NBER Working Paper No. 15013. Razin, A., Wahba, J., 2015. Welfare magnet hypothesis, fiscal burden, and immigration skill selectivity. Scand. J. Econ. 117, 369–402. Razin, A., Sadka, E., Swagel, P., 2002. The aging population and the size of the welfare state. J. Polit. Econ. 110 (4), 900–918. Razin, A., Sadka, E., Suwankiri, B., 2011. Migration and the Welfare State. Political-Economy Policy Formation. The MIT Press, Cambridge, MA. Rowthorn, R., 2008. The fiscal impact of immigration on the advanced economies. Oxf. Rev. Econ. Policy 24 (3), 560–580. Sandell, S.H., 1977. Women and the economics of family migration. Rev. Econ. Stat. 59 (4), 406–414. Sander, M., 2008. Changes in immigrants’ body mass index with their duration of residence in Germany. SOEP Papers on Multidisciplinary Panel Data Research No. 122, DIW Berlin. Sander, N., Skirbekk, V., Samir, K.C., Lundevaller, E., 2010. Prospects for later-life migration in urban Europe. PLUREL Project. Sjaastad, L.A., 1962. The costs and returns of human migration. J. Polit. Econ. 70 (Suppl.), 80–93. Stark, O., Taylor, J.E., 1991. Migration incentives, migration types: the role of relative deprivation. Econ. J. 101, 1163–1178. Stillman, S., McKenzie, D., Gibson, J., 2009. Migration and mental health: evidence from a natural experiment. J. Health Econ. 28, 677–687. Storesletten, K., 2000. Sustaining fiscal policy through immigration. J. Polit. Econ. 108, 300–323. Storesletten, K., 2003. Fiscal implications of immigration—a net present value calculation. Scand. J. Econ. 105 (3), 487–506. Tanaka, R., Farre, L., Ortega, F., 2014. Immigration, naturalization, and the future of public education. IZA Discussion Paper 8342. Tatsiramos, K., 2006. Residential mobility and housing adjustment of older households in Europe. IZA Discussion Paper No. 2435. Tienda, M., 2013. Multiplying Diversity: Family Unification and the Regional Origins of Late-Age Immigrants, 1981–2009. Mimeo. Tosun, M.S., 2009. Global aging and fiscal policy with international labor mobility: a political economy perspective. IZA Discussion Paper No. 4166. Tosun, M.S., 2015. Retiree migration and intergenerational conflict. IZA World of Labor 118. Tosun, M.S., Williamson, C.R., Yakovlev, P., 2012. Elderly migration and education spending: intergenerational conflict revisited. Public Budg. Financ. 32 (2), 25–39. Turra, C.M., Elo, I.T., 2008. The impact of salmon bias on the Hispanic mortality advantage: new evidence from social security data. Popul. Res. Policy Rev. 27 (5), 515–530. United Nations, 2001. Replacement migration: is it a solution to declining and ageing population? Executive summary. United Nations Population Division. United Nations, 2006. World population monitoring, focusing on international migration and development: Report of the Secretary-General. Commission on Population and Development. E/CN.9/2006/3. United Nations, 2010. Population Facts. International Migrants by Age No. 2010/6. Department of Economic and Social Affairs, Population Division, United Nations, New York. Available at: www. unpopulation.org.

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United Nations, 2012. Population Ageing and Development. Department of Economic and Social Affairs, Population Division, United Nations, New York. Available at: http://www.unpopulation.org. United Nations, 2013a. Department of Economic and Social Affairs. Trends in International Migrant Stock: The 2013 revision (United Nations database, POP/DB/MIG/Stock/Rev.2013). Population Division, United Nations, New York. Available at: www.unpopulation.org. United Nations, 2013b. Population Facts. International Migration 2013: Age and Sex Distribution No. 2013/4. Department of Economic and Social Affairs, Population Division, United Nations, New York. Available at: www.unpopulation.org. Vadean, F.P., Piracha, M., 2009. Circular migration or permanent return: what determines different forms of migration? University of Kent, Department of Economics Discussion Paper No. KDPE 09/12. van den Berg, G., Weynandt, M.A., 2013. Explaining differences between the expected and actual duration until return migration: economic changes. SOEP papers on Multidisciplinary Panel Data Research 497, DIW Berlin, The German Socio-Economic Panel (SOEP). Wadsworth, J., 2012. Mustn’t grumble: immigration, health and health service use in the UK and Germany. IZA Discussion Paper No. 6838. Wakabayashi, C., 2009. Effects of immigration and age on health for older people in the United States. J. Appl. Gerontol. 20, 1–23. Winkelmann, R., Zimmermann, K.F., 1993. Ageing, migration and labour mobility. In: Johnson, P., Zimmermann, K.F. (Eds.), Labour Markets in an Ageing Europe. CEPR, Cambridge University Press, Cambridge, pp. 255–283 (Chapter 10). Yahirun, J.J., 2009. Take Me “Home”: Determinants of Return Migration Among Germany’s Elderly Immigrants. University of California, Los Angeles Center for Population Research, On-Line Working Paper Series, Working Paper No. CCPR-2009-019. Zaiceva, A., Zimmermann, K.F., 2008. Scale, diversity, and determinants of labour migration in Europe. Oxf. Rev. Econ. Policy 24 (3), 428–452. Zaiceva, A., Zimmermann, K.F., 2016. Returning home at times of trouble? Return migration of EU enlargement migrants during the crisis. In: Kahanec, M., Zimmermann, K.F. (Eds.), Labor Migration, EU Enlargement, and the Great Recession. Springer, Berlin, pp. 397–418. Zimmermann, K.F., 1991. Ageing and the labor market: Age structure, cohort size and unemployment. J. Popul. Econ. 4, 177–200. Zimmermann, K.F., Hinte, H., 2005. Zuwanderung und Arbeitsmarkt, Deutschland und D€anemark im Vergleich. Springer Verlag, Berlin Heidelberg. Zlotnik, H., 2012. International migration and population ageing. In: Beard, J.R., Biggs, S., Bloom, D.E., Fried, L.P., Hogan, P., Kalache, A., Olshansky, S.J. (Eds.), Global Population Ageing: Peril or Promise. World Economic Forum, 2011, Geneva, pp. 97–102 (Chapter 20).

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CHAPTER 4

Global Demographic Trends: Consumption, Saving, and International Capital Flows O. Attanasio*,†,{,§, A. Bonfatti¶, S. Kitao║, G. Weber†,{,¶ * University College London, London, United Kingdom Centre for Economic Policy Research (CEPR), London, United Kingdom { Institute for Fiscal Studies (IFS), London, United Kingdom § National Bureau of Economic Research (NBER), Cambridge, MA, United States ¶ University of Padua, Padua, Italy ║ Keio University, Tokyo, Japan †

Contents 1. Introduction Part I. The Overlapping Generations Model 2. The Auerbach and Kotlikoff (1987) Model 2.1 Steady States and Transitions 2.2 Market Structure and Intergenerational Links 2.3 OLG Models and Demographic Trends 3. Extensions to the Model and Methodological Challenges 3.1 Expectations of Demographic Trends and Institutional Arrangements 3.2 Heterogeneity Within Cohorts 3.3 Aggregate and Idiosyncratic Uncertainty 3.4 Moving Away From the Simplest Preferences: Labor Supply and Habits 4. Demographic Trends and Savings 4.1 Closed Economy 4.2 Open Economy 4.2.1 Labor Mobility 4.2.2 Capital Mobility

Part II. A Multiregion Model of the World Economy 5. Demographic Data and Projections 6. Model 6.1 Economic Environment 6.1.1 6.1.2 6.1.3 6.1.4 6.1.5 6.1.6 6.1.7 6.1.8

Preliminaries Technology Demographics Household Preferences Household Endowments Household Budget Constraint Government Budget Constraint Commodities, Assets, and Markets

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7. Calibration 7.1 Preliminaries 7.2 The Four Regions 7.3 Technological Parameters 7.4 Demographic Parameters 7.5 Preferences and Endowments Parameters 7.6 Government Policy Parameters 8. Numerical Results 8.1 Baseline Scenario 8.2 Alternative Scenarios in Low-Income Region 8.2.1 8.2.2 8.2.3 8.2.4

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Fast Productivity Convergence Fast Convergence in Longevity in Low-Income Region Investment Risk in Low-Income Region Additional Experiments

8.3 Summing Up 9. Conclusion References

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Abstract In this chapter we review the recent literature on the effects of changing global demographic trends on consumption, factor prices and social security. We also construct an overlapping generation model with four regions of the world. The model is calibrated so that we match some basic statistics of the last few decades. We assume that the model was in a steady state in 1990, input projected demographic trends, which converge to common values across regions by 2200, and make suitable assumptions on productivity profiles and total factor productivity. This allows us to study the evolution of factor prices, current accounts, and welfare during the transition and explore the differences between open and closed economies, when we limit factor mobility to capital mobility and make different assumptions about future trends in demographics and productivity.

Keywords Capital flows, Demographic trends, Overlapping generations model, Social security reform, China

JEL Classification Codes E21, F21, F41, J11

1. INTRODUCTION Demographic trends in the last century or so have changed dramatically the size and composition of the world population. Developed and mature economies have experienced significant reductions in fertility rates and increases in longevity. Middle-Income countries have started on similar trajectories, although there is a sizeable delay in these trends. Developing countries still have relatively high fertility rates and lag behind in mortality but they are projected to reduce the former and increase the latter. China, which currently accounts for a large fraction of the world population, has gone through the most dramatic changes, induced by the one child policy, which has been followed until very

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recently. This implies large changes in the relative composition of the world population and its age structure in several regions over the next few decades. At the same time, many developing countries have experienced a very high rate of growth that caused their level of output and productivity to start to converge toward that of the developed countries. The experiences of China, India, and other middle-income countries have contributed to reduce the number of people living in poverty substantially over the past 25 years and changed the role that these countries play in the world, both in terms of their economic and political weight. The economic, political, and human consequences of these changes are far reaching. Deaton (2013) in his book The Great Escape vividly discusses some of the impacts that recent developments have had on the health, income, and more generally the well-being of very many people around the world. In a world that is ever becoming more connected and integrated, the interlinkages between the developments in different countries are of fundamental importance. The demand of raw materials sparked by the investment in China has had profound consequences on the performance of some parts of Africa. The demographic trends in Western Europe and the United States imply strong incentives to factor mobility (both labor and capital). And the list could continue. It may be useful, at the outset of this chapter that investigates the economic implications of international demographic trends to discuss some of the main channels through which these trends will affect economic variables. In a stationary equilibrium, in which the new cohorts that enter the economy and start a life cycle in which their productivity increases and then declines up to a point in which they retire from work, the length of the working life of a single individual and their productivity determines the amount that it is necessary to save to maintain certain standard of living in the last period of life. The way in which these savings are made affects in an important fashion various economic variables. For instance, depending on whether consumption during retirement is financed through individual savings held in real assets or through a Pay-AsYou-Go (PAYG) pension system in which part of the earnings of the current work are given to pensioners, the level of the capital stock (and the returns to capital and wages) will be different. Notice that when individual savings are important, during their working lives individuals acquire (through savings) assets, which they will sell (presumably to younger cohorts) during retirement. Dramatic shifts in demographic trends induce important changes in such a situation, regardless of how retirement consumption is financed. A large cohort that enters the economy will presumably face a market where labor is relatively abundant. If such a cohort is followed by a relatively small one, when it retires, it will face relatively unfavorable asset markets, and, therefore, realize relatively low rates of returns on their investment. If pensions, on the other hand, are financed via a PAYG system, the consequences for the large generation are not too dissimilar: there will be a small number of workers to finance each retiree. Indeed, a PAYG system has some similarities with a system financed by individual savings: one can consider the payments into the systems as investment whose return is directly linked to the rate

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of growth of the population. With declining or negative growth rates, the return to PAYG systems can be very low or negative. Until now we have sketched the issues faced by a closed economy whose demographic trends change. Particularly salient are changes brought about by a reduction in fertility and an increase in longevity. The situation becomes even more complicated if one considers open economies where demographic trends are relatively unsynchronized and where only some of the factors of production are (partly) mobile. In such a situation, the relative size of different economies, the productivity of their factors of production, and the degree of mobility of those factors are only relevant to establish the consequences that a certain set of demographic trends have on the economic welfare of the citizens of different countries and regions. There are many ways in which the economic impacts of demographic trends could be analyzed. One could, for instance, rely on a simple descriptive analysis which exploits variation across countries and over time to establish the relationship between demographic trends and economic variables. Such an analysis, however, would not provide an understanding of the mechanisms behind certain correlations. And, given the slowmoving nature of demographic trend, it would be difficult to extrapolate. Alternative theoretical models that consider the presence of individuals of different cohorts include dynastic models and the so-called model of perpetual youth used by Yaari (1965) and Blanchard (1985). In the former, individuals care about their offspring so that, under certain assumptions, a dynasty of individuals behaves like an infinitely lived agent. In the latter, in each year a fraction of the population currently alive dies and is replaced by new individuals. Both of these models, however, make very strong assumptions that all but preclude an in-depth analysis of changes in demographic trends.a The overlapping generation (OLG) model, instead, despite the many unrealistic assumptions that are typically made to make it tractable (analytically or even numerically), provides the natural theoretical structure to synthesize the changes of demographic trends. In this chapter, we will focus on the OLG model, which has been used widely in the literature. The model has a long history, starting with Samuelson (1958) and has been used in a variety of contexts, both to generate theoretical insights and for the empirical analysis of policy reform. The model, or at least the most sophisticated versions of it, makes the demographic structure of the economy under study very explicit, and it seems one of the most appropriate tools for analyzing changing demographic trends. We will therefore discuss both the use that the literature has made of the OLG model and present a quantitative exercise where we use it to understand the impacts of unsynchronized demographic trends in different regions of the world. A general theme that will be central to this chapter is the fact that a global view is key to a proper understanding of the phenomena we are studying, especially if one wants to draw a

Bloom et al. (2007) use the perpetual youth model to investigate the effects of increased longevity on savings. They find that, when retirement age is fixed, longer lives generate more savings. When retirement age is flexible, savings do not change.

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the implications for the design of economic and social policies. It could be extremely misleading to study the implications of the aging of Western societies and Japan for the design of, say, pension and health care reforms, ignoring what is happening to the demographic trends and to economic productivity in other parts of the world. Analogously, when studying the design of tax and benefit systems in middle-income countries where the informal sector still plays an important role, one needs to keep in mind the structure of world demand and the international mobility of factors. The global trends will move factor prices and modify the incentives of individual agents in reaction to specific policies. In a world with perfect mobility of production factors (labor and capital), one would expect factor prices to be quickly equalized, as a result of massive labor migration from high fertility, low capital areas to low fertility, high capital areas. In reality, however, one has to take into account obstacles to factor mobility, ranging from the costs of migration and adaptation, to the financial and political institutions that would guarantee capital mobility. In such a situation, economic models that are sufficiently sophisticated and able to capture the essence of the main economic forces at play are extremely useful and important. Obviously, the perfect model, representing all details and facets of a complex and ever-changing reality does not exist. But the very complexity of the world makes the construction of abstract and simplified models that are able to isolate the main factors affecting the impact of economic policies absolutely essential. This chapter is divided into two parts. We first discuss the existing literature on the use of large OLG models to understand demographic trends. We give examples of how the basic model has been extended in recent years to study global demographic trends and their impacts. We then construct one such model and discuss the results we obtain from calibrating it and simulating transition dynamics. In Part I we start by revisiting the multigeneration OLG model proposed by Auerbach and Kotlikoff (1987) that is ideally suited to study the general equilibrium of an economy that goes through profound demographic changes. We recall the main ideas of this model and discuss what can be learned from it. We then discuss the extensions that one needs to consider to the simplest model to make it sufficiently rich to capture some salient aspects of reality. We also discuss some of the methodological and computational challenges that one faces when developing such a model. We first focus on a closed economy, then explain how the model has been extended to study the global economy. In Part II, we present our calibrated model. This model explores the consequences of the high growth of China (and the high level of Chinese saving) and the possible outcomes of different scenarios for the growth of other regions, such as Africa, with very different demographics. It improves upon earlier work by Attanasio et al. (2006, 2007) that distinguished between developed and developing countries by adding two more world regions to the analysis. We consider explicitly four different regions in the world that have been previously aggregated: “High Income,” “Middle Income,” “Low Income,” and China. We keep separate regions that are at different stages of the demographic transition and have different levels of productivity and productivity growth.

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PART I. THE OVERLAPPING GENERATIONS MODEL As mentioned in the introduction, there are many ways to study the impact that demographic trends have on economic variables. In this chapter, we chose to focus on the OLG model, as it provides a natural framework to incorporate demographic trends in a meaningful and coherent economic analysis. OLG models have been used in economics for a long time. Since Samuelson (1958) contribution, economists realized that this type of models provide a very powerful tool that can be used effectively to describe complex dynamics in economic variables. For instance, the famous paper by Diamond (1965) illustrates how such a model can be used in a very parsimonious way to describe the impact of incomplete markets and the introduction of social security and government debt. Even in very simple incarnations, OLG models can generate extremely complex dynamics. In such models, factor prices are determined by the equilibrium in the capital market. The equilibrium interest rate guarantees that the supply of savings equals the demand for capital, which, at the same time is a factor of production and a way to move resources over time. This dual role of the capital stock and the fact that it is impossible to trade with future generations give a rise to the possibility of dynamic inefficiencies, as discussed, for instance, in Abel et al. (1989).b

2. THE AUERBACH AND KOTLIKOFF (1987) MODEL While the main economic forces at play in such models are evident even in the simplest version, where individuals live for two periods, interacting with their parents when young and with their children when old, to derive their quantitative implications and possibly to bring the models to bear on real world issues, it is necessary to complicate them considerably. The first contribution in a large literature that has extended the simple model to make it reasonably realistic and suitable for policy analysis is the monograph by Auerbach and Kotlikoff (1987) (AK henceforth). AK consider individuals living for 55 periods. In each period, a generation dies and is replaced by a newly born one. At each period, therefore, there are 55 different generations alive. Each individual generation makes consumption and labor supply choices, as in a standard inter-temporal model. Life cycle utility is an additively separable function of single period utilities (discounted geometrically at rate β) that depend on consumption and leisure in each period. Individuals are endowed with an exogenous productivity profile, which reflects the fact that their earning capacity varies with age. Declines in individual productivity (and possibly the presence of a social security system) will induce individuals to retire, that is, not to supply labor. Declines in productivity and therefore earnings over the last part of the life cycle will induce individuals to save in the earlier part b

Dynamic inefficiency cannot arise when there is a fixed factor of production, such as land. Whenever the interest rate falls, the price of land rises, and this absorbs the saving of young cohorts, leaving no room for overaccumulation of capital. See Imrohoroglu et al. (1999).

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of it. The level of savings will obviously depend on the presence of social security (see Feldstein, 1974). There is no uncertainty in the model: individuals know their productivity, their date of death, their wages, and interest rates until the end of their lives as well as government policies. The model considers two other sets of agents: firms and the government. Firms, which are owned by households, produce homogenous output with a neoclassical constant return to scale production function which uses capital and labor. Output can be used as consumption or as capital. Capital accumulates subject to some adjustment costs. Goods and labor markets are competitive, implying that wages are equal to the marginal cost of labor while the interest rate is equal to the marginal product of capital. Wages are also equal to the marginal disutility of labor. The government levies taxes on labor and capital income and consumption. The government might need to finance an exogenous flow of expenditure and might also run a pension (social security) system. The government is infinitely lived and subject to an infinite horizon budget constraint that rules out Ponzi schemes: the present discounted value of government revenues has to equal the present discounted value of its layouts. While extremely stylized, this model constituted an important contribution as it allowed the use of OLG models to analyze a number of policy-relevant issues, ranging from the effects of different demographic trends on the sustainability of the US Social Security system, to the choice of different fiscal instruments, in a realistic and quantitatively salient fashion. Obviously, even with the assumptions on the utility function (such as the CES specification AK use to represent preferences over consumption and leisure), the possibility of corner solutions in leisure (so that individuals retire) implies that it is not possible to derive analytical solutions for the equilibrium of the model. One of the innovations introduced by AK was a relatively simple and intuitive solution method that allows the simulation of this class of models and their use for policy analysis.

2.1 Steady States and Transitions The solution method proposed by AK starts with the derivation of the steady states of the model under different policies or demographic trends. The transition between the steady states is then computed exploiting the intuition that the evolution of the system can be summarized by a single state variable: the capital/labor ratio. Such variable determines factor prices, that is, interest rates and wages. Given a path of factor prices, individual households will choose labor supply, consumption, and savings. Aggregating the savings of different generations and their labor supply then generates the aggregate capital stock and aggregate labor supply. The equilibrium is determined by finding a fixed point in the capital labor ratio. While the solution method proposed by AK is very attractive, partly because it is very intuitive, it relies heavily on the assumption that a single state variable determines factor prices and, effectively, the supply and demand of capital and labor. Whenever such an

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assumption is violated, the method cannot be applied. There are many situations in which such an assumption is violated. An important case we discuss briefly below is the presence of aggregate uncertainty. Another interesting case, which we also mention below, is when demographic variables are themselves slow-moving random variables. In this situation, the current state of the demographic variables (which could be multidimensional) would also constitute an additional state variable.

2.2 Market Structure and Intergenerational Links In the basic model, the only asset available to individual households to transfer resources to the future (for instance to finance consumption in the last part of life when individual earning capacity declines) is the capital stock. Individuals therefore will accumulate capital in the first part of the life cycle and decumulate it in its last part. The relatively young will purchase capital from the relatively old. The net supply of capital and the demand for it by firms will determine the equilibrium capital stock which, together with the equilibrium labor supply, will determine the equilibrium interest rates and wages. This very simple market structure already imbeds, in a fairly natural way, a substantial deviation from the complete market paradigm that is sometimes used in aggregate models. The fact that is not possible to trade with future generation, as mentioned above, is at the origin of potentially important dynamic efficiency. With certain preference, specifications and assumptions about the production function can generate dynamic inefficiencies, situations where “too much capital” is accumulated to finance consumption in old age determining an inefficiently low level of the interest rate, possibly below the rate of growth of the population. In such a situation, as noted by Diamond (1965) the introduction of national debt or a social security system can alleviate and even eliminate the dynamic inefficiencies. The availability of national debt constitutes an alternative tool to move resources to the future which reduces this role of the capital stock. The introduction of an unfunded social security system, where social security contributions from individuals currently working are used to pay the pensions of individuals currently retired, reduces the incentive to save and, again, increases the equilibrium interest rate.

2.3 OLG Models and Demographic Trends Even the simplest OLG model has a well-specified demographic structure. It is relatively simple to introduce age-specific mortality and fertility rates. The model therefore constitutes a natural vehicle to study demographic trends. Individuals belonging to different generations will be on different sides of the market for assets. Therefore, changes in the size of different cohorts will have important consequences for the equilibrium in these markets, and therefore on the return to capital and, given the standard assumptions on the production function, on wages and labor income. Population aging induced by increases in longevity and reduction in fertility, can have particularly substantial effects

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especially during the transition from a steady state to another, as a large cohort is followed by a relatively smaller one. The AK model provides a useful tool to quantify these effects in a realistic fashion. A number of studies have looked at these effects, such as Geanakoplos et al. (1998), Abel (2001a,b, 2003), and Poterba (2001, 2004). In what follows we will explore similar ideas, using the basic intuition that demographic changes affect, on the one hand, the supply of labor and, on the other, the supply of saving. In a standard model, in the absence of pension systems, the young are savers and the old are dissavers. The relative sizes of these groups determine the supply of aggregate savings and, together with the supply of labor, the equilibrium interest rate. Demographic trends are important in the OLG model because they determine the supply and demand of production factors and, therefore, their prices. The papers cited so far have often focused on domestic demographic trends, often in the context of large developed economies, such as the United States. In the presence of large demographic shifts that might not be fully synchronized across different regions of the world, if there is some degree of factor mobility (either labor or capital—and possibly even commodities), it becomes important to consider the evolution of global demographic trends. To quantify the effects of these global shifts, however, it will be necessary to take a stance on the degree of factor mobility, on the specific old age arrangements in different regions, and on the level of factor productivity in different countries. We discuss these issues in detail in Section 4.

3. EXTENSIONS TO THE MODEL AND METHODOLOGICAL CHALLENGES While the model presented by AK is a rich one, it is also very stylized in many dimensions. In this section we briefly discuss extensions to the basic framework that have been considered in the literature. Some of these extensions present important methodological and numerical problems.

3.1 Expectations of Demographic Trends and Institutional Arrangements In most models in the literature, economic agents are endowed with rational expectations or perfect foresight about most of the model’s variables. However, they might be completely surprised by changes in demographic trends or public policies, in that they did not consider even the possibility of such changes. The standard OLG model starts from a steady-state equilibrium where agents assume that the current equilibrium (with certain fertility and mortality rates, pension arrangements, and taxation) will persist forever. These beliefs matter for their choices because, of course, future factor prices, including wages and interest rates, are affected by the behavior of future demographic trends and policy variables. Agents are, to an extent, not fully rational because they do not consider the possibility of such changes. That is, in the initial equilibrium they do not

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consider the possibility that the demographic structure of the economy (fertility and mortality rates) might change. When it does change it is the realization of a zero probability event. More sophisticated agents might take into account the fact that demographic variables (fertility, longevity) move, slowly, over time in an uncertain way. One of the few papers that addresses this issue is Rios-Rull (2001) that models demographic trends as slow-moving random variables over which economic agents form rational expectations. While it is debatable whether agents actually form expectations over such variables, fully understanding what their effects on future factor prices would be, such an approach is certainly intellectually coherent. Similar issues arise when considering the institutional environment. For instance, certain institutional arrangements for public pensions might be clearly financially unsustainable and should imply substantial adjustments in terms of benefit payments or contribution rates. However, these adjustments can occur in many dimensions. From the point of view of an individual agent belonging to a certain cohort, the consequences of a reduction of future benefits vs an increase of future contributions can be radically different. Boersch-Supan et al. (2006), for instance, consider the different consequences of reforming a PAYG pension system reducing benefits or increasing contributions. And yet, it is not clear how to model the way individuals perceive the possibilities of these alternative reforms. Some of these issues are obviously related to the political economy of economic reforms, as they affect different groups in the population differently. A few papers, such as Galasso (1999), have addressed this type of problems (see also Galasso and Profeta, 2002, for a survey).

3.2 Heterogeneity Within Cohorts Many of the papers that simulate large-scale OLG models focus on heterogeneity across cohorts (in, say, life expectancy or fertility) but assume that the members of a given cohort are homogeneous. For the analysis of certain policies, however, such as different ways of financing deficits or pension programs or pension reforms, it is important to allow for heterogeneity within a cohort. In the literature, there are important exceptions. The paper by Altig et al. (2001), for instance, allows for a substantial amount of heterogeneity within a cohort. In particular, Altig et al. assume that each cohort is made of 12 different groups of individuals that differ in term of their endowment of human capital and the rate of growth of human capital over the life cycle. These groups, which also differ in their preferences on bequests, are meant to capture different education groups in the population, whose earnings-age profile differ in shape and level. Labor supply is determined within the same maximization problem that determines consumption and saving choices: the utility function is assumed to depend on hours of leisure and consumption. Armed with this model, the authors consider the implications of different tax structures in the United States. This is an interesting study as it presents the consequences of alternative

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policies within a coherent framework which incorporates many different incentives and distortions, from the incentives to supply labor to the incentives to save. This paper, however, does not analyze the impact of changes in demographic trends, as it is focused on the differential effects of alternative taxation policies. Another strong assumption made in the Altig et al. (2001)’s paper is the presence of a unique type of human capital. In other words, different skills are perfect substitutes in the production function and different individuals differ only for the total amount of skills that they command. Alternatively, one could assume that different skills are less than perfect substitutes in the production function and, therefore, introduce another important margin of adjustment. In this case, one would have different wages for each skill type that would depend on the relative demand and supply of such skills as well as the parameters of the production function. This type of models can be particularly useful in modeling the impacts of the accumulation of different types of skills. Binelli (2014), for instance, uses an OLG models where individuals can acquire different levels of education and where the production function uses four different types of labor. She uses this model to explain what she calls the “convexification” of the returns to education in Latin America. A similar structure could be used to study the impact of different demographic trends in a richer way. Another interesting dimension of heterogeneity is that in preferences. Individuals within a cohort or in different countries might be different because of differences in discount factors, risk attitudes, or aspects such as altruism and reciprocity. In a recent paper, Falk et al. (2015) document important and systematic differences in preferences as elicited in a large and rigorous survey. Such evidence could be used in future research when building large global models. Differences in discount factors could, for instance, be able to match differences in observed capital labor ratios across different regions. The consideration of this level of heterogeneity, however, also involves some modeling challenges, especially when considering long-run simulations. For instance, if one allows for different level of discount factors in different regions, in the very long run, most of the capital stock will be allocated into the more patient region.

3.3 Aggregate and Idiosyncratic Uncertainty In the standard AK model, there is no uncertainty. Some sources of uncertainty, such as that about life span, are easily introduced into the model. Further elements of uncertainty, such as uncertainty about individual productivity, can also be introduced in a relatively straightforward manner, as long as there is no aggregate uncertainty. This is done, for instance, in Imrohoroglu et al. (1995) and Conesa and Krueger (1999). The introduction of aggregate shocks in general equilibrium models where markets are incomplete, however, is very hard. The difficulty arises because with aggregate shocks, factor prices are uncertain and depend not only on aggregate supply and demand

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of capital but also on their distribution in the population. Therefore, factor prices will depend on an infinitely dimensioned object. Krusell and Smith (1998) introduced an ingenious and useful solution method that allows the treatment of models with aggregate uncertainty and incomplete markets. In particular, they approximate the solution to the model assuming that, rather than on the entire distribution of assets in the cross section, aggregate prices depend on a few moments of the same distribution. This approximation allows a substantial reduction in the dimension of the problem and, therefore, the numerical study of this class of models. Krusell and Smith (1998) study an economy populated by infinitely lived consumers. In that context, the difficulty arises because the absence of complete markets does not allow the diversification of idiosyncratic risk. In the case of OLG models, market incompleteness arises naturally given the impossibility of writing contracts with future generations. In this context, several studies have considered different numerical methods to obtain a solution of the equilibrium. Storesletten et al. (2007), for instance, apply the Krusell and Smith method to OLG models. Krueger and Kubler (2003) use alternative numerical methods to solve this class of models. While we are not aware of multi country OLG models with aggregate uncertainty of the type we are considering below, it might be an interesting exercise to explore the extent to which some of the predictions of the existing models are robust to the introduction of these features. An important issue, of course, is the extent to which aggregate shocks are insured across countries. There exists a large empirical literature (see, for instance, Becker and Hoffmann, 2006; Kim et al., 2006; Kose et al., 2009; Baxter, 2012; Fuleky et al., 2015) that shows only very limited risk sharing of country-specific shocks.

3.4 Moving Away From the Simplest Preferences: Labor Supply and Habits The stylized (or stripped-down) version of the life-cycle model assumes that consumers supply labor inelastically (they work full time until they reach retirement age, then stop working completely, irrespective of the wage rate). This strong assumption is relaxed in the AK model, where consumption and leisure enter nonadditively in each period’s utility function—the elasticity of substitution between consumption and leisure governs the response of labor supply to the real wage rate, at least until retirement age (after retirement age consumers are not allowed to work any longer). Boersch-Supan et al. (2006) show that the exact value of this parameter is very important in assessing the response to—for instance—a pension reform that shifts the burden of a PAYG pension system from the workers (higher contributions) to the newly retired (lower benefits). Of course, once labor supply is endogenously determined one needs to be explicit about the way productivity (and wages) varies with age: endogenous retirement will occur if the wage offer is sufficiently low that the consumer prefers not to work (fixed participation costs may also play a role).

Global Demographic Trends: Consumption, Saving, and International Capital Flows

There is a large literature in labor economics that discusses the importance of extensive margins, especially when considering female labor supply (see, for instance, Chetty et al., 2013, for a recent contribution and citations). Family labor supply is rarely considered within large OLG models. And to a large extent, many contributions focus primarily on the intensive labor supply margin, rather than the extensive one. The reason for this simplification, of course, is that the individual decision problem becomes much more complex if one allows for different labor supply decisions.c And yet, labor supply is key to determine the extent to which certain demographic trends (such as the aging of the population) trickle into implications for factor prices and, ultimately, for the welfare of different generations. In some countries, the effect of the aging of the population on the size of the labor force might be muted if it is accompanied by an increase in the labor force participation by women. Moreover, reductions in fertility are likely to be associated with increases in labor force participation by women (opening up what is sometimes called “the demographic window”). Much work needs to be done in this dimension. All papers that follow the AK approach assume that preferences are additive over time, thus ruling out the type of history dependence in utility that is required for durability and habits (see Hayashi, 1985, for an early paper that argues history dependence is important). Habits in preferences have instead been extensively assumed in the macrofinance literature. For instance, Campbell and Cochrane (1999) show that a particular form of habit dependence (known as external habits) is required to explain a variety of dynamic asset pricing phenomena, including the equity premium puzzle. Habits in preferences can also explain some of the extremely high savings observed across all age groups in fast-developing countries like China, as pointed out in Attanasio and Weber (2010). A possible explanation for the tendency by older individuals in fast growing economies to keep saving is that their desired consumption level is heavily influenced by the low standard of living they were used to in their early years. If we add a bequest motive to the model we would predict that they keep saving in old age and then bequeath considerable wealth to their children, despite the fact that their children are much better off in a life-cycle sense than them. The model we present in Part II takes into account the existence of different propensities to save across world regions that converge to a common value in the very long run, but does not explicitly take habits into account.

4. DEMOGRAPHIC TRENDS AND SAVINGS As mentioned above, the OLG model is a very useful tool to study the impact of changes in demographic trends on various economic variables. In such a model (and in reality), as c

Another dimension that is neglected is how decisions are made within the household. Much evidence rejects the unitary model of individual decisions—see Browning et al. (2014) for a recent appraisal. We are not aware of any studies that have considered alternative intrahousehold allocation models within an OLG framework.

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individuals go through their life cycle they will accumulate and decumulate assets. This behavior, which is likely to be affected by pension arrangements and social security, will determine the demand and supply of assets in the economy. In this chapter we will briefly discuss the implications of demographic trends for savings and for the sustainability of different pension systems. In a closed economy, the demographic trends of that particular economy will determine, in conjunction with its institutional arrangements (such as the pension and social security system, the availability of annuity markets to diversify individual longevity risks), the demand and supply of assets and, therefore, will affect the equilibrium factor prices. The main forces at play will be the relative supply of human capital (possibly of different types of human capital) and physical capital, which is accumulated as the result of saving decisions by individual households, as well as changes in Total Factor Productivity, as emphasized in Chen et al. (2007). The link between demographic trends and the welfare of different generations is intuitive and very direct. In general, a large size generation, preceded and followed by smaller generations, due, for instance, to a temporary increase in fertility rates (as it happened with the baby boom), is likely to suffer in the OLG model: their relatively large size will imply relatively low wages during their active years. On the other hand, when they retire and live off their savings, capital will be relatively abundant and its return will be low. In an open economy these impacts can be reversed or attenuated if the demographic trends are not similar across countries or regions. The effects will depend on the relative size of the trends as well as on the specific institutions that limit (or facilitate) factor mobility. In what follows, we discuss some of the existing contributions that have looked at this set of issues. In our opinion, this is an area of research in which much progress is needed to incorporate more realistic models of factor mobility. Before discussing the studies that have analyzed open economies, however, we briefly summarize some of the papers that have considered demographic trends within closed economies.

4.1 Closed Economy The approaching retirement age of the baby boom generation (coupled with a marked overall increase in longevity) raises a concern on the sustainability of all Pay-As-You-Go public pension systems. The US Social Security System, for instance, would start paying out ever larger benefits, and this would require increasing contributions for currently working younger generations. De Nardi et al. (1999) tackle this issue by building a closed-economy applied general equilibrium model and incorporating the population projections made by the Social Security Administration to evaluate the macroeconomic and welfare implications of alternative fiscal responses to the retirement of the baby boomers. They calculate that maintaining benefits at (the then) current levels would be difficult because the increases in distortionary taxes required to finance them would reduce private saving and labor supply.

Global Demographic Trends: Consumption, Saving, and International Capital Flows

A possible response to this concern has been to push for privatization of the Social Security System, as discussed in the influential volume by Feldstein (1998) that also documents the experience of five countries that have taken this path in recent years. Geanakoplos et al. (1998) note that “advocates of social security privatization argue that rates of return under a defined contribution individual account system would be much higher for all than they are under the current social security system.” This claim, however, ignores accrued benefits already promised based on past payroll taxes, and underestimates the riskiness of stock investments. It is true that a reform toward a fully funded system would let the large fraction of (constrained) individuals, who do not own stocks reap the benefits of the equity premium, but this would raise current stock prices and lower future returns, thus hurting young (unconstrained) households. Abel (2001a) in fact notes that the aggregate capital stock could be reduced as a result. Suppose the fully funded defined-contribution Social Security system tries to exploit the equity premium by selling a dollar of bonds per capita and buying a dollar of equity per capita. In this context, consumers who save but do not participate in the stock market increase their consumption. The general equilibrium response to this policy could be a reduction of the aggregate capital stock that Abel computes to be about 50 cents per capita. The issue of whether a move toward a privatized social security system is welfare enhancing has been addressed in other papers, that explicitly consider the labor supply effects of such a reform, and stress the importance of the nature of the stochastic income process. Nishiyama and Smetters (2007) analyze one specific reform of the US Social Security system (a 50% privatization) and find that privatizing social security can not only produce efficiency gains by improving labor supply incentives but also reduce risk sharing. When there is purely idiosyncratic risk in wages and the earning process is dominated by transitory shocks they find that privatization produces small or no efficiency gains. Huggett and Parra (2010) consider not only the optimal reform of the Social Security and income tax systems together for a given cohort but also a more limited reform that chooses the Social Security benefit function but keeps income tax as is. In the more radical case, the social planner chooses a life-time income tax (that is present value neutral to the current system) under incentive compatibility constraints. The incentive problem arises because the social planner observes earnings but not hours of work or hourly wages. They also focus on idiosyncratic risk and find large efficiency gains when all shocks are permanent: high productivity workers work too little and low productivity workers work too much under the current US system compared to the solution of the planning problem. However, if all (or most) shocks are temporary, the radical reform produces almost no gain; the more limited one produces only a small gain.d d

McGrattan and Prescott (2015) address the politically sensitive issue of how to ensure that the transition toward a privatized system does not penalize the older cohorts, that are already retired and would not benefit from reduced payroll tax.

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The other concern that the retirement of the baby boom generation has raised has to do with the so-called “asset market meltdown” hypothesis. Financial market analysts associate the aging of this cohort to the rise in US asset values during the 1990s, and predict asset price declines when this group reaches retirement age and begins to decumulate its wealth. Abel (2001b, 2003) has used a two-period OLG model to analyze this issue— in this context, the price of capital first increases and then falls, in agreement with the hypothesis. Poterba (2001, 2004) argues that this type of models fails to capture the notion that most individuals do not in fact decumulate their assets in old age as fast as the OLG model assumes, and shows that demographic effects on asset prices are relatively minor. He concludes that there is “modest support, at best, for the view that asset prices could decline as the share of households over the age of 65 increases.” Pensions and the arrangement to finance the consumption of retirees are only one consequence of changing demographic trends and population aging in particular. The latter is likely to increase the need for medical care and health expenditure. Although in the exercise we perform we do not focus on this issue a number of recent interesting papers have looked at this set of issues. Kitao (2014), for instance, present reform options to make social security system in the US sustainable under aging demographics. Braun and Joines (2015) and Kitao (2015) investigate the fiscal imbalances due to population aging in Japan, considering both the increase in pensions and health care spending. Attanasio et al. (2011) study consequences of Medicare reforms. De Nardi et al. (2010) consider a model where medical expenses play an important role in the saving behavior of the old. Kopecky and Koreshkova (2014) study effects of nursing home expenses on life-cycle savings and Braun et al. (2016) consider welfare effects of social insurance at old ages. Recent papers address the issue of the likely increase in health care spending brought about by increased longevity—Dobrescu (2015) investigates its consequences on household saving once the choice between formal and informal insurance is considered, whereas De Nardi et al. (2016) investigate the distributional consequences of existing public programs, such as Medicaid.

4.2 Open Economy When considering the effect of changes in demographic trends it is important to consider the global economy, made of different regions with different levels of technological progress and factor endowments, especially if the focus of the analysis is on the impacts that demographic trends have on economic variables and intergenerational welfare under different fiscal policies and pension arrangements. A naive approach would be to consider the entire world as a closed economy. However, in the presence of limitations to production factors mobility (either labor or capital), such an analysis would be very misleading even if different levels of productivity are somehow allowed for using efficiency units. An important point to notice is that when considering a global model with some but not full

Global Demographic Trends: Consumption, Saving, and International Capital Flows

factor mobility and productivity differentials even when making the assumption of constant return to scale on production, the size of different economies will matter to determine the equilibrium factor prices. 4.2.1 Labor Mobility A few papers have considered the role of immigration policies aimed at countering the adverse effects of the retirement of the baby boom generation on the government budget and on the economy as a whole. For instance, Storesletten (2000) uses a calibrated general equilibrium OLG model of the AK type to investigate whether a reform of immigration policies could resolve the fiscal problems associated with the aging of the baby boom generation. His model captures the first-order effects of immigration: an inflow of working-age immigrants increases tax revenues per capita and reduces government debt and government expenditures per capita. When immigrants retire, these effects are reversed. A general equilibrium analysis is required since the government budget is also affected through increases in interest rates and decreases in wages due to a decline in capital–labor ratio (if capital does not flow into the country in response to immigration). Higher interest rates increase the cost of servicing the public debt, and lower wages reduce tax revenues. Storesletten notes that both age and skill levels of the new immigrants are potentially important. In fact, given the progressivity of the tax system, if skilled workers immigrate and pay taxes, the net fiscal effects are large and positive, even when the gains are traded off with the subsequent costs of retirement. Young immigrants, on the other hand, alleviate the demographic imbalance that characterizes most developed countries, but without a period of childhood. Therefore Storesletten argues that selective immigration can mitigate some of the fiscal burden associated with the aging of the baby boom generation and serve as an alternative to tax hikes or spending cuts for financing future fiscal deficits. Storesletten finds that an increased inflow of working age high- and medium-skilled immigrants can work. Fehr et al. (2004) question some of the policy implications of Storesletten’s analysis. They develop a three-region dynamic general equilibrium OLG model to analyze immigration policies during the demographic transition. They focus their analysis on three developed regions (the United States, Japan, and the EU)—the effects of migration on the developing (donor) countries are not considered. In this context, various factors are at play in general equilibrium that may limit the role played by immigration. First, increased immigration not only raises the size of the labor force but also lowers real wages. This limits the increase in the taxable wage base due to immigration. Second, Fehr et al. assume that immigrants arrive with some capital and they also accumulate more capital as they age, which raises labor productivity. Third, immigrants require public goods and become eligible for welfare state benefits. As pointed out by Storesletten, immigration of high-skilled workers is more beneficial for the government because taxes and transfer payments are collected and distributed on a progressive basis. Fehr at al.’s model confirms

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this point, but shows that a significant expansion of immigration, whether across all skill groups or among particular skill groups, does little to alter the major capital shortage, tax hikes, and reductions in real wages that can characterize the demographic transition. According to Fehr et al. (2004), even a doubling of high-skilled immigrants would leave the developed world with a major fiscal crisis in its hands. They also notice that increasing skilled immigration sounds easy, but is not. Most skilled workers live in the United States, the EU, and Japan: moving a high-skilled worker from one of these regions to another is not a solution for the developed world as a whole. In a follow-up paper, Fehr et al. (2006) add a fourth region to their model: China. This has a dramatic impact on their model’s predictions. In fact, even though China is aging rapidly, its saving behavior, growth rate, and fiscal policies are very different from those of developed countries. If this continues to be the case, China eventually becomes the world’s saver and helps resolve the developed world’s problems in terms of long-run supply of capital and general equilibrium prospects. 4.2.2 Capital Mobility Labor mobility is a possible solution to population aging of developed countries, but large-scale immigration poses important political and social challenges to the receiving, developed countries. Also, the supply of high-skilled workers that developed countries would ideally want to attract from developing countries is limited, and migration flows of this type of workers from developing to developed countries may increase world regional imbalances and threaten world growth and peace. A much less challenging solution to the demographic imbalance of the developed countries is capital mobility. Rather than importing labor, developed countries can invest part of their capital in developing countries, thus contributing to their growth now and generating capital income flows for their retirees in the future. Early papers that link the demographic world imbalances to capital flows across world regions include Miles (1999), Brooks (2000, 2003), and Lim and Weil (2003). Attanasio et al. (2006, 2007) and Boersch-Supan et al. (2006), instead, address the issue of pension reforms in a world with capital mobility but no, or limited, labor mobility. Attanasio et al. (2006, 2007) develop a two-region general equilibrium OLG model calibrated to the North (more developed countries) and the South (less developed countries). In their 2006 paper, Attanasio et al. evaluate quantitatively the impact of the observed demographic transition on aggregate variables (factor prices, saving rate, output growth), and on inter-generational welfare in developing economies. They find that the effects of the demographic trends for less developed regions depend on the degree of international capital mobility and the extent to which the large Pay-As-You-Go systems in place in the more developed world are reformed. In their 2007 paper, Attanasio et al. investigate the sustainability of the current social security systems in the developed economies, given the projected demographic trends, still using the two-region model

Global Demographic Trends: Consumption, Saving, and International Capital Flows

(South and North) of the world economy described above in the two polar cases where capital cannot or can freely flow across regions. Every country in the developed world (the North) faces quantitatively similar demographic trends and the same issue of how to reform their PAYG pension system. In contrast, in the developing world (the South), large-scale social security systems are absent and the demographic trends are markedly different from those of the North. Roughly speaking, the demographic transition in the South lags the one in the North by seven or eight decades. This lack of synchronization in the demographic trends between North and South generates, in a two-region open-economy model, major economic forces, that are suppressed in the closed economy model. The objective of the paper is to study whether the quantitative implications of various social security reforms for policy variables, factor prices, macroeconomic aggregates, and welfare of different cohorts in the North are sensitive to the benchmark adopted, i.e., closed vs. open economy. Attanasio et al. perform two types of policy experiments. First, they assume that the North retains a PAYG scheme and examines several options to finance the system through the demographic transition. Second, they assume that the PAYG will be gradually transformed into a fully funded system, and study alternative ways of financing this privatization. They perform all these experiments under both scenarios (open and closed economy). Their main conclusion is that if one is interested in quantifying the path of the fiscal variables needed to keep the social security system viable or to finance a transition toward a fully funded system, then these two scenarios yield similar results. However, if the focus is on quantifying the path of factor prices, aggregate variables and, ultimately, welfare, then the two scenarios can diverge significantly. Boersch-Supan et al. (2006) develop a multicountry computational general equilibrium model and discuss its public pension reform implications with special reference to three large European economies. They feed their multicountry overlapping-generations model with long-term demographic projections for seven world regions, and consider different degrees of flexibility in international capital markets (from no international capital flows allowed to full capital mobility across all regions, going through intermediate cases where capital mobility is restricted to the EU, or to EU and OECD countries only). They find that population aging and pension reform have profound effects on international capital markets. Aging results in decreases in saving rates when the baby boomers decumulate their assets. International capital flows follow this trend. The countries most affected by aging, such as those in the European Union, will initially be capital exporters, while countries less affected by aging, such as the United States and other OECD regions, will import capital. However, since it is older households that decumulate their assets, capital exports from the rapidly aging countries will decrease, and by around the year 2020, such countries are projected to start importing capital. Pension reforms with higher degrees of prefunding induce more capital exports; they also increase labor supply considerably, while their effects on the rate of return to capital are small. While the rate of

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return on capital is projected to decline in response to population aging, no ‘asset market meltdown’ is predicted. In their analysis of pension reform (from PAYG to fully funded systems in the three European countries under investigation), Boersch-Supan et al. highlight the role of labor supply responses. If the elasticity of substitution between leisure and consumption is sufficiently high, the effects of the reform are largely absorbed by changes in labor supply. Krueger and Ludwig (2007) also employ a multicountry large-scale OLG model to quantify the impact of the demographic transition toward an older population in industrialized countries on worldwide rates of return, international capital flows, and the distribution of wealth and welfare in the OECD. Their model has two key features: capital flows freely within the OECD (but not outside it), and there is uninsurable labor productivity and mortality risk. Uninsurable idiosyncratic uncertainty implies that some agents derive most of their income from returns to capital, while others mainly have labor income. This heterogeneity allows a meaningful analysis of the distributional consequences of changes in factor prices. They find that for the United States as an open economy, rates of return are predicted to decline by 86 basis points between 2005 and 2080 and wages increase by about 4.1%. Remarkably, they find that if the United States were a closed economy, rates of return would decline and wages increase by less. This is due to the fact that other regions in the OECD tend to age even more rapidly; therefore the United States is “importing” the more severe demographic transition from the rest of the OECD in the form of larger factor price changes. In terms of welfare, their model suggests that young agents with little assets and currently low labor productivity gain, up to 1% in consumption, from higher wages associated with population aging. Older, asset-rich households tend to lose because of the predicted decline in real returns to capital. The case of incomplete capital market mobility (subject to adjustment costs) is considered in other papers, such as Fehr et al. (2008).e

PART II. A MULTIREGION MODEL OF THE WORLD ECONOMY In this part of the chapter, we build and analyze a multiregion model of the world, where labor mobility is restricted, and compare what happens with and without capital mobility. Labor and capital prices are set competitively, and consumption goods are allowed to e

Fehr et al. (2013) instead use a model with three different skill levels of workers across five world regions to study the impact on income inequality of the worldwide increase in low-skill labor force brought about by the demographic transition. They assume that in each region the proportions of workers by skill level do not change over time and there are both tradable and nontradable goods. They compare the case where factor prices are equalized across regions (offshoring) to the case where they are instead region specific. Their key finding is that offshoring raises GDP and increases growth rates, but has a major negative effect on low-skill workers in developed countries (and a smaller, positive effect on low-skill workers in developing countries).

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travel without restrictions in the open economy. We take into account the existence of social security systems that are much more generous in developed countries compared to developing countries. We explicitly consider the presence of a large, fast developing country, China, that has a rapidly aging population structure due to much lower fertility than other countries at a similar stage of economic development. The purpose of this exercise is to provide a rigorous and quantitative account of the impacts that demographic changes can have on a variety of economic variables, ranging from wages and interest rates, to the life cycle welfare of different generations. While we are forced to make a number of simplifying assumptions to make the analysis feasible, the model we build and calibrate is useful because it allows us to perform a number of counterfactual exercises where we can vary both different demographic trends and different variables that determine the policy environment. We extend several papers that we discussed in the literature review part of this chapter, starting from the seminal contribution by Auerbach and Kotlikoff (1987). In particular, we build upon the existing general equilibrium, two-region OLG model pioneered in papers by Attanasio et al. (2006, 2007) by using more recent and more disaggregated data on demographic trends and economic growth in four different world regions. We also explore the consequences of the growth in China (and the Chinese saving behavior) and the possible outcomes of different scenarios for the growth of developing regions, such as Africa, with very different demographics. These issues are important at different levels. In equilibrium models with several regions, their relative size (which evolves as a consequence of differential demographic trends and differential productivity growth) matters both for factor flows and for their prices. And of course, the outcomes will depend on the degree of capital and labor mobility. In developing countries, where fertility rates are still relatively high but are projected to decrease quickly, there is also the issue of the so-called demographic window. It has been argued that decreases in fertility are associated with increased participation in the labor market by women, which might have important aggregate consequences in factor prices. To take into account these new developments we consider explicitly four different regions in the world that previously had been aggregated. The level of aggregation depends on the synchronization of projected demographic trends and productivity growth. We keep separate regions that are at different stages of the demographic transition and have different levels of productivity and productivity growth. Even though we do not explicitly model labor supply (and in particular female labor supply), we take into account that decreased fertility, and to a lesser extent increased longevity, may result in increased labor force participation. This demographic window is a mechanic consequence of the new demographic structure since there are more working age individuals in the overall population. An additional input to the demographic window can be the result of changes in female labor force participation, brought about by reduced child-care

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needs. The former mechanism has long exhausted its growth potential in most developed countries, but is playing an increasingly important role in many developing countries. The latter mechanism largely depends on how real wages change in response to population trends, the process of industrialization that is taking place in developing countries at the moment and capital as well as labor flows across the various world regions. Taking into account all these factors, we split the world in four regions: “High Income” (United States, Europe, Japan, Canada, Australia, and New Zealand), “Middle Income” (Latin America and the Caribbean, Russia, Turkey, India, South Korea, Taiwan, Thailand, and South Africa), “Low Income” (the rest of Africa, other parts of Asia, and Oceania), and China. Changes in demographic trends have important implications on factor prices and, as a consequence, on the relative welfare of different generations. The same trends that make Pay-As-You-Go systems unsustainable in the long run (or imply very high levels of labor taxation) induce, in closed economies with unfunded pension systems, factor prices movements that hurt certain generations. In particular, baby boomers are hurt in the labor market through lower wages and in the capital market after they retire through lower interest rate. But in open economies factor mobility may attenuate these effects if demographic trends are not fully synchronized. This is one of the issues we explore in this part. To summarize, in this part we construct an OLG model with four regions of the world. The model is calibrated so that we match some basic statistics of the last few decades. We start the model simulations in a steady state that approximates the economy of the four regions in 1960, input projected demographic trends and assume that a new steady state is reached in some hundred years, and make suitable assumptions on productivity profiles and total factor productivity. This allows us to study the evolution of factor prices, current accounts, and welfare during the transition and explore the differences in factor prices, current accounts, and welfare between open and closed economies, when we limit factor mobility to capital mobility and make different assumptions about future trends in demographics and productivity.

5. DEMOGRAPHIC DATA AND PROJECTIONS In this section we present some projections that motivate our choice to consider a fourregion model of the world economy. In the first graph (see Fig. 1) we show total fertility rates from 1950 until 2100. The bold line represents High-Income countries: we see a marked decline in fertility over the second half of last century, from a number close to three in 1950 to 1.5 in the 1990s. The demographic projections we use assume a slow convergence to the 2.1 fertility rate that is consistent with a steady population in a closed economy with stable life expectancy. The Middle Income dotted curve starts around 5.5 in 1950, but has already reached the 2.1 mark by the beginning of this century—the

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7 High Middle Low China

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Year

Fig. 1 Total fertility rates.

countries of this region have fully enjoyed the effects of the demographic window, and now face a fairly stable fertility path. Low-Income countries (represented by a broken line) saw a peak in their fertility rate around 1960—at a very high value (exceeding 6)—and are now experiencing a rapid decrease in fertility, but are still well above the 2.1 mark that will not be reached until the end of the century. Finally, China displays the most interesting fertility pattern: after a dip in the 1950s, there was an increase to values close to six, followed by an abrupt fall in the 1960s and 1970s, as a result of draconian governmental policies to limit population growth (the so-called one-child policy). This drop has continued in the first decade of this century—following mass migration from the rural to urban areas. The life expectancy patterns at birth of the four regions are displayed in Fig. 2. Life expectancy in High-Income region has grown from a number just below 70 in 1950, to over 80 in the 2010, and is projected to further increase to 87 years of age by 2100. Middle- and Low-Income countries are on lower, but similarly smooth increasing paths. China instead presents a marked dip in the 1950s, followed by a sudden rise in the next two decades, and is now on a steadily increasing path just above Middle-Income countries. The combination of fertility and longevity, together with migration, generates the population growth patterns displayed in Fig. 3. This picture takes into consideration a longer time period (until the year 2200). High-Income countries are currently experiencing small, negative population growth rates—Low- and Middle-Income

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90 85 80 75 70 65 60 55

High Middle Low China

50 45 1950

2000

2050

2100

Fig. 2 Life expectancy.

3 High Middle Low China

2.5 2 Percentage

202

1.5 1 0.5 0 −0.5 −1 1950

2000

2050

2100

2150

2200

Fig. 3 Population growth.

regions are instead growing at rates of 1% or more. Large negative growth rates are expected for China over the whole rest of this century, and Middle-Income countries will also see negative population growth from 2050 onward. The population levels consistent with these projections are shown in Fig. 4. The most striking feature is the massive decrease in the Chinese population that should fall back to 0.5 billion by the end of next

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4.5 High Middle Low China

4

Billions of individuals

3.5 3 2.5 2 1.5 1 0.5 1950

2000

2050

2100

2150

2200

Fig. 4 Population levels.

6

5

High Middle Low China

4

3

2

1

0 1950

2000

2050

2100

2150

2200

Fig. 5 Labor supply.

century, and the predominant role of Low-Income countries, that will account for more than a half of the world’s population already before the end of this century. The implications of these patterns for labor supply are shown in Fig. 5, under some assumptions that are detailed in the next section. In this figure, labor supply is expressed in efficiency units, and is normalized to unity in High-Income region in the initial year (1950). The most

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striking features are a steady increase in labor supply in Low-Income region until it reaches a plateau around the year 2100, and the bell shapes of labor supply in China (peaking around 2020) and Middle-Income countries (with a later peak around the year 2045). High-Income countries are much more stable over time, where after some growth over the 1950–2000 period, we observe a gentle decline until 2050 and a slow recovery afterward.

6. MODEL The model we present in this part updates and extends the one developed by Attanasio et al. (2006, 2007). It is a general equilibrium, OLG model of four interdependent economies. We exogenously limit migration flows, and compare the situation where there are no capital flows (closed economy) and where there are capital flows (open economy).

6.1 Economic Environment 6.1.1 Preliminaries The world economy is composed by four regions, (1) High-Income region H, (2) Middle-Income region M, (3) Low-Income region L, and (4) China C. The four regions differ in demographic structure, total factor productivity level, individual endowment profiles, and fiscal institutions. In what follows these differences are spelled out more in detail. There is no aggregate or region-specific uncertainty, but since we will model a deterministic transition across two steady states, equilibrium factor prices will be timevarying in a deterministic way. The only source of individual risk is related to the uncertain life span, which is region specific. We let t denote time, i individual’s age, and r the four regions, with r 2{H, M, L, C}. 6.1.2 Technology In each region r, a constant returns to scale, aggregate production function FðZtr , Ktr , Htr Þ produces output of a final good Ytr which can be used interchangeably for consumption Ctr and investment Xtr . Among the arguments of the production function, Ztr denotes the total factor productivity level in region r at time t, Htr is aggregate labor supply (i.e., the aggregate efficiency units of labor), and Ktr is the aggregate stock of physical capital used in production in region r. Physical capital depreciates geometrically at rate δ each period. The level of technology in region r grows exogenously at rate λrt between t and t + 1, but in the long run all regions reach the same productivity level and grow at the same constant rate λ. 6.1.3 Demographics Each region is populated by OLG of ex-ante identical “pairs of individuals” who may live for a maximum of I periods and their age is indexed by i ¼ 1,2, …,I . Pairs of individuals

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are dependent children for the first Id periods of their life and then they turn adult and form a household. For a pair of individuals born in region r, denote by sri, t the probability of surviving until age i at time t, conditional on being alive at time t  1 (with age i  1). Hence, in region r, the unconditional probability of surviving i periods up to time t is simply Sir, t ¼

i Y srj, t + ðjiÞ , j¼1

where S1r , t ¼ sr1, t  1 for all t by definition. In each period t, pairs of age i in region r have an exogenously given fertility rate (i.e., a probability of giving birth to another pair of individuals) equal to ϕri, t . During childhood, i.e., until age Id, fertility is assumed to be zero. For what follows, it is useful to define dir, t as the total number of (pairs of ) dependent children living in a (adult) household of age i at time t, i.e., 8 0 for i  I d < r di, t ¼ Xi : ϕr Sr for i > I d : k¼iI d + 1 k, tðikÞ ik + 1, t We denote by μri, t the size of the population of age i at time t in region r and by μrt the ðI  1Þ vector of age groups. Thus, in each region the law of motion of the population between time t and t + 1 is given by μrt + 1 ¼ Γrt μrt where Γrt is a time-varying ðI  I Þ matrix composed by fertility rates and surviving probabilities for households of region r described by 2 r 3 ϕ1, t ϕr2, t … … ϕrI
, t 6 sr2, t + 1 0 … … 0 7 6 7 r r 0 s 0 … 0 7 Γt ¼ 6 3, t + 1 6 7: 40 0 ⋱ ⋱ 0 5 0 0 … srI
, t + 1 0 The first row of this demographic transition matrix contains all the age-specific fertility rates, the elements (i + 1, i) contain the conditional surviving rates, whereas all the other elements are zeros. Lee (1974) shows that the largest eigenvalue of Γrt is the growth rate of the population between time t and t + 1, which we denote as γ rt (see also Rios-Rull, 2001). Since we are interested in the economically active population, we reshape the matrix r Γt and the vector μrt down to size I ¼ I
 I d and normalize the first period of adulthood (and economically active) life to be period 1 of life for households. We also restrict the parameters of the two matrices Γrt to converge across regions as t becomes large, in order to generate a common long-run growth rate of the population γ.f f

This restriction, similar to the one we impose for productivity growth, is necessary to achieve a long-run growth path where neither region is negligible in terms of output and population compared to the rest of the world.

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6.1.4 Household Preferences Households of age i at time t in region r are composed by a pair of adults and a number dir, t of pairs of dependent children living with their parents. The adults in the household jointly make consumption allocation decisions for themselves and their dependent children based on the intra-period utility function  a 1θ  1θ  r  cid, t ci, t r r a d (1) u ðci, t , ci, t Þ ¼ + di, t ω di, t , 1θ 1θ a d where  r ci, t denotes consumption for the adults, ci, t consumption per dependent child, and ω di, t is a positive function that weighs consumption of children in households’ utility. The intertemporal elasticity of substitution for consumption is 1/θ. This preference specification is convenient because it permits to express utility only as a function of the total consumption of the household ci, t ¼ cia, t + dir, t cid, t . From the optimality condition of the household with respect to cid, t one obtains  1 cid, t ¼ cia, t ω dir, t θ ,

(2)

which sets optimally the consumption of children to a fraction of the consumption of parents proportional to their weight in the utility function. Using (2) into (1), together with the definition of the total consumption of the household ci, t one obtains 1θ

r

u 

where

Ωri, t

 1 ¼ 1 + ω dir, t θ dir, t

θ

ðci, t Þ ¼ Ωri, t

ci, t , 1θ

(3)

and acts like an age- and time-dependent preference

shifter. To conclude, the intertemporal preference ordering for households born (adult of age i ¼ 1) at time t is given by U ¼ r

I X i¼1

1θ

c βi1 Sir, t + i1 Ωri, t + i1 i, t + i1 , 1θ

(4)

where β is the subjective discount factor. There is no explicit altruistic motive. 6.1.5 Household Endowments Households derive no utility from leisure. They have a fixed time endowment, normalized to one unit, that they can devote either to productive activities in the labor market or to child care at home. We denote by dri, t the (Id  1) vector of pairs of children’s by age groups for a household of age i at time t. Labor supply for households of region r at age i at time t is given by  r r  if i < I R Λt di, t r (5) li, t ¼ 0 otherwise;

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  Λrt dri, t is an exogenous fraction of time thateach household of age i in region r devotes to the market work at time t. The function Λrt dri, t is decreasing in the number of dependent children and captures the time trend and a rise in labor force participation of women. At age IR, households are subject to compulsory retirement from any working activity. Households of age i at time t in region r are endowed with εri, t efficiency units of labor for each unit of time worked in the market. Finally, we assume that the initial asset holding of each household is zero, i.e., a1,t ¼ 0 for any t in all regions. 6.1.6 Household Budget Constraint Let ari, t be the net asset holding of individual i at time t in region r. We assume that there are annuity markets to cover the event of early death. Every household has the right to keep the share of assets of the deceased in the same cohort; thus we can write the budget constraint as:       1 + τrc, t cir, t + sri + 1, t + 1 ari + 1, t + 1 ¼ yri, t + 1 + 1  τra, t rt ari, t : (6) We require households to die with nonnegative wealth once they reach age I, but otherwise we impose no borrowing constraint during their life. Net income yri, t accruing to households of age i in region r at time t is defined as 8   r < 1  τrw, t wtr εri, t lir, t ¼ 1  τrw, t y i, t if i < I R , (7) yri, t ¼ : r pi, t if i  I R , where wtr is the wage rate, εri, t is the efficiency units of labor of an individual of age i, and r pri, t is pension income. y i, t is the before-tax labor income. Households pay taxes τrc , t on consumption, τra, t on capital income, and τrw, t on labor income. Residents of region r pay capital income taxes in region r, independently of where capital was invested. Social security benefits are given by the formula Wir, t , IR  1 where κrt is the replacement ratio of average past earnings. Cumulated past gross earnings Wir, t are defined recursively as 8 r if i ¼ 1 y 1, t > > > > < r r R Wir, t ¼ y i, t + Wi1 (8) , t1 if 1 < i < I > > > > : r Wi1, t1 if i  I R : pri, t ¼ κrt

6.1.7 Government Budget Constraint In each region r, public expenditures and social security program are administered by the government under a unique consolidated intertemporal budget constraint. The

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  government can raise revenues through its fiscal instruments τrc , t ,τra, t , τrw, t and can issue one-period risk-free debt Brt . Government borrowing and tax revenues finance a stream of expenditures Gtr and the PAYG social-security program described above. The consolidated government budget constraint reads as Gtr + ð1 + rt ÞBrt +

I X pri, t μri, t ¼ i¼I R

τrw, t wtr

R IX 1

μri, t εri, t Λri, t

i¼1

I X   + μri, t τra, t rt ari, t + τrc , t cir, t + Brt + 1 :

(9)

i¼1

6.1.8 Commodities, Assets, and Markets There are three goods in the world economy: a final good which can be used either for consumption or investment, the services of labor, and the services of capital. The price of the final good (homogeneous across the four regions) is used as the world numeraire. Labor is immobile; thus wages are determined independently in regional labor markets. Physical capital is perfectly mobile across the four regions, so there is one world market for capital. We denote as Ntr the external wealth of region r, i.e., the stock of capital productive in other regions, which is owned by households of region r, with the convention that a negative value denotes ownership of capital used for production in region r held by households of the rest of the world. The sumP of the positive and negative external wealth across regions is zero by definition, that is, 4r¼1 Ntr ¼ 0 at any time t. Finally, in every region there is a financial market for government debt. The markets where these goods and assets are traded are perfectly competitive. An intuitive no-arbitrage condition between assets and the absence of aggregate uncertainty imply that the return on all regional bonds is equal to the return on physical capital, rt, as we have already implicitly assumed when we wrote the budget constraints of the government and households.g

6.2 Equilibrium Before stating the definition of equilibrium, it is useful to point out that, without further

∞ restrictions, the equilibrium path of the fiscal variables Gtr , κ rt , τrw, t , τra, t , τrc, t , Brt t¼1 is indeterminate, as there is only one budget constraint we can operate on. In what follows, we define an equilibrium for the case where the paths of all fiscal variables are given, except ∞ for τrw, t t¼1 : This case corresponds to our baseline experiment. It is straightforward to extend this definition to the case where the path of a different set of government policies is given exogenously. Finally, for brevity we omit the definition of the closed-economy equilibrium and state directly the equilibrium conditions for the open economy. g

In analogy with the definition of equilibrium stated in the next section, we report throughout the chapter the open economy interest rate rt, which by definition is equal in each region r to the world interest rate.

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A Competitive Equilibrium of the Four-Region Economy, for a given sequence of region

∞ ∞ specific demographic variables Γrt , Λrt t¼1 , TFP levels Ztr t¼1 , and fiscal variables n r r r r r ∞

I o∞ cir, t , ari, t i¼1 , Gt , κ t , τa, t , τc, t , Bt t¼1 , is a sequence of: (i) households’ choices t¼1 r ∞ r ∞ (ii) labor income tax rates τw, t t¼1 , (iii) wage rates wt t¼1 , (iv) aggregate variables r r r r ∞ Kt , Ht , Xt , Ct t¼1 in each region r, (v) world interest rates frt g∞ t¼1 , and (vi) external r ∞ wealth of each region Nt t¼1 such that: n

I o∞ , 1. Households choose optimally consumption and wealth sequences cir, t , ari, t i¼1 t¼1

maximizing the objective function in (4) subject to the budget constraint (6), the income process (7), and the time allocation constraint (5) 2. Firms in each region maximize profits by setting the marginal product of each input equal to its price, i.e., wtr ¼ FH ðZtr ,Ktr ,Htr Þ,

(10)

rt + δ ¼ FK ðZtr ,Ktr ,Htr Þ:

(11)

3. The regional labor markets clear at wage wtr and aggregate labor supply in each region is given by Htr

¼

R IX 1

μri, t εri, t Λri, t :

(12)

i¼1

4. The regional bond markets and the world capital market clear at the world interest rate rt, and the aggregate stocks of capital in each region satisfy Ktr

+ Ntr

+ Brt

¼

I X

μri1, t1 ari, t :

(13)

i¼2

∞ 5. The tax rates τrw, t t¼1 satisfy the consolidated budget constraint (9) in each region. 6. The allocations are feasible in each region, i.e., they satisfy the regional aggregate resource constraints Ktr + 1  ð1  δÞKtr + Ntr+ 1  ð1 + rt ÞNtr ¼ FðZtr , Ktr , Htr Þ  Ctr  Gtr :

(14)

Before concluding, it is useful to recall that aggregate gross investments in region r are given by Xtr ¼ Ktr + 1  ð1  δÞKtr ,

(15)

whereas aggregate (private plus public) savings in region r are, Str ¼ FðZtr ,Ktr , Htr Þ + rt Ntr  Ctr  Gtr :

(16)

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As a result, the current account surplus of region r (or, the net capital outflow from region r into the rest of the world) is given by Str  Xtr ¼ CArt ¼ Ntr+ 1  Ntr ,

(17)

and it equals the change in the net foreign asset position of region r. Moreover, in this four P region economy, 4r¼1 CArt ¼ 0.

7. CALIBRATION 7.1 Preliminaries We calibrate parameters of the model using demographic and economic data that are available for periods between 1960 and 2010 in the four regions. We assume that all demographic and productivity parameters in the four regions converge to the same values by 2200; thus all regions converge to the same balanced growth path some decades after 2200. We then let our world economy transit between the two steady states, by imposing a gradually converging path of mortality, fertility and female participation rates as well as the level of aggregate and individual productivities. The model’s period is set to 5 years.h

7.2 The Four Regions The world in our model consists of four regions that differ in the timing of demographic transitions and productivity growth. High-Income region includes United States, Canada, Europe, Japan, plus Australia and New Zealand. Middle-Income region encompasses countries that recently experienced high economic growth and includes those in Latin America and the Caribbean, as well as India, Russia, South Africa, South Korea, Taiwan, Thailand and Turkey. Low-Income region includes countries in Africa (except for South Africa), other Asia and Oceania. The fourth region is China.

7.3 Technological Parameters We choose a Cobb–Douglas specification FðZtr ,Ktr ,Htr Þ ¼ Ztr ðKtr Þα ðHtr Þ1α , for the production function with capital share α ¼ 0.30 and its constant depreciation rate of 5% on an annual basis. The growth rate of TFP, λrt in each region is set so that the region achieves the target average per capita output growth rate, as computed from the World Bank’s World Development Indicators (WDI, 2013) for the period of 1960–2010. We assume a constant growth rate until 2010 to match the historical average. h

The calibration strategy matches a set of moments in the data with the model’s counterparts in the closed economy equilibrium. The open economy equilibrium has the exact same parametrization, thus, for example, different levels of output, and capital stock.

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The initial value of TFP in High-Income region Z0H is set to 1.0 for normalization. Based upon the WDI data, income per capita in High-Income region was approximately 4.5  larger than that of Middle-Income region in 2010 and we set the value of Z0M , productivity in the initial steady state, to match this ratio. Similarly, High-Income region’s GDP per capita was 8.3  and 4.5  as large as that of Low-Income region and China, respectively. We set the TFP level of each region accordingly to match the relative size of GDP per capita. We assume that both the TFP level and the growth rate in the four regions converge to common values by 2200. We let the TFP growth rate of High-Income region remain the same after 2010 and calibrate the growth rate in each of the other three regions between 2010 and 2200 so that the TFP level will converge to that of High-Income region by 2200. Calibrated parameters are summarized in Table 1.

7.4 Demographic Parameters Since each model period corresponds to 5 years, we set Id ¼ 3 so that agents become adults and economically active at the model age of 4, which corresponds to 15–19 years old. We set I ¼ I
 I d ¼ 24  3 ¼ 21, so that households can live a maximum of 24 periods (120 years). We also set the retirement age IR ¼ 11 in the model, which corresponds to age 65–69. All these parameters are common in the four regions. Age-specific fertility rates are taken from data and projections for 1960–2100 of the United Nations (UN) World Population Prospects: The 2012 Revision (2013a). For the periods beyond 2100, we assume that fertility rate at each age converge by 2200 to those of HighIncome region projected for 2100, proportionally adjusted so that the total fertility rate is 2.1. Age-specific surviving probabilities in the four regions for the period 1960–2100 are computed from actual and projected data on population shares by age group in the UN database. After 2100, we make the surviving rates smoothly converge to those of HighIncome region by 2200. Another major demographic trend is the growth in female labor force participation rates. Our main data sources here come from historical labor market data of the International Labour Organization (2013, ILO). We focus on the ILO data since 1970s, when we have more comprehensive coverage of the countries and population in each region. Fig. 6 displays the trend in female labor force participation rates in the past four decades. Note that Table 1 Growth rate of TFP 1960–2010 GDP per capita growth, WDI 1960–2010, data (%) Region

TFP growth rate lrt 1960–2010 calibrated (%)

GDP per capita level, WDI 2010, data

Initial TFP level Zr0 calibrated

1. High income 2. Middle income 3. Low income 4. China

1.64 1.58 1.66 4.51

1 (normalization) 0.22 0.12 0.22

1.00 0.41 0.34 0.10

2.4 2.6 2.4 6.7

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80 75 70 65 Percentage

212

60 55 50 45 High Middle Low China

40 35 30 1975

1980

1985

1990 Year

1995

2000

2005

Fig. 6 Female labor force participation rate in four regions.

there are two data points available for China. In order to capture the time trend in the female labor supply, separately from the time requirements and impact of dependent children on their labor supply, we estimate the following equation for the participation rate of women Pir, t 2 ð0,1Þ with an exponential trend for all regions except for China. Pir, t ðdri, t Þ ¼ βr0

+ ðP

+ Ti  βr0 Þf1 

exp ½βr1 *ðt  1Þg +

Id X

^ j dir, j, t , α

(18)

j¼1

where βr0 measures the participation rate for a female worker with no children in the initial period.i P
¼ 0:68 is the long-run female participation rate, based on the projection of the Bureau of Labor Statistics (BLS) for the United States in 2020; T i is the long-run value of time devoted by a woman of age i to child care (common across regions) computed from the final steady-state value of the number of dependent children at age j, di, j, ∞ and the Pd ^ j dir, j, ∞: ; the parameter βr1 reg^ j , i.e., Ti ¼  Ij¼1 α estimated time to take care of children α ulates the speed of convergence toward the long-run rate P. The estimated parameters for M L High-, Middle-, and Low-Income regions are ðβH 0 , β0 , β0 Þ ¼ ð0:4191, 0:4412,0:4248Þ j M L and ðβH 1 ,β 1 , β 1 Þ ¼ ð0:1686,0:0482, 0:0810Þ, respectively. For China, female participation rates at available data points in the last few decades are high and remain stable at about 78% in 1980s and 1990s and decline slightly to 76% in 2000s. i j

Substituting t ¼ 1 and dir, j, t in Eq. (18) yields Pir, t ðdri, t Þ ¼ βr0 . Values for βr0 represent the participation rate of female workers with no children in each region in 1950.

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Therefore we estimate the function (18) without a time trend until 2000 and make the female participation rates change until 2000 only through the time-varying vector dri, t that indicates the number of dependent children. Thereafter, we assume that the participation rate of women without children will linearly converge to the level so that the average participation rate will reach the same long-run value of P
¼ 0:68 in the final steady state.k Once the female participation rates Pir, t ðdri, t Þ are computed for each region, we can derive Λri, t ðdri, t Þ, the fraction of the time endowment (normalized to one) worked by the household of spouses, i.e., Λri, t ðdri, t Þ ¼ 0:5½1 + Pir, t ðdri, t Þ, where the husband is assumed to work full time. As in Attanasio et al. (2006), the data from the Consumer Expenditure Survey (CEX) are used to estimate the marginal effects αj of the presence of a pair of dependent children at age j (0–4, 5–9, and 10–14 years old) on women’s probability of participation. The Probit regression, which controls for several individual characteristics including age, race, and education, yields α04 ¼ 0.146, α59 ¼ 0.0960, α1014 ¼ 0.0464. The coefficients are negative and significant and younger children have stronger impact on the probability of female participation. Fig. 7 displays the estimated participation rates of female from 1950 to 2200 in each region as well as the contribution of the fertility trend, relative to the value in 1950 which is set at zero. We normalize the total population in High-Income region in 1960 to one and set the initial population size for the other three regions to 1.031, 0.807, and 0.769, respectively, based on the UN population data. During the transition away from the initial steady state, the population size in the four regions is determined by the evolution of age-specific fertility rates ϕri, t and survival rates sri, t .

7.5 Preferences and Endowments Parameters We assume that preferences are common across regions and do not vary over time. Following the bulk of the literature on consumption (for a survey, see Attanasio, 1999), we set θ ¼ 2. We set the subjective discount factor β to match the capital output ratio of High-Income region in 2010 to 3.7, based on the data from Penn World Table (PWT, Feenstra et al., 2013). The weight parameter of children in the utility of adult parents is set to match the commonly used consumption adult-equivalent scales. The microevidence on equivalence scales summarized in Fernandez-Villaverde and Krueger (2007, table 1) points at a ratio between the consumption of a household with 1, 2, and 3 children compared to a k

Although we do not have the decomposition of the participation rates by occupations or regions, it is possible that high female workers’ involvement in the farming sector contributed to the high female labor force participation in earlier data, which may shift in future as a result of urbanization and a change in the Chinese industrial structure. Therefore, we assumed that the labor force participation rate will decline and converge to that of the other regions in the long run, rather than assuming it to remain high at around 80%.

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Participation rates

Contribution of fertility trend 0.15

High

0.8

0.1

0.6

0.05

0.4

Data

0.2 1950

0

Model 2000

2050

2100

2150

2200

Middle

Data

0.2

Low

2100

2150

2200

2000

2050

2100

2150

2200

2000

2050

2100

2150

2200

2000

2050

2100

2150

2200

0

Model 2000

2050

2100

2150

2200

−0.05 1950 0.15

0.8

0.1

0.6

0.05

0.4

Data

0.2

0

Model 2000

2050

2100

2150

2200

−0.05 1950 0.15

0.8

0.1

0.6

0.05

0.4

Data

0.2 1950

2050

0.05

0.4

1950

2000

0.1

0.6

1950

−0.05 1950 0.15

0.8

China

214

0

Model 2000

2050

2100

2150

2200

−0.05 1950

Fig. 7 Estimated female labor force participation rate in four regions.

household without children of 1.231,  1.470, and 1.694, respectively. Using equation (2), it is easy to see that our function ω dir, t should satisfy the three moment conditions 1

ωð0:5Þθ ¼ ð1:231  1Þ=0:5, 1

ωð1Þθ ¼ ð1:470  1Þ, 1

ωð1:5Þθ ¼ ð1:694  1Þ=1:5: Note that we need to make an adjustment for the fact that in our model children come in pairs. Given θ ¼ 2, setting ω ¼ 0.216 independently of the number of children yields an excellent fit. The calibration of the age profile of efficiency units is done separately for each region. The age-efficiency profile for High-Income region is estimated on weekly wage data from the US Consumer Expenditure Survey (CEX) for the period 1982–1999. For Middle-Income region, we have estimated an age-efficiency profile on Mexican data—precisely from the Encuesta Nacional de Ingreso y Gasto de los Hogares (ENIGH),

Global Demographic Trends: Consumption, Saving, and International Capital Flows

which is the equivalent of the US CEX, using the 1989, 1992, 1994, 1996, 1998, and 2000 waves.l The sample, across both surveys, is the universe of married couples headed by males and aged 17–69 and the derived “household wage” is an average of male and female wage weighted by hours worked. For Low-Income region, we use the age-efficiency profile in Bangladesh, estimated by Kapsos (2008), who uses a national occupational wage survey conducted by the Bangladesh Bureau of Statistics (BBS) in 2007 with the support of the ILO. We use the estimated coefficients of the hourly wage regression, that controls for age and education levels. Finally for China, we use Chinese Household Income Project (CHIP), a survey of Chinese households in urban and rural areas. We use individual data from the urban income, consumption and employment questionnaire and estimate the wage profile using a sample of household heads aged 20–65 in the 1995 and 2002 waves of the survey. The regression includes the age and education of an individual and we take the weighted average of spouses’ wages to derive a household wage. Fig. 8 shows estimated profiles for the four regions, where the wage at age 17 is normalized to 1 in each region. High-Income region has the steepest slope, followed by Middle-Income region, China and Low-Income region. The peak of the wage is at around 45–50 years old in High and Middle-Income regions, while the profile is much flatter and a mild peak arrives at age above 50 in the other two regions. We assume that the age–wage profiles will remain as in Fig. 8 until 2010, when they start to gradually converge to the profile of High-Income region by 2200. 2.5 High (USA) Middle (Mexico) Low (Bangladesh) China 2

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See Attanasio and Szekely (1999) for a detailed description of the Mexican survey data.

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7.6 Government Policy Parameters We obtain the ratio of the government debt Brt as a fraction of GDP from the International Monetary Fund (IMF)’s World Economic Outlook Database (WEO, 2013). We use the net debt variable that represents the gross debt net of financial assets. The average over the period 1990–2010 was 48%, 37%, and 51% in High-, Middle-, and Low-Income regions. For China, only gross debt data is available, which is 14% of GDP. Since we do not have the data for the government’s financial assets, we assume a net debt of 10% of GDP in the baseline calibration. The total government expenditures as a fraction of GDP are obtained from the WEO for the period 1980–2010, and from the IMF Government Finance Statistics (GFS, 2014) and the China Statistical Yearbook of the National Bureau of Statistics of China (n.d.) for earlier years (1970–1980). The average over 1970–2010 was 36%, 23%, 30%, and 22% of GDP in each of the four regions, respectively. Since these figures represent general public expenditures, which include spendings for social security and interest payment, we compute the ratio of the government expenditures Gtr to GDP so that the total expenditures match the ratios reported above. The ratios of Gtr to GDP are 29.2%, 22.5%, 28.8% and 21.4% for each of the four regions.m Based on the study of OECD, the replacement rate of pensions to the average earnn ings is set at κH t ¼ 58% in High-Income region. Unfortunately, similar systematic studies on the replacement rates for other regions are not available. The average replacement rate is likely to be much lower than in High-Income region due to two factors. First, the disproportionate role of self-employment and informal production means that a vast part of the working population is not covered by a public pension system. Second, the involvement of governments in the pension sphere is limited: in Asia, only Korea and Taiwan operate a defined benefits PAYG scheme with universal coverage; Latin America is the region with the largest number of pension systems already reformed toward substantial privatization (see Mohan, 2004, for the Asian experience; see Corbo, 2004, for the Latin American experience). We set the replacement rate of the three regions at κrt ¼ 10% in the first steady state, the value used in Attanasio et al. (2006).o For tax rates of each region, we use various data sources for the period of 2000–2010 and estimate effective tax rates following the method of Mendoza et al. (1994). We use m

n o

We assume that the ratio Gtr =Ytr is constant throughout the transition in closed economy. We then take the path of the government expenditures Gtr from the closed economy and assume that the same level of government expenditures in each year needs to be financed in the open economy. Our assumption is that the government expenditures do not vary with the openness of the economy and with the amount of capital flows across regions. OECD, Pensions at a Glance (2011). For the details on the scope of the public pension system in China, see He et al. (2015) on the replacement rate and the coverage of urban workers in China, and Song et al. (2015) on ongoing reforms of the nationwide pension system under aging demographics in China.

Global Demographic Trends: Consumption, Saving, and International Capital Flows

the OECD Revenue Statistics (2013a) database for tax revenues, in particular for HighIncome and Latin American countries, integrated with consistent data from IMF GFS for Low and other Middle-Income countries. Detailed national accounts data on households, enterprizes, and government are taken from the OECD National Accounts Statistics (2013b) and the UN National Accounts Statistics (2013b) databases. Equivalent data for China are not available and we use the estimates of Cui et al. (2011) for the effective tax rates of the country. Capital income tax rates τra are 35.7% for High-Income region, 15.5% for Middle-Income region, 13.5% for Low-Income region and 25.7% for China. Consumption tax rates τrc are set at 9.7%, 16.0%, 6.3%, and 7.7%, respectively. The labor income tax τrw, t in each region is determined in the equilibrium path of the model to satisfy the government budget constraint, as presented and discussed in the next section.

8. NUMERICAL RESULTS In this section, we present results for a number of simulations where we compare two scenarios: open and closed economies. We study the dynamics of key economic variables in the four regions of the world we have described above: High Income, Middle Income, Low Income, and China. The economic variables we look at include interest rates, wage rates, equilibrium tax rates, current account, and external wealth. On the basis of above, we shall be discussing some interesting welfare exercises. Comparing welfare along the transition path between the closed and the open economy scenarios allows us to quantify the importance of globalization (free capital mobility). After showing the results of the baseline model we described in the previous section, we shall consider different alternative scenarios for demographics and productivity.

8.1 Baseline Scenario In Fig. 9 we show interest rate paths that characterize the four regions when the economies are closed, and the world interest rate when instead there is full capital mobility. Even though we let the model start in 1960 and demographic and productivity parameters converge in 2200, we focus on and display results for a shorter time period of 2010–2100. The main purpose for going as far back as 1960 is to approximate the current and projected demographic structure better during the period of our interest. In the closed economy scenario, Low-Income region and China start with higher interest rates at around 5.7% and 8.2%, respectively.p The interest rate is lowest in High-Income countries to begin with. For several decades the interest rate continues p

According to Bai et al. (2006) the return to capital in China was very high in the period corresponding to the initial steady state, due to high TFP growth. Though, as stressed in Song et al. (2015), such high return seems not to be accessible to the government and most workers and employees. The large majority of Chinese households hold their wealth in bank deposits and bonds paying low returns, hence our equilibrium level of the real interest rate in closed economy seems to be a plausible figure.

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9 High Middle Low China Open economy

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to decline in all regions except High-Income region largely because of the demographic trends we saw in Section 5. Higher longevity calls for more saving to cover consumption expenditures for a longer retirement period. Lower fertility rates and fewer dependent children in households imply a larger fraction of disposable income allocated for savings. In High-Income region, fertility rates reached the bottom in 1990s and have been on the rise since then, which offsets the rise in savings driven by longer life expectancy. In the open economy scenario the world interest rate gently falls from slightly above 4% by about 2 percentage points over the century. In Fig. 10 we display the equilibrium wage paths separately for each region, where the solid line corresponds to the closed economy and the dotted line corresponds to the open economy. Wage rates are normalized to one in 2010 under the closed economy scenario in each region. Comparing the closed and the open economy outcomes, we observe that wages in the first three decades are higher in the closed economy scenario for HighIncome region workers. Only in around 2040 do wages benefit from capital mobility in this region. In Middle-Income region, wages are initially at similar levels in closed and open economies. Wages in the open economy eventually fall below the closed economy level as the capital starts to flow out of the region. Open economy wage rates remain above those of closed economy in Low-Income region throughout the century. In China, wages are higher in the open economy initially due to capital inflow, but the gap between wage rates in the two economies diminishes by mid-2020s and the trend reverses thereafter as more and more capital starts to flow out of China. Fig. 11 presents our simulation results for the equilibrium tax rates, that is, the tax rates that balance the consolidated government budget constraint in each year. Of particular

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interest is the difference in tax rates between closed and open economy scenarios. Taxes are lower in open economy for Low-Income region, even though the difference shrinks with time after 2020. In China the closed economy taxes are slightly lower until late 2030s but lie above the level in the open economy until the end of the century. In Middle-Income region, taxes are almost the same initially, but the tax rates in the open economy rise faster than in the closed economy. In High-Income region, taxes rise in both closed and open economies but the rates are lower in open economy. To understand these results we should first of all note that government expenditures are computed as a fixed percentage of output in each year in the closed economy and the path of expenditures is kept at the same level in the open economy. Labor tax adjusts to clear the government budget and the budget clearing tax rate depends also on the revenues raised by other taxes, all of which are endogenously determined in equilibrium. In China, for example, wages are higher in the open economy initially but a large decline in interest rate in the open economy during the initial decades reduces capital income tax revenues and equilibrium tax rates are higher than in the closed economy. Of course, the equilibrium labor tax rate depends not only on the interest rate and wage rate, but also on the amount of savings, total consumption and number of workers that affect the size of the labor income tax base. The dynamics of tax rates in High-Income region is largely driven by population aging. The rise in the old-age dependency ratio increases the fiscal burden to finance the region’s generous social security program. The tax rate has to rise by about 15 percentage points in closed economy to cover the rising pension expenditures. In open economy, tax rates also rise but are lower than in closed economy by a few percentage points. As we saw in Fig. 9, the interest rates are higher and the government generates more capital income tax revenues in open economy until 2030s. After that, higher wages and an expansion of the labor income tax base make up for the lower capital tax revenues in the open economy. In Fig. 12 we show how the current account evolves in the open economy scenario. Recall that the current account is defined as the difference between aggregate domestic savings and aggregate gross investments in each region. A surplus therefore indicates a net capital outflow from the region. Our model predicts a large surplus for China until 2060, a large negative balance for Low-Income countries until the middle of the century, an inflow for High-Income countries. Middle-Income countries start experiencing surpluses from 2020 onward. These capital flows and the underlying stocks (shown in Fig. 13, where external wealth is shown as a percentage of GDP) explain a lot of the differences between the closed and the open economy scenarios in terms of tax rates and capital per capita. Looking at the paths of capital per capita in each of the four regions (shown in Fig. 14), we notice a major difference between closed and open economies in High-Income region. Capital first rises with an increase in longevity and then (after 2030) declines in the closed-economy case. In the open economy case, instead, capital will continue

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to rise throughout the century. The difference between these scenarios is driven by the current account balance, partly by the higher interest rates in the closed economy compared to the open economy after 2040 as shown in Figs. 9 and 12. Fig. 13 shows that the external wealth of High-Income region monotonically declines throughout the century, which contributes to a rise in domestic capital in open economy as observed in Fig. 14. After mid-2040s, the external wealth turns negative, that is, people in other regions of the world will start to own claims against capital used in High-Income region. Open-economy capital in Middle-Income region starts at almost the same level as in the closed economy, but after 2030s it falls below the closed economy level as households start to shift the wealth abroad seeking higher returns. In the capital-starved Low-Income region, capital per capita is consistently higher in the open economy. Finally, in China capital per capita remains lower in open economy after mid-2020s as the country continues to be a lender of capital to the rest of the world. Fig. 15 presents our computations on the welfare gains brought about by an open economy. The welfare gain of being in open economy is quantified in terms of consumption equivalence. We ask what is the percentage change in consumption at each age that makes a representative agent in each cohort indifferent between being born into an open economy

Global Demographic Trends: Consumption, Saving, and International Capital Flows

14

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as opposed to a closed economy. A positive number implies that she likes the open economy better. Here “birth” is the age at which the agent enters the economy as an adult, which is 17.5 years (given that the first age group is defined to cover the age of 15–19). We notice that early cohorts in China gain significantly from being in open economy. This is due to the large capital inflow to the Chinese economy and increased economic activities and wages, as we saw in Figs. 10, 12, and 14. For opposite reasons, people in High-Income region currently alive will lose in the open economy, although generations entering the economy after mid 2020s will prefer the open economy due to the reversal of capital flow after 2040 and a rise in wages. Welfare effects on individuals in Low and Middle-Income region are smaller in magnitude but they all gain from the capital flow across regions. We also note that quantitative measures of welfare changes rely on the magnitude of capital that flows across regions and are sensitive to changes in economic environment. Changes in assumptions that affect cross-regional differences in saving incentives and interest rates, such as pension policies, heterogeneous preferences and factors that limit capital mobility, will affect the level of external wealth and welfare assessments.

8.2 Alternative Scenarios in Low-Income Region In the benchmark case, Low-Income region is dramatically different from the rest of the world in terms of endowment, demographics and key economic indicators driven by them and remains so for a very long time. In the baseline model we assume that TFP

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levels and growth rates as well as all the demographic parameters and preferences converge to those of High-Income region slowly and the convergence will be complete by as late as the year 2200. In this section, we simulate our model under alternative scenarios of convergence in productivity and demographics in Low-Income region. We also run an experiment in which there is return risk to investment in capital located in Low-Income region. 8.2.1 Fast Productivity Convergence The recent experience of China and of some Middle-Income countries (the so-called BRICS) suggests that convergence could very well be much faster than had been anticipated: after all, fertility rates are already dropping at a very high speed in most LowIncome countries, and it is perfectly possible that total factor productivity also catches up in a shorter time than we envisaged in our benchmark. The experiment we consider here is one where the level and the growth rate of total factor productivity of Low-Income region converge to those of High-Income region by the year 2100, rather than 2200. All remaining features of the model are unchanged. To facilitate comparison of values between the benchmark case and the experiment, the level variables (wage and capital) are normalized by the closed economy value of the initial year, 2010, in the benchmark economy. Fig. 16 compares the closed-economy interest rates in the four regions and the world interest rate of the open economy. Compared to the benchmark scenario shown in Fig. 9, 9 High Middle Low China Open economy

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Fig. 16 Fast productivity convergence in Low-Income region: interest rates. The thick solid line represents open economy.

Global Demographic Trends: Consumption, Saving, and International Capital Flows

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the interest rate initially rises for about a decade and then falls slowly in Low-Income region. Fig. 17 shows that Low-Income wage grows much faster in both closed and open economy scenarios, as one would expect with the higher productivity growth. The effects on other regions are only felt in the open economy case. Equilibrium tax rates and the current account balances are not dramatically different from the benchmark scenario, with the noticeable exception of current account in LowIncome region, which starts at a much more negative level and reaches parity at a later date, as shown in Fig. 18. The current account deficit amounts to about 17% of GDP in 2010, while it was about 12% of GDP in the baseline case. Important differences are observed when we look at capital per capita, shown in Fig. 19. In both closed and open economy scenarios, capital in Low-Income region grows much faster in this experiment compared to the benchmark case, and the difference between the two is also larger in percentage points of GDP as time goes by, since in the open economy scenario the region attracts larger capital inflows with the higher interest rates. Capital per capita is much lower in open economy compared to the benchmark case in High-Income region, Middle-Income region, and in China. The closedeconomy interest rate of High-Income region does not exceed that of open economy

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Global Demographic Trends: Consumption, Saving, and International Capital Flows

until close to 2050, implying that the external wealth remains positive much longer in the region and remains higher throughout the century. 8.2.2 Fast Convergence in Longevity in Low-Income Region Next we simulate a model assuming that the longevity in Low-Income region improves faster than in the baseline model and let the age-specific survival rates converge to the values of High-Income region by 2100, rather than 2200. The rapid increase in longevity strengthens saving motives of households in order to cover the cost of consumption for a longer retirement period. As shown in Fig. 20, closed economy interest rates of LowIncome region decline faster than in the baseline case. The interest rates go below those of High-Income region after 2060 and almost reach but do not yet intersect with the path of the open economy interest rates at the end of the century. The current account turns positive by 2040 as shown in Fig. 21, while it remains negative until 2060 in the baseline model. Low-Income region remains as a large borrower throughout the century, but the level of borrowing is significantly smaller as shown in the smaller amount of external debt in Fig. 22 compared to the baseline model. 8.2.3 Investment Risk in Low-Income Region In the baseline model we assumed free capital mobility with no risk involved in investment abroad. Here we introduce capital market risk in Low-Income region and assume 9 High Middle Low China Open economy

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Global Demographic Trends: Consumption, Saving, and International Capital Flows

that lenders to the region receive a return from investment which is lower than the return in a frictionless market. More precisely, the actual interest rate paid to the owners of capital is 80% of the gross return implied by the marginal product of capital. Fig. 23 shows the paths of interest rates, where the interest rates of Low-Income region represent the gross interest rates prior to the 20% reduction faced by the lenders. The capital will be lower with the investment risk and the gross return will be higher in Low-Income region than in the baseline case. In the open economy, Low-Income region will have less capital owned by foreigners and the current account improves slightly, as shown in Fig. 24. 8.2.4 Additional Experiments We simulated our model under a variety of alternative scenarios: (1) faster convergence in efficiency unit profiles in Low-Income region; (2) faster convergence in TFP in China; (3) faster convergence in fertility rates in Low-Income region and China; (4) faster convergence of longevity in China. By and large the effects on factor prices are not very significant under these experiments and paths of key economic variables look similar to those in the benchmark model.

8.3 Summing Up The model of the world economy we have discussed is obviously unrealistic in many ways and the results we have obtained should be taken and interpreted with care. 9 8 7

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However, the exercise we have performed is indicative of the way in which this type of medium-scale OLG models of open economies can be developed and used. Although they abstract from many realistic feature of the real economy, they are instructive of how demographic trends put pressures on fundamental economic variables and how these effects are mediated by other factors, such as the mobility of factors of production and the nature of institutions. An understanding of these forces and effects is crucial for the design of public policies. The main result is that the overall downward trend in real interest rates is somewhat smoothed out by factor mobility, as one would expect given the fact that the demographic trends in different regions are far from synchronized. The simulations also provide the implications for the tax rates that would be necessary to maintain a certain level of social security. In addition to a benchmark scenarios, we have also explored a variety of different alternatives that attempt to capture the high level of uncertainty about future trends in fundamental variables, such as relative productivity. Probably the most important omission in the exercise we have performed is that of labor mobility. In our model, we have assumed that labor is completely fixed. In reality, we know that labor flow is extremely important and that there are very powerful economic incentives to migration that in some regions in recent years have been accentuated

Global Demographic Trends: Consumption, Saving, and International Capital Flows

by conflicts and wars. The study of models that incorporate migration flows in a realistic fashion and develop the early contributions in this field, such as Storesletten (2000), would be extremely interesting and important.

9. CONCLUSION In this chapter we have reviewed the recent literature on the effects of changing global demographic trends on consumption and on factor prices. We have also constructed, calibrated and simulated an OLG model of the world with four regions. Although the exercise forces upon us many strong assumptions and simplifications, it provides a useful tool to quantify the effects of important demographic trends on savings, consumption, and factor prices. We find that capital mobility can attenuate some of the negative impacts of demographic trends in the High-Income region and, in general, can lead to important welfare gains in many regions. A large difference in interest rates across regions that would prevail in the closed economy could induce significant flows of capital in the open economy, changing factor prices, tax bases, and fiscal conditions of each region. For example, we have shown that a large inflow of capital to China in early years due to its demographic transition that is unsynchronized with other regions can bring a major welfare gain, although the reversal of capital flows in later years can reduce the gains from the openness. If we compare our model to the literature review, we notice that several questions could be addressed by extending the model in different directions. First, it remains an open question whether the very different saving behavior observed across regions is rooted in additional heterogeneity in preferences such as (long) habits. One needs to build a model in which the life-cycle decisions of households depend on their past behavior or the history of aggregate economy to address such questions. Second, the model we developed in the chapter assumes that a household acts as a unit of decision making and abstracts from the decision of household members and their interaction. By explicitly modeling female labor supply decisions, for example, the model would be able to assess whether there is a window of opportunity for Middle-Income and Low-Income countries associated with a rise in female participation rates. Third, the model assumes that capital is the only factor that moves freely across regions and labor is immobile. An interesting extension of course would be to allow for (at least some) labor mobility as well, in response to the unsynchronized transition of demographic across regions and study the impact on factor prices, consumption, and welfare. We trust that these open issues will be subject of more research in the near future. The following is the Supplementary material related to this chapter. DOI:10.1016/bs.hespa.2016.09.006

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REFERENCES Abel, A.B., 2001a. The effects of investing social security funds in the stock market when fixed costs prevent some households from holding stocks. Am. Econ. Rev. 91 (1), 128–148. Abel, A.B., 2001b. Will bequests attenuate the predicted meltdown in stock prices when baby boomers retire. Rev. Econ. Stat. 83 (4), 589–595. Abel, A.B., 2003. The effects of a baby boom on stock prices and capital accumulation in the presence of social security. Econometrica 71 (2), 551–578. Abel, A.B., Mankiw, N.G., Summers, L.H., Zeckhauser, R.J., 1989. Assessing dynamic efficiency: theory and evidence. Rev. Econ. Stud. 56 (1), 1–19. Altig, D., Auerbach, A.J., Kotlikoff, L.J., Smetters, K.A., Walliser, J., 2001. Simulating fundamental tax reform in the United States. Am. Econ. Rev. 91 (3), 574–595. Attanasio, O.P., 1999. Chapter 11. Consumption. In: Taylor, J.B., Woodford, M. (Eds.), Handbook of Macroeconomics. In: vol. 1. North-Holland, Amsterdam, The Netherlands. Attanasio, O.P., Szekely, M., 1999. Household savings and income distribution in Mexico. Inter-American Development Bank, Washington, DC. Research Department Working Paper 390. Attanasio, O.P., Weber, G., 2010. Consumption and saving: models of intertemporal allocation and their implications for public policy. J. Econ. Lit. 48 (3), 693–751. Attanasio, O.P., Kitao, S., Violante, G.L., 2006. Quantifying the effects of the demographic transition in developing economies. B.E. J. Macroecon. 6 (1), 1–44. Attanasio, O.P., Kitao, S., Violante, G.L., 2007. Global demographic trends and social security reform. J. Monet. Econ. 54, 144–198. Attanasio, O.P., Kitao, S., Violante, G.L., 2011. Financing medicare: a general equilibrium analysis. In: Shoven, J. (Ed.), Demography and the Economy. University of Chicago Press, Chicago, IL. Auerbach, A.J., Kotlikoff, L.J., 1987. Dynamic Fiscal Policy. Cambridge University Press, Cambridge. Bai, C.-E., Hsieh, C.-T., Qian, Y., 2006. The return to capital in China. National Bureau of Economic Research Inc. NBER working papers 12755. Baxter, M., 2012. International risk-sharing in the short run and in the long run. Can. J. Econ. 45 (2), 376–393. Becker, S.O., Hoffmann, M., 2006. Intra- and international risk-sharing in the short run and the long run. Eur. Econ. Rev. 50 (3), 777–806. Binelli, C., 2014. How the wage-education profile got more convex: evidence from Mexico. Department of Economics, University of Southamption. Working Paper No.1404. Blanchard, O., 1985. Debt, deficits and finite horizons. J. Polit. Econ. 93 (2), 223–247. Bloom, D., Canning, D., Mansfield, R., Moore, M., 2007. Demographic change, social security systems, and savings. J. Monet. Econ. 54 (1), 92–114. Boersch-Supan, A., Ludwig, A., Winter, J., 2006. Ageing, pension reform and capital flows: a multi country simulation model. Economica 73, 625–658. Braun, R.A., Joines, D.H., 2015. The implications of a graying Japan for government policy. J. Econ. Dyn. Control. 57, 1–23. Braun, R.A., Kopecky, K.A., Koreshkova, T., 2016. Old, sick, alone and poor: a welfare analysis of old-age social insurance programs. Rev. Econ. Stud. 1–33. http://dx.doi.org/10.1093/restud/rdw016. Brooks, R., 2000. What will happen to financial markets when the baby boomers retire? IMF Working Papers 00/18. Brooks, R., 2003. Population aging and global capital flows in a parallel universe. IMF Staff. Pap. 50 (2), 200–221. Browning, M., Chiappori, P.-A., Weiss, Y., 2014. The Economics of the Family Policy. Cambridge University Press, Cambridge. Campbell, J.Y., Cochrane, J., 1999. Force of habit: a consumption-based explanation of aggregate stock market behavior. J. Polit. Econ. 107 (2), 205–251. Chen, K., Imrohoroglu, A., Imrohoroglu, S., 2007. The Japanese saving rate between 1960 and 2000: productivity, policy changes, and demographics. Econ. Theory 32, 87–104. Chetty, R., Guren, A., Manoli, D., Weber, A., 2013. Does indivisible labor explain the difference between micro and macro elasticities? A meta-analysis of extensive margin elasticities. NBER Macroecon. Annu. 27 (1), 1–56.

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Conesa, J., Krueger, D., 1999. Social security reform with heterogeneous agents. Rev. Econ. Dyn. 2, 757–795. Corbo, V., 2004. Policy challenges of population aging and pension systems in Latin America. In: Ellon, G.H. (Ed.), Global Demographic Change: Economic Impacts and Policy Challenges. Economic Policy Symposium Proceedings, Jackson Hole, WY, Aug 26–28, 2004, issue Aug. Federal Reserve Bank of Kansas City, Kansas City, MO, pp. 257–280. Cui, Z., Wang, B., Guan, Q., 2011. The effects of the effective tax rates structure on economic growth: from structural VAR model. South China J. Econ. 29, 16–27. De Nardi, M., Imrohoroglu, S., Sargent, T.J., 1999. Projected U.S. demographics and social security. Rev. Econ. Dyn. 2, 575–615. De Nardi, M., French, E., Jones, J.B., 2010. Why do the elderly save? The role of medical expenses. J. Polit. Econ. 118, 37–75. De Nardi M., French E. and Jones J.B., 2016. Medicaid insurance in old age, Am. Econ. Rev. (in press). Deaton, A., 2013. The Great Escape: Health, Wealth, and the Origins of Inequality. Princeton University Press, Princeton, NJ. Diamond, P., 1965. National debt in a neoclassical growth model. Am. Econ. Rev. 55, 1126–1150. Dobrescu, L., 2015. To love or to pay: savings and health care in older age. J. Hum. Resour. 50 (1), 254–299. Falk, A., Becker, A., Dohmen, T., Enke, B., Huffman, D., Sunde, U., 2015. The nature and predictive power of preferences: global evidence. Working Paper. Feenstra, R., Inklaar, R., Timmer, M.P., 2013. The next generation of the penn world table. National Bureau of Economic Research, Inc., Cambridge, MA. NBER Working Papers 19255. Fehr, H., Jokisch, S., Kotlikoff, L.J., 2004. The role of immigration in dealing with the developed world’s demographic transition. National Bureau of Economic Research Inc. NBER Working Papers 10512. Fehr, H., Jokisch, S., Kotlikoff, L.J., 2006. Will China eat our lunch or take us to dinner? National Bureau of Economic Research Inc. NBER Working Papers 11668. Fehr, H., Jokisch, S., Kotlikoff, L.J., 2008. Fertility, mortality and the developed world’s demographic transition. J. Policy Model 30 (3), 455–473. Fehr, H., Jokisch, S., Kotlikoff, L.J., 2013. The world’s interconnected demographic/fiscal transition. J. Econ. Ageing 1-2, 35–49. Feldstein, M., 1974. Social security, induced retirement, and aggregate capital accumulation. J. Polit. Econ. 82 (5), 905–926. Feldstein, M., 1998. Privatizing Social Security. University of Chicago Press, Chicago, IL. Fernandez-Villaverde, J., Krueger, D., 2007. Consumption over the life cycle: facts from consumer expenditure survey data. Rev. Econ. Stat. 89 (3), 552–565. Fuleky, P., Ventura, L., Zhao, Q., 2015. International risk sharing in the short and in the long run under country heterogeneity. Int. J. Financ. Econ. 20 (4), 374–384. Galasso, V., 1999. The US social security system: what does political sustainability imply? Rev. Econ. Dyn. 2 (3), 698–730. Galasso, V., Profeta, P., 2002. The political economy of social security: a survey. Eur. J. Polit. Econ. 18 (1), 1–29. Geanakoplos, J., Mitchell, O., Zeldes, S., 1998. Would a privatized social security system really pay a higher rate of return? In: Arnold, R.D., Graetz, M., Munnell, A. (Eds.), Framing the Social Security Debate. Values, Economics, and Politics. National Academy of Social Insurance, pp. 137–157. Reprinted in: Altman, S.H., Shactman, D.I., (Eds.), 2002. Policies for an Aging Society, as Private Accounts, Prefunding, and Equity Investment Under Social Security. The Johns Hopkins University Press, Boston, London, pp. 266–292. Hayashi, F., 1985. The permanent income hypothesis and consumption durability: analysis based on Japanese panel data. Q. J. Econ. 100 (4), 1083–1113. He, H., Lei, N., Zhu, D., 2015. Rapid aging and pension reform: the case of China. Working Paper. Huggett, M., Parra, J.C., 2010. How well does the U.S social insurance system provide social insurance? J. Polit. Econ. 118 (1), 76–112.

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Imrohoroglu, A., Imrohoroglu, S., Joines, D., 1995. A life cycle analysis of social security. Econ. Theory 6, 83–114. Imrohoroglu, A., Imrohoroglu, S., Joines, D., 1999. Social security in an overlapping generations economy with land. Rev. Econ. Dyn. 2, 638–665. International Labour Organization, 2013. ILOSTAT Database. ILO, Geneva, Switzerland. International Monetary Fund, 2013. World Economic Outlook Database. IMF, Washington, DC. International Monetary Fund, 2014. Government Finance Statistics. IMF, Washington, DC. Kapsos, S., 2008. The gender wage gap in Bangladesh. ILO Asia-Pacific working paper series. Kim, S., Kim, S.H., Wang, Y., 2006. Financial integration and consumption risk sharing in East Asia. Jpn. World Econ. 18 (2), 143–157. Kitao, S., 2014. Sustainable social security : four options. Rev. Econ. Dyn. 17 (4), 756–779. Kitao, S., 2015. Fiscal cost of demographic transition in Japan. J. Econ. Dyn. Control. 54, 37–58. Kopecky, K.A., Koreshkova, T., 2014. The impact of medical and nursing home expenses on savings. Am. Econ. J. Macroecon. 6, 29–72. Kose, M.A., Prasad, E.S., Terrones, M.E., 2009. Does financial globalization promote risk sharing? J. Dev. Econ. 89 (2), 258–270. Krueger, D., Kubler, F., 2003. Computing equilibrium in OLG models with stochastic production. J. Econ. Dyn. Control. 28 (7), 1411–1436. Krueger, D., Ludwig, A., 2007. On the consequences of demographic change for rates of returns to capital, and the distribution of wealth and welfare. J. Monet. Econ. 54 (1), 49–87. Krusell, P., Smith Jr., A.A., 1998. Income and wealth heterogeneity in the macroeconomy. J. Polit. Econ. 106 (5), 867–896. Lee, R.D., 1974. Forecasting births in post-transition populations: stochastic renewal with serially correlated fertility. J. Am. Stat. Assoc. 69, 607–617. Lim, K.-M., Weil, D.N., 2003. The baby boom and the stock market boom. Scand. J. Econ. 105 (3), 359–377. McGrattan, E., Prescott, E.C., 2015. On financing retirement with an aging population. Federal Reserve Bank of Minneapolis. Staff Report 472. Mendoza, E.G., Razin, A., Tesar, L.L., 1994. Effective tax rates in macroeconomics: cross-country estimates of tax rates on factor incomes and consumption. J. Monet. Econ. 34 (3), 297–323. Miles, D., 1999. Modelling the impact of demographic change upon the economy. Econ. J. 109, 1–36. Mohan, R., 2004. Fiscal challenges of population ageing: the Asian experience. In: Ellon, G.H. (Ed.), Global Demographic Change: Economic Impacts and Policy Challenges. Economic Policy Symposium Proceedings, Jackson Hole, WY, Aug 26–28, 2004, issue Aug. Federal Reserve Bank of Kansas City, Kansas City, MO, pp. 299–357. National Bureau of Statistics of China, n.d. China statistical yearbook. Various Issues. Nishiyama, S., Smetters, K., 2007. Does social security privatization produce efficiency gains ? Q. J. Econ. 122 (4), 1677–1719. OECD, 2011. Pensions at a Glance 2011: Retirement-Income Systems in OECD and G20 Countries. OECD, Paris, France. OECD, 2013a. Revenue Statistics. OECD, Paris, France. OECD, 2013b. National Accounts Statistics. OECD, Paris, France. Poterba, J., 2001. Demographic structure and asset returns. Rev. Econ. Stat. 83, 565–584. Poterba, J., 2004. The impact of population aging on financial markets. National Bureau of Economic Research Inc. NBER Working Papers 10851. Rios-Rull, J.-V., 2001. Population changes and capital accumulation: the aging of the baby boom. B.E. J. Macroecon. 1 (1), 1–48. Samuelson, P.A., 1958. An exact consumption-loan model of interest with or without the social contrivance of money. J. Polit. Econ. 66 (6), 467–482. Song, Z., Storesletten, K., Wang, Y., Zilibotti, F., 2015. Sharing high growth across generations: pensions and demographic transition in China. Am. Econ. J. Macroecon. 7 (2), 1–39. Storesletten, K., 2000. Sustaining fiscal policy through immigration. J. Polit. Econ. 108 (2), 300–323.

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Storesletten, K., Telmer, C., Yaron, A., 2007. Asset pricing with idiosyncratic risk and overlapping generations. Rev. Econ. Dyn. 10 (4), 519–548. United Nations, 2013a. World Population Prospects: The 2012 Revision. United Nations, New York, NY. United Nations, 2013b. National Accounts Statistics: Main Aggregates and Detailed Tables. United Nations, New York, NY. World Bank, 2013. World Development Indicators Database. World Bank, Washington, DC. Yaari, M.E., 1965. Uncertain lifetime, life insurance and the theory of the consumer. Rev. Econ. Stud. 32, 137–150.

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CHAPTER 5

Insurance Markets for the Elderly H. Fang University of Pennsylvania, Philadelphia, PA, United States National Bureau of Economic Research (NBER), Cambridge, MA, United States ARC Centre of Excellence in Population Ageing Research (CEPAR), University of New South Wales, Sydney, NSW, Australia

Contents 1. Introduction 2. Risks Faced by the Elderly 2.1 Income Risks 2.1.1 2.1.2 2.1.3 2.1.4

Job Displacement and Labor Income Risks Investment Income Risks Housing Wealth Decline of Defined Benefit Pension Plans

2.2 Health and Health Expenditure Risks 2.3 Longevity/Mortality Uncertainty 2.4 Morbidity/Long-Term Care Risks 3. Insurance Markets 3.1 Health Insurance Market 3.1.1 US Health Insurance System for the Elderly 3.1.2 Health Insurance Reform in the United States 3.1.3 Health Insurance System in Other OECD Countries

3.2 Annuity Insurance Market 3.2.1 Theory of the Demand of Annuities 3.2.2 Under-Annuitization Puzzle and Its Solutions? 3.2.3 Reverse Mortgage

3.3 Life Insurance Market 3.3.1 Front-Loaded Premiums and Reclassification Risk Insurance 3.3.2 Life Settlement Market and Its Welfare Effects 3.3.3 Why Do Life Insurance Policyholders Lapse?

3.4 Long-Term Care Insurance Market 3.4.1 Basic Facts of Long-Term Care Arrangements 3.4.2 Why Is the Private LTC Insurance Market so Small?

4. Interactions Between Social Insurance and Private Insurance Programs 4.1 Medicaid and Long-Term Care Insurance 4.2 Medicare and Private Health Insurance 4.2.1 4.2.2 4.2.3 4.2.4

Medicare Medicare Medicare Medicaid

and and and and

Medigap Medicare Advantage Employer-Sponsored Health Insurance Medicaid Managed Care

5. Summary and Directions for Future Research

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5.1 Interaction Between Insurance Markets and Labor Markets 5.2 A Portfolio Approach to Households’ Insurance Demands 5.3 Insurer-Side Risks and Regulation Acknowledgments References

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Abstract We describe the risks faced by the aging population and survey the corresponding insurance markets for these risks. We focus on income risk, health expenditure risk, long-term care expenditure risk, and mortality risk. We also discuss the interactions between social insurance and private insurance markets.

Keywords Social insurance, Private insurance markets, Life insurance, Annuity insurance, Health insurance, Longterm care insurance, Risk

JEL Classification Codes D14 (personal finance), G22 (insurance), I13 (health insurance, public, and private)

1. INTRODUCTION Many nations, including almost all of the industrialized countries, are facing challenges from several demographic developments. First, the baby-boomer generation, the large cohort born within two decades after World War II, is approaching retirement and old age. Second, fertility rates have fallen in most countries. Third, mortality rates have also been falling, and life expectancies have been rising. These demographic trends will lead to a significant increase of both the number and percentage of the elderly population (those older than 65) and the very old population (those older than 85). Table 1 shows the number and percentage of the US population that are, respectively, aged 65 and over and 85 and over. It shows that the percentage of the population aged 65 and over in the United States has risen from about 8% in 1950 to 13% in 2010, and it is expected to further increase to close to 20% in the coming decades. Moreover, average life expectancies for both men and women at age 65 have been rising, which leads to an increasing proportion of the very oldest (age 85 and over). Table 1 shows that the percentage of population age 85 and over has risen substantially from 0.4% in 1950 to 1.8% in 2010 and is projected to increase to 4.3% in 2050. The aging population trend is by no means unique to the United States. In fact, the United States is relatively young compared to Europe and Japan. Table 2 shows, according to United Nations Population Prospects (2010), the percentage of the population aged 65 and over in 2010 and projections for 2030 and 2050. It shows that while Europe and Japan populations are currently the oldest, several Asian countries and regions will join the ranks of the oldest by 2030.

Insurance Markets for the Elderly

Table 1 Number and percentage of people age 65 and over and age 85 and over, selected years 1900–2010 and projected 2020–50 65 and over 85 and over Year

Number (millions)

Percent (%)

Number (millions)

Percent (%)

1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2005 2010 2020* 2030* 2040* 2050*

3.1 3.9 4.9 6.6 9.0 12.3 16.2 20.1 25.5 31.2 35.0 36.7 40.3 54.8 72.1 81.2 88.5

4.1 4.3 4.7 5.4 6.8 8.1 9.0 9.9 11.3 12.6 12.4 12.4 13.0 16.1 19.3 20.0 20.2

0.1 0.2 0.2 0.3 0.4 0.6 0.9 1.5 2.2 3.1 4.2 4.7 5.5 6.6 8.7 14.2 19.0

0.2 0.2 0.2 0.2 0.3 0.4 0.5 0.7 1.0 1.2 1.5 1.6 1.8 1.9 2.3 3.5 4.3

Source: US Census Bureau, 1900–40, 1970, and 1980, US Census Bureau, 1983, Table 42; 1950, US Census Bureau, 1953, Table 38; 1960, US Census Bureau, 1964, Table 155; 1990, US Census Bureau, 1991, 1990 Summary Table File; 2000, US Census Bureau, 2001, Census 2000 Summary File 1; US Census Bureau, Table 1: Intercensal Estimates of the Resident Population by Sex and Age for the US: April 1, 2000 to July 1, 2010 (US-EST00INT-01); US Census Bureau, 2011. 2010 Census Summary File 1; US Census Bureau, Table 2: Projections of the population by selected age groups and sex for the United States: 2010–50. For the years with *, the numbers are projected.

The increasing percentage of the elderly in the population will raise the dependency ratio (see Table 3 for selected OECD countries) and impose significant strains on the financing of social insurance programs, eg, the US Social Security system and the Medicare program (which is the government-provided medical insurance program for the retirees in the United States), that most of the retirees rely on. Fig. 1 plots the sources of income for married couples and nonmarried persons aged 65 and over. It shows that since the early 1960s, Social Security has provided the largest share of the total income for older Americans, at around 40%. It also shows that the share of income from pension withdrawals increased rapidly in the 1960s and 1970s to a peak in 1992, but has fluctuated since then at about a fifth of aggregate income. The share of income from assets peaked in the mid-1980s and has generally declined since then. The share from earnings has shown the opposite pattern—declining until the mid-1980s and generally increasing since then. In 2010 the aggregate income for the population aged 65 and over came largely from four sources: Social Security accounted for 37%, earnings 30%, pensions 19%, and asset incomes 11%. Given the rising elderly dependency ratio, projected for the United States

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Table 2 Sixteen oldest countries in 2030 according to the percentage of age 65 and over 65 and over (rank) Country

2010

Japan Germany Singapore Italy Hong Kong Finland Austria Slovenia Portugal France Belgium Switzerland Greece Netherlands Croatia South Korea

22.6% 20.5% 10.2% 20.4% 12.9% 17.2% 17.6% 16.4% 17.9% 17.0% 17.4% 17.3% 18.3% 15.4% 17.3% 11.0%

United States EU 27 World

13.0% 17.5% 7.6%

(1) (2) (51) (3) (41) (13) (8) (19) (6) (16) (10) (12) (4) (23) (11) (49)

2030

2050

30.8% (1) 28.2 (2) 27.5% (3) 26.8% (4) 26.3% (5) 25.1% (6) 24.8% (7) 24.6% (8) 24.5% (9) 24.3% (10) 24.1% (11) 24.1% (12) 24.0% (13) 23.8% (14) 23.8% (15) 23.2% (16)

37.8% 32.5% 32.6% 33.3% 32.6% 25.9% 29.4% 30.2% 32.1% 26.9% 26.6% 26.0% 31.3% 25.6% 28.2% 34.2%

19.8% 23.8% 11.7%

21.6% 28.7% 16.3%

(1) (6) (4) (3) (5) (27) (15) (13) (7) (20) (21) (24) (9) (29) (18) (2)

Source: United Nations, World Population Prospects: The 2012 Revision.

Table 3 Elderly dependency ratios in OECE countries Country 1975

2000

2025

Austria Belgium Denmark Finland France Germany Greece Ireland Italy Luxembourg Netherlands Portugal Spain Sweden United Kingdom Switzerland Turkey Japan United States OECD average

21 25 22 22 25 23 27 17 26 21 20 23 24 26 24 22 9 24 19 21

32 36 32 37 37 34 37 28 41 41 36 32 35 36 33 37 14 43 29 32

24 22 21 16 22 23 19 19 19 20 17 16 16 24 22 19 8 12 16 17

Note: Elderly dependency ratio is defined as the ratio of the population aged 65 and over relative to the population aged between 15 and 64. Source: Based on United Nations, Demographic Yearbook, various issues.

Insurance Markets for the Elderly

Percent

Percent

100

100 16

Other

10

Earnings

80

80 29 28 60

60 9

40

16

20

Pensions

12 15

31

34

1962

1967

0

Asset income

40

20

0 1976

Social Security

1980

1990

2000

2010

NOTE: A married couple is age 65 and over if the husband is age 65 and over or the husband is younger than age 55 and the wife is age 65 and over. The definition of “other” includes, but is not limited to, unemployment compensation, workers compensation, alimony, child support, and personal contributors. Reference population: These data refer to the civilian noninstitutionalized population. SOURCE: Current Population Survey, Annual Social and Economic Supplement, 1977–2011.

Fig. 1 Percentage distribution of sources of income for married couples and nonmarried persons age 65 and over: 1962–2010. Source: From Older Americans, 2012. Key indicators of well-being. Accessed at: http://agingstats.gov/agingstatsdotnet/mainsite/ (Indicator 8).

to be 29% in 2025, surveys have shown that there are serious concerns among babyboomers regarding the amount of sustainable benefits of Social Security when they retire (see Bernheim and Levin, 1989; Bottazzi et al., 2006; Dominitz and Manski, 2006; Delavande and Rohwedder, 2010 for survey evidence).a,b What Fig. 1 does not show is that retired households face a substantial drop in their income upon retirement. While it is true that the assets for the average household tend to peak at retirement, most assets are subject to significant rates of return risks (see Section 2.1). In fact, the elderly also face a multitude of other risks related to their health care expenditures, long-term care expenditures, and longevity, among others (see Section 2). a

b

In the most recent annual report, the US Social Security and Medicare Boards of Trustees (2014) projected that, under the current Social Security and Medicare benefits and tax rules, the Treasury would start to redeem the Social Security trust fund asset reserves from 2019 and the trust fund reserves would be depleted in 2033, from which point the tax income would be sufficient to pay about three-quarters of scheduled benefits (see http://www.ssa.gov/oact/tr/2014/index.html). See also Auerbach et al. (1989) for a quantitative analysis of the sustainability of the Social Security system in a computable dynamic general equilibrium model with an aging population.

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When there are risks, there is scope for insurance to protect individuals against the risks. Given the retirees’ diminishing earnings capacity over time, and the increasing risks (again over time) they expect to face, insurance is of the utmost importance for the welfare of the elderly. Indeed, most of the developed economies have instituted a variety of government-administered social insurance programs, for example, Social Security programs as a form of public annuity and Medicare as retirees’ health insurance, and so on. However, it is unlikely that public insurance will meet all of the insurance needs of the retirees; thus the retirees may still have to think about the costs and benefits of purchasing additional insurance from private insurance markets. Of course, retirees may also be insured through informal insurance, including self-insurance (ie, savings) and transfers from relatives and children.c While the details differ in terms of how each of the insurance products we subsequently describe impacts individuals’ welfare, the basic economics for the value of insurance to hedge against the risks is common to all and is very simple. Consider the simplest case where the relevant risk is related to out-of-pocket health expenditures, which will then impact the individuals’ level of consumption. Consumers are risk averse in the sense that their preferences can be represented by a strictly concave utility function u(c), where   c is level of consumption, and is given by c ¼ y  e , where y is the income
and e is the random out-of-pocket medical expenditures drawn from a distribution f e with mean  E e ¼ μe : Suppose that if the consumer purchases a health insurance at premium p, her out-of-pocket medical expenditure is reduced to 0. Her expected utility from purchasing the
insurance is simply uðy  pÞ, while her expected utility without insurance is   Eu y  e : If the insurance premium p is
actuarially fair, ie, if p ¼ E e , then we know   from Jensen’s inequality that uðy  pÞ > Eu y  e ; that is, the consumer is strictly better off by purchasing an actuarially fair insurance than not doing so.d In essence, the welfare gain from actuarially fair insurance is obtained by transferring resources from states with low marginal utility of consumption (ie, states without losses) to states with high marginal utility of consumption (ie, states with losses). While the preceding simple example illustrates the potential source of welfare gains from owning insurance, the reality for the elderly is a lot more complicated. First, the risks the elderly face are multidimensional, including health expenditure risks, income risks, mortality risks, and long-term care expenditure risks, to name the most important

c

d

We will focus on formal private and public insurance in this chapter, but clearly self-insurance via precautionary saving and informal insurance via family support are both important components of individuals’ strategy to deal with risks in retirement. See Chapter 4 by Attanasio et al. (this volume) for a focused discussion on consumption and saving. This simple argument assumes that the marginal utility of consumption u0 ð  Þ does not depend on health status. Also, self-insurance tends to complicate the welfare gains from insurance, though it is well known that saving is an imperfect substitute for insurance (see, eg, Baily, 1978).

Insurance Markets for the Elderly

ones. Second, the distributions of the risks are often affected by their own behavior; for example, health expenditure risks may depend on prior health investment, and income risks are affected by their retirement portfolio choices and labor supply decisions. Third, insurance markets are often subject to adverse selection and other forms of market failure (Arrow, 1963; Akerlof, 1970; Rothschild and Stiglitz, 1976). Fourth, individuals’ demand for and benefits from purchasing private insurance are often impacted by social insurance, leading to important and interesting interactions between public and private insurance markets, on both the demand and supply sides. The remainder of this chapter is structured as follows. In Section 2 we describe the major risks that the elderly face, including income risks, health risks, longevity/mortality risks, and morbidity/long-term care expenditure risks. In Section 3, we describe a variety of insurance products, offered either via the private markets or via governmentadministered programs, and the main theoretical and empirical findings regarding the workings of these insurance markets. In Section 4 we discuss the literature on the interaction between social insurance programs and the corresponding private insurance markets. Finally in Section 5 we conclude and discuss directions for future research. We would like to point out upfront that most of the literature we review in this chapter is about the US experience, though when appropriate we also discuss certain evidence from other OECD countries.

2. RISKS FACED BY THE ELDERLY In this section, we describe the multitude of risks the elderly face. We focus on income risks, health and health expenditure risks, longevity/mortality risks, and morbidity/longterm care expenditure risks.

2.1 Income Risks The income risks the elderly face can originate from a variety of sources. To the extent that the elderly still work, they face job displacement risks and labor income risks. But they also face risks in investment income, housing equity, and other pension incomes. An ever-growing fraction of elderly workers still participate in the labor force. According to the Bureau of Labor Statistics (2012a), the labor force participation rates for Americans aged 65 and over have been steadily increasing since the 1990s, a reversal of the long-standing prior trend toward ever-earlier retirement. The labor force participation rate for men aged 65 and over increased from 16.3% in 1990 to 22.1% in 2010 and is projected to increase further to 26.7% in 2020. Similarly, the labor force participation rate for women aged 65 and over increased from 8.6% in 1990 to 13.8% in 2010 and is projected to be 19.2% in 2020. The increase in labor force participation rates also applies to an even older population: the labor force participation rate for men (women, respectively) aged 75 and over increased from 7.1% (2.7%, respectively) in 1990 to 10.4%

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(5.3%, respectively) in 2010 and will further increase to 12.8% (8.0%) in 2020.e Of course, the labor force participation decision is endogenous, and working often constitutes an informal channel for the elderly to cope with risks they face; moreover, rising life expectancy also contributes to the increase in the labor force participation rates among those aged 65 and over.f 2.1.1 Job Displacement and Labor Income Risks Substantial literature documents the job displacement rates for near-retirement-age workers. Farber (2005) found that the 3-year job displacement rate for the 50–64 age group averages around 9–10% for the two decades from 1981 to 2003. There is evidence that older workers are less likely to become displaced from their jobs than the younger workers. For example, using Survey of Income and Program Participation data from the 1996, 2001 and 2004 panels, Johnson and Mommaerts (2011) found that, between 1996 and 2007, men aged 50–61 (respectively, men aged 62 and older) are 21% (respectively, 23%) less likely than those aged 25–34 to become displaced from their jobs each month. A similar pattern also applies to women. However, Johnson and Mommaerts pointed out that this is mainly driven by the tenure of their employment, not by their age. Once job tenure and other characteristics were held constant, they found that older workers are just as likely as younger workers to lose their jobs. Similarly, Munnell et al. (2009), using data from the Displaced Worker Survey over 1984–2006, found that the difference in the displacement rates between younger (25–54) and older (55+) workers disappeared. There is also strong evidence that older workers have a harder time finding a job, if they are displaced, than younger workers. Heidkamp et al. (2010) reported that, according to data from the Heldrich Center’s “No End in Sight” survey conducted in August 2009 of men and women who had been unemployed at some point in the previous 12 months, only 14% of the respondents who were aged 55 or above had found new jobs as of March 2010 compared to 37% of the younger job seekers. Two-thirds of the older job seekers are still actively looking for work as compared to only 52% of the prime age group. Statistics from the Bureau of Labor Statistics (2012b) showed that the median duration of unemployment for those aged 55–64 is 33.4 weeks, as compared to 21 weeks for those aged 34–44, and 27.6 weeks for those aged 45–54. Johnson and Mommaerts (2011) found that displaced men aged 50–61 are 39% less likely to become reemployed each month than otherwise identical men aged 25–34, and men aged 62 and older are 51%. Johnson and Kawachi (2007) examined older adults’ e f

See table 3 in Bureau of Labor Statistics (2012a). Fries (1980) and recently Cutler et al. (2013) documented evidence for significant compression of morbidity in the elderly US population, suggesting that increases in life expectancy are related to increases in healthy and productive lives.

Insurance Markets for the Elderly

employment opportunities by studying job changes at ages 45–75 using data from the Health and Retirement Study. They found that many older workers move to new occupations and industries when they switch jobs, often assuming positions that involve less stress and physical effort, and they generally experience sharp hourly wage reductions and often lose pension coverage and health benefits. Evidence also shows that older workers suffer from wage cuts in new jobs. Chan and Stevens (2001) focused on workers above age 50 in the Health and Retirement Study 1992.g They found that among reemployed workers, half receive wages at least 19% below their predisplacement wages, and almost 25% see their wages halved. On the other hand, nondisplaced workers enjoy about 5% earnings growth between the survey waves. They found that 6 or more years after displacement, earnings losses still ranged from 23% to 29%. Couch et al. (2011), using administrative earnings data from Connecticut unemployment insurance records, compared the experience of workers who were impacted in a mass layoff with those who remained continuously employed during the period of 1993–98. They found that on average that 6 years after job displacement caused by mass layoffs, older workers’ earnings remain 26% below those of the comparison group; workers aged 40 and above still have a 14% reduction in earnings, while the reduction in earnings is a more steep 37% for those aged 55 and above. Similarly, Johnson and Mommaerts (2011) found that older displaced workers who find a job usually experience a sharp wage decline: for those reemployed at ages 50–61, the new median wage falls 20% below the old median wage and the median wage fall is an even steeper 36% for people 62 or older. 2.1.2 Investment Income Risks Because wealth accumulation typically takes place over individuals’ entire working lives, elderly households have more assets on average than younger households. Household wealth includes housing, various forms of financial assets, Social Security, and pension wealth. Poterba and Samwick (2001), using data from the Survey of Consumer Finances, showed that both the median and the mean household typically enter a period of fairly rapid accumulation of financial assets when they are about 34 years old, and that median and mean holdings of financial assets peak at about ages 58 and 64, respectively. They also found interesting life-cycle patterns of asset accumulation: as a percentage of total assets, financial assets show a U-shaped pattern with age; specifically, they decline as households age and then begin to increase at advanced ages. However, investment real estate and equity in privately held business display a hump-shaped pattern, while owner-occupied housing does not decline at older ages. Also, Poterba and Samwick (2001) found that, within financial assets, the percentage in bonds, particularly tax-exempt bonds, significantly rise with age; but the portfolio share of all taxable equity exhibits a rather flat g

See also Chan and Stevens (1999).

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S&P 500 (1970–2012) 1800

1600

1400

1200

1000

800

600

400

200

5/ 1 1/ 970 5/ 1 1/ 972 5/ 1 1/ 974 5/ 1 1/ 976 5/ 1 1/ 978 5/ 1 1/ 980 5/ 1 1/ 982 5/ 1 1/ 984 5/ 1 1/ 986 5/ 1 1/ 988 5/ 1 1/ 990 5/ 1 1/ 992 5/ 1 1/ 994 5/ 1 1/ 996 5/ 1 1/ 998 5/ 2 1/ 000 5/ 2 1/ 002 5/ 2 1/ 004 5/ 2 1/ 006 5/ 2 1/ 008 5/ 2 1/ 010 5/ 20 12

0

1/

246

Fig. 2 S&P 500 index: 1970–2012.

age profile, suggesting that households do not necessarily follow the popular financial advice to switch from stocks to bonds as they approach retirement.h To the extent that risky investments, including equity or bond holdings in either taxable or tax-deferred accounts, are in the households’ financial portfolios, older individuals are thus more exposed, at least in absolute magnitude, to the volatilities in the asset market than younger workers (see Fig. 2 for the series of S&P 500 index at the beginning of each month between 1970 and 2012). For example, the Vanguard Report (2008) showed that about two-thirds of retirees’ 401(k) portfolios are invested in equities, and as a result stock market volatilities often would result in significant risks for older workers’ financial wealth, with little time for the market to recover. In fact, Glover et al. (2011), using 2007 Survey of Consumer Finances data, documented that the average net worth is 1.9 times the average labor income for 20–29 year olds, while it is 21.1 times the average for those 70 or older. The authors revalued these portfolios using relevant market indices

h

See also, Coile and Milligan (2009) for similar findings.

Insurance Markets for the Elderly

and found that during the Great Recession people between ages 60 and 69 lost the most: $310,000 on average, which is nearly four times their average annual income.i 2.1.3 Housing Wealth In 1998 households aged 50 and older held over $24.8 trillion in net worth, or 2.9 times the US GDP for that year (Kopczuk and Lupton, 2007). Most of that wealth was in the form of housing equity. At the household level, over 80% of households in their fifties are homeowners. Housing wealth accounts for over 50% of household wealth among homeowners, and it dominates other asset holdings for the majority of such households. Because of the significance of housing wealth in the portfolio of the elderly, housing market volatilities also contribute to the risks that the elderly face to the extent that they may be using housing equity to finance their retirement (see Fig. 3 for the S&P Case/Shiller home price indices from 1987 to 2013).j In a series of papers, 250

S&P/Case–Shiller Home Price Indices

20-city composite

225

250 225

200

200

175

175

150

150 10-city and 20-city Composites are both back to their mid-2004 levels

125

125

10-city composite

100

100

75

75

50 50 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009 2011 2013

Fig. 3 S&P/Case–Shiller home price indices: 1987–2013. Source: S&P Dow Jones Indices and CoreLogic.

i

j

However, Gustman et al. (2010) focused on the early boomer population (ages 53–58) and found a much smaller effect of the stock market decline on their wealth. Using Health and Retirement Study data, they reported that in 2006, those in their early to mid-fifties had only 15% of their total wealth in stocks, including 401(k) plans and IRAs. Poterba et al. (2011) also considered the role of housing equity in the portfolios of retirement-age households and explored the extent to which households draw down housing equity and financial assets as they age. They found that many households appear to treat housing equity and nonannuitized financial assets as “precautionary savings.”

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Venti and Wise (2001, 2004), using a variety of data sets, found that as they age households do not seem too willing to use housing equity to support their general nonhousing consumption. They found that large reductions in home equity are typically associated with the death of a spouse, retirement, or with other precipitating shocks. We will come back to housing wealth and its potential role in insuring risks associated with retirement in Section 3.2.3 when we discuss reverse mortgages. 2.1.4 Decline of Defined Benefit Pension Plans As shown in Fig. 1, incomes from employer pension plans constitute an important source of retirement income. There are two main categories of employer pension plans, the defined benefit (DB) plans and the defined contribution (DC) plans.k In a DB pension plan, workers accrue a promise of a regular monthly payment from the date of their retirement until their death or, in some cases, until the death of their spouse. The promised deferred life annuity is commonly based on a formula linked to an employee’s wage or salary and years of tenure at the sponsoring firm. In contrast, in a DC pension plan, workers accrue funds in individual accounts administered by the plan sponsor. The contributions of employees are typically deducted directly from their pay and frequently some portion of these contributions is matched by the employer. In contrast to a DB plan, it is the contributions rather than the benefit that is fixed in a DC pension plan; the retirement income that will be provided is unknown in advance. The pension benefit accumulated during the employee’s working career will depend on the contributions made while working and the investment returns earned on the plan balances. DB and DC plans also differ in how several important risks are distributed between the employers and the employees. Under a DB plan, the employer bears the investment return risk associated with the pension funds and, by promising a stream of annuity payments to the worker, bears the worker’s longevity risk. In contrast, under a DC plan, the employee is fully responsible for the investment return risk, as well as his/her own longevity risk. Traditional DB pension plans are gradually losing their dominance in the occupational pension systems of many countries. Over the past few decades, there has been a gradual shift toward DC pensions, and in some countries, DC plans now account for the majority of invested assets in private sector occupational pension plans. In 1983 more than 60% of US workers had some kind of DB plan; today, it is less than 20%.l Using the Form 5500 Annual Report data set, Fig. 4 shows that in the United States, the total k

l

See Chapter 14 by Mitchell and Piggott (this volume) for a detailed analysis of the economic aspects of occupational pensions. See Broadbent et al. (2006) for a detailed overview of the shift from DB to DC plans and the associated implications for asset allocation and risk management.

Insurance Markets for the Elderly

800,000 700,000 600,000 500,000 400,000 300,000 200,000 100,000 0 1975

1980

1985 Total

1990

1995

Defined benefit

2000

2005

Defined contribution

Fig. 4 Number of pension plans, by type of plan, 1975–2009. Source: Author's calculation from Form 5500 database.

number of DB plans peaked around 1983 and has been steadily declining; in contrast, the number of DC plans has been steadily increasing from 1975.m Fig. 5 shows that as a percentage of total number of employer pension plans, DB plans have been steadily losing ground to DC plans: in 1975, about 32% of all employer pension plans are DB plans, but in 2009 only 8% are DB plans. Notice that Figs. 4 and 5 are in terms of the number of employer pension plans unweighted by the asset levels in each plan. Fig. 6 shows the evolution of percentage share of pension assets in DB and DC plans, respectively, from 1975 until 2009, using data in the US Flow of Funds Accounts. It shows that the share of assets in DB plans has steadily declined over the past 30 years. A number of explanations have been offered for the shift from DB to DC pension plans (see Broadbent et al., 2006). Increased workforce mobility associated with demographic and industrial changes appears to be an important driver of the shift away from DB pension plans; all else being equal, mobile workers have less of a preference for DB pensions because traditional benefit formulas are “back-loaded,” favoring long-tenured employees, and because DB benefits are not portable from one employer to another. Other factors that may have contributed to the trend toward DC plans include pension m

The Form 5500 Annual Report is the primary source of information about the operations, funding, and investments of approximately 800,000 employer-sponsored retirement and benefit plans.

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100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2005 2006 2007 2008 2009

250

%DB plans

%DC plans

Fig. 5 Percentage of DB/DC plans among total pension plans, 1975–2009. Source: Author's calculation from Form 5500 database.

underfunding and its persistence because of a decline in long-term interest rates; the move to more market-based accounting; increasing regulatory burden; and the uncertainty and recognition of the effects of increased longevity on plan costs. It is also linked to the regulatory and accounting reforms that are making these risks more transparent. Since DC contributions can be fixed as a predictable share of payroll, migrating to a DC plan offers employers a means of reducing balance sheet and earnings volatility at least over the long term. As employers shift their pension plans from DB to DC, the risks and responsibilities associated with providing retirement income are increasingly shifted from the employer to the employee (Munnell and Sunden, 2004; Friedberg and Webb, 2005). In terms of responsibilities, the employee in a DC plan decides whether or not to participate, how much to contribute, how to invest the assets, and how to withdraw the money at retirement. However, Munnell and Sunden (2004) found that 26% of workers who are eligible

Insurance Markets for the Elderly

70% 65% 60% 55% 50% 45% 40% 35% 30% 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 DB

DC

Fig. 6 Percentage share of assets in US DB and DC pension plans: 1975–2009. Source: US Flow of Funds Account data.

do not participate; less than 10% of those who do participate contribute the maximum; over half do not diversify their investments, and almost none rebalance their portfolios in response to age or market returns; many cash out when they change jobs; and most do not annuitize at retirement.

2.2 Health and Health Expenditure Risks Older age is often accompanied by increased risk of certain diseases and disorders. Large proportions of older Americans report a variety of chronic health conditions such as hypertension and arthritis. According to Older Americans (2012), in 2009–10, 38% of people aged 65 and over were obese, compared with 22% in 1988–94; and total health care costs (including both out-of-pocket costs and costs covered by insurance) increased significantly among older Americans from $9850 in 1992 to $15,709 in 2008 (in 2008 constant dollars). From 1977 to 2009, the percentage of household income that people aged 65 and over allocated to out-of-pocket spending for health care services increased from 12% to 22% among those in the poor/near poor income category. French et al. (2006) found that death is often preceded by a costly illness; that out-of-pocket medical expenditures related to increased drug costs, doctor visits, and hospital and nursing home stays go up by about 200% in the few years before death; and that the increase in medical

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spending before death, combined with burial expenses, can explain about 24% of the decline in assets of the soon-to-be deceased and about 37% of the decline in assets in the last year of life.n In the United States, the retirees are almost all covered by Medicare (see Section 3.1.1 for details). However, Medicare pays just over half of total health care costs; thus retirees are still exposed to high out-of-pocket spending because Medicare has substantial deductibles and cost sharing.o For example, in 2012 Medicare Part A includes a deductible of $1156 per hospitalization; for hospital stays longer than 60 days, beneficiaries have cost sharing of $289 per day for days 61–90, $578 per day for days 91–150, and receive no coverage after 150 days. For Part B, beneficiaries pay a $140 deductible and 20% coinsurance per visit. There is also significant cost sharing and limited coverage for skilled nursing. Even with supplemental insurance for medical and prescription drug expenses, retirees face out-of-pocket expenses for cost-sharing obligations and for items or services not covered by Medicare or supplemental coverage. And, of course, they are subject to pay for the premiums for Medicare supplemental coverages. Hoffman and Jackson (2012) found that in 2006, the major components of out-of-pocket spending were premiums (39%); long-term care (19%); medical providers and supplies (15%); prescription drugs (14%); dental (6%); and inpatient and outpatient hospital costs (5%). Ample literature investigates the mean total medical expenditures or the mean out-ofpocket medical expenditure by age. Meara et al. (2004) used a combination of household surveys and total spending data to analyze the trends in medical spending from 1963 to 2000. They found that during this nearly 40-year period, total medical spending grew fastest among the elderly. Per person spending among the elderly grew rapidly from 1963 to 1987, but this trend was then reversed during the next decade. In contrast, Norton et al. (2006) focused on out-of-pocket health care expenditures paid by elderly Americans. Using data from the Medicare Current Beneficiary Survey (MCBS) (1992–98), Norton et al. (2006) show in Fig. 7, which is reproduced from their paper, that mean monthly out-of-pocket health care expenditures rise steadily as a function of age, from $85 per month at age 66 to $485 per month at age 95. It also shows that the increase in total out-of-pocket health care expenditures by age is driven almost entirely by long-term care; other out-of-pocket expenditures, such as primarily inpatient care, physician services, and pharmaceuticals, are essentially independent of age. Fig. 8 shows the ratio of out-of-pocket medical expenditures over income at different percentiles (25th, 50th, 75th, and 90th) for different ages. It shows an increasing range of out-ofpocket health care expenditures relative to income as retirees get older. Marshall et al. (2011) focused on the risk of out-of-pocket health care expenditures at the end of life n o

See also Kelley et al. (2013) for similar findings. See Department of Health and Human Services, What are the Medicare Premiums and Coinsurance Rates for 2012, at http://answers.hhs.gov/questions/3006.

Mean monthly out-of-pocket expenditures (1998$)

Insurance Markets for the Elderly

600 Total Others

Long-term care expup/expdn

400

200

0 65

70

75

80 Age (years)

85

90

95

Mean monthly total out-of-pocket expenditures/income

Fig. 7 Out-of-pocket health care expenditure (means) by age and type of expenditures. Source: From Norton, E.C., Wang, H., Stearns, S.C., 2006. Behavioral implications of out-of-pocket health care expenditures. Swiss J. Econ. Stat. 142 (Special Issue), 3–11 (figure 1).

2 25th percentile

50th percentile

75th percentile

90th percentile

1.5

1

.5

0 65

70

75

80 Age (years)

85

90

95

Fig. 8 Total out-of-pocket health care expenditures/income at different percentiles, by age. Source: From Norton, E.C., Wang, H., Stearns, S.C., 2006. Behavioral implications of out-of-pocket health care expenditures. Swiss J. Econ. Stat. 142 (Special Issue), 3–11 (figure 2).

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350

300

250

Millions

254

200

150

100

50

0 1

4

7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82

Fig. 9 Variance of total health care expenditures, by age. Source: Author's calculation based on Medical Expenditure Panel Survey data (2009).

using the Health and Retirement Study (HRS) 1998–2006. They found substantial variations in out-of-pocket expenditures near death, with the largest single category of the spending near death being nursing home care. For individuals who are thinking about insurance choices, the more relevant risk is total health care expenditures, not just the out-of-pocket expenditures given their current health insurance coverages; this is particularly true because of the uncertainty about the funding and coverage of government-provided health insurance programs. Fig. 9 shows the variances of unpredictable medical expenditures using data from the Medical Expenditure Panel Survey (MEPS) 2009. In constructing the graph, total medical expenditure information in MEPS data is regressed on self-reported health status, sex, and gender, and the variance of the residual expenditures for each age is calculated and plotted.p Fig. 9 shows that the variances of medical expenditures that cannot be easily predicted increase significantly after age 50.q

p

q

In order to smooth the graph because of small samples especially for children and the elderly, the sample used in the construction of variance at each age bin includes individuals within a 2-year bandwidth. See Capatina (2012) for an interesting study on the life-cycle effects of health risks.

Insurance Markets for the Elderly

100% Men Women

Probability of living to age x

90% 80% 70% 60% 50% 40% 30% 20% 10% 0%

65

70

75

80

85

90

95

100

Age

Fig. 10 The distribution of life expectancy for a 65-year-old. Note: The chart displays the probability of 65-year-old men and women living to age x. Source: Reproduced from Benartzi, S., Previtero, A., Thaler, R.H., 2011. Annuitization puzzle. J. Econ. Perspect. 25 (4), 143–164, which is based on the life expectancy data from Bell and Miller (2005): http://www.ssa.gov/oact/NOTES/pdf_studies/study120.pdf, table 6, pp. 60–61.

2.3 Longevity/Mortality Uncertainty Another important risk that the elderly face is their longevity/mortality risk. Mortality risk is simply the risk that an individual will die at any age. Longevity risk is the risk that a retired person will live significantly beyond her expected life span and thus run out of money for retirement. These two risks are important in determining how much individuals, including and particularly the retirees, should consume, how much they need to save, and how much bequest to leave to their children and loved ones. Brown (2000) documented the remaining life expectancy and probabilities of survival to selected ages for 65-year-olds in the year 2000: while men and women at age 65 can expect to live, respectively, an additional 16.4 and 19.6 years, 12% of men and 7.7% of women will die prior to their 70th birthday, and 17.5% of men and 31.4% of women will live to age 90 or beyond. More generally, Fig. 10, which we reproduce from Benartzi et al. (2011), shows a large variation in life expectancy at age 65. There is a 22-year difference between the 10th and 90th percentile of the distribution for men (dying at 70 vs 92). Similarly, there is a 23-year difference between the 10th and 90th percentile of the distribution for women (dying at 72 vs 95).r Not only is there significant uncertainty in the life expectancy, but there is also substantial heterogeneity in this uncertainty. Table 4 is reproduced from De Nardi et al. (2009). They used the AHEAD data set and found that rich people, women, and healthy r

Also see Brown (2000) for similar findings.

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Table 4 Life expectancy in years, conditional on being alive at age 70 Income percentile Healthy male Unhealthy male Healthy female

Unhealthy female

All

20 40 60 80

11.7 12.7 13.8 15.0

11.7 12.6 13.6 14.8

8.1 8.9 9.9 10.9

6.3 7.0 7.9 9.0

13.4 14.3 15.4 16.4

Source: From De Nardi, M.D., French, E., Jones, J.B., 2009. Life expectancy and old age savings. Am. Econ. Rev. 99 (2), 110–115. Papers and Proceedings.

Table 5 Percent living to ages 85 and 95, conditional on being alive at age 70 Income percentile Healthy male Unhealthy male Healthy female Unhealthy female

All

Percent living to age 85

20 40 60 80

12.3 15.8 20.3 26.0

8.2 10.8 14.5 19.4

39.2 44.0 49.9 55.8

32.5 37.6 43.5 49.7

31.4 36.3 41.6 47.5

0.5 0.8 1.2 1.9

7.2 8.7 10.9 13.8

6.0 7.5 9.4 12.3

5.4 6.9 8.7 10.9

Percent living to age 95

20 40 60 80

0.8 1.1 1.7 2.5

Source: From De Nardi, M.D., French, E., Jones, J.B., 2009. Life expectancy and old age savings. Am. Econ. Rev. 99 (2), 110–115. Papers and Proceedings.

people live much longer than their poor, male, and sick counterparts, conditional on being alive at age 70. Table 5, also from De Nardi et al. (2009), showed that there is a substantial variation in the probability of living to ages 85 and 95, conditional on being alive at age 70, and these variations are importantly related to income, gender, and health status at age 70.

2.4 Morbidity/Long-Term Care Risks An important risk that is specially pertinent to the elderly is the morbidity risk, which is related to the need for long-term care. Long-term care is a range of services and supports necessary for health or personal care needs over a long period of time (see Norton, 2000). It is important to note that most long-term care is not medical care, but rather assistance with the basic personal tasks of everyday life (sometimes called Activities of Daily Living,

Insurance Markets for the Elderly

Table 6 Percent distributions of limitation in activities of daily living (ADLs) and instrumental activities of daily living (IADLs) by age: United States, 2003–07 Limitations in ADLs Limitations in IADLs Age

None

1

2

3+

No

Yes

55–64 years

98.4 (0.07) 94.3 (0.13) 97.1 (0.11) 93.9 (0.21) 82.2 (0.62)

0.4 (0.03) 1.4 (0.06) 0.7 (0.05) 1.4 (0.10) 4.7 (0.33)

0.3 (0.03) 1.2 (0.05) 0.6 (0.05) 1.2 (0.09) 3.4 (0.28)

0.9 (0.05) 3.2 (0.09) 1.6 (0.08) 3.5 (0.16) 9.7 (0.49)

95.8 (0.12) 87.8 (0.21) 93.8 (0.18) 86.2 (0.31) 64.7 (0.81)

4.2 (0.12) 12.2 (0.21) 6.2 (0.18) 13.8 (0.31) 35.3 (0.81)

65+ years 65–74 years 75–84 years 85+ years

(1) Data source: National Health Interview Survey, 2003–07. Estimates are based on household interviews of a sample of the civilian noninstitutionalized population. (2) From National Center for Health Statistics: http://www.cdc.gov/nchs/ health_policy/ADL_tables.htm.

ADLs), and assistance with everyday tasks (sometimes called Instrumental Activities of Daily Living, IADLs).s The morbidity risk, and consequently the risk for long-term care needs, that the elderly face depends importantly on the number of limitations in ADLs and IADLs. Table 6, from the National Center for Health Statistics, shows that as retirees age, the limitations in ADLs and IADLs both increase substantially; and also importantly, there are substantial variations in the number of limitations in both ADLs and IADLs even conditional on age. As a result of experiencing the limitations in ADLs and IADLs, about 70% of people will need some form of long-term care at some point in their lives (Brown and Finkelstein, 2008). The duration and level of long-term care needs vary from person to person and often change over time. On average, an individual who is 65 today will need some type of long-term care services and supports for 3 years, and women need care longer (3.7 years) than men (2.2 years). However, about one-third of today’s 65-year-olds may never need long-term care support, but 20% will need it for longer than 5 years.t

s

t

ADLs include needing the help of other persons with bathing or showering, dressing, eating, getting in or out of bed or chairs, using the toilet (including getting to the toilet), and getting around inside the home; IADLs include everyday household chores, doing necessary business, shopping, or getting around for other purposes. See http://longtermcare.gov. Manton et al. (2006), however, showed that age-specific incidence of ADL limitations have been declining over time in the United States.

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The “very old” elderly receive long-term care either at home, or in community service organizations, or in long-term care facilities. Examples of home care services include an unpaid caregiver who may be a family member or a friend, or a nurse, home health or home care aide, and/or a therapist who comes to the home. Community support services include adult day care service centers, transportation services, or home care agencies that provide services on a daily basis or as needed. Outside the home, a variety of facility-based programs exist. Nursing homes provide the most comprehensive range of services, including nursing care and 24-h supervision. Other facility-based choices include assisted living, board and care homes, and continuing care retirement communities. Brown and Finkelstein (2008) use Robinson’s model to predict the probability distribution of longterm care utilization. Table 7, reproduced from Brown and Finkelstein (2008), shows that there is a considerable right tail risk to this distribution. For example, although 73% of 65-year-old men (and 56% of 65-year-old women) will never enter a nursing home, of those who do, 12% of men (and 22% of women) will spend more than 3 years there.u

3. INSURANCE MARKETS The elderly deal with the preceding risks in a variety of ways, particularly, they may use insurance products to help cope with these risks. In this section, we describe several important insurance markets. We will mostly focus on private insurance markets, but will discuss public insurances as well.

3.1 Health Insurance Market 3.1.1 US Health Insurance System for the Elderly The United States does not have a national health insurance system. However, the health insurance coverage for those aged 65 and older is almost universal. The sources of health insurance coverage for this population mainly consist of the following: Medicare, Medicaid, employer-provided coverage, and supplemental insurance (known as Medigap). According to Kaiser Family Foundation reports, on average basic Medicare benefits cover about 50% of the personal health care expenditures (excluding long-term care costs) of aged beneficiaries in the United States. Retirees must finance these costs not covered by Medicare by purchasing insurance coverage supplemental to Medicare or by paying directly for such costs out of pocket. Ninety percent of all retirees obtain supplemental insurance coverage from one of four main sources to help fill in these gaps: Supplemental Employer-Sponsored Insurance for Retirees (about one-third); Medicare Advantage (about one-fourth); Medigap policies (about 18%); and Medicaid for which u

However, see Friedberg et al. (2014), which updated and modified the Robinson model using the most recent National Long-Term Care Survey for 1999–2004.

Table 7 Care utilization for 65-year-old from the Robinson model Among users

Type of care

Nursing home Assisted living Home health care Any care

Men Women Men Women Men Women Men Women

Prob. of using care for

Prob. of ever using

Mean age of first use

Mean years in care

>1 year

>3 years

0.27 0.44 0.12 0.20 0.29 0.35 0.40 0.54

83 84 82 85 79 81 82 80

1.3 2.0 0.58 0.48 1.9 2.3 2.9 4.2

0.33 0.42 0.16 0.13 0.52 0.52 0.77 0.85

0.12 0.22 0.04 0.04 0.22 0.28 0.53 0.37

>5 years

Prob. of leaving care alive

Mean number of spells

0.05 0.12 0.01 0.01 0.09 0.15 0.17 0.31

0.65 0.66 0.90 0.93 0.67 0.77 0.33 0.35

1.28 1.39 1.18 1.26 1.45 1.68 1.20 1.27

Source: Reproduced from Brown, J.R., Finkelstein, A., 2008. The interaction of public and private insurance: Medicaid and the long-term insurance market. Am. Econ. Rev. 98 (3), 1083–1102 (table 1).

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about 15–16% of Medicare beneficiaries are “dually eligible” if they are disabled or meet the income and assets thresholds.v 3.1.1.1 Medicare

The main source of health insurance coverage for the elderly is Medicare. Medicare is a national social insurance program established in 1965 under Title XVIII of the Social Security Act that provides health insurance for Americans aged 65 and older.w Anyone who has, or whose spouse has, worked for at least forty quarters in Medicare-covered employment (ie, paid FICA taxes) is eligible for Medicare coverage. It is important to note that, as a social insurance program, the eligibility for Medicare does not depend on the retirees’ income and asset levels. Note that Medicare does not use any mechanism (either pricing mechanism or eligibility criterion) to select risk, which differs substantially from private health insurance programs that manage their risk portfolio by both pricing and underwriting mechanisms. Medicare has four parts. Part A provides coverage for hospital care, while Part B provides outpatient medical services (ie, doctor visits). Medicare enrollees also have the choice between what is called the “traditional Medicare” and Medicare Part C (also known as “Medicare Advantage”). Part D is for prescription drugs. Part A, known as “Hospital Insurance,” covers inpatient hospital stays (at least overnight stays). The maximum length of stay that Medicare Part A covers in a hospital inpatient stay is typically 90 days, where the first 60 days are paid for in full by Medicare but days 61 and 90 require a co-payment (as of 2012, $289 per day). The beneficiary is also allocated at most 60 days of “lifetime reserve days” that can be used after 90 days, which also requires a co-payment (as of 2012, $578 per day). Part A also covers brief stays for convalescence in a skilled nursing facility, and hospice benefits for terminally ill persons with less than 6 months to live as determined by the patient’s physician. Medicareeligible retirees are automatically covered for Part A. Part B, known as “Medical Insurance,” pays for some services and products not covered by Part A on an outpatient basis. Part B coverage includes physician and nursing services, and a list of diagnostic tests and other outpatient hospital procedures and medical treatments administered in a doctor’s office. Part B also covers the purchase of necessary durable medical equipment (DME). Part B coverage begins once a patient meets his or her deductible ($140 in 2012), and then typically covers 80% of approved services, while the remaining 20% is paid by the patient. Enrollment in Part B may be deferred if the beneficiary or his/her spouse is still working and has group health coverage through that employer. The retirees have to pay a small v

While varying across states, these thresholds are low across the board, which means that Medicaid coverage only protects a subset of the poorest retirees against significant out-of-pocket exposure. See French et al. (2012) for a discussion of the relationship between Medicaid and the elderly. w Medicare also provides health insurance coverage to younger people with disabilities as well as people with end stage renal disease and persons with Lou Gehrig’s disease (see Medicare.gov website).

Insurance Markets for the Elderly

premium, which does not depend on assets or on existing health conditions, for enrollment in Part B. Almost all Medicare enrollees who do not work enroll in Part B. Part C, also known as “Medicare Advantage,” was introduced in 1997, where Medicare beneficiaries were given the option to receive their Medicare benefits through private health insurance plans, instead of through the original Medicare (Parts A and B), which is sometimes also referred to as the “fee-for-service” (FFS) Medicare. Retirees face a trade-off in the choice between the traditional Medicare and the Medicare Advantage. The traditional Medicare allows enrollees access to any doctors and hospitals that accept Medicare patients, but its coverage is limited to the standard Medicare benefit package; enrollees of a Medicare Advantage plan, however, are restricted to access only the doctors and hospitals in the network of the private insurer who sells the Medicare Advantage plan, but the enrollees face lower co-payments and deductibles and may receive more benefits than offered by the traditional Medicare (for example, prescription drugs). For people who choose to enroll in a Medicare Advantage health plan, Medicare pays the private health plan a fixed amount every month; and the members may also have to pay a small premium in addition to the Medicare Part B premium for benefits not included in the traditional Medicare. In Section 4.2 we discuss the interactions between Medicare and Medicare Advantage plans. Part D covers prescription drugs. It was introduced in the Medicare Modernization Act enacted in 2003 and took effect in 2006. Anyone with Part A or B is eligible for Part D. To receive this benefit, a person with Medicare must enroll in a stand-alone prescription drug plan or Medicare Advantage plan with prescription drug coverage. These plans are approved and regulated by the Center for Medicare and Medicaid Services (CMS), but are actually designed and administered by private health insurance companies and private drug companies. Part D coverage is not standardized, and approved plans are allowed to choose which drugs (or even classes of drugs) they wish to cover, at what level (or tier) they wish to cover them, and are free to choose not to cover some drugs at all, though Medicare specifically excludes some drugs from coverage (see Duggan et al., 2008 for an extensive description of the Medicare Part D program). A large set of literature studies the Medicare Part D program, including causes of its increasing costs (eg, Duggan and Scott Morton, 2010), consumers’ choice of plans (Heiss et al., 2007; Abaluck and Gruber, 2009; Kling et al., 2009; Ketcham et al., 2010; Ericson, 2010; Heiss et al., 2012), and insurer behavior (Decarolis, 2013). 3.1.1.2 Medicaid

Medicaid is the health program for families and individuals with low income and resources in the United States. It is a government insurance program for persons of all ages whose income and resources are insufficient to pay for health care. In contrast to Medicare, Medicaid is a means-tested program that is jointly funded by the state and federal governments and managed by the states, with each state enjoying substantial discretion in determining eligibility and coverage. Because Medicaid is for individuals of all ages, as

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long as they are low income and meet the asset eligibility rules, many retirees also are on Medicaid. Importantly, if a retiree becomes eligible for Medicaid, the coverage provided under Medicaid is much broader than that under Medicare, particularly for long-term care (see Section 3.4). It should be noted that for beneficiaries who are dual eligible for both Medicare and Medicaid, Medicaid may pay for drugs not covered by part D of Medicare. As we will describe in Section 3.1.2, the recent Patient Protection and Affordable Care Act (ACA) health care reform significantly expanded both eligibility for and federal funding of Medicaid beginning January 1, 2014. Under the law as written, all US citizens and legal residents with incomes up to 133% of the poverty line, including adults without dependent children, qualify for Medicaid coverage. However, the US Supreme Court ruled in National Federation of Independent Business v. Sebelius that states do not have to agree to this expansion in order to continue to receive existing levels of federal Medicaid funding, and many states have chosen to continue with current funding levels and eligibility standards. 3.1.1.3 Employer Coverage for Retirees

Retiree health benefits are an important consideration for older workers making decisions about their retirement. Health benefits for retirees provide an important supplement to Medicare for retirees aged 65 or older. This constitutes another important source of health insurance coverage for retirees. However, the fraction of firms that offer retiree health coverage is fast declining. According to a recent report by the Kaiser Family Foundation and the Health Research and Educational Trust (2012), just 25% of employers with more than 200 workers even offered retiree health benefits to their workers in 2012. There has been a downward trend in the percentage of firms offering retirees coverage, from 66% in 1988 to 32% in 2005 (see Fig. 11). Moreover, the Kaiser Family Foundattion surveys found that the offering of retiree health benefits varies considerably by firm characteristics. For example, in 2012 it found that large firms are much more likely to offer retiree health benefits than small firms—25% vs 4%. Moreover, the rate of offering retiree health benefits among large firms also varies by industry, and by the fraction of lower-wage workers in the firm: large firms in the retail industry are less likely (9%) to offer retiree health benefits than large firms in other industries; and large firms with fewer lower-wage workers (those earning $24,000 or less annually) are more likely to offer retiree health benefits. Importantly, among firms offering retiree health benefits, most large firms offer them to early retirees under the age of 65 (88%). A lower percentage (74%) of large firms offering retiree health benefits offer them to Medicare-age retirees.x x

See Monk and Munnell (2009) for a study on the potential consequences of the declining retiree health insurance offering for both pre-Medicare and Medicare-eligible retirees.

Insurance Markets for the Elderly

100% 90% 80% 70%

66%

60% 50%

46% 40% 40% 40%

40%

36%

34%

37% 35% 36% 35%

30%

32% 34% 32%

29% 28% 26% 26% 25%

20% 10% 0% 1988 1991 1993 1995 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012

Fig. 11 Among all large firms (200 or more workers) offering health benefits to active workers, percentage of firms offering retiree health benefits, 1988–2012.

3.1.1.4 Medicare Supplemental Insurance

Medicare supplemental insurance, also known as “Medigap,” refers to various private supplemental health insurance plans sold to Medicare beneficiaries in the United States that provide coverage for medical expenses that are not or are only partially covered by Medicare, the “gaps” in the Medicare coverage. As of 2006, 18% of Medicare beneficiaries were covered by a Medigap policy. In order to enroll in Medigap, a person must be enrolled in parts A and B of Medicare. The Medigap insurance market is heavily regulated. Since 1992, the coverage and pricing of Medigap policies have been highly regulated by the US government. Specifically, in all but three states (Massachusetts, Minnesota, and Wisconsin) insurance companies can sell only ten standardized Medigap policy types; moreover, within the 6-month Medigap open enrollment period—which starts when an individual is both older than 65 and enrolled in Medicare Part B—an insurer cannot deny Medigap coverage, or place conditions on a policy, or charge more for preexisting health conditions. Outside of open enrollment, the issuing insurance company may require medical screening and may obtain an attending physician’s statement if necessary. Medigap plans are standardized by plan type, organized alphabetically from A to N. Although these plans often have high premium costs, most offer first-dollar coverage of many or all of the costs not covered by Medicare, leading to criticism that they invite moral hazard. The most popular plans (Plans C and F) cover nearly all costs that Medicare does not; some Plan F beneficiaries opt for a “high deductible” option where they pay the first $2000 in expenditures, after which the Medigap plan covers all costs. Premiums for these plans vary by plan type and by state, and by the gender and age of the enrollees, and can range from under $100 to over $400 per month. Some Medigap policies sold before

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January 1, 2006, may include prescription drug coverage, but after that date no new Medigap policies could be sold with drug coverage because of the introduction of the Medicare Part D benefit. 3.1.2 Health Insurance Reform in the United States In March 2010 the United States enacted the Patient Protection and Affordable Care Act, typically known as the Affordable Care Act, or the ACA, which represents the most significant reforms to the US health insurance and health care market since the establishment of Medicare in 1965. This legislation has many components, the four most important of which are as follows: • Individual mandate: All individuals must have health insurance that meets the law’s minimum standards or face a penalty when filing taxes for the year, which will be 2.5% of income or $695, whichever is higher.y,z • Employer mandate: Employers with more than 50 full-time employees will be required to provide health insurance or pay a fine of $2000 per worker each year if they do not offer health insurance, where the fines would apply to the total number of employees minus some allowances. • Insurance exchanges: State-based health insurance exchanges will be established where the unemployed, the self-employed, and workers who are not covered by employer-sponsored health insurance (ESHI) can purchase insurance. Importantly, the premiums for individuals who purchase their insurance from the insurance exchanges will be based on the average health expenditure risks of those in the exchange pool.aa Insurance companies that want to participate in an exchange need to meet a series of statutory requirements in order for their plans to be designated as “qualified health plans.” • Premium subsidies: All adults in households with income under 133% of federal poverty line (FPL) will be eligible for receiving Medicaid coverage with no cost sharing. For individuals and families whose income is between the 133% and 400% of the FPL, subsidies will be provided toward the purchase of health insurance from the exchanges. Most of the changes introduced in the ACA are for the purpose of reducing the uninsured rate, and thus increase the access to affordable health care, in the US population. y

z

aa

These penalties were implemented fully in 2016. In 2014 the penalty was 1% of income or $95 and in 2015, it was 2% or $325, whichever was higher. Cost-of-living adjustments will be made annually after 2016. Hardship exemptions are permitted if the least inexpensive policy available costs more than 8% of one’s income. This component of the ACA was one of the core issues in the United States Supreme Course case 567 US 2012 where the constitutionality of the individual mandate and the Medicaid expansion were challenged. The United States Supreme Court ruled to uphold the constitutionality of the individual mandate on a 5-to-4 decision. States that opt not to establish their own exchanges will be pooled in a federal health insurance exchange.

Insurance Markets for the Elderly

However as we mentioned earlier, because of the almost universal coverage of the elderly via Medicare, the ACA reform will have a rather small impact on the insurance coverage of those who are 65 and over. Nonetheless, two important changes introduced in the ACA are relevant to the elderly population, and we focus on them here. First, the “premium subsidies” component of the ACA represents a significant expansion of the current Medicaid system because many states currently cover adults with children only if their income is considerably lower, and do not cover childless adults at all. Apart from ACA, states differ in their income thresholds for Medicaid eligibility, and on average it is about 65% of the FPL. Thus raising the Medicaid income threshold to 133% of the FPL line represents a significant expansion of Medicaid coverage. Because Medicare enrollees can be dually eligible for Medicaid, this could impact the retiree population as well.ab The second important change relevant to the Medicare population is the introduction of a Medicare surtax on investment income for high-income households. Specifically, a new 3.8% Medicare surtax will be levied on the lesser of net investment income or the excess of modified adjusted gross income above $200,000 for individuals, $250,000 for couples filing jointly, and $125,000 for spouses filing separately. In additional, wages above $200,000 (individuals) and $250,000 (joint filers) will now have to pay an additional 0.9% on earned income above the thresholds previously mentioned. Emerging literature focuses on the impact of the ACA on both health insurance coverage and the labor market. Aizawa and Fang (2013) studied the equilibrium impact of the health insurance reform described in Section 3.1.2 on the labor market, with an emphasis of firms’ internal responses in their compensation package offerings in response to the ACA. Aizawa (2013) studied the optimal design of the health insurance exchange using an estimated life-cycle equilibrium labor market model. Handel et al. (2013) studied the equilibrium of the health insurance exchange under community-rating regulation; they argue that, on the one hand, community-rating regulation worsens the problem of adverse selection and leads to potential welfare loss, but on the other hand, it can generate welfare gains because it provides reclassification risk insurance to individuals. They find that welfare gains from reclassification risk insurance outweigh the welfare loss from adverse selection. Cole et al. (2013) argued that guaranteed issuance and community-rating regulations of the ACA will lead to reduced incentives for individuals to invest in their health. Pashchenko and Porapakkarm (2013) constructed and calibrated a general equilibrium life-cycle model that incorporates both medical expenses and labor income risks to evaluate the welfare effects of the community-rating regulation of the ab

The United States Supreme Court also ruled on June 28, 2012, that the law’s provision stating that if a state does not comply with the ACA’s new coverage requirements, it may lose not only the federal funding for those requirements but also all of its federal Medicaid funds, is unconstitutional. This ruling allows states to opt out of ACA’s Medicaid expansion, leaving each state’s decision to participate in the hands of governors and state leaders. As of the writing of this chapter, 25 states are moving forward with the Medicaid expansion, 22 states will not, and 4 are still weighing their options.

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individual health insurance market and an increase in income redistribution in the economy, both features of the ACA . Neither Cole et al. (2013) nor Pashchenko and Porapakkarm (2013) modeled the firm-side responses to the ACA. 3.1.3 Health Insurance System in Other OECD Countries According to OECD (2011a,b), among the 31 OECD countries, as of early 2010 all except four (Chile, Mexico, Turkey, and the United States) have universal health insurance. Among those, 13 (Australia, Canada, Denmark, Finland, Iceland, Ireland, Italy, New Zealand, Norway, Portugal, Spain, Sweden, and the United Kingdom) offer automatic national health insurance coverage to their citizens financed by general tax revenue. Twelve (Austria, Belgium, Czech Republic, France, Germany, Greece, Hungary, Japan, Korea, Luxembourg, Poland, and Slovakia) achieve universal coverage by mandating that all citizens purchase a single-pool national health insurance. But the financing of the coverage is not through general tax revenues; instead, except for Czech Republic and Slovakia, the premium is paid privately though the government provides an income-based premium subsidy. In the Czech Republic and Slovakia, the health insurance premium for working individuals is shared by the worker and the employer, while the premium for those who do not work is paid for by the government. Germany differs slightly from the other countries in this group: it allows high-income individuals to opt out of the national health insurance risk pool and purchase private health insurance. The Netherlands and Switzerland also achieve universal health insurance through a mandate; however, in these two countries, health insurance is not provided through the state, instead it is purchased from regulated private health insurers. Private insurance companies that operate in the health insurance market compete for enrollees, while subject to community-rating regulations. The government provides premium support to low-income individuals. Because of the lack of national health insurance or a mandatory health insurance requirement in Chile, Mexico, Turkey, and the United States (see the preceding US health insurance reform), a substantial percentage of people are uninsured in these countries. Even with national health insurance, primary health insurance does not cover all costs. Table 8, from OECD (2011a,b), summarizes the share of the costs for selected functions of care covered in 2008–09 by the basic primary health insurance in various countries.

3.2 Annuity Insurance Market Annuities are generally defined as contracts that provide periodic payments for an agreedupon span of time. They include annuities certain, which provide periodic payouts for a fixed number of years, and life annuities, which provide such payouts for the duration of one or more persons’ lives. As we described in Section 2.3, retirees face significant risks in longevity, which poses problems in ensuring sufficient savings for retirement. The principal role of life annuities is to protect individuals against outliving their resources. All developed countries have instituted some form of public annuity, eg, Social Security in

Insurance Markets for the Elderly

Table 8 Basic primary health insurance coverage of selected functions of care and share of typical costs covered, 2008–09 Outpatient Acute inpatient primary care and care specialist contacts Pharmaceuticals Dental care Australia Austria Belgium Canada Czech Republic Denmark Finland France Germany Greece Hungary Iceland Ireland Italy Japan Korea Luxembourg Mexico Netherlands New Zealand Norway Poland Portugal Slovak Republic Spain Sweden Switzerland Turkey United Kingdom

Covered, 100% Covered, 76–99% Covered, 76–99% Covered, 100% Covered, 76–99% Covered, 100% Covered, 76–99% Covered, 76–99% Covered, 100% Covered, 76–99% Covered, 100% Covered, 76–99% Covered, 100% Covered, 100% Covered, 76–99% Covered, 76–99% Covered, 76–99% Covered, 100% Covered, 100% Covered, 100% Covered, 100% Covered, 100% Covered, 100% Covered, 100% Covered, 100% Covered, 76–99% Covered, 100% Covered, 100% Covered, 100%

Covered, 76–99% Covered, 100% Covered, 76–99% Covered, 100% Covered, 76–99% Covered, 100% Covered, 76–99% Covered, 51–75% Covered, 76–99% Covered, 76–99% Covered, 100% Covered, 76–99% Covered, 100% Covered, 76–99% Covered, 76–99% Covered, 51–75% Covered, 76–99% Covered, 100% Covered, 100% Covered, 51–75% Covered, 76–99% Covered, 100% Covered, 100% Covered, 100% Covered, 100% Covered, 76–99% Covered, 76–99% Covered, 76–99% Covered, 100%

Covered, 76–99% Covered, 76–99% Covered, 76–99% Covered, 51–75% Covered, 51–75% Covered, 51–75% Covered, 51–75% Covered, 51–75% Covered, 76–99% Covered, 76–99% Covered, 1–50% Covered, 76–99% … Covered, 100% Covered, 76–99% Covered, 51–75% Covered, 76–99% Covered, 100% Covered, 100% Covered, 76–99% Covered, 76–99% Covered, 51–75% Covered, 1–50% Covered, 76–99% Covered, 76–99% Covered, 51–75% Covered, 76–99% Covered, 76–99% Covered, 100%

Not covered Covered, 100% Covered, 76–99% Not covered Covered, 1–50% Covered, 1–50% Covered, 76–99% Covered, 1–50% Covered, 76–99% Covered, 1–50% Covered, 76–99% Covered, 76–99% Not covered Covered, 1–50% Covered, 76–99% Covered, 51–75% Covered, 51–75% Covered, 100% Covered, 1–50% Not covered Not covered Covered, 100% Covered, 1–50% Covered, 51–75% Covered, 100% Covered, 1–50% Not covered Covered, 100% Covered, 76–99%

Source: From OECD: http://dx.doi.org/10.1787/888932526806.

the United States, pension schemes in the United Kingdom and Ireland, and superannuation plans in Australia and New Zealand. Retirement pensions are typically in the form of a guaranteed life annuity, thus insuring against the risk of longevity. Social Security and public insurance are the focus of Chapter 13 by B€ orsch-Supan et al. (this volume) as a result, here we focus on the private annuity insurance market. 3.2.1 Theory of the Demand of Annuities The theoretical literature on annuities started with the classic paper of Yaari (1965) where he considered the optimal consumption/saving/insurance problem for a consumer facing

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an uncertain lifetime in a continuous time model, and showed the classic result that in the absence of bequest motives, an individual should annuitize all of his income, in order to insure against the lifetime uncertainty.ac Yaari’s (1965) results were revisited in a simpler discrete time setting and under a somewhat more general asset structure by Davidoff et al. (2005). In what follows, we illustrate the economic benefit of annuitization in a simple two-period model as in Davidoff et al. (2005). Consider a consumer who is definitely alive in period 1 but may be alive in period 2 with probability 1  q 2 ð0,1Þ so q 2 ð0,1Þ is the death probability. Suppose that he has a utility function U ðc1 , c2 Þ over his consumption profile ðc1 ,c2 Þ, where c2 should be interpreted as his consumption level in period 2 if he is alive. Suppose that the consumer has access to two securities: the first is a bond that returns RB units of consumption in period 2 regardless of whether or not he is alive, in exchange for each unit of consumption good in period 1ad; the second is an annuity, which returns RA in period 2 if he is alive and nothing otherwise, again in exchange for each unit of consumption good in period 1. In this simple environment without asymmetric information (ie, the death probability q is known to the insurance company), an actuarially fair annuity was RA ¼

RB : 1q

However, suppose that we impose a weaker restriction: RA > RB : Let us denote by A the consumer’s choice of savings in the form of annuities and B his saving in terms of bonds. Suppose that he has no income in period 2 and his asset or income in period 1 is Y, his choice problem in period 1 is simply max U ðc1 , RA A + RB BÞ

fc1 , A, Bg

s:t:

c1 + A + B  Y A  0, B  0:

It immediately follows from the first-order conditions with respect to c1, A, and B that in the optimum, B* ¼ 0 as long as RA > RB, ie, all the consumption in the uncertain second period of the life should be funded by annuity, not bond. This is the well-known full annuitization result. The intuition is very simple: if B* > 0, then one can increase second-period consumption while holding c1 constant by reducing the bond holding

ac ad

See Sheshinski (2008) for a comprehensive review of the theory of annuities. Thus the bond can be interpreted as a riskless saving instrument with interest rate RB  1.

Insurance Markets for the Elderly

to zero, and use the proceeds B* to purchase B* units of annuity instead. This change of portfolio will increase c2 by B*ðRA  RB Þ > 0: The preceding full annuitization results can be generalized to environments with many periods and many states when the market is complete. To see this, let us generalize the utility function of the consumer to U ðc1 ,c2 Þ, where now c2 is a vector of date-state contingent consumption levels (eg, if there are T possible future periods and N states in each period, c2 will be a vector of length NT); let c2(t, ω) denote the element in vector c2 that corresponds to the consumption in a future period t 2 f2,…, T + 1g and state ω 2 Ω. The state ω can represent both uncertainty about aggregate issues such as the macro economy, the performance of the stock market, or individual issues including mortality or health. Suppose that we are in a complete market setting where we have “Arrow bonds” and “Arrow annuities” that pay out in ðt, ωÞ for all t 2 f2,…, T + 1g and ω 2 Ω with payout rates RBðt, ωÞ and RAðt, ωÞ , respectively. Suppose the individual chooses, respectively, Bðt, ωÞ and Aðt, ωÞ units of ðt, ωÞ-contingent bonds and annuities, then his consumption in ðt,ωÞ, if he is alive then, is c2ðt, ωÞ ¼ RBðt, ωÞ Bðt, ωÞ + RAðt, ωÞ Aðt, ωÞ : Thus the consumer’s problem is

s:t:

U ðc1 , c2 Þ max fc1 , ðAðt, ωÞ , Bðt, ωÞ Þg X
 c1 + Aðt, ωÞ + Bðt, ωÞ  Y ðt, ωÞ2f2, …, T gΩ

c2ðt, ωÞ ¼ RBðt, ωÞ Bðt, ωÞ + RAðt, ωÞ Aðt, ωÞ for all ðt, ωÞ 2 f2,…,T + 1g  Ω Aðt, ωÞ 0,Bðt, ωÞ  0 for all ðt, ωÞ 2 f2,…,T + 1g  Ω: Again, the first-order conditions for the preceding optimization problem immediately lead to the conclusion that optimally, it must be the case that for all ðt,ωÞ, Bðt, ωÞ ¼ 0 as long as RAðt, ωÞ > RBðt, ωÞ ; that is, all the consumption for the uncertain future periods and states should be funded through purchase of date and state contingent annuities. One may say that date and state continent annuities differ from the conventional life annuities that pay out in every date until death. But with complete markets, we can always create such conventional annuities by combining these date and state contingent Arrow annuities. Thus we have a very general result about the optimality of full annuitization: in a complete-market Arrow–Debreu equilibrium, it is optimal for a consumer without a bequest motive to annuitize all savings. The full annuitization result does not hold when markets are incomplete, or there are liquidity needs, or when individuals have bequest motives. However, the forces in favor of annuitization underlying the full annuitization result would imply that some annuitization would be optimal even under these circumstances. Let us consider the case of incomplete markets as an example. Markets are incomplete when there is not a sufficiently rich set of Arrow bonds and Arrow annuities to allow consumers to achieve a consumption profile by choosing appropriate combinations of

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these securities. For instance, most real world annuity markets require that a consumer purchase a particular time path of payouts, or the payouts are linked to the performance of the underlying portfolio of assets or to the actual mortality experience for the class of investors. We can model the restrictions on the available annuity products by assuming that the agent can purchase only annuity products that pay out in a set of states ω 2 ΩA, which is a strict subset of Ω. Denote by ‘ a row vector with one in states that belong to ΩA. Let RB denote the matrix of returns for the available set of bonds, and let B denote the collection of bond assets. If RAA ¼ RBB implies that A < ‘B (ie, any consumption vector that may be purchased strictly through annuities is less expensive when financed through annuities than when purchased by a set of bonds with matching payoffs), then an arbitrage-like dominance of the annuity over the matching combination of bonds, as long as such trade is feasible, which is the underlying force for the preceding full annuitization result, still holds. Therefore we can conclude that some annuitization is optimal and the optimal portfolio has zero bonds in at least one dated event. Similar arguments for the optimality of partial annuitization also apply in cases where consumers face liquidity needs, or when individuals have bequest motives. 3.2.2 Under-Annuitization Puzzle and Its Solutions? The theoretical predictions that individuals should annuitize their wealth are derived under a set of conditions, and calibrated life-cycle models taking into consideration bequest motives and other market frictions suggest that typical 65-year-olds would be willing to pay one-fourth of their wealth at retirement for access to actuarially fair annuities, which exceeds the usual 10–15% of annuity loads (see Mitchell et al., 1999, among others). However, in most countries voluntary annuitization is almost nonexistent. For example, Johnson et al. (2004) documented, using data from the Health and Retirement Study, that among people at least 65 years old in the US private annuities make up just 1% of total wealth. James and Song (2001) described the private annuity markets in Australia, Canada, Chile, Israel, Singapore, Switzerland, the United Kingdom, and the United States and concluded that in all of these countries, the annuities markets remain underdeveloped, especially relative to the life insurance market (which we describe in Section 3.3). The puzzle is not easily explained by the loadings of annuity products. For example, Mitchell et al. (1999) showed that annuity products in the United States offer very high “money’s worth”—the ratio of expected discounted lifetime benefits to initial capital cost of the annuity. Similar findings are obtained for other countries by James and Song (2001), who found that, when discounting at the risk-free rate, money’s worth for annuitants are greater than 95% in most countries and sometimes greater than 100%. The evidence has been termed the “underannuitization puzzle,”ae and a large set of literature has emerged to explain it (see, eg, Brown, 2007; Benartzi et al., 2011). The ae

Modigliani (1986), in his Nobel acceptance speech given in 1985, noted: “It is a well known fact that annuity contracts, other than in the form of group insurance through pension systems, are extremely rare. Why this should be so is a subject of considerable current interest. It is still ill-understood.”

Insurance Markets for the Elderly

existing explanations can be categorized into two groups, demand-side-based explanations and supply-side-based explanations. Supply-side explanations emphasize market failure because of barriers created by asymmetric information (Finkelstein and Poterba, 2004; Hendren, 2013) or because of the large loading factor that limits the annuity returns (Friedman and Warshawsky, 1990). Demand-side explanations, on the other hand, emphasize that the consumers may have substantial bequest motives that make them unwilling to annuitize (Lockwood, 2011), or they may suffer from behavioral biases in their decision making (Brown et al., 2008).af,ag 3.2.2.1 Information Problems in Annuity Insurance Market

The possibility of market failure because of private information has been well known since Akerlof (1970)’s classic paper on lemons. Thus underannuitization could be a result of private information in the annuity insurance market. It is indeed conceivable that informational barrier may be the reason for the low market penetration rate in the annuity insurance market. For example, Finkelstein and Poterba (2004) tested for evidence of private information using unique administrative data from an annuity insurance company in the United Kingdom. Hendren (2013) developed a theory of low penetration in certain insurance markets based on private information. He argued that if the adverse selection problem is sufficiently severe, then it is rational for insurance companies to reject insurance applications. His model is as follows. Suppose that there exists a unit mass of agents endowed with nonstochastic wealth w > 0. All agents face a potential loss of size l > 0 that occurs with random probability P (with realization denoted by p), which is private information to the agent. The random loss probability P is distributed in the population with cumulative distribution function F ð  Þ on the support Ψ ½0,1 : Suppose that agent with loss probability p has standard von Neumann–Morgenstern preferences with expected utility given by puðcL Þ + ð1  pÞuðcNL Þ, where cL and cNL are, respectively, the consumption in the event of loss and no loss. Denote an allocation by A ¼ fcL ðpÞ, cNL ðpÞgp2Ψ , which specifies the consumption level in the event of loss and no loss for each type p 2 Ψ . An allocation A is implementable if af

ag

Pashchenko (2013) used a quantitative model to assess the importance of many potential impediments to annuitization, including a large percentage of preannuitized wealth in retirees’ portfolios, adverse selection, bequest motives, medical expense uncertainty, government safety net in terms of means-tested transfers, illiquidity of housing wealth and restrictions on minimum amount of investment in annuities, and she found that quantitatively four explanations play a big role in reducing annuity demand: preannuitized wealth, minimum annuity purchase requirement, illiquidity of housing wealth, and bequest motives. Brown and Poterba (2000) recognized that longevity risk sharing by couples may reduce their willingness to pay for annuity products. They evaluated a married couple’s utility gain from joint-life annuitization using joint-and-survivor life tables and found that previous estimates of the utility gain from annuitization, which applied to individuals, overstate the benefits of annuitization for married couples.

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• A is resource feasible, ie, Z ½w  pl  pcL ðpÞ  ð1  pÞcNL ðpÞ dF ðpÞ  0; • A is incentive compatible, ie,



  for all p, p 2 Ψ ; puðcL ðpÞÞ + ð1  pÞuðcNL ðpÞÞ  pu cL p + ð1  pÞu cNL p • A is individually rational, ie, puðcL ðpÞÞ + ð1  pÞuðcNL ðpÞÞ  puðw  l Þ + ð1  pÞuðw Þ for all p 2 Ψ : The key theoretical result is the following no-trade theorem: Theorem The endowment, fðw  l,w Þ, for all p 2 Ψ g, is the only implementable allocation if and only if p u0 ðw  lÞ E ½PjP  p

 for all p 2 Ψ nf1g: 0 1  p w ðw Þ 1  E ½PjP  p

(1)

Conversely, if the preceding condition does not hold, then there exists an implementable allocation which strictly satisfies resource feasibility and individual rationality for a positive measure of types. The intuition for the preceding no-trade theorem can be described as follows. The left-hand side of (1) denotes the marginal rate of substitution between the consumption in the loss state and no loss state, evaluated at the endowment ðw  l, wÞ for a type-p agent. This is also type-p agent’s willingness to pay for a small amount of additional consumption in the event of the loss, in terms of consumption in the event of no loss. The actuarially fair cost of this transfer for type-p agent is p=ð1  pÞ, but such an actuarially fair price is not incentive feasible in an environment with private information. Instead, the relevant price is the average cost if all types with risks higher than p also obtain the transfer, ie, at the price E½PjP  p =f1  E ½PjP  p g, which is the right-hand side of (1). If no agent is willing to pay this cost, then endowment is the only implementable allocation. Based on condition (1), Hendren (2013) defines the pooled price ratio at p, T ðpÞ, as T ðpÞ 

E ½PjP  p 1  p , 1  E½PjP  p p

after which condition (1) can be succinctly stated as u0 ðw  lÞ  inf T ðpÞ: w 0 ðw Þ Ψ nf1g The statistic inf Ψ nf1g T ðpÞ, which is called the minimum pooled price ratio, can then be interpreted as a measure of informational barrier to trade in an insurance market. The higher the minimum pooled price ratio, the harder it is to implement trade.

Insurance Markets for the Elderly

Hendren (2013)’s idea to explain the low-penetration rate of some of the insurance markets—such as those for annuities, long-term care, and disability—is to estimate the distributions of F ðpjX Þ, where X is a vector of observable characteristics for those who are rejected by the insurance company and those who are served by the insurance company, respectively, and to show that the estimated risk distributions imply that the minimum pooled price ratio for the rejectees is higher than that for those who are served by the market. Indeed he found larger barriers to trade imposed by private information for the rejectees, for whom private information imposes a barrier to trade equivalent to an implicit tax on insurance premiums of 82% in long-term care, 42% in life insurance, and 66% in disability insurance; in contrast, he found that smaller implicit taxes for the nonrejectees that are not statistically different from zero in any of the three market settings. While Hendren (2013) provided conditions under which adverse selection in consumer’s risk type may lead to no trade, one of the major findings in the recent literature on the test of asymmetric information in insurance markets is that consumers may have multidimensional private information.ah For example, Finkelstein and Poterba (2004) examined a unique data set from a large annuity insurance company in the United Kingdom where retirees are required to annuitize at least a certain percentage of their tax-preferred retirement savings account balance, but have a choice over the annuity products that differ in guaranteed payout periods (0, 5, or 10 years) and in whether they are capital protected. They found evidence of systematic relationships between the ex-post mortality and some annuity characteristics such as the timing of payments and the possibility of payments to the annuitants’ estates, which suggests the presence of selection based on private information. Using the same data set, Einav et al. (2010b) estimated a structural model where individuals are hypothesized to have private information regarding their mortality risk as well as their bequest motive, and these two dimensions of private information are allowed to be correlated. They identify and estimate the two dimensions of private information based on the retirees’ choice of annuity guarantee length and their ex-post mortality experience. They found strong evidence of positive correlation between the two dimensions of private information. In related papers on the long-term care insurance market by Finkelstein and McGarry (2006), which we will discuss in Section 3.4, and on Medigap insurance market by Fang et al. (2008), which we discuss in Section 4.2, all found evidence that consumers’ insurance purchases are likely driven by their risk type, their preference type (eg, risk aversion), and even their cognitive ability. While selection based on risk type has been emphasized in the classic papers such as Akerlof (1970) and Rothschild and Stiglitz (1976), the recent empirical finding of the presence and importance of selection based on preference types—in particular, selection based on risk aversion—may offer a unified explanation for why different insurance ah

For a survey, see Einav et al. (2010a).

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markets vary so much in size: for example, markets for health, home, and life insurance are all large, while markets for annuities and long-term care insurance are quite small. To illustrate how selection based on multidimensional private information provides a potential unified explanation for size differences across insurance markets, it is useful to contrast the life and annuity insurance markets. These markets cover opposite risks: life insurance covers the risk of mortality, while annuities cover the risk of longevity. In life insurance markets, the “bad risks” from an insurer’s viewpoint are people with higher mortality probabilities. In a unidimensional model, less healthy people should have a greater demand for life insurance. But it is plausible that more cognitively able people or those with more income also demand more life insurance and tend to be healthier because they invest more in their health (similar to what we find in the health insurance market). If these two forces roughly balance, it is possible that overall there is no positive correlation between life insurance coverage and ex-post mortality risk, as empirically found by Cawley and Philipson (1999). Given the lack of adverse selection in the aggregate, this market can be expected to be large. In contrast, in an annuity insurance market, the “bad risks” from an insurer’s viewpoint are healthy people who expect to live long lives. People with private information that they are relatively healthy should be more likely to purchase annuities, creating an adverse selection problem. Now let us assume, as before, that (i) more cognitively able people and those with more income are both more likely to purchase annuities, just as they are more likely to purchase health or life insurance, and (ii) more cognitively able people and those with more income are healthier and live longer, because they invest more in their health. This creates an additional source of adverse selection. Thus, while selection based on cognitive ability and income alleviates the problem of adverse selection based on health risk in the life insurance market, it exacerbates the adverse selection problem in the annuity market. Similar patterns hold when we look at the other markets we mention previously (auto, health, long-term care). That is, in markets where we would expect selection based on cognitive ability or income to exacerbate selection based on risk type, the market is small and vice versa. Thus the theory of advantageous selection provides a plausible explanation of the size difference between life, annuity, and other insurance markets without relying on institutional assumptions.ai 3.2.2.2 High Loadings of Annuities

Friedman and Warshawsky (1990) argued that people may decide not to purchase individual annuities because such products are not priced fairly in the actuarial sense because of high loading factors. Such loading factors could reflect ordinary transaction costs, including taxes and competitive returns to the annuity insurer’s capital. However, Brown (2007) ai

Nevertheless, at this point these arguments are only speculative. Rigorous theoretical analysis of the relationship between equilibrium market size and the presence of advantageous selection is an interesting area for future research.

Insurance Markets for the Elderly

argued that this explanation for the underannuitization does not seem to square with the behavior of Social Security participants. He noted that in the United states, individuals are allowed to start claiming Social Security benefits as early as age 62 but do not have to begin claiming before turning age 70. As one delays longer before claiming benefits, the benefits are adjusted upward in an actuarially fair manner. Specifically, for each year after the normal retirement age that benefits are delayed up until age 70, the amount of benefits increases by roughly 8% a year.aj Effectively, the Social Security Administration is offering the participants, by delaying the start date of the Social Security benefits, to buy at an actuarially fair premium, a large annuity.ak However, Muldoon and Kopcke (2008) showed that most people begin claiming Social Security benefits within a year of becoming eligible, and less than 5% delay claiming benefits past age 66.al 3.2.2.3 Bequest Motives

As is known in Yaari (1965), bequest motives could be a reason not to annuitize all of the individual’s wealth. Several studies try to quantify how much bequest motive can explain the low-penetration rate of voluntary annuitization. For example, Friedman and Warshawsky (1990) and Vidal-Melia and Lejarraga-Garcia (2006) both showed that sufficiently strong bequest motives can eliminate purchases of annuities with high enough loads. Lockwood (2012) also quantified the strength of bequest motives needed to eliminate the demand for actuarially unfair annuity products. He found that moderate bequest motives, much weaker than those required to eliminate purchases of actuarially fair annuities, can eliminate purchases of available annuities. Even in a model in which the only reason to prefer nonannuity wealth to annuity income is that nonannuity wealth is bequeathable, altruists who wish to leave bequests gain little from actuarially unfair annuities and are in many cases better off not annuitizing any wealth at available rates. Moreover, in simulations of annuity decisions by single retirees in the United States, five of the six estimates of bequest motives from the saving literature significantly reduce the predicted demand for annuities.am aj

ak

al

am

The Social Security Administration describes the benefit adjustment for delayed retirement at http:// www.ssa.gov/oact/quickcalc/early_late.html. The premium is in the form of the forgone normal benefits the participants are entitled to receive had they retired at the normal benefit age. Since Social Security benefit is indexed for inflation and offers survivor benefits, one may even argue that the premium for delayed benefits is actuarially favorable. Sun and Webb (2011) showed that, for plausible preference parameters, the optimal age for claiming Social Security benefits for nonliquidity constrained single individuals and married men is between 67 and 70. Ameriks et al. (2011) also considered the possible role of what they referred to as “public care aversion” in underannuitization. The idea is that if people annuitize too much of their wealth, the probability of having insufficient wealth for private long-term care and therefore needing public care, which the individual is averse to, will increase. They administered a novel strategic survey instrument that includes hypothetical questions to disentangle the relative importance of public care aversion and bequest motive. They found that public care aversion is very significant, and that bequest motives are strong also for the middle class.

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3.2.2.4 Behavioral Explanations

Brown et al. (2008) provided experimental evidence that individuals’ aversion to annuities may be related to whether the annuity product is viewed by the consumer through the “consumption frame” or through an “investment frame.” When annuity is viewed through the consumption frame, the consumer focuses on the end result of what can be spent over time; but when it is viewed through the investment frame, the consumer instead focuses on the intermediate results of return and risk features when choosing assets and does not consider the consequences for consumption. For the sake of illustrating the potential differences of the two frames, consider a two-period case where the individual has probability q of dying. If an individual invests wealth W in a simple bond with a return R, he will be able to consumer W ð1 + RÞ in the second period if he stays alive. If, in contrast, he buys an actuarially fair annuity, he is able to consume W ð1 + RÞ=ð1  qÞ if he lives. Viewed from a consumption frame, the consumer will notice that what he is able to consume in the second period with an annuity, W ð1 + RÞ=ð1  qÞ, is higher than what he can consume with a simple bond, W ð1 + RÞ: However, viewed from an investment frame, the consumer may focus on the rate of return and the variance of payments of the two investment alternatives. In the preceding example, a bond has return of R and poses no risk, since it pays the same irrespective of the state; on the other hand, the annuity has a return of ð1 + RÞ=ð1  qÞ with probability q and a return of 0 with probability q. Even though the bond and the annuity have the same expected return, the annuity appears riskier than the bond. Brown et al. (2008) conducted choice experiments in which subjects are asked to choose to allocate a certain amount of money between a life annuity and a bond, but the choices are described randomly by using an “investment frame” or a “consumption frame.” They found that 72% of respondents prefer a life annuity over a savings account when the choice is framed in terms of consumption, but only 21% of respondents prefer a life annuity when the choice is framed in terms of investment features.an 3.2.3 Reverse Mortgage A reverse mortgage insurance, or sometimes called a reverse mortgage loan, can be a valuable retirement planning tool that can greatly increase retirees’ income streams by using their largest assets—their homes. As we described in Section 2.1, home equity is the dominant form of wealth for older Americans, particularly widows. Based on the 2001 Survey of Consumer Finances, Aizcorbe et al. (2003, quoted in Davidoff and Welke, 2004) showed that 76% of household heads 75 or over own a home, with a median value of $92,500, and only 11% of these households owe any mortgage debt. Among the majority an

Agnew et al. (2008) also used experiments to examine the role of gender, framing, and default on annuity choices.

Insurance Markets for the Elderly

of older single women in the 2000 AHEAD survey who own homes, the median ratio of home value to total assets was 79%.ao A reverse mortgage allows homeowners to borrow against their home equity, while still maintaining ownership of the home until they die. The modern reverse mortgage industry dates to 1961 in the United States and the early part of the 20th century in Europe.ap Reverse mortgage borrowers must be 62 or older, must be homeowners with very little outstanding mortgage debt, and must live in the house. The amount that homeowners can borrow via a reverse mortgage, called the initial principal limit, is larger if the house value is larger, if there is a lower (or zero) outstanding balance on other mortgage loans, if the borrower is older, and if the interest rate is lower. Once the lender calculates the initial principal limit, borrowers can generally take out up to 60% of their initial principal limit in the first year. Reverse mortgage borrowers can receive payments in several forms: a borrower may receive a single lump sum payment, or a line of credit with an increasing maximum outstanding balance, or monthly payments that last for a fixed period (term payments), or monthly payments that last as long as the borrower lives in the home (tenure payments). Borrowers may receive payments in a combination of any of these forms. The line of credit is by far the most popular option (and it includes lump sum payments as a subset). If a borrower decides to take a reverse mortgage with tenure payments, it may be considered as an annuity insurance with one’s home equity as the capital, which can potentially insure borrowers against the risks of housing market and their longevity risk. In the United States the most popular reverse mortgage is administered by the Federal Housing Administration (FHA), called a home equity conversion mortgage (HECM), while the private market for reverse mortgages has been shrinking.aq Shan (2011) reported that HECM loans represent over 90% of all reverse mortgages originated in the US market. It should be pointed out that with a reverse mortgage, borrowers are insured against substantial drops in house prices because the reverse mortgage loan includes an insurance in all HECMs administered by the FHA. Borrowers (or their heirs) can repay the loan either by letting the reverse mortgage lender sell the house or by paying in cash. Most use the first option. In the first case, a mortgage lender sells the house attached to the reverse mortgage loan and uses the proceeds of the sale to repay the loan and to pay for various costs. If the sale value of the house turns out to be greater than the sum of the total loan amount and the various costs of the loan, the borrowers receive the remaining value. In the opposite case, where the house value cannot cover the total costs ao

ap aq

See Davidoff and Welke (2004) for more discussions about the reverse mortgage market. Nakajima (2012) provided a very useful basic introduction. In French, reverse mortgage is known as a “viager.” In 2011 the two biggest lenders of reverse mortgage loans, Bank of America and Wells Fargo, exited the reverse mortgage market (see New York Times, “2 Big Banks Exit Reverse Mortgage Business,” June 17, 2011).

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2.5 2 1.5 1 0.5 0 1997

1999

2001

2003

2005

2007

2009

2011

Year

Fig. 12 Percentage of older (age 65) homeowners with reverse mortgages. Source: American Housing Survey, Various Waves. Reproduced from Nakajima, M., Telyukova, I.A., 2013. Reverse mortgage loans: a quantitative analysis. Working Paper, Federal Reserve Bank of Philadelphia.

of the loan, the insurance covers the difference and the borrowers do not need to pay anything extra (see Nakajima, 2012). The number of households with reverse mortgages has been growing. Fig. 12, reproduced from Nakajima and Telyukova (2013), shows the proportion of homeowner households of age 65 and above that have reverse mortgages, including both the HECM loans and private mortgage loans, between 1997 and 2011. Fig. 12 shows that the reverse mortgage market was very small before 2000. In 2001 the share of eligible homeowners with reverse mortgages was about 0.2%. This share increased rapidly since then, reaching 2.1% in 2011. There is growing economics literature that investigates various aspects of the reverse mortgage market. Davidoff and Welke (2004) empirically showed that the reverse mortgage market is characterized by advantageous selection; ie, reverse mortgage borrowers appear to exit their homes at a faster pace than the general population. The authors suggested that a higher discount rate among the borrowers combined with housing price appreciation may explain observed advantageous selection. Nakajima and Telyukova (2013) analyze reverse mortgages in a life-cycle model of retirement, calibrated to age-asset profiles. They found that the ex ante welfare gain from reverse mortgages is sizeable at $1000 per household. They also argued that bequest motives, nursing home moving risk, house price risk, and interest and insurance costs all contributed to the low take-up rate of reverse mortgages.

3.3 Life Insurance Market Individuals face mortality risks as described in Section 2.3. If they care for their dependents (eg, the spouse, the children, or sometimes the parents, or any other person), they

Insurance Markets for the Elderly

have a desire to ensure that their dependents’ quality of life is not affected by their death.ar Life insurance provides such protection. The basic economic theory of the demand for life insurance starts with Fischer (1973) and Karni and Zilcha (1986) and was summarized in a survey by Villeneuve (2000). There are two main types of individual life insurance products, term life insurance and whole life insurance.as A term life insurance policy covers a person for a specific duration at a fixed or variable premium for each year. If the person dies during the coverage period, the life insurance company pays the face value of the policy to the person’s beneficiaries, provided that the premium payment has never lapsed. The most popular type of term life insurance has a fixed premium during the coverage period and is called level term life insurance. A whole life insurance policy, on the other hand, covers a person’s entire life, usually at a fixed premium. In any period, life insurance is a contract between the insured and the insurance company that specifies a premium and a benefit amount payable to the beneficiary of the life insurance policy (known as the face amount) conditional on the death of the insured. Both term life and whole life are contracts that specify a sequence of such annual premium/death benefit combinations, and the difference is that under term life, the sequence has a fixed period (so, eg, a 20-year term life insurance policy has a sequence of 20 years), while under whole life, the sequence has a random length equal to the random longevity of the policyholder. In contrast to the rather small private annuity insurance market, as discussed in Section 3.2, the life insurance market is large and important.at According to Life Insurance Marketing and Research Association International (LIMRA International), 78% of American families owned some type of life insurance in 2004. By the end of 2008, the total number of individual life insurance policies in force in the United States stood at about 156 million; and the total individual policy face amount in force reached over 10 trillion dollars (see American Council of Life Insurers, 2009). In the United States at year-end 2008, 54% of all life insurance policies in force were term life insurance. Of the new individual life insurance policies purchased in 2008, 43%, or 4 million ar

as

at

As shown in Fang and Kung (2012a), the life insurance ownership rates are high among the Health Retirement Study respondents whose ages range from 54 to 84. In 1996, when the respondents are between 54 and 74 years old, life insurance ownership rate is at 88.1%; in 2006, when the surviving respondents are between 64 and 84 years old, the ownership rate remains high at 78.6%. It is somewhat a puzzle why elderly individuals continue to own life insurance. Brown (2001) provided evidence against the hypothesis that elderly individuals with strong bequest motives purchase term life insurance to offset mandatory annuitization by the existing Social Security system. The whole life insurance has several variations such as universal life (UL), variable life (VL), and variableuniversal life (VUL). UL allows flexible premiums subject to certain minimums and maximums. For VL, the death benefit varies with the performance of a portfolio of investments chosen by the policyholder. VUL combines the flexible premium options of UL with the varied investment option of VL (see Gilbert and Schultz, 1994). The discussion here borrows from Fang and Kung (2012a).

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policies, were term insurance, totaling $1.3 trillion, or 73%, of the individual life face value issued (see American Council of Life Insurers, 2009). Besides the difference in the period of coverage, term and whole life insurance policies also differ in the amount of receivable cash surrender value (CSV) if the policyholder surrenders the policy to the insurance company before the end of the coverage period. For term life insurance, the CSV is zero; for whole life insurance, the CSV is typically positive and prespecified to depend on the length of time that the policyholder has owned the policy. One important feature of the CSV on whole life policies relevant to our following discussions is that by government regulation, CSVs do not depend on the health status of the policyholder when surrendering the policy.au 3.3.1 Front-Loaded Premiums and Reclassification Risk Insurance An important feature of life insurance contracts is that life insurers often offer long-term insurance contracts with fixed premiums that are front-loaded; that is, the premium is higher than the actuarially fair premium in the early parts of the life insurance contract. Hendel and Lizzeri (2003) provided an elegant model that explains the front-loading of life insurance premiums. They showed that insurers require front-loaded premiums in order to provide reclassification risk insurance—insuring against the risk from stochastic second-period premium as a result of stochastic second-period health realization—which is valued by policyholders. Hendel and Lizzeri (2003) consider a perfectly competitive primary market for life insurance that includes individuals (policyholders) and life insurance companies.av There are two periods. In the first period, the policyholder has a probability of death p1 2 ð0,1Þ known to both himself and the insurance companies. In the second period, the policyholder has a new probability of death p2 2 ½0,1 , which is randomly drawn from a continuous and differentiable cumulative distribution function Φ() with a corresponding density ϕð  Þ. A consumer’s period 2 health state p2 is not known in period 1, but p2 is symmetrically learned by the insurance company and the consumer, and thus common knowledge, at the start of period 2. The policyholder’s income stream is y  g in period 1 and y + g in period 2, where y is interpreted as the mean life-cycle income and g 2 ð0,g with g < y captures the income growth over the periods. Both y and g are assumed to be common knowledge. The policyholder has two sources of utility: his own consumption should he live, and his dependents’ consumption should he die. If the policyholder lives, he derives utility u(c) if he consumes c  0; if he dies, then he has a utility v(c) if his dependents consume c  0. uð  Þ and vð  Þ are both strictly concave and twice differentiable. au

av

The life insurance industry typically thinks of the CSV from the whole life insurance as a form of a taxadvantaged investment instrument (see Gilbert and Schultz, 1994). This rendition of the Hendel and Lizzeri (2003) model follows Fang and Kung (2010).

Insurance Markets for the Elderly

However, in period 2, there is a chance that the policyholder no longer has a bequest motive. Denote by q 2 ð0,1Þ the probability that the policyholder loses his bequest motive.aw The bequest motive uncertainty is resolved at the same time as the period 2 health state; however, we assume that it is private information to the policyholder and cannot be contracted upon. If the policyholder retains his bequest motive, his utility in period 2 is again u() if he is alive and v() if he dies; if the policyholder loses the bequest motive, then his utility is u() if he stays alive, and some constant that is normalized to zero if he dies. Hendel and Lizzeri (2003) assume that there are no capital markets, thus the consumer cannot transfer income from period 1 to period 2. The only way for the consumer to ensure a stream of income for his dependents is to purchase life insurance. We now provide more details about the timing of events. At the beginning of period 1, after learning the period-1 health state p1, the consumer may purchase a long-term contract from an insurance company. A long-term contract specifies a premium and face value for period 1, hQ1 , F1 i, and a menu of health-contingent premiums and face values hQ2 ðp2 Þ, F2 ðp2 Þi for each period-2 health state p2 2 [0,1]. In contrast, a spot contract is simply a premium and a face value hQ,F i that earns zero expected profit for a given coverage period. The key assumption is that insurance companies can commit to these terms in period 2, but that the policyholders cannot. The one-sided commitment assumption has two important implications. First, it implies that the period-2 terms of the long-term insurance contract must be at least as desirable to the policyholder as what he could obtain in the period-2 spot market; otherwise, the policyholder will lapse the long-term contract into a new spot contract. This imposes a constraint on the set of feasible long-term contracts that consumers will demand in period 1. Second, if a policyholder suddenly finds himself without a bequest motive, he could lapse his policy by refusing to pay the second-period premium. In period 2, after learning the period 2 health state p2, the policyholder has three options. He can either continue with his long-term contract purchased in period 1, or he can let the long-term policy lapse and buy a period-2 spot contract, or he can let the long-term policy lapse and simply remain uninsured. To characterize the equilibrium set of contracts, we first consider the actions of a policyholder in the second period who no longer has a bequest motive. Given the absence of a secondary market, and we have not yet allowed the insurance companies to buy back contracts through CSVs, the best course of action for those who no longer have a bequest motive is to simply let the long-term policy lapse and become uninsured. Competition among primary insurance companies ensures that the equilibrium contract is a long-term contract hðQ1 , F1 Þ, ðQ2 ðp2 Þ, F2 ðp2 ÞÞ : p2 2 ½0,1 i that solves aw

A loss of bequest motive could result from divorce or from changes in the circumstances of the intended beneficiaries of the life insurance policy.

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max ½uðy  g  Q1 Þ + p1 vðF1 Þ

" # ) Z ( uðy + g  Q2 ðp2 ÞÞ + quðy + gÞ dΦðp2 Þ ð1  qÞ + ð1  p1 Þ +p2 vðF2 ðp2 ÞÞ Z s:t: Q1  p1 F1 + ð1  p1 Þð1  qÞ ½Q2 ðp2 Þ  p2 F2 ðp2 Þ dΦðp2 Þ ¼ 0, Q2 ðp2 Þ  p2 F2 ðp2 Þ  0, for all p2 2 0,1 ,

(2)

(3) (4)

where (2) is the expected utility the policyholders receive from the contract, (3) is the zero-profit constraint that reflects perfect competition in the primary market, and constraints in (4) guarantee that there will not be lapsation among policyholders with a bequest motive in the second period. Hendel and Lizzeri’s (2003) main results are summarized in the following proposition: Proposition (Hendel and Lizzeri, 2003) The equilibrium set of contracts satisfies the following: 1. There is a period-2 threshold health state p2 (which is higher than the period 1 death probability p1)  such that for all p2  p2 the period-2 premiums are actuarially fair, and for all
p2> p2 the period-2 premiums are constant, actuarially favorable and given by Q2 ðp2 Þ ¼ Q2 p2 ¼ Q1 + 2g; 2. When the income growth parameter g is sufficiently small, p2 is strictly less than 1, ie, reclassification risk insurance is provided for policyholders with low-income growth. Part (1) of the preceding proposition provides a theoretical justification for level-term and whole life insurance, which typically have fixed premiums for the duration of the contract. Fig. 13 depicts equilibrium premiums in the second period as a function of the period-2 health state p2.ax 3.3.2 Life Settlement Market and Its Welfare Effects A life settlement is a financial transaction in which policyholders sell their life insurance policy to a third party—the life settlement firm—for more than the cash value offered by the policy itself. The life settlement firm subsequently assumes responsibility for all future premium payments to the life insurance company and becomes the new beneficiary of the life insurance policy if the original policyholder dies within the coverage period.ay The life settlement industry is quite recent, growing from just a few billion dollars in the late 1990s to about $12–15 billion in 2007, and, according to some projections, it is expected to grow to more than $150 billion in the next decade (see Chandik, 2008). ax

ay

Hendel and Lizzeri (2003) made the ingenious observation that exactly the same outcome for the consumers would occur if the insurance company offers a contract that guarantees the second-period premium to be Q1 + 2g for all health states. The legal basis for the life settlement market seems to be the Supreme Court ruling in Grigsby v. Russell [222 US 149, 1911], which upheld that for life insurance, an “insurable interest” only needs to be established at the time the policy becomes effective, but does not have to exist at the time the loss occurs. The life insurance industry has typically included a 2-year contestability period during which transfer of the life insurance policy will void the insurance.

Insurance Markets for the Elderly

FI

Q2 (p2)

Q1 + 2g

Q2 (p2)

p2*

p2

Fig. 13 Equilibrium life insurance premium profile in the second period as a function of mortality rates. Source: Adapted from Hendel, I., Lizzeri, A., 2003. The role of commitment in dynamic contracts: evidence from life insurance. Q. J. Econ. 118 (1), 299–327.

The opportunity for the life settlement market results from two main features of life insurance contracts. First, most life insurance policies purchased by consumers, either term or whole life, have the feature that the insurance premium stays fixed over the course of the policy. Because policyholders’ health typically deteriorates over time, the fixed premium implies that policyholders initially pay a premium that is higher than actuarially fair, but in later years the same premium is typically actuarially favorable. This is the front-loading phenomenon we described earlier. Front-loading implies that policyholders of long-term life insurance policies, especially those with impaired health, often have locked in premiums that are much more favorable than what they could obtain in the spot market. This generates what has been known as the actuarial value of the life insurance policy (see Deloitte Report, 2005). Second, as we mentioned earlier, the CSV for life insurance policies is either zero for term life insurance or at a level that does not depend on the health status of the policyholder. Because the actuarial value of a life insurance policy is much higher for individuals with impaired health, the fact that the CSV does not respond to health status provides an opening for gains of trade between policyholders with impaired health and life settlement companies.az Life settlement firms

az

Deloitte Report (2005, p. 3) states that the CSVs of whole life insurance policies are, by regulation, not allowed to be conditioned on health impairments of the policyholder who surrenders the policy. Doherty and Singer (2002) also argue that regulatory constraints faced by life insurance carriers deter life insurance companies from offering health-dependent CSVs: “Such an offering of explicit health-dependent surrender values by a life insurance carrier, however, would be fraught with regulatory, actuarial, and administrative difficulties. Life insurance carriers do not offer health-adjusted surrender values, which suggests that these difficulties outweigh the benefits that carriers would obtain by offering healthdependent surrender values to consumers.” Life settlement firms so far are not yet regulated in their pricing of life insurance policies.

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operate by offering policyholders, who are intending to either lapse or surrender their life insurance policies, more cash than the CSV offered by the insurers. The emerging life settlement market has triggered controversies between some life insurance companies who oppose it and the life settlement industry who supports it. The views from the two opposing camps are represented by Doherty and Singer (2002) and Singer and Stallard (2005) on the proponent side, and the Deloitte Report (2005) on the opponent side. Doherty and Singer (2002) argued that a secondary market for life insurance enhances life insurance policyholders’ liquidity by eroding the monopsony power of the carrier. This will increase the surplus of policyholders and in the long run will lead to a larger primary insurance market. On the other side, life insurance companies, as represented by the Deloitte Report (2005), claim that the life settlement market, by denying them the return on lapsing or surrendered policies, increases the costs of providing policies in the primary market. They allege that these costs will have to be passed on to consumers, which would ultimately make consumers worse off. A key issue in the contention between the opposing sides is the role of lapsing or surrendering in the pricing of life insurance in the primary market (see Daily, 2004). Policyholders may choose to lapse or surrender in a variety of situations. First, the beneficiary for whom the policy was originally purchased could be deceased or no longer need the policy; second, the policyholder may experience a negative income shock (or a large expense shock) that leads him to favor more cash now over a bequest.ba In the absence of the life settlement market, when a health-impaired policyholder chooses to lapse or surrender its policy, the life insurance company pockets the intrinsic economic value of the policy, which potentially allows the life insurance company to offer insurance at a lower premium. In the presence of the life settlement market, these policies will be purchased by the life settlement firms as assets; thus the primary insurance company will always have to pay their face value if the original policyholder dies within the coverage period. Daily et al. (2008) and Fang and Kung (2010) studied the effect of life settlement on the primary life insurance market, using a dynamic equilibrium model of life insurance similar to Hendel and Lizzeri (2003), under the assumption that the lapsation of policyholders is driven by loss of bequest motives. Fang and Kung (2010) showed that the life settlement market affects the equilibrium life insurance contracts in a qualitatively important manner: with the settlement market, risk reclassification insurance will be offered in the form of premium discounts, rather than in the form of flat premiums as is the case without a settlement market, which we discussed in the previous section. This may lead to a smaller degree of front-loading in the first period. They also show a general welfare result ba

For example, the Wall Street Journal reports that older adults are turning to the “life settlement” industry to help them through tough times in an article titled “Source of Cash for Seniors Are Drying Up” (November 13, 2008).

Insurance Markets for the Elderly

that the presence of the settlement market always leads to a decrease of consumer welfare relative to what could be achieved in the absence of the settlement market. They also provide conditions under which the life settlement market could lead to a complete collapse of reclassification risk insurance as a result of unraveling. If one relaxes the assumption that prohibits endogenously chosen CSVs, Fang and Kung (2010) found that whether or not CSVs can be made health-contingent has crucial implications. If CSVs are restricted to be nonhealth contingent, Fang and Kung (2010) show that an endogenous CSV is an ineffective tool for primary insurance companies to counter the threat of the life settlement industry. Fang and Kung (2012b), however, shows that if policyholders’ lapsation is driven by income or liquidity shocks, then a life settlement market may potentially improve consumer welfare. The intuition for the difference in the welfare result is as follows. Life insurance is typically a long-term contract with one-sided commitment in which the life insurance companies commit to a specified death benefit provided that the premium payments are made, whereas the policyholder can lapse anytime. Because the premium of life insurance policies is typically front-loaded, the life insurance company pockets the lapsation profits whenever policyholders lapse their policy after holding it for several periods, which is factored into the pricing of the life insurance policy to start with because of competition (see Gilbert and Schultz, 1994). The key effect of the settlement firms on the life insurers is that the settlement firms will effectively take away the lapsation profits, forcing the life insurers to adjust the policy premiums and possibly the whole structure of the life insurance policy, since lapsation profits can no longer exist. In the theoretical analysis, we showed that life insurers may respond to the threat of life settlement by limiting the degree of reclassification risk insurance, which certainly reduces consumer welfare. However, the settlement firms are providing cash payments to policyholders when the policies are sold to the life settlement firms. The welfare loss from the reduction in the extent of reclassification risk insurance has to be balanced against the welfare gain to the consumers when they receive payments from the settlement firms. If policyholders sell their policies because of income shocks, then the cash payments are received at a time when the marginal utility of income is particularly high, and the balance of the two effects may result in a net welfare gain for the policyholders. If policyholders sell their policies as a result of losing bequest motives, the balance of the two effects on net results in a welfare loss. Thus, to inform policy-makers on how the emerging life settlement market should be regulated, an empirical understanding of why policyholders lapse is of crucial importance. 3.3.3 Why Do Life Insurance Policyholders Lapse? The theoretical prediction discussed above that the equilibrium effect of the life settlement market on consumer welfare depends on why policyholders lapse—loss of bequest motives or income shocks—motivate an empirical analysis on why do policyholders their life insurance policies in Fang and Kung (2012a).

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Lapsation is an important phenomenon in life insurance markets. Both LIMRA and the Society of Actuaries consider that a policy lapses if its premium is not paid by the end of a specified time (often called the grace period).bb According to LIMRA (2009, p. 11), the life insurance industry calculates the annualized lapsation rate as the ratio of the number of policies lapsed during the year over the number of policies exposed to lapse during the year. The number of policies exposed to lapse is based on the length of time the policy is exposed to the risk of lapsation during the year. Termination of policies because of death, maturity, or conversion is not included in the number of policies lapsing and contributes to the exposure for only the percentage of the policy year they were in force. Table 9 provides the lapsation rates of individual life insurance policies, calculated according to the preceding formula, both according to face value and the number of policies for 1998–2008. Of course, the lapsation rates also differ significantly by the age of the policies. For example, LIMRA (2009, p. 18) showed that the lapsation rates are about 2–4% per year for policies that were in force for more than 11 years in 2004–05.bc Fang and Kung (2012a) presented and empirically implemented a structural dynamic discrete choice model of life insurance decisions to study why life insurance policyholders lapse their policies using the limited life insurance holding information from the HRS data. They found that a large fraction of life insurance lapsation is driven by idiosyncratic choice-specific shocks, particularly when policyholders are relatively young. But as the remaining policyholders get older, the role of such idiosyncratic shocks gets less important, and more of their lapsation is driven by either income, health, or bequest motive shocks. Income and health shocks are relatively more important than bequest motive shocks in explaining lapsation when policyholders are young, but as they age, the bequest motive shocks play a more important role. These empirical findings have important Table 9 Lapsation rates of individual life insurance policies, calculated by face amount and by number of policies: 1998–2008 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008

By face amount By number of policies

8.3

8.2

9.4

7.7

8.6

7.6

7.0

6.6

6.3

6.4

7.6

6.7

7.1

7.1

7.6

9.6

6.9

7.0

6.9

6.9

6.6

7.9

Source: American Council of Life Insurers, 2009. 2009 Life Insurers Fact Book. Reproduced from Fang, H., Kung, E., 2012a. Why do life insurance policyholders lapse? Loss of bequest motives vs. liquidity shocks. NBER Working Paper No. 17899.

bb bc

This implies that if a policyholder surrenders his/her policy for CSV, it is also considered as a lapsation. Krebs et al. (2011) also studied the life insurance choices in a life-cycle macroeconomic model with physical and human capital, human capital risk, and limited contract enforcement and found both theoretically and empirically using Survey of Consumer Finance data that young households are the most exposed to human capital risk and are also the least insured.

Insurance Markets for the Elderly

implications regarding the effect of the life settlement industry on consumer welfare. As shown in theoretical analyses in Daily et al. (2008) and Fang and Kung (2010), the theoretical predictions about the effect of life settlement on consumer welfare crucially depend on why life insurance policyholders lapse their policies. If bequest motive shocks are the reason for lapsation, then the life settlement industry is shown to reduce consumer welfare in equilibrium; but if income shocks are the reason for lapsation, then life settlements may increase consumer welfare. To the extent that we found that both income shocks and bequest motive shocks play important roles in explaining life insurance lapsations, particularly among the elderly population targeted by the life settlement industry, our research suggests that the effect of life settlement on consumer welfare is ambiguous.

3.4 Long-Term Care Insurance Market As we mentioned in Section 2.4, retirees face significant risks in their morbidity and needs for long-term care. Long-term care in the United States is expensive. According to MetLife Mature Market Institute (2012), the cost for a semiprivate room in a nursing home is about $222 per day or $6753 per month, and $248 per day or $7543 per month for a private room in a nursing home. It is somewhat cheaper in an assisted-living facility at a cost of $3550 per month. A home health aide costs on average about $21 per hour, and it costs $70 per day for services in an adult day health care center.bd Not only is long-term care expensive, but also lifetime long-term care expenditures are spread unevenly across the population: as described in Table 7, between 35% and 50% of 65-year-olds will use a nursing home at some point in their remaining lives. Of those who use a nursing home, 10–20% will live there more than 5 years (Brown and Finkelstein, 2009).be As emphasized in Norton (2000), long-term care differs from acute medical care in four important ways: long-term care is care for chronic illness; the nursing home industry is dominated by for-profit facilities sometimes facing excess demand; long-term care is often provided by unpaid caregivers; and little private long-term care insurance is purchased.bf In this section, we will focus on the private long-term care insurance (or lack of it). 3.4.1 Basic Facts of Long-Term Care Arrangements Long-term care includes both home health care for people residing in the community and institutional care provided in nursing homes or assisted-living facilities. Expenditures on home health care account for about one-third of the total long-term care spending (Centers for Medicare and Medicaid Services, 2010). bd

be

bf

Cost of long-term care information is available at http://longtermcare.gov/costs-how-to-pay/costs-ofcare/. See Friedberg et al. (2014) for some new evidence on the probability of using nursing homes and the average duration of nursing home stays conditional on use. See also Chapter 16 by Norton (this volume), which summarizes the key connections between long-term care and population aging.

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Table 10, reproduced from Byrne et al. (2009), shows how the care arrangements for elderly parents vary across families.bg In their sample, which is from the 1993 wave of the AHEAD data set, 22% of elderly individuals receive formal or informal care in their homes. Among those receiving some type of care, 18% receive formal care, 90% receive informal care, and 8% receive both formal and informal care. Overall, 6% of unmarried, Table 10 Characteristics of care provision for families of various sizes Number of children Number of childrena Type of family

Single Married

Percentage of all families 17.8 Percent of families Receiving care 5.6 Receiving formal careb 100 Receiving informal careb Receiving formal and informal careb Percent of families where Children help pay for carec Spouse provides informal cared Children provide informal cared Multiple children provide informal caree Children and spouse provide informal cared Average hours per week Informal care provided by spousef Informal care provided by childreng

3.7 38.1 9.8 98.0 7.8

100

1

3

20.8 27.8 16.9

4

5

Total

9.0

3.9 100

26.3 24.7 25.7 26.1 22.9 21.8 12.9 12.2 8.2 3.1 88.3 93.5 96.8 100 100 10.2 6.5 9.0 8.2 3.1

22.3 17.8 89.9 7.7

11.6 12.5 5.3 48.9 62.9 63.6 54.0 40.1 43.7 9.7 16.7

0 63.5 42.4 19.4

0 68.8 40.6 23.1

8.7 62.6 41.7 14.4

7.3

5.9

9.4

4.6

25.8 25.8 24.3

27.1

34.4

26.2

21.3 23.7 27.5

21.9

16.8

23.5

2.9

26.8

2

3.0

a

Includes families with single and married respondents. As share of families with respondents receiving any care. c As share of families with respondents receiving formal care. d As share of families with respondents receiving informal care. e As share of families with children providing informal care. f Average over families with spouse providing informal care. g Average over families with children providing informal care. Source: From table 5 in Byrne, D., Goeree, M., Hiedemann, B., Stern, S., 2009. Formal home health care, informal care, and family decision-making. Int. Econ. Rev. 50 (4), 1205–1242. b

bg

Note that the target population for the AHEAD survey consists of US household residents who were born in 1923 or earlier. Persons in institutions (including nursing home, long-term medical care, or dependent care facilities, prisons, and jails) at the time of the Wave 1 survey are ineligible for AHEAD (see Heeringa, 1995). This initial sample selection could prejudice some of the statistics of the care utilization patterns.

Insurance Markets for the Elderly

childless respondents and 38% of married, childless respondents receive care in their homes. Regardless of the number of children, roughly one-fourth of elderly parents receive some type of care. Among families providing some type of care, the provision of informal care depends positively and the provision of formal care depends negatively on the number of adult children. Among elderly individuals receiving informal care, 63% receive care from their spouse, 42% receive care from their children, and 5% receive care from both their spouse and at least one of their children. Conditional on the receipt of informal care from at least one family member, the likelihood that the spouse and at least one adult child share informal caregiving responsibilities ranges from 3% of those with one child to 9% of those with five children. A more common type of shared caregiving involves two or more adult children. Among families with at least one informal care provider and at least two adult children, 14% include multiple caregivers among the younger generation. Not surprisingly, the likelihood that siblings share caregiving responsibilities depends positively on family size. Conditional on the receipt of informal care from at least one family member, 10% of elderly individuals with two children receive care from both children, whereas 17%, 19%, and 23% of elderly individuals with three, four, and five children, respectively, receive care from more than one child. Among families where elderly individuals receive formal home health care, 9% of elderly parents receive financial contributions for this care from their children.bh 3.4.2 Why Is the Private LTC Insurance Market so Small? Given the uncertain and expensive nature of the long-term care needs and expenses, we might have expected that there would be a large demand for long-term care (LTC) insurance. However, in the United States and in many developed countries, most of the longterm care expenditure risk is not insured. The private LTC insurance is rather small, at least relative to health insurance that covers acute health expenditure risks. The Congressional Budget Office (2004) estimates that in the United States, only 4% of long-term care expenditures are paid for by private insurance, while 33% are paid out of pocket; public insurance, including Medicare and particularly Medicaid, covers about 60% of long-term care expenditures.bi It is useful to describe briefly the means of payment for long-term care expenditures previously mentioned. Medicare is designed mostly to cover care costs associated with recovery from acute illness episodes following a hospital stay of more than three consecutive days, rather than chronic impairments. It only pays for care provided in skilled bh

bi

Byrne et al. (2009) note that these statistics understate the prevalence of informal and formal care, because only those AHEAD respondents reporting an ADL or IADL problem were asked about the provision of care. Furthermore, in the presence of an ADL or IADL problem, respondents were asked who provides care only if they reported receiving help with the problem “most of the time,” and the amount of care is recorded only if the caregiver provided help at least once a week during the month prior to the survey. For the related figures corresponding to other OECD countries, see OECD (2011b) .

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nursing facility for up to 100 days, but does not pay for nonskilled assistance with ADL, which makes up the majority of long-term care services.bj Medicaid serves as a second-payer insurance and pays for long-term care for individuals who meet Medicaid’s income and asset eligibility thresholds. Medicaid is a rather imperfect form of insurance for long-term care risks because its asset eligibility requirement is essentially a deductible of nearly all of one’s wealth.bk However, as we will discuss in Section 4.1, Brown and Finkelstein (2008) argued convincingly that the long-term care coverages provided by Medicaid contribute in an important way to the limited size of the private long-term care insurance market. Long-term care insurance is designed to cover long-term services and supports, including personal and custodial care in a variety of settings such as home, community organization, and other facility. Long-term care insurance policies typically reimburse policyholders a daily amount (up to a preselected limit) for services to assist them with ADL such as bathing, dressing, and eating. Many long-term care insurance policies have limits on how long or how much they will pay; most policies will pay the costs of the long-term care for 2–5 years. The premium of a long-term care policy is based on the age at the purchase of the policy, the maximum amount that a policy will pay per day, the maximum number of days (years) that a policy will pay. Importantly, individuals who are in poor health or already receiving long-term care services may not qualify for long-term care insurance as most individual policies require medical underwriting. It should be noted that private long-term care insurance policies typically set a relatively low maximum on the amount of covered expenses that the policy will reimburse per day in care. The average maximum daily benefit for nursing home care for policies sold in 2005 was only $142, which was substantially below the average daily nursing home costs of almost $200 per day in 2008 (MetLife Mature Market Institute, 2009). Moreover, since about one-quarter of policies have a maximum daily benefit that is fixed in nominal terms, the daily benefit caps are even more binding in practice. An important literature examines the question of why the private LTC insurance market is so small, which is analogous to the literature on the underannuitization puzzle discussed in Section 3.2. Similar to the proposed solutions to the underannuitization puzzle, the explanations for the small private LTC market can also be grouped into explanations based on supply- and demand-side imperfections. While the most compelling explanation for why private LTC insurance is so small is that of Brown and Finkelstein (2008), which we discuss in Section 4.1, we will now describe two

bj

bk

Most employer-sponsored or private health insurance plans cover only the same kinds of skilled, shortterm, medically necessary care as Medicare, if they cover long-term care at all. In 1988 the US Congress passed the Medicaid spousal impoverishment provisions under which a certain amount of a couple’s combined resources is protected for the spouse living in the community.

Insurance Markets for the Elderly

complementary explanations, one based on information barriers (and thus market failure) and the other based on a strategic lack of demand for long-term care insurance. 3.4.2.1 Informational Barriers in the LTC Insurance Market

Finkelstein and McGarry’s (2006) study of the long-term care (LTC) insurance market used panel data from a sample of Americans born before 1923 (the AHEAD study) and found that there was no statistically significant correlation between LTC coverage in 1995 and use of nursing home care in the period between 1995 and 2000, even after controlling for insurers’ assessment of a person’s risk type. This evidence, alone, is consistent with both no asymmetric information and multidimensional private information. To distinguish between these competing explanations, they first eliminated the no asymmetric information interpretation. Specifically, they found that a subjective probability assessment contained in the 1995 AHEAD questionnaire, “What do you think are the chances that you will move to a nursing home in the next five years?” is positively correlated with both LTC coverage and nursing home use from 1995 to 2000, even after controlling for insurers’ risk assessment. Since this variable is presumably unobserved by the insurer, these positive correlations suggest private information and adverse selection by the insured. Then Finkelstein and McGarry developed a proxy for risk aversion, using information on whether respondents undertake various types of preventive health care. They found that people who are more risk averse by this measure are both more likely to own LTC insurance and less likely to enter a nursing home—consistent with multidimensional private information and advantageous selection based on risk aversion. In fact, their findings suggest that, on average, adverse selection based on risk and advantageous selection based on risk aversion roughly cancel each other out in the LTC insurance market. This in fact presents an apparently larger puzzle: if adverse selection based on risk and advantageous selection based on risk aversion roughly cancel out, why is the LTC insurance market still so small? The no-trade theorem of Hendren (2013) discussed in Section 3.2 also applies to the LTC insurance setting. 3.4.2.2 Strategic Rational Nonpurchase

Pauly (1990) provided another explanation for rational nonpurchase of long-term care insurance, even for middle- or high-wealth individuals. He considered a model in which the parent prefers long-term care provided by her children over institutionalized care in nursing homes. The parent decides whether or not to purchase long-term care insurance before she becomes enfeebled, but her children determine the form of their parent’s longterm care once their parent incurs a chronic illness. The parent anticipates that the purchase of long-term care insurance reduces the price of the institutionalized care, thus encouraging her children to initiate more formal (nonfamily-provided) care than would be the case without insurance. More specifically, without insurance, the children know that the nursing home care expenditure will reduce their inheritance, but if full insurance

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is available, there is no such impact on the amount of their inheritance if nursing home care is chosen. Since the parent prefers family-provided care over institutionalized care, she will rationally choose not to purchase long-term care insurance. This explanation even predicts that the parent may not even permit the children to purchase long-term care insurance on her behalf. However, this explanation of strategic nonpurchase of LTC insurance does not apply to people without children.

4. INTERACTIONS BETWEEN SOCIAL INSURANCE AND PRIVATE INSURANCE PROGRAMS So far we have described how retirees rely on combinations of social insurance programs, such as Social Security, Medicare and Medicaid, and private insurance purchases to insure against the multitude of risks they face. Important literature describes the interactions between the social insurance programs and private insurance markets. We summarize some of the key studies in this area.

4.1 Medicaid and Long-Term Care Insurance Brown and Finkelstein (2008) argued that a potential explanation for the small size of the private long-term care insurance market is that the public insurance provided by Medicaid may crowd out the demand for private insurance. Recall that Medicaid is a public insurance program that provides health insurance, as well as long-term care insurance for the poor elderly. Brown and Finkelstein (2008) developed an optimization model of a 65-year-old risk-averse individual who chooses an intertemporal consumption path in an environment with long-term care expenditure risks. The individuals in their model face the typical state Medicaid rules, and they can buy long-term care insurance from the private market whose prices and coverages are also calibrated to the actual available policies. The model is as follows. Suppose that a consumer at care state s at month t derives utility from consumption Cs,t and some portion of the long-term care expenditures (eg, provision of food or shelter in a nursing home), denoted by Fs,t, according to Us ðCs, t + Fs, t Þ: The care state s can take five possible values: at home receiving no care, at home receiving home health care, residence in an assisted-living facility, residence in a nursing home, or deceased. At month t, the individual has an expectation that his care state will be s with probability Qs,t; and the monthly discount rate is ρ. The consumer thus chooses consumption paths to maximize Σ Tt¼1 Σ 5s¼1

Qs, t Us ðCs, t + Fs, t Þ ð1 + ρÞt

subject to three constraints: first, an initial level of nonannuitized wealth W0 and a given trajectory of annuitized income At from Social Security; second, a no-borrowing constraint imposed to eliminate the possibility that the individual dies in debt; and third, a

Insurance Markets for the Elderly

wealth accumulation equation that depends on whether the individual is eligible for Medicaid and whether he has purchased private long-term care insurance. Under assumed preference parameters and calibrated Medicaid rules and long-term care insurance premiums and coverages, Brown and Finkelstein (2008) estimated how much a risk-averse life-cycle consumer would be willing to pay, over and above the required premiums, to purchase a long-term care insurance contract. Their results suggest that Medicaid has a quantitatively large crowd-out effect on private long-term care insurance demand; specifically, they found that given the current structure of Medicaid, two-thirds of the wealth distribution would be unwilling to buy long-term care insurance even if it were offered at an actuarially fair price. Therefore the crowd-out effect of Medicaid seems to be a major contributor to the small size of the long-term care insurance.bl Moreover, their results show that Medicaid’s large crowdout effect mainly results from the combination of its means-tested eligibility and its secondary payer status for individuals with private insurance. Medicaid’s secondary payer status for long-term care expenses for those with private insurance imposes an “implicit tax” on long-term care insurance purchase because a large part of the premium for a private policy pays for benefits that would have been provided by Medicaid. The presence of public Medicaid insurance thus limits the market for private long-term care insurance, but because of the means-testing for Medicaid eligibility, Medicaid actually provides a rather inadequate consumption smoothing mechanism for all but the poorest of individuals.bm

4.2 Medicare and Private Health Insurance There is also substantial literature on the interaction between the social insurance program of Medicare and the private supplemental insurance known as Medigap, the Medicare Advantage plans (also known as Medicare Part C, see Section 3.1.1), and the employer-provided health insurance for workers. 4.2.1 Medicare and Medigap Using MCBS data, Fang et al. (2008) studied who among the Medicare eligibles are more likely to enroll in the supplemental Medigap insurance. Table 11, reproduced from Fang et al. (2008), reports two panels of results from regressing “Total Medical Expenditure” on Medigap status, along with controls for the determinants of price (gender, a thirdorder polynomial of age, and controls for state and year), with or without controlling bl

bm

Brown and Finkelstein (2008) predict that the LTC insurance purchase rate should be about one-third, still substantially higher than the 10% insurance rate in the data. Brown and Finkelstein (2008) used a care status transition matrix developed by Robinson (1996). However, Friedberg et al. (2014) showed that this understates the risk but overstates the conditional mean duration. They show that using a corrected transition matrix reduces the percentage with a positive willingness to pay to levels closer to those observed in the data.

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Table 11 OLS regression results of total medical expenditure on “Medigap” coverage in the MCBS (1) (2) (3) (4) (5) (6) Panel A: Without health controls Variables

All

4392.7*** (346.5) Female 270.0 (356.2) Age 65 387.5*** (138.0) (Age 65)2 1.9 (10.6) (Age 65)3 0.12 (0.22) State dummy Yes Year dummy Yes No. of obs. 15,945 Adjusted R2 0.073

Medigap

Female

Male

Panel B: With direct health controls All

6037.4*** 1863.4*** 1937.0*** (455.5) (538.8) (257.2) … … 751.6*** (283.3) 460.6*** 292.9 394.5*** (175.5) (228.5) (117.2) 1.8 5.6 27.5*** (13.2) (18.8) (9.2) 0.17 0.07 0.47** (0.27) (0.43) (0.21) Yes Yes Yes Yes Yes Yes 9725 6220 14,129 0.092 0.060 0.211

Female

Male

1677.3*** 2420.9*** (348.0) (395.8) … … 417.5*** (144.6) 32.0*** (11.4) 0.55** (0.25) Yes Yes 8371 0.196

355.4* (196.8) 22.8 (16.2) 0.47 (0.38) Yes Yes 5758 0.252

Note: The dependent variable is “Total Medical Expenditure.” All regressions are weighted by the cross-section sample weights. Health controls included in Panel B are described in detail in the Data Appendix in Fang et al. (2008) under the category “Health.” A total of 71 health indicators are included. Robust standard errors clustered at the individual level are in parentheses. *, **, and *** denote significance at 10%, 5%, and 1%, respectively. Source: Reproduced from Fang, H., Keane, M.P., Silverman, D., 2008. Sources of advantageous selection: evidence from the Medigap insurance market. J. Polit. Econ. 116 (2), 303–350.

for the health status of the individuals. Each panel reports results separately for the full sample, and for male and female subsamples. In Panel A where no health controls are included, we found a large and statistically significant relationship between total medical expenditure and Medigap status. Specifically, in the whole sample, those with Medigap have expenditures that are, on average, about $4000 less than those without Medigap; the negative relationship between Medigap coverage and total medical expenditure is stronger for women (about $6000) than for men (about $2000). The regressions in Panel B are analogous to those in Panel A, but with the addition of extensive controls for health (see the Data Appendix in Fang et al., 2008 for details). Conditional on observable (but not priced) health indicators, in the full sample those with Medigap have total health care spending of about $1900 more, on average, than those without Medigap. The positive association between Medigap and total medical expenditure seems to be stronger for males (about $2400) than for females (about $1700).bn bn

Monk and Munnell (2009) obtained similar findings.

Insurance Markets for the Elderly

The results in Panel A alone indicate the presence of multidimensional private information. The results of Panel A and B together imply, indirectly, that there is advantageous selection in the Medigap market—ie, those with better health are more likely to purchase Medigap. That is the only way to rationalize simultaneously the large negative correlation between Medigap and ex-post health expenditure in Panel A without health controls, and the large positive correlation with health controls in Panel B. The results in Panel B indicate that once we condition on health status, those with Medigap have higher total health expenditures. This is what we would expect, and it may be related to the effects of moral hazard; for individuals with the same health, those with Medigap insurance face a lower price for health care. To summarize, the results from Table 11 clearly illustrate two kinds of possible interactions between Medicare and Medigap. The first interaction is risk selection; namely, healthier Medicare eligibles are more likely to purchase Medigap plans. This type of risk selection has been called “advantageous selection” because it is favorable to the private insurers who sell the Medigap policies. Whether the advantageous selection is due to retirees’ themselves or it is induced by the private insurance company via, eg, advertising targeting the relatively healthier individuals, is somewhat understudied for the Medigap insurance market.bo The second kind of interaction between Medigap and Medicare is moral hazard. Medigap effectively reduces Medicare enrollees’ out-ofpocket costs to very low levels, thus increasing Medigap enrollees’ health expenditure beyond what they would have spent if they did not have Medigap. This interaction results in a rather significant fiscal externality by the supplemental Medigap on Medicare. Indeed, the US government has noticed the fiscal impact of Medigap on Medicare expenditures, and in 2013 the Obama administration proposed to impose a surcharge by adding an amount equal to about 15% of the average Medigap policy premium to a Medigap policy owner’s Medicare Part B premium to become effective in 2017. 4.2.2 Medicare and Medicare Advantage As we described in Section 3.1.1, the traditional FFS Medicare (Parts A and B) reimburses costs of each medical care utilized by a beneficiary. Medicare still leaves seniors at significant risk of health expenditure. On average, basic Medicare benefits cover about 50% of the personal health care expenditures of aged beneficiaries in the United States (Kaiser Family Foundation, 2005). Medicare Advantage, which is privately managed care plan (either health maintenance organizations, HMO, or preferred provider organizations), is a private alternative to traditional Medicare run by a qualified private insurer. Insurers wishing to enroll Medicare beneficiaries sign contracts with the CMS describing what coverage they would provide, and at what costs. A Medicare Advantage (MA) plan bo

See Aizawa and Kim (2013) discussed later for evidence of the role of insurer advertising in risk selection in the Medicare Advantage market.

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Table 12 Capitation payment and health expenditure by health status in Los Angeles County Self-reported health status Excellent Very good Good Fair Poor

Monthly capitation payment ($) Monthly health expenditure ($) Monthly overpayment ($)

601.0 266.0 335.0

619.5 347.8 271.3

646.6 575.4 71.2

708.0 923.7 215.7

796.3 2029.4 1233.1

Source: From Aizawa, N., Kim, Y.S., 2013. Advertising competition and risk selection in health insurance markets: evidence from Medicare advantage. Working Paper, University of Pennsylvania.

typically offers an enrollee more comprehensive coverage (eg, lower deductibles and co-pays) and provides benefits that are not available in traditional Medicare.bp However, enrollees in the Medicare Advantage plans can access only the provider network of the private insurer, which is more restricted than the network available under traditional Medicare—namely, any providers that accept Medicare payments. In 2011 about 25% of Medicare beneficiaries enrolled in MA. Private insurers that offer MA plans receive a capitation payment from the government for each enrollee and then bear their health care costs. The capitation payments account for most of the plans’ revenues because typically the MA plans charge zero to small premiums. However, it has been widely documented that the capitation payment received by private insurers does not fully reflect the cost of caring for an enrollee. Table 12 from Aizawa and Kim (2013) reports the average capitation payment and expected health expenditures by self-reported health status in Los Angeles County between 2000 and 2003, calculated from MCBS data.bq It shows that, from the perspective of the private insurers that offer MA plans, enrolling retirees with excellent or very good health is hugely profitable but enrolling those with fair or poor health leads to losses. This leads to strong incentives by the insurers to engage in risk selection. Indeed, Langwell and Hadley (1989), Mello et al. (2003), and Batata (2004) found that healthier individuals are systematically more likely to enroll in an MA plan. This pattern of selection could be a result of consumer-driven selection or be induced by insurers through, eg, targeted advertising or choices of plan characteristics. Consumer-driven risk selection occurs when healthier individuals, by themselves, are more likely than less healthy individuals to find the Medicare Advantage plans (which have lower co-payments and deductibles and more extensive benefits, but more restricted HMO networks than the traditional Medicare) preferable to the traditional Medicare. Lustig (2011) studied how MA insurers may internally choose MA premiums and plan generosity to induce advantageous risk selection. Aizawa and Kim (2013) studied the role played by the advertising spending choice of the private insurers in the advantageous risk selection (favorable to the private bp

bq

For example, many Medicare Advantage plans offer hearing, vision, and dental benefits, which are not covered by Medicare Part A or B. Before the introduction of Part D, prescription drug coverage was available in Medicare Advantage plans. The pattern is common in all markets.

Insurance Markets for the Elderly

insurers) in the Medicare Advantage market. They found that consumer-driven risk selection accounts for about 85% of advantageous risk selection, while insurer-driven selection (via advertising) accounts for 15% of risk selection. In 2004 Medicare began to base capitation payments on an individual’s “risk score,” generated by a risk-adjustment formula that accounts for over 70 disease conditions. Brown et al. (2011) showed, however, that this reform on the risk adjusted capitation payment formula in fact increased overpayments and thus the government’s total cost of financing the care of Medicare enrollees. They argued that this occurs for the following reason. The risk adjustment in the capitation payment indeed decreases insurers’ scope for advantageous selection along the dimensions included in the formula, but it increases their incentive to find individuals who are positively selected along dimensions excluded from the formula and are thus inexpensive for their risk score. 4.2.3 Medicare and Employer-Sponsored Health Insurance Even though Medicare provides health insurance for those 65 years and older, it can nonetheless affect their health behavior when they are dealing with working age because of life-cycle matters, generating both a fiscal and health externality from ESHI of the working-age population to Medicare. Fang and Gavazza (2011) provided evidence that workers in high turnover industries spend less on medical care than workers in lower turnover industries during their working years; however, the low level of medical expenditures during working years increases medical expenditures during retirement.br Moreover, workers in high turnover industries are less likely to receive employer-sponsored insurance than their counterparts in low turnover industries. Overall, medical expenditures over individuals’ life cycle in the United States seem to be rather inefficiently allocated. Based on their estimates, Fang and Gavazza (2011) found that overall medical expenditure in the United States is substantially increased as a result of the fragmented health insurance system: ESHI for the working-age population, but public Medicare for the elderly. Specifically, they found that one additional dollar of health expenditure during one’s working years may lead to approximately 2.8 dollars of savings in health expenditure during retirement. An employment-based system, as compared to a national health insurance system, steepens the increase of health expenditure over an individual’s life cycle, generating a substantial fiscal externality on Medicare, which covers retirees. An employment-based health system for workers also does not internalize the full longterm benefits of health investment, while workers are young, and this leads to an increase in the overall expenditure level.bs br

bs

Interestingly, Fang and Gavazza (2011) do not find a statistically significant relationship between the turnover rate of the industry and the quantity of medical care in the United Kingdom, which has a national health insurance system. Khwaja (2010) also found that Medicare leads to large increases in medical utilization because individuals defer their medical care prior to Medicare eligibility.

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4.2.4 Medicaid and Medicaid Managed Care The interaction between public and private health insurance also occurs in the Medicaid program. There is an increasing tendency for the state Medicaid program to contract the care of Medicaid beneficiaries to private insurance plans which are known as Medicaid Managed Care (MMC), instead of directly insuring them through a public FFS plan. These private insurers are regulated and receive a capitation payment for every Medicaid beneficiary they enroll.bt The MMC setting differs from the Medicare Advantage setting discussed previously in that the public FFS options are no longer available once MMC is adopted in a state, while in the MA setting, traditional Medicare is always available. Thus in the MMC setting, private insurers cannot engage in risk selection to leave unhealthy individuals on the public program, as occurs under the MA setting. Interestingly, Kuziemko et al. (2013) showed that insurers nonetheless try to retain low-cost clients and thus improve their care relative to high-cost clients, who they would prefer to switch to a competitor. Related to this, Duggan (2004) found that MMC increased Medicaid costs in California because competing MMC plans have limited ability to negotiate favorable rates with providers relative to a consolidated FFS system.

5. SUMMARY AND DIRECTIONS FOR FUTURE RESEARCH In this chapter we described the risks faced by the aging population and surveyed the corresponding insurance markets for those risks. We focused on income risk, health expenditure risk, longevity/mortality risk, morbidity/long-term care expenditure risk, and the corresponding insurance markets. We also discussed the interactions between social insurance and private insurance markets. Because of the challenges from several demographic developments that lead to significant population aging, retirees are likely to increasingly rely on private insurance markets to meet all their insurance needs in old age because the aging population will undoubtedly worsen the fiscal condition of many of the important social insurance programs. This chapter provides a selective overview of the important research on some of the key insurance markets for the elderly. Many open questions remain among the literature we discussed in detail in the survey. For example, for long-term care insurance, we presented several potential explanations for its small size: Brown and Finkelstein’s (2008) explanation based on Medicaid’s crowding out effect; Pauly’s (1990) strategic rational nonpurchase; and Finkelstein and McGarry’s (2006) and Hendren’s (2013) informational barriers. However, the literature lacks a comprehensive evaluation about the contributions of the various potential factors to the small LTC insurance puzzle. For example, Brown and Finkelstein (2008) predicted that the LTC insurance purchase rate should be about one-third, which is still substantially bt

Most of the ACA Medicaid expansion will occur under this type of private, capitated insurance plans with substantial government subsidies and regulation, instead of the public FFS option.

Insurance Markets for the Elderly

higher than the 10% insurance rate in the data. What accounts for the 23% or so of the population who should have purchased despite Medicaid? Why don’t the LTC insurance companies offer tailored insurance products to this population? Finkelstein and McGarry (2006) showed that adverse selection based on risk and advantageous selection based on risk aversion almost cancel each other out using their proxy measure of risk aversion, but then how does information asymmetry exactly create barriers to trade in this market? Building and estimating models that incorporate all these potential explanations, together with the possibility of informal care by children, will be an important area for future research. Similarly, we presented several potential explanations for the limited size of the voluntary annuity market in Section 3.2; yet it is fair to say that the literature still lacks a consensus. Developing more comprehensive data sets that reflect households’ overall incomes, expenditures, and financial assets and liabilities, as well as the portfolio of their insurance holdings, which we will discuss, can be an important first step for us to resolve the underannuitization puzzle. There are many interesting areas that pertain to the insurance markets for the elderly that we did not discuss in this chapter. Next we list three interesting areas for future research.

5.1 Interaction Between Insurance Markets and Labor Markets Because of space constraints, we did not discuss the interaction between insurance markets and the labor market. Social insurance programs such as Social Security, Medicare, and Medicaid affect individuals’ decisions regarding labor force participation, hours of work, retirement, and the equilibrium of the labor market in general. Of course, many interesting papers have already examined such interactions,bu but we believe that recent developments in the insurance markets, particularly the US health insurance reform, provide new opportunities and questions. Rust and Phelan (1997) studied how Social Security and Medicare affect retirement behavior in a world of incomplete markets. They found that Social Security creates significant disincentives to labor force participation, and Medicare eligibility at age 65 largely explains the peaks in retirement at ages 62 and 65 in an environment where there is significant market failure in the private health insurance market.bv The percentage of firms that offer retiree health insurance is declining—according to the Kaiser Family Foundation (2008), the percentage of firms with 200 or more employees offering retiree health insurance fell by more than half between 1988 and 2008—thus the incentives studied in Rust and Phelan (1997) are bu bv

See Chapter 8 by Blundell et al. (this volume) for extensive discussions on related issues. French and Jones (2011) provided an empirical analysis of the effects of employer-provided health insurance, Medicare, and Social Security on retirement behavior. Using data from the Health and Retirement Study, they estimated a dynamic programming model of retirement that accounts for both saving and uncertain medical expenses. The key difference from Rust and Phelan (1997) is that this paper accounted for internal savings. Also see French (2005).

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bound to be more important factors affecting the labor force participation rates for men at older ages. This drop in the percentage of firms that offer retiree health insurance dramatically changes the incentives facing workers in their late 50s and early 60s. If they stay with their employer, they will continue to receive health insurance. If they leave before 65 when they qualify for Medicare, they will be forced to purchase insurance on their own. Given the rapid rise in health care costs, the decline of retiree health insurance creates a strong incentive for workers to remain employed until 65.bw Madrian (1994) tested the hypothesis that employer-provided health insurance may lead workers to be “locked” into their jobs because preexisting condition exclusions make it expensive for individuals with medical problems to relinquish their current health insurance. She used data from the 1987 National Medical Expenditure Survey to estimate the degree of job lock by comparing the difference in turnover rates of those with high and low medical expenses for those with and without employer-provided health insurance, and found that job lock reduces the voluntary turnover rate of those with employer-provided health insurance by about 25%. Dey and Flinn (2005) proposed and estimated an equilibrium model of the labor market in which firms and workers bargain over both wages and health insurance offerings to examine the question of whether the employer-provided health insurance system leads to inefficiencies in workers’ mobility decisions (which are often referred to as “job lock” or “job push” effects). They found a relative small degree of job lock or job push. Bruegemann and Manovskii (2010) developed a search and matching model to study firms’ health insurance coverage decisions. In their model, firm sizes are discrete in order to highlight the effect of fluctuations in the health composition of employees on the dynamics of a firm’s coverage decision, and they argue that the insurance market for small firms suffers from adverse selection because those firms try to purchase health insurance when most of their employees are unhealthy. Aizawa and Fang (2013) study the equilibrium impact of the health insurance reform described in Section 3.1.2 on the labor market.bx Also, several papers by Kolstad and Kowalski (2012a,b) use prereform and postreform data to study the effect of the Massachusetts Health Reform, implemented in 2006, on medical expenditure, selection in insurance markets, and labor markets. Friedberg and Webb (2005) investigated how the decline in DB pension coverage in the United States influences retirement. Using HRS data, they found substantial changes in retirement patterns as a result of the spread of 401(k) and other DC plans in place of DB plans. Workers with DC plans are retiring significantly later, which helps explain why bw

bx

See Chapter 8 by Blundell et al. (this volume) for a detailed analysis of the labor force participation and the retirement decisions. One of the main reasons in Aizawa and Fang (2013) that more productive firms are more likely to offer health insurance to their workers are related to Fang and Gavazza (2011), which documents empirical evidence that worker turnover discourages a firm’s health insurance provision.

Insurance Markets for the Elderly

employment rates recently have risen among people in their 60s, after decades of decline. Workers with DB plans retire 2 years earlier on average than workers with DC plans. The authors’ simulation suggests that the continuing shift in pension structure will increase the median retirement age by about 10 months when comparing employees with pensions who will be aged 53–57 in 2015 vs those who were aged 53–57 in 1983. Friedberg and Webb argued that these changes arise because of major differences in accrual of pension wealth. Pension wealth in DC plans accrues smoothly, while gains to pension wealth in traditional DB plans spike sharply at older ages, then turn negative afterward, creating a financial incentive to retire at that point. The recent reform to the US health insurance system, described in Section 3.1.2, offers many interesting venues for further research. For example, in both Rust and Phelan (1997) and French and Jones (2011), near-retirees can access group-rated private insurance only if they continue working for employers that offer ESHI. This plays an important role in their models to explain the peaks in retirement at ages 62 and 65. Health insurance exchange under the ACA provides an opportunity to near-retirees to purchase community-rated private insurance without having to work for an employer that offers ESHI. How will this impact the retirement behavior? It is also important to study how the ACA can potentially impact employers’ incentives to offer health insurance benefits to spouses of the employees. There are several reasons for this. The first is related to how the ACA specifies that individuals are eligible to receive tax credits: (1) They have to purchase health insurance from their states’ health insurance marketplace. (2) Only individuals and families who make between 133% and 400% of the FPL are eligible for a tax credit. (3) The individuals do not have access to affordable ESHI, either from their own or from their spouses’ employers, or from another government program. To the extent that the spouse of an employee can get similar insurance from the health insurance exchange, net of tax credits, at less than the full cost of the spousal insurance offered by the employer, the spouse would have preferred that the employer did not offer spousal insurance benefits. The same could happen even for the employees themselves. Second, the availability of health insurance from a regulated health insurance exchange under the ACA can fundamentally change workers’ outside options and thus firms’ decisions to offer spousal health insurance benefits. How will the interaction between households’ job labor market decisions and firms’ decisions to offer employee and spousal insurance benefits be affected by the ACA?by

5.2 A Portfolio Approach to Households’ Insurance Demands So far, we have discussed individual or household demands for an insurance product that corresponds to a particular risk. For example, we studied the health insurance market for health and health expenditure risks, the life insurance market for mortality risk, the by

See Fang and Shephard (2014) for some attempt to study these issues.

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annuity insurance market for longevity risk, and the long-term care insurance market for morbidity/long-term care expenditure risk. However, households do not make insurance decisions to cover each risk in isolation. Instead, households most likely choose a portfolio of insurance products to address the insurance needs because of the multitude of risks they face. Yogo et al. (2010) provide a promising attempt to model individuals’ choices of life insurance, health insurance, annuity insurance, and so on in a unified framework as a portfolio problem.bz They consider a life-cycle model in which a household faces health and mortality risks that affect life expectancy, health expenses, and the marginal utility of consumption or wealth. The household has access to a risk-free bond market, as well as a complete set of health- and longevity-related insurance products that includes life insurance, annuities, and health insurance. The key simplification for Yogo et al. (2010) to analyze the households’ portfolio choice problem is to develop a pair of risk measures for the universe of life and health insurance products. Health delta measures the differential payoff that a product delivers in poor health, while mortality delta measures the differential payoff that a product delivers at death. This allows Yogo et al. (2010) to simplify a life-cycle model of insurance choice to replicate the optimal health and mortality delta through a portfolio of insurance products.ca The portfolio perspective to households’ insurance demands also calls for more innovation in insurance products. Umbrella or bundled, insurance products that offer policyholders protection against a multitude of risks are relatively rare. It is an interesting question of why the market for such insurance products, which may be called livelihood insurance products, is not yet emerging. It also calls for the need for collecting data that reflect households’ overall incomes, expenditures, and financial assets and liabilities, as well as the portfolio of their insurance holdings.cb It should also be noted that there is now substantial evidence that individuals experience cognitive declines as they age.cc For example, Fang et al. (2008) found that cognitive ability is the key driving force for advantageous selection in the Medigap insurance market (see Section 4.2). New insurance products must be easy to understand in both their benefits and their costs in order to be appealing to the aging population. Studying how the complexity of an insurance product design affects consumer demand is an important area of research for marketing.

bz ca cb

cc

See also Yogo (2007). See Washawsky (2011) for a discussion of the various strategies to deal with retirement income risks. For example, Webb and Gong (2010) evaluated the Advanced Life Deferred Annuity (ALDA), an annuity purchased at retirement that provides an income commencing in advanced old age, and they showed, using numerical optimization, that it would provide a substantial proportion of the longevity insurance provided by an immediate annuity, at much lower cost. See Chapter 11 by Keane and Thorp (this volume) for detailed discussions about decision making and cognitive decline.

Insurance Markets for the Elderly

5.3 Insurer-Side Risks and Regulation Finally, we have so far assumed that the insurance companies can rely on the laws of large numbers when it comes to meeting their payment obligations in the insurance products they sell. However, when it comes to forecasting the risks the insurers may be facing when they offer insurance products such as annuity insurance or long-term insurance, there is a significant level of aggregate uncertainty. For example, annuity insurers face significant aggregate risks regarding life expectancy, which could be affected by advances in new medical technology; and to the extent that insurers invest some of their premiums, they could face significant investment return risks.cd These risks faced by insurers in turn are intimately related to the aging population. How should government regulate the insurers when insurers face such aggregate risks that may impact their ability to meet payment obligations? What are the optimal strategies for life and annuity insurers to hedge against the aggregate longevity risks? These are interesting questions that deserve serious studies.ce

ACKNOWLEDGMENTS I would like to thank David Bloom, Olivia Mitchell, Edward Norton, and especially two anonymous reviewers and the editors (John Piggott and Alan Woodland), as well as participants in the Harvard-CEPAR Conference for the Handbook contributors for useful comments. I would also like to thank my coauthors, Naoki Aizawa, Alessandro Gavazza, Edward Kung, Michael P. Keane, and Dan Silverman, whose collaboration led me to better understand the issues discussed in this chapter. Junwen (Caroline) Liu provided capable research assistance on the preparation of this manuscript. I gratefully acknowledge the financial support from NSF Grant SES-0844845. All remaining errors are my own.

REFERENCES Abaluck, J., Gruber, J., 2009. Choice inconsistencies among the elderly: evidence from plan choice in the medicare part D program. NBER Working Paper 14759. Agnew, J.R., Anderson, L.R., Gerlach, J.R., Szykman, L.R., 2008. Who chooses annuities? An experimental investigation of the role of gender, framing, and defaults. Am. Econ. Rev. Pap. Proc. 98 (2), 418–422. Aizawa, N., 2013. Health insurance exchange design in an empirical equilibrium labor market model. Working Paper, University of Pennsylvania. Aizawa, N., Fang, H., 2013. Equilibrium labor market search and health insurance reform. NBER Working Paper No. 18698. Aizawa, N., Kim, Y.S., 2013. Advertising competition and risk selection in health insurance markets: evidence from medicare advantage. Working Paper, University of Pennsylvania. cd ce

see, eg, Bauer and Weber (2008) for a demonstration of the impact of longevity risk on life insurers. See Blake et al. (2008) for discussions regarding how annuity providers and pension funds may be able to transfer longevity risks to capital markets through securitization of longevity risks. Also, see Wong et al. (2013) for a study of how insurers may be able to naturally hedge the longevity risk, ie, the offsetting of risks in life insurance and annuity business, by selling life insurance products and annuity products as part of a product portfolio.

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CHAPTER 6

Intergenerational Risk Sharing R. Beetsma*,†,{,§, W. Romp* *

Amsterdam School of Economics, University of Amsterdam, Amsterdam, The Netherlands Network for Studies on Pensions, Aging and Retirement (Netspar), The Netherlands { Centre for Economic Policy Research (CEPR), London, United Kingdom § Center for Economic Studies and the Ifo Institute (CESifo), M€ unich, Germany †

Contents 1. Introduction 2. Intergenerational Risk Sharing and Aging 2.1 Types of Risks and Potential for Risk Sharing 2.2 Distinguishing Risk Sharing from Redistribution 2.3 Limits to the Scope of This Chapter 2.4 The Role of Population Aging 3. Intergenerational Risk Sharing Under Various Settings 3.1 The Closed Endowment Economy 3.2 Intertemporal Smoothing 3.3 The Production Economy 4. Pension Arrangements in the Market Economy 4.1 General Features of the Market Economy 4.2 Classification of Pension Arrangements 4.3 Retirement Arrangements 4.4 Individual and Firm Decisions 4.5 Macroeconomic Equilibrium 5. IRS Through Pensions 5.1 IRS in Stylized Pension Arrangements 5.1.1 5.1.2 5.1.3 5.1.4 5.1.5

Pay-As-You-Go Notional Defined Contribution Schemes Funded Pension Schemes Discussion of Demographic Risks Aging and the Role of Factor Prices

5.2 Optimal Pension Arrangements for IRS 5.2.1 5.2.2 5.2.3 5.2.4

Special Case: Period t Is the Final Period Generational Accounting An Infinite Horizon Links to the Literature

6. Alternative Channels for IRS 6.1 Informal Arrangements for IRS 6.2 IRS Through Public Debt and Taxes 6.3 Further Channels for IRS 7. Practical Limitations to IRS 7.1 Long-Run Correlation of Wage and Capital Risks

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7.2 Labor Market Distortions and IRS 7.3 Participation Constraints 7.4 Political Commitment 7.5 Budgetary Pressures, Fiscal Constraints, and Reversibility Risk 7.6 Further Complications in Putting Theory to Practice 8. Quantification of the Welfare Gains from IRS 8.1 Measuring the Welfare Gains from IRS 8.2 Complications in Measuring the Welfare Gains 8.3 Introducing or Changing a PAYG Social Security Scheme 8.4 DB Pension Funds 9. Policy Implications 9.1 The Scope for IRS 9.2 Aging and Pension Reform 9.2.1 9.2.2 9.2.3 9.2.4

Raising the Retirement Age The Introduction of DC Funded Pillars The Introduction of NDC Schemes Recent Changes in the Pension Reform Agenda

9.3 Flexibility, Mobility, and the Width of the Solidarity Circle 9.4 Dealing with the Consequences of Changes in Accounting Rules 9.5 The Role of Supervision 9.6 Building Confidence, Transparency, and Fairness 9.7 Reform of Health and Long-Term Care Financing 9.8 The Importance of Combining Risk-Sharing Arrangements 10. Literature Gaps and Directions for Further Research 11. Concluding Remarks Acknowledgments References

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Abstract This chapter reviews the literature on intergenerational risk sharing (IRS). We explore to what extent and how a market economy with an appropriate institutional setting can replicate a social planner's solution in models with increasing levels of complexity. In particular, we do this for different combinations of pay-as-you-go and funded pension arrangements, after which we turn to the role of public debt policy in promoting IRS. Existing studies show the potential welfare improvements of IRS. We highlight a number of real-world obstacles that limit the gains from IRS, including transitional issues, labor market distortions, participation constraints, and political factors. This is followed by a review of policy options to promote IRS and to deal with these obstacles. Finally, we identify a number of gaps in the literature on IRS.

Keywords Intergenerational risk sharing, Pay-as-you-go pensions, Funded pensions, Public debt, Social planner, Welfare, Ageing, Participation constraints

JEL Classification Codes: E20, E62, H31, H55, H63, J11, J26

Intergenerational Risk Sharing

1. INTRODUCTION Recent and prospective demographic trends are attracting attention to the allocation of resources across different generations. How much each cohort contributes to and receives from collective arrangements and which risk is born in what proportion by each cohort is a matter of increasing importance to policy-makers. This chapter reviews the literature on intergenerational risk sharing (IRS) in relation to population aging. Through IRS unexpected shocks that hit one cohort or that hit a particular cohort more than other cohorts can be spread out more evenly across cohorts. This way ex-ante welfare gains may be obtained compared to the situation in which a particular cohort absorbs a disproportionate part of a shock. Conceptually, IRS needs to be distinguished from intergenerational redistribution, which involves predictable shifts in resources across cohorts. But, as we will argue in this chapter, most real-world arrangements designed to promote IRS automatically also lead to redistribution, because of systematic differences in the characteristics of the participants in the arrangement. Hence, policy-makers may face the difficult task to cleverly design institutions to promote IRS, with as few unintended by-effects as possible. The review starts with a broad-based introduction about the types of risk individuals face and the role of market mechanisms and informal and formal arrangements in promoting IRS. Then, we set up a simple overlapping generations (OLG) model to illustrate how IRS works under a social planner who commands a closed endowment economy that does not allow for resources to be shifted across periods. An imbalance in the relative sizes of the coexisting cohorts, which may be driven by population aging, reduces the ex-ante benefits from IRS. We progressively complicate the framework by introducing the possibility to shift resources across periods or, equivalently, by borrowing from and lending to other countries, and, next, by allowing for a production economy. A laissez-faire economy fails to replicate the social planner’s IRS on two main accounts. When a new cohort is born some relevant shocks have already materialized, so that these shocks can no longer be shared with existing cohorts. The second main failure is that certain risks may not be traded in financial markets. The introduction of appropriate informal and formal institutions may alleviate these fundamental issues and helps to promote IRS in the decentralized market economy. We will mostly focus on IRS through pension arrangements, because IRS has been studied mostly in connection with pensions. Moreover, pension systems are often explicitly designed to promote IRS. However, we also discuss IRS through informal institutions, in particular the family, and IRS through formal institutions other than the pension system, in particular public debt management, the educational system, and the health care system. For example, IRS through the family takes place when the level of bequests depends on the financial fortune experienced by a deceased person, while IRS through the public debt is accomplished by adjusting issued debt in response to temporary shocks, thereby spreading

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the effects of these shocks also over future tax payers. As regards to IRS through pensions, we find that the appropriate combination of a pay-as-you-go (PAYG) and a defined benefit (DB)-funded pension pillar can replicate the above-mentioned planner’s solution. In particular, a defined wage-indexed funded scheme effectively makes human capital tradable, thereby ensuring that all fundamental shocks (population growth, productivity and financial market shocks) are optimally allocated over the cohorts. That benefits from IRS from an ex-ante welfare perspective are well known. However, it is much harder to assess their quantitative importance. This importance depends mostly on the specific institutional setting chosen to promote IRS. The literature generally does indicate that the magnitude of the benefits from IRS can be quite large, although in some instances those benefits may be overturned by losses during the transition to a system promoting IRS and by general equilibrium effects on the capital stock and factor prices in particular. In Section 7 we review a number of important practical limitations to the exploitation of the potential benefits from IRS. Major limitations are high long-run correlations between wage and equity risk, endogenous labor supply and the potential labor market distortions of arrangements that promote IRS, discontinuity risk that makes that individuals reluctant to participate, political risks, and public budgetary pressures that make the expropriation of accumulated pension savings more likely. There are also a number of real-world trends that make it harder, sometimes in relation to the aforementioned limitations, to maintain institutions that promote IRS. These are, in particular, population aging, increased labor mobility, and changes in accounting rules that require companies to put certain pension arrangements on the company’s balance. However, with the proper policies in place, there should still be sufficient scope for IRS. Strict monitoring of public debt policies would reduce default risk and stimulate countries to maintain sufficient margins in their finances to absorb negative economic and financial shocks. Further, while there is a trend toward individual defined contribution (DC) pensions, there is no reason why DB funded pension schemes cannot be maintained, as long as the effective retirement age follows life expectancy closely and the distribution of the shocks hitting the fund is sufficiently transparent and balanced across the different cohorts. We review other policy recommendations as well, and we close by identifying a number of gaps in the literature on IRS. The remainder of this chapter is as follows. Section 2 introduces the concept of IRS and provides a broad-based discussion of its relevance, while Section 3 explores the social planner allocation in progressively more complicated settings. Section 4 presents the market economy including the pension arrangements. This setup allows us to explore in Section 5 how pension arrangements can be designed to replicate the planner’s solution in the context of the market economy. Section 6 considers alternative (to pensions) channels for IRS. The discussion of the most important limitations undermining IRS is found in Section 7, while the quantification of the benefits from IRS is studied in Section 8. Section 9 explores how the policy-making can be deployed to promote IRS, in a world in which important trends, including that of an aging society, undermine the scope for

Intergenerational Risk Sharing

IRS. The penultimate section, Section 10, tries to identify the main gaps in the literature studying IRS. Finally, Section 11 concludes this review article.

2. INTERGENERATIONAL RISK SHARING AND AGING This section intends to provide a broad-based introduction to the analysis of IRS. We start by describing the potential for risk sharing, after which we discuss the distinction between risk sharing and systematic redistribution. Then, we turn to the limits to the scope of this chapter. Finally, we address explicitly the role of population aging for IRS.

2.1 Types of Risks and Potential for Risk Sharing Individuals are exposed to idiosyncratic risks and common risks. The former are independently distributed across individuals and average out when aggregating across the population. In principle, these risks can be diversified away by buying insurance. Examples are health insurance, fire insurance and car insurance. Common risks hit large groups of the population or the entire population and are much harder, or even impossible, to insure. For example, natural disasters are often excluded from insurance policies, because they hit such a large group of people that an insurance company would become bankrupt if it had to pay out all the claims. Still, in many instances common risks can be traded, because a common shock may not affect all members of the population to the same extent. For example, some risks may affect some cohorts more than others. That can be the case for financial market risks, which are likely to affect the elderly more than younger people, because the elderly have, on average, accumulated more financial assets. Another example is wage risk, which affects working cohorts more than the retired. Even when all individuals face an identical risk, there may still be scope for Pareto improving trade, because some agents are less risk averse than others and are, therefore, willing to take over the risk against an appropriate fee. In many instances risk sharing can simply be achieved through market mechanisms. This is the case for the insurance industry which, in return for a fee, takes over individual risks. Also asset markets allow individuals to share risks. For example, through the issuance of stocks, the risks associated with a company’s operations can be spread over a large group of market participants. Sometimes, though, some form of public intervention would be needed for risk sharing to materialize. First, asset markets are often incomplete, implying that there is a potential room for Pareto improving institutional arrangements that spread risks not traded in assets markets more evenly over the population. However, when certain obvious opportunities for risk sharing are not offered by the market, it is important to ask why this is not the case, because this can provide leads for specific remedies that policy-makers may offer. The most important reasons why the market mechanism may not work are the presence of moral hazard (eg, Shiller, 1999, p. 182) and of adverse selection. In the case of moral hazard, there may not be much that a government can do. However, when adverse

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selection is the source of the breakdown of the market, the government may be able to help by making participation in a risk-sharing arrangement compulsory. Ball and Mankiw (2007) focus on a second reason why markets may fail to reach an optimal allocation from an ex-ante perspective: the OLG structure of the population. The unborn cannot enter into potentially welfare-improving risk-sharing arrangements with those who are currently alive. The reason is that by the time this generation can commit itself to participation, the relevant uncertainties have materialized and are known. This problem occurs whenever overlapping cohorts are not simultaneously active in a securities market before an outcome is revealed (eg, Gordon and Varian, 1988). In principle, this creates a role for intervention by a government, who may commit future generations to sharing in current risks. Such commitment could be created through the issuance of public debt or by setting up social security arrangements. For example, if current generations are hit by a bad economic shock, the government could reduce taxes and allow for an increase in debt, which forces future generations to pay higher taxes and in this way share in the risks faced by current cohorts.

2.2 Distinguishing Risk Sharing from Redistribution The gains from risk sharing can in principle be evaluated by comparing expected utility with and without risk-sharing institutions. However, it is often a priori not entirely clear what we can consider as risk sharing and what as redistribution. This depends in particular on the perspective that we take. If we take a so-called “ex-ante perspective,” the benefit of risk sharing is measured by comparing expected utility under risk sharing and under no risk sharing before the Rawlsian veil of ignorance is lifted. That is, we compare expected utility using information available when setting up the risk-sharing arrangements at the beginning of time. If we take the perspective of someone after his birth, so when certain shocks have already materialized we take an “ex-interim perspective.” A reallocation of resources after shocks have materialized amounts to redistribution. For example, from an ex-interim perspective a high income tax rate could be seen as redistributive, because it mitigates income differences that result from differences in work effort and talent, while a high income tax rate may also be seen as a form of risk sharing if one takes the ex-ante perspective that productive abilities are randomly distributed. Hence, whether some policy intervention is seen as justified may depend strongly on the perspective that one takes. High income tax rates are likely to be politically more acceptable when most voters take the ex-ante perspective and incomes differ mainly as a result of a random allocation of differences in talent. Similar differences in view may be held with regard to bequests. High inheritance taxes are likely to count on more support if end-of-life wealth is seen as mainly driven by luck. However, even if it is conceptually completely clear what should be considered risk sharing and what should be considered redistribution, it may still be difficult to design policies aimed solely at achieving one or the other objective. This is, for example, the case in many funded pension

Intergenerational Risk Sharing

arrangements that intend to share risks across cohorts but that, as a by-product, produce systematic redistribution across fund participants if these differ in systematic ways from each other.

2.3 Limits to the Scope of This Chapter Generally, risks may be shared within a cohort, between cohorts and with individuals in other countries (Shiller, 1999; Beetsma et al., 2011). In practice, there are many institutional arrangements to promote intragenerational risk sharing, ie, risk sharing within a cohort. An example concerns the tax-transfer system, which taxes those who have a job and pays out part of the collected revenues as unemployment insurance. Another example concerns public health care. International risk sharing mainly takes place through the international trade of assets, while there are only very few public institutions actively promoting international risk sharing. Asdrubali et al. (1996) present a methodology to estimate how much various channels contribute to the sharing of income risks among US states. This methodology has subsequently been applied to quantitatively explore the different channels of international risk sharing. However, the international sharing of domestic shocks is found to be quite limited (for example, see Sorensen and Yosha, 1998). This contribution does not deal with intragenerational risk sharing nor with international risk sharing. This does not mean that we think that these channels of risk sharing are unimportant or that there is no scope for achieving welfare gains from improvements in intragenerational or international risk sharing. However, we have to limit the scope of this chapter. Hence, we will limit ourselves to studying IRS. Even when dealing with IRS only, there are many possible ways in which the benefits of this risk-sharing channel can be spread over the various cohorts, as, for example, pointed out by Bovenberg and Mehlkopf (2014). If we think of a social planner trying to maximize a weighted average of the expected utilities of current and future generations, then the relative weights the planner attaches to the various generations will determine the share of the welfare gains that will accrue to each generation.

2.4 The Role of Population Aging Old-age dependency ratios are rising rapidly across the world. In the developed countries this trend is driven by three factors, namely the post-World War II baby boom, a baby bust that started in the 1970s and continues until today, and lower mortality rates at older age. Since the start of the new century fertility rates have picked up slightly, though they remain well below the replacement rates for the population. In fact, over the period 2005–10, 26 developed countries, including Japan and most of the countries in Southern and Eastern Europe, still had fertility levels below 1.5 children per woman. Moreover, in these countries, average life expectancy is projected to increase from 77 years in 2005–10 to 83 years in 2045–50 and further to 89 years in 2095–100 (United Nations, 2013).

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An immediate consequence of these demographic changes is that old-age dependency ratios are set to double by 2050. Rising old-age dependency ratios may have consequences for the opportunities that exist for IRS. For example, financial risks are mainly born by elderly people, because they have accumulated relatively large amounts of financial assets. If the size of the elderly cohorts increases relative to that of the young cohorts, it becomes harder to spread financial risks across the population. A relative increase in the number of elderly also has implications for their political power, which might affect the way risks are shared among cohorts, possibly driving outcomes away from what would be seen as a “fair” way of spreading risks across cohorts.

3. INTERGENERATIONAL RISK SHARING UNDER VARIOUS SETTINGS This section illustrates IRS in the context of a simple Diamond–Samuelson OLG framework that we progressively make richer. We start with a closed endowment economy without savings possibilities. Then, we introduce intertemporal smoothing of resources and, finally, we consider a production economy. At each point in time, there are two generations alive, with each generation featuring a representative individual who lives for two periods. We thus assume away any intragenerational heterogeneity. At the start of a period a new, young cohort is born, while the other, old cohort dies at the end of the period. Then, at the start of the next period, the current young become old. The new generation born in period t is of size Nt ¼ ð1 + nt ÞNt1 , where nt is the (possibly stochastic) growth rate of this generation relative to the generation born in period t  1. In the first period of its life, the generation is young (indicated by “y”), while in the second period it is old (indicated by “o”). Hence, the total population size is Nt1 + Nt and the old-age dependency ratio in period t is Nt1 =Nt ¼ 1=ð1 + nt Þ.

3.1 The Closed Endowment Economy We start our formal illustration of IRS with the simplest case of a closed endowment economy. The representative individual of the generation born in period t faces the following expected lifetime utility function: Ut ¼ uy ðcty Þ + βEt ½uo ðcto+ 1 Þ,

(1)

where uy() is subutility when young, uo() subutility when old, cty  0 consumption when young, cto+ 1  0 consumption when old and Et ½: is the expectations operator taken in period t after period-t shocks have materialized. The subutility functions are increasing and strictly concave in their argument. Note that utility is separable in the consumption when young and when old.

Intergenerational Risk Sharing

Individuals receive endowments in each period of life. These endowments have a constant mean, but an age-specific variance: y

y

yt ¼ y + εt , yot ¼ y + εot , y

where y > 0 is a constant component of the endowment, and εt and εot are mean-zero shocks with respective variances σ 2y and σ 2o . For simplicity, we assume that these shocks are independently and identically distributed over time. Moreover, εyt and εot are independent at all leads and lags. For now, we assume that there is no possibility to transfer resources from one period to another. In other words, all endowments received in a period need to be consumed in that period and there is no possibility to save for storage or investment in domestic capital or in foreign assets. We also assume, for now, that population growth is nonstochastic, even though it may not be constant, ie, nt may vary over time. Hence, in the absence of any intergenerational transfers, the consumption variances when young and old will be given by σ 2y and σ 2o , respectively. Consider a social planner whose objective is to maximize the expected utilities of all the individuals under the condition that there are no systematic transfers across the individuals. In this chapter we assume that the weights of future generations reflect the discount factor of households and their demographic weights, so-called “dynastic” discounting. That is, the social planner maximizes W¼

∞ X

  βt E0 Nt1 uo ðcto Þ + ð1 + nt ÞNt1 uy ðcty Þ :

(2)

t¼0

Optimization takes place subject to the macroeconomic resource constraint (divided by Nt1) cto + ð1 + nt Þcty ¼ yot + ð1 + nt Þyyt  yt : The social planner can freely allocate consumption to the young and the old generation, so welfare maximization implies the first-order condition u0o ðcto Þ ¼ u0y ðcty Þ:

(3)

If the young and the old generation have the same subutility function, Eq. (3) reduces to cto ¼ cty : The social planner only needs to introduce lump-sum transfers between currently living generations to equalize their consumption or, with a more general utility function, to equalize the marginal utility of the currently living generations. The optimal allocation can be enforced with a suitably chosen intergenerational transfer. If we denote the

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transfer from an individual young person to the old by τt ¼ yyt  cty , with identical subutility functions of young and old consumption the optimal transfer is τt ¼

1 ðεy  εot Þ: 2 + nt t

The resulting individual consumption levels in period t are: ct  cty ¼ cto ¼ y +

1 + nt y 1 o εt + ε: 2 + nt 2 + nt t

If both contemporaneously living generations are of equal size, ie, nt ¼ 0, then it is optimal to have each individual, young and old, share equally in both shocks. However, if the young are more numerous, ie, nt > 0, then aggregate resources in the economy are affected relatively more by the shock initially hitting the young generation and, hence, each individual will optimally be more exposed to this shock. Given that resources cannot be transferred across periods, for a given average consumption level y in a period, individual utility from an ex-ante perspective is higher if the variance of consumption is lower. Hence, the IRS produced through the planner’s solution produces individual welfare gains if it reduces the variance of individual consumption. If the variances of both shocks are identical, ie, σ 2  σ 2y ¼ σ 2o , then the variance of individual consumption under the planner’s solution is given by: varðct Þ ¼

ð1 + nt Þ2 + 1 2 σ < σ2, ð2 + nt Þ2

where the term on the far right-hand side is the variance of individual consumption under autarky, ie, when individuals consume their own endowments. For a concave utility function, all individuals are expected to be better off by spreading each of the two shocks over the entire population. With identical variances of the two shocks, the variance of the common consumption level ct in period t is minimized when nt ¼ 0, that is, when both cohorts are of the same size. In this case, IRS can achieve the greatest welfare gains. Suppose now that the variances of the shocks are no longer equal, ie, σ 2y 6¼ σ 2o . Then, the variance of the common individual consumption level is:    2 1 + nt 2 2 1 σy + σ 2o : 2 + nt 2 + nt Differentiating with respect to nt, we see that the variance of the common consumption level ct is increasing in nt if: σ 2y >

1 2 σ : 1 + nt o

Intergenerational Risk Sharing

Hence, an increase in the relative size of the young cohort reduces welfare under the socially optimal transfer rule if the variance of the shock hitting the young cohort is relatively large compared to the variance hitting the old cohort. Or, vice versa, suppose that the size of the young cohort shrinks relative to the old cohort, as is the case in an aging population, then the benefit of IRS increases if the variance of the shock hitting the young is sufficiently large relative to the variance of the shock hitting the old, while the benefit of IRS shrinks if the variance of the shock hitting the old is relatively large. With unequal variances, it is no longer necessarily the case that both cohorts are better off under the above socially optimal transfer rule. The young (old) cohort would be worse off if the variance of the shock hitting the old (young) cohort is vastly larger than that of the shock hitting the young (old) cohort. The young trade the lower variance of their own shock for the higher variance of the other shock and this effect on the variance of consumption may dominate the benefit of IRS that comes about by the less-than-perfect correlation of the shocks hitting the two generations. In particular, the young cohort would be worse off under the above rule if σ 2o > ð3 + 2nt Þσ 2y . Notice that the bound ð3 + 2nt Þσ 2y on the variance of the shock hitting the old is smaller in a population that features a lower nt. The part of the shock to the old that is transferred away from them is spread over a smaller group of young individuals. To the young both the disadvantage of “importing” the higher shock variance and the benefit of shedding some of their own specific risk are raised. However, the former effect dominates if the young cohort becomes smaller. While the above socially optimal transfer rule may not improve upon autarky for all individuals, it is always possible to find a rule that does make all individuals better off. Essentially, the idea is as follows. Suppose that σ 2o is substantially larger than σ 2y . Then, the old cohort can already be made better off by shedding a small fraction of its own shock in return for a substantial fraction of the shock hitting the young. This trade would be acceptable for the young. To be concrete, let us focus on a transfer rule that is linear in the shocks:   τ ¼ τ εyt ,εot ¼ αεyt  βεot : It is easy to show that the young cohort is better off if β2 < αð2 + αÞσ 2y =σ 2o , while the old cohort is better off if β½2ð1 + nt Þ + β > α2 σ 2y =σ 2o : Given some value of α, it is easy to find a value for β that fulfills both inequalities. We see that for a given value of α, the admissible values for β become small as the variance of the shock to the old becomes relatively large compared to the variance of the shock to the young.

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3.2 Intertemporal Smoothing The key insight above is that it is socially optimal to expose all simultaneously living individuals to all generation-specific shocks. By construction, it was impossible to also share shocks with future generations. In this section we study the social optimum when it is possible to transfer resources across periods by introducing a savings opportunity and a long-lived institution. These transfers take place against a stochastic technology, for example, through trade in a risky international bond, at an exogenous return rts between periods t  1 and t. Future returns on savings are currently unknown. The economy has the possibility to save positive or negative amounts of resources, depending on whether endowments are unusually high or low, respectively. When there is such a savings opportunity, the macroeconomic asset accumulation identity is: St + 1 ¼ ð1 + rts ÞSt + Nt1 ðyot  cto Þ + ð1 + nt ÞNt1 ðyyt  cty Þ, where S denotes aggregate savings currently available. Dividing by (1 + nt)Nt1 gives st + 1 ¼ ð1 + rts Þ

st yo  c o + t t + yyt  cty , 1 + nt 1 + nt

with st  St/Nt1, the current asset position per elderly. We denote by ξt the vector of exogenous shocks that materialize at the start of period t before any decisions for that period have been made. Here, the endowments, the return  on savings, and population growth are stochastic, so that we have ξt ¼ yot ,yyt ,rtk , nt . For simplicity we assume that the shocks have the Markov property. That is, the distribution of the next period’s shocks is fully determined by the current shock vector. Maximizing welfare in Eq. (2) corresponds to solving the Bellman equation V ðs, ξÞ ¼ max uo ðc o Þ + ð1 + nÞuy ðc y Þ + βð1 + nÞE½V ðs0 ,ξ0 Þjξ co , cy s yo  c o with s0 ¼ ð1 + r s Þ + yy  c y , + 1+n 1+n where we have dropped the time subscript and used a prime to denote next-period variables. The maximization problem on the right-hand side yields the first-order conditions u0o ðc o Þ ¼ βE½Vs ðs0 , ξ0 Þjξ,

(4)

u0y ðc y Þ ¼ βE½Vs ðs0 , ξ0 Þjξ:

(5)

Together, these two conditions give the same intratemporal risk-sharing condition between simultaneously living cohorts as above: u0o ðcto Þ ¼ u0y ðcty Þ:

Intergenerational Risk Sharing

The intertemporal risk-sharing condition follows from the envelope theorem Vs ðs,ξÞ ¼ βð1 + r s ÞE ½Vs ðs0 ,ξ0 Þjξ: Combining with the above two first-order conditions yields the social planner’s Euler equation   u0y ðcty Þ ¼ βEt ð1 + rts + 1 Þu0o ðcto+ 1 Þ : (6) While the intratemporal condition spreads shocks optimally over simultaneously living generations, condition (6) spreads shocks optimally over current and future generations.

3.3 The Production Economy In the previous subsection we assumed that endowments and returns were exogenous. This corresponds to an open economy with exogenous endowments. In this section we study a production economy in which the returns are endogenously determined. In this economy the key conditions for optimal risk sharing, Eqs. (3) and (6), still hold. In Section 5 we will explore how to set up an institutional framework within a market economy that can replicate the social planner’s allocation that we will derive here. The representative individual of the cohort born in period t now faces the following expected lifetime utility function: Ut ¼ uy ðcty Þ  zðlt Þ + βEt ½uo ðcto+ 1 Þ:

(7)

For expositional reasons we assume a utility function time separable in consumption and leisure. This specification differs from the previous specification by the second term z(lt), which is the disutility from work lt  0. The function z() is increasing and strictly convex. Hence, z0 > 0 and z00 > 0. Aggregate production is given by a constant-returns-to-scale production function: Yt ¼ At FðKt , Lt Þ,

(8)

where At is stochastic and determines the productivity level, Kt is the capital stock, and Lt ¼ Ntlt is aggregate labor input, ie, the product of the number of young and the individual labor supply. Capital depreciates at a stochastic rate δt. Hence, the period-t resource constraint of the economy is Cty + Cto + Kt + 1 ¼ At FðKt ,Lt Þ + ð1  δt ÞKt ,

(9)

which states that the total consumption of the young, Cty ¼ Nt cty , plus the total consumption of the old, Cto ¼ Nt1 cto , plus the total amount of capital to be accumulated for use in the next period equals total production plus the net-of-depreciation existing capital stock.

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Again we use ξt to denote the vector of shocks, which by assumption fulfill the Markov property. Here, we have ξt ¼ fAt , δt ,nt g. Following the same steps as above for the endowment economy, we can write the Bellman equation as V ðk,ξÞ ¼ max uo ðc o Þ + ð1 + nÞ½uy ðc y Þ  zðlÞ + βð1 + nÞE½V ðk0 , ξ0 Þjξ co , cy , l   k k co 0 with k ¼ ð1  δÞ  cy, + AF , lt  1+n 1+n 1+n which yields the same first-order conditions as above, (4) and (5), plus the condition for optimal labor input z0 ðlÞ ¼ At Fl ð  ,  ÞβE½Vk ðk0 , ξ0 Þjξ: The envelope theorem in this case gives Vk ðk, ξÞ ¼ βðAFk ð  ,  Þ + 1  δÞE½Vk ðk0 , ξ0 Þjξ: Combining these first-order conditions yields the social planner’s intratemporal and intertemporal first-order conditions:   z0 ðlt Þ=u0y cty ¼ At FL, t , (10)   u0y ðcty Þ ¼ u0o cto , (11)      u0y cty ¼ βEt ðAt + 1 FK , t + 1 + 1  δt + 1 Þu0o cto+ 1 : (12) Conditions (11) and (12) correspond to the conditions we derived above for the model with exogenous returns. Condition (11) regulates the intratemporal allocation of resources over the young and the old. Condition (12) is the Euler equation, which captures the intertemporal trade-off between consumption now and next period’s consumption. Hence, this condition regulates the investment in capital. Condition (10) is new. It captures the intratemporal trade-off between providing work effort and consumption by the young. In the special case that the subutility functions of consumption when young and when old are identical, condition (11) implies equal individual consumption of the young and the old in each period: y

cto ¼ ct :

(13)

In order words, optimal risk sharing of any shock takes place by having contemporaneous consumption of both concurrently living generations move together (see also Bohn, 2006). However, with age-specific utility, ie, the subutilities of consumption when young and when old are not necessarily equal, equalizing consumption of young and old within each period is no longer optimal. Linearization of Eq. (11) yields

Intergenerational Risk Sharing

^c ot ¼

ρy y ^c , ρo t

(14)

 where ρy  u00y ðc y Þ= c y u0y ðc y Þ is the coefficient of relative  risk  aversion for the young evaluated at the median consumption level c y and ^c yt  ln cty =c y , which is roughly equal to the percentage deviation of actual consumption from its median. While it would still be optimal for the planner to equate the marginal utilities of the two coexisting generations, it is no longer optimal to equate their consumption responses to shocks. If the degrees of relative risk aversion of the young and the old are equal, optimal resource allocation requires the consumption levels of the two coexisting cohorts to respond to shocks equally in percentage terms. However, if the elderly are more risk averse, ie, ρo > ρy,a then their consumption response to shocks will be proportionally smaller than the response of consumption by the young. The optimality of setting (13) also breaks down when individuals feature nonstandard preferences, such as habit formation. Under habit formation, current utility depends on current consumption relative to past consumption. For example, this could be previous consumption or some weighted average of all past consumption levels. As a result, individuals not only want to smooth the level of consumption but also want to smooth the change in consumption. Hence, young individuals will behave as if they are less risk averse than the elderly, because the young have more flexibility in changing their habits in response to unexpected shocks (see Bovenberg and van Ewijk, 2013). In this setup, young individuals would not be constrained at all by past consumption, while old individuals would want to limit deviations from the level of consumption they experienced when they were young. Other generalizations may also lead to a breakdown of (13). For example, Bohn (2001) studies a model with three OLGs in which the middle-aged, working generation finances its own and its children’s consumption and in which its utility depends on both consumption levels. In this case, movements of aggregate consumption of the middle aged, ie, consumption of both parent and children, should be identical to movements in the consumption of the retired plus a term that depends on the variation in the number of children. In the following sections we assume that preferences continue to be given by (7). It is useful to put our planner’s outcomes into a broader perspective. First, it is important to realize that not all individuals would necessarily be better off under the planner than if they had to take their own decisions. This would depend on the initial allocation of resources, which we have not specified here. Condition (11) potentially requires substantial redistribution of the initial allocation of resources, implying that one of the cohorts may actually be worse off under the planner. Second, by definition the planner’s a

While it is often argued that older people are more risk averse, empirical evidence from experiments is not conclusive, eg, see Albert and Duffy (2012).

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solution is Pareto efficient, implying that no cohort can be made better off without making any of the other cohorts worse off. Varying the relative cohort weights in the planner’s objective traces out the Pareto efficient allocations of the economy.

4. PENSION ARRANGEMENTS IN THE MARKET ECONOMY The social planner allocation serves as a benchmark for the study of IRS in the real world, which in most cases is characterized as a decentralized market economy. In the special case of a laissez-faire economy, there is no intervention in the market economy through public institutions. Generally, the allocations in the laissez-faire economy will differ from those under the planner, and this may happen for various reasons. In particular, some risks may simply not be traded among generations, because there exist no markets for them, while other risks are spread suboptimally over the generations, even though there do exist markets on which they are traded. The reason is that cohorts may be born only after those risks have materialized. Hence, a priori there exists a case for introducing institutional arrangements that can facilitate optimal IRS.

4.1 General Features of the Market Economy The market economy is based on the production economy presented above. It specifies the individual budget constraints, including the contributions to and benefits from private and public collective arrangements. Here, collective arrangements are arrangements in which contributions and risks are pooled among the participants. It also introduces explicit rewards for the deployment of the production factors. Those rewards depend on the fundamental sources of risk introduced above. Further, there are two assets that are traded in the financial markets. One is equity, of which the total supply is Kt and which earns a market rate of return rtk . The other is risk-free debt, which is in zero net supply and earns a market rate of return rt. Because the economy is closed, the asset returns follow endogenously from the model. In the following we will refer to wage risk, which, in turn, depends on productivity risk, and to capital or equity risk, which, in turn, depends on both productivity and depreciation risk. The asset market is incomplete in that wage risk is not directly traded. This creates a potential for welfare-improving institutional reform. As argued earlier, we focus on pension arrangements as a way to improve IRS. Before moving to the formal model, we discuss briefly the various classifications of pension arrangements.

4.2 Classification of Pension Arrangements Before setting up the market economy with a pension arrangement, we provide a brief overview of the classification of possible pension arrangements, which may take place along various dimensions. The first dimension concerns the way pension benefits are

Intergenerational Risk Sharing

financed. The extreme cases are a PAYG and a fully funded pension scheme. Under a PAYG scheme the contributions by the current workers are used to finance the benefits of the current retired. In other words, a PAYG scheme is financially balanced on a period-by-period basis. By contrast, in a funded scheme contributions are invested and the benefits are financed out of the accumulated capital. A second dimension for classifying pension arrangements relies on the question who bears the consequences of unforeseen developments. Here, we distinguish between DC and DB pension plans. A DC plan fixes the contribution rate and allows benefits to absorb the risks associated with the plan. By contrast, in a DB plan, the benefits are fixed or linked to other variables as prespecified in advance,b while there may be a potential mismatch between contributions and benefits. A third way of classifying pension arrangements concerns their degree of actuarial fairness. This refers to the link between the present value of contributions and the present value of benefits at the individual level (Lindbeck and Persson, 2003). In a financially actuarially fair arrangement, a marginal increase in the individual contribution equals the present value of the resulting increase in the benefit in monetary units. This definition of “actuarially fair” ignores the insurance value that is often involved in participation. We will use a definition of actuarial fairness that differs from that in Lindbeck and Persson (2003). Under our definition, the utility-based valuation of a one-dollar increase of the contribution to a pension fund is the same as the valuation attached to investing the additional dollar in the financial markets. A final dimension to classify pension arrangements concerns the question who manages the scheme (Hassler and Lindbeck, 2005). Is this the government or a private entity? It may also be that both parties are involved. Often, pension funds are managed by private entities, but heavily regulated by the government.

4.3 Retirement Arrangements We assume that the retirement arrangements in the market economy consist of two pillars, a first pillar comprised of a PAYG scheme and a second pillar comprised of a pension fund. While the contributions of workers to the PAYG scheme are immediately spent on benefits paid to the elderly, the funded second pillar allows them to save for their retirement. In addition, individuals have the possibility to voluntarily save even more. These voluntary additional savings may also be negative. In practice, they often take place in the context of what is referred to as the third pension pillar, which are arrangements offered by private parties that specifically aim at the provision of additional retirement provision. Many countries feature a three-pillar combination of pension arrangements, thus being the combination of a PAYG first pillar, a mandatory funded second pillar and a voluntary b

For example, benefits could be specified in terms of purchasing power, in terms of dollars, or as a fraction of the wage rate.

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funded third pillar. The PAYG pillar is generally the more important one, although in some countries like Denmark, the Netherlands, and the United Kingdom, funded pensions constitute a substantial part of total retirement income. This is also the case for the public sector pension funds in the United States. Moreover, wary of the demographic developments, governments in many countries are trying to stimulate funded pension provisions. The setup that we present below ignores some elements that are potentially relevant in practice. First, we do not take a specific stand on who manages the retirement arrangements. In practice, PAYG arrangements are managed through the government, the mandatory funded pillar may be publicly or privately managed, and the voluntary funded third pillar is privately managed. For ease of reference, we will refer to the PAYG pillar as managed through the government. Second, because we have assumed away any heterogeneity within cohorts, we necessarily ignore the fact that employees mainly save for retirement through the mandatory funded pillar, while self-employed are usually forced to save through the voluntary funded pillar, or outside any specific scheme. This means that the scope for IRS among the self-employed is essentially absent. Indeed, third pillar schemes are usually DC schemes. Third, saving through funded pension schemes often benefits from favorable tax treatment, because the contributions can be deducted from income before taxes. Since we ignore here public spending other than that on PAYG pensions, we necessarily ignore the issue of the tax treatment of funded pensions. Moreover, as a result, the personal savings in our model cannot make a distinction between voluntary saving through the third pillar and voluntary saving outside any specific scheme. Hence, in the sequel we will refer to all voluntary savings as “personal savings” of the individual.

4.4 Individual and Firm Decisions The total individual contribution to the PAYG scheme consists of a wage-dependent component τwt wt , where τwt is the contribution rate and wt is the wage rate, plus a lump-sum component τlt . The total PAYG benefit is Υ ot . The individual contribution to the funded scheme contains a wage-dependent component θwt wt , which is intended to build up the future funded benefit. In addition, the contribution contains a lumpsum component θlt , which is used to absorb the mismatch between the pension fund’s assets and liabilities in period t. The value of θlt may be positive or negative. Our formulation of the full set of pension arrangements in the economy is rather general and allows quite a few specific cases to be considered. The budget identities of an individual born in period t are   p p (15) cty ¼ 1  τwt  θwt wt lt  τlt  θlt  bt + 1  kt + 1 , p

p

f

cto+ 1 ¼ ð1 + rt + 1 Þbt + 1 + ð1 + rtk+ 1 Þkt + 1 + Υ ot + 1 + ð1 + rt + 1 Þθwt wt lt ,

(16)

Intergenerational Risk Sharing p

p

where bt and kt are the personal investments in risk-free debt and capital, respectively, f and where rt+1 is the (known) return on the risk-free debt and rt + 1 is the individual’s return on the wage-dependent part of his contribution to the pension fund. All individual decisions are taken when young. Specifically, young individuals maximize their expected p p utility (7) over work effort lt and personal investments bt + 1 and kt + 1 , subject to (15) and (16). The first-order condition governing the intratemporal trade-off between consumption and leisure is given by:       f (17) wt 1  τwt  θwt u0 cty + βθwt wt Et ½ð1 + rt + 1 Þu0 cto+ 1  ¼ z0 ðlt Þ: The marginal disutility of labor on the right-hand side should be equal to marginal utility of higher consumption due to higher wage income when young, the first term on the left-hand side, plus the expected marginal utility of higher consumption when old, the second term on the left-hand side. An increase in labor raises old-age consumption, because it leads to a rise in the pension fund contribution and, hence, in the expected funded retirement benefit. We notice that an increase in the PAYG contribution rate τwt exerts a negative incentive effect on labor, caused by the fact that extra revenues extracted from this increase are transferred in their entirety to the other cohort. An increase in the funded contribution rate θwt exerts a similar negative work incentive through its effect on consumption when young and a positive work incentive through its effect on old-age consumption. The intertemporal trade-off between current and future consumption is governed by the first-order conditions for private investments in, respectively, risk-free debt and equity:     u0 cty ¼ βð1 + rt + 1 ÞEt ½u0 cto+ 1 , (18)     ð1 + rt + 1 ÞEt ½u0 cto+ 1  ¼ Et ½ð1 + rtk+ 1 Þu0 cto+ 1 :

(19)

The first condition is the standard Euler equation, while the second condition is the arbitrage condition that ensures indifference between the risk-free bond and the risky asset. Firms maximize profits, ie, the sum of production plus net-of-depreciation capital minus the compensation paid to its shareholders, who own the capital stock, and the suppliers of labor: At FðKt , Lt Þ + ð1  δt ÞKt  ð1 + rtk ÞKt  wt Lt : The firm selects the amount of capital and labor to be employed in the production process. Hence, its (standard) first-order conditions are: At FK , t  δt ¼ rtk ,

(20)

At FL , t ¼ wt ,

(21)

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which tell us that the net marginal product of capital must be equal to the market return on an investment in equity, while the marginal product of labor is equal to the wage rate. Both rtk and wt are endogenously determined in the model.

4.5 Macroeconomic Equilibrium The model is closed with the equilibrium conditions in the various markets in the economy. Equilibrium in the labor market is given by: Lt ¼ lt Nt , where the left-hand side is the total demand for labor and the right-hand side its total supply, ie, the individual supply multiplied by the number of young individuals. The equilibrium conditions for the bond, respectively, capital, or equity, asset markets are B ft + Bpt ¼ 0, Ktf + Ktp ¼ Kt , f

f

p

where B t and Kt are the pension fund’s investments in risk-free debt and capital, Kt ¼ p p p Nt1 k t are the aggregate personal holdings of equity, and B t ¼ Nt1 b t are the aggregate personal holdings of risk-free debt. Aggregate bond holdings in the economy must equal their zero net supply, while the total capital stock in the economy must be equal to the sum of the capital held by the pension fund and that held through personal investments.

5. IRS THROUGH PENSIONS This section first discusses the IRS properties of some specific pension arrangements in the context of our simple model of the market economy. Then, we turn to analyzing optimal pension arrangements taking the social planner’s solution as a benchmark. Throughout this section we assume that participation in the prevailing pension arrangements is mandatory. The potential consequences of relaxing this assumption are discussed in Section 7.

5.1 IRS in Stylized Pension Arrangements 5.1.1 Pay-As-You-Go The balancing requirement of a PAYG scheme imposes that     Nt lt wt τwt + τlt ¼ Nt1 Υ ot , Υ ot ¼ ð1 + nt Þ lt wt τwt + τlt :

(22)

The left-hand side of the first equation is the sum of the wage-linked and lump-sum contributions to the PAYG scheme, all made by the current young, while the right-hand side is the sum of the benefit payments to the current retired. Eq. (22) is influenced only by the old-age dependency ratio and uncertainty about the wage rate. The latter, in turn, is affected by productivity shocks and by demographic shocks that influence the marginal productivity of labor. Hence, it is these types of risk that the PAYG can potentially

Intergenerational Risk Sharing

redistribute among generations. Financial market shocks do not directly affect the budget balance equation and, hence, can also not be redistributed among the generations through this pension pillar.c A PAYG scheme admits both DC and DB pensions. Under DC the individual contribution parameters τwt and τlt are given and do not respond to stochastic shocks, implying that the benefit Υ ot absorbs all uncertainty in order to balance the scheme. Because τwt typically lies strictly between zero and one, part of the productivity risk and part of the demographic risk are shifted to the elderly, while the remainder of those risks stays with the young. Hence, the PAYG-DC scheme allows for IRS of these specific risks. Under a DB system, the benefit Υ ot is given and does not respond to shocks. Hence, in this case the contribution parameters τwt and τlt need to respond to shocks in order to balance the scheme. Hence, both productivity and demographic risks are fully born by the young, precluding IRS under the PAYG-DB scheme. For given contribution parameters τwt and τlt , population aging as captured by an increase in the old-age dependency ratio Nt1/Nt implies fewer workers per retired, hence a lower benefit Υ ot . By contrast, if the benefit is kept unchanged in the presence of a rise in the old-age dependency ratio, then the contributions paid by the workers have to be raised. 5.1.2 Notional Defined Contribution Schemes A specific type of PAYG system is the so-called notional defined contribution (NDC) system in which a notional stock of pension entitlements is accumulated by assigning a notional return to the individual contributions made into a system. A prominent example of an NDC system is found in Sweden. Also some other countries, such as Poland and Italy, have introduced similar systems.d Consider an NDC scheme in which the return on contributions is given by the growth rate of the total wage bill, Lt wt =ðLt1 wt1 Þ. Assuming that τlt ¼ 0 for all t, in the context of our model, we have:   Lt wt τw lt1 wt1 : Υ ot ¼ Lt1 wt1 t1 Because the system operates as a PAYG arrangement, it needs to be balanced on the period-by-period basis, which requires that Nt1 Υ ot ¼ Nt τwt lt wt . Substituting the above expression for Υ ot , and simplifying, yields: τwt ¼ τwt1 , where we have used that Lt1 ¼ Nt1lt1 and Lt ¼ Ntlt. Hence, in this two OLGs setting the contribution rate by the young can be kept constant in the presence of uncertainty, c

d

Obviously, in reality, financial market conditions influence the opportunities for undertaking new investments and, thereby, also the capital stock. This would, in turn, affect the marginal productivity of labor. However, in our discussion we abstract from these indirect channels. For a description, see, for example, Cichon (1999).

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implying that a constant fraction of the individual wage uncertainty is shifted from the young to the old generation.e The old generation thus absorbs part of the uncertainty in wage income. 5.1.3 Funded Pension Schemes While financial market risks do not directly affect PAYG schemes, they do have a direct bearing on funded pensions. Here, we consider actuarially fair funded pension schemes. Such schemes do not engage in systematic redistribution of resources among cohorts. Absence of redistribution is often seen as a desirable property in reality as funded pension arrangements are usually not specifically intended for the systematic redistribution. This requires that the fund obeys the so-called actuarial-fairness condition,f     f (23) u0 cty ¼ βEt ½ð1 + rt + 1 Þu0 cto+ 1 : Compare (23) with (18). If (23) holds, individuals are indifferent between saving an extra dollar through personal investment or through the pension fund. If the left-hand side of (23) were smaller than its right-hand side, the current young would be better off investing via the fund than directly via the financial market. The future young as the residual claimant on the fund would have to make up for the expected difference, thus implying an ex-ante redistribution of resources from the future young to the current young. Vice versa, if left-hand side of (23) exceeds its right-hand side. Like PAYG pension arrangements, also funded arrangements can be of the DC or the DB type. If the arrangement is DC, the gross market return on the individual payment into the fund accrues entirely to the individual. Hence, there is no deficit or surplus in the fund that needs to be absorbed by the working cohort, implying that θlt ¼ 0 and

 f f f (24) 1 + r t + 1 θwt wt lt ¼ ð1 + rt + 1 Þb t + 1 + ð1 + rtk+ 1 Þk t + 1 , where f

f

θwt wt lt ¼ b t + 1 + k t + 1 :

(25)

The left-hand side of (24) is what is paid out to the retired in period t + 1. By definition, this must be equal to the gross return on its contribution θwt wt lt . In a DC scheme, this must equal the gross return on the assets purchased with this contribution, ie, the e

f

The result of a constant contribution rate when the notional return is linked to the rate of growth of the total wage bill does not generalize to a setting with more than two OLGs. For a three-period OLG model in which individuals work during the first two periods of their life, one can show that in the special case of an exogenous and constant labor supply the contribution rate is constant through time if and only if the population growth rate is constant. The latter condition is typically violated in an aging society. See, eg, Beetsma and Bovenberg (2009) or Beetsma et al. (2013), where this condition is termed the “full funding condition.”

Intergenerational Risk Sharing

right-hand side of (24). Eq. (25) shows the pension fund portfolio consisting of the quanf tities of the available assets purchased with the contribution to the fund. Hence, b t + 1 and f k t + 1 are the fund’s investments in risk-free debt and equity on behalf of the fund’s participant. Clearly, for a DC fund there will never be any mismatch between its assets and liabilities. The liabilities always adjust so as to equal the gross return on the fund’s assets, because this is what is paid out to the participants each period. Hence, a DC fund has each individual save purely for him- or herself and does not admit any IRS. Because DC funded plans do not admit IRS, our discussion of IRS through funded pensions from now on focuses on DB plans. Compared to capital markets DB funded plans can potentially enhance the opportunities for IRS in two possible ways. While capital markets only allow for risk sharing between individuals who can trade with each other at the same moment (see Bohn, 2009), DB funded plans allow current participants to share certain risks with the future born. In fact, if the pension fund is allowed to maintain buffers, risks affecting current participants can in principle be shared with all future generations. Second, some risks, such as wage risks, are not (yet) traded on capital markets (for example, see Constantinides et al., 2002). However, pension funds allow these risks to be spread over different cohorts of participants. DB funded plans can be defined in various ways. One possibility is to define it in nominal terms. This is, for example, the case for most plans in the Netherlands, where a DB plan entitles the participants to a fixed annual benefit as of retirement age in term of euros. Those plans are in principle subject to inflation risk. However, the consequences of unexpected inflation are often mitigated by indexing the accumulated pension entitlements to recent inflation, so that effectively the plan becomes a hybrid between a defined nominal benefit plan and a defined real benefit (DRB) plan. Under a DRB funded system, the benefit is fixed in real terms. Hence, the net return on the f period-t contribution into the fund, r t + 1 , is nonstochastic at the moment the contribution is made. Some state-owned pension funds in the United States effectively operate as DRB plans. In those systems, pension entitlements include cost-of-livingadjustments. This is also the case for DB funded arrangements in the United Kingdom, where the indexation of pension entitlements to the cost-of-living index generally is mandatory. Because under a DRB plan the return on the contribution is no longer f uncertain when the contribution is made, we can take 1 + r t + 1 outside the expectations operator in the actuarial-fairness condition (23). Combining with the Euler equation (18), this implies: f

r t + 1 ¼ rt + 1 : Hence, given that the retirement benefit is certain in real terms, actuarial fairness requires the return on the pension contribution to equal the risk-free rate. Under a defined wage-indexed benefit (DWB) funded system, the aggregate benefits that the old generation receives from the funded pillar are proportional to the aggregate wage

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sum in that period multiplied by a proportionality factor θdwb t . Hence, the return r t + 1 on the pension contributions should be such that the following expression holds:

 f (26) 1 + r t + 1 θwt wt Lt ¼ θdwb t wt + 1 Lt + 1 , where the left-hand side are again total contributions by the cohort born in period t, multiplied by the gross return on these contributions. This needs to equal the aggregate DB paid to this cohort when it is old, the right-hand side of the expression. Combining condition (26) with the actuarial-fairness condition (23) yields the required contribution rate that is consistent with the DB:   0 o w dwb Et wt + 1 Lt + 1 u ðct + 1 Þ θt ¼ βθt : wt Lt u0 ðcty Þ is constant, then the contribution rate θwt must be stochastic, because the Hence, if θdwb t wage rate wt is stochastic. In practice, pension funds try to limit mismatch risk; that is, they try to limit deviations in the value of the assets relative to the value of the liabilities. However, within the simple setup presented here, the presence of mismatch risk in the fund is necessary to benefit from IRS. In the case of a DC fund the benefit paid out by the fund is exactly equal to the gross return on the contribution, implying that there will never be any mismatch risk. IRS within a DB funded scheme is possible precisely because the fund allows for a mismatch between its benefit payments and the gross return on its assets. The contribution component θlt by the young absorbs any mismatch in period t by making up for the difference between the fund’s benefit payments and the gross return on its assets. Specifically, this requires that: θlt ¼

     1  1 + r ft b ft + k ft  1 + rta b ft + k ft : 1 + nt

(27)

Here, rta denotes the average market return on the fund’s financial assets. Hence, the fund f features a deficit if the return r t that the retired receive on their contributions f f θwt1 wt1 Lt1 ¼ b t + k t exceeds the average market return on the investments made with these contributions. Young agents thus have to make up for the difference. The term in square brackets in (27) is the mismatch per old participant. Hence, the additional contribution θlt per young participant is this term divided by the relative size of the young cohort. A number of features may be noted. First, in an aging economy, characterized by a low value for nt, each young person has to absorb a relatively large amount of mismatch. After this “mismatch contribution” by the young has been made, the fund’s asset position is again equal to zero. The fund then receives the contributions that the young pay to build up their own pension entitlements. Second, in the case of a DRB pension fund,

Intergenerational Risk Sharing

mismatch risk arises when not all of the participants’ contributions are invested in the risk-free bond, while in the case of a DWB pension fund, there would always be mismatch risk in reality, because financial assets with a return linked to wage growth are not available. Finally, the assumption that the young absorb the mismatch between the assets and liabilities associated with the pension arrangement of the old implies that the potential gains from IRS between these two generations accrue to the old, in line with Bovenberg and Mehlkopf (2014). The current young then absorb the gains from IRS with the next cohort of young and so on. Given their limited liability, young workers generally find it difficult themselves to borrow against their human capital to obtain this risk exposure and can as a participant of a fund thus benefit from the risk premia in the financial markets. In principle, by linking contributions to their financial performance, pension funds can expose young workers to financial market risks. With a DRB or a DWB fund, the current young absorb all the financial market uncertainty initially faced by the old through their pension assets. If the old also hold financial assets through personal savings, they can in this way shed some of their exposure to financial market uncertainty. Further, by linking pension benefits to wage developments, as can be done under a DWB scheme, pension funds enable retired to share in the wage risks of younger participants. Since wage risks are a function of fertility and productivity risks, the DWB fund allows to shift these fundamental risks across cohorts. In a sense, the DWB fund completes the missing market for trade in human capital. 5.1.4 Discussion of Demographic Risks While funded systems are generally more vulnerable to financial market risks than PAYG schemes, the opposite is the case for demographic risks. Population aging undermines the scope for IRS through PAYG pension systems, because it makes it harder to maintain their current generosity. Even so, demographic risks also have a substantial bearing on funded schemes. Compared with financial risks, a problem with demographic risks is their persistence and the fact that their consequences propagate for a long time into the future. This difference is difficult to capture in our simple two-OLG model structure. Over a long time, forecasts have systematically overestimated realized mortality (Oeppen and Vaupel, 2002). This is a problem for DB funded schemes in particular, because if life expectancy increases after individuals have started to build up pension entitlements, the fund’s financial assets become insufficient to honor the entitlements, implying that contributions need to be raised, entitlements need to be cut, or the retirement age has to be raised. Changes in fertility also affect funded schemes. In particular, a shrinking workingage population would reduce the marginal product on capital and thus lower the return on the equity holdings of pension funds. Moreover, it raises the marginal product of labor and, thereby, the wage rate. To the extent that existing pension claims are indexed to wages, this drives up the liabilities of the fund without matching assets. A final

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complication is that in the case of a DB system, a possible mismatch will be divided over a smaller cohort, so the ex-ante variance of the young’s contributions will increase. 5.1.5 Aging and the Role of Factor Prices In exploring the role of aging in risk sharing an important question is to what extent the aging process can be foreseen. If movements in the demographic structure are seen as purely random, then it would be optimal to design risk-sharing arrangements that spread the consequences of these movements over the generations. However, in setting up such risk-sharing arrangements in response to demographic shocks, account must be taken of the effects that these shocks already have on factor prices. As pointed out by Bohn (2001), in a closed economy it is ex post better to be born in a small generation than in a large generation, even when taking account of the effect that this has on the intergenerational transfers produced under a DB social security system. Unless the contribution rate is unrealistically high, this effect is dominated by the factor-price effects of movements in the relative size of generations. Large generations of workers bid down the wage rate, while their desire to save lowers the future return on their investments.g

5.2 Optimal Pension Arrangements for IRS This section explores the optimal design of pension arrangements from the perspective of IRS. In particular, we explore whether it is possible to find pension arrangements that replicate the planner allocation studied above. We generalize the results in Beetsma and Bovenberg (2009) by allowing for an endogenous labor supply and an infinite horizon and those in Beetsma et al. (2013) by allowing for an endogenous labor supply. We investigate IRS for combinations of PAYG and funded arrangements. Such combinations offer additional flexibility in allocating the shocks over the different participant groups. Let us first explore the various incentives created by the arrangements in our model. An inappropriate design of the combined pension arrangement may cause distortions in the labor supply, thereby undermining the potential for replicating the social planner’s allocation. First, workers contribute a fraction τwt of their wage to the PAYG pillar. Even if income effect is partly offset by the benefit they receive when retired, this surely has a substitution effect on their labor supply. Second, from the PAYG pillar each member of the old generation receives an amount Υ ot regardless of his work history. This lump-sum benefit offsets the negative income effect of the contribution, but this is in general not perfect. Third, part of the residual value of the pension fund is spread in a g

Not taken into account here are political factors. If the political weight of the large generation is large enough, it could potentially expropriate other generations, making the latter worse off, in spite of the beneficial factor-price effects. Section 7 will discuss the effect of aging on the political equilibrium in more detail.

Intergenerational Risk Sharing

lump-sum fashion over all workers via the lump-sum term θlt . Also this has no incentive effect. Finally, each worker contributes a fraction θwt of his wage income to the pension fund, which could be perceived as a labor income tax and as such have an incentive effect. However, per dollar contributed to the fund, the individual also receives additional pension when old. The actuarial-fairness condition (23) ensures that these two effects cancel against each other. To see this, substitute (23) into the first-order condition (17) for the optimal labor choice, which reduces to:   z0 ðlt Þ w : ¼ w 1  τ t y t u0 ðct Þ

(28)

Hence, the funded pension pillar no longer affects the consumption–leisure trade-off. Summarizing, we have the following result: Proposition 1 When the actuarial-fairness condition (23) holds, the funded pension pillar does not affect the consumption–leisure trade-off. We can now see under what conditions a market economy with a pension arrangement mimics the social planner’s solution. For the equilibrium factor price for labor, wt ¼ AtFL,t, replication of the planner’s labor–leisure trade-off (10) requires the wage-based contribution rate to the PAYG pillar to be zero: τwt ¼ 0:

(29)

Next, forwarding (20) by one period, substituting into (19), and combining with (18), we obtain (12), implying that the intertemporal trade-off associated with capital investment in the market economy coincides with that under the planner. The final condition that needs to be fulfilled is (13). That is, the consumption levels of the generations that live at the same moment need to be equal. This requires that the consumption of the young and the old in each period responds in an identical way to the various shocks hitting the economy. But this, in turn, requires that the young and the old effectively, ie, directly through their personal savings or via the pension fund, hold identical amounts of equity and human capital. Under laissez-faire, ie, in the absence of any pension arrangement, the old receive all capital income, implying that they absorb all depreciation risk, while the young receive all the wage income. Hence, an optimal pension arrangement needs to be able to shift capital income in the right proportion from the old to the young and wage income in the right proportion from the young to the old. In addition, the pension arrangement needs to ensure that also in the absence of any shocks consumption levels are identical. With τwt ¼ 0, the condition in Eq. (6) requires that for all possible shock combinations   p p 1  θwt wt lt  τlt  θlt  bt + 1  kt + 1 (30) ¼ ð1 + rt Þbpt + ð1 + rtk Þkpt + ð1 + nt Þτlt + ð1 + rtf Þθwt1 wt1 lt1 :

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5.2.1 Special Case: Period t Is the Final Period Suppose that the world ends in period t and that this is known to all individuals. This is the situation studied in Beetsma and Bovenberg (2009) and Beetsma et al. (2013). Hence, all remaining resources, production plus capital net of depreciation, will be consumed in p p period t. Therefore, bt + 1 ¼ kt + 1 ¼ 0. This also implies that the young generation in period t does not contribute to the pension fund in order to build up a future pension. Hence, θwt ¼ 0. According to the planner’s optimal solution, the effect of each shock should be evenly spread over all individuals who are currently alive. Under laissez-faire the young are affected by productivity risk only, while the old are affected by both productivity risk and depreciation risk. Because productivity risks are not automatically distributed in the right proportion across individuals, the pension arrangement has to ensure that this is accomplished. In addition, the pension arrangement has to ensure that the right amount of depreciation risk is shifted from the old to the young. Obviously, the planner’s allocation is achieved when both wage and capital risks are evenly distributed across individuals. Beetsma et al. (2013) show that the replication of the planner’s allocation through a DRB fund is rendered impossible by the requirement that τwt ¼ 0. Therefore, we consider the DWB fund. Combining (26) lagged by one period and (27), and using (25) lagged by one period:      1  1 + r ft b ft + k ft  1 + rta b ft + k ft 1 + nt    1  ð1 + rt Þb ft + 1 + rtk k ft : ¼ θdwb t1 wt lt  1 + nt

θlt ¼

(31)

Hence, substituting (31), (26) backwarded by one period, and θwt ¼ 0 into (30) yields: wt lt  τlt  θdwb t1 wt lt + ¼ ð1 + rt Þbpt

   1  ð1 + rt Þb ft + 1 + rtk k ft 1 + nt

+ ð1 + rtk Þk pt p

f

+ ð1 + nt Þτlt p

(32)

+ ð1 + nt Þθdwb t1 wt lt : f

Hence, rewriting and using that b t ¼ b t and k t ¼ kt  k t , we obtain:  

2 + nt f k 2 + nt f b + ð1 + rt Þ wt lt + ð1 + rt Þ k  kt ¼ ð2 + nt Þτlt + ð2 + nt Þθdwb t1 wt lt : 1 + nt t 1 + nt t This leads us to the following proposition: Proposition 2 Assume that the world ends when period t is over. Then, the planner’s allocation is f achieved by setting τlt ¼ ð1 + rt Þb ft =ð1 + nt Þ, k t ¼ ð1 + nt Þkt =ð2 + nt Þ, and θdwb t1 ¼ 1=ð2 + nt Þ. Given the stock of capital Kt in the economy, the actuarial-fairness condition ties down the f size of b t .

Intergenerational Risk Sharing

The DWB arrangement effectively addresses the two sources of market incompleteness, namely (i) that the unborn cannot trade in financial assets, and (ii) that human capital is not traded on the financial markets. Under the DWB arrangement the young, before they are born, effectively sell wage-indexed bonds to the old and invest the proceeds of this sale for their own risk via the pension fund in risk-free debt and in equity. In this way, the DWB scheme is able to shift an appropriate amount of wage risk to the old generation, while at the same time allowing the young to absorb the appropriate amount of capital risk, thereby sharing the right amount of depreciation risk. Specifically, because the DWB scheme is able to shift wage risk, there is no need for having the PAYG pillar shift part of the wage risk. Hence, the wage-linked part of the contribution to the PAYG pillar can be set to zero (τwt ¼ 0) and, because the wage-linked part of the contribution to the funded pillar does not distort the labor supply, the full arrangement leaves the labor market undistorted. f f f f Given k t , the pension designer can vary the contribution θ t ¼ θwt wt lt ¼ b t + k t to the f fund by varying b t . However, to ensure that the consumption levels of the individuals of the two cohorts are identical, the designer needs to impose an offsetting lump-sum contribution τlt to the first pillar. Concretely, given the funded-pillar benefit paid to the old f generation, an increase in b t implies that a young individual as a residual claimant receives an additional amount ð1 + rt Þb ft =ð1 + nt Þ, which needs to be offset through an equal increase in τlt . However, the sizes of the contribution and the benefit are linked to each through the actuarial-fairness condition, implying that, given the benefit level, there is f only one value of b t that is consistent with replicating the planner’s allocation. Replicating the planner’s allocation requires that consumption of the young and the old reacts in identical ways to the fundamental shocks hitting the economy. This is achieved by giving individuals from each of the two generations identical exposure to both wage and equity risk. As can be seen from (32), by setting θdwb t1 ¼ 1=ð2 + nt Þ, each dwb young person’s exposure to wage risk is wt lt  θt1 wt lt ¼ ð1 + nt Þwt lt =ð2 + nt Þ, while using (26) each old person’s exposure to wage risk is ð1 + nt Þθdwb t1 wt lt ¼ f ð1 + nt Þwt lt =ð2 + nt Þ. Further, by setting k t ¼ ð1 + nt Þkt =ð2 + nt Þ, each young person’s   exposure to equity risk is 1 + rtk k ft =ð1 + nt Þ, while each old person’s exposure to equity     f risk is 1 + rtk kpt ¼ 1 + rtk k ft =ð1 + nt Þ, where we have used that k t ¼ ð1 + nt Þkt =ð2 + nt Þ p

f

f

and kt ¼ kt + k t together imply that k t ¼ ð1 + nt Þk pt . An interesting property of arrangement in Proposition 2 is that it allows to separate the objectives of redistribution and risk sharing between the two pension pillars. While all redistribution takes place through the PAYG pillar, the funded pillar focusses on risk sharing only. In practice, this facilitated by the fact that PAYG pension arrangements are designed and managed by the government and so can be relatively easily deployed to achieve redistributive objectives design, while funded pillars are usually the preserve of the private sector.

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In a more aging economy, ie, when nt is lower, wage risk can be spread more thinly over the entire population. Hence, the effective amount of wage risk born by each individual in the population can be lower. In other words, per young person a larger fraction θdwb t1 of the wage risk effectively needs to be shifted to the retired. Also, each worker as a residual claimant of the pension fund receives a relatively large fraction of the gross return on the fund’s debt holdings, so that the offsetting lump-sum contribution τlt to the PAYG pillar by each worker needs to be larger. Finally, with the relatively smaller number of workers as the residual claimants the fund needs to hold a smaller amount of equity for each retired. 5.2.2 Generational Accounting Generational accounting has been advocated in the work of, for example, Auerbach et al. (1994). A generation’s account is the present discounted value of the sum of its (past, present, and future) net benefits (ie, benefits minus tax payments or contributions). The optimality condition of equal consumption levels of the two generations in the final period t, assuming their momentary utility functions are identical, can be translated into a condition on their generational accounts. The consumption levels of the two generations can be written as p

p

cty ¼ wt lt  bt + 1  kt + 1 + gty ,

(33)

cto ¼ ð1 + rt Þbpt + ð1 + rtk Þkpt + gto ,

(34)

where gty

and gto are the individual generational accounts of a young and an old individual, respectively. All individual generational accounts sum to zero, implying that gto ¼ ð1 + nt Þgty : Substituting this expression into (34) and setting the right-hand sides of (33) and (34) equal to each other, we obtain the condition on how the individual generational accounts should move in response to shocks. 5.2.3 An Infinite Horizon Let us now consider the infinite-horizon case for the DWB pension fund. Substituting (31) and (26) backwarded by one period into (30) yields:  

  2 + nt f w k 2 + nt f 1  θt wt lt +ð1 + rt Þ b + ð1 + rt Þ k  kt 1 + nt t 1 + nt t p

p

p

f

¼ bt + 1 + kt + 1 + ð2 + nt Þτlt + ð2 + nt Þθdwb t1 wt lt : Using (25) and the condition bt + 1 + b t + 1 ¼ 0 for equilibrium in the market for risk-free debt, we can write this equation as:

Intergenerational Risk Sharing

 

2 + nt f k 2 + nt f b + ð1 + rt Þ wt lt +ð1 + rt Þ k  kt 1 + nt t 1 + nt t ¼ kt + 1 + ð2 + nt Þτlt

(35)

+ ð2 + nt Þθdwb t1 wt lt :

This yields the following proposition analogous to Proposition 2: Proposition 3 The planner’s allocation is achieved by setting τlt ¼ ð1 + rt Þb ft =ð1 + nt Þ f kt + 1 =ð2 + nt Þ, k t ¼ ð1 + nt Þkt =ð2 + nt Þ, and θdwb t1 ¼ 1=ð2 + nt Þ. Hence, the arrangement is very similar to that in the case when the world ends in period t, except that now τlt has to be modified for the burden of building up the new capital stock to be used in period t + 1. Initially, this burden falls on the young. However, via τlt an appropriate share of this burden is shifted to the old, so that individuals from both generations have identical consumption in period t. 5.2.4 Links to the Literature Early work on IRS in pension arrangements has focused mostly on PAYG systems. Examples of such studies are Enders and Lapan (1982), Thøgersen (1998), Krueger and Kubler (2006), Wagener (2004), Sanchez-Marcos and Sanchez-Martin (2006), and Ball and Mankiw (2007). Only relatively recently has the analysis of IRS via funded pension arrangements received substantial attention. Bovenberg et al. (2007) provide a literature review and analysis of the factors driving savings and the composition of investment over the life cycle, while also exploring the role of funded pensions in such a setting. Matsen and Thøgersen (2004) investigate the optimal division between PAYG and funding from a risk-sharing perspective, though they do not include funded systems of the DB type. Teulings and De Vries (2006) explore a funding arrangement in which each generation builds up and depletes its own pension account. In contrast to the above model, they assume a partial equilibrium setup with a given equity premium and a given risk-free interest rate. In addition, they assume that capital markets are complete so that young agents can invest in equity before they are born. Several other contributions study intergenerational risk sharing through pension funds. One example is Gollier (2008). He explores in the context of a multi-OLG model the joint optimization of the retirement benefit policy and the fund’s asset allocation strategy. He finds that it is optimal for the fund to invest a constant share of its wealth in risky assets and distribute a constant fraction of it to the retired. The paper also studies a secondbest strategy optimized under a minimum solvency ratio and a nonnegative required return to the participants. Compared to the first-best strategy, the second-best strategy accumulates reserves faster in order to limit the chance of a low payout necessitated by a low wealth level. Also, the investment strategy in the second best is more precautionary; hence the expected portfolio return is lower. This effect is also particularly strong at low wealth levels.

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6. ALTERNATIVE CHANNELS FOR IRS IRS can not only be generated by pension arrangements. In practice, there are other formal and informal arrangements that also produce IRS, although these arrangements are not necessarily designed for this purpose. One may expect informal arrangements, like IRS taking place through transfers within the family, to play a relatively more prominent role in developing countries and formal arrangements to be relatively more important in the industrialized world. In this section, we discuss channels for IRS other than through the pension system.

6.1 Informal Arrangements for IRS Informal risk sharing among generations can take the form of bequests, mostly from parents to children, or of “inter vivos” transfers between family members alive at the same moment. To the extent that bequests depend positively on the financial fortune of the parents over the past, parents effectively shift some of the financial risks they have incurred to their offspring. The same is the case when children spend resources (in time or financial) to take care of their elderly parents, while these expenditures depend on the children’s financial well-being. Especially in developing countries, investing in children (and their education) is a channel to ensure old-age income and can be seen as an alternative to an investing in financial assets or a formal pension arrangement. Kotlikoff and Spivak (1981) explore to what extent insurance against longevity risk within the family can substitute for the absence of complete public annuity markets. They solve for the optimal consumption paths of family members that maximize the (weighted) sum of individual utilities, taking into account individual survival probabilities and assuming that altruism is absent. The combination of family members can be a married couple or a combination of one or more parents and one or more children. The problem with the absence of annuity markets is that the danger of running out of resources prevents consumption smoothing and hence consumption will be downward sloping over one’s lifetime. By insuring each other against longevity risk, family members can bring their consumption profiles closer to that under complete annuity markets. Even with small numbers of family members, about 70% of the benefit associated with perfect risk pooling can be captured. IRS within the “extended family” has been empirically tested by Altonji et al. (1992) using data on food consumption from the Panel Study of Income Dynamics for the United States. The idea is that in the presence of an altruistic link between generations, only the collective family budget constraint matters for consumption. The altruism model is strongly rejected, as it turns out that the distribution of changes in food consumption depends strongly on the distribution of changes in incomes between parents and children. Because the empirical specification for the altruism model is indistinguishable from that when risks are pooled out of selfish motives, also this latter model is

Intergenerational Risk Sharing

rejected. The follow-up study by Altonji et al. (1996) also rejects intrafamily risk sharing (as well as interfamily risk sharing).

6.2 IRS Through Public Debt and Taxes Public debt management in combination with tax policy can be an important channel for IRS. For simplicity, let us start with the assumption of lump-sum taxes. The effectiveness of public debt management for IRS depends on whether Ricardian equivalence holds. If, given the path for public spending, the choice between tax and debt-financing is irrelevant, then public debt policy cannot contribute to IRS. One reason for Ricardian Equivalence to fail is exactly the finite lifetime that allows for IRS. Whether public debt can be used for IRS also depends on the storage technology. Consider an OLG setting in which individuals have no bequest motive. Start with the simple setting of a closed endowment economy without storage technology and assume that endowments are stochastic. Alternatively, one may assume that the government faces an exogenous stream of spending requirements. In addition, one may have demographic shocks. In this setting, all available resources in each period have to be consumed in that particular period. Hence, IRS is limited to the smoothing of shocks over the concurrently living cohorts, which implies that there is no role for public debt in transmitting endowment fluctuations into the future. Taxes and transfers can be set such that public expenditures are financed on a period-by-period basis and every person living in a given period has the same amount of resources for consumption in that period. This is the decentralized setting that corresponds to the setup in Section 3.1. Introducing a storage technology, but retaining the closed economy, creates a role for public assets in promoting IRS. When resources are unusually high, the government taxes the private sector and stores some of the resources for later use. Future negative shocks can then be dampened by releasing some of the stored resources. This way, the government can spread the consequences of the shocks over all future generations. Obviously, if stored resources are zero and a negative shock hits, this shock cannot be dampened. Generally, it would be optimal for the government to build up a stock of resources when endowments are sufficiently favorable and use this stock to (partially) absorb temporary bad shocks. Next, relaxing the assumption that the economy is closed, the need for building up a buffer disappears. Now, in the case of an unusually bad shock the government can borrow abroad and use the borrowed resources to provide the private sector with additional resources. Let us assume that shocks take the form of exogenous government spending requirements. The period resource constraint in Section 3.2 becomes St + 1 ¼ ð1 + rts ÞSt + Nt1 ðyot  cto  gt Þ + Nt ðyyt  cty  gt Þ, where gt is the stochastic per-capita level of required government spending, which indeed plays the same role as an endowment shock. Hence, the social planner’s optimality

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conditions are identical to the original ones. An unexpected increase in gt lowers the wealth and, hence, lifetime consumption of the current generations if they have to finance the entire increase through taxes. The government can shift part of this burden to the future generations by additional borrowing and raising taxes for all current and future generations. This debt will be serviced by newborn, unlinked generations, so the lifetime income of current generations is partly restored. The beneficial role of public debt becomes even larger when current consumption no longer depends on lifetime income, but on disposable income, for example, because individuals face borrowing constraints. An economic recession then leads to additional welfare losses that can be mitigated by alleviating the tax burden through the issuance of additional debt, thereby allowing for better smoothing of consumption over individual life cycles. By the same logic, an economic boom should lead to a reduction in debt. Public debt management not only smoothes consumption over the life cycle of the currently alive. It also allows future cohorts to share in current business cycle risks. While the management of nonindexed public debt may aid in promoting IRS, IRS can be improved further by expanding the menu of available public debt instruments. As shown in Beetsma et al. (2011, 2013), the presence of wage-indexed debt enhances the scope for designing welfare-improving pension arrangements. Effectively, by issuing wage-indexed debt, wage risks can be more effectively shared among cohorts. Similarly, the issuance of longevity-indexed debt allows longevity risks to be shared across cohorts. Also, a clever deployment of tax instruments can improve IRS. As Bovenberg and van Ewijk (2013) point out, by taxing the wages of the younger cohorts to finance wageindexed pension benefits of the elderly, wage risks are more evenly spread over the cohorts, and by taxing capital income, including bequests and imputed rents from owner-occupied housing and property, also the younger cohorts are made to share in the risks associated with capital income.h

6.3 Further Channels for IRS This section turns to other channels for IRS not reviewed so far. In particular, we discuss IRS through the health care and long-term care insurance system and through the educational system. Regarding the latter channel, Bohn (2013) points to the possibility of IRS if working generations finance the education of the young in return for a claim on their future earnings. When the current working generations have become old, they can share in the deviation from its expected level of their offspring’s wage. In fact, this form of IRS is implicit in real-world education financing when the burden of servicing the debt incurred through schooling depends on disposable income. For example, in the Netherlands, the repayment obligation is means-tested, implying that the general tax h

In the case of the taxation of bequests, it is mostly the young and oldest cohorts, as well as the poorer parts of the population that now share in these risks.

Intergenerational Risk Sharing

payer shares in the wage risk. It should be noted, though, that this concerns the individual wage risk rather than aggregate wage risk of the cohorts that earlier received financial support for their education. Public health insurance is often organized in a way that resembles the PAYG pension system. Expenditures are financed through current contributions that generally do not reflect individual health risks. In particular, the (younger) working cohorts contribute more than is spent on them, while the opposite is the case for the elderly. This implies a systematic redistribution from the former group to the latter group. Such an arrangement may be maintained if it is seen as a social contract: younger cohorts only agree to such an arrangement, if they can benefit from the same arrangement when they have become old themselves. Aside from systematic intergenerational redistribution, health insurance may help in promoting IRS if changes (eg, due to technological progress) in the cost of the treatment of certain diseases are born through contribution changes whose incidence is more evenly distributed across the different generations than the occurrence of the disease itself. This is the case, for example, for most forms of cancer. Medical insurance for the elderly in the United States (Medicare) is (half–half ) financed by contributions by employers and employees, suggesting that working generations absorb a substantial share of the aggregate “medical expense risks,” as Bohn (2006) terms these risks. In this connection, Bohn (2006) points to the danger associated with a DB interpretation of Medicare under which the young absorb any uncertainty about the costs associated with further progress in medical technology. It should be noted, though, that, since employers usually contribute to health insurance of their employees, they also absorb part of this risk. This way, because of their disproportionate equity holdings, the elderly share in the “medical expense risks.” As is the case with PAYG pension systems, population aging reduces the capacity of the young to share in the medical expense risks associated with the elderly. Insurance of long-term care needs to be distinguished from health insurance. Cutler (1996) finds that the demand for long-term care insurance in the United States is relatively low, which may be partly due to a crowding-out effect from Medicare and partly because insurance tends to come in the form of indemnity payments rather than service guarantees, so that the insured continues to be exposed to aggregate medical expense risks.

7. PRACTICAL LIMITATIONS TO IRS Above we have explored IRS in a stylized model. The benefit of this strategy was that it helped us to gain insight into the optimal allocation of aggregate risks across generations and the basic institutional design to support such allocation. However, our simple model setup ignored a number of relevant real-world imperfections that affect the scope for IRS. Moreover, there are substantial practical obstacles in putting theory to practice. This section discusses these imperfections and practical complications.

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7.1 Long-Run Correlation of Wage and Capital Risks Benzoni et al. (2007) show that labor income and dividends are cointegrated. While the contemporaneous correlation between labor income shocks and stock returns is low, long-run correlations may be high. Naturally, if wage and capital market risks are highly correlated, the gain from IRS will be relatively low, because the risks faced by the elderly, via their stock holdings, and the young, via their human capital holdings, are very similar. Under those circumstances, a collective DB fund might be less attractive than a DC fund that allows for investment policy to be tailored to the individual’s personal characteristics.

7.2 Labor Market Distortions and IRS In the market economy of Section 4, workers pay a share τw of their labor income as a PAYG contribution and θw to the pension fund as a normal contribution, plus a lumpsum contribution θl to offset mismatch risk. Proposition 1 showed that if the actuarialfairness condition holds for the normal contributions, then this component has no distorting effects. The distortionary effect of the PAYG pillar mostly depends on the perceived link between the contribution to this pillar and the resulting future pension entitlements. It also depends on how participants value their entitlements. When the continuity of a PAYG system is at stake, the wage-linked contributions to the system will be perceived as distorting taxation, which leads to deadweight losses. A negative shock, such as an adverse demographic shock, that causes these contribution rates to rise will only lead to larger distortions. Some authors, like Feldstein (2005), predict that due to the current aging problem, the generosity of PAYG system will have to be reduced to prevent unacceptable deadweight losses from high contribution rates. This would also reduce the scope for IRS. As we document in Section 9, most countries try to limit the costs of PAYG schemes by shifting to a funded pension system. This comes at the cost of at least temporarily increasing the deadweight losses associated with the distorting PAYG contributions. Contrary to a PAYG system, a funded system has assets to back up its liabilities. Nevertheless, as a fund must recover after a negative financial shock, new participants have to pay a markup over the normal contribution rate, while the financial returns on their contributions are partly used to cover the pension of the currently retired. As Romp (2013) shows, risk sharing via pension funds creates a time-varying implicit tax, thereby distorting the labor-supply decision. Active participants may also try to shift the burden of restoring the fund to the employers by requiring a higher wage as compensation. This effect is particularly harmful for employment during a recession, as the additional wage cost amplifies the negative shock from the recession itself. This creates an interesting trade-off. IRS via the pension system has the objective of reducing the variance of lifetime income, while the risk-sharing mechanism itself increases the variance of aggregate output.

Intergenerational Risk Sharing

Bonenkamp and Westerhout (2014) allow for labor-supply distortions in a twoperiod OLG model with a DB funded pension scheme and explore whether the welfare gains from IRS can overcome the losses associated with these distortions. They find that on net it is beneficial to have at least some IRS. Specifically, a DB fund is always Pareto improving compared to a DC fund, because the former can replicate the laissez-faire economy without IRS and labor-supply distortions by investing only in the risk-free asset. The benefits of IRS show up in an increased risk-bearing capacity of economy and, hence, an increased demand for risky assets. Moreover, there is a shift in the labor–leisure choice toward increased labor supply, because workers can only capture the equity premium if they work. While Bodie et al. (1992) and Farhi and Panageas (2007) find that flexibility in labor supply justifies more risky asset portfolios, Bonenkamp and Westerhout (2014) establish that it may actually reduce the risk appetite of individuals. With contributions a constant fraction of wage income, the lower demand for risky assets is driven by two effects. First, since risk-sharing transfers are accompanied by distortions in labor supply, this makes these transfers less attractive. Second, there is a substitution effect in the labor supply that introduces a positive correlation between labor income and asset returns and, hence, makes investment in equity less attractive. Specifically, if the stock return falls, the pension fund has to raise the contribution rate, which reduces net wage income. Aging affects the scope for IRS also through funded pension systems. To the extent that a fund is of the DB type, an increase in the share of fund participants that is retired means that pension contributions have to fluctuate more in order to absorb the effect of shocks on the retirees’ benefits. Obviously, there are limits to the extent to which pension contributions can absorb those shocks. In particular, larger fluctuations of pension contributions raise the losses of distortions when the labor supply is endogenous.

7.3 Participation Constraints The scope for IRS may depend on whether participation in some risk-sharing arrangement is voluntary or mandatory. The continuity of a pension system can be seen as the result of a social contract among subsequent cohorts. Young cohorts are only prepared to participate in the system on a voluntary basis, if they expect the future young to do the same. From this perspective, PAYG schemes are relatively vulnerable in the presence of changes in fertility. A fall in fertility may make the burden of paying the retirement benefits of the old so large that the young would prefer to give the system up. The fear among current young workers that the current benefit levels for the elderly will no longer be in place when they themselves have become old, seems to be growing, as reported in polls among Canadian (Nanos, 2012) and Dutch (Motivaction, 2011) respondents. This uncertainty about the future benefits alone could cause the system to unravel into a breakdown already now, implying that ex-ante welfare gains from IRS will be lost.

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Discontinuity risks are relevant not only for PAYG pension schemes but also for funded schemes. When a large negative shock hits the pension fund, the young workers in particular may have an incentive to leave the fund, because the burden of restoring its financial reserves falls mostly on them, while they may be uncertain that the future young would be prepared to make up for any future shortfalls. Again, if the current young feel sufficiently uncertain in this regard, they will try to leave the fund if they are called upon to pay more than they normally contribute in order to restore the fund’s reserves, and the ex-ante welfare gains from IRS will be lost.i However, not only underfunding can be a threat to a fund’s existence, but also large buffers can threaten its survival. In this case, it is the existing, rather than the new, participants that have an incentive to dismantle the fund and distribute the fund’s assets among themselves (Van Bommel, 2007).j Beetsma and Romp (2013) explore in a two-period OLG endowment model with financial market uncertainty whether equilibria with IRS exist if participation in a funded pension arrangement is voluntary. Equilibria are characterized by a threshold on the contribution made by the young beyond which it is optimal to quit the arrangement. An equilibrium threshold is one that is optimally applied by the current young under the assumption that the next-period young apply the same threshold. The only stable equilibrium is one in which the arrangement persists indefinitely. Beetsma and Romp (2013) find that the existence of such an equilibrium requires rather substantial risk aversion and uncertainty on the financial markets, so that the benefits in terms of IRS from participation are relatively large. Moreover, the maximum amount of IRS compatible with the sustainability of such equilibria may be less than what would be optimal if participation were mandatory. Not surprisingly, many countries impose some obligation to participate in a supplementary pension arrangement. For example, a legal obligation is imposed in Australia, Chile, Iceland, Sweden, and Switzerland, while participation is quasi-mandatory (through collective labor agreements) for Denmark and the Netherlands. Mandatory participation is usually motivated by the need to protect individuals against their own myopia leading to insufficient retirement savings. That this may create a scope for IRS is a beneficial side effect. The United Kingdom recently introduced a policy that obliges employers to enroll employees into an occupational pension arrangement. Employees are allowed to opt out. However, the idea behind the automatic enrollment is that most individuals will not make use of the possibility. The assets of a pension fund can be split up into two components: assets used to cover the existing liabilities and a buffer. As Beetsma and Romp (2013) show, i

j

The likelihood of a system breakdown would obviously depend on the existence of guarantees provided by other parties, in particular a corporation sponsoring the fund. An alternative to dismantling the fund is to reduce contribution rates. This has happened on a large scale in the Netherlands during the end of the 1990s when stock prices were rising fast and the economy was booming.

Intergenerational Risk Sharing

imposing a buffer requirement has interesting consequences for the sustainability of a funded pension arrangement. If the asset returns are high, the buffer creates some “free” money that can be used to lower the contributions by the young. However, if the asset returns are low, the incoming cohort not only has to guarantee the pension benefits of the retired, but it also has to replenish the buffer, implying a contribution that is actually higher than in the case without buffers and, hence, creating a distorting tax. Overall, the sensitivity of the contributions to the asset returns increases when buffer requirements are higher. Moreover, individual contributions may be increasing or decreasing in the size of the young cohort, depending on whether the fund has more or less reserves than required. When the fund has more reserves than required, the excess reserves per young individual are higher when the young generation is smaller and, hence, the contribution can be reduced. However, when reserves are too low, a smaller young generation requires a larger increase in the individual contribution to replenish the reserves. Low buffers are currently a problem of many DB pension arrangements—see, for example, Novy-Marx and Rauh (2009) for the United States. This is partly the result of the financial crisis and its depressing effect on the interest rates used to discount the future benefit payments. It is also the result of ongoing increases in life expectancy that were not anticipated when current participants started contributing.

7.4 Political Commitment A number of contributions have studied pension arrangements arising in a politicoeconomic equilibrium: Tabellini (2000) and Demange (2009) determine the equilibrium policy using the median-voter approach, while Gonzales-Eira and Niepelt (2008) and D’Amato and Galasso (2010) build on the probabilistic voting approach. In papers that consider a dynamic voting setting, a lack of commitment to an existing pension arrangement arises from the fact that every period a new vote takes place in which only the then-alive agents participate. As a result, the consequences of current choices for future generations are neglected. As Gonzales-Eira and Niepelt (2008) explain, the median-voter framework is less suited to study the political-economy effects of demographic change. In a standard Diamond–Samuelson model with only a few distinct generations, demographic change does not change the cohort to which the median voter belongs and extreme, but unrealistic, outcomes are easily produced. There is simply not enough heterogeneity in the age domain. Median-voter models with many different generations quickly become intractable. Authors like Tabellini (2000), who do use the median-voter framework to model social security, include another source of heterogeneity such as financial assets or human capital to explain why the majority age group still supports a system that redistributes income toward a minority of the population.

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In the probabilistic voting models of Gonzales-Eira and Niepelt (2008) and D’Amato and Galasso (2010) young and old voters not only select a candidate based on the political plans, but the voters also take other characteristics (like “ideology”) into account.k The valuation of these other characteristics is assumed to differ across generations and to be subject to random aggregate shocks, realized after candidates have chosen their platforms. Formally, the politicians maximize the following objective function   max Pðτt Þ ¼ ωuo ðcto Þ + ð1 + nt ÞEt uy ðcty Þ + βuo ðcto+ 1 Þ , (36) τt where ω is the density of the uniform ideology distribution function. This can be interpreted as a measure of how fiercely the elderly pursue their interest in the political arena. A high ω implies that the elderly get more weight in the political decision-making process and this will result into a higher transfer to them. Comparing the politicians’ objective function (36) with the social planner’s objective function (2) already shows that the time horizon of the politicians’ objective is much shorter. Both articles find that, without commitment, the political equilibrium results in optimal transfers if and only if the political weight of the old ω corresponds to a specific value f ð n , βÞ that is strictly smaller than one, where n denotes the average population growth. Given the involvement of the elderly in the political process, it is unlikely that the weight of the old generation in the political decision-making process is less than that of the young generation. Above this threshold, the relative weight of the retired in the political process lures the politicians into setting the transfer to the old at an inefficiently high value. This is the result of two factors. In Gonzales-Eira and Niepelt (2008), it results from the fact that the planner takes account of all future general equilibrium effects, while the politicians only look at the general equilibrium effect of lower savings in the next period. In D’Amato and Galasso (2010) the inefficiency results from the fact that the cost of a large transfer is partly compensated by a large transfer in the future, because the current young generation will be relatively poor as a result of the large transfer they have to make now. Gonzales-Eira and Niepelt (2008) use the market economy of Section 4 with demographic risk only, log utility, full depreciation, and a Cobb–Douglas production function. They find that the political benefit of taxes increases with the relative weight the political process attaches to the retired (ω), while the political cost of taxes and depressed capital accumulation increases with the weight attached to the future (β) and the relative number of individuals who care about the future, ie, the relative size of the young cohort as captured by nt. With exogenous labor supply, the PAYG transfer in the politicoeconomic equilibrium exceeds the socially optimal transfer if ω > 1  βαð1 + nÞ, where α measures the capital share of output. This inequality is more likely to hold if β is lower. The reason is that with higher β the planner attaches higher weight to future generations and, hence, k

See Persson and Tabellini (2002) for a discussion of probabilistic voting.

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lowers current transfers to the elderly. Even if both generations have the same weight in the political arena (ω ¼ 1), this inequality holds. Political competition resolves the conflict between old and young voters by shifting some of the cost of the social security system to future generations. As a consequence, intergenerational transfers are too large relative to a system balancing the interests of all generations. D’Amato and Galasso (2010) compare the PAYG transfer under a social planner and in the politicoeconomic equilibrium in an endowment economy with constant population growth and a stochastic return on savings (as in Section 3.2). To obtain analytical 1 results, they focus on the special case of uy() ¼ 0 and uo ðcÞ ¼ ðc  γÞ2 . Both the social 2 planner’s transfer function and the politician’s transfer function are decreasing in the wealth of the old generations. They show that for their specific setup, the two transfer functions only coincide if ω ¼ 1  (1 + n)/(β(σ 2 + R2)). Again, even if the old and young have the same weight in the politician’s objective function (ω ¼ 1), then the transfers from the young to the old via the PAYG system always exceed the transfer chosen by the social planner, while they are not responsive enough to shocks in the realized returns. The political weight of the old generations ensures that they are underexposed to financial shocks.l The young accept this because they realize that future politicians will compensate them when they are old themselves. Hence, this political mechanism typically produces suboptimal IRS relative to the social optimum. The mechanism behind this overinsurance of the old generation is that current policies affect future policy decisions by inducing changes in the state of the economy that shape the incentives of the future politicians and voters. Overspending stems from the strategic behavior of the politicians under dynamic voting. This overspending leads to a lower private wealth in old age in the following period, triggering more transfers by the future politicians. The policy response of the future politicians thus reduces the current (electoral) cost of transferring resources to the elderly and leads to too large current transfers—unless the young enjoy an unusually large political power. Current politicians exploit the expectations by current young voters, who anticipate that their current transfers will be compensated by offsetting transfers provided by future politicians. A PAYG system is more likely to be introduced during an economic crisis. Its size depends on the size of the new cohort and on the electoral strength of the old generation, as measured by the relative share of the swing (or undecided) voters among the elderly cohort that happens to face the crisis. In other words, after a financial crisis office-seeking politicians are urged to bail out” the elderly through the provision of generous public pensions. The politicians’ incentives to intervene in case of a negative shock effectively create a quasi asset—the PAYG social security—whose return is negatively correlated to l

As pointed out by Bohn, this underexposure is a typical feature of the US social security system. It is also a feature of purchasing-power guarantees in occupational pension schemes in the United Kingdom.

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the stock market return. Interestingly, this policy turns out to be quite persistent, since, as explained above, a reduction in net income of the current young lowers net private wealth in their old age, thereby inducing more government intervention in the future. Such persistence is not necessarily inefficient, as D’Amato and Galasso (2010) remark, because the essence of IRS is to spread current shocks over future generations (see also Gordon and Varian, 1988; Ball and Mankiw, 2007). By transferring the burden of a negative shocks to current workers, the politician triggers a reaction by all future politicians, who keep on transferring this shock into the infinite future.

7.5 Budgetary Pressures, Fiscal Constraints, and Reversibility Risk An important advantage of using public debt for IRS is that public debt generally suffers less from participation risk. In Section 7.3 we argued that merely the expectation that future generations will not participate in existing pension arrangements can lead to a collapse of the system. Public debt, by contrast, is serviced through taxes, the payment of which is always mandatory. The only (legal) way to escape taxes is to move abroad. This implies that a priori public debt is a more robust institution for realizing IRS. However, in practice there may be reasons why the public debt cannot be fully exploited for this purpose. First, there is the possibility of default risk on the public debt. In the presence of such risk, it may be possible to shift only part of a large negative shock to future generations, because financial markets would not be prepared to hold all the debt required to evenly smooth the shock over all cohorts. Second, fear that some member states cannot resist the (political) temptation to issue large amounts of debt, thereby threatening other members with the possibility of being forced to come to rescue, has led the European Union (EU) to impose nominal budgetary restrictions. This may limit the use of the public debt for the purpose of IRS. For this reason, the EU requires member states to aim at budgetary balance or even a surplus in the medium run, so that there is enough leeway to absorb economic downturns through the use of the automatic stabilizers and thus variations in the public debt. But, from an IRS perspective, the medium run defined in these EU treaties is too short. At the moment many countries are struggling to bring their structural balances to zero. Third, another obstacle in maximizing the degree of IRS is the uncertainty about the persistence of shocks. A higher degree of shock persistence requires a stronger response of taxes to a given shock and in the extreme case that the shock is fully persistent there is no role at all for debt in smoothing shocks across generations. This issue has acquired particular importance in recent years with the discussion about the question to what extent the Great Recession has led to a permanent loss of productivity.

7.6 Further Complications in Putting Theory to Practice As was made clear in the previous subsections, our simple modeling setup in Sections 4 and 5 abstracted from various aspects that limit the scope for IRS. However, as

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complicated as things are on paper, they are far more so in the real world. In particular, there are a number of practical complications in implementing the optimal arrangements found in Section 5. First, the equalization of the marginal utilities of consumption between cohorts would generally require substantial redistribution. This could easily be seen as “unfair” and, therefore, be politically infeasible in a democratic system. Even if the government decides to engage in large-scale redistribution, this is likely to fail, as individuals try to avoid taxes by hiding income or moving to another jurisdiction. Second, the parameters of our optimal arrangements are stochastic and would generally fluctuate over time. Productivity changes and depreciation shocks lead to changes in the capital stock and its return, thereby affecting the parameters of the optimal arrangement indirectly, while changes in the growth rate of the cohort of newborns affect the parameters of the arrangement directly. Such changes in the design parameters could be undesirable, because they would lead to a reopening of negotiations between groups that have different interests and, hence, prefer different parameter settings. Indeed, while we have modeled the pension designer as a single entity, in reality decisions may be taken by some board consisting of multiple individuals that represent different interests within the fund.m However, as Vos (2012) shows, if the parameters of the pension arrangement are constrained to remain constant over time, then the arrangement yields socially suboptimal outcomes. Third, quantities relevant for the choice of the design parameters, such as the capital stock, can only be measured with imprecision. Fourth, the arrangement imposes restrictions on the investment policy pursued by the pension fund. In particular, the amount that the fund invests in equity should be such that it allows for equity risk to be evenly spread among the individuals in the population. In practice, this would be difficult to achieve, because such decisions would be taken by the fund’s board which trades off the interests of the various fund participants. Fifth, the sharp assignment of redistribution and risk sharing between the PAYG and the funded pension pillars may in practice not be so easily be realized. For example, in spite of their heterogeneous population of participants, many DB funded arrangements use identical contribution and entitlement accrual rates, implying that those groups with a relatively high life expectancy are effectively sponsored by groups with a relatively low life expectancy.

8. QUANTIFICATION OF THE WELFARE GAINS FROM IRS It is important to obtain a quantitative assessment of the potential benefits from IRS. Such an assessment can help policy-makers in taking more informed decisions about the design of policy arrangements, in particular when trade-offs need to be made. For example, in comparing individual DC pension schemes with funded DB schemes, the additional IRS m

For example, in the Netherlands, the board of a pension fund consists of representatives from employer associations and trade unions.

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under the latter may need to be traded off against the distortions it causes in the labor supply and the limitations it imposes on individual choices, eg, in terms of the investment of the contributions. This section reviews estimates in the literature about the potential welfare gains from IRS. Here, we focus mostly on the gains from IRS associated with pension arrangements, as these gains have been mostly studied in this context.

8.1 Measuring the Welfare Gains from IRS A common measure of the welfare gain from some policy change is the change in “certainty-equivalent consumption.” Consider two policy regimes A and B (for example, a pension arrangement without IRS and one with IRS) and suppose that the equilibrium social welfare levels under the two regimes are given by VA and VB, respectively. Then, the certainty-equivalent consumption levels cA and cB are defined as the constant consumption levels in all periods and all states of the world, such that the utility levels associated with them are equal to, respectively, VA and VB. The gain from shifting from policy A to policy B is then given by the percent improvement in certainty-equivalent consumption: B  c (37)  1 100%: cA Obviously, there are other possible ways to express the welfare gain from a policy change, such as the percentage increase in the wage rate or in the initial wealth that would leave an individual indifferent between two policy options.

8.2 Complications in Measuring the Welfare Gains A realistic assessment of the magnitude of the benefits of IRS is complicated by the fact that our models may abstract from elements that are relevant in reality. First, two-period OLG models of the type we studied above may have a tendency to overestimate the welfare gains from IRS, because shocks necessarily last for as long as a generation lasts, while in reality responses to shocks are more immediate, thereby dampening misallocations and thus the need for risk-sharing arrangements. More realistic quantitative assessments of the welfare gains from risk sharing can thus be obtained by considering models with a larger number of OLGs. Second, it is important that all relevant sources of shocks be included in the model. The reason is that the benefit from sharing a specific type of risk will generally be mismeasured when other sources of risk are neglected. Moreover, correlations among shocks would need to be realistically modeled. After all, the potential gains from risk sharing between young cohorts, holding a relatively large fraction of human capital, and old cohorts, holding a relatively large fraction of equity, are larger when the correlation between wages and stock returns is lower.

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Third, how should preferences be modeled? Preferences have a great bearing on the need for risk sharing. In the extreme case in which individuals are risk neutral, there is no benefit at all to be gained from IRS. Assumptions about the degree of individual risk aversion are thus important. However, standard expected utility specifications with realistic assumptions about relative risk aversion are unable to explain the historical excess returns of stocks over bonds (the so-called “equity-premium puzzle,” first identified by Mehra and Prescott, 1985). Hence, most of the contributions quantifying the gains from IRS assume Epstein and Zin (1989) preferences, which are able to generate more realistic risk premia on equity by allowing for the intertemporal elasticity of substitution to differ from the degree of relative risk aversion. Finally, the benefits from IRS are often studied in connection with the introduction of a specific pension arrangement or a change in pension arrangements. This means that the benefits from IRS are restricted by the specific setup of the pension arrangement. Moreover, these benefits have to be traded off against other consequences that the introduction of or change in a pension arrangement brings about, such as the general equilibrium effects working through the capital stock or the labor supply.

8.3 Introducing or Changing a PAYG Social Security Scheme A number of contributions quantify the welfare consequences of introducing or changing a PAYG social security scheme. Examples are Krueger and Kubler (2006), SanchezMarcos and Sanchez-Martin (2006), and Olovsson (2010). These contributions all assume Epstein and Zin (1989) preferences and their calibrations are based on the United States. Krueger and Kubler (2006) investigate the welfare consequences of introducing PAYG social security in a stochastic economy with uncertainty in productivity and the price of the risk-free asset, while asset markets are incomplete. The potential benefit from social security arises from the opportunity it offers to trading human capital risk. For the benchmark partial equilibrium setting with a constant aggregate capital stock, a marginal social security scheme based on a 2% payroll tax produces a welfare gain for newborn agents equivalent to a 0.5–2.8% increase in consumption in each state of the world when relative risk aversion ranges from low to very high. The sources of these welfare changes are the “consumption insurance effect” arising from the lower consumption variability when old, because the return on social security is imperfectly correlated with the return on capital, and the effect on mean consumption when old. The latter may be negative or positive. On the one hand, the introduction of the payroll tax reduces the demand for risky capital implying lower asset income than without social security when old. On the other hand, the average return on social security exceeds that on the risk-free bond, so that, if individuals would borrow the full amount of the payroll tax they would end up with higher average consumption when old. Hence, the effect on mean consumption when old depends on how much

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individuals reduce their investment in risky investment and how much they increase their borrowing through risk-free debt. Ignoring general equilibrium effects, a switch from a DC to a DB social security system, assuming that the average tax rate under the latter is 2%, raises the welfare gains from social security by approximately 0.5 percentage points, the reason being that retirement consumption becomes less volatile. However, endogenizing the capital stock and asset returns, the same reform leads to overall welfare losses of 1.6–2.2% for newborns under the benchmark calibration. The effect is driven by the strong crowding out of the capital stock. Social security becomes a safe source of retirement income, which induces young individuals to offset the lower disposable income through additional borrowing and reduced investment in capital. Sanchez-Marcos and Sanchez-Martin (2006) quantify the benefits of PAYG pension systems in the presence of demographic shocks. These shocks cause fluctuations in factor prices that benefit relatively small cohorts. The higher wages enjoyed by these cohorts dominate the disadvantage of lower asset income, because they hold only limited capital during their working life. By charging higher contributions to small cohorts, a PAYGDB scheme counteracts the effects of these factor-price movements. The authors weigh this insurance effect of the scheme against its standard crowding-out effect on private savings, arising from the debt associated with the free gift to the first cohort of beneficiaries of the scheme and the additional reduction in precautionary savings due to the certain pension benefit. The crowding-out effect turns out to dominate. The benchmark simulation assumes a marginal PAYG scheme providing only a 2% replacement rate of the average wage. This results in an average long-run overall welfare loss equivalent to 1.2% of lifetime income. The insurance effect offsets less than 2% of the welfare loss itself. In the context of a three-period OLG model with productivity and capital depreciation risk, Olovsson (2010) explores the welfare effects of moving from the current US social security scheme to a PAYG scheme with efficient indexation to wages or capital returns. These optimized alternatives imply substantial welfare gains equivalent to an increase in per-period consumption on the order of 13.5–16.5%. A large part of these welfare gains stems from general equilibrium effects, ie, higher capital stocks than under the current US social security system. Those higher capital stocks protect individuals against the high volatility of the benefits associated with the optimized arrangements. However, when the transition from one steady state to the other is taken into account, the social welfare gains of the transition turn negative, due to a highly negative impact on the welfare of the middle aged. The welfare effects can be attributed to changes in current consumption, the return on the capital stock, and future consumption. Highly procyclical taxes under the new regime stabilize current consumption. However, the higher volatility in the benefit raises future consumption volatility, thereby leading to a precautionary buildup of capital. Overall, the positive effects of the higher stability of current consumption and higher average future consumption are dominated by the reduction in

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average current consumption and the lower future capital return. The welfare loss, including the transition effect, amounts to 6% of per-period consumption under optimal indexation to capital returns and to 12.5% under optimal indexation to wages.

8.4 DB Pension Funds Other works quantify the welfare consequences of the IRS provided by DB pension funds. Gollier (2008) does this in the context of a many-period OLG partial equilibrium model with uncertain equity returns. More concretely, in each period there are 40 overlapping working generations and a retired generation that consumes its pension wealth. All individual consumption is concentrated in the final period of one’s life. First-best risk sharing is achieved within a pension fund whose payout and investment policies are constant shares of the fund’s aggregate wealth, calculated as the sum of the fund’s financial assets plus the discounted sum of the future contributions to the fund. The author finds that the benefit of moving from individual DC to a fund with IRS amounts to an increase in the fund’s certainty-equivalent return from 3.23% to 3.76% per year. Importantly, the result of introducing IRS is not that it reduces the risk exposure of each generation, but rather that it raises the expected return to individual contributions, because for given overall risk more risky investment portfolios are possible. While children do not usually directly invest in equity markets, mandatory pension arrangements allow them to participate indirectly in the stock market. Through a collective pension scheme current participants share risks with future participants by transferring part of the pension buffer, which may be negative, to those future participants. This contrasts to the case of decentralized capital markets, which only allow OLGs to trade risks with each other. Teulings and De Vries (2006) and Bovenberg et al. (2007) explore the welfare gains from being able to make the optimal consumption–savings and portfolio allocation decisions before becoming economically active. Uncertainty is confined to the equity return, while wage income is nonstochastic. Both articles report that this leads to substantial gains. For the case in which there are no constraints, Bovenberg et al. (2007) report a welfare gain that ranges from 0.5% of certainty-equivalent consumption if the initial investment positions are anticipated by 1 year to 8.3% of certainty-equivalent consumption if the initial positions are anticipated by 20 years. Even when a constraint is introduced on the size of the deficit with which the economically active life can be entered, the welfare gains will be substantial. In the case where this deficit is restricted to half an annual salary, the welfare gains range from 0.3% to 3.3% of certainty-equivalent consumption when anticipating the initial investments by 1 year, respectively, 20 years. Bonenkamp and Westerhout (2014) also quantify the welfare gains from IRS by using, as in most of the literature, a nonexpected utility specification. Their model features two sources of uncertainty, namely uncertainty about wage income, also interpreted as productivity risk, and about equity returns. Importantly, in line with the findings by

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Benzoni et al. (2007) and Bohn (2009) the authors assume a substantial positive correlation between the two sources of uncertainty. Starting from an individual DC scheme, the introduction of a DB fund with a mismatch between assets and liabilities effectively allows the unborn to already invest in equity, thereby resulting in higher expected lifetime wealth. In other words, the risk-return trade-off improves for individuals, which, as in Gollier (2008), actually results in more risky, but also higher expected, consumption. For a funded DB scheme with proportional transfers, the authors find for their benchmark parameter combination, based on a degree of relative risk aversion of 5, an ex-ante welfare gain compared to individual DC of approximately 3% of wage income. The mismatch between assets and liabilities that makes it possible to share risks among generations distorts the labor supply. This distortion increases when the intratemporal substitutability between consumption and leisure increases. A higher substitution elasticity also causes the labor supply to become more pro-cyclical. This raises the correlation with the equity returns and thus induces the pension fund to invest a smaller share in equity. Varying the model parameters, the authors find that the ex-ante welfare gains from IRS through the proportional-transfers DB scheme range from a little more than 0.5% of wage income to about 7.5% of wage income. Somewhat counterintuitively, these gains are smaller when relative risk aversion is higher and the uncertainty about the shocks is higher. The reason is that these changes lead to lower equity investment by the fund and, thus, less scope for IRS.

9. POLICY IMPLICATIONS Major trends, in particular the ongoing aging of the populations around the world, require adequate responses from policy-makers to protect the benefits for IRS. After we have given an idea of the potential for IRS on the basis of existing arrangements, we take these major developments as a starting point to discuss their policy implications.

9.1 The Scope for IRS Many countries have substantial unfunded pension liabilities. Varying the current and future implicit pension debt is a way to absorb unforeseen developments. For a large number of EU countries, Kaier and M€ uller (2015) calculate the implicit pension debt for 2006, which ranges from 125% of GDP for Latvia to more than 360% of GDP for France. Overall, in the industrialized world, unfunded pensions are more important than funded pensions. However, many countries combine unfunded pensions with some degree of pension funding. The scope for IRS increases with the (average) amount of assets in this pillar. Some countries, like Denmark, the Netherlands, the United Kingdom, and the United States, have very substantial pension buffers, while for most countries the buffers are only limited, implying only a rather marginal potential scope for IRS.

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Table 1 Relative shares of DB, DC, and hybrid pension fund assets in selected OECD countries, 2010 DB hybrid/ DC protected (%) DC unprotected (%) DB traditional (%) mixed (%)

Australia Canada Chile Czech Republic Denmark Finland France Greece Hungary Israel Italy New Zealand Norway Poland Portugal Spain Switzerland United States

0 0 0 100 94 0 0 0 0 0 28 0 0 0 0 0 100 0

89 3 100 0 0 0 100 100 100 22 62 73 0 100 6 73 0 39

11 92 0 0 6 100 0 0 0 78 10 27 100 0 92 0 0 61

0 5 0 0 0 0 0 0 0 0 0 0 0 0 1 26 0 0

Source: From OECD, 2012. Pensions Outlook. OECD Publishing, Paris (table A16).

The potential for IRS also depends on the type of pension funded arrangements. Purely individual DC or pure DB funding, in which benefits are fixed in real terms, offer no scope for spreading shocks across generations. However, such extreme arrangements rarely exist in reality. For example, while legally most pensions in the Netherlands are of the DB type, in practice pension entitlements absorb all types of shocks hitting the funding ratio (the ratio of fund assets over liabilities). Table 1 reports the relative shares of assets in DC, DB, and hybrid pension arrangements for a selection of OECD countries in 2010. Clearly, DC funding is more common than DB funding. However, among those offering DC pensions, there are number offering some form of protection.

9.2 Aging and Pension Reform As discussed in Section 3.1 aging will generally affect the scope for IRS within given collective retirement arrangements. In addition, as explained in Section 7 it may undermine the continued existence of the arrangements themselves, thereby promoting a move toward individual arrangements. Policy-makers concerned with the financial sustainability of existing arrangements for old-age income provision have reacted to aging by increasing the retirement age and promoting pension funding.

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9.2.1 Raising the Retirement Age Absent a substantial reduction in the level of benefits or increase in contribution rates, the only way to maintain existing pension arrangements is to raise the retirement age. This is indeed what a number of countries are now doing. OECD (2011) contains an overview of the foreseen changes in the official retirement age up to 2050, with 11 OECD countries raising the retirement age of both men and women, while another two plan to raise that of women to that of men. For example, Australia, Denmark, and the United States will raise the retirement age to 67 years, while for the United Kingdom an increase to 68 years is foreseen. While increases in the retirement age are under way, the question is whether they go fast enough. The answer is most likely no. OECD (2011) predicts that by 2050 the average pensionable age for men and women is about 65 years, implying a rise between 2010 and 2050 by about 2.5 years for men and 4 years for women, while life expectancy at pensionable age is predicted to go up by approximately 3 years for men and 2.5 years for women. Hence, a large part of the burden of increased longevity will be shifted to the young. If we think of working lives of about 40 years and average retirement periods of about 15 years, then to sustain existing benefit levels without increases in contributions an increase in life expectancy by one year would require a shift in the retirement age by almost 8 months. In fact, a rise in the official retirement age in proportion to the increase in life expectancy may not even be sufficient. Also the average effective retirement age should at least rise in proportion to life expectancy. An actuarially fair benefit reduction in the case of premature retirement may stimulate employees to continue working until the official retirement age. Yet, the power of financial incentives is not unlimited, because an increasing fraction of workers may be forced by their physical condition to retire earlier if the retirement age is raised. Hence, much depends on the correlation between the change in life expectancy and the increase in productivity at higher ages. A more-thanproportional response of the official retirement age to life expectancy may actually be needed to maintain the financial sustainability of the pension arrangement. On top of this, the financial sustainability of DB funded schemes requires dealing with unanticipated increases in life expectancy that happen after a participant has started his work career and that are therefore not fully financed through additional contributions. Pension contributions are sometimes considered to be so high that it is no longer possible for them to respond to adverse shocks. With the retirement age responding fast enough to advances in life expectancy, contribution rates may be dampened and contribution policy may be revived as an instrument for IRS. 9.2.2 The Introduction of DC Funded Pillars The role of DC funded pensions has increased enormously since 1980 when Chile took the decision to set up such a system as the main pillar of its system of old-age income

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provision. Edwards (1998) describes the Chilean reform in detail. Formal sector workers are required to contribute to an individual account placed with a so-called Administradoras de Fondos de Pensiones (AFP), a company that manages a pension fund. These funds differ in terms of the riskiness of the assets they invest in. The AFPs compete among each other on the basis of the fees they charge and the services they offer. Individuals have the possibility to switch between AFPs and those that do not make an active choice for an AFP are assigned to the default AFP. For the elderly with no pension or a very low pension a means-tested first pillar was added. Past contributions made by workers who switched from the old system to the new pillar were recognized through the issuance of “recognition bonds” by the government that were placed in the individual AFP accounts. Since Chile, some 30 countries followed by also setting up funded mandatory pension pillars (see Holzmann, 2013). For example, in addition to Chile, Israel, Australia, Mexico, Denmark, the Slovak Republic, Poland, Sweden, Hungary, Estonia, and Norway are all characterized by a substantial role for mandatory DC private pensions. Moreover, other countries that already featured a large funded pillar have been shifting away from DB toward mandatory or voluntary DC funded pensions. Examples are the United Kingdom and the United States. Besides the latter two countries, voluntary DC private pensions play a substantial role in Ireland, Canada, Belgium, Germany, New Zealand, the Czech Republic, and Norway. Often, the buildup of voluntary DC accounts is stimulated through the tax system. In moving from DB to DC, the annuity as an important instrument for risk sharing is lost. Indeed, in its purest form, individual funded DC arrangements do not allow for any IRS, because each individual contributes to his own account and withdraws from the accumulated balance when he is old. However, real-world individual DC arrangements often have features that make IRS possible. First, benefits may be resource-tested. Pablo et al. (2012, p. 9) report that, for example, in Australia, each extra dollar of private pensions results in a 40 cent reduction in public pension. This way adverse shocks to the resources of the elderly are cushioned. In the case of Chile, the government guarantees a minimum pension to the participants of the funded pillar if accumulated funds fall below the minimum. Also, people who outlive their accumulated balance receive this minimum. Second, pensions-in-payment are subject to a personal income tax in most OECD countries. Taxes vary across countries and reach 30% for the average retirement benefit in Denmark and Sweden (Pablo et al., 2012). Hence, future generations share in the shocks hitting the accumulation of current private pensions. Finally, many schemes provide some form of guarantee. Depending on how the costs of the guarantee are paid for, younger cohorts of participants may effectively share in the riskiness of the retirement benefits. Return guarantees in DC funded pension schemes are quite widely applied in practice (Pablo et al., 2012). For example, plan providers have to offer a guarantee for the level of the return in Belgium, the Czech Republic, Germany, Japan, the Slovak Republic, and Switzerland, while relative (to some benchmark) return guarantees apply in Chile,

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Denmark, Hungary, Poland, and Slovenia. In the case of Chile, if the AFP fails to generate the minimum return, the shortfall has to be met from a specifically designated investment reserve, while once this reserve has been depleted, the state makes up for the gap and the AFP is liquidated. Return guarantees may offer a fixed or a variable minimum return and they may be applied throughout the accumulation phase or only on retirement date, while the relevant fee may be annually levied on the accumulated net balance or at the end of the accumulation period, or it may constitute a fraction of the contribution. Various studies (see, eg, Munnell et al., 2009; Grande and Visco, 2010; Pablo et al., 2012) compare the costs and benefits of different types of return guarantees. For example, a guarantee that can be invoked at any time makes it easier to transfer the account to another provider, thereby potentially reducing the cost of switching jobs when financial markets are depressed. The main advantage of a return guarantee is that it may take away fears associated with entering some DC pension savings scheme. However, a disadvantage of any return guarantee is that it may distort the fund managers’ investment strategies away from what is preferred by the participants. It has been argued by Munnell et al. (2009) and Grande and Visco (2010) that the government would be best placed to provide a guarantee, because it may have better access to financial markets in economic downturns and it can pool all claims to guarantees. Miles and Timmermann (1999) propose a government guarantee on the minimum annual return during retirement on the contribution of the workers to the fund. Effectively, workers receive a put option from the government on the return on their asset holdings in the fund. Obviously, this option needs to be paid for, so the government could fully tax the returns when they exceed a certain level, effectively implying that the fund participants write a call option. The combination of the two instruments imposes a band on the return on the assets held in the fund. While the lower bound on the return could induce excessive risk taking, a moral hazard problem, the upper bound on the return would in turn mitigate this problem. The proposal is interesting, though not without problems. First, the stochastic processes of the asset returns must be known to ensure a correct pricing of the options. Specifically, if the expected return is systematically overpredicted, the minimum return guarantee would be invoked too often and the system would become unbalanced over the long run. Second, the asset returns will be highly correlated across pension funds, implying that there may be periods during which the system will run a substantial overall deficit, while once the returns recover, there may be pressure to repeal the system from those who are to be taxed. 9.2.3 The Introduction of NDC Schemes A number of countries have introduced NDC schemes in the past two decades. Early moves into this direction where made by Sweden, Italy, Latvia, and Poland. Norway has also recently reformed its pension system into the direction of an NDC system, but maintained some of the DB elements like a means-tested guaranteed pension.

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The general structure of an NDC system is that the government sets a fixed rate for contributions that are credited to individual accounts. At retirement, the balance is transformed into a life annuity based on the individual’s or cohort’s remaining life expectancy. Finally, the internal rate of return should guide the system toward long-term financial stability. Holzmann et al. (2012) provide an elaborate analysis of experiences with NDC arrangements to date. They advocate NDC systems because of their fully transparent liabilities, their built-in approaches toward financial sustainability, and the flexibility they offer when to retire above a certain minimum retirement age. Moreover, due to the tight link between contributions and benefits, NDC arrangements are claimed to avoid distortions in the labor supply. As with all PAYG systems, this last advantage is lost when there is doubt about the long-term continuity of the system. One aspect to bear in mind is that in none of the countries mentioned here the NDC scheme is the only source of retirement income. The relative size of the NDC scheme is largest for Sweden. In Latvia, Poland, and Sweden the system is supplemented by a mandatory financial DC pillar. Italy features a voluntary financial DC scheme fed with contributions for severance pay. Upon termination of the contract, these resources can be put into an occupational DC pension fund. While theoretically the system would be financially balanced in the long run by setting a fixed contribution rate and indexing all entitlements to the growth of a wage base (see Section 5.1.2), in practice there are various reasons why the long-term financial stability of the system is not automatically guaranteed. The three crucial factors in this regard are the internal rate of return applied to the notional capital accumulated by workers, the coefficient to convert the notional capital into an annuity at retirement date, and the indexation of pension benefits. The internal rate of return is based on GDP growth for Italy, the growth of the contribution base for Latvia and Poland, and the growth of average percapita wage for Sweden. The appealing feature of the latter is that it keeps the average replacement rate constant. As regards the computation of the annuity, the important elements are the rate of return assumed for pensions-in-payment and the treatment of changes in life expectancy. For the latter a backward-looking approach is applied in all countries, except for Latvia, where the forward-looking approach takes explicitly into account that younger cohorts have a higher life expectancy. Finally, as regards to pensionsin-payment, these are indexed to prices for Italy, Latvia, and Sweden, where for Sweden there is an extra indexation component based on the difference between per-capita wage growth minus 1.6%. For Poland, indexation is also against prices, but there is an additional component based on wage growth. Importantly, by mostly indexing to price inflation, the scheme creates some extra financial slack, because real wage growth is on average positive. Because in practice financial sustainability is not automatically guaranteed, Holzmann et al. (2012) argue in favor of adopting an automatic balancing mechanism and setting up a reserve fund to head off liquidity problems associated with temporary shocks, such as an unexpected fall in the number of contributors or a temporary fall in wages due to a

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recession. To date, only Sweden has introduced an automatic balancing mechanism. It is based on a solvency ratio, ie, contribution assets over liabilities, with the former made up by projections of future contributions and the latter made up by the accounts of the participants. The contribution asset is revised on an annual basis, so that a new solvency ratio can be calculated. If it falls below one, a balancing index will be activated to bring it back to one. The mechanism works in a asymmetric way in that higher indexation is only given to make up for reductions in previous indexations, but not more than that. In principle, NDC systems allow for IRS of wage and demographic risks, because pensions-in-payment rise in line with the contribution base, given that workers contribute a fixed fraction of their wage to the payment of the current retired (see Section 5.1.2). This way, the elderly share in these risks. However, whether these risks are shared in optimal proportions is a priori unclear, because the amount of IRS depends on the size of the NDC scheme. Overall, it is difficult to assess the precise amount of IRS accomplished by real-world NDC schemes. However, one can make some general statements. First, real-world NDC schemes may forego potential gains from IRS if benefits are indexed only to price inflation, because this excludes the possibility of having the elderly share in productivity and demographic risks. Further, indexing only to wage growth means that demographic risks are likely to be imperfectly shared, because only the effect of demographic developments on the marginal product of labor is taken into account. Nevertheless, Sweden uses its downside balancing mechanism to absorb negative shocks to the labor force, implying that demographic shocks get spread over all cohorts. A more precise analysis requires detailed modeling and simulation of actual schemes. Such an exercise is undertaken by Auerbach and Lee (2011). To investigate how demographic and economic risks are shared among the various generations, they simulate several actual and hypothetical PAYG pension schemes, including variants of the US social security system, in which taxes, benefits, or a combination of both are adjusted to balance the system, the Swedish NDC system and variations on it, and the German system with annual tax adjustments to balance the system on an annual basis. The normal return on the notional balance in the simulated Swedish system is determined by the growth rate of the wage itself rather than that of the total wage bill, as prescribed in the stylized NDC description in Section 5.1.2. This implies that if the labor force growth rate drops below zero, the balancing mechanism has to be invoked and the return on the system is reduced below the normal level. Because the return is never raised above the normal level, this asymmetry permits the system to accumulate additional assets, which beyond a certain transition phase reduces the need to activate the balancing mechanism and thus keeps the rate of return on the system more stable. The stability of the return on the Swedish NDC system makes it rank favorably in expected utility terms if its participants are risk averse. The disadvantage of the asymmetry in the balancing mechanism is that the transitional generations during the building-up phase of the assets are relatively worse off.

Intergenerational Risk Sharing

9.2.4 Recent Changes in the Pension Reform Agenda Holzmann (2013) discusses recent changes in the pension reform agenda, changes that have partially been driven by the recent economic and financial crisis. One change has been a refocus on basic income protection for the elderly motivated by reductions in coverage that have taken place for various reasons, such as difficulties of youth entering the labor market and increasing mobility between formal and informal employment. This way poor and vulnerable individuals are better protected against shocks. Second, the insight has taken hold that funding does not by itself solve the aging problem. Like unfunded schemes, aging due to longevity requires an increase in the pension age, when contributions and benefits in a funded scheme are held constant. Several countries have maintained their unfunded pension arrangements by supporting them with public pension reserve funds in anticipation of further aging. In particular, for resource-rich countries like Australia and Norway this is a convenient way to spread the costs associated with aging over cohorts. Another case is that of Canada (see Bonenkamp et al., 2014), which in 1997 reformed its PAYG public pension scheme to start pre-funding the anticipated future increase in the pension outlays. This way pension contribution rates can be smoothed over time. The management of this task was assigned to the Canadian Pension Plan. It was through legislation made as independent as possible from the government. Finally, the global economic and financial crisis made the financing of the transition to funding more difficult as implicit debt is being turned into explicit debt. Further, policymakers have come to realize that asset returns can be low for protracted periods of time, although they have strongly recovered recently. Other challenges that lie ahead (see Holzmann, 2013) include increasing the portability of pension entitlements and the need to reform labor markets and provide employers with incentives in order to keep older workers employed.

9.3 Flexibility, Mobility, and the Width of the Solidarity Circle The shift to more flexible and temporary labor contracts in many countries, increasing (international) labor mobility, and faster sector dynamics all a priori reduce the scope for maintaining arrangements that promote IRS via collective pension arrangements. Hence, this may actually call for a greater role of public arrangements promoting IRS.n If policy-makers want to protect IRS through the pension system, then a possibility is to explicitly assign the fund’s financial buffer to the individual participants and to have individual entitlements respond in an ex-ante prespecified way to shocks. As a result, at each moment, the value of an individual participant’s stake in the fund’s assets is known and can be transferred to another fund upon acceptance of a new job. This way IRS can be n

For example, the US Bureau of Labor Statistics (2013, Charts 1 and 2) projects a wide range of changes in employment by major sectors for the period 2012–22. This suggests a substantial scope for labor movements across sectors in the coming decade.

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preserved, because the entitlements of all individuals continue to absorb the common shocks hitting the fund, while the aggregate value of the entitlements equals the value of pension assets on a continuous basis. In fact, it becomes even more transparent how IRS effectively works out. However, while the portability of the accumulated pension capital can be facilitated in this way, individuals may still have an incentive to move to another employer offering another pension scheme, if they fear a substantial change in their future pension benefits or in the contributions they have to make, for example, because of adverse demographic developments. Job mobility motivated by pension considerations is likely to be inefficient from a macroeconomic perspective. Hence, policy-makers may reconsider the width of the “solidarity circle” within which risks are shared. Should risks be shared within a company pension fund, an industry fund, or even a national fund? The wider is the solidarity circle, the larger is the scope for IRS, because shocks can be spread over a broader base and individual participants find it more difficult to escape their obligation to contribute to the scheme after a bad shock. However, broadening the solidarity circle also has disadvantages. First, in the most extreme case of a national funded pension scheme, close ties between the government and the single large pension fund increase the probability of confiscation of the fund’s assets, possibly via taxation. Second, the broader the solidarity circle, the wider the variation in life expectancies and incomes of the groups included and, hence, the larger the danger of systematic redistribution among different groups. Finally, a broader circle implies that the arrangement is less well targeted at the needs of individual participants. For example, some participant groups may prefer the fund to adopt a more risky investment strategy than other groups do. Another possibility would be to organize IRS along the lines of occupations. The advantages are that the group of participants is relatively homogeneous in terms of life expectancy as well as in terms of shocks to wages and that the requirement to contribute to the potential restoration of the pension buffers cannot so easily be escaped. Moreover, pension arrangements would be unlikely to interrupt the allocation of specialized workers to those employers where their marginal productivity is highest. In the case of certified occupancies fulfilled under self-employment the practical complications are very limited. However, in many instances it would be difficult to determine under what occupancy a person falls, while it would be costly for a firm to administer a number of different pension arrangements for its personnel simultaneously.

9.4 Dealing with the Consequences of Changes in Accounting Rules International bookkeeping rules now require large firms to account for the financial consequences of their pension obligations on their balance sheet.o In the case of a o

For example, since 2005 listed European companies with their own pension fund have been required to follow the International Financial Reporting Standards laid down in the International Accounting Standards (IAS). For pension obligations, in particular IAS-19 is relevant.

Intergenerational Risk Sharing

DB fund, the company is the residual claimant of the fund and the difference between the fund’s assets and liabilities needs to be reported. In aging sectors, the size of the pension obligations may become so large that they dominate the financial situation of the company. This occurred in the US car industry (see Sloan, 2005). Moreover, because pension assets are measured at market value, they are highly volatile and this volatility is transmitted to the company’s reported financial position. With imperfect financial markets, the company might be charged higher borrowing rates and face a reduced scope for making investments. It is, therefore, no surprise that there is a trend of companies putting existing collective pension arrangements at a legal distance, thereby eliminating the obligation to provide financial support if necessary, and of companies closing existing DB pension arrangements for new participants in favor of individual DC arrangements. It is difficult to quantify the consequences for IRS of this development. With a firm providing a financial backstop, its shareholders and creditors effectively share in the risks of the pension fund, although their role would be limited by the possibility of the firm going bankrupt.p Hence, the question is how much additional risk sharing the sponsor effectively provides on top of the risk sharing among the participants themselves. Even if there is no sponsor to provide a financial backstop, IRS is still possible, because the fund may be collectively organized with different cohorts participating in it.

9.5 The Role of Supervision In the context of our specific framework above with agents living for two periods, we saw that IRS requires a mismatch between the assets and the liabilities of our pension fund. In a multiple OLG setting such mismatch is not strictly needed for IRS. For example, consider a fund that starts with a funding ratio of 100% and is hit by some bad shock. Then, by marking down part of the accumulated pension entitlements by a uniform fraction, the funding ratio can be kept at 100%, while still all participating cohorts share in the bad shock. However, pension regulators tend to create incentives for funds to limit mismatch risk. In particular, they want to prevent the funding ratio from becoming so low that this would require drastic intervention in the form of higher contributions or less indexation of pension rights. In other words, they aim at preserving the confidence in the system by limiting the fluctuations in the funding ratio. Hence, as such, they make a trade-off between the likelihood that the fund continues to exist and the gains that may be obtained from IRS. Better exploitation of the pension buffers for IRS requires sufficient confidence and transparency in the policies to restore the pension buffers, for example, spelling out in advance how unexpected shocks will be handled. p

Actually, in the case of the United Kingdom, a separate guarantee fund would take over the fund’s obligations.

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As regards the above-mentioned trade-off between confidence and the scope for IRS, it is interesting to consider the case of the Netherlands, which features a large occupational funded DB pension pillar (accumulated assets substantially exceed GDP) of which the supervisory framework has undergone some major changes recently. In this system, workers accumulate entitlements to a future nominal pension based on the average wage during their career.q In a given year the accrual of new entitlements is equal to the nominal wage minus a franchise multiplied by the pension accrual rate. For example, if the annual wage exceeds the franchise by 50,000 euros and the accrual rate is 2% per year, then one additional year of work implies an increase in the annual pension as of retirement date of 1000 euros. Legally, the benefits are DB in the sense that the accumulated rights guarantee the holder a nominally fixed benefit in euros from retirement date until death. The crucial input for a fund’s decisions is the funding ratio, where assets are measured at their market value and liabilities as the sum of discounted projected future benefits based on accumulated entitlements, with discounting taking place against a risk-free market rate of interest. There are two main steering instruments that produce IRS in response to any shock to the funding ratio.r First, the contribution rate may be altered so that all working cohorts contribute to an adjustment of the fund’s buffers. Second, the indexation rate of the entitlements may be changed (and, as a last resort, even become negative), implying that all participating cohorts, working and retired alike, share in a shock, although the incidence differs because the stock of accumulated entitlements differs across participants. For example, unexpectedly high returns in the equity market raise the value of the fund’s assets, thereby likely producing a rise in the indexation of the entitlements. This way also the young share in the equity market risk. Further, to the extent that indexation is based on wage developments, the elderly also share in human capital risk. Rising life expectancies and the impact of the financial and economic crisis caused worries about the financial sustainability of the existing pension contract. As a result, the supervisory framework has changed as of 2015. This has had a number of consequences. First, indexation policy and the circumstances under which entitlements can be cut have to be laid down in advance. Moreover, a financial crisis plan has to be ex ante established. Although these adjustments do not a priori affect the scope for IRS, they effectively make the pension contract more complete. Second, a number of changes have been made to indexation policy. Indexation can now only be awarded when the funding q

r

During the first decade of this century there has been a massive shift away from benefits linked to the final wage before retirement to benefits linked to the career-average wage. This may be any type of shock, including demographic and financial market shocks. Note that, even in what is legally considered a DB scheme, participants are thus effectively exposed to any type of risk affecting the funding ratio. Note further that, while the individual component of longevity risk is shared, average longevity risk in the population of fund participants is not.

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ratio exceeds 110%. Moreover, the chosen indexation policy has to be sustainable also for the future. The more conservative indexation policy enhances IRS in response to a positive shock, as a larger share of the shock will be absorbed by the fund’s buffer. However, a negative shock leads more easily to foregone indexation, thereby putting a larger burden on the current participants, thus reducing IRS. Third, instead of a 15-year restoration period under the previous regime, restoration to the long-run target for the funding ratio of around 125–130% now has to take place within 10 years, while entitlements have to be cut immediately if it is clear in advance that this goal cannot be achieved. Unlike before, the restoration plan is rolling in the sense that the plan is adjusted to new shocks occurring in the meantime. The reduction in the restoration period from 15 to 10 years reduces the scope for IRS, while the rolling character enhances IRS. Fourth, the short-term restoration plan has been replaced by the requirement to take offsetting measures when the funding ratio falls short of some minimum required level (roughly 105%) uninterruptedly over a period of 5 years rather than only the two subsequent years of shortfall under the previous regime. This improves IRS. Finally, catching up indexation and compensation for entitlement cuts in the past can only be awarded once full regular indexation can be given. It is not a priori clear what all this implies for IRS. Overall, some elements of the change in the supervisory framework enhance IRS, while others reduce it.

9.6 Building Confidence, Transparency, and Fairness Optimal use of IRS imposes a number of requirements on a policy arrangement. First, participants in the arrangement should be confident that it will be continued if they have to make a net contribution. If such confidence is low, they will abandon the arrangement if possible or they will start to exert political pressure to dismantle it. In the case of a funded pension arrangement, individuals should be confident that their accumulated entitlements are safe from repudiation. Dangers of expropriation of pension assets in one way or the other are nothing new. During the 1980s, the Dutch government gradually reduced its contributions to its civil servant pension fund, while around the beginning of the 1990s it (unsuccessfully) tried to introduce a law that would skim off the “excessive” buffers of pension funds—see Hofs (2012). Recently, following the onset of the international financial and economic crisis, reforms aimed at more funding of pension systems have been partially or completely reversed in some countries. Substantial increases in budget deficits and public debt triggered a readjustment of the mandatory contributions intended for public and private pension schemes. Some governments have opted for a temporary (Estonia, Latvia, Lithuania) or permanent (Poland, Hungary) decrease in the mandatory contributions managed by private funds, or even for the expropriation of the assets of mandatory funded pension arrangements (Hungary, Argentina). Hungary imposed hefty penalties on all workers continuing to divert contributions to the private sector and expropriated the assets of

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the pension funds. Argentina transferred a large share of the pension funds’ assets into the state’s coffers. Further, some countries decided to postpone the planned transition toward more private funding of retirement income (Romania, Bulgaria). Hence, budgetary pressures have not only limited the direct use of public debt as an instrument for IRS, but they have also undermined the development of funded pension schemes as vehicles for IRS, both directly by shrinking the size of those schemes and likely indirectly by undermining the confidence that individuals have in such schemes. Most reversals of pension funding took place in the Central and Eastern European countries, young democracies where private property rights were ill-defined for a long period of time. While the Dutch case suggests that it seems safer to build up pension wealth in a private sector than in a public sector scheme, even in the former case the legal protection of the pension assets is far from guaranteed. Public support for funded risksharing arrangements requires that the property rights are sufficiently protected in the law. In fact, for EU countries, there may be a case for enshrining such protection in EU law. A second requirement for optimal use of IRS is that individuals should be confident that a risk-sharing arrangement operates in a fair way. In the current context, it is important that all cohorts share in both the bad and the good shocks. If more of the risk is assigned to the young, then it is important that they be compensated by assigning them a disproportionate part of potential good shocks. Within a pension arrangement, this can be done by having the indexation rate of the young respond more strongly to shocks, but also by assigning them higher (expected) indexation on average. This requires adequate governance of the arrangement with sufficient checks and balances. Alternatively, the rules for the assignment of shocks across cohorts need to be laid down ex ante and enshrined in the statutes or in the law. In other words, the arrangement is made (more) complete.

9.7 Reform of Health and Long-Term Care Financing The challenges affecting the financing of health care bear strong resemblance to those affecting pensions and, as in the case of pensions, experts have argued in favor of prefunding of medical expenditures. For example, Lasilla and Valkonen (2004) explore pre-funding rules that keep variations in future tax rates to a minimum. However, from time to time tax rates need to be reset on the basis of new information about the demography and medical cost developments. In fact, the financial uncertainties associated with the future health care spending may even be larger than those associated with future pension spending, because besides demographic risks, there are huge medical expense risks. Kotlikoff and Burns (2005) propose a PAYG system in which Medicare is replaced by a system in which each individual receives a capped voucher of which the size depends on his medical condition. The government can set the aggregate of the vouchers to grow

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with that of real wage growth. Health insurance contribution rates can then remain constant. If the government indeed manages to limit voucher growth to the real wage growth rate, then aggregate medical expenditures risk would mainly fall on the elderly as they make disproportionate use of the medical system. They would have to meet the additional costs out of their own pocket. However, it is doubtful that such a system remains politically sustainable when the available technology grows at a higher rate than the economy and large fractions of the population would be unable to afford it. Policy-makers will be interested in how risks associated with health insurance financing can be optimally shared. In a model with individual health risks and aggregate “medical expense risks,” Jack (1998) explores various health insurance financing mechanisms. IRS will be minimal with actuarially fair age-dependent contribution rates, while the scope for IRS is much larger under “community rating” when individuals all pay the same contribution. Bohn (2006) distinguishes between inelastic (“unavoidable”) lifesaving or life-lengthening treatments that are separable in utility from other consumption and “discretionary care” that makes individuals feel better and that is substitutable with nonmedical consumption. Efficient risk sharing in response to an unexpected improvement in the former type calls for sharing the cost among young and old generations and, hence, a reduction in current nonmedical consumption of both the young and the old. A decline in quality-adjusted prices of the second type (due to technological innovation) resulting in higher expenditures, because of more-than-unit elastic demand, would have to be absorbed by the elderly themselves. The positive income effect experienced by them would actually call for lower intergenerational transfers to them. Importantly, as Bohn (2006) argues, IRS is about sharing the risks of deviations from some baseline path. Hence, even if the central projection of unavoidable medical costs grows faster than the economy as a whole, IRS calls for sharing only the deviation of growth from this central projection among the different cohorts. To give an impression of the potential order of magnitude for IRS associated with health- and long-term care spending, we report in Table 2 figures for major EU countries and the EU as a whole of the level and the projected rise in these types of spending in percent(age points) of GDP. We do this for both the baseline and the AWG risk scenario, in which not only demography but also technological and institutional changes are taken account of in the case of health care and an upward convergence of countries below the EU average to the EU average in the case of long-term care. The data are from European Commission (2012). On average EU health care spending is projected to increase by 1.1%-points of GDP on the basis of demography alone and one-and-a-half times as much when the other factors are accounted for. If we think of IRS as only applying to deviations from the baseline, then the deviation between the risk and base scenarios provides an indication of the scope for IRS, although one needs to be careful here as part of the cost resulting from technological change is probably anticipated. Table 3 reports similar figures from the OECD (2013, table 8) under the “cost containment” scenario, under

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Table 2 Health care and long-term care spending as percent(age points) of GDP in selected EU countries Pensions Health care Long-term care

DE FR IT SP UK EU27 EA

Level

Change

Level Base change Change risk Level Base change Change risk

2010

2010–60 2010

2010–60

2010–60

2010

2010–60

2010–60

10.8 14.6 15.3 10.1 7.7 11.3 12.2

2.6 0.5 0.9 3.6 1.5 1.5 2.0

1.4 1.4 0.6 1.3 1.1 1.1 1.1

2.0 2.1 1.0 1.9 1.8 1.7 1.7

1.4 2.2 1.9 0.8 2.0 1.8 1.8

1.7 2.1 0.9 0.7 0.7 1.5 1.7

1.8 2.2 0.9 0.8 0.7 1.7 1.9

8.0 8.0 6.6 6.5 7.2 7.1 7.3

Source: From European Commission, 2012. The 2012 ageing report. European Economy, No. 2 (tables 2.5, 3.12, 4.8).

Table 3 Health care and long-term care spending as percent(age points) of GDP in OECD countries Health care Long-term care 2006–10

2060

2060

2006–10

2060

2060

Average

Containment

Pressure

Average

Containment

Pressure

7.9 4.4 7.4

11.8 8.3 11.3

0.8 0.1 0.7

1.6 0.9 1.5

2.1 1.4 2.0

OECD average 5.5 Non-OECD average 2.4 Total average 5.0

Source: From OECD, 2013. Public spending on health and long-term care: a new set of projections. Economic Policy Papers 6. OECD (table 8).

which policy-makers react to suppress spending increases, and the scenario of “cost pressure.” For health care the differences between the two scenarios are on the order of 4%-points of GDP and for long-term care they are on the order of 0.5%-point of GDP. This points to quite a substantial amount of risk to be potentially shared, all the more so because any unexpected cost changes as a result of medical advancements are likely to be highly persistent.

9.8 The Importance of Combining Risk-Sharing Arrangements The World Bank (1994) identifies three roles for retirement income systems: redistribution, savings, and insurance. Accordingly, it argues in favor of a three-pillar system of old-age security, consisting of a publicly managed first pillar with mandatory participation and aimed at limited redistribution, a privately managed funded second pillar with mandatory participation and a third pillar consisting of voluntary savings. The second and third pillars aim at promoting savings, while all three pillars aid in spreading risks across different cohorts. While a PAYG first pillar is relatively vulnerable to

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demographic shocks, funded arrangements are relatively vulnerable to financial markets shocks. Since these types of shocks are imperfectly correlated, from the perspective of limiting the overall risk exposure of individuals, it may indeed be beneficial to combine PAYG and funded pillars into a complete arrangement. Yet, the analysis in Section 5 showed that it was possible, at least in the context of the simple framework studied there, to set up a combination of a first PAYG pillar and a DWB funded second pillar, such that the tasks of redistribution and providing for optimal IRS are completely separated between the respective pillars. Ideally, in assessing IRS one should also consider the full pension arrangement in combination with public debt management and tax policy, and the health care system. In particular, when the scope for IRS through pension arrangements shrinks, the role of other instruments for IRS may need to increase. The most obvious alternative channels are public debt management and tax policy. However, as discussed above, the scope for deploying public debt for IRS is restricted by private-sector fears of debt default. In principle, mutual debt repayment guarantees can reduce the danger that a country defaults on its debt, thereby increasing the potential for IRS. Various types of guarantees have been discussed in the context of the EU (Claessens et al., 2012; Beetsma and Mavromatis, 2014). However, resistance to such guarantees is strong (Issing, 2009), because the traditionally more fiscally disciplined countries fear that guarantees may stimulate moral hazard. Hence, they may only be politically acceptable under more intensified monitoring by the European Commission and the EU Ministers of Finance of the budgetary policies of individual member states or, even more far-reaching, by delegating the decisions about debt issuance at the national level to the union level. Also tax policy may assist in promoting IRS. For example, Smetters (2006) explores how an appropriately chosen capital tax can substitute for a US government social security trust fund investment in equities, thereby potentially improving financial risk sharing across generations that do not directly trade with each other. The capital tax creates an implicit investment of the government in equity. To generate equivalence, risk and expected return for the government must be the same as under a trust fund investment in equity, while also households must be enticed to hold the same portfolio of assets in both cases. The precise tax treatment of pensions is important for IRS (see Chen et al., 2016). The two main formats are the exempt-exempt-tax (EET) system, in which contributions can be subtracted from income before taxes, pension wealth accumulation is untaxed and the pension benefits are taxed, vs the TEE system in which contributions are paid from after-tax income, while pension wealth accumulation and pensions-inpayment are untaxed. The EET regime allows the financial market risks incurred by the retired during the accumulation phase of their pension capital to be shared with the wider population, including the younger individuals. The scope for IRS under TEE is less obvious, although also in this case an appropriate design of the taxation regime can allow for IRS. To see this, suppose that current financial market returns are unusually

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high, implying relatively high expected future pensions. With individuals as life-cycle maximizers, this would allow for an increase in labor income taxes, the revenues of which can be used to lower labor income taxes for future cohorts when financial market returns are less favorable.

10. LITERATURE GAPS AND DIRECTIONS FOR FURTHER RESEARCH While quit a substantial amount of research has been devoted to IRS during the past two decades, especially in the context of pension arrangements, the literature still features a number of gaps, in particular when it comes to making concrete policy recommendations. In this section we aim at identifying some of these gaps. Most studies focus on IRS in the context of a specific institutional pillar. This approach is useful to obtain insight into the way this institutional pillar promotes IRS. However, in reality, it is the combination of all relevant arrangements affecting an individual that determine how much IRS there is. A variety of articles, some of which have been discussed above (eg, Bovenberg and van Ewijk, 2013), have explored IRS in the context of multipillar pension schemes. However, the integration of debt and tax policy into the models studying combinations of pension pillars has been rare so far. This would allow a policy-maker to, for example, make a well-informed assessment of the valueadded of a funded DB instead of a DC pension pillar. If debt and tax policy take over the role of a DB pillar in terms of IRS, then on net a DC pension pillar may be relatively more attractive than a DB pillar, because a DC scheme allows for smaller violations of actuarial fairness, hence smaller labor market distortions. The more general conclusion is that to assess how much IRS there actually is and how individuals can maximally benefit from IRS, it is important to construct realistic models that capture all relevant channels through which the financial position of individuals is affected and see how IRS is influenced by varying one or more arrangements away from the baseline setting and simulating the model outcomes under these alternative settings. A second area for fruitful further research, closely related to the previous one, concerns the consequences of alternative tax treatments of pension contributions and benefits, and in particular the timing of taxation. The previous section discussed the EET vs the TEE regime. However, a more systematic and complete investigation of the role of the complete design of the tax code would be welcome. Third, further research into the design of pension arrangements that allow for the separate assignment of redistribution and risk sharing to the individual pension pillars is desirable. This is important, as the political rulers may assign an explicit redistribution objective to a first PAYG pension pillar, but expressly not so for the other pillars. The analysis in Section 5 indicated how such separation can be achieved in a simple setting that combines a PAYG pension pillar with a DB funded pension pillar. However, in practice, funded DB plans often cause unintended redistribution among groups of

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participants, because contribution and accrual rates tend to be uniform across participants. This implies that individuals with a longer life expectancy, ie, female and/or highereducated individuals, benefit financially from the other groups with a lower life expectancy. As these systematic redistributions become more transparent, the political sustainability of such plans may get undermined. So far, there has been little formal analysis of settings that combine DB pension arrangements with systematic heterogeneity among participant groups. Fourth, there is still relatively little known of IRS in the presence of voluntary and involuntary exits from a funded pension arrangement. Consider, for example, a DB pension fund in which participants are subject to some exogenous risk of having to leave the fund. This reduces the ex-ante benefit from participation, because it raises the uncertainty about the amount of pension wealth at the moment of retirement. The reason is that in a DB funded arrangement with uniform contribution and accrual rates, during the first part of their career, individuals contribute more than their actuarially fair share, while their contribution is less than actuarially fair during the second part of their career.s Hence, those who quit mid-career have been accumulating too few entitlements in relation to their contributions and this benefits the individuals who do not quit. From an ex-ante perspective the spread in pension assets increases, as it is not known beforehand whether one will quit or not. Also, the option to switch jobs voluntarily naturally limits the scope for IRS, as explained above. Overall, there is a need for more research into the welfare consequences of forced or unforced movements between pension arrangements and how the gains from IRS can be preserved in spite of these movements. Finally, and related to the previous paragraph, the (increasing) role of labor mobility for the design of institutions facilitating IRS has so far been underinvestigated. Enhanced labor mobility implies that it becomes more difficult to impose additional contributions on participants when an IRS-promoting institution is hit by a bad shock. This may have consequences for the organization of solidarity circles, in particular for which groups to include in the circle and at what level in the economy they should be organized. More analysis of the relevant trade-offs in this regard is desirable.

11. CONCLUDING REMARKS This chapter has tried to provide an up-to-date review of the literature on IRS. IRS may take place through various channels; the most obvious are pension arrangements and public debt management. However, also the health care system, the educational system, as well as informal channels may provide for IRS. We have explored IRS under a social s

For younger participants the contribution can earn a return over the risk-free rate over a longer period than for older participants.

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planner for various progressively more complicated settings and we have shown how a proper design of pension arrangements can replicate the planner allocation. While it is not hard to see intuitively that IRS can be beneficial from an ex-ante perspective, an important question concerns the quantification of its benefits. As the literature reviewed here suggests, these benefits are potentially quite large, though so far it has not been possible to come up with precise numbers. The benefits depend on the setting under consideration and, to reap those benefits, they may actually require a costly transition from existing systems. Future work that aims at quantifying the gains from IRS should take account of the various factors that limit the scope for IRS. These include positive long-run correlations between wage and equity risk, the potential labor market distortions associated with arrangements that promote IRS, discontinuity risks that tighten constraints on the participation in IRS-promoting institutions, political risks, and budgetary pressures that impede public debt management. In addition, such an analysis should take account of the fact that it is the combination of various arrangements that determine the overall amount of IRS. The scope for reaping the benefits from IRS depends a lot on the confidence of individuals in the institutions promoting IRS. For example, participants in a DB funded pension arrangement, especially the young ones, should be sufficiently confident that the arrangement is financially sustainable in the long run, hence that planned increases in the official retirement age do actually take place, and that the shocks that hit the arrangement are allocated in a balanced and transparent way over the participating cohorts. Policies should also aim at other channels to promote IRS. In particular, the availability of a sufficiently rich menu of public debt instruments can go a long way spreading shocks across cohorts. However, this requires governments to be sufficiently forward-looking in the sense that in good times they create enough budgetary margin to be able to relieve the consequences of future economic downturns. Tight monitoring of public debt policies at the international level could be helpful in this regard. This chapter has on purpose abstracted from intragenerational risk sharing and intragenerational heterogeneity. Intragenerational risk sharing comes almost automatically through institutions that allow for IRS, such as most health insurance schemes. A priori we would expect the additional reduction in individual risks to enhance the support for such arrangements. By contrast, we expect intragenerational heterogeneity to make it harder to find support for such arrangements, because IRS comes almost automatically with systematic redistribution. This is, for example, the case for a DB pension fund in which life expectancies differ systematically across participant groups, while contribution and accrual rates are uniform. Another example concerns a health insurance scheme that covers groups with systematically different health risks. We have closed this review article by trying to identify some important gaps in the literature on IRS. Important directions for further research are the study of (i) IRS under combinations of relevant arrangements, which include not only the various pension

Intergenerational Risk Sharing

pillars but also public debt, health care, and housing arrangements; (ii) the role of the tax treatment of benefits and contributions for IRS; (iii) arrangements that can explicitly separate risk sharing from redistribution, which is complicated by systematic differences among participants of such arrangements; and (iv) how forced and unforced switches between retirement arrangements as well as increased labor mobility affect the design of IRS-promoting institutions.

ACKNOWLEDGMENTS We thank two anonymous referees, the editors John Piggott and Alan Woodland, Ed Westerhout, and the participants of the Harvard-CEPAR Workshop on Population Ageing for many helpful comments. The usual disclaimer applies.

REFERENCES Albert, S.M., Duffy, J., 2012. Differences in risk aversion between younger and older adults. Neurosci. Neuroecon. 1, 3–9. Altonji, J.G., Hayashi, F., Kotlikoff, L.J., 1992. Is the extended family altruistically linked? Direct tests using micro data. Am. Econ. Rev. 82 (5), 1177–1198. Altonji, J.G., Hayashi, F., Kotlikoff, L.J., 1996. Risk sharing between and within families. Econometrica 64 (2), 261–294. Asdrubali, P., Sorensen, B.E., Yosha, O., 1996. Channels of interstate risk sharing: United States 1963–1990. Q. J. Econ. 111 (4), 1081–1110. Auerbach, A.J., Lee, R., 2011. Welfare and generational equity in sustainable unfunded pension systems. J. Public Econ. 95 (1), 16–27. Auerbach, A.J., Gokhale, J., Kotlikoff, L.J., 1994. Generational accounting: a meaningful way to evaluate fiscal policy. J. Econ. Perspect. 8, 73–94. Ball, L., Mankiw, N.G., 2007. Intergenerational risk sharing in the spirit of Arrow, Debreu, and Rawls, with applications to social security design. J. Polit. Econ. 115 (4), 523–547. Beetsma, R.M.W.J., Bovenberg, A.L., 2009. Pensions and intergenerational risk-sharing in general equilibrium. Economica 76 (302), 364–386. Beetsma, R.M.W.J., Mavromatis, K., 2014. An analysis of eurobonds. J. Int. Money Financ. 45, 91–111 Beetsma, R.M.W.J., Romp, W.E., 2013. Participation constraints in pension systems. Discussion Papers DP9656. CEPR. Beetsma, R.M.W.J., Bovenberg, A.L., Romp, W.E., 2011. Funded pensions and intergenerational and international risk sharing in general equilibrium. J. Int. Money Financ. 30 (7), 1516–1534. Beetsma, R.M.W.J., Romp, W.E., Vos, S.J., 2013. Intergenerational risk sharing, pensions, and endogenous labour supply in general equilibrium. Scand. J. Econ. 115 (1), 141–154. Benzoni, L., Collin-Dufresne, P., Goldstein, R.S., 2007. Portfolio choice over the life-cycle when the stock and labor markets are cointegrated. J. Financ. 62 (5), 2123–2167. ISSN 1540-6261. http://dx.doi.org/ 10.1111/j.1540-6261.2007.01271.x. Bodie, Z., Merton, R.C., Samuelson, W.F., 1992. Labor supply flexibility and portfolio choice in a life cycle model. J. Econ. Dyn. Control 16 (3-4), 427–449. ISSN 0165-1889. http://dx.doi.org/10.1016/01651889(92)90044-F. Bohn, H., 2001. Social security and demographic uncertainty: the risk-sharing properties of alternative policies. In: Campbell, J.Y., Feldstein, M. (Eds.), Risk Aspects of Investment-Based Social Security Reform. University of Chicago Press, Chicago, IL, pp. 203–246. Bohn, H., 2006. Who bears what risk? An intergenerational perspective. In: Blitzstein, D., Mitchell, O.S., Utkus, S.P. (Eds.), Restructuring Retirement Risks. Oxford University Press, Oxford, UK, pp. 10–36.

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Bohn, H., 2009. Intergenerational risk sharing and fiscal policy. J. Monet. Econ. 56 (6), 805–816. Bohn, H., 2013. Private versus public risk sharing: should governments provide reinsurance? In: Bovenberg, A.L., van Ewijk, C., Westerhout, E. (Eds.), The Future of Multi-Pillar Pensions. Cambridge University Press, Cambridge, UK, pp. 187–223. Bonenkamp, J., Westerhout, E., 2014. Intergenerational risk sharing and endogenous labour supply within funded pension schemes. Economica 81, 566–592. Bonenkamp, J., Meijdam, L., Ponds, E., Westerhout, E., 2014. Reinventing intergenerational risk sharing. Netspar Panel Paper 40. Netspar, Tilburg. Bovenberg, A.L., Mehlkopf, R., 2014. Optimal design and regulation of funded pension schemes. Mimeo, Tilburg University. Bovenberg, A.L., van Ewijk, C., 2013. The future of multi-pillar pension systems. In: Bovenberg, A.L., van Ewijk, C., Westerhout, E. (Eds.), The Future of Multi-Pillar Pensions. Cambridge University Press, Cambridge, UK, pp. 373–418. Bovenberg, A.L., Koijen, R., Nijman, T., Teulings, C., 2007. Saving and investing over the life cycle and the role of collective pension funds. De Economist 155 (4), 347–415. ISSN 0013-063X. Bureau of Labor Statistics, 2013. News release: employment projections—2012–2022. http://www.bls. gov/news.release/pdf/ecopro.pdf. Chen, D.H.J., Beetsma, R., Ponds, E., Romp, W.E., 2016. Intergenerational risk-sharing through funded pensions and public debt. J. Pension Econ. Finance 15 (2), 127–159. Cichon, M., 1999. Notional defined-contribution schemes: old wine in new bottles? Int. Soc. Secur. Rev. 52 (4), 87–105. ISSN 1468-246X. http://dx.doi.org/10.1111/1468-246X.00055. Claessens, S., Mody, A., Vallee, S., 2012. Paths to eurobonds. IMF Working Paper WP/12/172. International Monetary Fund. Constantinides, G.M., Donaldson, J.B., Mehra, R., 2002. Junior can’t borrow: a new perspective on the equity premium puzzle. Q. J. Econ. 117 (1), 269–296. Cutler, D.M., 1996. Why don’t markets insure long-term risk? Mimeo. D’Amato, M., Galasso, V., 2010. Political intergenerational risk sharing. J. Public Econ. 94, 628–637. Demange, G., 2009. On sustainable pay-as-you-go contribution rules. J. Public Econ. Theory 11 (4), 493–527. Edwards, S., 1998. The chilean pension reform: a pioneering program. In: Feldstein, M. (Ed.), Privatizing Social Security. University of Chicago Press, Chicago, IL, pp. 33–62. Enders, W., Lapan, H.E., 1982. Social security taxation and intergenerational risk sharing. Int. Econ. Rev. 23 (3), 647–658. Epstein, L.G., Zin, S.E., 1989. Substitution, risk aversion, and the temporal behavior of consumption and asset returns: a theoretical framework. Econometrica 57 (4), 937–969. European Commission, 2012. The 2012 ageing report. European Economy, No. 2. Farhi, E., Panageas, S., 2007. Saving and investing for early retirement: a theoretical analysis. J. Financ. Econ. 83 (1), 87–121. Feldstein, M., 2005. Structural reform of social security. J. Econ. Perspect. 19 (2), 33–55. Gollier, C., 2008. Intergenerational risk-sharing and risk-taking of a pension fund. J. Public Econ. 92 (5–6), 1463–1485. Gonzales-Eira, M., Niepelt, D., 2008. The future of social security. J. Monet. Econ. 55, 197–218. Gordon, R.H., Varian, H.R., 1988. Intergenerational risk sharing. J. Public Econ. 37 (2), 185–202. Grande, G., Visco, I., 2010. A public guarantee of a minimum return to defined contribution pension scheme members. Temi di discussione (Economic working papers) 762. Bank of Italy, Economic Research and International Relations Area. Hassler, J., Lindbeck, A., 2005. An overview of notional defined pensions plans. Working Paper CISS/WP/ 05112. Inter-American Conference on Social Security. Hofs, Y., 2012. ABP kreunt onder last van verleden. Volkskrant 19 January. Holzmann, R., 2013. Global pension systems and their reform: worldwide drivers, trends and challenges. Int. Soc. Secur. Rev. 66 (2), 1–29. Holzmann, R., Palmer, E., Robalino, D., 2012. Nonfinancial Defined Contribution Pension Schemes in a Changing Pension World: Volume 1. Progress, Lessons, and Implementation. World Bank, Washington, DC.

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Issing, O., 2009. Why a common eurozone bond isn’t such a good idea. White Paper III, Center for Financial Studies, University of Frankfurt. Jack, W., 1998. Intergenerational risk sharing and health insurance financing. Econ. Rec. 74 (255), 153–161. Kaier, K., M€ uller, C., 2015. New figures on unfunded public pension entitlements across Europe: concept, results and applications. Empirica 42 (4), 865–895. Kotlikoff, L.J., Burns, S., 2005. The Coming Generational Storm. MIT Press, Cambridge, MA. Kotlikoff, L.J., Spivak, A., 1981. The family as an incomplete annuities market. J. Polit. Econ. 89 (2), 372–391. Krueger, D., Kubler, F., 2006. Pareto-improving social security reform when financial markets are incomplete!? Am. Econ. Rev. 96 (3), 737–755. Lasilla, J., Valkonen, T., 2004. Pre-funding expenditure on health and long-term care under demographic uncertainty. Geneva Pap. Risk Insur. 29 (4), 620–639. Lindbeck, A., Persson, M., 2003. The gains from pension reform. J. Econ. Lit. 41 (1), 74–112. Matsen, E., Thøgersen, Ø., 2004. Designing social security—a portfolio choice approach. Eur. Econ. Rev. 48 (4), 883–904. Mehra, R., Prescott, E.C., 1985. The equity premium: a puzzle. J. Monet. Econ. 15 (2), 145–161. Miles, D., Timmermann, A., 1999. Risk sharing and transition costs in the reform of pension systems in Europe. Econ. Policy 14 (29), 251–286. Motivaction, 2011. Grote meerderheid jongeren verwacht dat pensioenen en zorgkosten onbetaalbaar worden. Munnell, A.H., Golub-Sass, A., Kopcke, R.W., Webb, A., 2009. What does it cost to guarantee returns? Issues in Brief No. ib2009-9-4. Center for Retirement Research. Nanos, 2012. Jobs top priority, pensions and taxes trending up. http://www.nanosresearch.com/library/ polls/POLNAT-W12-T525E.pdf. Novy-Marx, R., Rauh, J.D., 2009. The liabilities and risks of state-sponsored pension plans. J. Econ. Perspect. 23 (4), 191–210. OECD, 2011. Pensions at a Glance 2011: OECD and G20 Indicators. OECD Publishing, Paris. OECD, 2013. Public spending on health and long-term care: a new set of projections. Economic Policy Papers 6. OECD. Oeppen, J., Vaupel, J.W., 2002. Broken limits to life expectancy. Science 296 (5570), 1029–1031. http://dx. doi.org/10.1126/science.1069675. Olovsson, C., 2010. Quantifying the risk-sharing welfare gains of social security. J. Monet. Econ. 57 (3), 364–375. Pablo, A., Stphanie, P., Whitehouse, E.R., Yermo, J., 2012. The role of guarantees in defined contribution pensions. OECD Working Papers on Finance, Insurance and Private Pensions 11. OECD, Paris. Persson, T., Tabellini, G., 2002. Political Economics: Explaining Economic Policy (0262661314). The MIT Press, Cambridge, MA. Romp, W.E., 2013. Procyclicality of pension fund regulation and behaviour. Discussion Paper DP 11/2013068. Netspar. Sanchez-Marcos, V., Sanchez-Martin, A.R., 2006. Can social security be welfare improving when there is demographic uncertainty? J. Econ. Dyn. Control 30 (9–10), 1615–1646. Shiller, R.J., 1999. Social security and institutions for intergenerational, intragenerational, and international risk-sharing. Carnegie-Rochester Confer. Ser. Public Policy 50 (1), 165–204. Sloan, A., 2005. No free lunch. Bus. Week. Column, 20 April. Smetters, K., 2006. Risk sharing across generations without publicly owned equities. J. Monet. Econ. 53 (7), 1493–1508. Sorensen, B.E., Yosha, O., 1998. International risk sharing and European monetary unification. J. Int. Econ. 45 (2), 211–238. Tabellini, G., 2000. A positive theory of social security. Scand. J. Econ. 102 (3), 523–545. Teulings, C.N., De Vries, C.G., 2006. Generational accounting, solidarity and pension losses. De Economist 154 (1), 63–83. ISSN 0013-063X. http://dx.doi.org/10.1007/s10645-006-6486-y. Thøgersen, Ø., 1998. A note on intergenerational risk sharing and the design of pay-as-you-go pension programs. J. Popul. Econ. 11 (3), 373–378.

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United Nations, Department of Economic and Social Affairs, Population Division, 2013. World population prospects: The 2012 revision volume I, comprehensive tables. ST/ESA/SER.A/345. Van Bommel, J., 2007. Intergenerational Risk Sharing and Bank Raids, Universite du Luxembourg— School of Finance, Luxemburg. Vos, S.J., 2012. Essays in pension economics and intergenerational risk sharing. University of Amsterdam PhD thesis Wagener, A., 2004. On intergenerational risk sharing within social security schemes. Eur. J. Polit. Econ. 20 (1), 181–206. World Bank, 1994. Averting the Old Age Crisis: Policies to Protect the Old and Promote Growth. Oxford University Press, New York.

CHAPTER 7

The Political Economy of Population Aging
G. Casamatta, L. Batte Toulouse School of Economics (GREMAQ-CNRS and Centre for Economic Policy Research (CEPR)), Toulouse, France

Contents 1. Introduction 1.1 The Political Challenges of Population Aging

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1.1.1 Facts on Aging, and Political Consequences 1.1.2 Policies at Stake with Aging

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1.2 Features of Social Security Systems and Recent Reforms

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2. Why Individuals Support PAYG Social Security 2.1 Dynamic Inefficiency 2.2 Reduced Time Horizon 2.2.1 Central Argument 2.2.2 Population Aging in the Browning Model

2.3 Effect of Social Security on Prices 2.4 Within Cohort Redistribution 2.4.1 2.4.2 2.4.3 2.4.4 2.4.5 2.4.6

Individually Optimal Tax Rates Variation of the Optimal Tax Rates with the Wage Level Majority Voting Tax Rate Effect of a Drop in the Fertility Rate Myopic Individuals Other Dimension of Individual Heterogeneity: Differing Life Expectancies

2.5 Risk-Sharing 3. Endogenous Retirement 3.1 Implicit Taxation and Early Retirement 3.1.1 The Political Support for Early Retirement Provisions 3.1.2 The Implicit Taxation on Continued Activity

3.2 Voting on the Retirement Age 3.2.1 One-Dimensional Voting 3.2.2 Joint Determination of the Retirement Age and the Contribution Rate

4. The Social Contract 4.1 Sustainability of the PAYG System 4.2 Dynamics of the Political Equilibrium

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4.3 Markov Perfect Equilibria 4.3.1 A Median Voter Model with Capital as the State Variable 4.3.2 Probabilistic Voting 4.3.3 The Evolution of Retirement

5. The Transition to a Fully Funded System 6. Quantitative Analysis 6.1 Empirical Estimations 6.2 Simulating the Future Political Evolution of Social Security 6.2.1 Political Sustainability and the Evolution of the Contribution Rates for the Current Systems 6.2.2 Political Sustainability with Endogenous Retirement Age

7. The Political Impact of Aging on Other Public Programs 7.1 Aging and Political Support for Education 7.1.1 Theory 7.1.2 Empirical Evidence

7.2 Aging and Support for Health Care 7.3 Aging and Long-Term Care 7.4 Aging and the Environment 7.5 Capital vs Labor Taxes 8. Conclusion Acknowledgments References

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Abstract This paper reviews the latest developments in the political economy literature that are concerned with the consequences of population aging, with a primary focus on the threat posed by aging to the continued existence of public pension programs in developed countries. After briefly recalling why pay-as-you-go (PAYG) public pensions are supported by a political majority in the first place, we turn to analyzing how a drop in fertility or mortality rates will change the contribution rates and pension sizes at the political equilibrium, by first assuming a constant retirement age. Other theoretical works are discussed that are mainly concerned with endogenizing the retirement age choices and exploring the opportunity to transition to a fully funded (FF) system. Empirical assessments of the relationship between a population age structure and the size of its pension programs are also presented. Additionally, we explore the impact of population aging on the political support for other public programs, such as education, heath care (including long-term care), capital taxation, or environment protection. We also give an account of some empirical analyses of the joint determination of education and pension programs.

Keywords Demography, Public pensions/social security, Retirement, Political equilibrium/voting, Intergenerational transfers

JEL Classification Codes: H55 (Social Security and Public Pensions), J11 (Demographic Trends, Macroeconomic Effects, and Forecasts), D72 (Political Processes: Rent-Seeking, Lobbying, Elections, Legislatures, and Voting Behavior)

The Political Economy of Population Aging

1. INTRODUCTION 1.1 The Political Challenges of Population Aging 1.1.1 Facts on Aging, and Political Consequences Population is aging rapidly in all regions of the world, and even faster if one considers the most developed countries. Individuals aged 65 years or more represented 5.1% of the world population in 1950 and 8.3% in 2015. According to recent projections (United Nations, 2015), this ratio should rise to 16.0% in 2050. What are the reasons for this evolution? Population aging finds its roots in two contemporaneous phenomena: a drop in mortality and fertility rates. In developed countries, the drop in fertility has mainly occurred before the 1980s and 1990s, and the fertility rate seems to have stabilized since then. In the least developed countries, however, there remains considerable room for further fertility reductions. The global total fertility rate fell from approximately 5 children per woman in 1950 to just over 2.5 in 2015, and the UN projects that it will fall to 2.2 children per woman by 2050 (United Nations, 2015). Most of the yet-to-come decline will occur in the developing world; this will contribute to a near halving of the share of children in the population of developing countries between 1965 and 2050. The drop in mortality, or increase in longevity, is however a long-lasting trend. Average world life expectancy at birth (both sexes combined) has risen from 46.5 years in 1950 to 70.5 years in 2015. It is forecasted to continue to increase up to 77.8 years by 2050. The aging of the world population introduces several major policy challenges (Bloom et al., 2010). People aged 60 or above usually have different needs and behaviors than younger individuals. Older individuals tend to work and save less, thus negatively impacting the long-term growth potential of the economy. They also require more health care and, in many countries, rely on publicly funded pensions for a large part of their income. As older populations become larger and politically stronger, adopting certain policies (such as cutting health and pension benefits) will prove difficult, as the older generations will be more able to impose their views on political agendas, be it through their sheer weight in the electorate, or by mobilizing themselves through lobbies or interest groups (Mulligan and Sala-i Martin, 1999; Hanley, 2012). Sinn and Uebelmesser (2003) even estimate that in one of the countries most concerned by aging, Germany, the age of the median voter will increase so quickly that it will soon become extremely hard to secure a political majority to pass pension reforms: according to them, “gerontocracy” will be a fact in Germany as soon as 2016. Individuals aged 80 or over also have different needs. With declining health the need for full-time, long-term care increases. In many cases, this also increases the need for financial support, as private savings tend to vanish rapidly for individuals with particularly long life spans. As their numbers increase, they place further demands on government resources, familial resources, and personal savings.

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1.1.2 Policies at Stake with Aging In this chapter, we will focus on the impact of population aging on public programs, such as social security, health care, and education, that entail substantial transfers of resources between generations. It should be noted from the outset that our survey will not explore the diversity of institutional frameworks under which these programs are shaped, nor the interplay between political parties, interest groups, social movements, or expert advice in defining and reforming them. We feel that the study of these important subjects is best left to political scientists (see Pierson, 2007; Goldstone et al., 2011; Vanhuysse and Goerres, 2012), and that the need to make quantitative predictions on the future evolution of these key programs requires that the political economy literature should stick to models where individual preferences aggregate into a collective vote on a limited number of features of the programs, and abstract away from the particularities of each country’s and each policy’s institutional features. The main part of the chapter will be devoted to social security. Aging has a direct and dramatic impact on the functioning of unfunded, or pay-as-you-go (hereafter PAYG), pension systems. In these systems, pension benefits are financed with the contributions of the workers. Population aging implies that the proportion of recipients increases while the proportion of contributors decreases, and thus threatens the financial viability of the system. The magnitude of this phenomenon is captured by the change in the old-age dependency ratio, which is defined as the ratio of elderly (aged 65 years or more) to adult individuals (aged between 15 and 64 years): according to the United Nations (2015), it will jump from 12.6% in 2010 to 25.6% in 2050 for the world taken as a whole, and from 26.7% to 45.8% for developed economiesa over the same time frame. Meier and Werding (2010) give an order of magnitude of the increased burden that would represent if the system (and notably the replacement rate)b was left unchanged: for a subset of OECD economies, the increase in pension spending to GDP would spread from 3% (for the UK) to 21% for Poland, over the 2000–2050 period. In many cases, this pensionspending-to-GDP ratio would be more than doubled over the period, should no reform be enacted. Together with these changes in the age composition of the population, most OECD countries have also experienced a large drop in the labor force participation of middleaged and elderly workers, which contributes to aggravating the financial difficulties of pension systems. As we will see later in this chapter, this drop is mainly due to the design of social security systems, which induces people to retire early, as well as other programs of the welfare state (among which unemployment benefits and disability insurance).

a b

As defined in the report cited above: Europe, Northern America, Australia, New Zealand, and Japan. The replacement rate of a pension system is defined as the average ratio of individual pensions to wages before retirement.

The Political Economy of Population Aging

Confronted to this demographic evolution, pension systems thus need to be reformed. A substantial part of this chapter will be devoted to the political sustainability of such reforms. In a democratic society, this amounts to identifying the reforms which are likely to receive the support of a majority of the voters. Two kind of reforms of PAYG systems can be envisioned. The first one consists in keeping the system unchanged, but simply adjust its parameters, that is the contribution rate, the pension benefit level, or the retirement age. This is called a parametric reform. The other possibility consists in changing the system and move to a fully funded (hereafter FF) or a notional definedcontribution (NDC, see below) system: this is called a structural reform. An analysis of the political sustainability of social security under aging needs to examine the individuals’ position on social security. Preferences over social security typically depend on an individual’s age—since different cohorts of people have different remaining periods of contributions and benefits, but also on the redistributive design of the system. To assess the political sustainability of social security, one has to aggregate these preferences into a collective choice procedure. In this chapter, we focus almost exclusively on majority voting. Once we have determined how these individual preferences shape the collective choice that arises out of majority voting, we can study how population aging affects this democratic choice. Demographic dynamics impact the majority voting equilibrium over social security in essentially two ways. It modifies individuals’ preferences—through, for example, the change in the rate of return of the pension system or equilibrium prices. But it also changes the identity of the decisive voter: when population ages, the median voter becomes older and therefore individuals at or close to retirement get more political power.

1.2 Features of Social Security Systems and Recent Reforms Most industrialized countries feature an unfunded social security system that collects contributions from the workers’ labor income and uses the revenue raised to provide pension benefits to current retirees. The first unfunded public program of retirement income was introduced in Germany in the late 19th century; several other countries followed at the beginning of the 20th century—often with the creation of small funded systems targeted to workers in specific sectors. By the end of World War II, most systems had become unfunded. Until the beginning of the 1990s, these systems have constantly grown, either because of the extension of coverage among workers or due to an increase in the generosity of pension benefits. Since then, governments, recognizing the long-term financial effect of the aging process, have started to adopt retrenching measures. 1.2.1 Features of Social Security Systems Social security systems are designed to provide replacement income for old age under a variety of circumstances and, as such, need to combine different mechanisms called

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pillars or tiersc that each functions in a specific way and provides for different needs. For ease of exposition, we will retain here only two main roles played by the pension systems. The first role or tier typically refers to noncontributory provision of basic income for persons older than a certain threshold, with a clear aim at alleviating old-age poverty. It is usually financed out of general taxation. The second tier, in contrast, provides an amount of income that is linked to past contributions made to the system, and has an insurance (rather than a redistributive) objective. This second tier of the social security system of a given countryd can be classified into four broad categories, as a combination of two key features: (a) pension systems are either fully funded or unfunded (henceforth referred to as pay-as-you-go or PAYG) and (b) a system can provide payments based on either defined benefits or defined contributions. A system is deemed “defined benefits” (henceforth DB) if the benefits accrued at retirement are predetermined based on a formula that takes into account mainly life earnings, years of contribution, and age, while a “defined contribution” system does not guarantee future pension levels, which are calculated by applying a (market-based or fictitious) rate of return on contributions. Additionally, it should be noted that some countries feature both a funded and an unfunded component in their pension system, making any attempt at a general typology of pension system rather obscure.e 1.2.1.1 Funded Defined-Contribution System

Chile’s social security reform in 1981 remains the best known international example of a FF defined-contribution system. Under the Chilean system, all workers are required to contribute 10% of their salary into a savings plan of their choice, which is administered and regulated by the Administradora de Fondos de Pensiones. Eligibility for retirement is based on age, and early retirement is available to those with sufficient accumulated savings. At retirement, workers can choose monthly withdrawals or purchase an annuity. Furthermore, workers are guaranteed a minimum pension paid from the general revenue fund. The benefits of such a system include reduced exposure to political and demographic risks. Several other countries, including most of Latin America, have a funded definedcontribution pillar that follows Chile’s example. Vald
es-Prieto (1999) presents, among other things, a summary of the reforms that took place in seven Latin American countries, following Chile’s example. He offers five reasons why Chile’s model is so successful, including low levels of private-sector corruption, little political pressure on investment c

d

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The pillar denomination seems to originate from the World Bank (see, for instance, World Bank, 2008), while the classification in tiers emanates from the OECD (see, for instance, OECD, 2015). We henceforth only refer to this second tier of the pension system of a given country as “the system” for brevity. The interested reader will find in Section 1.2.2 some useful references that describe the pension systems of given countries using a coherent typology.

The Political Economy of Population Aging

options, and successful implementation of a redistributive means-tested benefit to workers not covered by the Administradora de Fondos de Pensiones. In Australia also the system is funded with defined contributions. The peculiarity of this system is that it offers the choice of either a lump-sum payment or an annuity at retirement. The UK system also offers a privatized, funded defined-contribution system but a unique one, in that it allows workers to opt out of their public, unfunded, definedbenefit system. 1.2.1.2 Funded Defined-Benefit System

More traditional pensions, similar to those awarded to older US workers during previous decades, are good examples of funded defined-benefit systems. Workers pay into the pension system, and the corporation manages how these contributions are invested. Workers then receive a defined benefit at retirement, which is usually based on years of service or some other related measure. Switzerland currently offers a hybrid system: a funded defined-contribution system with a guaranteed minimum return. 1.2.1.3 Unfunded Defined-Benefit System

A publicly operated, unfunded defined-benefit plan constitutes the main system of social security among a majority of OECD countries, including, for instance, France and Spain. Pension benefits may be granted to every individual that complies with the age and contribution range requirements, or may be means-tested (such that only workers below an income threshold are eligible). 1.2.1.4 Unfunded Defined-Contribution System

Sweden and Italy are concrete examples of countries with an unfunded definedcontribution social security system. In recent years, both countries have switched to a so-called NDC (notional defined contribution) plan. The government credits each worker for the taxes he or she and the employer contribute, and then pays upon retirement a benefit equal to the worker’s contributions plus a notional (ie, not market-based) interest rate. 1.2.1.5 Pension Benefits and Eligibility

Benefits are computed based on the number of years of contributions and on a reference wage, which typically depends on the worker’s past wages. However, even countries with a defined-benefit system differ in how pensions relate to the reference wage and in how this reference wage is obtained. France, Germany, and Spain feature a tight link between wages and benefits. In these so-called Bismarckian systems, the benefit formula is constructed so as to entitle the retirees to a pension income that replaces a certain share (called the replacement rate) of their previous labor income. On the contrary, the United Kingdom exhibits an essentially redistributive system (often referred to as Beveridgean).

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The basic state pension is not related to any reference wage, and depends mostly on the number of years of contributions only. Benefits are most of the time indexed on inflation or to the net wage growth, to reflect the increase in the cost of living. Eligibility to these benefits may depend on the years of contributions and/or on a minimum retirement age. 1.2.1.6 Retirement Age

All countries feature an official retirement age, when people are allowed, if not forced, to exit the labor market and receive their pension benefits. Most countries also have early retirement provisions that allow workers to retire before the official age on a reduced pension benefit. On top of that, some countries (like France) allow workers to enjoy full pensions even if they did not contribute to the system during the required amount of years, provided they have reached an age that is slightly higher than the official retirement age. 1.2.2 Recent Reforms It is outside the scope of this chapter to provide a detailed account of the state of pension program reformsf in any economy taken individually, as every country exhibits specific provisions linked to the history of its public pension system development, the national public debate on the subject, and other idiosyncrasies such as how much the recent crisis hit public finances. We refer the reader interested by very up-to-date information on any particular country to periodic reports made by international or specialized institutions to cover the specifics of recent reforms on all aspects of pension programs. Notably, the “Social Security Programs Throughout the World” reports, issued by the American Social Security Administration jointly with the International Social Security Association, give detailed accounts of most features of the pension system of every country in a given area of the world, every six months on a rotating basis for the different regions (see, eg, the latest report for the Americas: US Social Security Administration (2016)). Other international organizations are also publishing reports on the situation of pension programs in their member states for policy coordination purposes: see, for instance, OECD (2014, 2015) for OECD countries, or European Commission (2010) for the EU. OECD (2015), for instance, examines pension reforms in its member countries between 2013 and 2015, noticing a trend toward less favorable indexation mechanisms, rather than direct cuts in pensions, and increased incentives to work longer in many member states. Another feature common to OECD member states is, according to the report, renewed effort to provide social assistance to the old poor in the form of minimum, noncontributory pensions, or increased levels of pensions for people having worked short careers. Additionally, past trends aimed at financial sustainability are still present: minimum f

To get an overview of recent reform trends, see Holzmann (2012).

The Political Economy of Population Aging

retirement age keeps being more and more tied to life expectancy, and benefits levels are increasingly tied to the whole contribution history rather than the last years (or best years in terms of wage) of an individual’s career. European Commission (2010) also adds that eligibility criteria now more and more include a statutory number of contribution years on top of the minimum age. Recent reforms are also shown to be aimed at lengthening working lives, either through increases in statutory retirement age, provision of financial incentives to work while in retirement, or the retrenchment of generous early retirement schemes. These reforms are sometimes coupled with labor market reforms aimed at promoting employment of older workers from the labor demand side, with incentives given to firms that hire workers close to retirement. Finally, furthering diversification and security of the pension plans available to workers has been brought through the establishment of voluntary pension plans and increase in competition between private providers, or by relaxing restrictive regulations over investment choices made by the individuals (when saving to a private fund) and pension funds (to increase diversification of their portfolios). In this respect, European Commission (2010) notes an “increased complexity of pension systems [meaning] a transfer of risk from pension scheme sponsors to the beneficiaries.” Additionally, European Commission (2010) notices a trend toward the prefunding of future pension outlays, which consists in frontloading parts of the adjustments costs linked to aging in order to distribute them over a longer period and over several generations. This prefunding typically is made by establishing a pension reserve fund, paying down national public debt,g or reforming the systems from defined benefits to defined contributions.

1.3 Contribution of This Chapter and Outline 1.3.1 Contribution of This Survey This chapter naturally builds on previous surveys of the literature on the political economy of intergenerational transfers, notably Breyer (1994b), Galasso and Profeta (2002), or De Walque (2005).h Among other things, Breyer (1994b) provides a clear classification of the assumptions made by the various theoretical models that deal with our topic: the time structure of the model, the validity of the decision (once-and-for-all voting or not), the decision rule, or the characteristics of voters in the same cohort are some of the assumptions that are discussed. He also compares the political decisions regarding the pension system to the decision to accumulate some government debt, an issue rarely tackled elsewhere. Galasso and Profeta (2002) review works that aim to study the interactions between social security systems and other redistributive programs of the welfare state. They also g

h

Once we take into account the fact that the state is financing the deficits of universal unfunded systems in many countries, it becomes clear that social security deficits add up each year to the implicit public debt, so that reducing public debt now in order to run social security deficits in the future is as effective as building up a pension reserve fund. A more recent survey on some aspects of this literature can be found in Pamp (2015).

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briefly analyze the first multidimensional voting models involving social security that were used to understand the joint determination of several features of social security systems. Another notable contribution is their review of the early literature on the political sustainability of social security following a demographic shock, as well as on the feasibility of reforms. This survey expands on those cited above, first by giving an account of more recent work that aims at explaining the emergence of social security: for instance, one issue that has received increased attention in the last decade is the existence of within-cohort heterogeneity, especially concerning life expectancy at retirement. Heterogeneity within the cohort of current workers may help explain why there is a political majority that supports the existence of a (partly redistributive) pension system in equilibrium. We also review recent work on the political determination of the retirement age, whether as a stand-alone policy dimension or in conjunction with the size of pensions. Besides, we give an account of theoretical models in which the once-and-for-all-voting assumption is relaxed, this assumption being a clear limitation of the early literature on the political economy of pensions. In this chapter, we also report on the recent empirical analyses and simulations of the effect of aging on the political determination of the size of pension programs. In particular, we show that the choice of the variables used in empirical studies to represent the changing age structure of population has a tremendous impact on the conclusions drawn by these studies. Additionally, the use of simulations allows to make quantitative predictions on the future evolution of the retirement age, contribution, and replacement rates in a selection of major OECD countries, of which we give a brief summary. Finally, we believe this chapter contributes to the understanding of how population aging impacts other public programs beyond (or in conjunction with) social security. We give an account of the complementarity at the political decision-making level between public funding of education and pensions, a mechanism that was first recognized as important from a normative point of view a decade ago: the recent political economy literature envisions the possibility that voters may take into account such a relationship between the two policies when stating their policy preferences. 1.3.2 Outline In a first step, we consider that the retirement age is fixed, so that a PAYG pension system is characterized by its contribution rate and its level of benefits, and examine in Section 2 the reasons why a majority of the population may sustain a PAYG pension system. These reasons are the following. First of all, the economy may be dynamically inefficient. This implies that the rate of population growth exceeds the interest rate. In other words, the rate of return of the PAYG system is larger than the rate of return of a FF system.i i

We assume for simplicity that there is no wage growth.

The Political Economy of Population Aging

It follows that individuals find the PAYG system to be a better “investment” opportunity than the FF system. Browning (1975), in his seminal paper, noted that the economy need not be dynamically inefficient for a majority of the population to support the PAYG system. His argument relies on the idea that past contributions to the social security system are a sunk cost for individuals. These latter, in evaluating the relative return of a PAYG and a FF system, compare the contributions that remain to be paid to the future pension benefits they expect to receive. It is then clear that an individual close to retirement receives a very high return from the PAYG system. If the median voter (who is the median age individual) is close enough to retirement, he will therefore vote for a PAYG system. Previous arguments were developed in a partial equilibrium setting. In a general equilibrium, the introduction of a PAYG system depresses savings and thus makes the interest rate increase. This provides an additional reason for the voters to support PAYG. Besides, pension systems not only redistribute wealth across generations, they also redistribute within cohorts. As a consequence, a sufficiently redistributive PAYG system may be sustained by a coalition of the retirees and the poor workers. Finally, a PAYG system may constitute a device to insure individuals against the fluctuations of the interest rate. We then turn in Section 3 to the political determination of the retirement age. Two different frameworks are considered. In the first one, individuals freely decide when to retire. They however vote on some features of the PAYG system that affect their retirement decision. In the second framework, we consider that the majority vote applies to the retirement age, which is unique and common to all individuals. The previous arguments were made under the once-and-for-all voting assumption: when voting on the contribution rate, individuals anticipate that the chosen tax rate will apply to their retirement period. A strand of the literature has shown that this assumption can be rationalized as the equilibrium outcome of an infinitely repeated game. In each period, the young voters sustain the system because of the fear to be punished by the subsequent generations. This game, which allows to explain the social contract between generations, is analyzed in Sections 4.1 and 4.2. Its main drawback is that it has many (subgame perfect) Nash equilibria. Section 4.3 develops a recent literature on social security as a Markov perfect equilibrium, which is a refinement of the Nash equilibrium. The payroll tax rate is assumed to be a function of some state variables, for example, the capital stock. This creates a link between generations: if some generation decides to alter the tax rate in a given period, it will impact the capital stock in the next period and, through the Markov link, the tax rate in this next period. A widely discussed reform of the social security system consists in moving from a PAYG to a FF system. This latter having a larger rate of return, many observers propose to change the system. Some authors have however shown that this transition cannot be Pareto improving, as it only results in making the implicit debt of the PAYG system explicit. Only when the PAYG system generates some distortions could the transition to a FF system be Pareto improving. We discuss this reform in Section 5.

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Section 6 presents quantitative, rather than theoretical, analysis of the consequences of population aging, by first reporting empirical evidence and then turning to simulation work. Section 7 deals with other public programs that are likely to be affected by population aging, mainly health care and education. Lastly, Section 8 concludes.

2. WHY INDIVIDUALS SUPPORT PAYG SOCIAL SECURITY 2.1 Dynamic Inefficiency We present the basic two-period overlapping generations (hereafter OLG) model that is used for analyzing pension policy. We consider a small open economy, so that the wages and the interest rate are given. Individuals live two periods. In any given period, two generations thus coexist: the young y and the old o. The size of each cohort at time t is denoted Nty and Nto , y respectively. Let assume that population grows at a constant rate n, so that Nt ¼ ð1 + nÞNto . Lifetime utility of the generation born in t depends on consumptions in young and old ages and is assumed to be additively separable: Uðcty ,cto+ 1 Þ ¼ uðcty Þ + βuðcto+ 1 Þ, where β is the discount factor. Assuming each individual earns the same income, normalized to 1, when young,j he chooses savings st in order to solve: max Uðcty , cto+ 1 Þ st

st cty ¼ 1  st cto+ 1 ¼ st ð1 + rt + 1 Þ where rt is the interest rate. This leads to the first-order condition on savings: u0 ðcty Þ ¼ βð1 + rt + 1 Þu0 ðcto+ 1 Þ:

(1)

Consider now the introduction of a PAYG social security system. Each individual contributes a fraction τ of his income when young and receives a pension benefit p when old. The budget constraint of the system in each period is: τNty ¼ pNto , p ¼ τð1 + nÞ: With the PAYG system, consumptions in both periods are cty ¼ 1  τ  st and cto+ 1 ¼ st ð1 + rt + 1 Þ + τð1 + nÞ. The effect of introducing a PAYG system at any time t0 on the welfare of generations born after t0 is given by:
@V

¼ u0 ðcty Þ + βð1 + nÞu0 ðcto+ 1 Þ, (2) @τ
τ¼0 j

Wage growth is thus ruled out by assumption. This is for expositional simplicity, results continue to hold with this assumption relaxed.

The Political Economy of Population Aging

where V is the indirect utility function. From (1), we see that this expression is positive when n > rt, a condition known as dynamic inefficiency. Noting that the introduction of the PAYG system constitutes a windfall for the old of the initial period, it is found that the PAYG system is Pareto improving when the economy is dynamically inefficient (Samuelson, 1958; Aaron, 1966). Whether the economy is dynamically efficient or not is a debated issue (Abel et al., 1989; Homburg, 1991; Geerolf, 2013). However there exist other reasons, that we examine in the next sections, why individuals support social security even when the economy is dynamically efficient.

2.2 Reduced Time Horizon 2.2.1 Central Argument Browning (1975) provided the first analysis of a majority vote over pensions. He considers a small open economy (in which the interest rate is given) with individuals differentiated according to age only (in particular there is no income heterogeneity). They live three periods, meaning that three generations coexist in each period, the young y, the middle-aged m, and the old o. Under this setup, preferences are single-peaked over the payroll tax rate, implying that a Condorcet winner exists (Black, 1948).k This policy is the majority-voting equilibrium of a standard two-party Downsian electoral competition game (Roemer, 2001). With three generations, noting that Nto ¼ ð1 + nÞ2 Nty and Ntm ¼ ð1 + nÞNty , the budget constraint of the PAYG system writes: Nto pt ¼ Nty τt + Ntm τt , pt ¼ τt ð1 + nÞð2 + nÞ: It is assumed that there are no future re-voting opportunities. In other words, individuals vote with the belief that the contribution rate chosen today will not be modified in the future (τt+1 ¼ τt  τ). Under this assumption, the optimal payroll tax rate of the decisive voter (who is a median-aged individual) solves: max Vtm ðτÞ  uðctm Þ + βuðcto+ 1 Þ τ

st ctm ¼ 1 + syt ð1 + rÞ  smt  τ cto ¼ smt ð1 + rÞ + τð1 + nÞð2 + nÞ:
He chooses a positive payroll tax rate if @Vtm =@τ
τ¼0 > 0: Using the optimality condition on private savings, (1), this will be the case when (1 + n)(2 + n) > 1 + r. In words, this implies that he may sustain the PAYG system even when the economy is dynamically efficient. The reason for this is that past contributions to the system are sunk cost. k

The Condorcet winner is the tax rate that is preferred by more than one half of the population, when confronted to any other possible tax rate.

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At the time of the vote, he compares the benefit of the system, τ(1 + n)(2 + n), to its cost, τ. The rate of return of the system is thus (1 + n)(2 + n), which is larger than the rate of return of the young, 1 + n.l More generally, the closer the individuals are to retirement, the higher the rate of return of the system. As a consequence, optimal tax rates are increasing with age. Noting that the steady-state socially optimal tax rate is the one maximizing life cycle utility at birth, Browning reaches the conclusion that the voted tax rate, that corresponds to the preferences of the middle-aged, is too high. In other words, voting leads to a pension system excessively generous. In this stylized economy, middle-aged individuals vote for a 100% tax rate. They prefer to “invest” all their income in the social security system and finance current consumption by borrowing. There exist however obvious limits to the size of the system. First of all, when borrowing is constrained, agents need to keep resources for consumption in the working period (Boadway and Wildasin, 1989). The presence of uncertainty about future voting outcomes may also dissuade them to adopt too high tax rates (Hu, 1982). Finally, distortions caused by taxation are absent from Browning’s analysis. With distortionary taxation, the voted tax rate lies strictly between 0 and 1 (Breyer, 1994a). 2.2.2 Population Aging in the Browning Model We consider the impact of population aging in the framework just described. In this purpose we formulate a simple continuous version of this model. Assuming no time discounting and no savings for simplicity, the life cycle utility of an aged a worker writes: Z R Z T uð1  τÞdt + uðpÞdt ¼ ðR  aÞuð1  τÞ + ðT  RÞuðpÞ, a

R

where R is the age of retirement and T the length of life. The budget constraint of the PAYG system is: p¼

FðRÞ τ, 1  FðRÞ

where F(.) is the c.d.f. of the age distribution and we denote Ny ¼ F(R) the number of workers (recall that the retirement age is assumed to be fixed). The optimal contribution rate of an aged a worker solves the following first-order condition: ðR  aÞu0 ðc y Þ + ðT  RÞ

Ny 0 o u ðc Þ ¼ 0, 1 Ny

where cy ¼ 1  τ and co ¼ p. l

These latter vote for a zero tax rate in a dynamically efficient economy.

(3)

The Political Economy of Population Aging

Obviously, and for the reason explained in the previous section, @τy/@a > 0, so that the majority voting tax rate is the preferred tax rate of the individuals with median age am. Now consider a change in the fertility rate that makes the ratio η  Ny/(1  Ny) decrease. As a consequence the median age increases and the total effect on the majority voting tax rate is:m dτ* @τy @τy dam + : ¼ dη @η @am dη As explained before, the second term is negative. The first term is obtained by differentiating (3): @τy ðT  RÞu0 ðc o Þð1  εÞ ¼ , @η Dτ where ε ¼ xu00 (x)/u0 (x) is the coefficient of relative risk aversion and Dτ < 0 is the derivative of the first-order condition (3) with respect to τ. One can show that ε is equal to the inverse of the intertemporal elasticity of substitution. Individually optimal tax rates increase with η when ε < 1. When η decreases, the rate of return of the PAYG system becomes lower. In other words, the price of second-period relatively to first-period consumption increases and individuals are induced to substitute first- for second-period consumption. This is achieved by decreasing the tax rate. But the income effect goes in the opposite direction. With a high enough intertemporal elasticity of substitution, the substitution effect dominates so that individuals react to a drop in the fertility rate by increasing the tax rate. In this case, we see that the total effect of an increase in the dependency ratio (equal to 1/η) on the equilibrium tax rate is ambiguous. The direct, economic effect calls for a reduction in the size of the system. But at the same time, in a graying society the increased political power of the old pushes toward a higher tax rate. What is the consequence of an increase in life expectancy? This change leads to a reduction in η and therefore has similar effects as previously. There is however an additional economic effect. Because individuals live longer and thus spend more time on retirement (for a given retirement age), they should invest more resources in PAYG to ensure a decent standard of living at retirement: @τy ηu0 ðc o Þ ¼ > 0: @T Dτ

m

We are interested here in the comparison of steady states and do not address the question of the demographic transition.

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2.3 Effect of Social Security on Prices Diamond (1965) extended the analysis of Samuelson (1958) to a model with production. In this context, the introduction of PAYG social security crowds out private savings and thus lowers the capital stock. This in turn implies lower wages and a higher interest rate. It follows that social security may, through its positive effect on the interest rate, be sustained by a majority of voters in a dynamically efficient economy (Cooley and Soares, 1999; Boldrin and Rustichini, 2000). Consider the extension of the simple model in Section 2.1 to a closed economy with wage in period t denoted wt. The program of the representative young agent in period t remains the same with consumptions in both periods equal to cty ¼ wt ð1  τÞ  st and cto+ 1 ¼ st ð1 + rt + 1 Þ + τwt + 1 ð1 + nÞ. Denoting f the production function from per capita capital k, the equilibrium conditions on the production side are wt ¼ wðkt Þ ¼ f ðkt Þ  kt f 0 ðkt Þ 1 + rt ¼ rðkt Þ ¼ f 0 ðkt Þ kt + 1 ¼ st =ð1 + nÞ: The effect of the introduction of a PAYG system is now given by:
  @V

@wt + 1 @kt + 1 @rt + 1 @kt + 1 0 y ¼ wt u ðct Þ + β ðwt + 1 + Þð1 + nÞ + st u0 ðcto+ 1 Þ: @kt + 1 @τ @kt + 1 @τ @τ
τ¼0 There are two new terms with respect to (2). The introduction of the PAYG system depresses savings: @kt+1/@τ < 0. With less capital, the wage rate in period t + 1 decreases (first term negative), but at the same time the interest rate increases (second term positive). If this second effect dominates, introducing a PAYG system has a positive effect on prices from a welfare perspective.

2.4 Within Cohort Redistribution Even in a dynamically efficient economy, poor young individuals may support the PAYG system because of its (intragenerational) redistributive properties (Meltzer and Richard, 1981; Tabellini, 2000; Casamatta et al., 2000). We consider a two-period OLG model of a small open economy. There is wage heterogeneity within cohorts: w 2 [w, w+], with the average wage larger than the median (w > wm ) and agents are assumed to be credit constrained.n The pension formula is

n

In order to have interior optimal tax rates, see discussion at the end of Section 2.1.

The Political Economy of Population Aging

pðwÞ ¼ ð1 + nÞτðαw + ð1  αÞwÞ,  where α 2 ½0,1 is a parameter that represents the link between contributions and benefits. It is a measure of the redistributiveness of the pension system. A low value of α implies a highly redistributive, or Beveridgean, pension system (for α ¼ 0, everyone receives the same pension, whatever the level of contributions). Large values of α correspond to a contributory, or Bismarckian, system. The analysis is conducted at steady state under the once-and-for-all voting assumption. 2.4.1 Individually Optimal Tax Rates We first determine the tax rates that maximize the life cycle utility of the different agents, considering first the retirees and then the workers. 2.4.1.1 The Retirees

Private saving is the result of past decision. The retirees choose the value of τ, τo, that maximizes their consumption: c o ¼ ð1 + rÞs + ð1 + nÞτðαw + ð1  αÞwÞ.  The solution is straightforward: τo ¼ 1, the same tax rate for all retirees. 2.4.1.2 The Workers

A worker with earning w chooses τy(w) in order to maximize V ðτ,wÞ ¼ uðwð1  τÞ  sy Þ + βuðð1 + rÞsy + ð1 + nÞτðαw + ð1  αÞwÞÞ  where sy  0 is the optimal level of private saving. If 1 + r >(resp. 0) and sy > 0 (resp. ¼ 0). Put differently, for an individual to prefer private saving to PAYG pensions, his wage must be strictly higher than w^ defined as: 1α w   w:  1+r α 1+n One easily checks that w^ ¼ w if n ¼ r, @ w=@n ^ > 0, and @ w=@α ^ < 0. Indeed, a larger n means a higher return of the PAYG system. It thus explains why more workers support the system (@ w=@n ^ > 0). Moreover a less redistributive system (α increases) receives less political support (@ w=@α ^ < 0). One can also check that the indirect utility function V (.) is concave in τ, meaning that preferences are single-peaked and therefore that the median voter theorem applies. w^ ¼

2.4.2 Variation of the Optimal Tax Rates with the Wage Level Let us now take a look at how the optimal tax rate changes with the individual wage w  w. ^ Differentiating the first-order condition on τy,

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wu0 ðc y Þ + βð1 + nÞðαw + ð1  αÞwÞu  0 ðc o Þ ¼ 0,

(4)

we obtain w 0 o @τy βð1 + nÞð1  αÞ w u ðc Þð1  εÞ ¼ V 00 ðτÞ @w where ε is the coefficient of relative risk aversion. Optimal tax rates increase with wages if and only if ε > 1. A variation of the wage level generates an income and a substitution effect. When the wage increases: 1) The individual is richer. Because consumption in the second period is a normal good, he wants to increase it. This is achieved by increasing the tax rate (income effect). 2) The price of first-period consumption with respect to second-period consumption, ð1 + nÞðαw + ð1  αÞwÞ=w,  decreases. By this effect, richer individuals are induced to buy more first-period consumption and this is achieved by reducing the tax rate (substitution effect). When the intertemporal elasticity of substitution is small (ε > 1), the income effect dominates: individually optimal tax rates are increasing with wages. 2.4.3 Majority Voting Tax Rate The workers are divided into two classes, those who prefer a zero tax rate and positive savings and those who prefer a positive tax rate and no saving. A fraction 1/(2 + n) of citizens, the retirees, is in favor of τR ¼ 1. Furthermore, all workers with earnings above w^ are in favor of a zero tax and the preferred tax rate of the workers with earnings below w^ increases (resp. decreases) with w if ε > 1 (resp. < 1). For the majority voting tax rate to be positive, it must be that the number of individuals who want a positive rate is larger than half the total population: Z w^ Nty + Nto y Nt f ðwÞdw + Nto  2 Z w^ w n , f ðwÞdw  : 2ð1 + nÞ w Under this condition,o the majority voting equilibrium tax rate is the rate preferred by the  workers with earning w , such that the number of people who prefer a higher tax rate is exactly half the total population. For ε > 1 (increasing tax rates), it solves:

o

Note that this condition is always satisfied when n  r. It could however be violated in the converse case.

The Political Economy of Population Aging

Z Nty

w^

f ðwÞdw + Nto ¼  w Z w^ , f ðwÞdw ¼ 

w

Nty + Nto 2 n : 2ð1 + nÞ

(5)

This corresponds to an ends-against-the-middle equilibrium (Epple and Romano, 1996): a coalition of the middle-class and the retirees support a larger PAYG system, whereas the poor and rich workers would like to downsize it.  For ε < 1 (decreasing tax rates), w is implicitly defined by: 

Zw

f ðwÞdw ¼

n : 2ð1 + nÞ

(6)

w

It corresponds to the situation in which the PAYG system is supported by a coalition of the retirees and the poor workers. 2.4.4 Effect of a Drop in the Fertility Rate A change in the fertility rate has both a direct and an indirect effect on the majority voting tax rate. The direct effect is obtained by differentiating the first-order condition (4): @τy βðαw + ð1  αÞwÞu  0 ðc o Þð1  εÞ ¼ : @n V 00 ðτÞ Optimal tax rates increase with n if and only if ε < 1. When n decreases, the rate of return of the PAYG system becomes lower. In other words, the price of second-period relative to first-period consumption being larger, individuals are induced to substitute first for second-period consumption. This is achieved by decreasing the tax rate. But the income effect goes in the opposite direction. With a large enough intertemporal elasticity of substitution, the substitution effect dominates so that individuals react to a drop in the fertility rate by decreasing the tax rate. Following a change in the fertility rate, not only optimal tax rates are modified but also  the identity of the decisive voter. When the intertemporal elasticity is low, w is given by (5). Differentiating this condition, we obtain: 

dw  1 dw^ f ðw Þ ¼ f ðwÞ: ^ 2 dn dn 2ð1 + nÞ Noting that @ w=@n ^ > 0, this effect has an ambiguous sign. In the case of a high intertemporal elasticity, we differentiate (6) to obtain: 

dw  1 f ðw Þ ¼ > 0: dn 2ð1 + nÞ2

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The total effect on the majority voting tax rate is given by: 

dτ* @τy @τy d w + : ¼ @n @w dn dn When ε > 1 the direct effect is negative and the indirect one ambiguous. When ε < 1 the direct effect is positive and the indirect effect negative. Therefore, one cannot conclude unambiguously about the effect of a drop in fertility. The direct and indirect effects go in opposite directions and one needs to evaluate the magnitude of these countervailing effects to be able to conclude about the global direction of the change. 2.4.5 Myopic Individuals Cremer et al. (2007) develop a political economy analysis that describes the majority vote over PAYG pensions when some individuals are myopic, in the sense that they do not discount the future “correctly.”p They consider a model which is basically the same as the one presented in the previous sections, except that now part of the individuals that compose society are myopic, meaning that they do not discount the future when making their private economic decisions (savings and labor supply). The vote takes place sequentially on the two parameters that characterize the PAYG pension system. Individuals first vote on the Bismarckian factor (α) and then on the size of the pension system (τ). When they vote, individuals are placed under the “veil of ignorance,” meaning that they vote as if they were not myopic and thus rationally anticipate the future. Two main results emerge from this analysis. First, it is shown that, while a Beveridgean system (α ¼ 0) is always chosen in a homogeneous society, a Bismarckian system (α ¼ 1) may be adopted in a society composed of both farsighted and myopic individuals. Second, the generosity of the pension system (τ) is not a monotonic function of the proportion of myopic individuals, as one would expect. The reason is that the type of the pension system may endogenously switch when the proportion of myopic individuals in society is altered. 2.4.6 Other Dimension of Individual Heterogeneity: Differing Life Expectancies Income heterogeneity is certainly not the only dimension in which individuals differ within each cohort. Differences in life expectancy also play a key role when analyzing the design of pension systems and their political support. We have seen in the previous sections that the redistributiveness of the pension system has an impact on its political support: a redistributive system is likely to be supported by the poor and middle-class workers. It should be p

Diamond (1977) emphasized the need for the state to provide a mandatory pension system stemming from the fact that individuals may be myopic and do not save adequately for their retirement.

The Political Economy of Population Aging

clear that a pension system that provides annuities also redistributes from the short-lived to the long-lived. For instance, Coronado et al. (2000) and Liebman (2001) in the US case and Bommier et al. (2006) in the French case have shown that part of income redistribution operated by the pension system is neutralized by mortality differentials. Bommier et al. (2006) also estimated that in France, differential mortality offsets between one-fourth and one-half of aggregate redistribution. Consequently, longevity is one of the many dimensions, other than productivity, which should affect the design of pension schemes. De Donder and Hindriks (2002) consider a model in which individuals differ both with respect to productivity and mortality rate. They analyze how the political support for social security depends on the link between contributions and benefits (characterized by the parameter α in the previous sections). Their main finding is that tightening the link between contributions and benefits may lead the median voter to raise the equilibrium contribution tax rate, thereby increasing the distortions associated to the social security program. Borck (2007) also considers individuals heterogenous in income and longevity. He assumes a positive correlation between the two and finds that, depending on the magnitude of this correlation, individually optimal tax rates may increase or decrease with income. Cremer and De Donder (2016) extend these works by endogenizing through a majority vote the Bismarckian factor (α).

2.5 Risk-Sharing In a dynamically efficient economy, a FF system provides a higher return than PAYG in expectation. However fluctuations in the interest rates make investments in the FF system risky. In the absence of private markets for insurance, the PAYG may constitute an insurance device. This occurs when the returns to capital and wages are imperfectly correlated. This argument has been formalized by Bohn (2001) and Krueger and Kubler (2006). We present here a simple version of the model by Krueger and Kubler (2006). In the following simplified version, agents live two periods but value consumption in the second period only, according to the utility function u(.). The indirect utility function writes: V ðτÞ ¼ E ðu½ð1  τÞwR + τwGÞ, where R and G are the (stochastic) returns of savings and PAYG, respectively, and E(.) is the expectation operator. It is welfare improving to introduce a PAYG system if dV =dτjτ¼0 > 0. With a logarithmic utility function and a joint log-normal distribution for R and G, this condition reduces to:   G EðGÞ ½cvðRÞ2 + 1 E > 1, ¼ R EðRÞ ½ ρG, R  cvðGÞ  cvðRÞ + 1 where cv designates the coefficient of variation and ρ the correlation coefficient. This condition can be met even when the expected return from PAYG is lower than the

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return of savings. This occurs if the stochastic savings returns are very volatile (cv(R) is large) or the correlation between G and R is small.

3. ENDOGENOUS RETIREMENT Pensions systems are characterized by three key parameters: the payroll tax rate, the benefit level, and the retirement age. So far, we have considered the retirement age to be given and common to all individuals. We address in this section the endogenous determination of the retirement age and envisage two main modeling assumptions: either the retirement age is chosen collectively through a vote; or individuals decide freely when to retire.

3.1 Implicit Taxation and Early Retirement 3.1.1 The Political Support for Early Retirement Provisions In the last 30 years, most OECD countries have experienced a dramatic drop in the labor force participation of their middle-aged and elderly workers. In the OECD countries, the average labor force participation rate of male workers aged between 55 and 64 years has decreased from 84.2% in 1960 to 66.8% in 2015. The extent to which male elderly workers have decreased their participation in the labor market may also be captured by the reduction in the average retirement age. A comprehensive study on 11 OECD countries edited by Gruber and Wise (1999) suggests that generous early retirement provisions are largely responsible for this drop in the (male) participation rates. Gruber and Wise (1999) and a parallel study by Blondal and Scarpetta (1998) identify two features of the early retirement provisions, which display a strong correlation with the departure of the elderly workers from the labor force: the early (and normal) retirement age and the tax burden which is imposed on the labor income of the individuals who continue to work after reaching the early retirement age. Gruber and Wise (1999) and Blondal and Scarpetta (1998) argue that individuals are often induced to retire early because of the large implicit tax imposed on continuing to work after early retirement age. Individuals’ early retirement decision thus represents the optimal response to the economic incentives provided by the social security system. Conde-Ruiz and Galasso (2003) develop a positive theory of why early retirement age provisions have been introduced in the first place and sustained over time. They analyze a majority voting game over two dimensions: the payroll tax rate and the decision to introduce or not an early retirement provision. Focusing on the (simultaneous) issue-byissue voting equilibrium,q they show that early retirement is sustained by a coalition of the q

The political process being multidimensional, there is no Condorcet winner (Plott, 1967). A possible solution is to determine the issue-by-issue voting equilibrium (Shepsle, 1979). This consists in deriving the voting equilibrium on each policy (for given the other policy). The full equilibrium is then given by the intersection point of these reaction curves.

The Political Economy of Population Aging

young poor and of the old with an incomplete earning history. The latter obviously sustain the system as it makes them eligible for pension benefits. The former vote for early retirement because, due to substitution effects between leisure and consumption, they tend to retire earlier than the rich. It should be noted that the equilibrium is self-sustained over time (or subgame perfect) as, by retiring earlier, the current poor young will continue to sustain the system when becoming old. In a subsequent paper, Conde-Ruiz and Galasso (2004) note the (negative) macroeconomic consequences of early retirement provisions which, by inducing individuals to retire earlier, depress human capital accumulation and growth. 3.1.2 The Implicit Taxation on Continued Activity Gruber and Wise (1999) point a second feature of social security, besides the existence of an early retirement age, that induces individuals to retire early: the implicit tax on continued activity created by the pension system. When an individual decides to work one more year, he is deprived of one year of pension benefits. Furthermore he has to pay social security contributions for that year. Increased pension benefits and decreased contributory taxes represent the net social security accrual. When it is negative, the pension system encourages early retirement through an implicit taxation on continued activity. In the words of Crawford and Lilien (1981), the pension system is not marginally fair. Sheshinski (1978) and Crawford and Lilien (1981) were the first to analyze the individual retirement decision. They show that the income and substitution effects of the implicit tax on continued activity go in opposite directions. Leisure being a normal good, the loss in income generated by the tax induces individuals to work longer. But, faced with a lower price of leisure in terms of consumption, they tend to substitute leisure for consumption, ie, to retire earlier. Under the common assumption that the substitution dominates the income effect, the implicit taxation built in the pension system encourages individuals to retire earlier. We present here the model by Crawford and Lilien (1981). They consider a continuous time model in which individuals work for time 0 to R and then retire from R to T. Assuming for simplicity no time discounting, life cycle utility is: Z R Z T Z T uðct Þdt + ½uðct Þ + vdt ¼ uðct Þdt + ðT  RÞv, 0

R

0

where v is the utility of leisure. Normalizing wage income to 1 and assuming a zero interest rate and a perfect capital market, individuals wish to equalize consumption in all periods. Thus, the worker’s problem can be written as max TuðcÞ + ðT  RÞv R, c subject to

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Tc  Rð1  τÞ + ðT  RÞp: Social security benefits obey the following formula: p ¼ ½ðT  Rð1  BÞÞA + RBτ=ðT  RÞ: For B ¼ 1, social security is marginally fair. For B ¼ 0, benefits per period are constant, p ¼ A. In such a case, the pension system implicitly taxes individuals: those who work one more year not only have to contribute for that year but also lose one year of pension benefits. Substituting this formula into the constraint of the individual optimization problem yields: c  ðR=T Þ½1  ð1  BÞðA + τÞ + A: Assuming an interior solution, the conditions for a solution of the individual program are: u0 ðcÞω ¼ v and c ¼ ðR=T Þω + A, where ω ¼ 1  (1  B)(A + τ) is the relative price of leisure in terms of consumption. Differentiating these conditions, we obtain:   dR R T u0 ðcÞ ðA + τÞ: ¼ + dB ω ω2 u00 ðcÞ An increase of B raises the implicit price of leisure, with an ambiguous effect on R. There is a substitution effect, Tu0 (c)(A + τ)/ω2u00 (c), which tends to delay retirement; and an income effect, R(A + τ)/ω, which acts to induce earlier retirement. If we make the usual labor supply assumption that the substitution effect of a shift in wages dominates the income effect, then dR/dB > 0. Casamatta et al. (2005) develop a model with no income effects. The pension benefit formula is such that total benefits do not depend on the age of retirement. An implicit tax, or bias, is however present in the form of the contributory tax. They prove the existence of an issue-by-issue voting equilibrium with a positive bias. The bias is sustained by the poor (both young and old) who benefit from the (intragenerational) redistribution of the system. Numerical simulations show that the bias chosen at the political equilibrium might be excessive with respect to the second-best optimum. Casamatta et al. (2006) distinguish between the two components of the implicit tax: the payroll tax rate τ and the reduction in pension rights, represented by a parameter α. When α > 0 (resp. < 0), pension rights decrease (resp. increase) with the retirement age. They show that individuals prefer α < 0, as well as a Rawlsian or Utilitarian planner. A positive tax is however possible when the planner maximizes a weighted sum of utilities

The Political Economy of Population Aging

and the weight on the rich is sufficiently high, which corresponds to a political process biased toward the rich. This is indeed the outcome of a “bargaining” process between the poor and the rich. These latter ask for a low τ. In exchange they accept to set a positive α, which is a second-best instrument for the poor to redistribute income. Leroux (2010) considers a model in which individuals differ according to longevity. She studies first a pension system with the retirement age uniformly set by the government. In such a setting the PAYG pension system receives the support of the majority of the voters only if the distribution of longevities is left-skewed. The intuition is clear : as the pension system redistributes from the short-lived (with below average longevity) to the long-lived (above average), it receives the support of the majority of the voters if the median longevity is larger than the mean. She then allows the individuals to decide freely when to retire and finds that voluntary retirement reduces the size of the system (characterized by the payroll tax rate), as the taxation of labor income now generates distortions on the retirement decision. She finally analyzes the impact of an increase in longevity on the majority voting equilibrium tax rate: the median voter having a larger life duration, he chooses a larger tax rate. Leroux (2010) shows that this increase in the payroll tax rate is accompanied by a rise in the pension benefit level.

3.2 Voting on the Retirement Age 3.2.1 One-Dimensional Voting Lacomba and Lagos (2007) study the one-dimensional vote on the retirement age, mandatory and common to all individuals, while other parameters of the pension system (payroll tax rate, benefit level) are held fixed. The main insight of their analysis is to emphasize the dependency of individually optimal retirement ages on the status quo retirement age. If the status quo retirement age is low, individuals anticipate to receive a small pension for a long period of time and therefore tend to save a lot. Therefore an individual who is close to the (current) retirement age at the time of the vote has accumulated a large wealth. Due to the associated income effect, he will tend to favor a lower retirement age than a young individual at the start of his working life. In the words of Lacomba and Lagos, the status quo retirement age “acts like a magnet.” While Lacomba and Lagos (2007) consider individuals with different income levels, we present here a simplified version with only age heterogeneity (wage income is normalized to 1). Population is assumed to be constant and age uniformly distributed on ½0,T . The interest rate is assumed to be 0 and individuals do not discount the future. The vote on the legal retirement age takes place at an arbitrary moment of time t. It is unanticipated and the newly voted retirement age is believed by everybody to remain permanent. Denoting Rsq the retirement age before the vote, accumulated wealth of an aged a worker at the time of the vote is

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πðaÞ ¼ að1  τ  cðRsq ; 0ÞÞ, where c(Rsq; 0) is planned consumption at the beginning of the life cycle when the anticipated retirement age is Rsq:r Rsq ð1  τÞ + ðT  Rsq ÞpðRsq Þ cðRsq ; 0Þ ¼ : T Substituting this expression in the former, we get:   T  Rsq πðaÞ ¼ a ð1  τ  pðRsq ÞÞ: T The level of pension benefits, for given τ and R, is determined by the budget constraint of the pension system: τR : T R Replacing p(Rsq) in the previous expression gives   Rsq : πðaÞ ¼ a 1  τ  T pðRÞ ¼

Accumulated wealth thus depends on age, life expectancy, the payroll tax rate, and the status quo retirement age. We now turn to the preferred retirement ages of the different individuals. 3.2.1.1 The Retirees

It is assumed that the retirees do not return to work if the newly voted retirement age is lower than their age. Therefore postponing the retirement age is always favorable to the retirees, as the number of contributors increases and there are fewer retirees who receive a pension. This implies that the retirees always vote for the largest possible retirement age. 3.2.1.2 The Workers

First of all, it is clear that the workers never prefer a retirement age lower than their own age. We therefore have R*(a)  a, where R*(a) is the optimal retirement age of an aged a worker. Indeed choosing R*(a) < a or R*(a) ¼ a in both cases results in these individuals being on retirement. But in the second case the dependency ratio is lower, meaning a higher level of pension benefits. The optimal consumption decision of an aged a individual when the retirement age is R is: r

Remind that, with a 0 interest and discount rates, individuals optimally choose a constant stream of consumption.

The Political Economy of Population Aging

ðR  aÞð1  τÞ + ðT  RÞpðRÞ + πðaÞ T a R  að1  τÞ + πðaÞ ¼ T a R  ða=T ÞRsq , ¼ T a and his indirect utility function: cðR; aÞ ¼

(7)

V ðR; aÞ ¼ ðT  aÞuðcðR; aÞÞ + ðT  RÞv: The first-order condition on R is u0 ðcÞ  v ¼ 0:

(8)

Differentiating, this implies @R Rsq  R ¼ if R ðaÞ > a: @a T a Then two cases are possible (see Fig. 1). Either R*(Rsq) > Rsq, in which case optimal retirement ages decrease with age, or R*(Rsq) ¼ Rsq and the converse holds. The status quo retirement age acts as a magnet: as workers get older, their optimal legal retirement ages are closer to the status quo age. The reason is the following. Denote   R ¼ R ð0Þ the optimal retirement age at birth. Consider the case where R > Rsq and sup pose that all the workers have the same optimal retirement age: R ðaÞ ¼R . In such a case, optimal consumption levels would be increasing with age (simply differentiate (7) with respect to a). But this would violate the first-order condition (8), which implies that,

Fig. 1 Optimal retirement ages of the workers.

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at their optimal retirement age, all the workers have the same consumption level. To attain this optimal consumption level, older workers vote for a lower retirement age. In less technical terms, older workers, under the status quo retirement age, have overaccumulated with respect to the newly born. They thus vote for a lower retirement age to achieve the desired life cycle consumption level. A symmetric reasoning can be made for the case  R < Rsq . 3.2.1.3 Aggregation of Preferences Through Majority Voting

It can be shown that preferences are single-peaked, implying the existence of a Condorcet winner. If optimal retirement ages increase with age, a coalition of the retirees and middle-age workers will join to support a higher retirement age. For decreasing optimal retirement ages, the retirees will form a coalition with the youngest workers. 3.2.1.4 Population Aging

Lacomba and Lagos (2006) analyze the impact of a change in the fertility rate on the optimal retirement age of individuals at the beginning of the life cycle. We present here a simplified two-period model, in which individuals spend a fraction 1  z of the second period on retirement (z is thus interpreted as the retirement age).s Life cycle utility is   uðcty Þ +β uðcto+ 1 Þ + vð1  zÞ ¼uð1  τ  sÞ + β½uðsð1 + rÞ + zð1  τÞ + pð1  zÞÞ + vð1  zÞ, where β ¼ 1/(1 + r). Assuming a perfect capital market, individuals equalize first- and second-period consumptions: ð1  τÞð1 + r + zÞ + pð1  zÞ 2+r and the optimal retirement age solves c¼

max z

(9)

2+r 1 uðcÞ + vð1  zÞ: 1+r 1+r

The budget constraint of the PAYG system is N y τ + N o zτ ¼ N o ð1  zÞp , τð1 + n + zÞ ¼ ð1  zÞp: In a defined contribution (DC) pension system, the pension benefit level depends on the value of the tax rate: s

Contrarily to the continuous time model analyzed above, we consider nonzero discount and interest rates, denoted, respectively, β and r.

The Political Economy of Population Aging

pðτÞ ¼

τð1 + n + zÞ ð1  zÞ

while in a defined benefit (DB) system, this is the tax rate that adjusts: τðpÞ ¼

ð1  zÞp : ð1 + n + zÞ

Using (9), we obtain cτ ¼

1 + r + z  τðr  nÞ 2+r

(10)

and 1+r +z cp ¼

ð1  zÞp ðr  nÞ ð1 + n + zÞ , 2+r

(11)

where cτ and cp are the optimal consumption levels in the defined contribution and defined benefit systems, respectively. The impact of a change in the retirement age is different in a DB or in a DC system, unless r ¼ n. It can indeed be shown that: @c τ 1 ¼ @z 2 + r and

" # @c p 2+n ¼ 1+p ðr  nÞ =ð2 + rÞ: @z ð1 + n + zÞ2

The change in consumption in a DC system is “neutral”: if individuals work one more year, their lifetime consumption increases by 1/(1 + r).t The change is however not neutral in a DB system. As soon as r > n, consumption increases by more than the change in income. The reason is that when p is fixed, total pension p(1  z) is reduced when individuals postpone retirement. This means that the amount of resources devoted to the PAYG system (the “size” of the system) decreases. These resources can be invested at a better return in private savings when r > n. Observe also that the optimal retirement age differs in DC and DB. This latter is the solution of the first-order condition: ð2 + rÞ

t

@c 0 u ðcÞ  v ¼ 0: @z

Lifetime consumption is c + c/(1 + r) ¼ c((2 + r)/(1 + r)).

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Looking at conditions (10) and (11), it is clear that @cτ/@z < @cp/@z (as soon as r > n) and thus that the optimal retirement age is larger in a DB system. The reason for such a difference between the two systems is that the DB system is biased in the sense that the net pension wealth p(1  z)  τz (equal to τ(1 + n) from the budget constraint) varies with z. In a DC system on the contrary it is fixed and depends on the chosen value of the contribution rate τ. The impact of a change in the population growth rate in a DC system is straightforward: @z* τu00 ðcÞ 1 ¼ < 0: @n Dz 2 + r The intuition is simple. Due to a drop in the fertility rate, the PAYG system has a lower rate of return. Therefore, lifetime consumption is reduced. Leisure being a normal good, individuals choose to postpone retirement to counter this (negative) income shock. One can show (after quite tedious calculations) that the same conclusion holds in a DB system: the optimal retirement age is decreasing with the rate of population growth. 3.2.2 Joint Determination of the Retirement Age and the Contribution Rate Galasso (2008) considers the joint determination of the size of the PAYG system (given by the contribution rate) and the retirement age through an issue-by-issue voting procedure. He calibrates the model on economic data for the year 2000 in various OECD countries and uses forecasted values to construct the politico-economic equilibrium in year 2050.u Due to population aging and absent any political reaction (ie, for unchanged contribution rate and retirement age), the economy has to adjust: pension benefits drop and individuals increase their savings, making the stock of capital larger. As a consequence, wages increase and the interest rates fall dramatically. These aggregate effects are dampened when political reactions are taken into account. The political equilibrium is given by the intersection of two reaction curves: τ(R), the majority voting tax rate for a given retirement age and R(τ), the majority voting retirement age for a given tax rate. To understand the impact of population aging, one thus need to analyze how each of these reaction curves is affected by aging. How does the majority voting tax rate react to population aging? For a given retirement age, population aging is known to have two opposite economic and political effects on the determination of the contribution rate (see Casamatta et al., 2000; Razin et al., 2002; Galasso and Profeta, 2004, 2007).v The political effect is positive: the median voter u

v

See Section 6.2.2 for a quantitative assessment of the effects of aging when contribution rates and retirement age are voted upon at the same time, on a model very similar to the one discussed here. These effects have been studied in Section 2.2.2.

The Political Economy of Population Aging

being older, he chooses a larger tax rate. The economic effect is however ambiguous and depends on the comparison of an income and a substitution effect. Simulation results reported in Galasso suggest that the political push dominates in all countries: aging shifts the reaction function τ(R) upward. What is the effect of aging on the majority voting retirement age? Again, one should compare an economic and a political effect. The economic effect has been studied in the previous section: aging reduces the average profitability from social security, which generates a reduction in the lifetime income of all generations. This negative income effect encourages individuals to postpone retirement. The political effect is however ambiguous: the analysis in Section 3.2.1 suggests that, the median voter being older, he may choose a larger or lower retirement age, depending on the status quo retirement age. In the numerical simulations presented by Galasso (2008), aging generates a political push for postponing retirement: the reaction function R(τ) shifts upward. Two main insights emerge from this simulation exercise. First, the retirement age increases dramatically in all countries. As emphasized above, the income effect associated to aging pushes for delaying retirement. This is reinforced by the economic consequences of aging: the opportunity cost of retiring, as represented by the wage rate, increases. Second, in all countries but Italy, both the contribution rate and the level of benefits increase. The rise in the contribution rate is not that surprising: in the face of aging, individuals must invest more in social security to maintain a decent level of retirement consumption. Moreover the interest rate is lowered, reducing the gap between the profitability of savings and PAYG social security. The increase in the level of benefits is more surprising. While it is difficult to disentangle the various effects at play in these numerical simulations, the aging of the median voter, and the associated increased demand for social security, is certainly one of the main reasons driving this result.

4. THE SOCIAL CONTRACT 4.1 Sustainability of the PAYG System In the Browning analysis and subsequent papers on the vote over pensions, it is assumed that agents vote once and for all. This assumption, while convenient, is strong. Why young individuals should support the system, if the tax rate is re-voted tomorrow and there is therefore no direct link between the contributions they make and the benefits they receive? The answer is that there exists an implicit contract between generations: the young support the system because of the threat to be punished by future generations. If they break down the system, they incur the risk of receiving no pension benefits in old age (although of course they could rely on savings). This idea has been first formalized by Hammond (1975) and then adapted to the pension game by Sjoblom (1985) and Boldrin and Rustichini (2000).

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To illustrate the argument, we consider an infinitely repeated voting game with individuals living two periods. Assuming a positive rate of population growth, the young are more numerous than the old and therefore are decisive in the vote. Indirect life cycle y utility is denoted vt ðτt , τt + 1 Þ. w Consider the sequence of tax rates ðτ i Þ∞ i¼1 and the strategies if τsi ¼ τ si for all i ¼ 1,…, s  1 τ y σs ¼ s 0 otherwise: The social contract prescribes the choice of τ i . According to this strategy profile, young individuals comply with this implicit contract if everybody has done the same in the past. Otherwise, they break the contract by choosing a 0 tax rate. Denote ðvi Þ∞ i¼1 the resulting payoffs for the young. We have to check two conditions to obtain a subgame perfect equilibrium. 1) No player should want to deviate in any time period. The best deviation for a young in period s is to choose τs ¼ 0. By choosing a tax rate different from τ s , he breaks the contract and receives no pension. He has therefore no interest in contributing to the system. Consequently, if vs  vsy ð0,0Þ, a young individual has no interest in breaking the contract. 2) Subgame perfection: if player t deviates, player t + 1 must have an incentive to punish him. Because once a player has deviated, the system is permanently abolished, player t + 1 will receive no pension and should thus not contribute: punishment is credible. This leads to the conclusion that the strategies above constitute a subgame perfect equilibrium as soon as vs  vsy ð0,0Þ, 8s. This condition simply states that the young are better off with the social security system implemented. It is satisfied in the different cases described in Section 2.x It should however be kept in mind that there exist many other equilibria.y This game thus generates a high degree of indeterminacy.

4.2 Dynamics of the Political Equilibrium In the recent historical experience of many countries the immediate cause for the general alarm surrounding the social security system seems to be the long run fall in the growth rates of population and labor productivity. Boldrin and Rustichini (2000) show that, even if one knows that the PAYG system will be dismantled in a finite future and therefore that some generation will contribute to it but will never receive any benefit, this system can be sustained by a majority of the voters. This follows from introducing in the previous game w

x y

Players of this game are generations of individuals. In other words, it is assumed that there exists a coordination mechanism for individuals belonging to any given generation. This equilibrium could easily be extended to the case of three generations analyzed by Browning (1975). In particular, no social security is always an equilibrium: if a player believes that the following generation will not contribute, it is optimal not to contribute, even if it is Pareto improving that every generation contributes.

The Political Economy of Population Aging

a stochastic process for the growth rate of population. They consider a sequence of growth rates fnð jÞg∞ j¼0 satisfying n( j + 1) < n( j), for all j, and lim j!∞ nð jÞ ¼ 0, and a transition probability Prðnt + 1 ¼ nð jÞjnt ¼ nð jÞÞ ¼ 1  p Prðnt + 1 ¼ nð j + 1Þjnt ¼ nð jÞÞ ¼ p, with 0 < p < 1. With a linear production function, f(k) ¼ ak + b, and logarithmic utility, they show that there exists an equilibrium with a sequence of tax rates fτð jÞg∞ j¼0 , such that τ( j) > 0 for some j and τ( j + 1) < τ( j) for all j. This means that a PAYG is sustainable even though one knows that it will be dismantled for sure in the future (but not when). The condition for having this equilibrium is a < (1  p)(1 + n0). Noting that a ¼ 1 + r in this model, the intuition is clear: even though there is a risk of not receiving pensions in the next period, the expected return of the PAYG system dominates private savings (as long as a < (1  p) (1 + nt)).

4.3 Markov Perfect Equilibria The game described in Section 4 has many equilibria. Furthermore, it is quite poor in making predictions and does not allow to do comparative statics. A way to select among these equilibria is to consider the concept of Markov perfect equilibrium. A Markov strategy is such that the action played in a given period only depends on some fundamental state variables, such as the level of the capital stock or the ratio of the number of retirees to workers.z This approach has generated a considerable interest in the last years. We review in the next sections the main work in this direction. 4.3.1 A Median Voter Model with Capital as the State Variable Forni (2005) has developed a model close to Boldrin and Rustichini (2000). It is a standard two-period OLG model. Agents work, consume, save, and pay taxes in the first period. They retire, consume, and receive old-age benefits in the second one. A logarithmic utility function is assumed, as well as a Cobb–Douglas production function: Y ¼ KαL1α. In per capita terms: y ¼ kα with k ¼ K/L. It is assumed that capital depreciates completely in one period. The utility maximization program of a young agent in period t is: max uðcty , cto+ 1 Þ ¼ ln ðcty Þ + β ln ðcto+ 1 Þ y

ct , cto+ 1

subject to z

See Fudenberg and Tirole (1991) for a precise definition of Markov equilibria.

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cty ¼ wt ð1  τt Þ  st cto+ 1 ¼ st ð1 + rt + 1 Þ + pt + 1 : Given the Cobb–Douglas production function, the profit maximizing conditions imply that: wt ¼ ð1  αÞkt

(12)

rt + 1 ¼ αkα1 t + 1  1:

(13)

and

The budget constraint of the PAYG system also implies: pt + 1 ¼ τt + 1 wt + 1 ð1 + nÞ:

(14)

With a logarithmic utility function, the utility maximization program has closed-form solutions:    1 pt + 1 y (15) wt ð1  τt Þ + ct ¼ 1 + rt + 1 1+β   β o ct + 1 ¼ ½wt ð1  τt Þð1 + rt + 1 Þ + pt + 1  (16) 1+β    1 pt + 1 st ¼ : (17) βwt ð1  τt Þð1 + rt + 1 Þ  1 + rt + 1 1+β The last equilibrium condition is the capital formation dynamic equation: ð1 + nÞkt + 1 ¼ st :

(18)

Collective decisions are made through majority voting. The young being more numerous than the old, they decide on the payroll tax rate in each period. Strategies are assumed to be Markov and moreover to be time-invariant: the policy function is of the type τt ¼ τ(kt). In words, the payroll tax rate chosen in period t only depends on the capital stock in this period. Using the optimality conditions (12), (13), (15)–(17) as well as the PAYG budget constraint (14), we can write the indirect utility function of the young in period t as  Ψ ðkt , τðkt Þ, τ ðkt + 1 ÞÞ. This depends on the capital stock in periods t and t + 1, on the policy function chosen in period t, τ(.), and on the expectation on the next period policy  function, τ ð:Þ. The optimal strategy of the median voter in period t (a young) solves the following program: 

max Ψ ðkt , τðkt Þ, τ ðkt + 1 ÞÞ,

0 τt ¼ τ, people retire earlier, zt + 1 < zt ¼ z, and the per capita pension is unaffected, pt + 1 ¼ pt ¼ p. At steady state, the contribution rate is larger, τ 0 > τ, implying z0 < z. This political economy analysis thus suggests that aging will lead to a larger social security system and more early retirement. This result was however obtained with a quasi-linear utility function with only substitution effects on labor supply taken into account. Conde-Ruiz et al. (2013) note that the introduction of income effects may mitigate these results: the loss of income following the drop in the PAYG rate of return induces individuals to work more and therefore to postpone retirement.

5. THE TRANSITION TO A FULLY FUNDED SYSTEM Previous sections considered only parametric reforms of the PAYG system that is modifications of the parameters that characterize the pension system. By contrast, systemic reforms change the very nature of the pension system: this is the case for transitions toward a FF system, where current contribution is saved to provide for benefits later in the life cycle. Due to the drop in fertility rates, population grows at a slower rate. This implies a lower rate of return for the PAYG system. Therefore many believe that it is desirable to move to a FF system. The mere comparison of steady states is however misleading. It has been shown that, absent labor supply distortions, the transition to a FF system cannot be Pareto improving (Breyer, 1989): when moving to the FF system, the implicit debt of the PAYG system is simply made explicit; the PAYG system is nothing more than an intergenerational redistribution scheme. In other words, some generations gain from the reform but others lose. Only when there are some labor market distortions, the reform can yield a Pareto improvement (Homburg, 1990; Breyer and Straub, 1993; Rangel, 1997). We illustrate this argument with a simple two-period representative agent OLG model in a small open economy. We denote Nty and Nto the number of young and old individuals in period t. Population grows at a constant rate n, so that Nty ¼ ð1 + nÞNto . Wages are assumed to be constant (normalized to 1). Consider a steady state with a constant contribution rate τ and constant labor supply l. The PAYG pension benefit in this steady state is: ppayg ¼ τlð1 + nÞ:

The Political Economy of Population Aging

Clearly, if r > n, individuals would be better off in the steady state with a FF system in which they invest τl in every period. Their payment when young would be the same, namely τl, and the pension benefit level would be: p ff ¼ τlð1 + rÞ: However this is not the answer to the question we are interested in. We wish to know whether, starting from a steady state with a PAYG system, it is possible to operate a transition to a FF system that improves the welfare of all generations. We now show that it is possible to make the transition in a Pareto-neutral way. Consider a reform that occurs at time T. With a fixed labor supply l (normalized to 1), the mechanism to obtain a welfare-neutral transition is the following. The retirees at time T receive the promised pension p payg so that they are indifferent between reforming the pension system or not. This pension is financed by a mix of time T workers contributions and government debt. The new contribution rate at time T is such that: τ T ¼ τ  p payg =ð1 + rÞ 1+n : 1+r Suppose that the government borrows NTy τð1 + nÞ=ð1 + rÞ in period T and that the time T workers invest τ(1 + n)/(1 + r) in the FF system. Their pension in period T + 1 is thus τ(1 + n) ¼ p payg and their payment in period T is τ T + τð1 + nÞ=ð1 + rÞ ¼ τ. They are thus indifferent between the PAYG and the FF system. Suppose now that time T + 1 workers pay a tax to reimburse part of the government debt. This tax is: ¼ττ

1+n : 1+r Moreover they invest τ(1 + n)/(1 + r) in the FF system. Their total payment when young is thus τ and their pension benefit when old (in period T + 2) is τ(1 + n) ¼ ppayg. Therefore generation T + 1 gets the same life cycle utility as in the initial steady state with the PAYG system. The government needs to borrow the difference between its debt, y y NT τð1 + nÞ=ð1 + rÞ, and the taxes paid by the young in period T + 1, NT + 1 τ T + 1 . This y difference is equal to NT + 1 τð1 + nÞ=ð1 + rÞ. This process can be repeated infinitely with all generations having the same welfare level in the initial steady state with the PAYG system and in the new one with the FF system. We thus have presented a Pareto-neutral transition to a FF system when labor supply is fixed. This suggests that no Pareto improvement is possible (the reader can refer to Breyer (1989) for a formal proof ). What happens when labor supply is endogenous? It should be noted that the tax rate in the new scheme, τ t , is lower than τ. This implies that the new scheme is less distortive τ T + 1 ¼ τ  τ

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and that it is therefore possible to use this efficiency gain to raise strictly the welfare of all generations. Homburg (1990) goes even further by noting that these efficiency gains can be used to reimburse the government debt in finite time. It is thus possible to completely abolish PAYG and to restore the economy’s net wealth to the level which is associated with a pure capital reserve system. Conesa and Garriga (2008) use these results to construct numerical simulations in which all generations benefit from the reform (transition generations receive no pension but are compensated with a debt-financed transfer).ac They however consider a representative-agent economy. When individuals differ with respect to labor income within cohorts, efficiency gains have to be compared to the insurance benefit of the PAYG system (Conesa and Krueger, 1999; Nishiyama and Smetters, 2007).

6. QUANTITATIVE ANALYSIS 6.1 Empirical Estimations Several empirical estimations of the relationship between the age structure of population and the share of income devoted to pension programs—and other types of social spending as well—have been conducted in recent years. We detail their most salient features hereafter. Lindert (1994) provides a long-term, historical point of view on the link between aging and pension transfers, by providing panel estimates on industrial countries for the period 1880–1930. The role played by demographics to explain the rise in social spending over the period is measured, including controls for income levels and growth, political determinants (indicators of democratization, women’s suffrage, rate of executive turnover), and religious affiliation. He shows that the share of population aged 65 and more had a positive impact on the share of GDP devoted to total social spending (a notion that encompasses all social transfers such as pensions, health care; and educational spending): this type of evidence concurs with the insight that longevity should induce an increase in total spending (and thus taxation). The effect on social transfers only is also positive. On the contrary, the share of population aged between 20 and 39 has a significant negative impact on the share of social transfers in GDP. The main results are confirmed in a similar analysis of the 1960–1980 period by Lindert (1996): over this period, a higher share of older people in the total population exerts a positive impact on the share of GDP spent on pensions, while the share of school-age individuals does not affect significantly the share of educational spending on GDP. We also briefly mention Durevall and ac

Before them, all quantitative analyses have found welfare gains in the long run, but losses for the transition generations. Conesa and Garriga (2009) follow the same optimal taxation approach. They however do not address the question of the transition to a FF system, but maintain the PAYG system and look for the optimal adjustment of its parameters following a temporary demographic shock.

The Political Economy of Population Aging

Henrekson (2011) as a more recent analysis of the relationship between social spending and the age structure of the population based on long-run historical data. Breyer and Craig (1997) conduct an analysis on 20 OECD countries over the 1960–1990 period, using pension spending over GDP or average pension per capita as dependent variables. Among the explanatory variables, the age of the median voter in each country and the ratio of the population aged 40–60 to the elderly are meant to capture the effects of aging. A strong and significantly positive effect of the age of the median voter on the size of pension programs is found in all specifications. The estimate implies that an increase in median voter age by one year would lead to a 0.5% increase in the share of social security payments to GDP, to be compared with a sample mean of 9% for this variable. The support ratio (reduced to the 40–60 age group for the numerator) has a negative effect on pension program size, when it is added into the regression. Another paper also using OECD panel data, Sanz and Velazquez (2007), indicates that public spending in several areas of government (social welfare, health, but also education and defense) increases with the share of the elderly of the population. However, benefits per capita are not reported to be affected in any significant way. Profeta (2002) reports similar findings using a large cross-country data set which is not restricted to OECD countries: when the share of elderly in the population increases, total social security expenditure increases. The share of elderly in the overall population has more contrasted effects at the individual level, however: while the average length in retirement is reported to increase, and the labor force participation of the elderly decreases when population ages, the pension annuity is, again, not affected. The empirical relationship between population structure and pension spending has been at the center of a controversy, started by a paper by Razin et al. (2002). They estimate a panel data of the USA and 12 European countries over the period 1965–1992, with the average tax rate on labor income and the per capita transfers (including pensions, unemployment, and disability compensation) as dependent variables. The explanatory variables used are the dependency ratio (measured as one minus the share of labor force in the population), a measure of income skewness, real growth in GDP, and other controls. Both regressions yield a negative impact of the dependency ratio on the dependent variable. Indeed, in the main specification, a 1% increase in the dependency ratio is shown to lead to a 0.4% decline in the labor tax rate: this means that the 4% decline in the dependency ratio that happened over the 1970–1991 period accounts for roughly 1.5% of the 11% increase in the labor tax rate then. Again, all specifications point to a higher dependency ratio, leading to lower per capita government transfers: over the same period, the decrease in the dependency ratio accounts for 30% of the increase in transfers. Razin et al. (2002) also introduce a theoretical model to account for the nonstructural relationships they find. In this two-period OLG model, a single labor tax is used to finance a lump-sum transfer to both generations, which is used by the young to acquire education and by the old as a pension. In this context, while the young want some tax to

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finance their education, the chosen level is limited by the fiscal “leakage” going to the old. Therefore when population growth increases (equivalent in the model to a reduction in the dependency ratio), this leakage is reduced, potentially leading to a higher chosen tax rate if the distortionary effect of taxation is not too strong on the opposite side. The findings of Razin et al. (2002) have been questioned by Bryant (2003), Disney (2007), Simonovits (2007), and Shelton (2008), mostly for the use of the dependency ratio as a measure of population aging. In particular, Disney (2007) proceeds to a new test of the model introduced by Razin et al. (2002) on a data set of 21 countries for the 1970s to 1990s decades, redefining the variables used in the regression: the old-age dependency ratio (defined as the share of 65+ to the 15–64-year-old population) and the inverse of the support ratio (namely, the share of pensioners to people participating to the labor market) are used instead of the simple dependency ratio, and the share of labor taxes in GDP and the average contribution rate to social security. In all specifications, the measures of age dependency are this time positively associated with tax rates, with strong statistical significance in the case of the pension contribution rate: the typical specification indicates that the pension contribution rate paid by workersad would increase by around 0.6% if the oldage dependency ratio were to be increased by 1%, on average. Moreover, by introducing proxies that capture to which degree social security systems link contributions and entitlements, Disney (2007) shows that the positive relationship between aging and tax rates becomes weaker when contributions made by individuals start to match less their future entitlements. In the limit case where current contributions bear no link to future benefits (as is the case in the model by Razin et al. (2002) where decision on tax rates is purely static), this relationship may then be reversed. In practice, though, most pension systems around the world entail some actuarial component.

6.2 Simulating the Future Political Evolution of Social Security 6.2.1 Political Sustainability and the Evolution of the Contribution Rates for the Current Systems Galasso (2006) is, to the best of our knowledge, the only successful attempt so far at simulating the evolution of the social security systems of several key countriesae until 2050, by taking into account both the economic and the political effects of changes in the age structure of population.af To this end, the author builds a closed-economy ad

ae

af

In this paper, the contribution rate is defined as the ratio between the social security replacement rate and the support ratio of the pension scheme, and is meant to measure the share of the average worker’s labor income that needs to be paid to balance the pension scheme. The countries concerned by the simulation exercise are: the USA, the UK, Germany, France, Italy, and Spain. It should be noted that Galasso and Profeta (2004) was actually the first attempt at simulating the politicoeconomic dynamics of social security systems recorded in the literature. However, Galasso (2006) presents, among other things, an updated version of the simulations performed in Galasso and Profeta (2004), which is why we do not report Galasso and Profeta (2004)’s results here.

The Political Economy of Population Aging

model with several overlapping generations of agents that differ in age and education, supply work elastically, save, and consume. The pension system is modeled in such a way that its budget is balanced in each period, with a fixed age of retirement. The other main institutional features of each national system considered are either held fixed across the years or not taken into account, to ensure tractability. This way, policy choices are reduced to a single dimension in each period: by voting on a pension contribution rate τt, all the other features of the system at date t are determined. The equilibrium of the voting game is sustained by stationary strategy profiles as in Section 4, with the median voter (in age but also in education) choosing the equilibrium value of τt in each period. The methodology used to investigate the effects of aging is twofold. First, the author assumes that each economy is initially at steady state at the starting point of the simulations (around the year 2000), and calibrates the model parameters to target the key variables of the economy then (such as the dependency ratio, pension contribution rate, labor force participation, capital-output ratio). In a second step, the author then feeds the model with forecasted values of the relevant economic and demographic variables (among which labor productivity growth, population growth, and median voter age) for the year 2050. The output of the simulations is, for each country and for two different effective retirement ages in 2050 (either unchanged with respect to 2000 or increased to 65 years old), an equilibrium pension contribution rate (which is voted upon) and the corresponding replacement rate. In the words of the author of the study himself, “these simulations give a gloomy picture of the future of social security: under the political constraints imposed by a graying electorate, pension expenditure is forecasted to increase in all countries” (Galasso, 2006, p. 207). In Germany, Italy, and Spain, the (sometimes massive) increase in contribution rates is however not enough to yield higher replacement rates absent any increase in the effective retirement age, due to the extent of aging happening in these countries. Higher replacement rates are achieved in all countries only when the effective retirement age is postponed to 65. Yet, even in this case, most countries see an increase of their contribution rate over the 50-year time span of the simulations, albeit less stark than if the effective retirement age is left untouched. Indeed, for instance, Galasso (2006) computes that postponing the retirement age in Italy or France from 58 (the effective age in both countries at the time of the study) to 65 years would limit the increase in the contribution rate by 11% and 12%, respectively. In Italy, this would even be enough to allow the contribution rate to decrease from 38% to 35.5%, instead of increasing to 46.3% if the retirement age was kept untouched. Interestingly, as the model incorporates savings and capital, the composition of retiree income between private and public pension plans can be computed: it is forecasted that future retirees will rely more on public pension programs than before, probably given to the fact that they are able to extract more resource from the working generations under the new circumstances.

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6.2.2 Political Sustainability with Endogenous Retirement Age Galasso (2006) also tackles the next question that comes to mind:ag since raising the retirement age is the only way to prevent contribution rate hikes from being massive and replacement rates from decreasing sharply, is there a political majority to raise this retirement age in the concerned countries? To answer this question, the author extends the model discussed in the previous section to allow individuals to vote both on the contribution rate and the retirement age. Given that the multidimensionality of the policy space may be troublesome for the existence of a Condorcet winner, the author models the voting process as an issue-by-issue simultaneous voting game, which yields as output of the model a structure-induced political equilibrium (see Shepsle, 1979). Under this setup, it is clear that the age profile of preferences for the retirement age will be similar to the one studied in Section 3, holding the contribution rate fixed. Besides, if the agents are faced with a higher contribution rate, the opportunity cost of retiring will be lower, meaning older agents will vote for a lower retirement age, all else being equal. The author mentions, however, that since “social security is a dominated asset, a higher contribution rate reduces the overall income of the young, hence inducing them to postpone retirement” (Galasso, 2006, p. 215). Moreover, population aging will affect the preferences for the retirement age in the same way as described in Section 3.2.2: the retirement age R voted in equilibrium will then inevitably rise. Quantitatively, the simulations feature rises in the effective retirement age that match almost one-to-one the projected rises in the age of the median voter over the contribution rate dimension. Depending on the severity of forecasted aging, the retirement age is projected to be increased between 5 years (for the USA) and 9 years (for France and Italy) over the study period, thus closing a big part of the initial gap between countries. Notably, the political equilibria in this case feature retirement ages that are systematically above 65 years old, the benchmark used in the previous exercise. This seems to indicate that fears over the sustainability of our pension systems and their capacity to be reformed toward a longer worklife might be overrated. A side effect of this strong increase in retirement age is to mitigate the rise of social security contribution rates (from 9.7% in 2000 to a forecasted value of 13.5% in 2050 for the USA, for instance). Concerning the replacement rate, the results are quite contrasted and depend largely on the scope of aging projected to happen in each country:ah while it is forecasted to decrease from 98.9% to 69.4% in Italy between 2000 and 2050, it is expected to rise by modest amounts in France (from 55% to 63.3%) and the USA (from 40.8% to 46.1%) over the same time period.

ag

ah

Galasso (2008) essentially presents the same model and results, and has already been discussed from a theoretical point of view in Section 3.2.2, to which we refer the reader. Source: Galasso (2008).

The Political Economy of Population Aging

7. THE POLITICAL IMPACT OF AGING ON OTHER PUBLIC PROGRAMS Of course, the most widespread concern linked to aging is the continuous funding of the generous pension programs that have been set up in the second half of the last century, for all the reasons outlined before. Nonetheless, other public programs may also be at stake due to the way in which they are currently funded (when these programs entail transfers from the young to the old generations), or simply because these public programs are not a priority for a graying electorate. In the following section, we review recent developments in the theoretical and quantitative analysis of the political impact of aging on these various policies, which range from education to health care, from environment conservation to the composition of taxes falling on labor and capital.

7.1 Aging and Political Support for Education 7.1.1 Theory 7.1.1.1 With Education Only

In the political economy literature, there seems to have been few attempts at studying the impact of demographic structure on education subsidies. Kemnitz (1999) provides an early example of such an attempt. In his two-period OLG model, the size of subsidies to privately purchased education is chosen so as to maximize a weighted sum of the utilities of the two generations (young and old) living in each period. Results are driven by a rather ad hoc assumption made on these so-called political weights: they are assumed to be an increasing but concave function of the size of each generation. The rationale for introducing such a function is that there may exist larger free-rider problems in bigger groups, when these groups try to organize themselves politically: hidden there is a model of lobbying for public resources. In steady state, it is found that a decline in population growth leads to an increase in education subsidies. When the fertility rate decreases, the decrease in the relative political weight of subsidy recipients is lower than the decrease in their share numbers because of the concavity of the political weight function. Since the relative size of the young with respect to the old is itself linked to the tax price of subsidies, in equilibrium the political costs to the government of subsidizing education fall more than the political gains, and the government is led to increase these subsidies. Gradstein and Kaganovich (2004) incorporate into a two-period OLG model two opposing effects of population aging. On the one hand, aging increases the proportion of older voters, who cannot reap off the benefits of investing into the productivity of the future workforce. On the other hand, the currently working adults, upon which the current tax falls, can expect to benefit from their investment into future labor productivity through an increase in future PAYG pension payments, and increase interest payments on their savings. Gradstein and Kaganovich (2004) find that the second effect dominates in their setup, so that aging should lead to increased education funding. However, by

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introducing a version of this same economy with two geographical districts or constituencies, the authors are able to show that constituencies with a (exogenously determined) higher fraction of elderly would be less willing to finance education, at a given time period. The apparent contradiction in these two results is solved if one considers that in the two-district version of the model, education is financed locally, while productivity increases due to education are transmitted to the aggregate level (through perfect capital mobility between the districts). The discrepancy between the costs and benefits of education finance then explains why districts with more old people are more reluctant to finance public education in cross section, as evidenced by Poterba (1997) (see Section 7.1.2); however, it also shows that cross-sectional evidence has little external validity when one wishes to investigate the effect of population aging on education spending at the aggregate level through time. Levy (2005) brings into the picture the interaction of education policy with general, nonage-related income redistribution. She sets up a model in which agents are not only heterogeneous in terms of age but also in terms of income. It is shown that, all else being equal (and notably the pretax income distribution), a larger young group will lead to decreased education spending, which is crowded out by the untargeted income redistribution. 7.1.1.2 Joint Education and Social Security

Since Rangel (2003) and Boldrin and Montes (2005), the existence of strong linkages between publicly funded education and social security has become obvious, and analysis of these linkages has been extensive since. We believe it is important to understand precisely the nature of these linkages, if one is to be able to make predictions on the impact of aging on both these programs that constitute a large share of public spending. Common features of the models discussed belowai are the necessity of publicly provided education to enhance human capital accumulation, and its beneficial impact on future PAYG pensions through the size of the wage bill, but also on fully funded ones through the increase in the return on savings. The papers discussed below share some additional characteristics which are worth emphasizing: they usually feature a working generation, which is taxed to finance the two types of public transfers (education and pensions), and the generations which benefit from them. The policies determined in equilibrium have two dimensions: the amount of resources spent on each program or, equivalently, the tax rate falling on the ai

We voluntarily omit from the discussion below papers that do not explicitly tackle the impact of aging on policy choices, even though these papers have interest on their own in that they help understanding the existing complementarity/competition at the political level between education and pensions; see for instance Poutvaara (2006), Soares (2006), or Kaganovich and Meier (2012). Additionally, other recent papers (Kaganovich and Zilcha, 2012; Iturbe-Ormaetxe and Valera, 2012), while not focused on exploring the impact of aging on the size of social security, deliver interesting insights into the relationship that exists between the design of social security and political support for public education.

The Political Economy of Population Aging

working generation and a rule to allocate public resources between the two programs. Depending on the model, the political outcome is determined through a vote in which the currently alive generations take part, or results from lobbying from each generation; in case of a vote, the assumption of once-and-for-all voting is usually relaxed, and the two-dimensional nature of the choice to be made sometimes dictates the use of political equilibrium concepts which are alternative to the standard Downsian framework (ie, assuming probabilistic voting, or using structure-induced equilibria). Lancia and Russo (2015) offer a good example of the type of arguments that explain the coexistence of the two policy programs under this setup: even if agents vote in each period on the size of both pension programs and there is no reputational effect linked to dismantling social security in a given period, they show that pensioners manage to extract some pensions from the working generation in equilibrium, and that current workers collectively invest in public education because they know this will pay off in the future in the form of higher pensions for themselves. In terms of forecasts of the impact of aging, these various models typically make a distinction between predictions on the size of each governmental program at the aggregate level, and the actual amounts of transfers which are received by individuals. To the best of our knowledge, Kemnitz (2000) was the first attempt at formalizing the interactions between these two types of intergenerational transfers, and characterizing the policy outcome as that of a game between old and active generations. In this paper, the policy decision is made to maximize the support politicians receive from middle-aged workers and old people, this support being a function not only of their respective numbers but also on their lobbying activities. Lobbying by individuals of a given generation is costly in terms of their current consumption. While the elderly only favor pensions, the current contributors to the system (ie, the workers) favor education finance even though no commitment on future pension benefits is possible, since they anticipate they will in turn be in a position to extract these benefits from their children later in the game. In steady state, population aging is shown to lead to higher per capita income growth: the pension contribution rate increases as a consequence of a decrease in fertility or mortality (through the increased political power of pensioners), which in turn increases the incentives to fund public education to benefit from these higher future pensions. It should be noted, however, that only the amount devoted to education per child is supposed to increase here, but not necessarily the share of national income devoted to education in the case of fertility reduction: education per child might only increase due to the increased effectiveness of public spending. To put it differently, the tax price of spending on education falls when the relative number of children falls, so willingness to fund education increases. Batt
e (2015) also aims at studying how demographic changes impact our collective willingness to finance social security and education. Contrary to other papers, the economy is assumed here to be closed, and the impacts of aging on capital accumulation and

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the relative prices of the different inputs are taken into account explicitly. Another distinguishing feature, common only with Naito (2012), is the existence of intragenerational heterogeneity. Individual preferences for taxation and spending are aggregated through probabilistic voting. Under the assumption of nonstrategic voting between periods, Batt
e (2015) derives predictions on the impact of fertility and mortality rate changes on the level and composition of public spending: in particular, population aging (whatever the cause) points out to a rising tax burden, and thus a bigger size of government. Analytical results fail to unambiguously state which type of policy is likely to be expanded as population ages, but simulations under plausible parameters point out to rising pension and education expenditures as a share of GDP. At the same time, higher expenditures at the level of the whole economy may fail to translate into higher pensions per capita when longevity rises. Gonzalez-Eiras and Niepelt (2007) also study the joint determination of the size of education and pensions, and incorporate the study of capital taxation as well. Their model is calibrated to US data to generate predictions about the effects of fertility decrease and longevity extension on labor supply, labor and capital income taxes, pensions, and human and physical capital investment: the aging of population is found to induce a reallocation of public spending toward excessively large levels of pensions (with a GDP share of retirement benefits going from about 5% in 2005 to 10% in 2075), at the cost of education spending (with the education spending over GDP ratio going from 6% to 5% over the same period of time). This results in the productivity growth of the economy being severely slashed down, due to the endogenous growth component present in their model. Gonzalez-Eiras and Niepelt (2012) build on a standard two-period OLG model with endogenous growth based on physical and human capital accumulation. Its main contribution is to incorporate retirement age as a policy choice. Individuals are successively modeled as young and old adults, and homogenous in dimensions other than age. The young have to determine their labor supply and their choice of savings; a fraction δ of the young get to live to the next period, in which they consume their savings but can also work part-time.aj The share of time spent working while old, denoted ρ (envisioned as a proxy to retirement age policy), is a policy variable as well as τe and τp, the tax rates on labor income used to finance education of the next-generation young and the pensions of the current old, respectively. Preferences on those three policy choices are aggregated assuming probabilistic voting. Population aging is shown to act on policy decisions through different channels. First, population aging, by increasing the political power of the elderly, tends to raise τp but to decrease τe and ρ: elderly voters use their bigger political clout to increase the transfers they receive at the expense of productive aj

It is noteworthy that the effect of fertility is also taken into account here, even though the effects of fertility and longevity cannot be analytically disentangled on a two-period OLG structure.

The Political Economy of Population Aging

investment, while trying to reduce their labor force participation. This effect is countered by the fact that the bigger share of elderly in the population makes it more profitable (from a government finance point of view) to raise the retirement age ρ, which allows to decrease τp and increase τe. Third, increased longevity makes forward investment more profitable for young households, which in turn would tend to increase public investment in education τe. Finally, since there are dynamic linkages between policies at successive periods, future anticipated demographic change can lead to deviations in current policy: this implies that permanent demographic change can lead to nonmonotone dynamics in policies. Based on this analysis, the authors make quantitative predictions for a stylized aggregate of rich OECD economies: it turns out that projected demographic change over the 2000–2080 period would lead to a modest increase in both τp and τe (by, respectively, 2% and 3% of taxable labor income), with a larger increase in ρ corresponding to a 6-year increase in the retirement age (to be put into perspective with the expected 8-year increase in life expectancy over the same period). However, if one shuts down the retirement age adjustment mechanism, the contribution rate for pensions would sharply increase in equilibrium, while the tax rate to finance education would barely decrease over the 2000–2080 time range. Taking into account the possibility to enact changes in the retirement age thus leads to important insights on the future evolution of retirement and education policies, as already outlined in Section 3. Ono (2015) also formulates a three-period OLG model where public education funding and social security coexist as the outcome of a political process. Key distinguishing features are the existence of altruism toward children, and the possibility to invest privately in education (on top of standardized, public education). The model sheds light on the key role of longevity (proxied as usual by an exogenous survival probability into old age δ) as a determinant of these two types of spending. Depending on the relative efficiency of private vs public education, two political equilibria may coexist, one featuring only private education with public spending focusing exclusively on pensions, while the other one is distinguished by no private education spending and positive public spending on education (along with pensions). Population aging (an increase in δ in this setting) induces several effects, which may or may not exist depending on the equilibrium selected:ak first, greater longevity implies middle individuals attach more weight to their offsprings’ acquisition of human capital, implying an increased incentive to invest in private education. Second, an increase in the number of pensioners has the direct political effect of increasing their weight in the political process, hence a tendency to increase pensions at the expense of both types of human capital accumulation. Third, higher survival probability into old age means middle-aged individuals have a greater incentive to enact

ak

Note that the author remains silent on equilibrium selection. Multiplicity of equilibria is only explored to rank policies in terms of human capital accumulation and welfare.

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public education funding for their children, whose human capital they have a higher chance of enjoying later in life. Naito (2012) elaborates on the political linkages between public education and pensions, by setting up a tractable model in which the level of inequality in initial human capital endowments plays a role on the comparative statics with respect to demography. It considers a canonical three-overlapping-generation economy with exogenous and constant fertility rate n, but without mortality. The assumptions on production technology and openness of the economy are such that human capital accumulation is the only source of growth, and provides the only dynamic linkage between policies at different periods. For each individual, human capital is produced using parental human capital and public education. The only policy subject to a vote is the total labor income tax rate τ: the share of tax receipts that goes to education and pensions is assumed to be fixed from the outset. The conflict about policy is here both inter- and intragenerational: as individuals of a same generation differ in their human capital, and since both types of policies redistribute income intragenerationally, the policy outcome reflects the interests of a coalition of poor active workers and retirees against the higher-endowed workers. The author restricts his attention to a subclass of stationary, fully forward-looking Markov equilibria with a constant tax rate τ over time. Interestingly, a rise in the fertility rate n has two opposite effects on the equilibrium tax rate: on the one hand, for a given decisive voter, a rise in n decreases the optimal funding rate for education (mainly because education expenditures have to be shared among more people). On the other hand, when n increases, the old generation loses weight so that the willingness to fund education expenditures increases; this latter effect is shown to be stronger when inequality in human capital is higher. As a whole, it is shown that because of these various political effects, human capital accumulation rate increases with n for high levels of initial inequality, while it decreases when n increases for low levels of inequality. 7.1.2 Empirical Evidence 7.1.2.1 Empirics with Education Only

Miller (1996) performs a panel estimation of the impact of the population structure on educational spending for US states. She explicitly tests for interest-group determination of spending, by including as explanatory variables the proportion of parents of school-age children, and of retirees, in the electorate. The dependent variable is the log of real per adult expenditures on education (state and local) for the years 1960, 1970, 1980, and 1990. While most specifications show a positive effect of the proportion of parents on spending, elderly proportion seems insignificant. A similar analysis on Texas counties, conducted for the years 1970 and 1980, finds both variables to be significant with the expected sign, however. Poterba (1997) similarly uses panel data on K-12 education spending on the US states, over the 1960–1990 period, using (log of ) education spending per child as the dependent

The Political Economy of Population Aging

variable. The proposed explanatory variables this time include the proportion of schoolaged children and elderly in the state population of each state. It is estimated that per-child spending has an elasticity with respect to the over-65 population share of approximately 0.25: in other terms, “a one standard deviation change in the share of elderly in the population, a shift from 0.108 to 0.130, results in almost a 5% decline in per-pupil education spending,” which is sizeable. This also needs to be put into perspective with the fact that other governmental programs are rising with the share of the elderly in the population. On the other hand, per capita education spending has a negative elasticity (varying between 0.4 and 1.0) with respect to the fraction of school-age children in the population. While this result may seem surprising, the author emphasizes that other types of public spending are more negatively affected by increases in the share of the young: thus, the share of public spending that goes to the young increases when the share of the young in the population increases. Fernandez and Rogerson (1997) perform a similar analysis on US states from 1950 to 1990. In their main specification, the logarithm of schooling expenditures per student is regressed on the log of income per capita, the fraction of the population of school age, and the fraction of the adult population over 65. While the coefficient on the share of students is insignificant, the one on the share of elderly is consistently negative and significant (around 0.2). On the other hand, per student education expenditures go hand in hand with income per capita. Ladd and Murray (2001) explicitly build on the approach of Poterba (1997), while shifting the unit of observation away from states to local counties. They start by presenting descriptive evidence, showing that elderly residential choices may be related to the level of spending on education by the county. In order to try to eliminate the bias created by this Tiebout sorting of elderly with respect to local taxes, they then proceed to estimating a panel equation where the share of the elderly in a county is instrumented by the same share in previous census. By so doing, Ladd and Murray (2001) obtain a significantly smaller estimate of the elasticity of educational spending with respect to the share of pupils; more importantly, the share of the elderly now becomes statistically insignificant, suggesting that elderly actually do not exert any downward pressure on spending per child. Harris et al. (2001) use panel data on spending and demographic structure at the school district level to reconcile the findings in Poterba (1997) and Ladd and Murray (2001). Indeed, they show that the elderly are much less likely to support state funding than funding at the local, school district level. This, the authors remark, is consistent with the widely accepted observation that the quality of local schools is capitalized in housing values. Grob and Wolter (2007) perform a panel analysis of spending on compulsory education for Swiss Cantons, between 1990 and 2002. It shows that under a Canton fixed-effect specification, the percentage of retired in the population has a negative, yet significant at the 10% level only, effect on educational spending per child. Using first differences, the authors find that variations in the number of pupils (resp. the number of retirees) have a positive (resp. negative) impact on total education spending.

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7.1.2.2 Empirics with Several Public Programs

Borge and Rattso (2008) use a specification very similar to that of Poterba (1997), to evaluate the impact of population structure on three welfare programs of the 275 Danish local governments, over the 1989–1996 period. The welfare programs considered are child care, compulsory education, and elderly (institutionalized) care. The demographic variables are the fraction of the potential recipients of each of the three programs (ie, resp. the 0–6 years, 7–15 years, and 80+ age groups) over the total population. Using as dependent variables the spending per capita on each program, the authors first find that being part of a large age cohort is a disadvantage in terms of transfers received. They also shed into light that while the elderly exert significant crowding-out on spending toward the younger generations, the opposite is not true. 7.1.2.3 Surveys of Voter Preferences

All the aforementioned papers attempt to analyze the empirical impact of the age structure of the population on the size of these public programs, which is the outcome of the political process concerning them. Meanwhile, a complementary approach has been developed by some other papers (Brunner and Balsdon, 2004; Berkman and Plutzer, 2004; Cattaneo and Wolter, 2009; Busemeyer et al., 2009; Sorensen, 2013) that have used individual surveys about the likelihood to vote for specific, age-related transfer policies, in order to analyze the role of age on the individual preferences on these policies. For instance, Cattaneo and Wolter (2009) use a representative survey of Swiss voters to show the elderly are less likely to be willing to fund education programs, and prefer spending on health and social security. They find that these result still hold after controlling for the fact that the elderly are less supportive of public spending in general. The interest of this type of analysis is to establish a possible causal link between the age structure of the population and the policy outcome that goes through individual preferences, and not only through the tax cost of spending on the different programs as the age structure varies.

7.2 Aging and Support for Health Care Surprisingly enough, the recent political economy literature contains few articles linking the aging of the electorate and the evolution of public health-care provision, even though it may be considered as hot a topic as pensions. We will focus here on only one significant contribution, although other recent papers on the political economy of health care without direct focus on aging may be worth mentioning here, such as Moreno-Ternero and Roemer (2007) or De Donder and Hindriks (2007): indeed, the results and insights obtained can be extended to a situation with a changing composition of the population with regard to aging. Bethencourt and Galasso (2008) emphasize a political complementarity between two transfer programs, namely pensions and public health care. It is known for some time

The Political Economy of Population Aging

already (Philipson and Becker, 1998) that the existence of pensions as annuity encourages investment in health care. Here, expenditure in health care reduces the longevity differential between rich and poor individuals, thereby making pensions more attractive for the poor individuals with lower longevity. The authors support their analysis by pointing out the existence of a health gradient in income and the fact that publicly provided health care increases more longevity for the low-income than for the high-income individuals (in other words, the health production function is concave). Essential to the establishment of a political equilibrium supporting a large welfare system is the intragenerational redistribution element of both programs. Their model features a two-period OLG endowment economy where young agents do not take any economic decisions (they only participate in the vote over social security and health care). Old agents (who are heterogeneous in the endowment they received) use their income to finance private health care and nonhealth expenditures. They are taxed linearly to finance noncontributory pensions and public healthcare. Only public health care raises the life expectancy, which is modeled as the fraction of the second period during which agents will enjoy their pension payments. On the political side of the model, the authors assume that a majoritarian vote takes place over the size and composition of the welfare state. They use subgame perfect structure-induced equilibrium to reduce the game to a (degenerately) dynamic, issue-by-issue voting game. Under adequate parameter restrictions, an equilibrium with positive taxation is supported by a coalition of the old and the young poor, provided the amount devoted to health care is sufficient to increase the young poor life expectancy up to the point where they support pensions. Concerning the determination of the composition of the system, the authors find that the preferred policy mix depends solely on income. For any transfer size, richer agents prefer a purely pensionbased system, since it is the one which provides the widest longevity gap in income and thus redistributes income the least. As agents become poorer, they prefer a bigger part of the welfare system to be spent on health care, in order to make receiving pensions more worthwhile. The authors also find out that an increase in health-care technology leads to a larger welfare state and a larger pension share. Using a calibrated version of the model for the US economy in the early 1980s, they find that such a technology improvement would then cause an increase in aging, and also higher per capita welfare spending. An interesting potential development of this line of research would be to analyze the impact of a change in fertility, which enters the model here as an exogenous parameter.

7.3 Aging and Long-Term Care Long-term care can be broadly defined as the supply of help to elderly, dependent people, regarding basic daily activities such as eating, dressing, and bathing. It can be extended to include help to perform activities that are instrumental to day-to-day life like cooking, cleaning, taking medication, or going to places which are further than walking distance.

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The risk of long-term care (hereafter LTC) needs showing up at the individual level strongly increases around the age of 80 years. As it turns out, the “80 years and above” category is the fastest growing segment of population in many aging, industrialized societies. It is then no wonder that the number of dependent elderly, and the cost of providing for their LTC are expected to increase dramatically over the coming years: according to European Commission (2015), the baseline scenarioal for the future evolution of LTC expenditures in the European Union implies a hike of public outlays from 1.6% of GDP in 2015 to 4.1% in 2060, if coverage rates and cost per dependent remain the same throughout the period. An important issue concerns the provision of LTC: in many countries, the bulk of LTC is still provided informally by family members, a feature which may change in the future due to evolutions of family structure or female labor force participation. Formal care can also be provided by the state or the market: it should be noted, however, that the market for LTC (and especially LTC insurance) is currently quite thin, as evidenced by Brown and Finkelstein (2011) and Pestieau and Ponthie`re (2011). The question of our collective willingness to fund public provision of LTC is thus a pressing issue, which has received some increased attention in the recent literature: indeed, most recent papers on the political economy of LTC are devoted to finding the reasons why public financing of LTC remains underdeveloped in many countries. A pervasive argument (Nuscheler and Roeder, 2013; De Donder and Pestieau, 2016; De Donder and Leroux, 2015) is the crowding-out of social financing of LTC by direct care provision or purchase, be it through financial transfers from the family, depletion of the concerned individual’s own savings, or informal care from relatives. Another line of explanation (De Donder and Leroux, 2013) stresses out the fact that agents may be myopic when making decisions regarding LTC, in the sense that they underestimate their probability to become dependent in old age: this argument tends to explain both the low level of market coverage and the low political demand for a publicly funded system. Nuscheler and Roeder (2013) and De Donder and Pestieau (2016) both consider setups in which agents differ in income and LTC needs, even though they adopt a different perspective in terms of the realization of LTC needs. In Nuscheler and Roeder (2013), dependence risk is already realized, so that families either have to support a dependent parent or they do not. The political conflict then pits families with healthy parents against families with a sick parent, but also poor families against rich families, since a vote also occurs on the level of income redistribution. In this setup, the impact of aging on the level of public LTC financing is ambiguous, and depends on the tax elasticity of the supply of informal care. Indeed, population aging is shown in the model to make the income tax more distortionary, so that income taxation is lower at the political al

The scenario mentioned here assumes that half of future gains in life expectancy will be spent in good health, and half in disability.

The Political Economy of Population Aging

equilibrium; as a result, the opportunity cost of giving informal care to one’s parent (instead of participating to the labor market) increases, which decreases the supply of informal care in equilibrium. If informal care decreases sufficiently, then agents may ask for public financing of LTC to step in. On the opposite, De Donder and Pestieau (2016) adopt an ex ante perspective, in which agents rather differ in the probability to become dependent (as well as the probability to get family help and the extent of that help). The only policy chosen at the political equilibrium is here the income tax rate, where all the income tax is used to fund social LTC insurance. In this setting, the interaction between family help, market insurance, and social insurance is fairly complex; however, agents are shown to prefer social insurance to market insurance if they have a relatively low level of income or a relatively high level of risk of being dependent, ceteris paribus, which is due to the fact that social insurance redistributes across income and risk levels while private insurance is actuarially fair. Besides, good prospects of family help (ie, a high probability to receive help from the family and/or a high level of help) reduce demand for any kind of insurance, all else being equal, as expected. In this context, aging (which can be represented by a higher probability to become dependent) unambiguously increases the need for total LTC provision; however, the effect on social LTC insurance is ambiguous, given that its return can be shown to decrease with the average probability to become dependent at the scale of the entire population.

7.4 Aging and the Environment Although some may consider the subject of environment conservation very loosely related with our subject, we argue that its characteristics make it a subject with important intergenerational dimensions. Indeed, to use the terminology introduced by Rangel (2003), a healthy environment can be considered a “forward intergenerational good” in the sense that it is financed by a given generation to be consumed mainly by the next one (as opposed to “backward intergenerational goods” like pensions for instance), especially if one considers climate change. In this sense, the way in which a society decides on the funds to allow for environment conservation may well be impacted by the age structure of its population as well. Ono (2005) is, to the best of our knowledge, the first significant contribution on this topic. It focuses on the impact of greater longevity and lower growth rate of population may affect the level of a politically determined environmental tax, and through it the quality of environment over time. This paper uses a two-period OLG model with environmental quality and uncertain lifetimes. Lifetime uncertainty is represented by an exogenous probability δ to survive into old age. It is assumed this uncertainty cannot be completely hedged against in the savings decision of young agents, as they can only save a fixed fraction γ of their savings

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in the form of annuities. On the production side, it is assumed that firms create environmentally harmful emissions as by-products, in the form of a fixed fraction ηy of the output of the firms. To repair the damage made by emissions, an environmental tax τ on each unit of production is levied in each period. The proceeds of the tax are used to improve environmental quality, which is modeled as a stock that depletes with emissions and is maintained by tax receipts. Finally, agents care about consumption and environmental quality when old, in a separable fashion. The political process boils down to a short-lived representative government that sets up τt in each period, so as to maximize a weighted sum of the utilities of currently living generations: representatives are assumed to have rational expectations about future policies, but to act in a myopic fashion with regard to the impact of current decisions on future ones. A first insight from the model is that longevity has no impact on the level of the environmental tax at steady state, while a slower level of population growth n will reduce the level of the tax. However, the final impact on environmental quality is more complex. Indeed, increased longevity leads to a lower level of environmental quality under partial annuitization of savings, while having no effect at all in the case of full annuitization. On the other hand, environmental quality increases when the rate of population growth decreases: indeed, a lower n enhances capital accumulation, in a way that increases environmental investment more than emissions for a given level of τ. This effect outweighs the negative effect of n on τ described above, hence the result. As is already the case for pensions, it is worth stressing that in this case too, one needs to take into account the effect of population change on capital accumulation decisions as well as their more politically proximate effects, if one is to get a full understanding of the consequences of political aging.

7.5 Capital vs Labor Taxes Bassetto (2008) studies a setup slightly more complex than an OLG model with pensions, including capital taxes (that fall on the old) along with labor taxes (falling on the young), and tax proceeds that can be used to finance a public good and lump-sum transfers to either generation (or both). The argument for looking at this broader picture comes from generational accounting: changing demographics will probably affect what each generation pays to the system, thereby possibly offsetting the changes in what they receive as a consequence of the demographic shock. An interesting feature of the model used in this paper is the modeling of the political process as a bargaining game. In each period, citizens are drawn randomly to make proposals that have to be accepted unanimously to be implemented, with a small probability that the game terminates with a government shutdown for the period each time a proposal is rebuked. In this environment, each generation holds a veto power over the decisions, such that the outcome

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must somehow balance the gross contributions from and transfers to both the old and young. Moreover, concerning the public good financing, it can be seen that if a generation values less the good than the other one, this generation benefits from hold-up power (here, the threat of a shutdown), which it may use to extract larger transfers. Under a setup where the young only supply labor and the old only capital to the production process, the author points out that the young will be willing to reduce the size of both their contribution and the transfers they receive (since the labor tax base is sensitive to the tax rate), while the old will accept large contributions in exchange for big transfers (as the capital tax base is predetermined by past decision and is thus insensitive to the tax rate chosen). Let us now convey the intuition of the consequences of population aging, under the assumption that young people value more the public good than the oldam: in this case, as the old agents become relatively more numerous, their decision power increases and is used to decrease the overall size of the government, and in particular decrease public good financing. Moreover, and even though they manage to negotiate higher overall transfers from the young, this is not enough to counteract the fact that transfers have to be shared between more old people, so that the per capita transfer they get will decrease. This effect on the transfer side needs to be added to the fact that the capital tax rate also increases, so that the overall net transfer per capita to the old is further degraded. From the point of view of the young, aging leads to increased labor tax rate and increased net contributions per capita, on top of the reduction in public good consumption, so the overall effect is unambiguously negative for them. On top of this comparative statics on the steady state of the economy, the author conducts two comparative dynamics exercises to explore what happens to these taxes and transfers when a demographic shock hits, whether anticipated or unanticipated. It is shown that the output of the model is consistent with the historical experience if one considers an anticipated aging shock at the time of the baby boomers generation, with transfers to the old going upward when this generation is active (ie, young), before an eventual contraction. Contrary to the intuitions conveyed by the preceding paper, Mateos-Planas (2010) sets up a general equilibrium model to predict a link between aging and increased capital taxation, in a model where both labor and capital can be taxed. For the prediction to hold, the young need to hold less capital than the old, which appears reasonable, and the aging process needs to be large enough to shift the identity of the median voter to induce a movement of the tax rate in equilibrium.

am

This would be the case, the author argues, if the public good is itself somehow a forward intergenerational good, like environmental quality (see Section 7.4).

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8. CONCLUSION Summary of Previous Sections In the previous sections, we have thus given an account of the recent literature on the political economy of pensions, and more precisely how population aging is compelling electoral democracies to rethink collectively the size and design of their pension systems. A first, and essential step according to us, was to remind the reader why public PAYG pensions were supported by a majority of the electorate in the first place: arguments of reduced time horizon of the median voter, or the existence of a within-cohort redistribution component in PAYG pension schemes, are the most compelling reasons why these programs exist in the first place. Once this theoretical framework for the political sustainability of pensions has been established, we have been able to give an account on the impact of aging on the size of the programs. The effects at play are slightly different depending on whether population aging is caused by fertility decreases or life expectancy increases: in any case, they fall into two categories. The political effect of aging is unambiguous: as population ages, the weight of old voters in the electorate increases, which will give incentives to politicians seeking votes to propose electoral platforms with more generous retirement packages. What we call the economic effect of aging is less clear cut, but essentially hinges on how the internal return of the PAYG system is modified as the age structure of the economy changes. The theoretical literature essentially associates higher life expectancy to higher sizes of pension programs, while lower fertility yields more ambiguous results. Empirical evidence suggests that measures of population aging such as the old-age dependency ratio can be estimated to cause higher pension spending. Considering other public programs alongside pensions does not seem to modify the broad sense of this result: it adds to the previous analysis the finding that education funding is generally at risk with a graying electorate. This chapter has also studied the impact of aging on the retirement age: to sum up, aging acts as a negative shock on the return of the PAYG pension system. Then, agents faced with aging suffer a negative income shock, which will result in their optimal retirement age being higher than before (retirement, or leisure, being a normal good). Therefore, aging is predicted to induce the electorate to choose a higher retirement age. The Way Forward As stated in Section 7.2, further research is warranted on the political economy of health care and long-term care, especially since recent increases in life expectancy make the financing of these governmental program an ever more pressing issue. As shown in Galasso (2006), work on the joint political determination of the size of the pension system and the retirement age seems a promising avenue of research. Galasso and Profeta (2004) also suggest that the importance of family ties (and hence altruism considerations) should be taken into consideration, if one is to make sense of the political decisions taken by individuals as regards the pension system. Indeed, they indicate that countries with relatively more frequent multigenerational living arrangements would

The Political Economy of Population Aging

tend to choose larger pension systems, as adult children living with their parents are more likely to be in favor of pensions than their alone-living counterparts for intra-household transfer reasons. It can be argued that this effect is sizable, especially when comparing countries: in Southern Europe or Japan, a high fraction of elderly individuals (around 40% or more) live with their adult children, compared with just less than 15% in the USA.an Another overlooked characteristic of pension systems is its intragenerational redistribution component. Galasso and Profeta (2004) recall the distinction between Beveridgean and Bismarckian pension systems, the former aiming at giving a base income at retirement independently from past contributions, while the latter tends to provide equal replacement rates for all individuals. Indeed, recent reforms go in the direction of extended coverage and increased minimum pensions to fight poverty among elders, while at the same time tightening the eligibility criteria and containing the increases in spending by tinkering with benefits formula for the general population. It therefore appears worthwhile to ask the question whether most pension systems are not becoming increasingly Beveridgean (or at least progressive in some dimensions), as well as to investigate the political reasons behind this institutional evolution. We would also like to add that further theoretical work should consider including the possibility for the electorate to choose to run some deficits on its pension system: indeed, most theoretical papers assume from the outset that the electorate determines the size of a system by merely setting the contribution rate on labor income, the value of pension benefits being merely set so that the pension system budget is in equilibrium at all times. Such formulations have several drawbacks, the most important one being that pension systems are never exactly in budgetary equilibrium for any fiscal year. It also significantly blurs the distinction between defined-benefit and defined-contribution systems. It would probably be a hard process, as there would be several decision dimensions (including the size of the system and its degree of financing by current contributions) to consider, and would most likely require precious insights from the political economy literature on inaction and reform delay, and debt (see Drazen, 2000, chapters 3 and 10, but also Tepe and Vanhuysse (2012) for the point of view of political science). More generally, every step should be made in terms of modeling or quantitatively assessing the future evolutions of the pension systems to better explain the institutional details of these systems, and how these are likely to be impacted by the coming demographic shockwave.

ACKNOWLEDGMENTS We would like to thank the editors, Alan Woodland and John Piggott, as well as two anonymous referees, for very helpful comments. an

Source: Howe and Jackson (2003), as cited in Galasso and Profeta (2004).

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Casamatta, G., Cremer, H., Pestieau, P., 2005. Voting on pensions with endogenous retirement age. Int. Tax Public Financ. 12 (1), 7–28. Casamatta, G., Cremer, H., Pestieau, P., 2006. Is there a political support for the double burden on prolonged activity? Econ. Gov. 7 (2), 143–154. Cattaneo, M.A., Wolter, S.C., 2009. Are the elderly a threat to educational expenditures? Eur. J. Polit. Econ. 25 (2), 225–236. Conde-Ruiz, J.I., Galasso, V., 2003. Early retirement. Rev. Econ. Dyn. 6 (1), 12–36. Conde-Ruiz, J.I., Galasso, V., 2004. The macroeconomics of early retirement. J. Public Econ. 88 (9–10), 1849–1869. Conde-Ruiz, J.I., Galasso, V., Profeta, P., 2013. The role of income effects in early retirement. J. Public Econ. Theory 15 (3), 477–505. Conesa, J.C., Garriga, C., 2008. Optimal fiscal policy in the design of social security reforms. Int. Econ. Rev. 49 (1), 291–318. Conesa, J.C., Garriga, C., 2009. Optimal response to a transitory demographic shock in social security financing. Fed. Reserve Bank St. Louis Rev. 91 (1), 33–48. Conesa, J.C., Krueger, D., 1999. Social security reform with heterogeneous agents. Rev. Econ. Dyn. 2 (4), 757–795. Cooley, T.F., Soares, J., 1999. A positive theory of social security based on reputation. J. Polit. Econ. 107 (1), 135–160. Coronado, J.L., Fullerton, D., Glass, T., 2000. The progressivity of social security. Working Paper 7520, NBER. Crawford, V.P., Lilien, D.M., 1981. Social security and the retirement decision. Q. J. Econ. 96 (3), 505–529. Cremer, H., De Donder, P., 2016. Life expectancy heterogeneity and the political support for collective annuities. Scand. J. Econ. 118 (3), 594–615. ISSN 1467-9442. Cremer, H., De Donder, P., Maldonado, D., Pestieau, P., 2007. Voting over type and generosity of a pension system when some individuals are myopic. J. Public Econ. 91, 2041–2061. De Donder, P., Hindriks, J., 2002. Voting over social security with uncertain lifetimes. In: d’Aspremont, C., Ginsburgh, V.A., Sneessens, H.R., Spinnewyn, F. (Eds.), In: Institutional and Financial Incentives for Social Insurance. Kluwer Academic Publishers, Dordrecht, pp. 201–220. De Donder, P., Hindriks, J., 2007. Equilibrium social insurance with policy-motivated parties. Eur. J. Polit. Econ. 23 (3), 624–640. De Donder, P., Leroux, M.-L., 2013. Behavioral biases and long-term care insurance: a political economy approach. B.E. J. Econom. Anal. Policy 14 (2), 551–575. De Donder, P., Leroux, M.-L., 2015. The political choice of social long term care transfers when family gives time and money. CESifo Working Paper Series 5384, CESifo Group Munich. De Donder, P., Pestieau, P., 2016. Private, social and self-insurance for long-term care in the presence of family help. J. Public Econ. Theory. forthcoming. De Walque, G.D., 2005. Voting on pensions: a survey. J. Econ. Surv. 19 (2), 181–209. Diamond, P.A., 1965. National debt in a neoclassical growth model. Am. Econ. Rev. 55 (5), 1126–1150. Diamond, P.A., 1977. A framework for social security analysis. Am. Econ. Rev. 8, 275–298. Disney, R., 2007. Population ageing and the size of the welfare state: is there a puzzle to explain? Eur. J. Polit. Econ. 23 (2), 542–553. Drazen, A., 2000. Political Economy in Macroeconomics. Princeton University Press, Princeton, NJ. Durevall, D., Henrekson, M., 2011. The futile quest for a grand explanation of long-run government expenditure. J. Public Econ. 95 (7–8), 708–722. Epple, D., Romano, R.E., 1996. Public provision of private goods. J. Polit. Econ. 104 (1), 57–84. European Commission, 2010. Progress and key challenges in the delivery of adequate and sustainable pensions in Europe (A Joint Report on Pensions). Occasional Papers 71. European Commission, Directorate-General for Economic and Financial Affairs. European Commission, 2015. The 2015 ageing report: economic and budget projections for the 28 member states (2013-2060). European Commission, Directorate-General for Economic and Financial Affairs. Fernandez, R., Rogerson, R., 1997. The determinants of public education expenditures: evidence from the states, 1950-1990. Working Papers 97-16, C.V. Starr Center for Applied Economics, New York University.

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Forni, L., 2005. Social security as Markov equilibrium in OLG models. Rev. Econ. Dyn. 8 (1), 178–194. Fudenberg, D., Tirole, J., 1991. Game theory. In: MIT Press Books, vol. 1. The MIT Press, Cambridge, MA. Galasso, V., 2006. The political future of social security in aging societies. In: MIT Press Books. The MIT Press, Cambridge, MA. Galasso, V., 2008. Postponing retirement: the political effect of aging. J. Public Econ. 92 (10–11), 2157–2169. Galasso, V., Profeta, P., 2002. The political economy of social security: a survey. Eur. J. Polit. Econ. 18 (1), 1–29. Galasso, V., Profeta, P., 2004. Lessons for an aging society: the political sustainability of social security systems. Econ. Policy 19, 63–115. Galasso, V., Profeta, P., 2007. How does ageing affect the welfare state? Eur. J. Polit. Econ. 23, 554–563. Geerolf, F., 2013. Reassessing dynamic efficiency. Working Paper. Goldstone, J.A., Kaufmann, E.P., Toft, M.D., 2011. Political Demography How Population Changes Are Reshaping International Security and National Politics. Oxford University Press, Oxford. Gonzalez-Eiras, M., Niepelt, D., 2007. Population ageing, government budgets, and productivity growth in politico-economic equilibrium. CEPR Discussion Papers 6581. Gonzalez-Eiras, M., Niepelt, D., 2008. The future of social security. J. Monet. Econ. 55 (2), 197–218. Gonzalez-Eiras, M., Niepelt, D., 2012. Ageing, government budgets, retirement, and growth. Eur. Econ. Rev. 56 (1), 97–115. Gradstein, M., Kaganovich, M., 2004. Aging population and education finance. J. Public Econ. 88 (12), 2469–2485. Grob, U., Wolter, S.C., 2007. Demographic change and public education spending: a conflict between young and old? Educ. Econ. 15 (3), 277–292. Gruber, J., Wise, D., 1999. Social Security and Retirement Around the World. University of Chicago Press, Chicago. Hammond, P., 1975. Charity: altruism or cooperative egoism. In: Phelps, E.S. (Ed.), Altruism, Morality and Economic Theory. Russell Sage Foundation, New York, pp. 115–131. Hanley, S., 2012. Chapter 2: Explaining the success of pensioners’ parties: a qualitative comparative study of 31 polities. In: Vanhuysse, P., Goerres, A. (Eds.), Ageing Populations in Post-industrial Democracies: Comparative Studies of Policies and Politics. Routledge, Oxford, pp. 23–53. Harris, A.R., Evans, W.N., Schwab, R.M., 2001. Education spending in an aging America. J. Public Econ. 81 (3), 449–472. Holzmann, R., 2012. Global pension systems and their reform: worldwide drivers, trends, and challenges. IZA Discussion Papers 6800, Institute for the Study of Labor (IZA). Homburg, S., 1990. The efficiency of unfunded pension schemes. J. Inst. Theor. Econ. 146, 640–647. Homburg, S., 1991. Interest and growth in an economy with land. Can. J. Econ. 24 (2), 450–459. Howe, N., Jackson, R., 2003. The 2003 Aging Vulnerability Index: An Assessment of the Capacity of Twelve Developed Countries to Meet the Aging Challenge. CSIS and Watson Wyatt Worldwide, Washington, DC. Hu, S.C., 1982. Social security, majority-voting equilibrium and dynamic efficiency. Int. Econ. Rev. 23 (2), 269–287. Iturbe-Ormaetxe, I., Valera, G., 2012. Social security reform and the support for public education. J. Popul. Econ. 25 (2), 609–634. Kaganovich, M., Meier, V., 2012. Social security systems, human capital, and growth in a small open economy. J. Public Econ. Theory 14 (4), 573–600. Kaganovich, M., Zilcha, I., 2012. Pay-as-you-go or funded social security? A general equilibrium comparison. J. Econ. Dyn. Control. 36 (4), 455–467. Kemnitz, A., 1999. Demographic structure and the political economy of education subsidies. Public Choice 101 (3–4), 235–249. Kemnitz, A., 2000. Social security, public education, and growth in a representative democracy. J. Popul. Econ. 13 (3), 443–462.

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Krueger, D., Kubler, F., 2006. Pareto-improving social security reform when financial markets are incomplete!? Am. Econ. Rev. 96 (3), 737–755. Lacomba, J., Lagos, F., 2006. Population aging and legal retirement age. J. Popul. Econ. 19, 507–519. Lacomba, J., Lagos, F., 2007. Political election on legal retirement age. Soc. Choice Welf. 29, 1–17. Ladd, H.F., Murray, S.E., 2001. Intergenerational conflict reconsidered: county demographic structure and the demand for public education. Econ. Educ. Rev. 20 (4), 343–357. Lancia, F., Russo, A., 2015. Public education and pensions in democracy: a political economy theory. Memorandum 01/2015, Oslo University, Department of Economics. Leroux, M.-L., 2010. The political economy of social security under differential longevity and voluntary retirement. J. Public Econ. Theory 12 (1), 151–170. Levy, G., 2005. The politics of public provision of education. Q. J. Econ. 120 (4), 1507–1534. Liebman, J.B., 2001. Redistribution in the current U.S. social security system. Working Paper 8625, NBER. Lindert, P.H., 1994. The rise of social spending, 1880-1930. Explor. Econ. Hist. 31 (1), 1–37. Lindert, P.H., 1996. What limits social spending? Explor. Econ. Hist. 33 (1), 1–34. Mateos-Planas, X., 2010. Demographics and the politics of capital taxation in a life-cycle economy. Am. Econ. Rev. 100 (1), 337–363. Meier, V., Werding, M., 2010. Ageing and the welfare state: securing sustainability. Oxf. Rev. Econ. Policy 26 (4), 655–673. ISSN 1460-2121. Meltzer, A.H., Richard, S.F., 1981. A rational theory of the size of the government. J. Polit. Econ. 89 (5), 914–927. Miller, C., 1996. Demographics and spending for public education: a test of interest group influence. Econ. Educ. Rev. 15 (2), 175–185. Moreno-Ternero, J.D., Roemer, J.E., 2007. The political economy of health care finance. CORE Discussion Papers 2007031, Universit
e catholique de Louvain, Center for Operations Research and Econometrics (CORE). Mulligan, C.B., Sala-i-Martin, X., 1999. Social security in theory and practice (I): facts and political theories. Economics Working Papers 384, Department of Economics and Business, Universitat Pompeu Fabra. Naito, K., 2012. Two-sided intergenerational transfer policy and economic development: a politicoeconomic approach. J. Econ. Dyn. Control. 36 (9), 1340–1348. Nishiyama, S., Smetters, K., 2007. Does social security privatization produce efficiency gains? Q. J. Econ. 122 (4), 1677–1719. Nuscheler, R., Roeder, K., 2013. The political economy of long-term care. Eur. Econ. Rev. 62 (C), 154–173. OECD, 2014. OECD pensions outlook 2014. Technical Report, OECD Publishing. OECD, 2015. Pensions at a glance 2015: OECD and G20 indicators. Technical Report, OECD Publishing. Ono, T., 2005. The political economy of environmental taxes with an aging population. Environ. Resour. Econ. 30 (2), 165–194. Ono, T., 2015. Public education and social security: a political economy approach. Econ. Gov. 16 (1), 1–25. Pamp, O., 2015. Political Preferences and the Aging of Populations: Political-Economy Explanations of Pension Reform. Springer VS, New York. Pestieau, P., Ponthie`re, G., 2011. The long term care insurance puzzle. In: Courbage, C., Costa-Font, J. (Eds.), Financing Long Term Care in Europe: Institutions. Markets and Models. Palgrave Macmillan, London, pp. 41–52. Philipson, T.J., Becker, G.S., 1998. Old-age longevity and mortality-contingent claims. J. Polit. Econ. 106 (3), 551–573. Pierson, C., 2007. Beyond The Welfare State?: The New Political Economy of Welfare. Penn State University Press, University Park, PA. Plott, C.R., 1967. A notion of equilibrium and its possibility under majority rule. Am. Econ. Rev. 57, 787–806. Poterba, J.M., 1997. Demographic structure and the political economy of public education. J. Policy Anal. Manage. 16 (1), 48–66. Poutvaara, P., 2006. On the political economy of social security and public education. J. Popul. Econ. 19 (2), 345–365.

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Profeta, P., 2002. Aging and retirement: evidence across countries. Int. Tax Public Financ. 9 (6), 651–672. Rangel, A., 1997. Social security reform: efficiency gains or intergenerational redistribution. Mimeo, Harvard University. Rangel, A., 2003. Forward and backward intergenerational goods: why is social security good for the environment? Am. Econ. Rev. 93 (3), 813–834. Razin, A., Sadka, E., Swagel, P., 2002. The aging population and the size of the welfare state. J. Polit. Econ. 110 (4), 900–918. Roemer, J.E., 2001. Political Competition: Theory and Applications. Harvard University Press, Cambridge, MA. Samuelson, P.A., 1958. An exact consumption-loan model of interest with or without the social contrivance of money. J. Polit. Econ. 66 (6), 467–482. Sanz, I., Velazquez, F.J., 2007. The role of ageing in the growth of government and social welfare spending in the OECD. Eur. J. Polit. Econ. 23 (4), 917–931. Shelton, C.A., 2008. The aging population and the size of the welfare state: is there a puzzle? J. Public Econ. 92 (3–4), 647–651. Shepsle, K., 1979. Institutional arrangements and equilibrium in multidimensional voting models. Am. J. Polit. Sci. 23 (1), 27–59. Sheshinski, E., 1978. A model of social security and retirement decisions. J. Public Econ. 10 (3), 337–360. Simonovits, A., 2007. Can population ageing imply a smaller welfare state? Eur. J. Polit. Econ. 23 (2), 534–541. Sinn, H.-W., Uebelmesser, S., 2003. Pensions and the path to gerontocracy in Germany. Eur. J. Polit. Econ. 19 (1), 153–158. Sjoblom, K., 1985. Voting for social security. Public Choice 45, 225–240. Soares, J., 2006. A dynamic general equilibrium analysis of the political economy of public education. J. Popul. Econ. 19 (2), 367–389. Sorensen, R.J., 2013. Does aging affect preferences for welfare spending? A study of peoples’ spending preferences in 22 countries, 1985-2006. Eur. J. Polit. Econ. 29, 259–271. Tabellini, G., 2000. A positive theory of social security. Scand. J. Econ. 102 (3), 523–545. Tepe, M., Vanhuysse, P., 2012. Chapter 6: Accelerating smaller cutbacks to delay larger ones? The politics of timing and alarm bells in OECD pension generosity retrenchment. In: Vanhuysse, P., Goerres, A. (Eds.), Ageing Populations in Post-industrial Democracies: Comparative Studies of Policies and Politics. Routledge, Oxford, pp. 127–144. United Nations, 2015. World population prospects: the 2015 revision, key findings and advance tables. Technical Report, U.N. Department of Economic and Social Affairs, Population Division. US Social Security Administration, 2016. Social security programs throughout the world: the Americas, 2015. Technical Report, Social Security Administration. Vald
es-Prieto, S. (Ed.), 1999. The Economics of Pensions. In: Cambridge Books. Cambridge University Press, Cambridge, UK. ISBN 9780521666121. Vanhuysse, P., Goerres, A. (Eds.), 2012. Ageing Populations in Post-industrial Democracies: Comparative Studies of Policies and Politics. Routledge, Oxford. World Bank, 2008. The World Bank pension conceptual framework. Technical Report, World Bank Pension Reform Primer Series.

CHAPTER 8

Retirement Incentives and Labor Supply R. Blundell, E. French, G. Tetlow University College London and Institute for Fiscal Studies (IFS), London, United Kingdom

Contents 1. Introduction 2. Trends in Employment Among the Elderly 2.1 Postwar Trends in Employment 2.2 Historical Context 2.3 Trends in Hours of Work 2.4 Trends in Self-Employment 3. The Retirement Decision 3.1 The Life-Cycle Profile of Hours and Employment 3.2 The Distribution of Hours Worked Near Retirement Age 3.3 Potential Explanations for the Abruptness of Retirement 4. Retirement Incentives 4.1 Declining Health 4.1.1 4.1.2 4.1.3 4.1.4

Measurement Issues Key Findings Trends in Health Summary

4.2 Substitution Effects, Wealth Effects, and Liquidity Effects 4.3 Retirement Incentives from Falling Wages 4.3.1 Measurement Issues 4.3.2 Key Findings

4.4 Retirement Incentives From Public Pensions 4.4.1 4.4.2 4.4.3 4.4.4 4.4.5

Common Features of Public Pension Schemes Across Countries A Detailed Example: Public Pension Programs in the United States Public Pension Programs in Other Developed Countries Key Findings Trends in Public Pension Incentives

4.5 Retirement Incentives From Private Pensions 4.5.1 Defined Benefit Pensions 4.5.2 Trends in Private Pension Incentives

4.6 Retirement Incentives From Disability Insurance 4.7 Retirement Incentives From Health Insurance 4.8 Expectations, Salience, and Focal Points 5. Models of the Retirement Decision 5.1 Early Structural Models 5.2 A Structural Model With Savings and Uncertainty Handbook of the Economics of Population Aging, Volume 1B ISSN 2212-0076, http://dx.doi.org/10.1016/bs.hespa.2016.10.001

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5.3 Estimated Life-Cycle Labor Supply Elasticities

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5.3.1 Retirement Elasticities

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5.4 Policy Experiments 5.5 Recent Structural Models

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5.5.1 5.5.2 5.5.3 5.5.4 5.5.5 5.5.6

Liquidity Constraints Health Disability Insurance Medical Spending Risk Explaining Differences in Retirement Across Countries and Over Time Optimal Pensions Policy

5.6 Retirement and Financial Decision-Making 5.7 Option Value Models 5.8 Structural Models: Key Limitations and Challenges for the Future 6. Families and Households 6.1 Evidence on Retirement in Couples 6.2 Modeling Retirement Decisions in Couples 6.3 Separating Preferences and Financial Incentives for Joint Retirement 6.4 What Have We Learned About Joint Retirement? 7. Conclusions and Challenges Acknowledgments References

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Abstract In this chapter, we review the evidence on retirement and study the role of incentives in the retirement decision. The key patterns of withdrawal from the labor market are presented and some of the factors that might explain the large and discrete drops in hours of work at the point of “retirement” are presented. We study the main retirement incentives that individuals face and place these financial and other incentives in the context of a structural approach to modeling retirement. We use this approach to frame issues of how government and private pension schemes affect retirement behavior. Noting that the typical household nearing retirement today in most developed economies is one in which both husband and wife work, we examine the theory and evidence on modeling incentives in couples and for joint decision-making. We conclude with a discussion of some of the gaps in our understanding of the employment of the elderly and raise some central questions that should be addressed by future research.

Keywords Retirement, Aging, Labor supply, Pensions, Retirement models

JEL Classification Codes H55 (social security and public pensions), I38 (government policy, provision and effects of welfare programs), J08 (labor economics policies), J14 (economics of the elderly), J26 (retirement, retirement policies), J32 (nonwage labor costs and benefits, retirement plans, private pensions)

1. INTRODUCTION Virtually all developed countries face challenges to the affordability of public (and, in some cases, occupational) pension programs. The shortfalls arise for two reasons. First,

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populations in developed countries are aging rapidly. Second, until recently, older individuals in developed countries have been retiring earlier. These two developments created serious strains on public pension programs. In order to address these issues and help public and occupational pension programs to remain solvent, there have been significant reforms across many countries to pensions and regulations relating to older workers. These policy changes have been accompanied by nontrivial increases in the labor supply of the elderly over the same period. This trend has occurred in multiple countries, raising the question of whether the policy reforms have caused the increases in labor supply. Employment among the elderly is an important factor in helping developed countries to deal with the ongoing demographic transition toward an older population. It is therefore a topic that has attracted significant attention from policymakers and researchers. In this chapter, we review the evidence on how employment rates among the elderly have changed in developed countries over recent decades and discuss the main factors that are thought to influence older workers’ labor supply. We do this within an economic framework of life-cycle decisions about consumption, saving, and labor supply. In addition to the policies discussed in this chapter, many countries have also changed regulations affecting labor demand. In particular, many have abolished mandatory retirement ages, meaning employers can no longer make workers redundant or refuse to hire them on the grounds of age alone. Such demand-side policies are also likely to have been important in affecting employment rates, but discussion of these is beyond the scope of this chapter. We start, in Section 2, by describing trends in employment of older women and (in particular) men over the last few decades and put these patterns in the context of a longer historical context. Most of our focus in this chapter is on the extensive margin of labor supply among the elderly. We motivate this focus in Section 3 by describing patterns of withdrawal from the labor market and some of the factors that might explain the large and discrete drops in hours of work that are seen for most people at the point of “retirement.” In order to better understand whether policy reforms have been important for explaining the rise in employment among the elderly, it is essential to know how sensitive labor supply is to the financial incentives caused by these reforms. To further examine these incentives, Section 4 discusses some of the key retirement incentives that individuals face and summarizes key papers that have examined the retirement response to these incentives. We then place these financial and other incentives in the context of a structural retirement model in Section 5. We use the model to frame issues of how government and private pension schemes affect retirement behavior. The discussion in that section builds upon French and Jones (2012). Lumsdaine and Mitchell (1999) also provide a useful survey of similar issues. In recent years, increasing attention has been paid to joint decision-making within families. This has largely been motivated by the fact that individuals in couples are often observed to exit work at roughly the same time as each other, in a way that cannot simply

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be explained by the individual incentives to retire that each member of the couple faces— suggesting instead that some interactions between the behavior of the two members of a couple are important in determining when each quits employment. The growing labor force attachment of women over recent decades means that the typical household approaching retirement today in most developed economies is one in which both husband and wife work. As a result, understanding how the circumstances and behavior of one member of a couple affects those of the other member has become an increasingly important part of understanding employment among the elderly. Section 6 examines the theory and evidence on the joint retirement behavior of couples—extending the discussion of the life-cycle model presented in Section 5 to allow for one partner’s behavior and/or incentives to affect the other. Different motives for retirement in couples are considered, focusing on attempts to separate preferences from financial incentives. We find that ignoring the role of family decisions in modeling retirement can distort the picture of retirement and bias the analysis of retirement policies. Our main conclusion is that the labor supply of older workers is responsive to changes in retirement incentives. This means that the trend toward lower effective taxes on older workers in many developed countries is likely to continue to fuel the recent trend toward later retirement. This, in turn, is likely to reduce the financial strain on public pension schemes. But we are still some way from fully understanding the precise channels through which external factors (such as reforms to public pension schemes) affect retirement behavior. Despite a large body of important evidence that has been assembled, new patterns of retirement raise new questions about retirement behavior. For example, although the research we review has established that financial incentives from pension schemes have significant effects on the employment of older people, in many countries (such as the United States (US) and the United Kingdom (UK)) retirement incentives from pension plans are now much smaller than in previous years, yet many people in those countries still retire at certain announced “retirement ages”. There remains much to be learned. Section 7 concludes with a discussion of some of these gaps in our understanding of the employment of the elderly and raises some central questions that should be addressed by future research.

2. TRENDS IN EMPLOYMENT AMONG THE ELDERLY 2.1 Postwar Trends in Employment In the last 20 years, we have seen a rapid increase in employment rates of the age 55+ population in developed countries. All 14 countries listed in Table 1 saw an increase in the employment rate of 55- to 64-year olds between 1999 and 2007 and Table 2 shows that this trend has continued for most countries over the 2007–2013 period that covered the global financial crisis. Tables 3 and 4 show employment patterns of the population aged 15–54. Table 3 shows that, over the period 1999–2007, employment rose for those aged 15–54 in most

Retirement Incentives and Labor Supply

Table 1 Changes in employment rate of 55- to 64-year olds, 1999–2007 Change in employment rate, 1999–2007 Employment Men Women All rate in 1999 Country

Employment rate in 2007

New Zealand The Netherlands Germany Australia Canada France Belgium Spain United Kingdom Sweden Italy Denmark United States Japan

71.8 48.8 51.3 56.5 57.0 38.2 34.4 44.5 56.8 70.1 33.7 58.9 61.8 66.1

13.5 12.8 12.6 9.2 6.9 8.6 7.8 7.2 6.5 6.1 3.8 5.0 1.3 2.0

17.1 14.8 14.6 16.0 13.4 11.1 11.3 11.3 8.4 6.1 8.0 5.2 6.5 3.1

15.3 13.8 13.5 12.5 10.2 9.9 9.7 9.5 7.4 6.1 6.0 4.7 4.1 2.7

56.5 34.9 37.8 44.0 46.8 28.3 24.7 35.1 49.3 64.0 27.6 54.2 57.7 63.4

Note: Countries listed from largest increase in employment to smallest. Employment rate shown is calculated across both men and women. Source: Authors’ calculations using data from the OECD and the UK Labour Force Survey.

Table 2 Changes in employment rate of 55- to 64-year olds, 2007–2013 Change in employment rate, 2007–2013 Employment Men Women All rate in 2007 Country

Employment rate in 2013

Germany The Netherlands Italy France Belgium Australia Sweden Canada Denmark United Kingdom New Zealand Japan United States Spain

63.6 60.1 42.7 45.6 41.7 61.4 73.7 60.3 61.7 59.5 74.3 66.8 60.9 43.2

10.5 10.2 7.8 7.9 4.9 3.3 3.9 1.2 1.6 0.7
1.4
1.7
1.4
9.1

14.2 12.6 10.3 7.0 9.8 6.8 3.3 5.4 3.9 4.6 6.4 3.0
0.4 6.1

12.3 11.3 9.0 7.4 7.4 4.9 3.6 3.3 2.7 2.7 2.5 0.7
0.9
1.3

51.3 48.8 33.7 38.2 34.4 56.5 70.1 57.0 58.9 56.8 71.8 66.1 61.8 44.5

Note: Countries listed from largest increase in employment to smallest. Employment rate shown is calculated across both men and women. Source: Authors’ calculations using data from the OECD and the UK Labour Force Survey.

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Table 3 Changes in employment rate of 15- to 54-year olds, 1999–2007 Change in employment rate, 1999–2007 Employment Men Women All Country rate in 1999

Employment rate in 2007

Spain Italy France New Zealand Australia The Netherlands Canada Belgium Japan Sweden Denmark Germany United Kingdom United States

70.5 64.2 69.8 75.7 76.0 80.2 76.8 68.0 72.0 75.2 81.5 73.0 74.1 73.1

6.7 3.1 2.4 3.9 2.5 0.2 1.5 0.9 0.4 1.6
0.4
1.1
0.9
3.2

18.3 8.6 6.5 4.6 5.5 6.7 5.0 4.9 3.2 0.7 2.5 2.5 0.5
2.7

12.6 5.7 4.4 4.2 4.0 3.3 3.3 2.9 1.8 1.2 1.0 0.7
0.2
2.9

57.9 58.4 65.4 71.5 72.0 76.9 73.5 65.2 70.2 74.1 80.5 72.3 74.3 76.0

Note: Countries listed from largest increase in employment to smallest. Employment rate shown is calculated across both men and women. Source: Authors’ calculations using data from the OECD and the UK Labour Force Survey.

Table 4 Changes in employment rate of 15- to 54-year olds, 2007–2013 Change in employment rate, 2007–2013 Employment Men Women All rate in 2007 Country

Employment rate in 2013

Germany Japan Sweden France United Kingdom Australia The Netherlands New Zealand United States Italy Denmark Spain

75.9 73.1 74.7 68.5 72.6 74.2 77.8 72.5 68.3 59.0 75.0 57.5

1.6
0.8
1.1
2.7
2.7
2.9
5.3
4.2
5.5
8.3
7.8
18.5

4.3 2.9 0.0
0.0
0.4
0.8 0.4
2.3
4.0
2.0
5.2
7.1

2.9 1.0
0.5
1.3
1.5
1.8
2.5
3.2
4.8
5.2
6.5
13.0

73.0 72.0 75.2 69.8 74.1 76.0 80.2 75.7 73.1 64.2 81.5 70.5

Note: Countries listed from largest increase in employment to smallest. Employment rate shown is calculated across both men and women. Source: Authors’ calculations using data from the OECD and the UK Labour Force Survey.

countries we consider, with the US being a major exception. There is an active debate in the US about what factors explain the historically unprecedented steady decline in labor force participation of both men and women since the turn of the century (Moffitt, 2012). However, as Table 3 suggests, this phenomenon is somewhat peculiar to the US. The US

Retirement Incentives and Labor Supply

was one of only two countries (the other being the UK), of the 14 developed countries shown, to have experienced a decline in overall employment rates of adults aged 15–54 between 1999 and 2007. All other countries saw increases and in some cases substantial increases. Though Denmark and Germany saw a decline in the employment rate of men, this was more than offset by rising employment rates among women—in contrast to the US, where employment rates for both men and women declined significantly. However, comparing Tables 1 and 3 shows that, with the exception of Spain, the employment increase was larger for those aged 55–64 than for those aged 15–54. Comparing Tables 2 and 4 shows that the differences in employment changes by age are even more dramatic over the 2007–13 period. For all countries except Japan, employment grew more rapidly for the 55–64 age group than for the 15–54 age group over this period. For most countries, employment rates rose for the 55–64 population, which is in stark contrast to what happened to the employment rates of younger adults.a Increases in employment rates of older individuals since 1999 continue a trend that began in (at least) the 1980s for women and the mid 1990s for men in most of the countries, as Figs. 1–4 show. Over the last half a century, trends in employment of older men and trends in employment of women have followed remarkably similar patterns in many developed countries. For example, as Fig. 2 shows, between 1960s and the mid 1990s there was a steady decline in employment rates of men in their early 1960s in many developed economies. For men, the declines were larger in some countries than in others: the employment rate of men aged 60–64 in the Netherlands dropped from 72.3% to 20.5% (or 51.8 percentage points) between 1971 and 1995, while in the US the drop over the same period was 20.2 percentage points. Since the mid 1990s, employment rates of older men have started to increase again in virtually all developed countries. Though the magnitudes of the decline and the following increase differ across countries, the regularity of the patterns is striking. Trends in employment of women during the postwar period have been rather different from those of men. Employment rates of older women have increased steadily and significantly across all developed countries over the last few decades. Rising labor force attachment of successive cohorts of women at all ages dominates the picture. For example, as Fig. 5 suggests, in the UK rising employment rates at older ages reflect the fact that successive cohorts of women have been more likely to be in paid work at younger ages too. There was a particularly sharp increase in employment rates of women in their 30s and 40s between those born in the 1920s and those born in the 1960s. The fact that employment rates ceased to increase further between those born in the 1960s and those a

While employment rates of younger adults did increase between 2007 and 2013 in Germany, the 2.9 percentage point increase seen for younger adults was well below the 12.3 percentage point increase in employment rates among those aged 55–64.

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Fig. 1 Employment of those aged 55–59. Source: Authors’ calculations using data from the OECD and the UK Labour Force Survey.

Retirement Incentives and Labor Supply

Women — Anglo-Saxon, Scandinavia & Japan

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Fig. 2 Employment of those aged 60–64. Source: As Authors’ calculations using data from the OECD and the UK Labour Force Survey.

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Fig. 3 Employment of those aged 65–69. Source: Authors’ calculations using data from the OECD and the UK Labour Force Survey.

Retirement Incentives and Labor Supply

Women — Anglo-Saxon, Scandinavia & Japan

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Fig. 4 Employment of those aged 70–74. Source: Authors’ calculations using data from the OECD and the UK Labour Force Survey.

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Fig. 5 Employment rates of successive cohorts of women in the UK. Source: From Figure 2.7 of Chandler and Tetlow (2014b).

born in the 1970s might suggest that the rapid rise in older women’s employment rates that has been seen over recent decades in the UK might slow down as these later cohorts age. These cohort trends in female employment began at different points in different countries. In particular, as Figs. 1 and 2 show, the rise in older women’s employment rates began later in Italy and Spain than it did in Australia, Canada, the US, and many northern European countries. In the 1970s, employment rates of older women were well below those of men in developed countries. However, steady increases in employment rates of women over the following four decades, coupled with declines in employment of older men up to 1995, mean that employment rates of older women are now much closer to those of men. Among women aged 55–59, employment rates in northern European countries, the US, and Canada are virtually the same as those among men of the same age. For example, in Sweden in 2014, 79.9% of women aged 55–59 were in paid work, compared with 84.0% of men. However, the gaps remain larger in southern European countries: in Italy in 2014, just 48.6% of women aged 55–59 were working, compared with 72.4% of men. The facts described above suggest that the factors driving employment among older groups may be different from the factors affecting younger groups, but they also suggest that there may be common factors underlying the similar trends among the old in

Retirement Incentives and Labor Supply

Fig. 6 Employment rate of men aged 65+ in the UK and the US. Source: Data for the UK from Matthews et al. (1982) and the Labour Force Survey. Data for the US from Moen (1987) and OECD.

different countries. There are many possible explanations for these trends, which we explore in Sections 3–6.

2.2 Historical Context The concept of retirement as a significant period of leisure at the end of life is a relatively recent phenomenon. As Fig. 6 shows, in the late 19th century, over three-quarters of all men aged 65 and over in the US were engaged in gainful employment. This fraction declined steadily over the following century, reaching an employment rate of less than one-fifth by the mid 1990s. Very similar patterns were seen in the UK and other European countries over the same period (Costa, 1998). In the 19th and early 20th centuries, policymakers envisaged retirement as reflecting the point at which older workers (principally men) became incapable of working sufficiently productively. The public pension schemes that were established across much of the developed world at around this time were introduced with the intention that the state should insure individuals against the risk that they would live beyond the point at which they could contribute productively in the labor market. For example, as Costa (1998) summarizes, the statistician Frederick Hoffman argued in 1906 that a country’s productive potential could be maximized if people ceased working at age 65; in a similar vein, the economist (and eventual architect of the UK’s postwar welfare state) William Beveridge argued in 1909 that older workers lacked the adaptability to cope with rapid technological change.

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Germany, under Otto von Bismarck, was the first country to introduce an old-age social insurance program, which came into force in 1889. This pension was founded on the principle that, as Kaiser Wilhelm I wrote to the German Parliament in 1881, “those who are disabled from work by age and invalidity have a well-grounded claim to care from the state.” Reflecting this notion of a pension insuring against disability for work, the eligibility age was initially set at 70. The same eligibility age was adopted by the British, in 1909, when they too introduced an old age pension. For those who were reaching pension age in the UK system’s first year of operation, life expectancy at birth had been just 40 years for men and 43 years for women. Only one-in-four of those born in 1838 in the UK would actually have been alive to receive a pension.b It was only somewhat later that pension eligibility ages were reduced to 65, which subsequently became widely accepted as an appropriate age to retire in many countries. The pension eligibility age was reduced to 65 in 1916 in Germany and in 1925 in the UK, and it was 65 from the inception of Social Security in 1935 in the US.c When the pension age was set at 65 in the UK, in 1925, life expectancy for men at that age was 11.2 years (as Fig. 7 shows). This figure had changed little over the preceding 80 years. However, over the following 90 years (and particularly after 1960), it was to increase rapidly, reaching 18.9 years by 2012. This, coupled with the sharp fall in employment rates of older men described in Section 2.1, led to a rapid expansion of the period spent in “retirement.” The same coincidence of rising life expectancy and falling employment rates led to similar expansions in the prevalence and length of retirement across most developed countries after the Second World War. Most people in developed countries now expect to have a period of leisure at the end of their lives, with the date of their exit from employment determined not only by declining productivity and capacity to work but also by other factors such as their access to publicly and privately provided pensions.

2.3 Trends in Hours of Work As Figs. 8 and 9 show, the pattern of part-time work follows a U shape over the life cycle, at least in the US and the UK. Part-time work in the US is very common at young ages, as many young people attend school and work at the same time. But part-time work is very common at older ages in the US as well: about 40% of working men and 60% of working b

c

In contrast, over four-in-five of the men born in 1943 and the women born in 1948 (who reached the eligibility age for public pensions in 2008) were still alive. Source: Department for Work and Pensions (2008). Age 65 had also been used by the Pensions Bureau in the US as the age of pension eligibility for Union army veterans from 1890 onward (Costa, 1998).

Retirement Incentives and Labor Supply

Fig. 7 Life expectancy of men at age 65 in the UK and the US. Source: UK data from the Office for National Statistics. US data from the Human Mortality Database.

ages 65–70 women are part-time. Part-time work among older workers is even more common in the UK. Part of this increase late in life is related to the trend toward higher self-employment in the late 60s. Many workers are part-time self-employed individuals after age 65. However, conditioning on being an employee, part-time work rises after age 65 too. We do not show part-time rates in France above age 64, because very few French people work after age 65. However, the U-shaped profile in France does seem to be less pronounced. Figs. 8 and 9 also show that part-time work was more common in 2012 than in 1977, especially in France but in the UK too. This trend, however, occurs at all ages. Part-time work after age 65 was common in the US and the UK in 1977.

2.4 Trends in Self-Employment Self-employment constitutes only a small share of total employment across the population as a whole in most developed countries. However, among older workers, it is a much more significant phenomenon. As Figs. 10 and 11 suggest, the fraction of workers who are self-employed rises sharply with age in France, the UK and the US. For example, in France in 2012, fewer than one in ten male workers aged under 30 were self-employed, compared with around one in three workers aged 60–64.

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Fig. 8 Prevalence of part-time working among male workers. Note: Part-time work is defined as working no more than 1500 h a year. Source: From authors’ calculations using Enqu^ete Emploi for France, the Labour Force Survey for the UK, and the Current Population Survey for the US.

There are a number of reasons why self-employment may play a greater role among older people than among younger people. First, historically, employers in many countries have imposed mandatory retirement ages (determined either by government or by company-specific policies). As a result, older people who wished to work beyond that age often had to turn to self-employment instead. Mandatory retirement ages were

Retirement Incentives and Labor Supply

Fig. 9 Prevalence of part-time working among female workers. Note: Part-time work is defined as working no more than 1500 h a year. Source: From authors’ calculations using Enqu^ete Emploi for France, the Labour Force Survey for the UK, and the Current Population Survey for the US.

common across developed countries in the early 1990s but many countries have made them illegal in recent years—for example, Australia, Canada, New Zealand, and the UK (Wood et al., 2010). Second, self-employment may allow greater scope for flexibility in hours and conditions of employment (Banks et al., 2012).

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Fig. 10 Prevalence of self-employment among male workers. Source: From authors’ calculations using Enqu^ete Emploi for France, the Labour Force Survey for the UK, and the Current Population Survey for the US.

3. THE RETIREMENT DECISION 3.1 The Life-Cycle Profile of Hours and Employment Before turning to examine factors that influence individuals’ retirement decisions (in Section 4), it is important to start by characterizing the nature of the retirement process in developed countries. For much of the post-Second-World-War period,

Retirement Incentives and Labor Supply

Fig. 11 Prevalence of self-employment among female workers. Source: From authors’ calculations using Enqu^ete Emploi for France, the Labour Force Survey for the UK, and the Current Population Survey for the US.

retirement has been an abrupt transition for many workers. That is, it typically manifests as a sharp change from working many hours a week to not working at all, rather than workers gradually reducing their hours from full-time to not working. Figs. 12 and 13 show how employment rates and hours of work among the employed differed with age in France, the UK, and the US in 2012 (for men and women,

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Fig. 12 Employment rates and hours of work, by age: men in France, the UK, and the US. Note: Figures for hours of work at ages 70–74 in France are excluded due to small sample sizes. Source: Modified from Blundell et al. (2013), updated using data from Enqu^ete Emploi (France), the Labour Force Survey (UK), and the Current Population Survey (US).

respectively).d In all three countries, employment rates drop sharply at older ages. While the average hours of work per year among those who are employed also decline slightly d

These figures use updated data similar to those presented by Blundell et al. (2013). We are very grateful to Antoine Bozio for providing access to their data to allow us to produce these figures.

Retirement Incentives and Labor Supply

Fig. 13 Employment rates and hours of work, by age: women in France, the UK, and the US. Note: Figures for hours of work at ages 70–74 in France are excluded due to small sample sizes. Source: Modified from Blundell et al. (2013), updated using data from Enqu^ete Emploi (France), the Labour Force Survey (UK), and the Current Population Survey (US).

with age (particularly from age 60 onward), hours of work still remain reasonably high at older ages. For example, in the US, workers on average work over 1500 h a year (equivalent to more than 31 h a week for 48 weeks a year) even in their early 70s. This suggests that many people make a sharp transition in hours of work at the point of retirement.

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The ages at which hours and labor force participation rates decline most rapidly differ across countries. Employment rates decline at a younger age in France than in the UK, which in turn sees an earlier decline in employment than the US. As we will discuss, the declines in each country typically coincide with the ages at which there are large pension and other policy-related disincentives to work and also coincide with the age at which wages decline.

3.2 The Distribution of Hours Worked Near Retirement Age Several papers have noted that a common retirement transition is from full-time work to no work at all. This is an observation that is consistent with the more general finding that much of the variability of labor supply is on the margin of whether or not to work, rather than in the number of hours conditional on working (see, for example, Chang and Kim, 2006; Ljungqvist and Sargent, 2006; Rogerson and Wallenius, 2009; Chetty et al., 2011; Erosa et al., 2014; and Ljungqvist and Sargent, 2014). Much of the literature on the labor supply response to tax reforms has considered only the decision of whether or not to work, sometimes called the “extensive margin.” Other papers assume that everyone works until a fixed and exogenous retirement age and focus on the number of hours worked by workers, sometimes called the “intensive margin.” Figs. 12 and 13 show that—even though both margins are important—most changes in life-cycle labor supply occur along the extensive margin. For example, while in the US participation rates drop dramatically between ages 62 and 65, hours worked among those in employment drop much more modestly. Similarly, employment rates in France drop sharply at age 60, while hours of work among those in work decline only slightly at this age. Table 5 shows the distribution of hours worked by older men and women in France, the UK and the US. The table reveals that in all countries, even at ages 60–64, most working men are working over 1500 h per year, which would correspond to 30 h per week for 50 weeks per year. This finding is corroborated by other studies. Rupert and Zanella (2015) show the density of hours worked at different points in the life cycle in the US. They show that part-time work is rare until ages 64–68. Similarly, for the UK, Chandler and Tetlow (2014a) show that fewer than one-in-ten men in their early 50s work part-time (defined in their analysis as fewer than 30 h a week), but this rises to over half among employed men in their late 60s. Part-time work is more prevalent among women but, as Fig. 13 suggests, this is true at all ages (particularly in France and the UK). Using data from the Current Population Survey, the Panel Study of Income Dynamics, and the Health and Retirement Study, Fan (2015) shows that about 75% of all men who exit the labor force at older ages were working at least 35 h per week in the year prior to retirement. Blau and Shvydko (2011) and Rogerson and Wallenius (2013) report similar facts. Using data from the English Longitudinal Study of Ageing, Chandler and

Retirement Incentives and Labor Supply

Table 5 Distribution of hours worked, by country, age, and sex (2012) Men

Women

Ages 50–54

Ages 60–64

Ages 50–54

Ages 60–64

25.2 0.6 2.1 5.8 26.1 23.5 16.7

77.5 0.9 1.7 2.1 6.3 5.4 6.0

35.5 2.1 5.9 11.0 25.9 13.8 5.9

80.3 1.8 2.4 3.2 6.1 3.9 2.3

24.5 0.9 2.5 4.4 19.0 30.0 18.6

53.0 2.0 4.0 5.9 12.1 15.1 7.9

32.8 2.8 8.4 13.2 24.3 13.1 5.4

70.1 4.0 6.6 6.8 7.3 3.6 1.6

22.9 1.2 1.6 3.4 7.1 42.1 21.7

44.7 1.4 2.5 4.1 6.4 28.3 12.7

32.7 1.9 3.1 6.5 12.0 34.9 8.7

52.6 1.8 3.7 5.9 9.2 21.8 4.9

France

0h 1–500 h 501–1000 h 1001–1500 h 1501–2000 h 2001–2500 h 2501+ h United Kingdom

0h 1–500 h 501–1000 h 1001–1500 h 1501–2000 h 2001–2500 h 2501+ h United States

0h 1–500 h 501–1000 h 1001–1500 h 1501–2000 h 2001–2500 h 2501+h

Source: Blundell et al. (2013), updated using data from Enqu^ete Emploi (France), the Labour Force Survey (UK), and the Current Population Survey (US).

Tetlow (2014b) show that, of those who moved from full-time work into retirement between 2002–2003 and 2012–2013, 68% of men and 60% of women moved straight from full-time work to retirement, without experiencing an intervening period of part-time work, self-employment, or unemployment. However, this does not mean that most individuals make the transition from a fulltime career job to permanent nonwork. Ruhm (1990) shows that less than two-fifths of household heads retire directly from career jobs, over half partially retire at some point in their working lives, and a quarter reenter the labor force after initially retiring. Maestas (2010) shows that nearly 50% of retirees follow a nontraditional retirement path that involves partial retirement or unretirement, and at least 26% of retirees later unretire.

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3.3 Potential Explanations for the Abruptness of Retirement Why does there appear to be so little labor supply variability along the hours of work margin? Perhaps the most important reason is that there are fixed costs to working. It takes time to commute to work. Estimates of mean commuting time in several countries range from about 7% to 10% of market work time (Juster and Stafford, 1991). Furthermore, work involves extra monetary costs, such as food at restaurants and work clothes. Spending falls on average by about 20% at retirement in Britain (Banks et al., 1998), and similar declines in spending have been documented in other countries as well. Part of this fall comes from declines in transportation and food bought in restaurants, suggesting that working imposes fixed costs on workers.e There might also be fixed costs of work on the part of employers. Employers might incur fixed costs to recruit, hire, and train employees, and they might have to pay fixed administrative costs to keep records on each worker. Desk and office space is costly as well. Because these fixed costs must be spread over fewer hours of work for part-time employees, firms are likely to pay lower wages to part-time workers. For example, Aaronson and French (2004) find that a part-time worker makes about 25% less per hour than a full-time worker, which is similar to what is found by Gustman and Steinmeier (1986) and others. Rogerson and Wallenius (2009) stress the importance of this issue in their analysis of participation and life-cycle labor supply. To illustrate how fixed costs of work affect individuals’ decisions about whether to work or not, Fig. 14 shows the labor–leisure tradeoff that arises (in a static model) when there are fixed costs of working. The vertical axis shows the individual’s total income; the horizontal axis shows hours of time, which are divided between leisure and work. The indifference curve ICR (which passes through the point where no labor is supplied) shows that at the reservation wage, wR, the individual is indifferent between working 0 h and the amount of hours of work at wR. If the wage falls below wR, the individual will not work. If the wage rises, the individual will work for sure and, moreover, work a large number of hours. For those who are almost indifferent between working and not, small changes in the wage can induce large changes in hours. However, once wages are high enough to justify working, further wage increases will cause much smaller increases in hours. As an example, in Fig. 14, raising the wage from wR to w1 yields higher utility but leaves hours of work unchanged. French (2005) and French and Jones (2011) find that, in order to fit the decline in hours of work seen among older workers in practice, fixed costs must be high. Depending e

This decline in spending does not necessarily represent a decline in retirees’ standard of living. Aguiar and Hurst (2005) have argued that, even though spending on food declines after retirement, the nutritional quality of the food actually rises as individuals replace the fast food they ate when working with more nutritious home-cooked meals. However, Banks et al. (1998) and others have shown that the declines do not seem to be entirely explained by work-related expenses.

Retirement Incentives and Labor Supply

Fig. 14 The labor supply decision with fixed costs of working.

on the specification, a fixed annual cost of work is estimated at 240- to 1313-h per year by French (2005) and at 826 h per year by French and Jones (2011). Most of these estimates are much higher than the estimates of commuting times in Juster and Stafford (1991), for example. The lower estimates in French (2005) are the estimates that account for a parttime wage penalty: both part-time wage penalties and fixed costs of work imply that it is not advantageous for an individual to work part-time. Rogerson and Wallenius (2013) show that either fixed costs must be large or labor supply very elastic (with an intertemporal elasticity of substitution of labor supply in the range of 0.75) in order to explain the abruptness of retirement. The importance of participation decisions in determining labor supply and the apparent importance of fixed costs in affecting participation lead us to believe that labor supply elasticities are not constant over the life cycle. Instead, they are likely higher at ages when individuals are nearest to the participation margin. Given that the decision to retire by definition implies that the participation margin has been crossed, it is almost surely the case that older workers are nearer the participation margin than younger workers, whose participation varies much less. It is thus plausible that labor supply elasticities are higher at older ages. Many empirical studies confirm this, as we discuss in Section 5.3. However, fixed costs of work are not the only potential explanation for the abruptness of the hours decline at retirement. For example, Fan et al. (2015) develop a retirement model with endogenous human capital accumulation. In such a model, because human

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capital depreciates, individuals have an incentive to cluster their hours in a small number of years. Reductions in work hours lead to reductions in future wages. Thus individuals have an incentive to keep work hours high until retirement.f There are also more institutional reasons for remaining in the labor market. For example, in the US, many individuals work for firms that provide defined benefit pensions, where the value of the pension benefit is a function of final salary, among other variables. Thus, in such schemes in the US, a decline in work hours would lead to lower earnings and thus pension benefits.g Fan (2015) shows that those with pension benefits are more likely to make a discrete jump from full-time work to nonwork than those without a pension. There might also be firm-based constraints. For whatever reason (such as coordination of work schedules), many firms do not let workers reduce their hours at a fixed wage schedule. Consistent with this view, Hurd (1996) shows that the share of the population who are self-employed (who are less likely to face these constraints) rises with age. The self-employed also tend to retire much more gradually than those employed by others. Banks et al. (2012) also find that—in both England and the US—reductions in hours of work are more common among those who change jobs or who move into selfemployment than among those who remain employed in the same job with the same employer. This suggests that there is some rigidity in the employment contracts offered by employers to existing employees. Beffy et al. (2014) formulate and estimate a model with restricted hours choices. Figs. 8 and 9 show that many people who are working at older ages are working parttime. However, in most developed countries, it is still common for people to experience a sharp reduction in hours worked at the point of retirement, rather than gradually reducing their hours of work to zero. The next section discusses the key factors that have been highlighted by the literature as being important determinants of when people retire.

4. RETIREMENT INCENTIVES There are many factors that are likely to incentivize individuals to continue or to cease working at older ages. In this section, we review the main factors that have been identified as being important, describing why these factors might matter in theory and reviewing the reduced form evidence on their importance in practice. Section 5 then f

g

Fan (2015) integrates time nonseparabilities in preferences for labor supply. He shows that these nonseparabilities can create work habits that create a tendency for either high hours of work or no work at all. In the UK, in most defined benefit schemes, pension benefits are a function of final salary calculated on a “full-time equivalent” basis. Consequently, periods of part-time work at the end of a career may have a less detrimental effect on a scheme member’s pension than is the case in the US. However, there may still be a disincentive to move into part-time work if a scheme member would experience a reduction in hourly pay from doing so.

Retirement Incentives and Labor Supply

shows how these factors can be incorporated into structural models of life-cycle consumption and labor supply and assesses the structural evidence on the quantitative importance of these factors. Our focus in both sections is on factors affecting the supply of labor among older workers. We do not devote much attention to factors potentially affecting the demand for older workers. Our focus on the supply side is in part motivated by the evidence presented in Section 2, which suggests that trends in employment of older workers have been rather similar across a large number of countries over recent decades, despite the fact that labor market institutions (such as the nature of employment contracts) are very different in these countries. This suggests that supply-side factors may be the most important.

4.1 Declining Health Both health and employment decline as people get older. For this reason, it seems natural to suspect that health declines are one cause of exits from work. There are several reasons why we might expect health to impact retirement behavior. First, declining health makes work less pleasant. Second, it can reduce an individual’s productivity and thus the individual’s wage. Third, health shocks might reduce life expectancy and thus the amount of savings that an individual needs for retirement. Finally, declining health means that an individual often becomes eligible for benefits from firm- or government-based disability programs, which often stipulate that the individual cannot work while drawing disability benefits. French (2005) shows the life-cycle pattern of hours in the US for those in good and bad health, using data from the Panel Study of Income Dynamics (PSID). The PSID is a panel data set, covering 1968 to the present, which allows us to track individuals over extended periods. Using a fixed effects procedure that accounts for measurement error in health status, discussed in greater detail in French (2005), Fig. 15 shows how wages and hours change for the same men over the course of their lives—distinguishing between those in good and bad health. The top panel of the figure shows the life-cycle profiles of hours worked, conditional on working. Hours begin to decline rapidly after age 59 but this is true of those in good health as well as those in bad health. The bottom panel of Fig. 15 shows life-cycle profiles for employment. Health appears to affect employment rates more than hours worked. Nonetheless, the effect of health on employment rates is modest. The fraction of individuals who report bad health rises from 20% at age 55 to 37% by age 70. French (2005) shows that this decline in health would, with the participation profiles shown in Fig. 15, lead to a 7 percentage point drop in the employment rate, and would thus explain a small share of the drop in participation rates from 87% to 13% between ages 55 and 70. Disentangling the different channels by which health impacts retirement is difficult. Much of the literature focuses on the simpler questions of whether health impacts

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Annual hours worked by health status, workers only 2800 2400

Hours

2000

1600

1200

800 400 30

Healthy Unhealthy 34

38

42

46

50

54

58

62

66

70

66

70

Age Labor force participation rate by health status 1.0 0.9 Labor force participation rate

484

0.8 0.7 0.6 0.5 0.4 0.3 0.2 Healthy Unhealthy

0.1 0.0 30

34

38

42

46

50

54

58

62

Age

Fig. 15 Life-cycle profiles for hours and employment for men in the US. Source: From French (2005).

retirement decisions and of quantitatively how important these impacts are. The literature tends to find that health is an important predictor of retirement. However, most studies find that declining health can only explain a modest share of the decline in employment after age 50. The estimates shown above are some of the higher estimates within the literature. O’Donnell et al. (2015) and French and Jones (2016) provide a range of the recent

Retirement Incentives and Labor Supply

estimates within the literature and also review some of the same measurement issues we discuss below. 4.1.1 Measurement Issues The literature measuring the effect of health on labor supply, starting with Bound (1991) and Stern (1989), has focused on two main issues in interpreting the effect of subjective and objective health measures on labor supply. The first of these is measurement error, which can take multiple forms. One problem is that most data sets have only limited health measures, and thus may only capture one dimension of health. This issue is especially important when considering the effect of objective measures on labor supply. For example, even if studies conclude that certain conditions—say, diabetes—have no significant effect on labor supply, we cannot conclude that health more broadly is unimportant for labor supply, since other (unmeasured) health conditions could still impact on labor supply behavior. Many large surveys—such as the Health and Retirement Study (HRS), the English Longitudinal Study of Ageing (ELSA), the Survey of Health, Ageing and Retirement in Europe (SHARE) and related surveys—now contain a battery of subjective and objective health measures. These are designed to capture the variety of factors that might be important in understanding older people’s behavior. These data have greatly expanded the opportunities to conduct empirical research on this question (Gustman and Steinmeier, 2014). However, even with very detailed and wide-ranging measures of health, problems can arise in estimating how health affects employment. People may, for example, errantly misreport their health status because they misinterpret a question, or interpret the question differently from others. For example, Kapteyn et al. (2007) show that differences in reported work disability between the Dutch and the Americans largely stem from the fact that Dutch respondents have a lower threshold in reporting whether they have a work disability than American respondents. Most likely, measurement error bias leads to an attenuation of the estimated effect of health on labor supply. The second main issue that arises in interpreting the effect of subjective and objective health measures on labor supply is that estimates of the effect of health status on labor supply potentially suffer from “justification bias,” as those who are not working might claim to be unhealthy in order to justify their work status (see, for example, Butler et al., 1987). This would likely lead to an overstatement of the effect of health on labor supply. In most studies, the estimated effect of health on labor supply is found to be larger when using subjective measures than when using objective ones. These differences in estimates could be attributable to either measurement error in the objective measures or justification bias in the subjective measures. Bound (1991) and subsequent papers have found that these differences can be large, and using subjective measures can yield estimates of the effect of health that are several times or more larger than objective measures.

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Finally, the relationship between health and employment could be driven by factors other than health causing employment. It could be that past employment (which is highly correlated with current health) increases economic resources, which in turn causes better health. Alternatively, it could be that health and employment are both caused by other factors earlier in life. For example, income in childhood predicts both income and health as an adult, presumably because the family has more resources to invest in health and human capital of the child. These factors are likely to give rise to persistent heterogeneity, biasing up the effect of health on employment. A popular approach to addressing this problem is to use first differences or fixed effects estimation procedures. These procedures focus on how changes in health impact changes in employment. Blundell et al. (2016a) show that first differences and fixed effects deliver estimates that are several times smaller than OLS. On the surface of it, this may suggest that the usual OLS estimates overstate the effect of health. However, as Blundell et al. (2016b) show, first differences are likely to exasserbate issues of measurement error. Furthermore, they (and Bound et al., 1999) show that not only current health is important, but lagged health is also important. First differences will only capture the effect of changes in current health, not lagged health. Furthermore Blundell et al. (2016b) point out that if lagged health is important for employment, OLS estimates may understate the effect of health on employment also if lagged health is not captured in the OLS regression. 4.1.2 Key Findings Bound (1991) suggests using objective health measures (which are arguably free of justification bias, but suffer from measurement error) to instrument for more subjective measures. He shows that this procedure produces estimates that are close to simply using subjective health measures. This suggests that, for the subjective health measures, the effects of measurement error and justification bias roughly offset. Kreider and Pepper (2007) and Blundell et al. (2016b) come to similar conclusions. For example, Blundell et al. (2016b) find that declining health, measured using a battery of subjective health measures, can explain 11% of the fall in employment of low-education men in England between ages 55 and 70. However, when instrumenting for subjective health using more objective measures, health can explain 14% of the fall. Gustman and Steinmeier (2014) find that health is an important factor in driving early retirement. They find that average retirement ages in the US are about 1 year younger than they would be if everyone were in good health. However, using both cross-sectional and time-series data from 12 developed countries, Wise (2016) presents two types of evidence to make the case that declines in health cannot explain either the sharp drops in employment that still occur at older ages or the steady declines in employment at older ages that occurred up to the mid 1990s. First, the papers in Wise (2016) show that the trends in “health” (as measured by 1-year mortality probabilities) of older men across many developed countries are very different from the

Retirement Incentives and Labor Supply

trends in employment. Steady declines in mortality rates since the mid 1970s were accompanied first by declining employment rates and then (from the mid 1990s onward) by steadily rising employment. Second, the papers compare employment rates of older people with those of similarly healthy younger people—using the detailed health measures from the HRS, ELSA and SHARE (described above) to define health. Evidence from all 12 countries suggests that health does decline on average across successively older age groups but that the declines seen are far from sufficient to explain the large differences in employment rates by age. 4.1.3 Trends in Health Recent results from Vos et al. (2015) suggest improvements in health among the aged. Life expectancy is rising among the elderly, and the Global Burden of Disease Study suggests that much of the rise in life expectancy represents an increase in healthy life expectancy. 4.1.4 Summary Taken together, the literature suggests that falling health is an important determinant of retirement and—as we discuss in Section 5—it is a feature that is worth capturing in a retirement model. Recent and projected future trends of improving health among older people might also suggest that employment rates of older people will continue to increase in future. However, the available evidence clearly suggests that the great majority of variation in retirement is not explained by health.

4.2 Substitution Effects, Wealth Effects, and Liquidity Effects There are many financial incentives for retirement that individuals face, coming from declining wages, public and private pensions, other government programs, and (in some countries, notably the US) health insurance. They can create incentives that affect retirement decisions for three main reasons. • Substitution Effects. Changes in wage opportunities as people age, as well as the operation of the tax, benefit, and pension systems in a country, can affect the relative attractiveness of working vs not working at different ages. For example, public pension schemes in many countries generate high implicit tax rates on labor income after a certain age. These encourage households to work less when old. Similarly, if individuals’ productivity declines as they age, they may be able to command higher wages at younger ages than at older ages and so find it less attractive to work as they get older. • Wealth Effects. All public pension schemes have an insurance aspect, which implies redistribution between individuals. Moreover, most public pension plans are pay-asyou-go systems, where taxes collected from the working young are used to finance current retirees’ benefits. Even if a system lacks an insurance aspect, the actuarial value of a retiree’s benefits rarely equals the actuarial value of the taxes he/she paid while

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working. Public pensions can therefore increase (decrease) a household’s lifetime wealth, allowing it to finance its retirement with fewer (more) years of work. The redistribution/insurance aspect of pension schemes is particularly large for those with low income. • Liquidity Effects. Public pension benefits tend to be illiquid: that is, households cannot borrow against future benefits. As a result, many households cannot finance their retirement until pension benefits become available. If public pensions crowd out private savings that would otherwise have been more liquid, they may delay retirement. Understanding the quantitative importance of substitution effects, wealth effects, and liquidity effects is difficult because pension schemes are complex and individuals are likely to be affected by incentives from many different public programs and private pension schemes at the same time. Furthermore, each program induces substitution effects, wealth effects, and liquidity effects, making it difficult to disentangle the relative importance of each effect. In the following sections, we examine the main factors and institutional features that result in important financial incentives to remain in or leave work at older ages. In each case, we describe how the financial incentives might operate in theory and then summarize the empirical evidence.

4.3 Retirement Incentives from Falling Wages One often-discussed fact is that wages follow a hump shape over the life cycle: wages rise at younger ages and fall near retirement age. Falling wages are a potentially powerful retirement incentive that individuals face. A number of reasons have been put forward for why people might face lower wages as they get older (Weiss, 1986). If health affects productivity, then declines in health with age—discussed in Section 4.1—could result in declining productivity and thus declining wages with age. The human capital model (Mincer, 1974; Becker, 1975) suggests that wages vary over the life cycle because of differences in investment in depreciable human capital. This theory postulates that older people will perceive less benefit from investing in their human capital—because they have fewer years remaining to reap the rewards—and so their human capital (and thus the wage that employers will pay them) will decline more rapidly than for younger workers. However, while there are numerous theoretical reasons why we might expect to see wages falling as people get older, the empirical evidence on this is not conclusive. 4.3.1 Measurement Issues Measuring the extent to which wage offers fall with age near retirement appears superficially to be a simple question. However, for several reasons, measurement of whether wage offers fall with age is a challenging task. First, cross-sectional comparisons of wages of the old with those of the young compare older individuals born in earlier years with younger individuals born more recently. Since younger people born more recently have higher lifetime wages than older people born long ago, failure to account for this problem likely leads to an understatement of

Retirement Incentives and Labor Supply

wage growth with age. This problem can be solved by tracking wage growth of birth cohorts, and how wages change with age. The best papers in the literature address this important issue. A second and more difficult problem is that we do not observe the wages of those who do not work. Those exiting the labor market may be earning more or less than those who remain in the labor market. If high-wage people are more likely to remain in the labor market to old age while low-wage people retire early, then estimates of wage growth will come from comparisons of all potential workers when young with only high-wage individuals when old. This will likely lead us to overstate wage growth when old. If the reverse is true, we would understate wage growth when old. To help understand this issue, consider the following model of wages, where the logarithm of wages, lnWt , is a function of age, t, plus an autoregressive component of wages, ωt: ln Wit ¼ W ðtÞ + ωit

(1)

W(t) is the age-specific component to wages that we wish to recover, and the idiosyncratic component of wages is ωit. The selection problem is that wages are observed for workers but not for nonworkers. French (2005) and French and Jones (2011) attempt to address this problem using a fixed effects estimator. The idea here is to decompose the idiosyncratic component of wages ωit into a permanent person-specific component αi (which is potentially correlated with employment) and a stochastic component uit: ωit ¼ αi + uit

(2)

αi summarizes time-invariant factors (such as education and ability) and uit is the part that is orthogonal to αi by construction. The fixed effect (αi) can be eliminated using first differences or a fixed effects estimator. However, first differencing or fixed effects on Equation (1) will not eliminate the average change in uit in a given year. The average value of uit might not be equal to 0 if those who received a bad wage shock dropped out of the labor market, for example. Therefore, using fixed effects estimation or first differencing to estimate Equation (1) will not on its own be sufficient to identify the object of interest, which is the relationship between age and wage offers, W(t). Formally, even if E½ ln Wit
ln Wit
1  ¼ ½W ðtÞ
W ðt
1Þ + E½ðαi + uit Þ
ðαi + uit
1 Þ ¼ 0

(3)

among all (whether in work or not), most likely the expected change among those continuously working is not 0: E½ln Wit
ln Wit jworking at t and t
1 ¼ ½W ðtÞ
W ðt
1Þ + E½ðαi + uit Þ
ðαi + uit
1 Þjworking at t and t
1 ¼ ½W ðtÞ
W ðt
1Þ + E½uit
uit
1 jworking at t and t
1 6¼ 0

(4)

Thus, first differencing eliminates the fixed effect αi but does not address the fact that those who work in periods t and t
1 are a selected sample.

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Because the fixed effects estimator is identified using growth rates for wages and not levels of wages, composition bias—the problem that persistently high-wage and lowwage individuals drop out of the labor market at different times—is not a problem if wage growth rates for workers and nonworkers are the same. However, if individuals leave the market because of a sudden wage drop, such as from job loss, then wage growth for workers will likely be greater than wage growth for nonworkers. This problem will likely bias wage growth upward, thus understating the amount of wage declines late in life. French (2005) and French and Jones (2011) estimate structural life-cycle models with realistic wage shocks estimated from the data. Consistent with intuition, they find that the fixed effects estimator modestly understates the extent to which wages decline late in life. A third issue is whether measured wage differences between old and young individuals reflect only the potential productivity of these individuals or whether they also pick up (potentially unobserved) characteristics of the types of jobs they each do. Although declining productivity is one potential explanation for declining wages, (unobserved) differences in the types of jobs that older and younger people choose to do could provide an alternative explanation. For example, some of the measured declines in wages with age appear to come from people switching from higher-paying full-time jobs to lowerpaying, less strenuous part-time jobs (Johnson and Neumark, 1996; Haider and Loughran, 2010). Aaronson and French (2004) show that taking a part-time job causes individuals to receive a lower offered wage. They estimate this using arguably exogenous variation in hours caused by the Social Security rules. The Social Security rules provide incentives to reduce work hours exactly at ages 62 and 65. It is exactly at these ages that we observe the sharpest decline in wages. Thus the decline in wages may merely reflect a transition from full-time jobs to part-time jobs. Other papers have also made the point that parttime workers earn lower wages than full-time workers. If the decline in wages represents a decline in productivity, then declining wages near retirement provide an incentive to work more when young and less when old. However, the other explanations for why wages decline near retirement often imply that there is no strong work disincentive to retire at older ages. 4.3.2 Key Findings Some papers find that wages fall rapidly near retirement age, whereas other papers find that wages do not fall near retirement age. This is true even when using similar methods and data. For example, French (2005) uses data from the Panel Study of Income Dynamics (PSID) with a fixed effects estimator and finds that wages fall with age after age 60 in the US. Fig. 16, taken from French (2005), shows predicted wages, conditional on health and age, using these procedures when including a full set of age dummy variables and age dummy variables interacted with health status. Fan et al. (2015) use Survey of Income and

Retirement Incentives and Labor Supply

Average hourly wage by health status, 1987 dollars 16

14

Hourly wage

12

10

8

6

4 20

Healthy Unhealthy 30

40

50

60

70

80

Age

Fig. 16 Life-cycle profiles for wages for men in the US. Source: From French (2005).

Program Participation (SIPP) and Current Population Survey (CPS) data and find that wages fall in the US when not accounting for fixed effects, but do not fall when accounting for fixed effects. Casanova (2013) uses data from the HRS and finds that—after using a fixed effects estimator with an additional selection correction to address transitory shocks and controlling for part-time employment status—wages do not fall. It is unclear what drives these discrepancies in the estimates described above. Some recent papers have noted that, over recent years, the negative relationship between age and wages toward the end of working life appears to have weakened and that wages of older workers have been growing more rapidly than those of younger workers. Rupert and Zanella (2015) use data from the PSID and the CPS to measure how wages change near retirement for different cohorts of individuals. They find that cohorts born before the Second World War (who entered the labor market before the 1960s) experienced a decline in wages toward the end of working life. In contrast, those born during or after the Second World War appear to have experienced no such fall in wages as they have aged. Consistent with this, Aaronson and French (2004) find, using fixed effects estimators, that wages decline between ages 60 and 65 by approximately 4% per year in the PSID data over the period 1968–1997, 3% per year in the HRS data covering the 1992–2000 period, and only 1% per year in the matched March and Outgoing Rotation Group samples from the CPS starting in 1979. Thus whether wages fall or not in the US appears to vary with sample period and data set.

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Fig. 17 Growth in median gross hourly wages for men in the UK. Source: From authors’ calculations using the Annual Survey of Hours and Earnings.

Fig. 18 Growth in median gross hourly wages for women in the UK. Source: From authors’ calculations using the Annual Survey of Hours and Earnings.

Figs. 17 and 18 show data on wages for the UK, relative to the base year of 2004. They show that older workers have fared comparatively well in recent years, certainly compared with young workers. This may suggest that—if declining wages used to act as an incentive for older people to leave work—this incentive has perhaps weakened in more recent years.

4.4 Retirement Incentives From Public Pensions Public pension schemes likely affect employment patterns of older people across many developed countries. As we discussed in Section 2, public pension schemes were introduced in many developed countries from the late 19th century onward. These were originally intended to provide an income to the minority of people who survived to very old

Retirement Incentives and Labor Supply

age but were unable to continue working. However, as life expectancies increased, more and more people reached the eligibility ages—increasing the importance of these schemes in affecting incentives to work. 4.4.1 Common Features of Public Pension Schemes Across Countries Although the precise details of public pension schemes differ across countries, many of them have common features. We begin by describing these. For most developed countries, public pension schemes are defined benefit (DB) in nature—that is, pension benefits are a function of the age at which the individual begins drawing benefits and of earnings when working (as well as other factors, such as date of birth and marital status). Although a number of countries, such as Italy and Sweden, have now moved toward defined contribution (or notional defined contribution) systems, we focus in this section on features of DB schemes. This is because DB schemes can have strong effects on incentives to leave work at older ages, which are typically not present in defined contribution schemes. Public pension programs in most countries impose an early and/or normal “retirement” age. These are, respectively, the earliest age at which an individual can receive any income from a public pension scheme and the earliest age at which an individual can receive an unreduced pension. Although these are typically referred to as “retirement” ages, in some countries’ public pension systems these ages simply relate to the date at which pension income may be claimed and have a weak or nonexistent relationship to employment. In many countries, individuals can draw benefits and work at the same time with little tax penalty. The effect of the public pension scheme on individuals’ incentives to participate in paid work typically changes at the early and normal retirement ages. This happens for a number of reasons, some of which relate to other common features of public pension schemes. First, public pension schemes are typically “contributory”— that is, by continuing to work and contribute to the system, individuals can accrue entitlement to a higher future pension income. There is typically a greater incentive to continue working while it is still possible to accrue additional rights. In many countries, the ability to accrue additional rights ceases at the normal retirement age. Second, employment incentives can be affected by whether or not the public pension system offers any adjustment to pension benefits for early/late claiming (i.e., before/after the normal retirement age). If benefits are adjusted, this can increase the incentive to delay claiming (and possibly also the incentive to carry on working). Finally, in many countries, pensioners will have their benefits reduced if they have income from earnings, often referred to as an “earnings test.” This reduces the incentive to engage in paid work once a person is in receipt of her public pension income. A further common feature of public pension programs is that individuals are unable to borrow against future public pension income. This can induce liquidity constraints on

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individuals’ behavior, particularly in countries where (or for individuals for whom) public pension programs constitute a very large share of retirement saving. We discuss these incentives with reference to the specific case of the U.S. Social Security system. We then discuss important differences between the workings of a number of European public pension schemes and the US one. Table 6 provides a summary of public pension scheme rules in a number of countries. We discuss some of these in the text below. 4.4.2 A Detailed Example: Public Pension Programs in the United States The American public pension program is a pay-as-you-go pension scheme called Social Security. On average, Social Security replaces about 40% of preretirement earnings; the replacement rate is higher for those with low lifetime income. Private pensions, which are discussed in more detail in Section 4.5, also replace a large share of preretirement earnings. Private pension replacement rates tend to be higher for those with relatively high lifetime income. Gustman and Steinmeier (1999) and Scholz et al. (2006) both found that mean private pension wealth and mean Social Security wealth (that is, the expected discounted value of the pension benefits) at the end of working life are just over $100,000 each in 1992 dollars, although median private pension wealth is much smaller than median Social Security wealth. Social Security distorts labor supply in four ways. First, Social Security benefits depend on total contributions to the system during the worker’s 35 highest-earning years. Once a worker has paid into the Social Security system for 35 years, additional years of work increase his/her benefits only if earnings in those years exceed earnings from earlier years. Thus an important work incentive may disappear after 35 years in the labor force. Second, Social Security is financed by a payroll tax of 5.3% on both workers and firms (so the total tax is 10.6%). In addition, workers and firms each pay a 0.9% tax for disability insurance and 1.45% for Medicare, resulting in a 7.65% tax on both workers and firms. These taxes reduce the after-tax wage and thus the incentive to work. Although tax payments into the Social Security system usually lead to higher benefits, the links are indirect and variable. For example, tax payments made by younger workers translate into higher benefits only after they retire, a substantial delay; tax payments made by older workers translate into higher benefits much more quickly. In short, the net tax rate imposed by Social Security is higher for younger workers and higher earners (see, for example, Feldstein and Samwick, 1992). Third, until recently, the basic benefit formula encouraged workers to claim benefits by age 65. The age at which the individual applies for Social Security affects the size of the annual benefit. Most individuals can begin drawing benefits at age 62. Between 62 and the normal retirement age (which, as Table 6 describes, was 65 until 2002 and is currently 66), benefits are reduced by 5.0-6.7% for every year before the normal retirement age that benefits are drawn. This is roughly actuarially fair for single men: that is, the reduction in

Table 6 A summary of country-specific public pension scheme rules Increase in pension rights if Normal retirement age continue working Early retirement (NRA) beyond ERA/NRA? Country age (ERA)

Deferral rate/ actuarial adjustment?

Australia

65 (increasing to 67, 2017–23).

n/a

No: pension is noncontributory, eligibility based on being resident for 10+ consecutive years.

No

Belgiuma

Until 2012: 60 (subject to 35 years’ contributions). Gradually rising to age 63 in 2019 (with 42 years’ contributions).

M: 65. W: increased from 60 to 65, 1997–2008. M&W: to be increased to 66 in 2025 and 67 in 2030.

Only if it boosts best 45 years’ earnings.

No penalty for claiming before NRA. No bonus for deferring beyond NRA.

Canada

60

65

Yes, until age 70.

Until 2011:b 0.5% per month. From 2014: 0.7% boost for claim after NRA. From 2017: 0.6% reduction for claim before NRA.

Earnings test?

Generosity

Pension is means tested against any income above AUD 4200/7500 p.a. (singles/couples); 50% withdrawal rate. Yes. From 2016, earnings test does not apply to those aged 65+ or those with 45+ years’ contributions before NRA.

Benchmarked to 28%/42% of male total average weekly earnings (singles/ couples).

Until 2011, necessary to have a period of at least 1 month without earnings to claim public pension.

75% of average lifetime earnings for one-earner couples, 60% for singles. (Floors and ceilings also apply—benefits are becoming increasingly flatrate.) Replaces up to 25% of average lifetime earnings up to a cap. Average calculated between ages 18 and 65/70. Maximum monthly benefit CAD$1021.50 (2013). Continued

Table 6 A summary of country-specific public pension scheme rules—cont’d Increase in Normal pension rights if retirement age continue working Early retirement (NRA) beyond ERA/NRA? Country age (ERA)

Denmark

France

Germany

Can claim postemployment wage (efterløn) from ERA. 1979–2014: 60. 2014–2017: increased to 62. 2017–2023: increased to 64. 2023 onward: increasing with longevity projections. 60 (with 41 years’ contributions). 2010–2016: increased to 62.

Efterløn ceases and folkepension starts from NRA. 1979–2004: 67. 2004–2006: reduced to 65. 2014–2017: increasing to 67. 2023 onward: increasing with longevity projections. 65 (to get full rate without meeting contributory conditions). 2010–2016: increased to 67.

63 if have 35 years’ contributions. Until 2012: 60 (W) if had 15 years’ contributions with 10 after age 40.

Until 2012: 65. 2012–2029: increasing to 67.

Deferral rate/ actuarial adjustment?

Earnings test?

Generosity

Entitlement is residence based (maximum 40 years).

Between ERA and NRA: more than actuarially fair. Beyond NRA: actuarially fair (using official life tables). Maximum 120 months beyond NRA. Must work 83+ h per month to defer.

Efterløn and folkepension benefits are earnings tested.

Folkepension: DKK 12,462 per month for a single person (2016); compares with median equivalized monthly disposable income of DKK 19,000 (2014).

Yes, even after NRA.

5% p.a. penalty for claiming before NRA. 5% p.a. bonus for delaying claim (maximum 5 years post-NRA).

No, provided do not work for same employer as before claiming pension.

Yes: yearly pension rights increase with each year of service as long as no benefits have been claimed (amount depends on relative income position).

Since 1997, 3.6% p.a. if claim before NRA. 6% bonus for deferring beyond NRA.

Only for those between ERA and NRA. Pension fully withdrawn if earn above €450 per month.

Replaces 50% of best 25 years’ earnings. (Additional mandatory pension benefits increase this to around 75%.) Earnings related. Current pensioner with 45 years’ service at average wage receives pension worth 44.4% of current economy-wide average earnings (2014).

Italyc

From 2002: 57 with 35 years’ contributions; any age with 37 years’ contributions. Gradually increased from 2011 to 60 with 36 years’ contributions; any age with 40 years’ contributions. Contribution condition rising to 46 years (M)/45 years (W) by 2050.

From 2000: 60 (W) and 65 (M) (with 20 years’ contributions). M and W: increasing to 66 years and 7 months by 2018. Eligibility age now linked to changes in life expectancy— expected to increase to 69 years and 9 months (M/W) by 2050.

Japan

Flat-rate benefit (M): increased from 60 to 65, 2001–2013. Flatrate benefit (W): increased from 60 to 65,

n/a

Yes. If had more than 18 years’ contributions by end of 1995: –up to 2012, can increase average wage of last 5/10 years, and increases number of years’ contributions (if 0),am by contrast, would induce the adults born at t to pass the subsidy on to their children in the form of larger bequests, because they would regard the subsidy to themselves as a tax on their children (“Ricardian equivalence”). The present and the future cohorts’ lifetime consumption plan and utility level would consequently be unaffected.an If fertility is endogenous, however, the adult member of cohort t will free-ride on each other by reducing their own fertility, and more than compensating each of their own children for the extra (social security) tax burden they will have to bear in future life. Therefore, Ricardian equivalence will not apply in full. As usual, free-riding will cause inefficiency. As the effect on the utility of cohort t is nonetheless positive, however, it must be the case that the efficiency cost is more than compensated by the implicit pension subsidy.

3.4 Pensions in the Presence of Ascending Altruism Given the additional complexities associated with social security, we will examine the effects of pension policy in the basic version only of the ascending-altruism model set out in Section 2.3. In Nishimura and Zhang (1992), Zhang and Zhang (1995), and Zhang (1995), the utility function is a log-linear version of (24),ao U t ¼ ln c1t + β ln c2t + η ln c2t1 , 0 < β < 1, 0 < η < 1:

(50)

The marginal cost of children is increasing (μ > 1) in n . The amount of money or goods that an adult born at t transfers to her elderly parent is expressed as a share of the former’s full income, t ap

pt ¼ qt ð1  θÞw, 0  qt  1: Unlike ψ, qt is a choice variable. The budget constraints are now μ

c1t + st + ½ψ ðnt Þ + qt ð1  θÞw ¼ ð1  θÞw, al

am

an

ao

ap

(51)

Utility would be negatively affected only if the pension contribution were larger than voluntary savings, and current adults were credit rationed. That is the case actually examined by Barro in the article cited, and again and again by many others after him. Incidentally, if everybody were altruistically linked to everyone else (and not only to their own children) as hypothesized by Bernheim and Bagwell (1988), all public transfers would be neutralized by private transfers of opposite sign. Wigger (1999) adds a term increasing in nt and thus introduces a demand for children as a consumption good in addition to a demand for children as an asset. To keep the two mechanisms separate, we do not follow him in this. Were it not so, the solution would be at a corner, with fertility equal either to zero or to the lower of the maximum number of children that can be financed on credit and the physiological maximum.

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μ  w + δt , c2t ¼ rst + nt ð1  θÞqt + 1 + θ 1  ψ nt + 1

(52)

and μ

c2t1 ¼ rst1 + nt1 fð1  θÞqt + θ½1  ψ ðnt Þ gw + δt1 : At an interior solution,aqðnt , qt , st Þ satisfy the FOCs 
μ  μ1 ð1  θÞqt + 1 + θ 1  ψ nt + 1 ¼ rψμðnt Þ ,

(53)

(54)

μ

and

rst1 + nt1 fð1  θÞqt + θ½1  ψ ðnt Þ gw + δt1 μ ¼ ηnt1 fð1  θÞw  st  ½ψ ðnt Þ + qt ð1  θÞwg,

(55)

 
μ  t +δ rst + nt w ð1  θÞqt + 1 + θ 1  ψ nt + 1 μ ¼ rβf½1  ψ ðnt Þ  qt ð1  θÞw  st g:

(56)

In steady state, these conditions become ð1  θÞq + θð1  ψnμ Þ ¼ rψμnμ1 ,

(57)

rs + nw½ð1  θÞq + θð1  ψnμ Þ ¼ ηn½ð1  θÞð1  ψnμ  qÞw  s,

(58)

rs + nw ½ð1  θÞq + θð1  ψnμ Þ ¼ rβ½ð1  ψnμ  qÞð1  θÞw  s:

(59)

and

Dividing (58) by (59), we find β n ¼ r: η

(60)

As in the descending-altruism model, therefore, n is independent of θ. Assuming that people care about their own old-age consumption at least a little more than they care about that of their parents (β > η), n will again be larger than r. Therefore, social security will raise steady-state utility. On the other hand, in view of (57), ð1  θÞq + θð1  ψnμ Þ η ¼ n: ψμnμ1 β As n is independent of θ, this equation makes q a decreasing function of θ. With n and q so determined, (58) tells us that s is increasing in θ. In steady state, therefore, social security has no effect on fertility, but raises savings and lowers filial support for elderly parents.

aq

We are ruling out the possibility, considered in Section 2.3, that the marginal return to children could be larger than r and st consequently equal to zero.

Conflict and Cooperation Within the Family

Table 3 Pension policy effects in the ascending-altruism model Fertility Savings Transfer to child

Transfer to parent

Utility

θ δt

0 0

0 0

>0 0, dδt H and dst ð1 + ηÞð1  μÞrψμðnt Þμ2 nt1 ð1  θÞw ¼  < 0, dδt H where H is the Hessian determinant, positive at a maximum. This tells us that an adult receiving a windfall from the pension administration will donate part of this windfall to her elderly parent and consume the rest. As the return to children is not affected, her fertility behavior will not change, but her utility will rise. In a closed economy,ar the effect of θ on s will again be moderated by endogenous changes in r and w. Given that (60) still holds, however, n will again be larger than r, and social security will again raise steady-state utility.as These results are summarized in Table 3.

4. FAMILY RULES In reality, individual actions are constrained not only by the law of the land but also by cultural, familial, or religious norms. In the theoretical economics literature, such norms ar

as

The analysis is in Barro and Becker (1989). There, the production function (not necessarily Cobb–Douglas) displays constant returns to scale, and y grows at the constant Harrod-neutral technical progress rate g. To make the results comparable with those of the models examined in the last subsection, we assume g ¼ 0. Wigger (1999) finds a nonlinear relationship between θ on the one hand, and n and U on the other. Given, however, that he assumes endogenous technical progress, and that the model is a hybrid of the ascending-altruism and the augmented life-cycle models because children yield direct utility, his results are not easily comparable with those of the basic ascending-altruism model examined here. Besides, he assumes that p is proportional to w rather than ð1  θÞw, and that pension contributions are levied on full rather than actual income. These assumptions are hard to justify and do not allow the small-open-economy effects of θ to be signed.

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are usually ignored or taken as given (as, for example, in the “punishment” model examined at the end of Section 2.3). In the empirical literature too, they are usually taken to be exogenous and controlled for by introducing variables such as ethnicity, religion, and marital status. An early theoretical analysis of the consequences these norms can have is in Neher (1971). The author models a primitive economy where property rights are vested in families, rather than individuals, and family income is distributed according to a “ …share alike ethic whereby all members of the family have equal claim to the product whether they work or not.” This ethic reduces the individual incentive to work hard and refrain from immediate consumption, because the benefit is shared with other family members, and increases the incentive to have children, because the cost of raising them is similarly shared. Production, consumption, and asset accumulation will consequently be inefficiently low, and fertility inefficiently high. Arguably, norms like the one envisaged by Philip Neher have lost currency because they make everyone poorer. If a norm persists and is obeyed without or even against the enforcement apparatus of the modern state, it must be that it helps to solve a coordination problem, and is thus seen by everyone concerned as beneficial. There have been several attempts, including Esteban and Sakovics (1993), Cigno (1993), Cigno et al. (2006), Caillaud and Cohen (2000), Rangel (2000), Rangel (2003), Guttman (2001), Anderberg and Balestrino (2003), Lindbeck et al. (2003), and Lindbeck and Nyberg (2006), at explaining the emergence and persistence of social or family norms as the outcome of some kind of intergenerational game. Rangel models the provision of what he calls “backward intergeneration goods” (BIGs) and “forward intergeneration goods” (FIGs) as an infinitely repeated game between generations. As examples of the former, the author mentions unfunded social security and individual care of elderly parents.at As examples of the latter, he gives parental or public investment in education, investment in infrastructure, and the preservation of the environment. He shows that the provision of FIGs is sustainable as an equilibrium (not necessarily efficient) because these goods generate a surplus. BIGs, by contrast, do not generate a surplus, and their provision is sustainable as an equilibrium only if combined with the provision of FIGs. Cigno (1993) and Cigno et al. (2006, 2016) reach analogous conclusions by a different route. The 1993 paper establishes conditions such that a set of family rules will be selfenforcing in the sense that it is in every family member’s interest to obey them and have them obeyed. The 2006 paper takes the analysis further by establishing conditions such at

As pointed out in Section 3, the first example is somewhat misleading. The pension benefits received by a cohort of individuals who did not pay pension contributions (“inaugural gains”) are indeed BIGs, but those received by subsequent cohorts are not. In steady state, the net benefit of participating in the system is the same for every cohort (or increasing at the technical progress rate if there is any).

Conflict and Cooperation Within the Family

that the rules not only self-enforcing but also renegotiation–proof and may thus be regarded as the family-level equivalent of the political constitution that restricts the legislative powers of successive parliaments (in particular, their power to pass legislation that benefits present electors at the expense of future ones) at the national level.au The 2016 follow-up introduces sex differentiation, sexual reproduction, and marriage. In the following subsections, we will look at this “constitutional” approach in more detail and examine the way in which family-level arrangements stand up to the competition of publicly provided old-age security.

4.1 Family Constitutions In its simplest form, a family constitution prescribes (a) the minimum amount of money or goods, z  ξ, that an adult must transfer to each of her children if she has any, and (b) the minimum amount of money or goods, x  0, that she must transfer to her parent if the latter obeyed the constitution in her turn.av This gives each adult a choice of two strategies: cooperate (“comply” with family rules), or defect (“go it alone” in the market). The model assumes rational expectations. The utility function is (1) as in the basic lifecycle model. For a go-it-aloner, the cost of having n children is ξn + wc ðnÞ. As her children, if she decided to have any, would give her nothing when she got old (because, even if they chose to comply, the family constitution would allow them to give their parent nothing), this person will then choose n ¼ 0. Given that she is past infancy, and that u0 ðc0 Þ is consequently a by-gone, the payoff of the go-it-alone strategy is V ðr, wÞ ¼ max u1 ðw  sÞ + u2 ðrsÞ s

and her choice of s will thus satisfy u01 ðw  sÞ ¼r u02 ðrsÞ

(61)

as in the basic life-cycle model. For a compiler, the cost of children is x + zn + wc ðnÞ, higher than for a go-it-aloner even if z is equal to ξ because she must pay her parent a fixed amount x. Next period, however, if her children also comply, she will receive x from each of them. In equilibrium, the payoff of the comply strategy is thus au

av

One instance of such behavior is the accumulation of public debt, that will have to paid by future generations. A constitutional clause prescribing that the government must break even every year, or every legislature, will stop that. We can safely assume that zwill be at least as large as ξ, and x at least as large as ξ divided by the number of children the parent has.

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V  ðr, w, x, zÞ ¼ max u1 ðw½1  c ðnÞ  s  x  znÞ + u2 ðrs + xnÞ: nc , s The associated choice of ðn,sÞ will equate the MRS of adult for old-age consumption to the marginal return of children, u01 ðw ½1  c ðnÞ  s  x  znÞ x ¼ , u02 ðrs + xnÞ z + wc 0 ðnÞ

(62)

and satisfy the portfolio condition that the said return must be at least as large as the return to savings, x  r: (63) z + wc 0 ðnÞ This condition differs from the analogous one we encountered in the ascending-altruism model only in that the numerator of the LHS term is fixed by family rules, rather than chosen by the children as in that model. Here too, the condition will be satisfied as an equation, and the optimization will have an interior solution, if c 0 ð:Þ is an increasing function. Like the generic adult in the ascending-altruism model, a compiler will have children to the point where her marginal valuation of current consumption equals the marginal return to children. If the marginal cost of children is increasing, (63) will hold as an equation (interior solution), and the adult in question will save. Otherwise, she will set s ¼ 0 and rely entirely on her children for old-age support. Notice that, if the marginal cost of children is increasing, the return to children will be equal to r for the marginal child, but will be greater than r for inframarginal ones. Therefore, children generate a surplus. For complying to be the winning strategy, this surplus must be at least equal to the fixed cost of complying, x.aw If that is the case, V  ðr, w,x,zÞ  V ðr, wÞ

(64) ax

and the set of comply strategies is a subgame perfect Nash equilibrium. Otherwise, go-it-alone will be the winning strategy, and the adult in question will behave as in the basic life-cycle model. Given that an infinite number of ðx, zÞ pairs may satisfy (64), which will prevail? Cigno (2006a) adapts the renegotiation-proofness selection criterion developed by Bernheim and Ray (1989) and Maskin and Farrell (1989) for a repeated game where the players are always the same, to a game like the present one where the players change aw

ax

In Cigno (1993) and Cigno et al. (2006), the marginal cost of children is constant as in the models examined in the last section. For (64) to hold, the return to children, also constant, must then be strictly larger than r. As a result, compilers do not save. By allowing for an increasing marginal cost of children, the version presented here generalizes the original slightly, and makes it more realistic. For a demonstration, see Cigno (1993).

Conflict and Cooperation Within the Family

at each round (as a cohort enters adulthood and another leaves it). Compared with all the other constitutions which also satisfy (64), a renegotiation-proof constitution has the additional property that it is not Pareto-dominated by any of them. A constitution prescribing ðx,zÞ will then be renegotiation-proof if and only if it maximizes U ðn, s, x, zÞ ¼ u0 ðzÞ + u1 ðw ½1  c ðnÞ  s  x  znÞ + u2 ðrs + xnÞ

(65)

subject to (64). The associated allocation will satisfy (62) and (63), u00 ðzÞ u01 ðw ½1  c ðnÞ  s  x  znÞ  u01 ðw ½1  c ðnÞ  s  x  znÞ u02 ðrs + xnÞ

(66)

u01 ðw ½1  c ðnÞ  s  x  znÞ x ¼ ¼ n: u02 ðrs + xnÞ z + wc 0 ðnÞ

(67)

and

If (64) is not binding, (66) will be satisfied as an equation, and the allocation will be a Pareto optimum. Otherwise, the allocation will be a constrained Pareto optimum. The analysis can be extended in a number of directions. Rosati (1996) shows that allowing for a child’s survival beyond infancy (or, more generally, for her future ability to support her elderly parent) to be uncertain may give rise to a precautionary demand for savings, but does not alter the model’s predictions in any substantive way. Cigno and Rosati (2000) let a person’s utility depend not only on money or market goods but also on the personal services (“care”) this person receives from her parent during infancy, and from her children in old age. The constitution is reworded so that it requires every adult to give each of her children a basket of personal services and market goods yielding at least the same utility as a sum of money z, and her parent a basket of personal services and market goods yielding at least the same utility as a sum of money x. By allowing adults to pick the cost-minimizing mix of money and personal services with which to satisfy the constitutional requirements, this extension reduces the cost of complying and makes it more likely that a self-enforcing family constitution exists. Anderberg and Balestrino (2003) interpret z as education. Cigno (2006a) shows that little of substance changes if we put the number and utility of children in the parent’s utility function (“descending altruism”), in which case the constraint that an adult must give each of her children at least z may be slack, but the constraint that she must give her parent at least x will be tighter than ever. With this extension, the family-constitution model becomes directly comparable with Becker’s (see Section 2.2). Given that an adult has two strategies (comply or go it alone) in the former, but only one (go it alone) in the latter, maximized utility will be at least as high in the present model as in Becker’s. Descending altruism, however, brings back the incentive and sibling rivalry problems encountered in Section 2.2. Chang and Luo

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(2015) argue that these problems will go away if the family constitution is reworded to say that each adult must divide her wealth into two parts, one to be bequeathed and shared equally among her children, and the other to be transmitted to them, while the parent is still alive in accordance with the amount of care each of them gives to the parent. The authors demonstrate that this constitution will generate the right incentives and be selfenforcing. They also conjecture that it will discourage grown-up children from colluding to give their elderly parent as little care as possible (the problem raised at the end of Section 2.2). The hypothesis that a share of the adult population is governed by something resembling a family constitution is tested by a micro-econometric study of interhousehold transfer behavior in Italy. Using a Bank of Italy household survey that, for a particular year, records monetary transfers to friends or relatives (rather than from them as for all previous and subsequent years), and thus allows the probability and size of the transfer to be related to the donor’s characteristics, Cigno et al. (2006) find that, other things being equal, both the probability and the size of the transfer are higher if the donor is credit rationed than if she is not.ay This rejects the hypothesis that transfers are either gifts (“altruistic motive’) or the visible counterpart of an unrecorded personal service (“exchange motive”),az because in either of those cases the probability and the size of a transfer would be positively related to the donor’s wealth and thus, controlling for assets and earnings, lower if the donor is credit rationed than if she is not. By contrast, the finding does not reject the hypothesis that the transfers are made in compliance with family rules (nor does it reject the hypothesis that transfers are generated by the demonstration or the punishment models examined in Section 2.4). Consistently with descriptive evidence in Crimmins and Ingegneri (1990), Davis et al. (1997), and Cigno and Rosati (2000) that, in developed economies where people have ample opportunities to accumulate material wealth by saving or contributing to a public pension system, elderly parents receive primarily personal services, Cigno et al. (2006) find that monetary interhousehold transfers go primarily to noncoresident children.

4.2 Family Constitutions with Sex Differentiation Sex differentiation raises more fundamental difficulties than descending altruism, because the actor is then the couple rather than the individual, and each couple has two sets of parents to contend with. The problem does not arise in traditional societies where one of the partners (usually the woman, but in some cases the man)ba leaves the family of origin ay az ba

The probability of being rationed is endogenized using appropriate instrumental variables. See Cox (1987). For example, in Japan at least until the Meji revolution, and in India still today, if the bride’s family has no male heirs, her parents may effectively adopt the groom.

Conflict and Cooperation Within the Family

and joins (“marries into”) the other’s family.bb It arises in modern societies where both partners may retain their links with their families of origin. If that is the case, the two families are interlinked. The issue is taken up in Cigno et al. (2016). Because of the complexities associated with this setup, the authors restrict the generality of the analysis by using a specific utility function. As the focus is on developed societies, it is further assumed that the old are sufficiently well provided with money through saving or the public pension system not to be interested in receiving material support from their grown-up children (there is indeed evidence that the elderly subsidize their children and grandchildren). As in the more recent formulations of family theory reviewed in this chapter,bc what elderly parents want of their children’s is essentially personal services (“attention”), because such services have no perfect market or government-provided substitute. If children are not altruistic toward their parents, however, those services will not be forthcoming unless it is in the children’s own interest to provide them. The same would be true if children were altruistic toward their parents as in Pezzin et al. (2007), already examined in Section 2.3, because the parents’ welfare is a local public good, and the children will be tempted to free-ride. In order to have children, the generic adult i must now marry an adult of the opposite sex. This will give i a daughter D and a son S. Adults know their own wage rates before they decide whether and whom to marry, but do not know their children’s future wage rates. It is assumed that the wage rate of child k ¼ D, S will be high (wk ¼ wH) with probability π k, and low (wk ¼ wL) with probability ð1  π k Þ, where π k is a concave function π ðzk Þ of the amount of education zk that k receives from her or his parents. Given that children are the only source of uncertainty, if the generic adult i decides to stay single, her or his utility is Vi ¼ c1i + ln c2i for certain.bd Maximizing Vi subject to the budget constraints c1i + si ¼ wi and c2i ¼ rsi , where si is the amount that i saves in period 1, r is the interest factor, and w is the wage rate, yields the payoff of singlehood

bb

bc bd

Typically, there are also at-front payments, by the man to the woman’s family of origin (“bride-price”) if the woman is seen as an asset, the other way round (“dowry”) if she is seen as a liability. See Pestieau and Sato (2006), Pezzin et al. (2007, 2009), and Cremer and Roeder (2017). We write Vi rather than Ui because it does not include the utility that i enjoyed as an infant.

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Ri ¼ max ðwi  si + ln si r Þ ¼ wi  1 + lnr: si

If i were to marry, her or his expected utility would be EVi ¼ c1i + ln c2i + δð ln tDi + ln xSi Þ + ðEWD + EWS Þ, 0 < δ < 1,

(68)

where tki is the amount of attention she or he will receive in period 2, and EWk the pleasure of giving attention, gk, education, zk, and money (bequests),be bk, to k,  EWk ¼ α ϕ lngk + ln b + π k ln w H + ð1  π k Þ lnw L , 0 < α,ϕ < 1: Notice that ðEWD + EWS Þ has the nature of a local public good. Take the couple formed by a particular woman f, and a particular man m. Assume that adults are matched by their preferences (ie, have the same α, δ, and ϕ) and maximized utilities as singles (Rf ¼ Rm ¼ R), so that wf ¼ wm ¼ w. The domestic allocation of resources conditional on marriage is Nash-bargained between f and m. Assuming that parents do not discriminate between their children, gk ¼ g, zk ¼ z, and bk ¼ b, so that EWk ¼ EW for k ¼ D, S. To simplify, it is further assumed that f provides the whole of g and pays for the whole of z, while m gives the whole of b. Given that m is at liberty to make a compensatory monetary transfer T to f, however, the full cost of the children may be effectively shared between the parents. Of course, T can take either sign. As in much of the economics of marriage literature, it is taken for granted that neither party can commit to compensate the other in period 2, and thus that any such payment would have to be made in period 1.bf The couple will marry if and only if the payoff is at least as large as R for both of them. In the absence of a family constitution, the Nash-bargaining equilibrium maximizes
 N ¼ EVf  R ðEVm  RÞ, where


 EVf ¼ wð1  2gÞ  2z  sf + T + ln rsf + 2EW

and EVm ¼ w  sm  T + ln ðrsm  2bÞ + 2EW : Given that i will not get any present from k, and assuming that buying k’s attention would be prohibitively expensive for the reasons set out toward the end of

be

bf

The money a child receives in period 0 is treated as a constant and normalized to unity as in the many of the models reviewed in this chapter. Cigno (2012, 2014) show, however, that this restriction is relaxed if divorce courts tend to mandate compensation for the economically weaker party.

Conflict and Cooperation Within the Family

Section 2.2, tki will be zero. As marriage expands the utility-possibility set nonetheless, because it generates two local public goods, EUD* and EUS* , the ðR,RÞ point will lie inside the utility-possibility frontier, and a Nash-bargaining equilibrium without a family constitution consequently exists (the couple will marry). In equilibrium, ^g ¼

2αϕ , w

(69)

b^ ¼ 2αr, ^sf ¼ 1, ^sm ¼ 1 + 4α, 1 , 2αΔw T^ ¼ z^  2αð1  ϕÞ,

π 0 ðz^Þ ¼

(70)

where an apex denotes the Nash-bargained value of a variable, and Δw  ln wH  ln w L , Given that π 0 ð:Þ is a decreasing function, z^ is increasing in Δw. The payoff of marriage is EV^ ¼ w  2αϕ  z^  1  2α + ln r

 2αϕ H L z Þ lnw + 2α ϕ ln + ln2αr + πð^ z Þ ln w + ½1  πð^ w for both parties. Could it be in f’s and m’s interest to marry and comply with a rule stipulating how much attention each adult must give her or his elderly parents? Given that, if a constitution exists, it must hold for ever, and given that the wage rate is a random variable, the amounts due may well be conditional on the realized value of this variable. Let the amount that an adult woman F (man M) must give her (his) elderly mother be xH FF L L (xH MF ) if the giver’s wage rate is high, and xFF (xMF ) if that wage rate is low. Similarly, H let the amount that F (M) must give her (his) elderly father be xH FM (xMM ) if the giver’s L L wage rate is high, and xFM (xMM ) if it is low. The rule applies not only to f and m but also to D and S, and all their descendents. The paper starts by assuming that the couple barH gains over g, b, z, and T taking xH FF , xMF , etc., as given. Having established that marrying without a constitution is better than not marrying at all, i’s outside option is now E V^ rather than R. Given that the rule gives the couple access to an otherwise unattainable good (filial attention), but imposes further restrictions on the couple’s choices, the existence of a Nash-bargaining equilibrium is not guaranteed (ie, the ðEV^ , EV^ Þ point does

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not necessarily lie inside the utility-possibility frontier). The paper starts by characterizing a Nash-bargaining equilibrium under the assumption that a constitution exists, then finds the renegotiation-proof rule, and finally checks that marrying in the presence of this rule makes the couple at least as well-off as marrying in its absence. The Nash-bargaining equilibrium is now found maximizing

 N ¼ EVf  E V^ EVm  E V^ , where


   EVf ¼ wð1  2g  xFF  xFM Þ  2z  sf + T + ln rsf  H L L + δ π ðzÞ½ ln xH FF + ln xMF  + ½1  π ðzÞ½ lnxFF + ln xMF  + 2EW

and EVm ¼ ½wð1  xMF  xMM Þ  sm  T  + ln ðrsm  2bÞ  H L L + δ π ðzÞ½ ln xH FM + ln xMM  + ½1  π ðzÞ½ lnxFM + ln xMM  + 2EW :
 C C H H H Substituting the solution gC , bC , sC , and the rule that tFF ¼ xH FF , tFM ¼ xFM , i ,z ,T etc., into i’s expected lifetime utility function 
H  
L  EVi ¼ π ðzÞ ϕ ln gi + δ ln tDi + ln tSiH + ½1  π ðzÞ ϕ ln gi + δ lntDi + ln tSiL + c1i + ln c2i + 2EW , H and maximizing the expression thus obtained with respect to xH FF , xMF , etc., they find j

j

j

j

xFF ¼ xFM ¼ xMF ¼ xMM ¼

δ , j ¼ H,L wj

(71)

and 2αϕ , w bC ¼ 2αr, gC ¼

M sC f ¼ 1, sm ¼ 1 + 4α,


 π 0 zC ¼

1 , 2αΔw + δΔx T C ¼ zC  2αð1  ϕÞ,

where



 H H H L L L L Δx ¼ ln xH FF + ln xFM + ln xM + ln xMM  ln xFF + ln xFM + ln xM + ln xMM :

Conflict and Cooperation Within the Family

If a constitution exists, it then prescribes that each adult should give the same amount of attention to each of her or his elderly parents. As this amount is decreasing in the giver’s realized wage rate, Δx is negative, and consequently zC < z^: For α  δ, zC will be actually zero. The intuition is that, as the amount of attention the parents will receive from each of their grown-up children will be larger if the latter’s realized wage rates are low, parents have no interest in increasing the probability that their children’s wage rates will be high. The only reason for giving children an education is then altruistic. If this sentiment is not strong enough to outweigh the desire to receive filial attention in old age, parents will give their children no education at all. They will only give them money. A constitution exists if the payoff of marrying and obeying the constitution, EV C ¼ w  2αð1 + ϕÞ  2δ  zC  1 + lnr


C 
C  δ δ ln L + 2δ π z ln H + 1  π z w w

2αϕ + πðzC Þ lnw H + 2α ϕ ln w   + 1  πðzC Þ ln wL + ln2αr ,

(72)

is at least as large as EV^ . Depending on preference parameters, this may or may not be true. Let us then take a couple whose common preferences are compatible with the existence of a family constitution. Will this couple abide by a constitution (71) reflecting their common preferences? Not necessarily, because all their ascendants and descendants must also have those same preferences. What makes us think that this would be the case? If preferences were purely random, the probability that a child is born with the same preferences as her or his parents would be very small. Another possibility, suggested by Stark (1993, 1995) and Cox and Stark (2005), is that preferences are inculcated, rather than genetically inherited. We argued in Section 2.4 that children would not be fooled by their parents behaving as if they loved the grandparents just to impress on the grandchildren that they should love their parents. Seen against the background of a family constitution that requires stable preferences of a certain kind, however, it may make sense to say that people brought up in families where adults appear to enjoy making presents of various sorts to their children, and the elderly appear to enjoy the attention of their children, are likely to appreciate the advantages of

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acquiring their parents and grandparents tastes. It may also make sense to say that adults so brought up will look for marriage partners with similar upbringing. What about people who did not inherit this kind of preferences, nor had them inculcated at a tender age? These persons may well marry, but it is not possible to demonstrate that they will have a family constitution with which to comply. They may even marry persons with preferences different from their own, but there is then no guarantee that a Nash-bargaining equilibrium will exist, because the utility-possibility frontier and thus the game will be asymmetrical. This conclusion has a certain intuitive appeal. Cigno et al. (2016) examine also the proposition put forward in Bernheim and Bagwell (1988) that, if everybody were altruistically linked to everybody else by blood or marriage, any public action, no matter whether distortionary or nondistortionary, would be neutralized by a private action.bg Does this proposition carry over from a world where private actions affecting others are motivated by altruism alone, to one where this sentiment is tempered by strategic self-interest? We have seen several models like this in Section 2.4, but none of them is designed to address the neutrality issue. Cigno et al. (2016) examine three policies, one nondistortionary and the others distortionary, within the model that we have just reviewed, where individuals marry and bargain with their spouses, and may or may not be constrained by a family constitution. They find that the first policy, a lump-sum subsidy to the old paid for by a lump-sum tax on adults, is neutralized by a private transfer of opposite sign. This policy does not affect the conditions for the existence of a family constitution. By contrast, a subsidy on low-wage rates financed by a tax on high-wage rates and compulsory education, are generally nonneutral. Unlike the first one, this policy affects the condition for the existence of a family constitution and thus the share of the adult population that abides by such an arrangement.

4.3 Social Security vs Family Constitutions The effects of social security are more complex in the constitution model than in the lifecycle and altruistic models considered earlier, because the policy affects individuals differently according to whether they do or do not abide by a family constitution, and may also affect their decision to abide by one. The same is true of the policies considered in Section 4.2. Here, however, we will use the simpler model without sex differentiation outlined in Section 4.1. We start by assuming that every adult complies with some family constitution, so that the aggregate fertility and savings rates coincide with the fertility and savings rates of the representative compiler (identified by the c superscript),

bg

See the end of Section 2.3.

Conflict and Cooperation Within the Family

n ¼ nc and s ¼ sc : We further assume that the allocation brought about by the constitution is a Pareto optimum (as already noted, that is always true in the extended version of the model, but not necessarily in the basic one). The constitution ðxc , zc Þ complied with by the representative adult, and the associated choice of nc and sc, found maximizing U ðxc ,zc , θ, δÞ ¼ u0 ðzc Þ + u1 ðð1  θÞw½1  c ðnc Þ  sc  xc  znc Þ + u2 ðrsc + xc nc + θw½1  c ðnc Þnc + δÞ, satisfy u00 u01 ¼ ¼ nc u01 u02 and nc ¼

x + θw ½1  c 0 ðnc Þ ¼ r: z + ð1  θÞwc 0 ðnc Þ

(73)

Under present assumptions, therefore, the aggregate fertility rate would be the same with or without social security, and equal to the interest factor. No matter whether r is exogenous or endogenous, the policy would then leave U unchanged. The effects of an exogenous change in either r or w on nc, sc, xc, and zc, found differentiating the FOCs totally and solving by Cramer’s rule, are @sc @sc @xc @xc @zc ¼ ¼ ¼ ¼ ¼0 @θ @δ @θ @δ @δ and

(74)


2 rw ½1  c ðr Þ u001 + r 2 u002 @zc (75) ¼ > 0, @θ H where H is the Hessian determinant (negative at a maximum). The economic intuition is straightforward. With the return to children fixed at r, the policy does not affect portfolio choice. On the other hand, as the return to children is increasing in θ and xc, and decreasing in zc, xc must fall relative to zc for that return to remain constant as θ rises. Changes in δ do not affect the return to children and thus the choice of sc, xc, and zc (they will only affect adult consumption). Let us now relax the assumption that (64) is slack for everybody. Let there be a continuum of individuals differentiated by a parameter, ζ, which raises the marginal cost of

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children. There will be a threshold value of this parameter, ζm, such that the payoff of the comply strategy equals the payoff of the go-it-alone strategy. For all individuals characterized by a value of ζ higher than ζm, (64) will not hold. These individuals will go it alone. All individuals characterized by a value of ζ lower than or equal to ζm will comply. For those with ζ equal to ζm, (64) will be slack and the domestic resource allocation will be a Pareto optimum. For those with ζ greater than ζm, (64) will be tight, and the domestic resource allocation will be a constrained Pareto optimum. Diversity carries two implications. The first is that compilers with different ζ may have different x and z (different constitutions). The second is that, as not everybody will follow the same strategy, we can no longer talk of a representative adult, but we can still talk of a representative go-it-aloner and a representative compiler. Further assuming that at least some individuals go it alone (have ζ greater than ζm), the aggregate fertility rate will then be lower, and savings per adult higher than, respectively, the number of children and the savings of the representative compiler, n < nc and s > sc : With social security, the payoff of the comply strategy for an individual with cost parameter ζ (ζ for short) is

 ζ ζ ζ r u ð 1  θ Þw ½ 1  c ð r Þ   s  x  ζ + z V  ðr, w, xζ , zζ ,θ,δ,ζÞ ¼ max 1 si
 + u2 sζ r + xζ r + nθw½1  c ðr Þ + δ : Having established (in the last subsection) that every compiler has r children, we have substituted r for nζ. For that same individual, the payoff of the go-it-alone strategy will be

 V ðr, w, θ,δÞ ¼ max u1 ð1  θÞw  sζ + u2 sζ r + n½1  c ðr Þθw + δ : i s

The effects of a small change in θ on the payoffs of the two strategies are
 n
Vθ* ¼ w ½1  c ðr Þ 1  u01 ð1  θÞw ½1  c ðr Þ  sζ  xζ  ζ + zζ r r and n o
 n Vθ ¼ w 1  ½1  c ðr Þ u01 ð1  θÞw  sζ , r both negative because n is smaller than r (and the policy is thus inefficient). Those of a small change in δ are
 Vδ* ¼ u02 sζ r + xζ r + nθw½1  c ðr Þ + δ

Conflict and Cooperation Within the Family

and


 Vδ ¼ u02 sζ r + n½1  c ðr Þθw + δ ,

both positive.

u01 will be equal to r in both strategies. Given that the u02 comply strategy has a fixed cost xm (absent in the go-it-alone strategy), however, u01 will be higher, and u02 lower, in the former than in the latter. For this person, therefore, Vθ* is more negative than Vθ, and Vδ* less positive than Vδ. If either θ or δ increases, marginal compilers (those with ζ equal to, or a little smaller than, ζ m) will turn into go-it-aloners.bh Notice that the higher is r, the more strongly negative is the effect of θ on V* and thus on the share of compilers in the adult population. If we compare two alternative steady states, one with a high θ and the other with a low θ, we will then find that the share of compilers is lower in the former than in the latter. In the absence of other effects, and given that a person has fewer children, makes smaller transfers, and saves more if she goes it alone than if she complies, s will then be higher, and n, x, and z lower at the high than at the low θ. These are composition effects. But there are also other effects. In view of (74) and (75), an inframarginal compiler (one who would comply at either value of θ) would in fact have the same number of children, save the same amount, and give her parent as much at the high as at the low value of θ, but would give each of her children more at the former than at the latter. Conversely, and recalling that a go-it-aloner behaves in the way described by the basic life-cycle model, an inframarginal go-it-aloner would have no children and make no transfers to anyone at the high as at the low θ, but would save less at the former than at the latter. These within-strategy adjustments will tend to offset the composition effects on per-adult savings, s, and per-adult transfers to each every old person, x, and each infant, z. As utility is lower with than without the policy for both compilers and go-it-aloners, it is clear that, in the presence of family constitutions, social security reduces social welfare in the long run. As pointed out in the last section, it does not make sense to talk of steady-state effects of δ because, in steady state, the deficit must be equal to zero for the pension system to be financially viable. It does make sense, however, to talk of the off-steady-state effects of making the pension deficit positive for one cohort and negative for another. In the presence of such a policy, family constitutions would instruct each adult to make a larger transfer to each of her children (hence, to each future adult) if she belongs to a cohort For an individual with ζ ¼ ζm,

bh

Put more formally, m is increasing in θ and δ.

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Table 4 Pension policy effects in the presence of family constitutions Fertility Savings Transfer to child Transfer to parent

Utility

θ δ

P) > 0 and @E ð f j WTP > P Þ=@P > 0. Intuitively, consumers who are willing to pay very high prices for an insurance plan will tend to be (on average) making mistakes such that they are overvaluing the plan. Eliminating these mistakes would therefore flatten the demand curve. See also Erdem et al. (2008), who discuss various mechanisms through which advertising can alter both the slope and level of demand curves for differentiated products.

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perception errors. Similarly, Handel et al. (2015) look at a stylized market with one plan. In numerical experiments, they show that confusion reducing policies are most likely to be welfare enhancing if the mean and the variance of risk aversion is high, while the variance of costs (ex ante risk) is relatively low. Using the estimates from Handel and Kolstad (2015), which imply low risk aversion, their simple calibrated model implies a $47 welfare loss per person from eliminating inertia, which is 99% of consumer surplus. Polyakova (2015) does a similar sort of analysis using data from the Medicare Part D market. But, in contrast to the Handel (2013) and Handel et al. (2015) papers, which use a simple “cost plus fixed administrative expense” pricing rule, Polyakova (2015) estimates a reduced form pricing rule based on observed pricing behavior of insurers. She then estimates a structural discrete choice model of consumer demand. Finally, she combines the demand model and the reduced form pricing rule to solve for market equilibrium prices and quantities. This “quasi-structural” approach is very similar to that used by Ching (2010a,b) to study equilibrium in the market for name brand and generic drugs.ab Another key difference is that Polyakova’s choice model does not assume that plans differ only by ex ante mean and variance of OOP costs. Rather she allows for consumers to have heterogeneous preferences over a number of horizontal attributes of drug plans. Finally, she distinguishes between preference heterogeneity and inertia, a distinction which our previous discussion suggests may be very important for welfare calculations. Polyakova’s (2015) results are quite striking in that she finds very large consumer welfare gains from reducing confusing in the Medicare Part D market. When she shuts down inertia she estimates a $455 per person increase in welfare due to better matching, which is 23% of annual drug spending. There is a further $10 increase in welfare due to a modest drop in premiums. We conjecture this occurs because, in a market with horizontal differentiation, removing inertia raises the price elasticity of demand and this outweighs any upward price pressure due to increased adverse selection. Ericson and Starc (2013) examine a specific mechanism for reducing consumer confusion: product standardization. They look at the Massachusetts Health Insurance Exchange (HIX), a program started in 2006 to help match uninsured individuals with health insurance plans.ac Initially firms had wide latitude with respect to product ab

ac

Interestingly, the issues studied by Ching (2010a,b) are fundamentally identical to those studied in the several papers discussed here. He noted the puzzle that many consumers remain loyal to brand name drugs even after identical but much lower priced generics become available. Furthermore, the brand names raise their prices at this point. This appears to be explained by the fact that the loyal customers who stay with the brand names even after low-priced generics enter are very insensitive to price, so the brand name firm faces smaller market share but less elastic demand after generic entry. These loyal name brand drug customers are, in a different context, behaving like the inertia bound consumers in the Ericson (2014) and Handel (2013) studies. This matching also served to aggregate individuals so they could buy insurance at lower group rates. Ericson and Starc (2013) look specifically at the unsubsidized part of HIX (called “Commonwealth Choice”) that dealt with people about 300% over the poverty line.

Complex Decision Making

offerings, and in 2009 there were 6 insurers offering 25 plans, many of which were differentiated in rather subtle ways. The HIX design was changed substantially from 2009 to 2010 in an effort to make it easier for consumers to see the differences between plans. In 2010 each insurer was required to offer six plans with different levels of coverage, with financial characteristics identical across all insurers (within each level). A choice platform made this structure transparent. Strikingly, the mean OOP cost declined by $259 per year poststandardization, as consumers tended to shift to plans with more comprehensive coverage. Furthermore, adjusted for generosity, monthly premiums were roughly $12 higher in 2010 (suggesting the greater salience of financials led to a slight worsening of adverse selection). Ericson and Starc (2013) go on to fit separate choice models for both 2009 and 2010. They find that the parameters of the choice model change with the change of choice environment. In particular, the financial aspects of plans, which were now more clearly distinguished, became much more salient. The authors take the parameters from the second “simpler” environment as the “true” representation of preferences for welfare calculations. They then conclude that product standardization greatly increased welfare. While not necessarily doubting this conclusion, we disagree about the correct interpretation of the change in parameters after the change in the choice environment. In our view, the correct interpretation is that the parameters we see in both models (before and after) are reduced form parameters that are functions of preferences, the choice set, and the information platform. This is precisely why they changed. There presumably exist deeper structural parameters of preferences that would not have changed. A recurring challenge for this literature is how to properly evaluate welfare when our estimated decision rules reflect not true preferences but rather reduced form parameters that also vary with the choice context.ad ad

In a context where consumers are uncertain or confused about true attribute levels (say, because of the number and complexity of alternatives) the true “structural” model might specify that choice depends on perceived attributes, and the econometrician might then attempt to estimate utility weights on perceived attributes. Unfortunately the econometrician cannot see perceived attributes. If he/she simply uses the true attributes instead, it creates an errors-in-variables problem, and the estimated model will have no structural interpretation. [Note: This is exactly the sort of problem that Harris and Keane (1998) or Erdem and Keane (1996) try to handle by allowing for a distinction between true and perceived attributes in choice models, in different contexts]. Given such a misspecified model, if perceived attributes change we would expect the coefficients on actual attributes to change as well (precisely because those coefficients are reduced form functions of both (i) actual utility weights and (ii) the mapping between true and perceive attributes). To give a concrete example, if true and perceived premiums are uncorrelated, we would expect a zero coefficient on true premiums. If we improve information so that true and perceived premiums are highly correlated, the estimated coefficient on true premiums would presumably increase in magnitude—moving closer to the structural utility weight. In Ericson and Starc (2013), this may well explain why the weights on financial characteristics increase in the 2010 model.

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2.1.5 Summary In summary, the findings reviewed here have important implications for the design of “competitive” health insurance markets. As Angell and Kassirer (1996) note: “According to the theory, if consumers are given full information about the quality of the health plans they are considering, they will opt for higher-quality plans, or at least when they trade-off quality for lower costs, they will be able to do so knowingly. In a competitive system, consumers can then vote with their feet—that is, change plans if they believe that they can obtain better quality for the same price …” But, as Hall (2004) notes: “to choose rationally across insurers, [consumers] must be well informed about … the plans offered. … [but] many consumers … have not had substantial experience in obtaining health care until they face … illness.” The evidence that consumers have important misperceptions about their health insurance and health care options undermines a key tenet of the standard “choice is good” argument.

2.2 Evidence of “Confusion” in Making Health Care Choices We turn next to the issue of how senior citizens, and consumers more generally, make choices about health care services (as opposed to health insurance). For instance, people are often faced with the need to make choices among alternative providers (i.e., physicians, surgeons, and hospitals), alternative treatment options (e.g., surgery vs noninvasive treatment), different drugs (e.g., brand name vs generic—see, e.g., Ching, 2010a,b), elective tests (e.g., cancer screening—see, e.g., Fiebig et al., 2010; Keane and Wasi, 2013), vaccination, and so on. Harris and Buntin (2008) give an excellent review of the substantial literature on this topic, so here we just highlight some key points. A key problem is that is the quality of a physician or hospital, or the effectiveness of a treatment, is very difficult to measure. For instance, doctors can be graded based on process measures (e.g., what fraction of patients are screened for high cholesterol?) and/or outcome measures (e.g., what fraction of patients have cholesterol in a desired range?). Since 2004, the National Health Service in the UK has based 25–30% of physician pay on such measures (see Roland and Campbell, 2014). But the problems with such an approach to measuring quality are manifold. Which aspects of care or outcomes should be considered? And what perverse incentives are created? Will physicians be tempted to “teach to the test” and work to improve what is measured while neglecting other important aspects of health care quality? Even if such problems can be overcome, and we develop measures of quality that make sense from an expert point of view, how can these measures be communicated to consumers in an understandable way? The understanding of quality measures requires a great deal of health-related knowledge that few people possess. If a surgeon has a certain success rate in a certain type of operation, is that good or bad? By analogy, the quality of a baseball batter can be well summarized by his batting average (BA), on-base percentage (OBP), and slugging average (SA). But if you are a person with

Complex Decision Making

only a passing knowledge of the game, and you are told a batter has BA ¼ 0.251, OBP ¼ 0.314, and SA ¼ 0.386, you will have no idea what that means. In fact, only a person with a substantial knowledge of baseball and baseball statistics could interpret these figures.ae Given the difficulty of understanding health care quality measures, it is not surprising that most studies reviewed in Harris and Buntin (2008) find that people rely primarily on factors like quality of personal interactions when choosing a doctor. It is not surprising that people tend to ignore technical information they do not understand, and instead rely on factors like interpersonal skills which they do understand. Harris and Buntin (2008) describe a number of experiments that attempt to present provider quality information to consumers in a more useful way, but success in this area has been limited.

3. RETIREMENT SAVINGS AND INVESTMENT PLANNING Next, we consider the evidence on whether people in general—and the elderly in particular—can understand the complex choices they face in regard to retirement planning. Standard economic models assume that people plan optimally for retirement. But if instead people have difficulty making decisions about retirement savings vehicles (e.g., pension, 401(k), or superannuation plans), we may see a growing population of senior citizens and elderly whose well-being is adversely affected by failure to plan ahead optimally. Retirement planning influences macroeconomic income and productivity as well as individual welfare. As populations age, income and insurance provision for the elderly take a larger share of public funds, increasing the size of the public sector (Poterba, 2014). The diminishing government investment, rising taxes, and perverse labor market incentives that follow can reduce aggregate efficiency (James, 1995). In addition, population aging can hamper entrepreneurship, making it less likely that rising productivity will compensate for slower growth (Liang et al., 2014). In that case, it is important to develop policies to help people plan better for retirement right now.

3.1 Evidence of “Confusion” in Retirement Planning In theory, efficient life-cycle planners should have hump-shaped lifetime wealth profiles, adequate retirement income, and judiciously chosen insurance against mortality, longevity, and health shocks. In fact, there are striking inconsistencies between theoretical predictions and actual behavior. Many households retire with inadequate savings, even when contributions to plans are mandatory,af the voluntary take up of longevity insurance is ae

af

In fact, these were the average values across all major league players in 2014. But no doubt more than a small handful of baseball aficionados would be aware of that. Skinner (2007) surveys evidence for and against inadequate retirement savings. Studies showing inadequate savings include, among others, Laibson et al. (1998), Mitchell and Moore (1998), Knoef et al. (2015), and for a more recent empirical scan, see Poterba (2014).

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low (Mitchell et al., 2011), and many elderly decumulate at very modest rates (see, e.g., Guiso et al., 2002; B€ orsch-Supan, 2003; Milligan, 2005; Love et al., 2009; Poterba et al., 2011; Ooijen et al., 2014; Wu et al., 2015a). These outcomes are hard to reconcile with rational planning. Strikingly, only 43% of surveyed American adults say they have ever tried to figure out what they need for retirement, including only 57% of 50–65-year-olds (Lusardi and Mitchell, 2011). Studies from across the developed world consistently find fewer than half of adults have attempted any financial planning for retirement (see, e.g., Alessie et al., 2011; Bucher-Koenen and Lusardi, 2011; Fornero and Monticone, 2011; Agnew et al., 2013a). To make good retirement savings decisions, consumers need both: (i) to know and understand the attributes of the products/services they are evaluating and (ii) to possess the cognitive capacity and skills to make good choices among those products/services. They are likely to become confused if they do not have the facts about investment returns, survival, pension plan structures, and government support to hand. They also need the basic numeracy, financial literacy, patience, and personal efficacy to design and implement a plan. Empirical studies have highlighted both misperceptions about the key facts and serious deficits in the capacity of many people to make a plan and follow through. We will first discuss the question of whether people have adequate information and accurate perceptions, and then turn to the question of their cognitive capacity for planning: 3.1.1 Evidence That Consumers Hold Biased Expectations There is clear evidence that many consumers hold biased expectations of variables that are critical to retirement planning, including investment returns, longevity, and retirement dates. Subjective expectations of equity market returns show marked pessimism and heterogeneity, despite the fact that they are readily observed public information. For example, data from Dutch adults put the average expected 1-year-ahead return to equities at 0.3% when the historical median rate of return was actually 14% (Hurd et al., 2011). Other studies show that returns expectations tend to track recent stock market performance, and severe crashes increase uncertainty and disagreement (Hudomiet et al., 2011). High subjective pessimism and uncertainty may explain low stock market participation by risk averse investors, which, in turn, could account for low lifetime investment earnings. Similarly, many people are excessively pessimistic about their survival prospects. Numerous international studies find that people underestimate their life expectancy by around 5 years on average. These errors are larger for women and younger cohorts—groups who should anticipate living longer (Hurd, 2009; Wu et al., 2015b; Teppa and Lafourcade, 2013; Kutlu-Koc and Kalwij, 2013). Individuals also misestimate the shape of the survival curve, showing too much pessimism at near ages and too little at

Complex Decision Making

distant ages. This means that they are more likely to misjudge retirement consumption and longevity insurance decisions (Wu et al., 2015b; Teppa and Lafourcade, 2013). In contrast, reported retirement intentions are optimistic compared with realized retirement outcomes. Hurd (2009) studied responses from the HRS showing that middle-aged people’s subjective expectations of still working at age 62 were upward biased: the forecast rate of full-time work was 46% compared with a realized rate of only 32%. This difference between realizations and expectations persisted even up to within a year or two of the target age. People who expect to retire later and die sooner than they actually do are likely to save less than they would need to finance retirement consumption. 3.1.2 Evidence That Consumers Misunderstand Pension Plan Rules and Entitlements The findings discussed in Section 3.1.1 are perhaps not surprising, given the evidence already noted in Section 2 that that people have difficulties understanding probabilities in general (e.g., Johnson et al., 1993; Peters et al., 2007b). However, peoples’ misunderstanding of retirement planning is not limited to probabilistic outcomes like returns or survival. It extends to objective quantities that can, in principle, be known with certainty: For example, several studies have shown that many preretirees have a weak grasp of their pension plan rules and social security entitlements. Mitchell (1988) compared Survey of Consumer Finance responses of employees with administrative data on their pension plans, and found major gaps in what employees knew. For example, this included knowing whether their employer contributed to their DC account, as well as the rules governing early retirement. Similarly, Gustman and Steinmeier (2005) found that only about half of respondents could report an estimate of their pension and Social Security benefits, and that those who could often made large errors. Bottazzi et al. (2006) report a similarly large range of expectations errors by Italian workers around replacement rates. Although superannuation is compulsory for almost all workers in Australia, mistakes about preservation ages—i.e., the age at which superannuation accounts can first be accessed—are common among middle-aged workers (see Agnew et al., 2013b). Similarly, less than one-third understand the basic features of standard decumulation products like lifetime annuities (Bateman et al., 2015). The value of plan-specific knowledge rises with the stakes, and wealthier, older, higher income, better educated males and whites do tend to know more. But significant errors persist.

3.2 Evidence That Consumers Lack Financial Literacy Hypothetically, suppose we could design informational interventions that would fill the gaps in knowledge that we have described. The question remains whether people would have the cognitive capacity and skills to engage in (near) optimal retirement planning. As is well known, even simple versions of the theoretical life-cycle problem can only be solved using dynamic programming (DP) methods and substantial computing

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power—see Geweke and Keane (2001). By contrast, fewer than half of adults in developed countries can correctly answer three questions about financial basics such as interest rates, inflation, and risk diversification (Lusardi and Mitchell, 2014). So, as with health insurance, the assumption that most people can make (near) optimal choices regarding objects as complex as pension plans and annuities does seem to strain credulity.ag Cognitive ability and acquired human capital, in the form of financial literacy, are powerful influences on retirement welfare (Jappelli and Padula, 2013; Lusardi and Mitchell, 2014). For example, Dohmen et al. (2010) find that higher cognition is associated with more risk tolerance and patience, and hence more wealth. Banks et al. (2010) find that households with higher numeracy exhibit steeper rates of accumulation and decumulation of assets over the life cycle, consistent with life-cycle theory. Poor numeracy and financial literacy are also related to low rates of stock market participation (Christelis et al., 2010; van Rooij et al., 2011), higher rates of mortgage delinquency and defaults (Gerardi et al., 2013), and higher rates of mistakes in processing investment risk (Bateman et al., 2016b). Unfortunately, however, measured numeracy among adults, like other forms of financial literacy, is generally weak. For example, in simple questions about proportions, percentages, and probabilities, tests of Australian adults show median scores of two out of three correct answers (e.g., Bateman et al., 2015). Galesic and Garcia-Retamero (2010) report similar results for the United States and Germany, finding that probabilities are particularly poorly understood. Consequently a large minority of people probably lack the skill to understand compounding and risk, concepts that are critical to savings and investment decisions. Cognition varies within individuals over time as well as in the cross-section. Agarwal et al. (2009) find an inverse u-shaped pattern of financial skill that peaks in middle age. The decline in cognition at older ages makes managing retirement increasingly hard for the very elderly. Stock picking and diversification skills of investors in their ‘60s and ‘70s drop off sharply compared with middle age (Korniotis and Kumar, 2011), and rates of credit card mistakes rise (Agarwal et al., 2009). Perhaps even more concerning is the evidence that worsening cognition does not bring with it any less confidence in one’s ability to manage finances (Gamble et al., 2014a). This makes the elderly especially susceptible to scams and fraud (Gamble et al., 2014b; Blanton, 2012). Beyond general cognitive ability and numeracy, people need some specific skills to make and execute good savings plans. For example, an understanding of compounding is fundamental but not easy: only 18% of early baby boomers surveyed in the HRS could answer a simple question about compound interest correctly, with 43% of those who got ag

As discussed in Geweke and Keane (2001) and Houser et al. (2004), optimal solutions of life-cycle problems can often be well approximated by simple (but clever) rules of thumb. So the issue is not really whether people can solve DP problems, but whether they can behave in a sophisticated enough way so as to approximate such a solution.

Complex Decision Making

it wrong giving a simple linear interest answer (Lusardi and Mitchell, 2007). Administrative data, as well as laboratory and field experiments confirm individuals’ tendency to linearize interest growth and so underestimate the benefits of long-term savings (Song, 2015; Stango and Zinman, 2009). 3.2.1 Evidence That Consumers Make Passive Choices Not only are financial calculations difficult for many people, but there is also evidence that many have problems even thinking about delayed payoffs. This is especially true for people who are prone to procrastination or who have a poor connection with their future self (Weber, 2003; Ersner-Hershfield et al., 2009; Bartels and Urminsky, 2011). As a result, people will delay, refuse, or oversimplify long-term savings and investment decisions, like joining a pension plan, until some event triggers it, such as changing jobs. Others may be paralyzed by worry about making mistakes and incurring financial losses (Rangel, 2005). Conversely, cognitive biases such as overoptimism or overconfidence can also lead to inaction, by creating an attitude that one is invulnerable and the future will take care of itself. An important practical way to deal with procrastination and lack of financial planning ability is the use of automatic enrolment in retirement plans. Another is default settings for contributions and investment strategies. Defaults have been shown to have large and long-lasting effects, especially on unsophisticated savers (Madrian and Shea, 2001; Beshears et al., 2009; Choi et al., 2002, 2003). They simplify a complex decision by reducing it to a comparison between the default and everything else, rather than a comparison between many possibilities. Defaults are sometimes also interpreted as an endorsement by an expert (Beshears et al., 2009). When asked why they choose defaults, many retirement plan members cite their own lack of skill for making a choice or their wish to delay a complicated task (Butt et al., 2015; Brown et al., 2015). In general, passive behavior channels operating through defaults are far more effective for increasing savings than incentives such as tax rebates that require active decisions (Chetty et al., 2014). 3.2.2 Evidence That Consumers Are "Confused" by Investment Decisions Not everyone procrastinates or lacks financial capability, but the fact that “nudges” such as default options are so effective is implicit evidence that many households avoid thinking about their future needs (or find the problem very hard). If making savings decisions can be a challenge, investment choices are even harder. The advanced normative theory of optimal portfolio allocations proposes highly individualized strategies consisting of complex dynamic hedges (see Bodie et al. (2009) for a survey). It goes without saying that unsophisticated investors cannot design and implement these investment programs on their own, and that default investment options will be, at best, rough approximations to the ideal. Even the simplest version of modern portfolio theory predicts that investors should choose a well-diversified portfolio to maximize expected risk-adjusted returns. However, each of these three factors, returns, risk, and diversification, present challenges to naı¨ve investors.

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In regard to returns for example, there is evidence that retirement savers: fail to take up matching offers that offer risk-free returns (e.g., Saez, 2009; Choi et al., 2011), fail to minimize fees that reduce expected returns when choosing between otherwise identical index funds (Choi et al., 2010), and make different decisions about investments depending on whether fees are shown as gains or losses (Hastings et al., 2011), whether returns are shown as long or short term (Benartzi and Thaler, 1999), and whether equivalent returns are shown as dollars and cents, ratios, or percentages (Rubaltelli et al., 2005). As noted earlier, many people cannot answer questions about basic probabilities correctly, so it is not surprising that long horizon investment risk is also hard to grasp. For example, most individuals cannot infer outcomes of repeated gambles, overestimating the probability of a loss. As a result, they make much higher allocations to stocks when shown the distribution of 30-year returns than that of 1-year returns (Benartzi and Thaler, 1999; Klos et al., 2005). Comparing changes in investment risk is difficult for many people. Bateman et al. (2016b) observed modifications to retirement savings portfolio allocations of individual investors in an experiment where investment risk increased but returns stayed constant. They recorded that about 30% of allocation decisions violated basic expected utility axioms, indicating misunderstandings of increasing risk. In general, investment decisions are susceptible to the way that risk is framed. So much so that Bateman et al. (2013), using portfolio allocation experiments, show that changing the way that investment risk for retirement accounts was described caused much more variation in allocation decisions than even a doubling of the actual volatility of investment returns. More fundamentally, it is not clear exactly how “investment risk” is understood by retirement savers, but the conventional measure of volatility is probably not what most people have in mind. Portfolio theory emphasizes both upside and downside risk, but unsophisticated investors may be more focused on losses. Some studies show that such perceived risk is a better predictor of asset choices than return variance (Weber et al., 2005).ah Weber (2003) further argues that the abstraction and distance of the consequences of retirement savings decisions means that the affective (emotional) response needed to evoke action is often missing. Thus, retirement “risk” does not seem “risky.” Even setting aside the psychological distance between retirement investment decisions and their consequences, ordinary investors struggle to understand both what investment risk is and how it relates to returns. Other studies show that unsophisticated investors know that diversification is a good principle but do not understand the risk-return trade-off. Many think that diversified ah

Other work has found that probability-weighted ranges of outcomes are better understood and result in fewer mistakes than information about negative return frequencies (Goldstein et al., 2008; Vlaev et al., 2009; Bateman et al., 2015). Fewer mistakes are unsurprising given the additional information ranges offer over negative return frequencies. Even so, regulators often stipulate that risk is reported as a likelihood of losses. See Bateman et al. (2016b) for a review of regulator and industry use of risk framings.

Complex Decision Making

portfolios actually have higher risk and higher expected returns than concentrated portfolios (see, Weber et al., 2005; Reinholtz et al., 2015). The widespread use of diversification heuristics further highlights misunderstandings. When investors are confronted with large, complex, investment menus, choices can degenerate into ad hoc strategies. For example, people divide their wealth evenly between some or all investment options even though this actually reduces diversification (Benartzi and Thaler, 2001; Huberman and Jiang, 2006; Brown et al., 2007; Morrin et al., 2012; Agnew et al., 2011; Bateman et al., 2016a,c). Overall, empirical studies of investment decisions by ordinary consumers show that people want higher returns and diversification but are confused about how to achieve them.

3.3 Can Disclosures, Education, or Advice Reduce Retirement Planning “Confusion”? Informational asymmetries, search costs, complexity of contracts, and a lack of trust imply that financial markets are prone to failure (Campbell et al., 2011). Consumers’ lack of information, their cognitive limitations or their behavioral biases can exacerbate the effects of market failure. This can mean that some households are more affected than others. Planning and investment mistakes are more common among poorer, less educated households; these households are also less likely to participate in risky asset markets (Campbell, 2006). However, the effects of mistakes or failures are not limited to one group of households. When unsophisticated households confront complex products with shrouded attributes, such as bank account or credit card fees, the outcome can be cross-subsidization from naı¨ve to sophisticated households (Gabaix and Laibson, 2006). This can also limit financial innovation. Sophisticated households that tend to be early adopters of new products are also unlikely to forego the cross-subsidies from less aware consumers that extant products offer. What is the solution? Is poor retirement planning a problem that could be solved by improved disclosure, simplified products, education, or advice? Regulators wanting to minimize restrictions on consumer financial choices while ensuring some degree of protection have tended to rely on disclosure rules. However, this has often resulted in lengthy and complicated disclosures mainly designed to minimize legal risk rather than to communicate clearly. More recently, regulators have drawn up templates for financial product disclosures that aim to make information easier for unsophisticated investors to understand.ai But ai

The G20 endorsed a set of common principles on consumer financial services including the principle that consumers should be given information on the fundamental benefits, risks, and terms of products. The US Securities and Exchange Commission (SEC) adopted a new simplified (or enhanced) disclosure document for mutual funds in 2007; and the European Commission implemented a key investor information document for collective investment vehicles, such as mutual funds, that aimed to make information comparable across jurisdictions and easy for consumers to understand. In Australia, the regulator, the Australian Securities and Investments Commission (ASIC) prescribed a short form for investment product disclosures limited to eight pages and fixed structures.

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simplified disclosures do not ensure better decisions. For instance, tests of the way consumers use the Securities and Exchange Commission (SEC) summary prospectus find no significant difference over the long form of disclosure that it was designed to replace— except that consumers spent less time on their decisions. Investors in the experiment still did not minimize fees and loads in their choices of mutual funds (Beshears et al., 2011). Similarly, tests of the short form disclosures in Australia (Bateman et al., 2016a) showed that retirement plan members focused on very few of the information items on the form, had difficulty integrating the information on returns, risk, and asset allocation, and retreated to a simple diversification rule. In general, it is hard to predict how people will respond to simplifications and unintended consequences can follow (Navarro-Martinez et al., 2011; Agarwal et al., 2015). As well as controlling information disclosure, regulators can attempt to simplify choices by standardizing products or setting defaults. These strategies tend to rely on passive choice rather than active use of disclosures. In Australia, for example, regulators concerned about complexity stipulated a standardized form for default retirement plans (called “superannuation funds”). They implemented “MySuper” regulations that aimed to support a simple, low-fee, scalable default structure. Default plan member contributions must be invested in a constant balanced or life-cycle (target date) portfolio (Super System Review, 2010). Many plans have lowered fees and switched to life-cycle investment strategies in response to the standardization regime (Butt et al., 2015). Similarly, Keim and Mitchell (2016) showed that streamlining defined contribution pension fund investment menus reduced turnover rates, expense ratios, and systematic risk factors of plan members, potentially improving savings outcomes. Despite the observed correlation of knowledge and financial capability with improved wealth management and planning outcomes, it is not clear that general education is an effective solution to poor decision making. Financial literacy is often measured by simple tests of objective knowledge about interest rates or inflation. However, when confronted with novel and complex choices, people need “consumer expertise” (Fernandes et al., 2014). Expertise is the appropriate set of skills, knowledge, acquired experience, and psychological traits needed for specific financial decisions. General financial education, especially if it is not applied to an immediate decision, tends to decay quickly (Fernandes et al., 2014). What about expert advice? Usage rates of financial advice vary across countries, but for the United States, Sabelhaus et al. (2008) found 55% of retiring DC account-owning households use an advisor, either one they found on their own (42%) or one provided by their employer (13%). In theory, advisors can bring better knowledge and financial practices to unsophisticated clients, while giving them the benefits of economies of scale in skill and knowledge—see Hackethal et al. (2012). In practice however, advisors often have the role of both expert and salesperson, so conflicted incentives affect the benefit of their relationship with clients—see Inderst and Ottaviani (2009).

Complex Decision Making

Empirical studies of advisor–client relationships show both costs and benefits. Broker directed mutual fund investments, for example, including investments in retirement portfolios, underperform direct investments, or age-appropriate target date funds. They exhibit return chasing, higher risk, and higher turnover (Bergstresser et al., 2009; Chalmers and Reuter, 2012). Field studies of personal financial advice find evidence that advisors who gave poor quality advice were still trusted by clients, and that advisors confirm clients’ biases to their own advantage (ASIC, 2012; Mullainathan et al., 2012). On the other hand, unbiased computer generated advice has been shown to result in better outcomes for the few clients who take it up, typically wealthier and more sophisticated clients (Bhattacharya et al., 2012). Less educated and unskilled clients are less likely to pay for advice, but they are more likely to rely on it when they do (Hackethal et al., 2010; Holden, 2013). So, while advice holds promise for assisting retirement planning, the cheapest, and most unbiased sources, such as online and automated advice, appear to be unattractive to the less sophisticated consumers who could potentially benefit the most. In summary, it seems clear that many people make suboptimal preparations for retirement or do not plan at all. This is partly because they lack information, but also because the retirement planning problem is intrinsically difficult (e.g., it involves matters such as investment risk that are very difficult for many people to understand). As in the case of health insurance, retirement savings decisions are very complex, and consumers appear to exhibit confusion when making them.

4. MODELS OF CHOICE BEHAVIOR THAT INCORPORATE IRRATIONAL BEHAVIOR AND CONFUSION As we have seen, there is a substantial body of work showing that consumers exhibit confusion when making choices about complex products like health insurance, health care, and retirement planning. They both: (i) fail to understand key attributes of the choice objects and (ii) exhibit choice behavior that appears to be nonoptimal and subject to an array of behavioral biases. Examples include choice of dominated alternatives, sensitivity to default options, sensitivity of choices to the framing of information, delay, and so on. As a result, traditional models of rational choice may not be adequate to understand or predict how consumers make choices in these areas. But, while there exists a large literature criticizing the rational choice paradigm, relatively few papers have developed positive (predictive) models of how people actually behave in very complex choice environments. Thus, in this section, we discuss some attempts to build behavioral models of how people actually make choices about complex choice objects like health insurance and retirement plans. In general, these models depart from the standard “rational choice” paradigm and incorporate confusion and cognitive limitations into the choice process.

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4.1 Allowing Perceived Attributes to Differ From True Attributes In Section 2, we argued that the model of Harris and Keane (1998) was a promising approach to relaxing the assumption that people know and understand the attributes of choice alternatives perfectly. Instead, their procedure allows one to estimate the “perceived” attributes of choice alternatives as distinct from the true attributes. To do this requires that one have available not just data on consumer choices but also auxiliary data on how consumers value (or rate) the attributes. Subsequently, Harris et al. (2002)—henceforth HFS—provided additional evidence on the validity of the HK methodology. They analyzed insurance plan choices of employed workers who were under 65, and hence not yet eligible for Medicare. They used data from the Buyers Health Care Action Group (BHCAG), a coalition of twodozen employers in Minneapolis/St. Paul that contracts directly with health care providers. The employees of BHCAG member companies have a choice among several alternative health plans. They were surveyed about their plan choices in 1998, and they were also asked a series of questions about how much they valued various plan attributes. A key aspect of the HFS study is that they pretended they did not observe premiums, in order to ascertain if the HK methodology could successfully uncover premium differences across plans by using data on survey respondents’ stated importance of premiums. They found that true premium differences were accurately uncovered by the HK methodology. And, like Harris and Keane, HFS found that the use of stated attribute importance data led to dramatic improvements in model fit. These results are encouraging for the HK method. Substantively, the HFS results showed (yet again) that consumers pay relatively little attention to various measures of provider quality.aj

4.2 Relaxing Theoretical Constraints on Choice Model Parameters Abaluck and Gruber (2011) proposed a way to incorporate “irrational” behavior into a standard choice model. In an application to Medicare Part D, they argue that when fully rational consumers compare drug plans they should only care about the level and variability of out-of-pocket costs (net of premiums), not the details of how this is achieved. To test this, they estimate a choice model of the form: Uij ¼ Pj α + E ðopc Þij β1 + σ 2ij β2 + cj β3 + Qj β4 + εij , j ¼ 1,…,J

(4)

Here Pj is the premium of plan j, E(opc)ij is expected out-of-pocket costs for person i under plan j, σ 2ij is the variance of out-of-pocket costs, cj is a vector of plan financial characteristics that affect out-of-pocket costs, and Qj is a vector of plan quality measures. aj

Parente et al. (2004) also use the HK approach to study health plan choices of University of Minnesota employees. I will not describe this work in detail, but simply note that they again find that attitudinal data are very predictive of consumer choices.

Complex Decision Making

The stochastic term εij is assumed iid type I extreme value, giving a multinomial logit model.ak Normative theory predicts that: (1) α ¼ β1 < 0 because consumers should be indifferent between plans with equal values of net expected out-of-pocket cost, Pj + E ðopc Þij , conditional on risk, (2) β2 < 0, provided that consumers are risk averse, and (3) β3 ¼ 0, as consumers should be indifferent among plan financial characteristics once one conditions on E(opc)ij and σ 2ij. Of course, rational consumers may also care about various plan quality measures (β4  0). The Abaluck–Gruber estimates indicate that jαj ≫ jβ1 j, implying excessive sensitivity to premiums, β2 < 0 but insignificant, giving only weak evidence of risk aversion, and β3 6¼ 0, implying that people do care about the particular assortment of features (e.g., premiums vs copays vs deductibles) by which a health plan achieves a given expected level and variability of out-of-pocket costs. They take these results as evidence against rational behavior.al While the Abaluck–Gruber approach seems intuitively appealing, Ketcham et al. (2015a), henceforth KKP, present some criticisms of their work that are worth considering. First, they argue there may be important omitted variables in (4). In particular, rational consumers may care about the identity of the firm offering a plan—i.e., a plan’s “brand name”—because some firms are perceived as more reliable, less likely to dispute claims, etc.am The failure of the theoretical restrictions on coefficients may be due to such misspecification. For this reason they propose to add brand indicators to the vector Qj in Eq. (4). But more general misspecifications of utility are also possible. In order to examine this issue, KKP implement a RP test which does not rely on a particular utility function. First, one must specify the (complete) set of plan attributes that consumers care about. Then, a person’s behavior cannot be rationalized if he/she chooses a dominated plan (i.e., one that is worse on all relevant attributes than another plan in his/ her choice set).an As long as a person passes this (weak) RP test, there exists some utility function that can rationalize his/her behavior. To begin, assume that consumers only care about premiums, expected out-of-pocket costs, and the variance of out-of-pocket costs. In that case, KKP find that 75% of consumers made dominated choices in 2006. This figure remains rather stable through 2010. However, when KKP assume that consumers also care about the brand name of a plan, ak al

am

an

This is a first order Taylor approximation to a CARA utility function. Another possible explanation of the jαj ≫ jβ1 j and β3 6¼ 0 result is that the consumers are using the financial rules of the plans to form E(opc)ij and σ 2ij via a different method from the econometrician. It is quite difficult to rule this out, or to determine if the consumers’ approach is superior or inferior. In principle, such plan differences should be captured by the quality measures Qj already included in (4). But Abaluck–Gruber use the CMS “star” measures, which are thought to be weakly related to true quality—see Harris and Buntin (2008). Formally, plan A is dominated by plan B if A is strictly worse than B on at least one attribute, and weakly worse than B on all other attributes.

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they find that only 20% of consumers made dominated choices in 2006, and this fraction is again stable through 2010.ao A naı¨ve response to these results would be to debate: (i) whether the 20% of irrational consumers detected by KKP is large or small and (ii) whether allowing “brand” to be a relevant attribute of drug plans is “too generous” to the rationality hypothesis (in the sense that a fully rational consumer would perhaps be able to parse the true “quality” of a plan in a way that is more precise than just relying on brand name as a portmanteau signal). Apropos of both points, Bhargava et al. (2015) look at a more controlled environment where a single insurer offers a large set of plans to employees of a private firm (thus eliminating brand as a confound) and where the plans only differ on four financial characteristics (thus also eliminating quality measures like network size from consideration). They nevertheless find that 55% of the employees made dominated choices. Interestingly, employees who were older, lower income, female or who had more health problems were more likely to choose dominated plans. In our view, the most important point of KKP and Bhargava et al. (2015) is they provide clear evidence that consumer behavior is heterogeneous. Both studies find that a significant fraction of consumers (i.e., 20% or 55%) behave quite irrationally, in that they make dominated choices. And, presumably, there is another group of consumers who make choices that can be rationalized, but only using utility functions that exhibit attribute trade-offs most of us would consider “odd.” A well-specified econometric model should account for such heterogeneity in behavior. An obvious problem with (4) is that it assumes homogeneous consumers. A naı¨ve test of the theoretical restrictions α ¼ β1, β2 < 0, β3 ¼ 0, is in fact a test of a complex joint hypothesis: (i) coefficients are homogenous across consumers, (ii) the theoretical restrictions hold for all these homogeneous consumers, and (iii) as KKP note, there are no other types of misspecification (e.g., omitted variables). Notably, given heterogeneity in parameters, the theoretical restrictions that α ¼ β1, β2 < 0, β3 ¼ 0, could hold for every consumer in the sample, but be violated in the pooled data.ap Finally, it is worth noting that if perceived attributes differ from true attributes it could explain both failure of theoretical parametric restrictions and failure of RP tests.

4.3 Allowing for Heterogeneity in the Choice Process In our view, a promising approach to behavioral heterogeneity is a model of “process heterogeneity.” This builds on and extends earlier work by El-Gamal and Grether ao

ap

In an additional test, KKP consider a choice model that imposes the theoretical restrictions α ¼ β1, β2 < 0, β3 ¼ 0 on (4), while also including brand dummies. They find that this model forecasts out-of-sample at least as well as the Abaluck–Gruber model. This is a version of a point made in Keane and Runkle (1990). Even if every person in a sample is making rational forecasts (that are heterogeneous due to private information), the pooled data will generate evidence of irrational behavior.

Complex Decision Making

(1995), Geweke and Keane (1999, 2000, 2001), Houser et al. (2004), and Keane and Wasi (2013). For example, consider a model with two types of people, a rational type and a nonrational type: n o w:p: p1 (5a) Uij ¼ Eðopc Þij + Pj β1i + σ 2ij β2i + Qj β4i + εij Uij ¼ Pj αi + E ðopc Þij β1i + σ 2ij β2i + cj β3i + Qj β4i + εij

w:p: 1  p1

(5b)

Eq. (5) says that a fraction p1 of consumers are “rational,” and make decisions based on the utility function in (5a), while a fraction 1  p1 are “irrational” or “confused” and make decisions according to (5b). Eq. (5a) incorporates the restrictions of rational choice theory as suggested by Abluck and Gruber, αi ¼ β1i, β2i < 0, β3i ¼ 0, but at the individual level, while (5b) does not impose these restrictions. Aside from allowing for two behavioral types, Eq. (5) also generalizes (4) by allowing for heterogeneity in utility function parameters within each type. We would not expect the parameter distributions to be the same for each type, so we might write: h i 0 if type ¼ 1 (6a) ðβ1i β2i β4i Þ0  N βr1 βr2 βr4 , Σ1 h i 0 (6b) ðαi β1i β2i β3i β4i Þ0  N αc βc1 βc2 βc3 βc4 , Σ2 if type ¼ 2 where the superscript “r” denotes rational while “c” denotes confused. Finally, the stochastic term εij is assumed iid type I extreme value in both (5a) and (5b). Thus, if we condition on a person’s type and his/her preference parameters, we have a simple multinomial logit model. But, given that we do not observe a person’s true type and preference parameters, in order to form his/her likelihood contribution we must form the unconditional probability of his/her choice by integrating over these unobservables.aq This is closely analogous to how one forms the unconditional choice probabilities in the Harris and Keane (1998) model, which we describe in Appendix A, so we will not repeat the details here. Estimation of the model (5) and (6) would give an estimate of the fraction of rational consumers in the population (1  p1). It is important to note, however, that it would not categorize particular consumers as either rational or irrational. Rather, given the likelihood, we could construct the posterior odds, for each person in the data, that his/her behavior is described by (5a) or (5b). A useful specification check on the model in (5) and (6) is that we would expect consumers’ posterior probabilities of being “irrational” to be closely related to whether they pass the rationality tests proposed by aq

The model in (5) and (6) is a type of “mixed” logit model, with two stages of mixing. The individual level logit models are mixed using both (i) the mixing distribution determined by (6) and (ii) the type proportions p1 and 1  p1.

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Ketcham et al. (2015a),ar as well as to variables like cognitive ability that we would associate with decision-making ability. As we have discussed at several points in Sections 2 and 3, the question of how to do welfare analysis if consumers’ “decision utility” departs from their “true utility” remains difficult and unresolved. One option that one might consider is to estimate a model of process heterogeneity as in (5) and (6) and then use the estimates for the “rational” type (i.e., the type whose estimated utility parameters obey theoretical restrictions) to perform welfare analysis. Such an approach relies on the theory restrictions being correct, and on the distribution of taste parameters among the sophisticated type being representative of the whole population.as More generally, given estimates of the distribution of taste parameters as in (6), we could do many interesting exercises, such as: (i) assess the magnitude and welfare consequences of departures from rational choice behavior, (ii) assess the welfare implications of changing product attributes, or restricting choice sets, and (iii) predict the demand for (and welfare consequences of ) introducing new products. Of course, the conclusions of such an analysis will depend on the parametric forms in (5) and (6). But it is not possible to do quantitative welfare analysis without parametric assumptions on utility.at

4.4 Incorporating Confusion in the Choice Process In the standard interpretation of the multinomial logit model due to McFadden (1974), the error terms εij represent unobserved attributes of products for which consumers have heterogeneous tastes. For example, Blue Cross Blue Shield (BCBS) may have a high value of Qj because it is widely perceived as high quality. But BCBS would only have a high εij if person i has a personal reason for liking that brand (e.g., person i had a very good previous experience with BCBS). It is important to emphasize that consumer ar

as

at

Ketcham et al. (2015b) propose to divide consumers into “rational” vs “suspect” groups based on whether they pass the RP test in Ketcham et al. (2015a), and whether they can answer a basic knowledge question about Medicare drug plans. They find the probability of being labeled “suspect” is systematically related to demographic variables that may proxy for cognitive ability (e.g. age, education, health status). They show that choice models like (4) estimated on the “rational” vs “suspect” groups have very different parameters, with those for the “rational” group coming much closer to satisfying the restrictions suggested by Abluck and Gruber. They also show how to treat the parameters of the “rational” group as the true utility weights in evaluating welfare effects of policies aimed at helping the “suspect” group make better choices. The main limitation of their approach is they continue to assume homogeneous parameters within the “rational” and “suspect” types. In other words, the difference between the sophisticated and unsophisticated types lies in decisionmaking ability, quality of information, and so on, but not in preferences themselves. Indeed, even “nonparametric” RP analysis, which allows one to test for rational behavior (but not to do quantitative welfare analysis), is not fully “nonparametric” as it requires assumptions about what attributes of products do or do not generate consumer utility.

Complex Decision Making

choice behavior is not “random” in the logit model. It only appears that way to an analyst who cannot observe εij. An important extension of our model is to allow for confusion in choice behavior. One way to capture confusion is to introduce genuine randomness into choices. We propose to do this by adding a source of randomness to Eq. (5b). We then have: Uij ¼ Pj αi + E ðopc Þij β1i + σ 2ij β2i + ci β3i + Qi β4i + ωij ρðAi Þ + εij

ð5b0 Þ

Here, ωij  N ð0, 1Þ captures a mistake in how consumer i evaluates the “true” utility that he/she will derive from choice of option j. The parameter ρðAi Þ  0 is a scaling factor that captures the magnitude of the consumer’s mistakes.au Ai is a vector of both (i) individual characteristics, such as cognitive ability, financial knowledge, age, etc., that may influence a person’s level of difficulty in making decisions, and (ii) contextual variables like size of the choice set or number of attributes, that influence the complexity of the choice situation. The assumption that the scale of optimization errors is related to cognitive ability is motivated by the results of Fang et al. (2008). In their model of demand for health insurance they included a set of “behavioral” variables that would not be included in a typical rational choice model. Most importantly, they included a measure of cognitive ability. They found that, ceteris paribus, cognitive ability has a strong positive effect on demand for insurance. We hypothesize that people with higher cognitive ability are better able to understand the benefits of insurance, and better able to evaluate different plan options.av, aw The model in (5a), (5b0 ), and (6) can be used to study a number of different types of possible departures from rationality: First, the model generates an estimate of the proportion of rational consumers in the population (p1). Second, by examining the estimates of ρ(Ai) we can learn about the extent of “confusion” in choice behavior, as well as discovering whether some types of people exhibit more confusion than others. Third, by looking at the distribution of the parameter vector (αi β1i β2i β3i β4i) we can learn a great deal about the nature of departures from rational behavior. For instance, do a large fraction of people have jαi j ≫ jβ1i j, meaning they place excessive weight on au

av

aw

The inclusion of the scale factor in the model is motivated by the work of Fiebig et al. (2010), who find strong evidence of scale heterogeneity in consumer choice behavior. Fang et al. (2008) find not only that high cognitive ability people are more likely to buy insurance, but also that they tend to be healthier. Together, these two factors mean that healthier people are more likely to buy insurance. This phenomenon—which contradicts the standard prediction of adverse selection models—is known as “advantageous selection.” A number of studies have also found that proxies for cognitive ability are related to the probability of rational decision making. Recent examples are Ketcham et al. (2015b), discussed earlier, and Bateman et al. (2015, 2016c), who study allocation of retirement funds to annuity vs phased withdrawal plans, and find that measures of numeracy and financial literacy predict rational allocations.

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premiums vs out-of-pocket costs? Or are these excesses statistically significant but quantitatively quite modest? If the latter, this would cast the statistical finding that many people overweight premiums in quite a different light (as the problem would appear to be fairly modest).ax Fourth, we can simulate the estimated model to learn how much choice behavior would be affected if the confusion term ωijρ(Ai) were shut down. If we assume that the confusion term is not part of “true” utility, this exercise would allow us to assess the welfare loss due to confusion.ay Another interesting exercise is to simulate behavior under a simpler menu of choice options than that which exists in the data. In a rational choice model restricting choice must reduce utility, but, in the presence of confusion, restriction (or simplification) of the choice set can potentially lead to an increase in consumer welfare.az Finally, note that other extensions of the process heterogeneity model are possible. For example, there is no reason to limit the mixture model to two types. One could add other processes like “always choose the default,” or other heuristics that are prevalent in the data.ba

4.5 Simple Methods to Model Dynamics That Relax Optimizing Assumptions As we discussed in Section 3, optimal life-cycle planning requires the solution of a complex DP problem. But actual decision making in the domain of retirement planning often departs in obvious ways from normative principle, and people often seem to react to the difficulty of the problem with delays or procrastination. Next, we discuss models of choice behavior that accommodate such features. ax

ay az

ba

For example, we might find α2 only slightly greater than β21 but with the difference significant and Corr(αi, β1i) very high (but significantly less than one). Together, these results would imply statistically significant but economically negligible departures from rationality. This is analogous to Kahneman et al. (1997)’s distinction between decision vs hedonic utility. To give a simple example, consider a choice set consisting of only two plans A and B. Plan B is dominated on all attributes observed by the econometrician. In the rational version of the logit model a tiny fraction of consumers do choose B just because they have very large values of εiB. However, if ρ(Ai) is very large—indicating consumers are very confused by this choice—the probability of choosing B will be close to 50%. A paternalistic social planner could improve social welfare by banning plan B (provided of course that he/she does not put enormous weight on the small fraction of consumers with very large values of εiB). A precedent is Bateman et al. (2016c), who consider a model of process heterogeneity in allocation of funds to annuities vs phase withdrawal plans. They let the mixture components include always choosing the default, making a 50/50 allocation, making a 100% allocation to one alternative (or the other), or drawing allocations from a beta-binomial. Their model differs fundamentally from (5) to (6), however, in that it is essentially descriptive (no option corresponds to optimizing behavior). But they do find that lower cognitive ability people are more likely to use the naı¨ve heuristics.

Complex Decision Making

Interestingly, methods that appear to be relevant for retirement planning problems have already been developed in marketing research for the closely related problem of inventory planning. Specifically, Ching et al. (2009, 2014)—henceforth CEK—develop a model of consumer demand for a storable (or semidurable) branded commodity. In this context, optimal behavior involves: (i) checking the prices of all brands of a product in every period, (ii) solving a DP problem to determine both (ii-a) the reservation price for purchase of each brand and (ii-b) the optimal quantity to buy in the event that the price of a brand is below its reservation price. Of course, the reservation prices and optimal purchase quantities both evolve in a complex way with inventories. CEK argue that a normative model is unrealistic for two reasons: (i) for most products, consumers presumably do not have the time, interest, or mental capacity to check all prices in every period and (ii) in those periods when consumers do pay close attention to a category, they presumably make decisions using more or less sophisticated rules of thumb, not by literally solving a DP problem. Thus, CEK develop a two-stage model of demand for a storable branded product. In the first stage, consumers decide whether or not to pay attention to the product category. If they do decide to pay attention then, in stage two, they use a rule of thumb that may or may not provide a good approximation to the DP problem (depending on parameter estimates), as in Geweke and Keane (2000, 2001). In CEK’s empirical applications, the decision whether to consider a category is modeled as a simple probit or logit discrete choice model, where the factors that drive consideration are cues like advertising, displays, and low inventory.bb Their work was originally motivated by the observation that brand choice conditional on category purchase is very sensitive to price, while the decision to make a purchase in a category is quite insenitive to price. CEK showed that these seemingly contradictory facts could be explained if consumers only occasionally look at (i.e., consider) a category. It seems fairly clear how one might apply the CEK framework to financial products like annuities, life insurance, or choice of retirement plans. As we discussed in Section 3, there is clear evidence that most consumers are averse to thinking about these products on a regular basis. For example, as is well known, the typical consumer does not engage in a frequent rebalancing of his/her stock portfolio as the state of the world changes. It is natural to think of a framework where, in a first stage, consumers decide on, say, a quarterly or annual basis, whether to consider financial products in a certain category. The decision to consider could be driven by advertising, as well as by major life events such as retirement, children leaving home, a spouse passing away, selling a house and/or moving house, or reaching a milestone birthday. In the second stage, it would again be possible to estimate a behavioral rule of thumb from the data, rather than imposing an optimal DP solution. bb

In the optimal solution consumers should consider a category in every period regardless of their inventory. Even if inventory is high, a low enough price would make it optimal to stock up even more.

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Given such an estimated model, one could simulate behavior under the model vs under a normative solution to the planning problem. One could then evaluate whether or not the wealth losses from following the simplified decision process rather then the optimal DP solution are substantial (as in Houser et al., 2004).

4.6 Summary and Directions for Future Work To summarize, in this section we have described several approaches to modeling choice behavior that depart in different ways from the standard rational choice paradigm. It is not difficult to see how these different approaches could be combined into a more general framework. Consider the demand for a PHI plan. One could adopt the CEK approach of assuming that consumers only occasionally consider such products, and adopt a firststage consideration model that depends on factors like major life events. Then in the second stage, one could adopt a framework like our mixed logit model of Eqs. (5) and (6), where some fraction of consumers make choices rationally while others do not, and there is heterogeneity in the nature of departures from rationality.bc Next, it is important to recognize that, if perceived attributes differ from true attributes, then a model that falsely assumes consumers know true attributes will not be a structural representation of behavior (see Section 2.1.4). But, if attitudinal data were available one could incorporate the Harris–Keane approach to relax the assumption that all product attributes are correctly observed by consumers. One could, for instance, treat expected out-of-pocket costs and product quality as latent variables in (5), provided that one had available measures of how much individuals value these attributes. Furthermore, if data on consumers’ information sets were available, one could model how consumers learn about product attributes, as in Erdem and Keane (1996). Finally, in dynamic choice contexts, where the value of each option includes not just a current payoff but also an expected stream of future payoffs (so that optimal choices would require a DP solution), we could, in the second stage, use a rule-of-thumb approximation to the value of each option, as in Geweke and Keane (1999, 2000) and Ching et al. (2014). The approaches to modeling choice behavior that we have described in this section are “constructive” in the sense that they attempt to provide positive models of behavior that would be useful for prediction and policy analysis even if rationality assumptions fail. We hope that such models will prove useful for empirical work in areas such as demand for financial products and insurance products, just as they have already proven useful in areas such as experimental economics, labor economics, marketing, and health economics. bc

Furthermore, as noted earlier, one could adopt additional behavioral modes, such as choice of defaults and other heuristics, as additional components of the mixture.

Complex Decision Making

5. CONCLUSION In this chapter, we have reviewed evidence on how people make decisions in complex choice situations. This may refer to situations where the object under consideration is complex, in that it has many attributes, or some attributes that are difficult to understand or evaluate, and/or situations where the choice set itself is complex because there are a very large number of alternatives. We focus on three particular areas that are of special relevance to senior citizens: health insurance, health care, and retirement planning. The well-being of senior citizens depends critically on people making “good” choices in these areas, not just in old age but over the whole life cycle. The idea that consumers are capable of making informed choices in markets for health care, health insurance, and retirement benefits rests on assumptions that they both (i) know and understand the attributes of the products/services they are evaluating and (ii) possess the cognitive capacity and skills to make good choices among those products/services. Our review suggests that consumers in general, and the elderly in particular, fall far short of this ideal. For instance, the evidence suggests that consumers have a very difficult time understanding the attributes of both public and private health insurance plans. Both the quality of care and expected out-of-pocket costs under alternative health care plans are very difficult for experts to measure, let alone for consumers to understand. There is ample evidence, for example, that most senior citizens in the United States do not understand cost-sharing requirements of the Medicare program, or how these are affected by supplemental insurance. The evidence also suggests that informational interventions have very modest impacts on health insurance and health care decisions. A similar story holds in the area of retirement planning. Fewer than half of adults have attempted any financial planning for retirement. Consumers show misunderstandings and biases in critical areas of retirement planning knowledge, including life expectancy, investment returns and risk, retirement dates, pension ages, and entitlements. Confusion extends to evaluating investment decisions and is exacerbated by low financial literacy. Improved disclosure, education, and advice go some way toward improving outcomes, but impacts of education are often temporary, disclosure simplifications have unpredictable effects, and advice is affected by agency problems. In light of these findings, we discuss ways to extend standard rational choice models to account for consumer confusion. For example, Harris and Keane (1998) and Erdem and Keane (1996) develop approaches to choice modeling where perceived attributes may depart from true attributes. Geweke and Keane (2000, 2001) develop a method where consumers are assumed to use a mixture of heuristics to solve a dynamic model. And Ching et al. (2009, 2014) develop a method that can account for consumer inattention, delay, and procrastination.

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In standard choice models in economics, the error term is assumed to arise from person-specific tastes for the alternatives—tastes that the researcher cannot see. Thus, choice behavior is deterministic from the point of view of the consumer. We have proposed a new type of choice model in which one component of the error term captures genuine randomness or confusion in consumer behavior. Under this “hybrid” view of the error term, randomness will arise primarily from taste heterogeneity in the case of simple products like laundry detergent. But as we move to more complex choices like health insurance or super funds, more randomness will be attributable to confusion. Existing work has shown that randomness in choice due to confusion, and the extent of departures from rationality more generally, is moderated by nontraditional variables like cognitive ability, age, numeracy, education, and financial literacy. These findings contrast sharply with traditional rational choice models where all consumers are assumed to be able to make optimal decisions, regardless of the complexity of the situation. In all the models we have described, people make choices subject to optimization errors, so they do not base decisions on a normatively correct solution to the optimization problem. This leaves open the potential for carefully designed paternalistic interventions. For instance, there is some evidence that product standardization enables consumers to make better choices in both health insurance and financial product markets. We are however, quite cognizant of the potential for unintended consequences of such interventions.

APPENDIX A. LIKELIHOOD FUNCTION OF THE HARRIS–KEANE MODEL It is straightforward to estimate the Harris and Keane (1998) model in Eqs. (1)–(3) using simulated maximum likelihood. If the attribute importance weights βi and Wi were known, the choice probability for a person would have a simple multinomial logit form. Since βi and Wi are unobserved (we are estimating the parameters of their distribution), the simulated probability that person i chooses plan j is just the average over draws for βi and Wi of multinomial logit choice probabilities: 2  d  3 D d X   exp X β + A W j i j i 4X (A1) P jjθ,Si ,Si ¼ D1  5 5 d d exp X β + A W d¼1 k i k i k¼1 Here θ is the vector of all model parameters and Si and Si* are the vectors of attitudinal measures for person i. Draws are indexed by d ¼ 1,…, D. A technical point, explained at some length in Harris and Keane (1998), is that it is difficult to estimate both the scale of W1p in Eq. (3) and the scale of the unobserved attribute levels A for each plan. To deal with this problem, Harris and Keane restricted W1p to equal the inverse of the estimated standard deviation of the measurement error in Eq. (3), which, in turn, was restricted to be the same as the standard deviation of the measurement error in Eq. (2). Intuitively, these restrictions imply that the stated attribute

Complex Decision Making

importance measures are just as good at predicting peoples’ preference weights on the unobserved attributes as they are at predicting peoples’ preference weights on observed attributes.

APPENDIX B. SIMULATIONS OF HARRIS–KEANE HEALTH PLAN CHOICE MODEL Given an estimated choice model, one can use it to simulate the impact of a change in plan attributes on the market shares of the various plans. One can also use the model to predict whether there would be substantial demand for new plans with particular attributes. Some examples of this type of exercise are provided in Table B.1. The first row of Table B.1 reports a “baseline” simulation of the model—i.e., the model predictions of the market shares of the various plans. The second row of Table B.1 reports the model prediction of what would happen if Basic Medicare were to add prescription drug coverage. The model predicts its market share would increase substantially, from 9.1% to 17.7%. Similarly, the third row shows that if the IPA were to add drug coverage its market share would increase from 25.6% to 41.7%. These results imply that many consumers find prescription drug coverage to be a very attractive feature of a health plan. The fourth row of Table B.1 presents the model’s prediction of what would happen if the IPA plan were to remove provider choice. The model predicts that its market share would dwindle to almost zero (2.3%). Thus, most consumers place great value on provider choice. In other simulations (not reported), Harris and Keane (1998) found that moderate changes in premiums (i.e., $20 per month increases) would have very small effects on plan enrollments. Thus, consumers appear to care greatly about provider choice and drug Table B.1 Some Illustrative Experiments Using the Model Basic Medigap Medigap Medicare Without With Drugs (%) Drugs (%) (%)

Baseline market shares Medicare adds drug coverage IPA adds drug coverage IPA plan removes provider choice Add “New Plan”

IPA (%)

HMO (%)

9.1

9.4

12.4

25.6

43.6

17.7

8.2

10.9

22.2

41.2

6.7

7.1

9.1

41.7

35.5

11.4

12.1

16.3

2.3

57.7

6.8

7.4

9.9

19.6

30.6

“New Plan” (%)

25.8

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coverage, but not very much about premiums (at least within the modest range of premiums covered in the data). In the bottom row of Table B.1, the model is used to predict what would happen if a new health insurance plan were introduced. The “New Plan” is designed to fill a gap that existed in the Minneapolis/St. Paul insurance market. Consider a segment of consumers who place a high value on provider choice and preventive care, but little value on prescription drug coverage. The plan best tailored to these tastes was the IPA. However, the IPA was perceived as being of very low quality (as well as having very high cost sharing), thus leaving these consumers without a very appealing option. The fact that so many people choose the IPA anyway (21.7%) suggests this configuration of preferences is rather common. The “New Plan” was designed to be like the IPA on observed attributes, but to have the same perceived quality as the group HMO (A62 ¼ 0.161) and to have less perceived cost sharing (A61 ¼ 0.150). The model predicts that the “New Plan” would be very popular, with a market share of 25.8%. Note that the “New Plan” differs from the group HMO primarily in that it allows provider choice but does not cover drugs. The model implies that a substantial segment of the population likes that option, provided it is also of reasonably high quality.

ACKNOWLEDGMENTS M.P.K.’s work on this project has been supported by Australian Research Council grants FF0561843 and FL110100247. S.T.’s work on this project has been supported by Australian Research Council grant DP120102239. We thank the editors and two anonymous referees for exceptionally useful comments.

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Gustman, A.L., Steinmeier, T.L., 2005. Imperfect knowledge of social security and pensions. Ind. Relat. J. Econ. Soc. 44, 373–397. Hackethal, A., Inderst, R., Meyer, S., 2010. Trading on advice. CEPR Discussion Paper No. DP8091. Hackethal, A., Haliassos, M., Jappelli, T., 2012. Financial advisers: a case of babysitters? J. Bank. Financ. 36, 509–524. Hall, J., 2004. Can we design a market for competitive health insurance?. CHERE Discussion Paper No. 53. Handel, B., 2013. Adverse selection and inertia in health insurance markets: when nudging hurts. Am. Econ. Rev. 103, 2643–2682. Handel, B., Kolstad, J., 2015. Health insurance for ‘humans’: information frictions, plan choice and consumer welfare. Am. Econ. Rev. 105, 2449–2500. Handel, B., Kolstad, J., Spinnewijn, J., 2015. Policy interventions in health insurance markets. NBER Working Paper No. 21759. Hanoch, Y., Rice, T., Cummings, J., Wood, S., 2009. How much choice is too much? The case of the Medicare prescription drug benefit. Health Serv. Res. 44, 1157–1168. Harris, K., Buntin, M.B., 2008. Choosing a health care provider: the role of quality information. Research Synthesis Report 14, 1-25, Robert Wood Johnson Foundation. Harris, K.M., Keane, M.P., 1998. A model of health plan choice: inferring preferences and perceptions from a combination of revealed preference and attitudinal data. J. Econ. 89, 131–157. Harris, K.M., Feldman, R., Schultz, J., 2002. Measuring consumer perceptions of quality differences among competing health benefit plans. J. Health Econ. 21, 1–18. Harris-Kojetin, L.D., McCormack, L.A., Jael, E.F., Sangl, J.A., Garfinkel, S.A., 2001. Creating more effective health plan quality reports for consumers: lessons from a synthesis of qualitative testing. Health Serv. Res. 36, 447–476. Hastings, J., Mitchell, O.S., Chyn, E., 2011. Fees, framing, and financial literacy in the choice of pension manager. In: Mitchell, O.S., Lusardi, A. (Eds.), Financial Literacy: Implications for Retirement Security and the Financial Marketplace. Oxford University Press, Oxford, pp. 101–115. Hensher, D.A., Louviere, J., Swait, J., 1999. Combining sources of preference data. J. Econ. 89, 197–221. Hertzog, C., Kramer, A.F., Wilson, R.B., Lindenberger, U., 2008. Enrichment effects on adult cognitive developments. Can the functional capacity of older adults be preserved and enhanced? Psychol. Sci. Public Interest 9, 1–65. Hibbard, J.H., Slovic, P., Peters, E., Finucane, M.L., 2002. Strategies for reporting health plan performance information to consumers: evidence from controlled studies. Health Serv. Res. 37, 291–313. Holden, S., 2013. When, why, and how do mutual fund investors use financial advisers? In: Mitchell, O.S., Smetters, K. (Eds.), The Market for Retirement Financial Advice. Oxford University Press, Oxford, pp. 249–272. Houser, D., Keane, M., McCabe, K., 2004. Behavior in a dynamic decision problem: an analysis of experimental evidence using a Bayesian type classification algorithm. Econometrica 72, 781–822. Huberman, G., Jiang, W., 2006. Offering versus choice in 401 (k) plans: equity exposure and number of funds. J. Financ. 61, 763–801. Hudomiet, P., Kezdi, G., Willis, R.J., 2011. Stock market crashes and expectations of American households. J. Appl. Econ. 26, 393–415. Hurd, M.D., 2009. Subjective probabilities in household surveys. Ann. Rev. Econ. 1, 543–564. Hurd, M., Van Rooij, M., Winter, J., 2011. Stock market expectations of Dutch households. J. Appl. Econ. 26, 416–436. Inderst, R., Ottaviani, M., 2009. Misselling through agents. Am. Econ. Rev. 99, 883–908. Isaacs, S.L., 1996. Consumer’s information needs: results of national survey. Health Aff. 15, 31–41. James, E., 1995. Averting the old age crisis: an international perspective. Aging Int. 22, 15–22. June. Jappelli, T., Padula, M., 2013. Investment in financial literacy and savings decisions. J. Bank. Financ. 37, 2779–2792. Johar, M., Jones, G., Keane, M., Savage, E., Stavrunova, O., 2011. Waiting times for elective surgery and the decision to buy private health insurance. Health Econ. 20 (S1), 68–86. Johnson, E.J., Hershey, J., Meszaros, J., Kunreuther, H., 1993. Framing probability distortions, and insurance decisions. J. Risk Uncertain. 7, 35–51.

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Kahneman, D., Wakker, P., Sarin, R., 1997. Back to Bentham? Explorations of experienced utility. Q. J. Econ. 112, 375–405. Kaiser Family Foundation, 2000. National Survey on Americans as Health Care Consumers: An Update on the Role of Quality Information. Available at http://www.ahrq.gov/downloads/pub/kffsummary00.pdf. Keane, M., Runkle, D., 1990. Testing the rationality of price forecasts: new evidence from panel data. Am. Econ. Rev. 80, 714–735. Keane, M., Wasi, N., 2013. Comparing alternative models of heterogeneity in consumer choice behaviour. J. Appl. Econ. 28, 1018–1045. Keane, M., Wasi, N., 2016. How to model consumer heterogeneity? Lessons from three case studies on SP and RP data. Res. Econ. 70, 197–231. Keim, D.B., Mitchell, O.S., 2016. Simplifying choices in defined contribution retirement plan design. NBER Working Paper No. 21854. Ketcham, J., Kuminoff, N., Powers, C., 2015a. Which models can we trust to evaluate consumer decision making? Comment on choice inconsistencies among the elderly. NBER Working Paper No. 21387 (American Economic Review). Ketcham, J., Kuminoff, N., Powers, C., 2015b. Estimating the heterogeneous welfare effects of choice architecture: an application to the Medicare prescription drug insurance market. Working Paper, Arizona State University. Kling, J.R., Mullainathan, S., Shafir, E., Vermeulen, L., Wrobel, M., 2008. Misperception in choosing Medicare drug plans. Harvard University Working Paper. Klos, A., Weber, E.U., Weber, M., 2005. Investment decisions and time horizon: risk perception and risk behavior in repeated gambles. Manag. Sci. 51, 1777–1790. Knoef, M., Been, J., Alessie, R., Caminada, K., Goudswaard, K., Kalwij, A., 2015. Measuring retirement savings adequacy: developing a multi-pillar approach in the Netherlands. J. Pension Econ. Financ. 15, 55–89. Kolstad, J., Chernew, M., 2009. Quality and consumer decision making in the market for health insurance and health care services. Med. Care Res. Rev. 66, 28–52. Korniotis, G.M., Kumar, A., 2011. Do older investors make better investment decisions? Rev. Econ. Stat. 93, 244–265. Kutlu-Koc, V., Kalwij, A., 2013. Individuals’ survival expectations and actual mortality. Discussion Paper No. 2013-013, Netspar. Laibson, D.I., Repetto, A., Tobacman, J., Hall, R.E., Gale, W.G., Akerlof, G.A., 1998. Self-control and saving for retirement. Brookings Pap. Econ. Act. 29 (1, Spring), 91–196. Liang, J., Wang, H., Lazear, E.P., 2014. Demographics and entrepreneurship. NBER Working Paper No. 20506. Louviere, J., 1988. Conjoint analysis modelling of stated preferences: a review of theory, methods, recent developments and external validity. J. Transp. Econ. Pol. 22, 93–119. Louviere, J., Hensher, D.A., Swait, J.A., 2000. Stated Choice Methods: Analysis and Application. Cambridge University Press, Cambridge. Love, D.A., Palumbo, M.G., Smith, P.A., 2009. The trajectory of wealth in retirement. J. Public Econ. 93, 191–208. Lucarelli, C., Prince, J., Simon, K., 2009. The welfare impact of reducing choice in Medicare Part D: a comparison of two regulation strategies. Available at SSRN, http://ssrn.com/abstract¼1217662. Lusardi, A., Mitchell, O.S., 2007. Baby boomer retirement security: the roles of planning, financial literacy, and housing wealth. J. Monet. Econ. 54, 205–224. Lusardi, A., Mitchell, O.S., 2011. Financial literacy and retirement planning in the United States. J. Pension Econ. Financ. 10, 509–525. Lusardi, A., Mitchell, O.S., 2014. The economic importance of financial literacy: theory and evidence. J. Econ. Lit. 52, 5–44. Madrian, B.C., Shea, D.F., 2001. The power of suggestion: inertia in 401 (k) participation and savings behavior. Q. J. Econ. 116, 1149–1187. Maestas, N., Schroeder, M., Goldman, D., 2009. Price variation in markets with homogeneous goods: the case of Medigap. NBER Working Paper No. 14679. Mather, M., Carstensen, L.L., 2005. Aging and motivated cognition: the positivity effect in attention and memory. Trends Cogn. Sci. 9, 496–502.

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Mazzonna, F., Peracchi, F., 2012. Ageing, cognitive abilities and retirement. Eur. Econ. Rev. 56, 691–710. McCall, N., Rice, T., Sangl, J., 1986. Consumer knowledge of Medicare and supplemental health insurance benefits. Health Serv. Res. 20, 633–657. McCormack, L.A., Garfinkel, S.A., Hibbard, J.H., Norton, E.C., Bayen, U.J., 2001. Health plan decision making with new Medicare information materials. Health Serv. Res. 36, 531–554. McFadden, D., 1974. Conditional logit analysis of qualitative choice behavior. In: Zarembka, P. (Ed.), Frontiers in Econometrics. Academic Press, New York, pp. 105–142. McFadden, D., 1986. The choice theory approach to market research. Mark. Sci. 5, 275–297. McFadden, D., 2006. Free markets and fettered consumers. Am. Econ. Rev. 96, 3–29. McFadden, D., Morikawa, T., Ben-Akiva, M., 2002. Discrete choice models incorporating revealed preferences and psychometric data. In: Franses, P.H., Montgomery, A.L. (Eds.), In: Econometric Models in Marketing, vol. 16. Elsevier Science, Oxford, pp. 27–53. Milligan, K., 2005. Life-cycle asset accumulation and allocation in Canada. Can. J. Econ. 38, 1057–1106. Mitchell, O.S., 1988. Worker knowledge of pension provisions. J. Labor Econ. 6, 21–39. Mitchell, O.S., Moore, J.F., 1998. Can Americans afford to retire? New evidence on retirement saving adequacy. J. Risk Insur. 65, 371–400. Mitchell, O.S., Piggott, J., Takayama, N., 2011. Securing Lifelong Retirement Income: Global Annuity Markets and Policy. Oxford University Press, Oxford. Morrin, M., Inman, J.J., Broniarczyk, S.M., Nenkov, G.Y., Reuter, J., 2012. Investing for retirement: the moderating effect of fund assortment on the 1/n heuristic. J. Mark. Res. 49, 537–550. Mullainathan, S., Noeth, M., Schoar, A., 2012. The market for financial advice: an audit study. NBER Working Paper No. 17929. Navarro-Martinez, D., Salisbury, L.C., Lemon, K.N., Stewart, N., Matthews, W.J., Harris, A.J.L., 2011. Minimum required payment and supplemental information disclosure effects on consumer debt repayment decisions. J. Mark. Res. 48, S60–S77. Neuman, P., Cubanski, J., 2009. Medicare Part D update—Lessons learned and unfinished business. N. Engl. J. Med. 361, 406–414. Ooijen, R., Alessie, R., Kalwij, A., 2014. Saving behavior and portfolio choice after retirement. Panel Paper 42, Network for Studies on Pensions, Aging and Retirement. Parente, S.T., Feldman, R., Christianson, J.B., 2004. Employee choice of consumer-driven health insurance in a multiplan, multiproduct setting. Health Serv. Res. 39, 1091–1111. Peters, E., 2008. Numeracy and the perception and communication of risk. Ann. N. Y. Acad. Sci. 1128, 1–7. Peters, E., Hess, T., V€astfj€all, D., Auman, C., 2007a. Adult age differences in dual information processes: implications for the role of affective and deliberative processes in older adults’ decision making. Perspect. Psychol. Sci. 2, 1–23. Peters, E., Hibbard, J., Slovic, P., Dieckmann, N., 2007b. Numeracy skill and the communication, comprehension, and use of risk and benefit information. Health Aff. 26, 741–748. Polyakova, M., 2015. Regulation of insurance with adverse selection and switching costs: evidence from Medicare Part D. NBER Working Paper No. 21541. Poterba, J.M., 2014. Retirement security in an aging population. Am. Econ. Rev. Pap. Proc. 104, 1–30. Poterba, J.M., Venti, S.F., Wise, D.A., 2011. The composition and draw-down of wealth in retirement. J. Econ. Perspect. 25, 95–117. Rangel, A., 2005. Comment on passive decisions and potent defaults. In: Wise, D.A. (Ed.), Analyses in the Economics of Aging. University of Chicago Press, Chicago, pp. 73–78. Reinholtz, N., de Langhe, B., Fernbach, P.M., 2015. Almost everyone misunderstands the benefits of diversification. Working Paper, Center for Research on Consumer Financial Decision Making, University of Colorado, Boulder. Roalf, D.R., Mitchell, S.H., Harbaugh, W.T., Janowsky, J.S., 2012. Risk, reward, and economic decision making in aging. J. Gerontol. B Psychol. Sci. Soc. Sci. 67, 289–298. gbr099. Roland, M., Campbell, S., 2014. Successes and failures of pay for performance in the United Kingdom. N. Engl. J. Med. 370, 1944–1949. Rubaltelli, E., Rubichi, S., Savadori, L., Tedeschi, M., Ferretti, R., 2005. Numerical information format and investment decisions: implications for the disposition effect and the status quo bias. J. Behav. Financ. 6, 19–26.

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Sabelhaus, J., Bogdan, M., Holden, S., 2008. Defined Contribution Plan Distribution Choice at Retirement: A Survey of Employees Retiring Between 2002 and 2007. Investment Company Institute Research Series, Investment Company Institute, Washington. Saez, E., 2009. Details matter: the impact of presentation and information on the take-up of financial incentives for retirement saving. Am. Econ. J. Econ. Pol. 1, 204–228. Samanez-Larkin, G., Kuhnen, G., Yoo, D., Knutson, B., 2010. Variability in nucleus accumbens activity mediates age-related suboptimal financial risk taking. J. Neurosci. 30, 1426–1434. Skinner, J., 2007. Are you sure you are saving enough for retirement? J. Econ. Perspect. 21, 59–80. Song, C., 2015. Financial illiteracy and pension contributions: a field experiment on compound interest in China. Available at SSRN 2580856. Spinnewijn, J., 2016. Heterogeneity, demand for insurance and adverse selection. Working Paper, London School of Economics. Spranca, M., Kanouse, D.E., Elliott, M., Short, P.F., Farley, D.O., Hays, R.D., 2000. Do consumer reports of health plan quality affect health plan selection? Health Serv. Res. 35, 933–947. Stango, V., Zinman, J., 2009. Exponential growth bias and household finance. J. Financ. 64, 2807–2849. Stern, Y., 2002. What is cognitive reserve? Theory and research application of the reserve concept. J. Int. Neuropsychol. Soc. 8, 448–460. Super System Review, 2010. Super System Review—Final Report. 30 June 2010. Canberra. Swait, J., Andrews, R., 2003. Enriching scanner panel models with choice experiments. Mark. Sci. 22, 442–460. Teppa, F., Lafourcade, P., 2013. Can longevity risk alleviate the annuitization puzzle? Empirical evidence from survey data. Working Paper, De Nederlandsche Bank (DNB). Tumlinson, A., Bottigheimer, H., Mahoney, P., Stone, E., Hendricks, A., 1997. Choosing a health plan: what information will consumers use? Health Aff. 16, 229–238. Uhrig, J.D., Harris-Kojetin, L., Bann, C., Kuo, T.M., 2006. Do content and format affect older consumers use of comparative information in a Medicare health plan choice? Results from a controlled experiment. Med. Care Res. Rev. 63, 701–718. Van Rooij, M., Lusardi, A., Alessie, R., 2011. Financial literacy and stock market participation. J. Financ. Econ. 101, 449–472. Vlaev, I., Chater, N., Stewart, N., 2009. Dimensionality of risk perception: factors affecting consumer understanding and evaluation of financial risk. J. Behav. Financ. 10, 158–181. Weber, E., 2003. Who’s afraid of a poor old age? Risk perception in risk management decisions. In: Mitchell, O.S., Utkus, S.P. (Eds.), Pension Design and Structure: New Lessons from Behavioral Finance. Oxford University Press, Oxford, pp. 54–65. Weber, E.U., Siebenmorgen, N., Weber, M., 2005. Communicating asset risk: how name recognition and the format of historic volatility information affect risk perception and investment decisions. Risk Anal. 25, 597–609. Winter, J., Balza, R., Caro, F., Heiss, F., Jun, B., Matzkin, R., McFadden, D., 2006. Medicare prescription drug coverage: consumer information and preferences. Proc. Natl. Acad. Sci. U.S.A. 103, 7929–7934. Wu, S., Asher, A., Meyricke, R., Thorp, S., 2015a. Age pensioner profiles: a longitudinal study of income, assets and decumulation. CEPAR Working Paper 2015/17. Wu, S., Stevens, R., Thorp, S., 2015b. Cohort and target age effects on subjective survival probabilities: implications for models of the retirement phase. J. Econ. Dyn. Control 55, 39–56.

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Taxation, Pensions, and Demographic Change A. Woodland School of Economics, The University of New South Wales, Sydney, NSW, Australia ARC Centre of Excellence in Population Ageing Research (CEPAR), The University of New South Wales, Sydney, NSW, Australia

Contents 1. Introduction 2. Fiscal Implications of Demographic Change 2.1 The Issue 2.2 Modeling the Impacts of Demographic Change 2.2.1 Population Aging and Demography 2.2.2 An Overview of Methods

2.3 National Studies 2.3.1 2.3.2 2.3.3 2.3.4

Some National Studies USA Japan Australia

2.4 International Studies 2.5 Role of Sources of Demographic Change 2.6 Summary 3. Taxation Design 3.1 Introduction 3.2 Age-Dependent Taxation 3.2.1 3.2.2 3.2.3 3.2.4

Why the Interest in Age-Dependent Taxation? The Ramsey Approach to Age-Dependent Taxation The Mirrlees Approach to Age-Dependent Taxation Summary

3.3 Taxation Design Issues 3.3.1 3.3.2 3.3.3 3.3.4

Taxation Reform and Analysis The Taxation of Capital Income Optimal Taxation Optimal Taxation Over the Transition

4. Pension Design 4.1 Introduction 4.2 Means Testing of Pension Benefits 4.2.1 4.2.2 4.2.3 4.2.4

Why Is Means Testing an Issue? Types of Means Tests The Economics of Means Testing Optimal Means Test Design

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4.2.5 Modeling and Implications of Means Testing

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Privatization of Social Security Optimal Pension Design Political Support for Social Security Relating Pensions to Demographic Change

5. Conclusions Acknowledgments References

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Abstract This chapter provides a review of some implications of demographic shift arising from population aging for fiscal policy, taxation policy, and social security settings. The key implications of population aging that have been forthcoming from the many national and international macroeconomic modeling studies are presented. These implications are that population aging will put significant stress on governments’ fiscal situations under current policy settings. Consideration of policy options to accommodate population aging leads to examination of age-dependent taxation, the means testing of social security benefits, general taxation and pension design, and the analysis of taxation policy over time. The chapter concludes with some comments on the nature of the literature reviewed and on possible directions for future research.

Keywords Population aging, Taxation, Social security, Means testing, Age-dependent taxation, Optimal policy, Overlapping generations, Life cycle

JEL Classification Codes E60, E17, H21, H30, H60, J11

1. INTRODUCTION Much has been said, and written, about the fiscal stress that many nations will face consequent upon demographic shift. But there is little research on the relationship between this change and taxation design, except insofar as analysts have calculated how social security tax rates must change to meet the pension promises made to cohorts approaching retirement. Yet the public finance implications of an aging demographic reach well beyond labor taxation, and the associated revenue requirement involves a wider spectrum of government outlays than just social security payouts. We therefore begin with a review of some empirical and modeling analyses to identify the quantitative importance of demographic change for the various elements of a tax revenue system, treating social security systems not as separate government entities, but as part of an overall tax–transfer system. Given this backdrop, we turn to the analytic public finance literature to discover what light it sheds on taxation reform and aging, with an

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emphasis on demographic change. While research focused on taxation and demographic transition has been relatively thin, there are several recent developments in the public finance literature that bear upon this intersection. Partly guided by our initial review of quantitative studies of the fiscal impacts of demographic change and the related literature, the chapter is framed around several important questions. 1. Does age-dependent policy design hold any promise for moderating the fiscal impacts of demographic change? It is often assumed that age-dependent taxation is infeasible. But in the context of retirement policy, in particular, age dependence is often built into policy. If social security payouts are treated as simply transfers (or negative taxes) then this constitutes the most widespread example. While there is an analytical literature built around the idea of age dependence (see Weinzierl, 2011 for a recent example) this literature is typically not linked to social security payouts. 2. Is the means testing of pensions a good idea? Resource testing, means testing, or targeting public pensions is a controversial policy reform. It clearly reduces the revenue requirement for older cohorts, but is also frequently criticized for the implied very high marginal tax rates imposed over the entitlement withdrawal range. An important initial question is whether means testing can be designed in a conventional model to improve welfare relative to a demogrant. Means or resource testing of public pensions is equivalent to imposing a capital income tax on retirement capital. Recent research has challenged the policy implication of research undertaken in the 1980s and 1990s (for example, Judd, 1985 and Chamley, 1986) that capital should not be taxed. The role of personal capital income taxation in tax design depends upon more complex institutional settings. In a life cycle framework, and where age-varying tax rates are infeasible, Erosa and Gervais (2002) prove that it is optimal for a government to tax or subsidize interest income, as a second-best response to setting optimal taxes as individuals’ optimal consumption-work plans change over the life cycle. It has also been shown (Hubbard and Judd, 1986; Aiyagari, 1995; Imrohoroglu, 1998; Fuster et al., 2007; and Conesa et al., 2009) that if there are incomplete credit and/or insurance markets, i.e., individuals are liquidity constrained and/or face uninsurable idiosyncratic income risk, then the optimal capital tax rate might not be zero. To what extent can means testing a pension be seen as efficiency improving, through its equivalence with a tax on retirement capital? 3. To what extent does the changing relative importance of tax bases and the increasing revenue requirement associated with population aging indicate adjustments in tax design? What are the implications for efficiency and for equity, both within and between generations? Would a tax–transfer system, financed by general tax revenue, be more efficient than financing retirement incomes through a social security tax?

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To what extent do taxation and pension policy settings provide social insurance when individuals face uninsurable earnings, health, and longevity risks? These questions and issues motivate the contents of this chapter. In Section 2, the issue of taxation, social security, and demographic change is put into context by first asking why population aging is likely to have fiscal implications. Since analyses of the impacts of population aging have been based upon a range of modeling frameworks, the section continues with a brief overview of such models including generational accounting, microsimulation models, and overlapping generations (OLG) models of the economy incorporating life cycle behavior of individuals and intertemporal general equilibrium. With that in hand, various studies of the fiscal and other impacts of population aging are reviewed. There are a large number of such studies, with broadly similar overall conclusions, so only some are reviewed in detail. While many are purely national studies, which focus on national issues, some others are for groups of countries and these focus on international aspects of demographic change, such as through international capital markets. The main message from these studies is that population aging is expected to have major impacts upon many economies, including macroeconomic, household welfare, and government fiscal impacts. This highlights the desirability of policy adjustments on the part of governments to manage and alleviate the impacts of population aging. These policy adjustments are particularly focused on the taxation instruments used to raise government revenue and on the expenditures of this revenue on age-dependent public programs such as health and social security. Accordingly, Sections 3 and 4 consider, respectively, several different taxation and social security topics that are of policy relevance for population aging. There are two topics that are drawn out of the literature for special and more detailed treatment. The first of these is the concept of age-dependent taxation arising initially out of the Ramsey approach to optimal taxation. Age-dependent taxes seem particularly relevant in the context of population aging, which alters the proportions of people in the various age groups with greater proportions moving to higher age groups, since it is shown to produce efficiency gains if different age groups have different elasticities of response to taxation. This idea is a type of tagging, whereby tax rates are distinguished by a characteristic of those being taxed. The discussion of age-dependent taxation leads to a more general consideration of taxation design and analysis in Sections 3. Here the review covers such topics as the analysis of various tax policy reform proposals, the differential taxation of capital income and labor earnings, other optimal taxation designs, and how fiscal policy might evolve over time due to population aging. The second topic given special treatment is that of the means testing of pension or social security benefits. The means testing of social security benefits is prevalent in many countries such as the UK, Denmark, and Australia but is being increasingly discussed in other countries such as the USA. Means testing may also be interpreted as a form of tagging, whereby pension recipients are identified as a group to receive specially designed

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implicit taxation via the pension taper or withdrawal rate applied to income or assets above a threshold. Means tests are often justified on the grounds of limiting government expenditure on publicly provided age pensions, but also raise many issues, including the impacts of the resulting distortions to household labor supply and saving decisions upon welfare and the economy. On the other hand, they may have valuable social insurance roles when households face uninsurable earnings and longevity risks. In addition to discussing means tests, Section 4 also discusses other pension and social security design issues such as privatization of social security and optimal pension structures. There are, of course, a large number of taxation and pension policy instruments available to governments. In this chapter, focused as it is on taxation, pensions, and population aging, attention will be concentrated on a relatively small subset of such tax instruments. There are three main taxation instruments that researchers in the area have considered. The first two are income taxation rates applied to the earnings of labor and capital. Typically, models distinguish between the two and there is an extensive literature, some of which is discussed further below, on whether the income from capital should be taxed along with the taxation of labor earnings. It is also common in the literature to simply have linear labor and capital income taxes, meaning that the tax rates are constant with taxation being proportional to income. Extensions of this restrictive assumption to deal with a progressive tax structure, as is common in many countries, do appear in the literature, such progressivity generating another source of potential labor market distortion. The optimal nonlinear income taxation literature initiated by Mirrlees (1971) is one such an example, but nonlinear income tax schedules appear in other literature. Since most models dealing with population aging and taxation are macroeconomic models, they deal with consumption as a single aggregate rather than a vector of consumption of various commodities. Accordingly, they often incorporate a single tax rate on consumption—a goods and services, consumption, or a value added tax rate. While a consumption tax rate can have differential age-distributional effects on the population, this tax is usually viewed as a source of government revenue rather than a tax rate targeted at population aging per se. Fiscal policy instruments that play important roles in some macroeconomic models are, of course, the size of the government budget deficit and the level of government debt. These are inherently dynamic in nature and allow intertemporal substitution in fiscal policy and the smoothing of taxation policies. Models used in this area vary significantly in their assumptions with some models based upon the assumption that governments balance their budgets in every period and others allowing budget deficits and surpluses over transition paths but requiring a long-term intertemporal government budget constraint to hold. The literature dealt with in this chapter provides a strong link between the taxation policy instruments indicated above and the nature and structure of the social security system. Indeed, it is the intersection of these two areas that is especially important in the

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analysis of population aging. Accordingly, taxation policy can quite reasonably be interpreted as including the tax and structural aspects of the social security system. Many countries have a publicly provided old age pension scheme that is funded by some form of contributions and taxation. For example, a percentage of labor earnings may be mandated to be paid into a pension fund. There may be concessionary tax rates applied to these contributions. The earnings within pension funds may be taxed at concessionary rates, as may the pension withdrawals from these funds upon retirement. The pension payments that retirees receive might be means tested, a topic dealt with in some detail further below, so that those with higher other income or assets receive lower pensions. All these tax rates, means tests, and other pension rules constitute policy instruments available to governments and with fiscal implications. Additionally, governments may provide tax incentives for individuals to save in special retirement funds outside the public pension program and these also may have concessionary taxes on fund earnings and payouts. All these taxes and schemes therefore constitute policy instruments of relevance for the literature examined in this chapter. The chapter finishes in Section 5 with some concluding remarks and observations. Provided first are some views on the main features of the literature covered in this review, followed by some comments on what the different tax and social security ideas covered may imply for population aging responses. The chapter concludes with a brief discussion of potential developments in research on taxation and demographic change.

2. FISCAL IMPLICATIONS OF DEMOGRAPHIC CHANGE 2.1 The Issue The demographic change currently being experienced by many countries is due to substantial increases in the longevity of people arising largely from better health care and reductions in fertility. These two factors have manifested themselves in a significant change in the age distributions of populations, with relatively fewer young people and relatively more older people than was previously the case. The result is that the old age dependency ratio, defined as the number of people aged 65 years and over divided by the number of people aged 15–64 years, has increased markedly. As the “baby boomers”—those born in the post-World War II decade—move into the 65 and over age group, this age dependency ratio is projected to increase further over the next 30 years in many countries.a Accordingly, the relatively shrinking working age populations are faced with the prospect of supporting relatively increased numbers of retirees. This demographic change generates many important issues and adjustments for the economy, for individuals, and for government policy. One such issue concerns the fiscal a

See Chapter 1 by Bloom and Luca (this volume) for a detailed account and discussion of the anatomy of population aging.

Taxation, Pensions, and Demographic Change

implications for governments and for retirement and taxation policy responses to demographic change. Governments in most countries have extensive taxation, welfare, and transfer programs that will be impacted by demographic change in the form of an aging population. Increased funding requirements for welfare and transfer programs will put pressure on the taxation system. A primary concern of governments is with the funding of age pension programs, since increased numbers of retirees will increase the benefit payments and, hence, the funding requirements. Another area of special concern is with health programs, which are heavily subsidized by governments. Since health expenditures are strongly correlated with age (with a local peak for fertility ages), since health demands are likely to be strongly increasing in income, and since technical improvements in health care increase the range of health services, an aging population is expected to require greater government expenditures on health programs. The fiscal and other implications of an aging population have been investigated in many government reports and in increasing numbers of academic papers. Government commissioned national enquiries have been made, for example, for Australia (Productivity Commission, 2005; Australian Treasury, 2015), New Zealand (NZ Treasury, 2003), the United Kingdom (HM Treasury, 2003), the USA (Congressional Budget Office, 2005; Congressional Budget Office, 2016), and Europe (European Commission, 2012) to name just a few. Typically, these reports on the consequences and implications of population aging are based upon demographic projections and scenarios using accounting and budget data and do not involve a formal economic model with behavioral and market responses. To put the magnitude of the potential fiscal impacts of population aging over the next half century into some concrete context, it is useful to report some of the results from the type of studies just mentioned. To this end, Fig. 1 shows for selected OECD countries (Australia, Belgium, Germany (DEU), Italy, the UK, and the USA) the projections of the percentage point GDP shares of several age-related government expenditures—health care, long-term care, and pensions—over the period 2006–2060.b While long-term care starts off at a low base for countries other than Belgium, the trend is clearly upward with the percentage point share of GDP doubling over this period of population aging. For Belgium, the increase is projected to be from a little over 1.5% to around 3% of GDP. Similarly, health care expenditures are projected to rise from around 6% to around 12% of GDP for all these countries, the variation between them being rather small. The levels and trends in projected expenditures on public pensions exhibit much more variability over these countries. Apart from Belgium, whose pensions as a percentage of GDP are projected to increase from 12% to around 15%, and Germany, where the increase is from 10% to 12% of GDP, the percentage point increases over this period are modest and actually decline for Italy (from a very high base). Australia’s age pension b

The figure is based on data from De la Maisonneuve and Oliveira Martins (2013) and OECD (2015).

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Fig. 1 Projections of public spending on age-related programs for selected countries, 2006–2060 (% of GDP). Based on projections drawn from De la Maisonneuve and Oliveira Martins (2013) and OECD (2015).

as a percentage of GDP is the lowest of these countries, primarily as a result of a modest maximum pension and an effective means test. These graphs underline the importance of health and long-term care as sources of fiscal stress as the population continues to age in these OECD countries. While the increases in these as a percentage of GDP are large, it is also relevant that public pensions are already significant components of GDP and, hence, of government expenditures.c More broadly, the implications of population aging for the fiscal imbalances for 2050 as a percentage of the present value of GDP are projected to be severe. As illustrated by Nishiyama and Smetters (2014), these estimates for developed countries are around 9–10% for the UK and USA, 12% for Japan, and with considerable variation around a 9% average for 25 EU countries.

2.2 Modeling the Impacts of Demographic Change 2.2.1 Population Aging and Demography At the heart of analyses of population aging is the economy’s demography. Individuals are distinguished by their age j 2 f1,…,J g, where J is the maximum age. At time t, there are Njt individuals of age j in the population. The dynamics of the population may be expressed formally as c

A detailed recent account of population aging and the US government budgetary implications is provided in Congressional Budget Office (2016).

Taxation, Pensions, and Demographic Change

2

3 2 N1, t + 1 0 6 N2, t + 1 7 6 π 2, t 6 7 6 6 7¼6   6 7 6 4 NJ1, t + 1 5 4 0 0 NJ , t + 1

f2, t 0  0 0

 fJ1, t  0    0  πJ , t

3 32 fJ , t N1, t 6 7 07 76 N2, t 7 6 7  76  7 7 0 54 NJ1, t 5 0 NJ , t

(1)

where fj, t is the fertility rate for individuals of age j and π j, t is the conditional probability of a person of age j surviving at age j + 1 at time t. This equation may be expressed compactly in terms of the matrices At and vectors nt as nt+1 ¼ Atnt, which constitutes a system of J first order, linear difference equations. Given an initial vector n0, the future path of vectors nt evolves given assumptions about the survival probabilities and the fertility rates. The equation can also be expressed in the μt+1νt+1 ¼ At μt, where νt+1 ¼ Nt+1/Nt is Pform J the population growth factor, Nt ¼ j¼1 Nj, t is the population at time t and μt ¼ (μ1, t, …, μJ,t) is the vector that gives the proportions of the population at the J ages. Population aging is the situation where the proportion of the population in the older age groups is increasing over time. Clearly, this process depends on the changes in fertility and survival probabilities over time. If the fertility rates and survival probabilities are unchanged over time (or stop changing), then the population dynamics specified above converge to a constant age structure of the population. In this case, the difference equation becomes μν ¼ Aμ, which is a set of homogeneous equations. These can be written as ðνI  AÞμ ¼ 0, thus defining ν as the eigenvalue and μ as the eigenvector for matrix A, the solution satisfying the determinant equation jνI  Aj ¼ 0. In this situation, ν is the constant population growth factor (1 plus the population growth rate). The growth rate factor is the largest eigenvalue.d The above description of age population dynamics ignores immigration, but this aspect can be readily incorporated. Define the vector mt ¼ ðM1, t , M2, t , …,MJ , t Þ0 as the immigration vector denoting the number of immigrants (net immigration) by age. Dividing through this vector by the total number of immigrants, Mt, gives mt ¼ Mt ðη1, t ,η2, t ,…,ηJ , t Þ0 . The difference equation for population then becomes nt+1 ¼ Atnt + mt. Behind this vector lies the economy’s fertility, mortality, and immigration history. 2.2.2 An Overview of Methods A variety of methods used to make use of the demographic structure and its evolution over time to obtain fiscal and other implications of interest exist. Many government agencies with access to government data sources make assumptions about the age structure of expenditures and taxation receipts, growth rates for the economy and labor force participation rates, and so forth. They then compute projections of expenditures, taxes, d

See Lee (1974), Rios-Rull (2001), and Attanasio et al. (2007) for this specification.

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and government debt over time assuming no change in policies or possibly assuming some projected change in policies. More detailed methodologies have been developed via the concepts of intergenerational accounting and microsimulation. The former provides a formal framework for computing net government expenditures (payments minus taxes) for each age group in the population and, hence, providing implicit transfers between generations over time. While these models focus on government fiscal measures, they can also provide private intergenerational transfer measures. For the methodology on intergenerational accounting, see Auerbach et al. (1994) for example. A more microeconomic approach leads to microsimulation models. These take detailed information on particular types of households (e.g., couples with no children) as the basis of calculations and then construct measures of the implications of changes in population structures and policy for variables of interest at different levels of aggregation. Their advantage is their ability to embed very detailed and disaggregated information about households into the models, and consequently are not constrained so much by the “curse of dimensionality” that limits behavioral models. EUROMOD, described by Sutherland (2007) and Sutherland and Figari (2013), is one such microsimulation model and a recent application of a dynamic microsimulation model to the analysis of population aging has been provided by Lawson (2016). OLG models of economies explicitly model the behavior of households over the life cycle, the behavior of firms, government budget constraints, and market equilibrium. Accordingly, the impacts of the age structure of the population and its change through population aging upon households, government, and macroeconomic variables embody endogenous behavioral responses. In a similar fashion, the impacts of changes in taxation and retirement policy parameter settings also take into account behavioral responses. Households are assumed to make decisions over their life span about consumption, labor supply and saving taking as given market prices for goods and labor, the interest rate, and government policy settings. Typically, it is assumed that they do this by solving an intertemporal expected utility maximization problem, taking account of future retirement options and idiosyncratic uncertainty regarding future productivity. The production sector in most OLG models used for demographic change and retirement studies is quite simple, comprising a single economy-wide production function in which capital and labor combine to produce output. The capital stock evolves through investment. The government sector is normally described by the government budget and its components—taxation revenue, expenditures, and debt. The main expenditures are on government consumption (goods and services needed to operate the government and the provision of public goods), transfers to households, and pension benefit payments. Many of these items, such as health service expenditures, transfers, and pensions are age dependent, and so are impacted quite directly by demographic change. As part of the government sector specification, there are details about the structure of various taxes

Taxation, Pensions, and Demographic Change

and welfare settings. These include income taxes on capital income and labor earnings, payroll taxes, direct taxes on goods and services (sales and value added taxes, for example), and pension and retirement fund taxes (on contributions to, earnings within, and benefits from pension funds). In addition, an important component of such policy settings concerns age pension benefit rules, such as means tests for access to pensions and other retirement fund vehicles. If governments are permitted to issue debt, the government budget constraint is intertemporal and involves the issuing of new debt via bonds and the servicing of that debt through taxation. The model is closed by requiring all markets— goods, labor, and capital—to clear in all years. Analysts of demographic change and policy have sometimes focused on the comparison of initial and final steady states, thus considering long run impacts. Others have also considered the impacts of demographic change and policy setting changes over the transition path. Importantly, these analyses allow evaluations for presently alive generations and immediately subsequent generations, not just those in the distant future. There are, of course, many variations and extensions of OLG models that provide the bases for the analyses of taxation and population aging discussed in this chapter. For an introduction to the theory of OLG models and their use in economic growth and policy analysis, see De La Croix and Michel (2002). A recent exposition of large scale, numerical models used to analyze population aging and social security policy issues, based upon the pioneering modeling by Auerbach and Kotlikoff (1987), has been provided by Fehr (2016).

2.3 National Studies 2.3.1 Some National Studies This general class of OLG model has been used by many other researchers to investigate the potential economic effects of population aging in various countries. These include De Nardi et al. (1999), Kotlikoff et al. (2007), Nishiyama (2004), Nishiyama (2015), Imrohoroglu and Kitao (2009), Jung and Tran (2016), and Lee and Edwards (2002) for the USA; Miles (1999) for the United Kingdom and Europe; Kulish et al. (2010) using a generic model for developed countries; Fehr and Habermann (2008) and Fehr (2000) for Germany; Faruqee and Muhleisen (2003) and Kitao (2015) for Japan; Beetsma et al. (2003) and Bovenberg and Knaap (2005) for The Netherlands; Oksanen (2003) for the European Union; Fougere and Merette (1999) for the OECD; Aaberge et al. (2004) for Norway; Dı´az-Gim
enez and Dı´az-Saavedra (2009) for Spain; Fougere et al. (2007) and Fougere et al. (2009) for Canada; Guest (2006), Guest (2007), Kudrna et al. (2015), and Kudrna et al. (Forthcoming) for Australia; and Jones (2009) for Korea. In the following, several studies are summarized and discussed to give an appreciation of the type of model detail employed, of the fiscal impacts of demographic change arising from population aging, and hence, of the desirability of accommodating tax and retirement policy changes by national governments. Three countries are chosen as example case studies, each providing its own special features—the USA, Japan, and Australia.

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2.3.2 USA An example of such a study is that by Kotlikoff et al. (2007) for the United States of America. They construct an OLG model for the USA that starts from an initial position that is not a steady state, allows for demographic changes in longevity and fertility and incorporates important features of social security and taxes.e Conditioning on the observed initial distribution of assets over several household types, the model generates an intertemporal equilibrium over a period of 275 years converging to a steady state solution. Since the initial position is not a steady state and since there is assumed demographic change, the benchmark transition path solution embodies both changes towards a steady state and to the demographic shift. The model provides the implications for macroeconomic variables, household decisions and welfare, and for the government budget and social security. Under the assumptions of the model, adjustments to demographic change (and to the steady state) imply that capital becomes relatively scarce, despite the aging of the population, raising its rate of return. The payroll tax payments rise substantially, limiting national saving, and capital accumulation. To maintain the government’s real expenditures, the average labor tax rate increases. Thus, this study demonstrates the potential for population aging to have substantial macroeconomic effects and for there to be interactions between the social security and tax systems. Population aging focuses attention not just on retirement systems such as social security, but also on the tax system and its interaction with social security. This study builds on and extends various other studies of the impacts of population aging for the US economy, including De Nardi et al. (1999). This latter study also assumes time-varying profiles for survival probabilities and fertility over a long period starting in 1970 and compute transition paths under various policy scenarios. A main conclusion reached is that the demographic changes postulated will require increases in distortionary taxes to maintain existing social security benefits. These distortionary taxes will, in turn, reduce private saving and labor supply that negatively impact the economy. Accordingly, the impact of demographic change on fiscal requirements is severe. More recent analyses of the impacts of demographic shift in the USA are provided by Kitao (2014) and Nishiyama (2015). While Kitao calibrates her model to a steady state equilibrium for 2010, Nishiyama begins with a steady state solution in 1975 and then calibrates the transition path to the 2014 US economy to capture the nonstationary demographic structure of the population and economy in 2014 and to compute the transition path to 2200. Both models are then simulated under various policy assumptions. Both studies confirm the conclusions from previous studies that the aging of the e

The model allows for technical change, bequest motives, children, and 12 household types defined by income class. The essential features of the federal, state, and local tax system are included in the model. The government produces a fixed amount of real goods and services and maintains a debt that grows with the population and technical change by endogenous changes in income tax rates.

Taxation, Pensions, and Demographic Change

US population makes the current social security and taxation policy settings unsustainable. They also establish that various tax policy options to finance the increased social security benefit payments are likely to have distortionary impacts on the economy and on household welfare. Moreover, even though various policy options may have similar long run effects and be effective in financing the demographic change, they may have quite different transitional effects. While population aging impacts on social security payments is important, it is arguable that the impacts on health spending by governments is potentially equal or more important, as suggested in Fig. 1 discussed further above. Recently, Jung and Tran (2016) have undertaken an OLG modeling quantitative study of the impacts of population aging upon medical spending for the USA assuming that social security benefits are financed from payroll taxes, while medical spending is part of the overall government budget constraint which is balanced by adjustments in the consumption tax rate. They calculate that, under their assumptions regarding demographic change, medical expenses as a percentage of GDP will increase from the base level of around 13% in 2010 to over 16% of GDP by the year 2040, after which the percentage remains fairly constant. In percentage changes from the base year, the increase in medical expenses is over 30% by 2040 and 37% by 2060. These represent substantial increases in expenditures as a result of population aging in the USA. An interesting channel by which medical spending is expected to increase is provided by Zhao (2014), who argues that the projected increases in social security expenses will have a spillover impact on medical expenses. Higher social security payments represent a transfer of resources from the young to the old, who have a relatively higher marginal propensity for health services, and provide a more secure retirement, thus increasing the payoff from investing in heath services that increase longevity. The model, which allows for endogenous medical spending and longevity, calculates that a third of the projected increase in medical spending arises from these social security impacts. These studies highlight the role played by population aging in health expenditure projections and, importantly, the interaction between social security and health expenditures. 2.3.3 Japan Japan is a country in which the aging of the population is further advanced than most other countries, to the extent that the population size is declining and is expected to continue to do so for some time. Accordingly, Japan provides an apposite case study for analysts and for policy makers in other countries where the population aging process is less developed. Such an analysis has been provided by Kitao (2015) in a recent study on the fiscal cost of demographic transition in Japan using an OLG model. In this model, individuals are assumed to have an economic life from age 25 to 110, to face mortality risk and to have idiosyncratic age-dependent labor efficiencies that comprise permanent components and stochastic components that follow an autoregressive time structure. On the

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production side, productivity grows at a constant rate. The fiscal side of the model has the government operating a pay-as-you-go public pension system providing a social security payment to retirees, providing medical insurance for health and long-term care (with individuals making contributions), funding its expenditures by taxes on the earnings of capital and labor and on consumption and issuing debt. Within this economic framework, Kitao embeds the essence of population changes being experienced by Japan. Taking the structure of the population in 2010 as given, assumptions are made about projected changes in fertility and longevity over the subsequent 50 years. With these demographic projections in hand, the future path of the Japanese economy is computed using the OLG model under the assumption that the impacts of population aging upon the government budget are financed by suitable changes in either the consumption tax rate or the income tax rate. The projected long run increase in the old age dependency ratio from around 40% to 56% leads to an increase in the ratio of social security expenditures to output from about 10% in 2010 to over 13%, while government medical expenditure ratio increases from around 6% to over 8% in the long run. The required tax rate adjustments to fund the impacts of population aging on the government budget are from 5% to 19% for the consumption tax, or from 35% to 48% if the labor income tax rate is used as the accommodating tax instrument. Clearly, these are substantial tax rate adjustments. Overall, there is a reduction in the size of the economy and in the population. The long run results, while interesting, hide some of the important results that are found when analyzing the transition path. Importantly, the old age dependency ratio rises to a peak of about 90% in the 2080 decade before falling to its long-term level. As a result, the impacts of demographic shift in Japan along the transition path are correspondingly more dramatic than the long run impacts. The consumption tax rate rises from 5% to just under 50% around the end of the current century, where it stays for several decades before gradually falling to its long-term level. The wage–rental ratio rises substantially and then falls, with a corresponding time profile generated for the capital-labor ratio. Government social security and medical expenditures have a similar profile to that for the old-age dependency ratio, unsurprisingly. Another recent study of the fiscal implications of aging in Japan is that of Braun and Joines (2015). Like Kitao (2015), these authors consider an OLG model that embodies future reductions in fertility and increases in longevity leading to a much lower long run population and carefully model social security, medical payments, and taxation. The basic conclusion is that the existing policy settings are not sustainable and therefore they consider a range of policy options to raise tax rates (e.g., labor income tax and the consumption tax rate) and to reduce government spending (e.g., pensions and medical payments). It is shown that increases in the consumption tax rate to over 50% would be needed toward the middle of the century to establish fiscal balance, a result similar to that of Kitao (2015).

Taxation, Pensions, and Demographic Change

The results from Kitao (2015) and Braun and Joines (2015) clearly demonstrate the substantial impact that population aging is projected to have on the Japanese economy. These impacts have severe fiscal implications and substantial macroeconomic adjustments. The role for appropriate responses in the form of taxation and retirement policy design is underlined by studies such as this. 2.3.4 Australia Australia provides an interesting example of a small open economy experiencing population aging, and one that has a special age pension and retirement saving system. The impacts of population aging for the fiscal aspects of the Australian economy has recently been undertaken by Kudrna et al. (2015) using an OLG model incorporating the dynamics of population change projections, a detailed structure of the taxation and retirement policy settings and the age structure of various government expenditures. The age pension, which is eligible for all Australians but subject to income and asset means tests, is clearly age dependent and is funded from current taxes and so has potentially severe implications from population aging. Other government services such as health care, aged care, education, and family benefits have distinct age distributions, which the study takes as given, and levels that depend on the size of the economy. Accordingly, these also are modeled and the implications for them of population aging are examined by the authors. The model’s assumed age distribution of the Australian population changes over time from its observed distribution in 2010, the base year, as a result of projected changes in fertility rates, mortality rates, and in the size and age structure of net immigration. These projected changes in rates, based on the Productivity Commission’s projections, cease in 2018 for fertility rates and in 2053 for mortality rates, while the level of immigration simply moves to a different level immediately. It takes a long time—well into the 2100s—for the age distribution to closely approach its long run state. The OLG model takes various assumed (high, medium, and low aging) scenarios for the population dynamics as given and generates long run and transition path solutions for the macroeconomic and fiscal variables of interest. The model simulation results show that, not surprisingly, projected population aging results in increased old-age-related expenditure by government, with per capita expenditures on health care increasing over the 2010–2050 period by around 25%, on the age pension by about 63% and on age care services by a massive 126%. To maintain balanced government budgets, these increases in age-related expenditures, which far exceed the small reductions in education costs and family benefits, require a reduction of nonage-related government expenditures of around 32% by 2050. By 2100, further increases in age-related expenditures shift this budgetary impact to around 58%. If, alternatively, the budget is balanced by changes in the consumption tax rate rather than changes in nonage-related expenditures then the simulation results show that the consumption tax rate would be required to increase from its 2010 rate of around 15% to about 19% by 2050 and

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to over 22% by 2010. This tax is distortionary, and the required rate increase has negative effects upon consumption and leisure decisions, leading to an overall increase in labor supply and asset holdings. In either case, the results how that the projected population aging is likely to have a significant impact on the government budgetary situation and upon the economy.

2.4 International Studies In addition to single country modeling, there is a small series of studies of the impacts of population aging using multicountry or -region models. Examples include B€ orsch-Supan et al. (2006) using a multiregion model for seven regions (France, Germany, Italy, rest of the EU, USA and Canada, and the rest of the world), Fehr et al. (2008b) for the OECD countries (USA, Japan, and 15 EU countries), and Floden (2003) for 15 OECD countries and the rest of the world. Additionally, the international aspects of demographic change has been analyzed by Aglietta et al. (2005), Attanasio et al. (2007), Krueger and Ludwig (2007), B€ orsch-Supan et al. (2014), and Vogel et al. (2016). These international studies are particularly valuable for several reasons. First, different countries have different demographic structures and different population dynamics in terms of fertility, longevity, and immigration. Accordingly, their age distributions are different and evolve differently over time. Since the age distribution affects consumption, labor supply, savings, and age pension payments, the paths of national economies will be different. Taking this into account is both interesting and important. Second, countries are interconnected through international trade, capital mobility, and technological spillovers. These interconnections will have impacts upon the market prices for internationally traded goods and capital, thus impacting national economies. Different demographic dynamics affect these international flows and prices and so affect national economies. Attanasio et al. (2007) construct an OLG model that incorporates population age distributions that differ between countries (regions) and change over time as a result of assumed changes in fertility and mortality rates. The rates converge over time and country, thus ensuring a common and constant population growth rate in the long run. In particular, the South’s higher fertility and mortality rates converge downward toward lower rates for the North region. In each region, individuals make consumption and saving decisions while labor supply is assumed to be exogenously given, but depending on household structure. The production sectors use both labor and physical capital that is financed via bonds. Each region has a pay-as-you-go social security system with benefits given by a replacement rate based on average past earnings. While labor markets are national, the model allows for international flows of bonds. Accordingly, there is an international bond market that determines the world interest rate, thus connecting regions. The model is calibrated to a world of two regions—the North comprising developed countries (North America, Europe, Japan, Australia, and New Zealand) and the South

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comprising the rest of the world. The authors compare results from closed and open models as well as pay-as-you-go and privatized (fully funded) social security schemes and alternative financing schemes. The simulations of the various scenarios begin with an assumed steady state in 1950 being perturbed by the baby boom and baby bust, with fertility and longevity rates changing up to 2200 and transition paths to the new long run steady state computed. Given the regional differences and the projected changes in population aging parameters, the model simulation shows considerable variation in the time profile of international capital flows and world interest rates. To accommodate the differing demographic structure, northern ownership of southern assets initially increases and then falls. Eventually, under the pay-as-you-go social security scheme foreign ownership is reversed with the South owning increasing amounts of the assets of the North. In all of the scenarios, the world interest rate declines over time (from 2010), the fall for the initial benchmark case being from around 8% to about 4%. As a result, endogenous variables in each region also alter over time. Typically, the capital stocks per capita increase and wages rates increase. Overall, the authors conclude that consideration of a trading world with frictionless movement of capital compared to using a closed economy model with no international capital movements does not lead to major differences in deciding between alternative policy means to deal with the demographic transition. However, a difference of note arises when consideration is given to welfare implications, the open economy seeming to mitigate negative welfare impacts. Krueger and Ludwig (2007) also formulate a multiregion model for the OECD comprising the USA, the EU, and the rest of the OECD as three regions. In contrast with Attanasio et al. (2007), their model incorporates uninsurable idiosyncratic productivity of households over the life cycle and endogenous labor supply. They focus upon the role of different demographic changes in the three regions and the operation of international markets and linkages upon the return to capital and wage rates and, hence, upon household welfare. Vogel et al. (2016) have a similar interest in the implications of different demographic changes, but their particular focus is on the role played by endogenous human capital formation in their two-region (France–Germany–Italy and the rest of the world) framework. The main conclusion is that endogenous human capital formation can significantly ameliorate the impacts of population aging in the presence of pension reform. Some other studies have previously formulated multicountry models to capture the idea that different national demographic patterns could lead to different saving rates and hence to international flows of capital that would, in turn, affect each country’s demographic change impact. These include the studies by B€ orsch-Supan et al. (2006) and Fehr et al. (2008b), both of which focus on developed OECD countries. B€ orsch-Supan et al. (2006) have a model with seven regions that are connected via capital markets. They, like

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Fehr et al. (2008b), show that population aging has significant effects on saving choices and hence upon international capital flows, a result for developed country regions that was confirmed by Attanasio et al. (2007) for their two region model with countries in one of the regions (South) being in the less developed category. They also conclude that analyses based on closed economy models miss these important impacts of population aging operating through international capital markets.

2.5 Role of Sources of Demographic Change A question arises as to the relative importance of the primary sources of demographic shift in the determination of the macroeconomic, welfare, and budgetary consequences for economies. Put differently, are the roles played by the several sources of demographic change—fertility, longevity, and immigration—different in their impacts? The study by Kudrna et al. (2015) of the impacts of population aging on the Australian economy (discussed further above) considers the issue of the sources of demographic change and the disaggregation of the total impacts of population aging into the separate impacts of the several sources. They do this by considering several different population dynamics specifications—having no fertility or mortality rate changes, having just fertility rate changes, and having just mortality rate changes in addition to having both sets of changes. Several conclusions emerge from their simulation study. First, the shutting down of both fertility and mortality sources of population dynamics change still leads to macroeconomic changes over the transition path due to the impacts of fertility and mortality rate changes prior to the experimental period starting in 2010. Second, the remaining impacts of population aging on the economy are then split into those due to projected fertility rate changes and those due to projected increases in longevity. It is established that the impacts of the fertility changes are relatively minor compared to the substantial changes in the economy simulated for the case where only projected mortality rates change. This indicates that the main driving force of the population aging phenomenon in Australia is the projected increase in longevity, not the changes in fertility. The third main conclusion derived by Kudrna et al. (2015) was that immigration, which is often seen as a means to lessen the impacts of population aging, seemed to play a rather minor role and so should not be regarded as a solution. A contrasting conclusion is reached by Attanasio et al. (2007) concerning the role played by fertility changes. In their two-region trading world model, fertility changes were found to be more important than changes in longevity (immigration was not directly considered) the reason being that fertility in the two regions moved in quite different ways over time whereas longevity moved in a similar way in the two regions. The assumed rise in fertility to normal replacement rates in the North and the rapid drop in fertility rates in the South to these same levels resulted in substantial capital flows from the

Taxation, Pensions, and Demographic Change

South to the North. This international difference in fertility rate profiles is, of course, missing from studies using closed economy or small open economy (as in Kudrna et al., 2015) models. Using general equilibrium models, various authors including Fehr et al. (2008b), Kulish et al. (2010), and Zhang and Zhang (2005) have investigated macroeconomic effects of improved survival rates and longevity. For example, Fehr et al. (2008b) undertakes modeling analyzes of OECD countries (USA, Japan, and 15 EU countries) and is concerned with the impacts of projected changes in fertility and longevity upon fiscal and macroeconomic variables. A primary conclusion is that assumed increases in fertility will relieve the fiscal pressures while assumed increases longevity will exacerbate them, but that these impacts are not particularly large in the short and medium terms (the current century). They conclude that changes in fiscal policies are needed to relieve fiscal pressures arising from population aging in the OECD countries.

2.6 Summary The literature reviewed in this section comprises various studies of the impact of demographic change being experienced by many countries, particularly those countries that are classed as developed, upon the fiscal sustainability of current social security retirement programs under current taxation settings. The demographic change, brought about primarily by a sharp rise in fertility following the Second World War followed by a fall in fertility and by a prolonged period of reduced mortality rates that is projected to continue into the foreseeable future, has been termed population aging. The shift in these countries population age distributions from younger to older age groups means that a greater proportion of people in the traditional retirement phase increases social security benefit payouts, health, and long-term care expenditures and so places additional fiscal demands upon governments. The studies reviewed here all confirm that current social security and fiscal settings are largely unsustainable and have provided quantitative measures of these fiscal demands for a selection of countries and regions; there are many other studies for particular countries and time frames with similar conclusions. With this backdrop, the purpose now is to consider some of the issues that arise as a result of these fiscal demands. These relate to both the financing side through taxation dealt with in the next section and the social security expenditure side through pension and social security design dealt with in Section 4.

3. TAXATION DESIGN 3.1 Introduction Given that the projected increases in population aging are predicted to increase pressure on government budgets, there is an incentive to determine more efficient tax structures

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and settings to alleviate this pressure. While piecemeal tax policy reform is a clear option, and one that is likely to be politically palatable, much of the recent literature has focused attention on optimal tax policies using particular social welfare functions. This section is devoted to a review and assessment of this literature. It will become apparent that much of the literature is generic in the sense that it applies to a world with stationary population dynamics. Only some of the literature specifically addresses the issue of tax design in a world with a dynamically changing demographic structure. This is partly because the latter world is much more difficult to analyze. It is also because dynamic models typically specify household behavior within the context of making decisions over the whole life cycle and stochastic household incomes vary over the life cycle. That is, the outcomes are history dependent, making the task of designing optimal taxation much more difficult than within a static framework, as pointed out by Mankiw et al. (2009) in his survey of optimal taxation. Mankiw’s survey provides a valuable overview of and insight to the optimal taxation literature and presents it in terms of eight lessons. Several of those are particularly pertinent to the current task. The fifth lesson is that taxes should depend on personal characteristics as well as income, based largely upon the work by Akerlof (1978) on “tagging.” This topic will be discussed below in terms of the means testing of the age pension in Section 4 and in terms of age-dependent taxation in this section. His eighth lesson relates to the complications arising from stochastic dynamic considerations alluded to immediately above and discussed further below in this section. The seventh lesson relates to the argument that capital income should not be taxed, a topic that is also addressed in this section. While there are various principles that can be used to underlie the design of taxation systems, the one that is commonly used in the literature surveyed in this chapter is that taxes are chosen to maximize a suitable social welfare function, subject to the government budget constraint and to the constraints imposed by individuals’ behavior. The pressures of population aging highlight the importance of such optimality, which can help relieve the fiscal pressure that population aging brings and help establish the sustainability of taxation settings. Other important aspects of taxation concern redistribution implications— redistributions both across generations and across cohorts and household types in any period. Models that do not embody such features as uninsurable future income, health, or longevity risks but do have heterogeneous households are primarily concerned with the distributional aspects of taxation. On the other hand, the introduction of uninsurable future income, health, or longevity risks raises the question of the extent to which the taxation design affects the provision of social insurance. The studies discussed in the remainder of this chapter vary in their model specifications in these aspects and so vary in the extent to which each addresses the issues of sustainability, redistribution, and social insurance. They also vary in many other respects, such as the degree and nature of heterogeneity among households and the restrictions imposed on various tax instruments, including whether taxes are linear or nonlinear or whether there are lump-sum taxes

Taxation, Pensions, and Demographic Change

permitted. Moreover, they differ in whether the tax system is analyzed within a partial or general equilibrium setting and in whether the context is a static (steady state) equilibrium or a dynamic (transitory path) equilibrium. Given this backdrop, the remainder of this section is concerned with several main taxation issues. The first is that of age-dependent taxation, which is based on well-known optimal taxation principles developed by Ramsey and Mirrlees. The former is concerned with the choice of linear tax rates to maximize a social welfare function, subject to budgetary, and behavioral restrictions. Within a life cycle model for households, this leads to tax rates that differ by age if behavioral responses differ by age. The Mirrlees approach is to consider nonlinear income tax functions to maximize social welfare where individuals vary in earning abilities, and these tax schedules may differ by age. The second main topic concerns general taxation design issues under various assumptions and foci, including the desire for efficiency, distributional concerns, and the role of taxes for social insurance. Starting with various analyses of tax policy options, the remaining content concentrates on optimal tax policy.

3.2 Age-Dependent Taxation 3.2.1 Why the Interest in Age-Dependent Taxation? The standard principle applied to the taxing of individuals is that of anonymity, in the sense that the tax code applies equally to all individuals. An interesting digression from this principle has been investigated in the recent literature on optimal taxation, a digression that raises the possibility that taxes on consumption, labor earnings, and interest earnings might be conditioned upon the age of the individual. Such age-conditioned taxes have the convenient property that individuals can only avoid the tax by altering their behavior, not their age. They are also of particular interest in the context of population aging, since that phenomenon has concentrated attention on individual aging within the context of life cycle models and on intergenerational effects of taxes and other variables. Accordingly, attention is now given to the desirability or otherwise of age-conditioned taxes. It will become evident that the nature and structure of agedependent taxes will depend significantly on the elasticities (for example, the elasticity of labor supply) of their behavioral responses to taxes, and how these elasticities vary by age over the life cycle. 3.2.2 The Ramsey Approach to Age-Dependent Taxation The first observation to make is that it is generally optimal for a government to impose age-dependant taxes on individuals, a result derived from optimal tax theory. To see this, consider a simple model of a country in steady state equilibrium with a stationary population and a government that has a fixed revenue requirement as in Alvarez et al. (1992). Households (individuals) have an intertemporal utility function given by u(c, l), where c ¼ (c1, …, cn) is the time profile for consumption and l ¼ (l1, …, ln) is the time profile

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for leisure over a fixed lifetime of n years. Assuming no borrowing constraints, the intertemporal budget constraint may be expressed as p0 c + w0 l ¼ w 0 T , where p and w are the vectors of consumption prices and wages rates discounted to the present using market interest rates, and T is a vector of time endowments. Households choose the consumption and leisure profiles to maximize the utility function subject to the budget constraint. In terms of the expenditure function, e(p, w, u), and using Shepherd’s lemma, the solutions are c ¼ ep(p, w, u) and l ¼ ew(p, w, u), where utility, u, solves the budget constraint eðp, w, uÞ ¼ w 0 T and subscripted functions ep and ew denote gradient vectors with respect to p and w, respectively. The government is assumed to choose age-dependent taxes on both consumption and labor earnings, thus creating a wedge between fixed market prices and wage rates, ρ and ω, and the after-tax prices and wage rates faced by the households, p and w. The optimal tax problem is to choose the price vector faced by the households, q ¼ (p, w), to maximize household utility while respecting household behavior and obtaining the required amount of tax revenue. This problem is   max u : eðq, uÞ ¼ w 0 T , ϕ0 eq ðq,uÞ ¼ ð1  γÞω0 T , (2) u, q where ϕ ¼ (ρ, ω) is the market price vector and γ is labor earnings not spent on goods as a proportion of the value of the time endowment. The first-order necessary conditions for a solution are θeu + λϕ0 equ ¼ 1

(3)

 θe q + λeqq ϕ ¼ 0

(4)

0

together with the two constraints, where e q ¼ ðe0p ,e0w  TÞ is the vector of optimal consumptions and labor supplies over the life cycle, eu ¼ @e/@u, equ ¼ @eq/@u, eqq is the Hessian or matrix of second derivatives of e with respect to q, and θ and λ are Lagrange multipliers. These conditions constitute a set of 2n + 3 equations in the 2n + 3 variables, u, q, θ, and λ. Since the Hessian of the expenditure function with respect to prices satisfies the homogeneity condition e0qq q  0, the second first-order condition may be expressed as 

eqq t¼ ðθ=λÞe q ,

(5)

which is the familiar Ramsey rule for optimal taxes, t ¼ q  ϕ. Setting the first tax rate equal to zero, without loss of generality, the Ramsey rule can be expressed as 2n X eij ϕj j¼2

 ei

τj ¼ ðθ=λÞ,

i ¼ 2 : 2n:

(6)

This states that the optimal ad valorem tax rates, τj ¼ tj/ϕj, must satisfy stringent linear  equations; weighted by the “elasticities,” eij ϕj =e i , they must sum to the same constant for

Taxation, Pensions, and Demographic Change

every good i. In general, the tax rates will be different. Accordingly, the optimal tax regime is to have tax rates that are age dependent. The above discussion demonstrates that the motivation for age-dependent taxes is built upon the basic principles of optimal taxation of goods as initiated by Ramsey (1927). According to that principle, the tax rates on goods are generally different and are closely related to their price elasticities of demand. Goods with lower elasticities attract higher tax rates as the distortion created by the tax is then lower. The same ideas apply to the taxation of consumption and labor over the life cycle, as demonstrated by Alvarez et al. (1992). Since the household’s responsiveness of hours of work to the after-tax wage rate will generally vary over the life cycle, so should the optimal tax rates on earnings vary over the life cycle. Alvarez et al. (1992) draw upon results in Deaton (1979) and Deaton (1981), who shows that the concept of implicit separability is the key to determining whether uniform taxes are optimal in a static framework.f In the present life cycle context, the implicit separability assumption applies to consumption goods and leisure. However, since leisure cannot be taxed the results of Deaton can’t be automatically applied to the taxation of earnings. Thus, the issue of whether uniform earnings taxes are optimal reverts back to determining whether the Ramsey rule expressed in (6) has a solution with all tax rates for labor, τj, i ¼ n + 1 : 2n, being equal.g The basic framework underlying the above discussion of the Ramsey approach to agedependent taxation is built on rather restrictive assumptions. The government’s spending is exogenously given, households are homogeneous, lump-sum taxes are not permitted, and the purpose is to determine linear tax rates to finance the given government expenditure by maximizing social welfare. More recent literature has extended the Ramsey approach to age-dependent taxation to more general settings such as with OLG, heterogeneous households, progressive income tax schedules, human capital formation, and the incorporation of retirement support schemes. Some of these extensions are considered below. Erosa and Gervais (2002) have theoretically analyzed optimal taxes within a fairly standard OLG growth model of a closed economy. The household sector comprises individuals who live for J periods with certainty and choose consumption and labor supply (at both intensive and extensive margins) throughout their life cycle without borrowing constraints. Labor productivity is age dependent. A constant population growth rate ensures a time-invariant age structure. There is a simple production sector producing a single output using labor and capital, which changes through time via investment and depreciation. All markets are perfectly competitive. The government chooses f

g

Deaton’s definition, in the present life cycle context, states that leisure and goods are implicitly separable when the distance function for preferences, d(u, c, l), has the structure d(u, c, l) ¼ G(u, l, g(u, c)). The distance function is defined by dðu,c,lÞ ¼ max λ fλ : uðc=λ, l=λÞ  ug. Alvarez et al. (1992) express the Ramsey optimal tax condition in terms of the Hessian of the distance function, which is called the Antonelli matrix.

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age-dependent tax rates on consumption and on labor and capital earnings, issues debt and maintains an intertemporal budget constraint. The objective function for the government when choosing its tax policy instruments is a discounted sum of lifetime utilities of all current and future generations. Their analysis yields the result that age-dependent taxes are optimal in general. As with Alvarez et al. (1992), Erosa and Gervais (2002) establish conditions under which the optimal taxes are age independent, conditions that are very strict concerning preferences (see their proposition 2.3). In addition to this general result, Erosa and Gervais (2002) also derive the optimal taxation profiles in the steady state for a reparameterized version of the model formulated by Auerbach et al. (1983) for the USA and consider various special cases. Each of these examples, with one exception, has the age profile for labor earnings taxes falling with age until retirement. Thus, young individuals are taxed at higher rates than older individuals. This is different from the result in Blomquist and Micheletto (2008), who get that the young face lower marginal tax rates. The idea that age-dependent taxation can be a substitute for other forms of taxation or as a second-best policy when first-best policies are not available has been a recurring theme in the literature. An example is provided by Gervais (2012), who argues that a progressive tax system is an appropriate second-best tax policy when age-dependent taxation is not available. The reasoning is that a progressive income tax system imposes higher marginal tax rates on those with higher incomes and empirically incomes typically vary with age. Accordingly, a progressive tax system indirectly imposes different marginal tax rates on people of different ages. Using an OLG model calibrated to the USA, Gervais (2012) computes optimal taxes under alternative assumptions—that they can be age dependent or not and progressive or not. As is typical in OLG models, the productivity of individuals is hump-shaped over the life cycle generating a hump-shaped labor supply. The author finds that optimal labor age-dependent income taxes are also hump-shaped, with lower tax rates for the young, increasing in middle age and then reducing, a result similar to that obtained by Lozachmeur (2006). When age-dependent taxes are not permitted, the optimal nonlinear income tax schedule (parametric) exhibits progressivity. This corresponds roughly to age-dependent taxation, since labor income is humpshaped. Another example is provided by Kifmann (2008), who examines optimal taxes and retirement benefits simultaneously in an age-dependent context, using a model in which productivity varies over individuals and is not observable. Building on Wrede (1999) and Fenge et al. (2006), he characterizes the conditions for, and discusses, optimal agedependent taxes and retirement benefits. One of his results is that if age-dependent labor taxes are not permitted then a retirement benefit formula is a requirement for implementing an optimal policy. In other words, a retirement benefit scheme can act as a secondbest substitute for age-dependent labor income taxation. This result complements that of Gervais (2012), who showed that age-dependent taxation and progressive taxes could be

Taxation, Pensions, and Demographic Change

substitutes, and the idea that capital taxes might also substitute for age-dependent labor income taxation (since the old typically have higher assets and hence higher capital income than the young). The Erosa and Gervais (2002) model assumes that individuals are homogeneous (same productivity and preferences) and face no borrowing constraints. These shortcomings have been dealt with by Lozachmeur (2006), but in the context of a simple partial equilibrium model with households that face a borrowing constraint and make endogenous choices regarding the amount of education and length of retirement. His model comprises individuals who live three periods and a government with a fixed revenue requirement. Young individuals choose the allocation of time between work and education, the latter generating greater productivity and a greater wage rate, middle-aged individuals work, and older individuals choose the allocation between work and leisure (retirement). Thus, unlike in Erosa and Gervais (2002), the productivity of individuals is endogenous. When the borrowing constraint is nonbinding, it turns out that the optimal age-dependent tax rates on earnings are fully characterized. They involve a zero tax rate on the old and a tax rate on the young lower than the tax rate on the middle aged. The zero tax rate ensures that the retirement decision is not distorted, while the tax rate on the middle aged is higher than that for the young to minimize the distortion on the educational choice. When the borrowing constraint is binding, an analytic characterization of the tax rates is not forthcoming; nevertheless, the author shows that the young continue to pay a lower tax rate than the middle aged, but the old now face a nonzero tax rate, which can be positive or negative depending on the interaction between education and retirement. This theme is supported by da Costa and Santos (2015), who develop an OLG model in which the endogenous choice of human capital investment plays an important role. The resulting age-dependent labor efficiency exhibits the usual hump-shape. The study computes optimal taxes, assuming a linear tax function with a threshold that permits limited nonlinearity, under the assumptions of age dependence and age independence of the tax function. The results from their calibrated model indicate that optimal taxes should increase with age. This result is primarily due to the endogeneity of human capital (lower taxes when young encourages investment) and the implied higher elasticity of labor supply when young. The lower tax rate for the young when human capital is endogenous complements a similar result of Lozachmeur (2006). Very recently, Karabarbounis (2016) has also emphasized the role of the variation of the elasticity of labor supply over the life cycle in the determination of optimal agedependent taxation. The model used for the analysis is a typical OLG model extended to include labor supply, consumption, and saving decisions by couples with agedependent productivities based upon endogenous human capital investment decisions. The calibrated model exhibits the usual hump-shape for productivities and labor supply, with the elasticity of labor supply varying over the life cycle. Among other things (assets and income tax filing status), the nonlinear parametric tax function is permitted to be age

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dependent. The resulting optimal age-dependent taxes are also shown to exhibit a humpshape that is related to the implied age dependence profile for the labor supply elasticity. The young attract the lowest tax rate, which increases with age and then begins to fall at older ages. The author also makes the observation that age-dependent labor taxes and nonlinear asset taxation are, to some extent, substitutes. A fundamental feature of the Ramsey tax formulae is that goods with high price elasticities should attract low tax rates, while those with low responsiveness to price changes should be taxed more heavily. In the context of labor income taxes that are permitted to be age dependent, the elasticity of labor supply becomes an important element. Several recent papers have addressed this relationship. For example, French and Jones (2012) have undertaken empirical work on the impact of government pensions and wages upon the labor supply and retirement decisions of individuals over the life cycle. They provide evidence that labor supply and retirement decisions of older workers are more sensitive to incentives than the labor supply decisions of younger workers. An implication is that there is value of having age-dependent taxes that are lower for older people. Recent empirical evidence on the elasticities of labor supply with respect to wages has been provided by Keane and Wasi (2016) in a model incorporating endogenous human capital formation. When human capital formation is endogenous, the price of time is no longer just the net wage rate but also depends on the future returns to work experience (investment in human capital) and the labor supply elasticities depend on both preferences over consumption and leisure and the evolution of wages over the remaining ages in the life cycle. Using results from an econometrically estimated life cycle model, the authors provide estimates of Hicks and Marshallian elasticities of labor supply with respect to tax rate changes that exhibit a U-shaped age profile. That is, the elasticities are typically higher at early ages, relatively low throughout the main working life ages (25–60) and then rise fairly sharply at older ages. They suggest that this U-shaped age pattern combines the expected effects of human capital, for which elasticities should rise with age as human capital becomes less important (Keane, 2016), and of the extensive margin (retirement) decision, which yields a U-shape. An implication of these results for optimal agedependent taxation is that the young should be taxed at relatively low rates, the middle aged at higher rates, and those at older ages at lower rates.h 3.2.3 The Mirrlees Approach to Age-Dependent Taxation There are basically two different strands of the literature dealing with age-dependent taxation, based upon two different approaches to the issue. One strand of the literature, discussed in some detail above, is based upon the Ramsey approach to optimal taxation. In such modeling, the tax rates are assumed to be linear (proportional) so these tax rates are h

For a review of the literature on the estimation of labor supply elasticities and responses to taxes, see Keane (2011).

Taxation, Pensions, and Demographic Change

treated as policy variables to be optimally chosen to maximize a social welfare function. These tax rate policy variables may be constrained to be the same for people of all ages and so are age independent, or this assumption may be relaxed to allow for the tax rates to differ by age so that they are then age dependent. In contrast, the second strand of literature is based upon the Mirrlees (1971) approach to optimal taxation. Mirrlees was concerned with the construction of an optimal (income) tax function T(y), which was subjected to only weak conditions, chosen to maximize a social welfare function. The question of interest concerned the properties of the optimal tax function, in particular, its shape and progressivity. While it might be the case that assessable income, y, is correlated with age, Mirrlees was not concerned with an age dependant tax function. However, Mirrlees’ optimal taxation approach has been extended in many ways by subsequent researchers to allow for an age-dependent taxation function, T(y, a), where a denotes age. Since the Mirrlees model is static, these extensions have been made to life cycle models of households to enable explicit treatment of households of different ages. The basic objective is to allow the optimal tax function with respect to income depend on age as in T(y, a), and to determine how it is influenced by age. This strand of the literature based upon Mirrlees’ optimal taxation approach seems to have begun with the unpublished paper by Kremer (2001). Kremer (2001) provides the conclusion that the young should be taxed at a lower rate than the old. This argument is based upon the principles from the Mirrlees approach that the marginal tax rates should be high when labor supply responses are relatively small, the government is keen to redistribute income from the rich to the poor and at incomes in the distribution where there are few taxpayers relative to those with higher incomes. Kremer argues that empirical evidence suggests that the labor supply elasticity is higher for the young than the old, and that the hazard rate (density function at an income divided by the proportion of the population with higher incomes) is much higher for the young than the old. Accordingly, marginal tax rates should be lower for the young than for the old. Subsequent studies based on Mirrleesian principles include (in chronological order) Blomquist and Micheletto (2008), Weinzierl (2011), Farhi and Werning (2013), and Bastani et al. (2013). The issue of age-dependent taxes has been investigated by Blomquist and Micheletto (2008) in a model that incorporates a skill heterogeneity among households. They consider a simple life cycle model of households that live two periods and a government that chooses a nonlinear (discrete point) income tax schedule to redistribute income between households, the interest rate, and wage rates being exogenously given. Thus, in essence, their model is different from that of Alvarez et al. (1992) in having households distinguished by skill (in the second period of life) and considering progressive income taxes in the Mirrlees tradition rather than linear consumption and earnings taxes as in the Ramsey approach. The authors show that, compared with an age-independent tax system, an age-dependent tax system yields a Pareto improvement in welfare. When households are not permitted to save, the welfare

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improvement is achieved by lowering the marginal tax rate for young individuals. When saving is permitted, optimality requires a positive tax on interest income as well as agedependent progressive income taxes. Weinzierl (2011) extends the ideas in Kremer (2001) to a dynamic setting, undertakes numerical simulations for the US economy and provides welfare calculations for the different policy scenarios considered. The model is, however, partial in that it comprises only the household sector and a government, with no general equilibrium determination. In his model, households live many periods and are heterogeneous, their skill levels changing over the life cycle according to either a deterministic or a stochastic process. The government chooses nonlinear income taxes to maximize a social welfare function (weight sum of household lifetime utilities), subject to a government budget constraint (that is purely redistributive) and incentive compatibility constraints. A primary conclusion to come out of the analysis is that, when age-dependent taxes are permitted, it is optimal for young high earners to have lower marginal tax rates than the old, a conclusion supporting that of Kremer (2001). The optimal average tax functions are increasing in income for each age group, but the functions are higher for higher age groups. A second major conclusion, obtained by comparing the welfare arising from optimal age-independent taxes with welfare arising from optimal age-dependent taxes, is that there are significant gains from the latter policy; age dependence of the tax function yields large welfare gains, especially for low-skilled households. The Mirrlees approach to optimal taxation is extended by Farhi and Werning (2013) to a dynamic life cycle model that incorporates age-dependent labor productivities, which follow a stochastic autoregressive process over the age of individuals. The planner chooses an optimal allocation that satisfies local incentive compatibility conditions and that takes account of the uncertainty created by the stochastic productivity process. A focus of the paper is to understand more fully the role played by uncertainty concerning future productivity, and hence labor earnings, with taxes perhaps acting to perform an insurance role as well as a redistributive role. An outcome from the analysis is that the age profile of labor income taxes is strongly related to the stochastic process generating the productivity profiles. An implication is that if there is persistence in the productivity shock process so that there is a strong positive correlation between productivity and age, labor taxes should increase with age. Simulation results show that average labor taxes start close to zero at low ages and increase with age over the working age portion of the life cycle. By contrast, the average tax on savings falls with age to zero. Moreover, the authors’ simulations demonstrate that there are significant welfare gains from having age-dependent taxes compared to having age-independent taxes, thus confirming the welfare efficacy of age-dependent taxes reported by earlier studies. Another study of the welfare implications of age-dependent taxation in a life cycle context and based upon the Mirrlees approach is that of Bastani et al. (2013). This paper builds on the earlier model and theoretical analysis of Blomquist and Micheletto (2008), who show the potential welfare improvements in moving from age-independent to

Taxation, Pensions, and Demographic Change

age-dependent taxes. Bastani et al. (2013) construct a more detailed model calibrated to the US economy (but with only three periods in the life cycle) and to use it to provide quantitative calculations of optimal tax functions and welfare gains. Unlike Weinzierl (2011) and Farhi and Werning (2013), who analyze partial equilibrium models with only the household and government sectors, Bastani et al. (2013) introduce a production sector with capital accumulation and deals with the steady state for a dynamic closed economy model. It also features heterogeneous households, distinguished by discrete productivities that evolve stochastically over the life cycle through a transition probability matrix. In terms of taxation policy settings, Bastani et al. (2013) also consider optimal linear taxes as well as optimal nonlinear taxes and, like Farhi and Werning (2013) but unlike Weinzierl (2011), the model allows for a linear tax on income from saving. Of special interest is that they consider four main labor income tax policy options—agedependent nonlinear taxes, age-independent nonlinear taxes, age-dependent linear taxes, and age-independent linear taxes—and compare them assuming that the government sets each optimally to maximize the expected value of a social welfare function. While the welfare gain obtained by moving from optimal age-independent linear taxes to optimal age-dependent linear taxes is modest, large welfare gains accrue as a result of a shift from optimal age-independent nonlinear taxes to optimal age-dependent nonlinear taxes. The latter gain is calculated to be around 4% of GDP using a social welfare function that maximizes the minimum expected utility for a young person, while the former is around 2% of GDP. These figures indicate the gains from making the income tax system age dependent. While these gains are substantial, they are less than the gains accruing from a move from optimal linear taxation to optimal nonlinear taxation. These latter gains are calculated to be in the order of 4.6% in the case of age-independent taxation and of 6.6% of GDP in the case of age-dependent taxation. Together the gains from making taxes both nonlinear and age dependent are calculated to be very large. The age-dependent marginal tax rate functions are shown to be lower for young workers than for middle-aged workers, confirming results obtained by others such as Weinzierl (2011). In addition, the marginal tax functions for both young and middleaged workers are decreasing in income, indicating that the tax schedules are highly regressive. The lower tax rate for young workers encourages their saving and so leads to a higher rate of capital accumulation and output. An interesting approach to age-dependent taxation was taken by Cremer et al. (2004), who deal with the optimality of the income tax system in a model where the income tax function is assumed to depend on income and the age of retirement. The model has individuals heterogeneous in productivity and whose preferences depend on health. With neither variable observable to the government, the second-best optimal tax function differs from the first-best. The authors argue that the optimal policy implies some distortion to the retirement decision in a model where individuals’ productivity and health status are not observable. This optimal policy is an example of age-dependent taxation and may induce early retirement.

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3.2.4 Summary It has been demonstrated that the concept of age-dependent taxation is firmly grounded in the theory of optimal taxation when applied to life cycle models of individual behavior. One strand of literature is based upon optimal taxation theory following the Ramsey tradition. The other strand of literature follows the Mirrlees approach to optimal nonlinear tax functions. Both strands establish that age-dependent taxation can be optimal in a whole range of situations. This, of course, should not be surprising since the assumption of age-independent taxation involves a restriction on the optimization problem not required under the assumption of age-dependent taxation. Rather, the primary issue is to what extent the relaxation of the age independence restriction increases welfare. The literature surveyed above typically indicates that the gains can be substantial. The literature has not, it seems, addressed age-dependent taxation over the transition path arising from demographic shift from, say, one stable population age structure to another. The issue of how an optimal age-dependent tax system would change over the transition path has not been attacked by researchers, this being computationally extremely demanding. Nevertheless, the existing results based upon steady states have lessons. Given that population aging creates pressure upon government budgets, improvements in the efficiency of the tax system will partially relieve that pressure. Age-dependent taxation offers one such improvement. While the literature has mainly focused on taxation over the working period of the life cycle, it is apparent that taxation and retirement benefit rules after retirement may constitute another form of age-dependent taxation. Attention will be turned to the postretirement treatment of pensions further below in Section 4.

3.3 Taxation Design Issues 3.3.1 Taxation Reform and Analysis Before proceeding to the optimal tax analysis literature, attention is now directed to consideration of the nature and impacts of various policy reforms that have been analyzed as a response to the fiscal and welfare challenges brought about through population aging. These policy reforms involve changes to the tax structure by replacing existing taxes by others such as the move from progressive income taxes to proportional income taxes or flat rate income taxes.i In addition, attention is paid to tax and system reforms involving the health and medical programs in the USA, since these represent significant fiscal challenges as a result of population aging. Finally, the roles of endogenous technical change i

In contrast to the studies by Altig et al. (2001) and Nishiyama and Smetters (2005), who consider changes from one type of tax to another, Kudrna et al. (Forthcoming) consider the switch between a reduction in pension benefits and an equal increase in taxes as alternative policies in response to population aging using their OLG model for Australia. The first policy involves gradual changes to the pension eligibility age, the maximum pension and the taper rate, all acting to reduce pension expenditures. The second policy is to increase tax rates, either the consumption tax rate or the income tax schedule.

Taxation, Pensions, and Demographic Change

and endogenous human capital in the analysis and evaluation of tax policy reforms are briefly considered, since they represent channels through which population aging and taxation impacts might be ameliorated. Altig et al. (2001) have simulated the effects of five different tax policy options using an OLG model calibrated to the US economy. These include a move to a “proportional income tax, a proportional consumption tax, a flat tax, a flat tax with transition relief,” and another system that combines flat taxes with proportional relief subsidies. The results are obtained over the transition path from the initial steady state to the final steady state. This is not directly related to population aging, but is relevant within the context of tax policy reform. In particular, it simulates the impacts of these various tax reforms over the transition path from an initial to a final steady state solution and computes the welfare effects for 12 different categories of households distinguished by income profiles. The main conclusions reached from the simulation analysis of the several taxation reforms for the US economy are that the reforms can yield substantial increases in output and macroeconomic outcomes, but that there are potentially difficult distributional trade-offs. In most cases the long run welfare impacts differ by income class, with some benefiting and others losing in terms of welfare. Moreover, there are generational differences at play. The current older generations are impacted differently from future generations since they have limited time to adjust behavior. These differential intra- and intergenerational welfare impacts are prevalent in many such studies for other countries and so reflect the political quandary facing taxation reform even in models without demographic change, as here, let alone in models in which demographic change adds another dimension to the issue. Tax reform has also been investigated for the USA by Nishiyama and Smetters (2005), who consider a shift in taxation from a progressive tax system to one with a flat rate consumption tax. They formulate an OLG model of the USA that involves heterogeneous (by productivity) households living from age 20 to 109, with wage profiles that embody an idiosyncratic stochastic process, stochastic mortality, and an exogenous population growth rate. To permit an overall measure of welfare, they adopt the methodology of Auerbach and Kotlikoff (1987) and make use of a hypothetical lump-sum redistribution authority (LSRA) whereby currently alive households are provided with a lump-sum transfer to ensure that they are not adversely affected by the policy change and a common lump-sum transfer is provided to future households. If the latter transfer is positive there is an efficiency gain, and if negative then an efficiency loss ensues. They establish two fundamental results. The first is that, if the model is restricted so that there are no uninsurable idiosyncratic wage risks (the wage profiles become deterministic) then the switch in tax scheme from progressive income taxes to a flat rate consumption tax increases efficiency with the LSRA scheme generating a net welfare gain to society. Without lump-sum transfers, older currently alive generations suffer a welfare loss while younger generations gain from the policy change. However, when the LSRA scheme is implemented, current

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generations are left indifferent while future generations obtain a substantial welfare gain amounting to about $154,000 for each future household. The second main result is that if there are uninsurable stochastic wage profiles for household, the policy change is unable to generate an aggregate welfare (efficiency) gain through the LSRA scheme. Indeed, while current generations remain indifferent, future generations experience a welfare loss amounting to $85,900 per household. Given these two results, the authors conclude that the welfare loss arises because the progressive income tax schedule provides an indirect insurance role that the flat rate consumption tax cannot provide. Hence, the switch from the progressive tax scheme removes the social insurance role and so welfare is reduced. Thus, just as will be observed further below regarding the social insurance role provided by means-tested pensions, so too is there a social insurance role performed by a progressive income tax system. As discussed briefly in Section 2, health and medical expenses (such as Medicare in the USA) have contributed significantly to the fiscal burden faced by many countries due to population aging. As a result, there is a growing interest in the economic analysis of medical support programs and of their interaction with insurance and taxation. In many countries, public medical programs are financed, partially or wholly, by a tax levy (such as for Medicare in the USA), while household contributions to private health insurance are subsidized through the tax system and through income tax deductions. This interaction with the income tax schedule yields distributional and welfare implications. Since older individuals have a higher demand for health services, population aging has potentially important interactions with the health system and the structure of taxation. Recent contributions to this literature include Jeske and Kitao (2009), De Nardi et al. (Forthcoming), Jung and Tran (2016), and Jung et al. (2016). The interactions between US health insurance and tax policy were analyzed by Jeske and Kitao (2009), who were especially concerned with the tax deductibility of contribution to employer-based health insurance. Since this deductibility is from income, the progressive income tax schedule implies that higher earners benefit more from the policy. They calibrate their model to the USA and undertake several policy experiments— abolishing the tax deductibility of premiums, providing lump-sum transfers instead, extending deductibility to private health insurance and providing credits to the insurance market. Removing deductibility for employer-based health insurance leads to widespread welfare losses due to reduced coverage for health risks, with only some (about 19%) younger individuals obtaining a welfare gain. Extending tax deductibility to private health insurance provides relatively strong and widespread welfare gains for the young (80% gain), as does the policy of providing credits. While the lump-sum transfer yields widespread gains, they are very modest. One possible economic mechanism that could alleviate some of the fiscal and welfare implications of the aging of the population operates through endogenous technical change. The basic idea is that the aging of the population will reduce the labor supply

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and so increase the real wage rate, thus inducing the investment of funds into labor augmenting technical progress, which, in turn, raises the rate of growth and alleviates the labor shortage. While most macroeconomic analyses of population aging, taxes, and pensions assume an exogenous rate of technical progress, authors such as Heer and Irmen (2014) have explicitly modeled endogenous technical change and have assessed its importance when analyzing the impacts of population aging and social security policy settings. The model is calibrated to match the US economy and then used to compute the transition path between a 1950 steady state to another steady state in 2400 taking as given a projected path for the US population, which is assumed to become stationary by 2200. The population growth rate increases initially followed by a long period over which the growth rate (mostly) declines, thus inducing an aging of the population. This benchmark solution exhibits an increase in the growth rate for the technology due to an induced increase in labor productivity. The equilibrium time paths for the economy under two different social security policy changes are then compared with this benchmark solution, which assumes a constant replacement rate for the pay-as-you-go social security. These policy variations are, first, adjustments in the contribution rate to balance the social security budget (becoming constant) and, second, an adjustment in the replacement rate (becoming constant) combined with a higher future retirement age of 70 years. These policies reduce the replacement rate for pensions and act to encourage labor supply. The rate of technological progress increases in the long run under the first policy scenario but does not change much under the second policy scenario, indicating that the impacts of policy can vary significantly when technical change is endogenous. This differential effect of endogenous technical change is further reflected in the welfare outcomes, showing that future generations benefit significantly from the first policy variation while the second variation results in welfare losses. One related source of endogenous growth that has received increasing attention within the context of population aging is that due to endogenous human capital formation. Not only does endogenous human capital investment have implications for the impacts of population aging, but it also has implications for tax and pension policy analysis and design. The implications for the impacts of population aging for the USA were drawn out by Ludwig et al. (2012). They compared results from model specifications with and without the human capital investment channel operating and showed that the resulting macroeconomic and welfare implications were substantially different. The difference was quantitatively important, especially for welfare losses; the losses arising from demographic change fell from about 12.5% to 8.7% as a result of the human capital channel operating. Fougere et al. (2009) similarly find that human capital investment can significantly mitigate the economic implications of population aging in Canada. The importance of human capital investment for the analysis of population aging has been taken up by Vogel et al. (2016) in their recent study of pension policy reform, via an increase in

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the retirement age. By comparing the intertemporal equilibrium for their model— calibrated to represent the European countries of France, Germany, and Italy—with the retirement age fixed and then with the retirement age linked to life expectancy, they conclude that the combination of the human capital investment channel and the retirement age adjustment substantially alleviate the macroeconomic and household welfare implications of projected population aging. The increased longevity and pension policy change induce more human capital and more labor supply resulting in a smaller welfare loss for households arising from population aging. 3.3.2 The Taxation of Capital Income An important strand of the literature on optimal taxation in dynamic economies concerns the proposition that the income tax rate on income from capital should be zero. This proposition was initiated by Judd (1985), who considered a closed economy producing a single product that could be used for consumption by infinitely lived consumers or invested in physical capital. Judd argued that, in the short run capital is fixed and adjusts slowly over time and so a positive tax rate on capital income can be beneficial for redistribution purposes. In the long run, a tax on capital income discourages capital accumulation resulting in a reduction in the capital–labor ratio and the wage rate (labor is now relatively more abundant). The smaller capital stock and the lower wage rate have detrimental affects upon consumer welfare. Accordingly, the optimal policy is to have a zero tax on income from capital in the long run. This proposition is supported by Chamley (1986). He shows that, in his model, the optimal policy is for a positive capital income tax along the transition path, jumping to zero in finite time. Again, the result is that it is optimal for capital income not to be taxed in the long run. These papers spawned further research into the generality of the zero capital income tax proposition. Some papers, such as Jones et al. (1997), show that the result is fairly robust, extending to zero taxes on labor income and consumption, but exceptions arise when taxes are restricted or there are positive profits. There are several pertinent reasons why the capital income tax rate will be nonzero optimally. Drawing heavily upon the discussion in Conesa et al. (2009), there are three main reasons. First, a nonzero tax rate can arise if households face borrowing constraints and/or in which the households face uninsurable labor income risk. This point is emphasized by Imrohoroglu (1998), who considers a model with borrowing constraints, uninsurable wage income risk, and longevity risk and by Hubbard and Judd (1986), who has borrowing constraints. Other papers include Aiyagari (1994) and Aiyagari (1995), who have uninsured idiosyncratic risks, incomplete markets, and borrowing constraints. A second reason is that nonzero capital income taxes may arise in OLG models. This is established by various authors, including Alvarez et al. (1992), Erosa and Gervais (2002),

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and Garriga (2003)—the optimal capital tax rate is not zero in life cycle model especially if the tax code cannot be conditioned on the age of a household. Third, the optimality of capital income taxes might depend on whether the government is able to implement progressive income taxes. See Conesa et al. (2009), who used their OLG model for the USA to show that the optimal capital tax rate is 36%, while the optimal labor income tax rate is 23% with a $7200 deduction. The intuition for some of these results is along the following lines. It was previously established that it is generally optimal to tax young agents’ labor income lightly (leisure heavily) and to tax older agents’ labor income more heavily (leisure lightly) if agedependent taxes are available. If it is not possible to have age-dependent taxes, capital income may be a second-best option. Since older agents typically have greater capital income than young agents (due to past saving), a heavier tax on capital income indirectly taxes the leisure of the old more heavily and leisure of the young more lightly. In a similar fashion, if age-dependent taxes are not available, a progressive income tax structure acts a second-best option if earnings are age related. As a final point, it may be that the means testing of the age pension (as in Australia) also acts as a type of capital income tax, since pensioners’ nonpension income is mainly derived from asset holdings (capital income). The analysis of capital taxation by Conesa et al. (2009) has been extended in the more recent contributions of Peterman (2013) and Fehr and Kindermann (2015). Peterman (2013) distinguishes his model from that of Conesa et al. (2009) in several ways and then investigates various potential reasons for obtaining a large optimal tax on the income from capital. He finds that the most important reason is an assumption that the Frisch elasticity of labor supply is variable over the individual’s life cycle, which induces governments to condition labor income taxes upon age. If they cannot, a capital income tax can provide a second-best policy. The imposition of preferences with a Frisch elasticity that is constant over the life cycle removes the incentive to condition labor income taxes on age and so reduces the optimal capital income tax. In addition, the restriction of capital income and bequest income taxes to be the same also induces a reduction in the optimal capital income tax. Together, these two restrictions reduce the optimal tax from about 30% to about 16%. Other potential reasons investigated are found to be quantitatively less important. Fehr and Kindermann (2015) extend the long run analysis of Conesa et al. (2009) to a detailed consideration of the impacts of optimal taxation on the economy and the welfare of different cohorts over the transition path from one long run equilibrium to another. Basing an optimal tax on the welfare implications for all members of all cohorts requires a careful specification of the social welfare function. Using a fairly general specification that has several special cases of interest, they show that a high optimal capital income tax rate depends crucially on having a welfare function that is utilitarian, which supports redistribution across cohorts. A high capital income tax thus facilitates redistribution from current older generations to younger and future generations. It is also found that the social

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welfare function based upon individuals does not embody such a redistributive aspect. Rather, it concentrates upon the economic efficiency and social insurance impacts of policy and generates a zero capital income tax. These results highlight the role of the chosen social welfare function for the determination of optimal tax policies, which are sensitive to the assumed weights given to individuals in current and future cohorts. The relationship between changes in the age structure of the population, voting for political parties, and the structure of taxation—particularly capital vs labor income taxation—has been recently analyzed by Mateos-Planas (2010) for the USA. The model used for the analysis is one of an OLG in a perfectly competitive economic environment with capital accumulation and a political economy specification in which voters have preferences for tax rates. These preferences differ by age, with younger voters preferring capital income taxation and older voters preferring labor income taxation. In equilibrium, the tax structure (mix between labor and capital taxation) is determined politically by the median voter. A change in the age structure of the population (demographic change) will alter the equilibrium median voter and so alter the equilibrium tax mix. The author points out that there are two opposite effects that determine the outcome—tax preference effects and general equilibrium effects. In the two period theoretical analysis, it is shown that a reduction in the decisive voter’s age leads to a higher capital tax rate, while an increase in the proportion of older voters will reduce the tax rate on capital. This theoretical analysis is then extended to a large scale model with many age groups and calibrated for the USA, with numerical simulation results for two main scenarios. Comparing steady state solutions—so there are no transition dynamics—for 1990 and 1965, it is shown that the relatively younger population in 1990 results in a lower capital tax rate. While the younger population lowers the median voter’s age, which augers well for a higher capital tax rate, this effect is dominated by the general equilibrium effect that encourages a lower capital income tax rate. This general equilibrium effect operates via the larger share of asset poor younger age groups having less saving and so discouraging capital formation and raising the return to capital, thereby encouraging the median voter to reduce the tax rate on capital. The second simulation compares the steady state solutions for 1990 and 2025, over a period where there is a projected increase in population aging. In this case, population aging leads to an increase in the tax rate on capital income, thus moving the tax mix toward capital and away from labor. The upshot of this analysis, applied generally to other countries, is that projected increases in the proportion of older age groups in the populations of many countries (population aging) is likely to lead to increases in the tax rate on capital income and, thereby, a shift in the tax base from labor to capital. A question that has arisen with respect to the taxation of capital vs labor income is whether the means testing of the age pension may be regarded as a partial substitute for capital income taxation. With this in mind, Kumru and Piggott (Forthcoming) investigate the relationship between capital income taxation and the means testing of the age

Taxation, Pensions, and Demographic Change

pension based partly upon assets and asset income. They argue that an age pension that is means tested so that the pension payment reduces as the pensioner’s assets become larger and/or as the pensioner’s asset income (in the form of interest or dividends, for example) acts as an indirect means of taxing capital income. This is an extension of the idea that capital income taxation acts as a partial substitute for age-dependent taxation, since assets are strongly correlated with age. Kumru and Piggott (Forthcoming) calibrate an OLG model, incorporating a means-tested pension and capital income taxation, to the UK economy and undertake a range of simulation exercises computing optimal tax rates. One of the important results to come from these exercises is that there is a strong negative relationship between the taper rates (withdrawal rates) applying to the means-tested pension and the capital income tax rates that help generate revenue to fund the age pension. This means that higher capital income tax rates partially substitute for lower taper rates. That is, capital income taxation and means testing are partial substitutes. Another implication of this relationship is a confirmation that taxation policies and social security policies are intimately connected and that they need to be jointly considered. 3.3.3 Optimal Taxation The issue of determining optimal income tax functions within a life cycle framework has been addressed by various authors including Pirttila and Tuomola (2001) and Gorry and Oberfield (2012), though not with a particular focus on population aging.j Pirttila and Tuomola (2001) develop a theoretical OLG model with a public good in which two types of households differ in their productivities, both working in the first period of life and consuming in both periods. Allowing for separate tax schedules for capital and labor income, optimal nonlinear tax schedules are characterized. A primary result is to show that the optimal marginal tax rates for the capital income of high ability households should be positive (negative) if an increase in capital reduces (increases) the real wage of the low ability worker. Thus, the capital income tax rate should not be zero and the result indicates that its sign depends upon the endogeneity of wages in the economy. The marginal tax rate on the capital income of low ability households is also nonzero in general, the sign depending on different labor market outcomes. On the other hand, the marginal labor income tax rate is unambiguously negative for high ability workers and positive for low ability workers. Gorry and Oberfield (2012) also characterize optimal nonlinear taxation schedules, but restrict attention to labor income. Their theoretical analysis of a continuous life cycle model with heterogeneous households (the heterogeneity being based upon ability) and supplemented by numerical examples, establishes that the optimal nonlinear income tax schedule exhibits a positive marginal tax rate at the highest income, in contrast to the j

For an earlier survey of optimal fiscal (and monetary) policy see Chari and Kehoe (1999); for a very recent contribution to optimal taxation, see Saez and Stantcheva (2016).

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Mirrlees (1971) result that has received much attention. The authors explain the intuition behind this outcome by noting that, while an extension of the tax function with a zero marginal tax rate would encourage greater work effort and consumption by those with highest ability, they would also react by reducing labor effort at earlier stages of the life cycle when they were less productive. This would impact negatively upon government taxation revenue; accordingly, the zero marginal tax rate at the highest income could not be optimal. Using numerical specifications of the model matched to the US social security and tax system, the authors compare results under the current progressive US tax schedule with the optimal nonlinear tax function and compute welfare gains from moving from the current system to the optimal tax function. Surprisingly, the welfare gains appear to be rather modest. The interaction between taxation and social security policies, and the relationship of these with endogenous retirement decisions, are also the subjects of the study by Cremer et al. (2004). Their model incorporates two essential sources of heterogeneity among households, namely productivity and health heterogeneity, and endogenous labor supply (intensive margin) and retirement (extensive margin). The model also permits nonlinear taxation of labor income, the taxation function being optimally chosen subject to incentive compatibility constraints. The theoretical analysis supplemented by numerical calculations indicates that the second-best taxation and transfer policy is to have a positive tax on low ability and low health individuals. Moreover, the optimal second-best policy encourages earlier retirement, irrespective of whether the source of heterogeneity is via productivity or health. The recent literature has paid some attention to the role of human capital in life cycle models of individuals’ choice and its implications for optimal taxation. Empirical evidence for the importance of human capital decisions and their role in determining lifetime income and wealth has been documented by, for example, Huggett et al. (2011). The implications of endogenous human capital for optimal policy formulation have recently been highlighted in the studies by Gottardi et al. (2015), Krueger and Ludwig (2016), Stantcheva (Forthcoming), and Stantcheva (2016). Gottardi et al. (2015) emphasize that the returns to human capital are riskier than the returns to physical capital and show that the optimal taxation policy for the USA involves taxes on both labor and capital income as well as the issue of public debt. Krueger and Ludwig (2016) use a calibrated OLG model for the USA to show that optimal policies involve generous subsidies to undertake education along with a moderately progressive income tax schedule that provides a social insurance role. Stantcheva (Forthcoming), also for a model calibrated to the USA, finds that the optimal net human capital tax/subsidy wedges are relatively small and, interestingly, that the resulting welfare gain could instead be achieved by simple age-dependent taxes and subsidies. This literature is potentially of great importance within the context of population aging, since greater longevity may, arguably, increase the return to human capital investment through education and so encourage

Taxation, Pensions, and Demographic Change

individuals to stay longer in the work force. As a result, endogenous human capital may have important implications for how optimal taxes are designed. 3.3.4 Optimal Taxation Over the Transition In this subsection, attention is concentrated on the analysis of optimal taxation policies over the transition path from one initial equilibrium (usually a steady state) to a final equilibrium. Since this task is computationally very demanding in calibrated OLG models, few papers have reported such research. Exceptions are provided by Conesa and Garriga (2008a), Conesa and Garriga (2008b), Bielecki et al. (2015), and McGrattan and Prescott (2016). Conesa and Garriga (2008b) assume that the economy in an initial steady state equilibrium is subjected to an unanticipated policy shock that changes the financing of the social security scheme in the USA from a PAYG system to a fully funded system. The government is assumed to have available a set of taxation policy instruments that it can use to assist this fundamental social security policy change. The set of such taxation instruments include tax rates on labor income, tax rates on capital income and income transfers to households. In addition, the government faces an intertemporal budget constraint, permitting government debt as a fiscal instrument. In this research, the authors abstract from any change in the demographic structure, maintaining a stationary age distribution for the population. Accordingly, they focus exclusively on the intertemporal aspects of tax and fiscal policy. To construct the optimal tax policy problem, a social function to be maxiP welfare t2 mized needs to be specified. This is defined as U ¼ ∞ λ U t , where Ut denotes t¼2 the expected lifetime utility of the generation born in period t and λ is the discount factor that the government assigns to future generations. Thus, the government maximizes the discounted sum of expected lifetime utilities of all future generations, the change of policy being initiated in period t ¼ 1. The research strategy is to express the welfare optimization problem in primal space, in which all variables are quantities and to incorporate restrictions that reflect those derived from the economy (such as the requirement that supply is at least as great as demand for consumer goods and labor supply, etc.) and from the policy setting (choice of instruments and the requirement that the first generation must achieve its baseline expected lifetime utility level). This quantitative solution can then be implemented by a suitably constructed tax and fiscal policy, thus decentralizing this central planning or Ramsey solution. Thus, the optimal policies are obtained indirectly, being “backed out” from the optimal primal problem solution. The main outcome from the simulations is the result that a Pareto improvement in welfare for future generations without any loss of welfare for the current generation is possible by an appropriate design of policy. The policy comprises intertemporal changes in labor income tax rates, transfers to households, and in the level of national debt. The labor income tax rates initially decline, since social security funding moves from PAYG to

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fully funded, while income transfers are required to compensate households who would otherwise be harmed. This requires the issue of more government debt to cover the costs of the transfers, so the level of government debt immediately jumps and is gradually reduced over time. Additionally, the authors consider the extension of the policy instruments to age-dependent labor and capital income tax rates. Age-dependent labor income taxes, in particular, offer significant increases in welfare. The optimal policy is to tax the young lightly, increasing the tax rate with age, reducing it in middle age and then raising it again for older households, the variation being particularly pronounced along the transition path. This additional policy instrument generates substantially greater welfare gains over the earlier part of the transition path. In a companion paper, Conesa and Garriga (2008a) relax the assumption of a stationary demographic population and consider the optimal policy response to a transitory demographic shock. They assume an initial stationary demographic population and steady state equilibrium and then consider an unexpected shift in the dependency ratio over two periods (each of 5 years), which then reverts to its original value. Given that the financial demands upon the government will increase with a higher dependency ratio as a result of pensions being funded by a PAYG scheme, the purpose of the paper is to determine the government’s optimal policy response and to show that, contrary to standard thought, no generation needs to suffer a loss in welfare. Proceeding in the same way and using a similar model to that used in their other paper discussed above, the optimal policy response is computed to ensure that no generation loses from the demographic shock. The permissible policy instruments comprise the mandatory retirement age, the labor income tax rate and fiscal policy through government debt. The main policy change is to remove the mandatory retirement age of 65 years, making retirement voluntary at all ages. The optimal accompanying policies are to reduce labor income tax rates, make these rates age dependent, and to issue more government debt so that the level of debt increases early on during the transition period and then gradually declines over time. Labor income taxes increase with age until dropping somewhat for the more elderly. Welfare of current generations is unchanged but future generations benefit from the optimal policy response. Future gains beyond the transitory demographic shift arise from long-term policy adjustments from the initial suboptimal policy settings. The idea of establishing policy responses chosen to generate Pareto improving changes in welfare over the complete transition path has been considered further more recently by Bielecki et al. (2015) and McGrattan and Prescott (2016). Like Conesa and Garriga (2008b), Bielecki et al. (2015) are concerned with a shift in policy from a defined benefit to a defined contribution public pension system and are cognizant of the problem that current generations may suffer welfare losses from such a shift. They consider a context in which there is demographic change in the form of decreasing mortality over time and exogenous technical change and, within this context, construct an optimal policy response that phases in the shift from a defined benefit to a defined contribution pension

Taxation, Pensions, and Demographic Change

scheme. This is achieved by introducing indexation of both contributions and pension benefits through a “generosity” variable gt that varies by year; gt denotes the generosity of pension benefits over those implied by a defined contribution scheme. This generosity factor may be specific to either the year t (in which case all cohorts alive at t receive the same level of generosity in year t) or to the cohort t (in which case cohorts born in year t receive the same level of generosity). The generosity profile is chosen optimally to minimize the loss of the maximal loser from the policy shift. When the policy shift is introduced very gradually, the optimal generosity profile is able to compensate current older generations so that they do not lose in welfare, but it is unable to prevent some younger and future generations from suffering welfare losses. Thus, the optimal generosity policy is not Pareto improving. Though unable to achieve this goal, the method indicates how to optimize welfare using a particular policy variable over the transition path without relying on lump-sum transfers or government debt as an instrument.

4. PENSION DESIGN 4.1 Introduction The design of pension support for individuals in retirement varies significantly by country, both in the benefits paid and in the way by which they are financed. Some have contributions paid out of earnings while working, while others have no such contributions but are financed out of current income taxes (such as in Australia). Some are Beveridgean in that the payments are the same for all recipients, while others are Bismarckian in that the payments are linked to earnings. Some have means-tested benefits, while others have a flat rate payment (universal pensions). With this backdrop, the current section is devoted to some particular aspects of pension structure and design. Of special concern is the issue of the means testing of age pension benefits. While means tests have been used in various countries for some time, they are becoming increasingly analyzed and discussed in terms of implementation more generally. Accordingly, a substantial discussion of means testing is provided below. This is followed by a more general, but not comprehensive, discussion of various pension issues. These include the privatization of social security, optimal pension design, the political support for public pension programs, and the role of population aging in pension design. Throughout, many of the same issues that concern the analysis of taxation also apply in the analysis of pensions and social security. There are potential distortions to the labor supply and saving behavior of individuals arising from the structure of pension systems. There are redistribution aspects, such as the transfer of incomes from young to old, from workers to retirees, and from the rich to poor. Similarly, when individuals face uninsurable earnings, health and longevity risks the issue of whether pensions contribute a social insurance role arises. Within the context of saving for retirement and access to pensions, assumptions regarding the behavior of individuals are of special importance, since the

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existence of individuals who have myopic behavior or are subject to temptation may significantly affect the role and impacts of pension systems. These issues arise throughout the discussions below.

4.2 Means Testing of Pension Benefits 4.2.1 Why Is Means Testing an Issue? Given the projected significant increase in the proportion of populations aged 65 years and over during the next several decades, there will be more attention given by policy makers to the concept of the means testing of social security benefits in general and government funded age pensions in particular. The primary reason for this is, of course, to limit the projected increase in the proportion of government tax receipts going into these social programs. While increasing the eligibility age is one obvious policy measure, another is to introduce means testing of benefits or to strengthen an existing means test, perhaps by decreasing the free (income or assets) threshold or by increasing the taper rate whereby the benefit is reduced with additional income or assets. The Australian age pension provides a good example of a government provided benefit that is likely to have severe funding implications. This age pension has had an eligibility age (for men) of 65 years since its inception in 1908 until very recently, when the Australian government legislated to increase the eligibility age gradually to 67 years. The eligibility age for women was previously set at 60 years, but has recently been increased to that of men. The increased longevity of the population, with over 80% of the eligible population getting at least a part pension, has led to a major increase in funding requirements with further increases expected in the future. Means testing of the age pension has, however, dampened the funding requirement increase. Accordingly, means testing is an important tax–transfer policy issue. While means testing has been the subject of much research, it is only more recently that attention has focused on means testing of retirement programs. 4.2.2 Types of Means Tests Means tests applied to age pensions can be of various types and can be contrasted with a universal age pension scheme. Under the latter, all individuals satisfying an eligibility rule (such as being at least a certain age and having a suitable residential or citizenship status) will receive the same age pension benefit. In contrast, a means-tested age pension scheme provides a pension benefit that depends upon the persons “means” or ability to consume in retirement. Broadly, the pension may be asset tested or income tested. Under the assets test, if assets are above some threshold the pension benefit is reduced using a taper or withdrawal rate, eventually becoming zero. Similarly, under an income test the benefit is reduced by a taper rate for incomes above some threshold, eventually becoming zero. Clearly, variations within each of these two types of tests occur depending upon the definitions of assessable assets and assessable income. Special cases of the income test include

Taxation, Pensions, and Demographic Change

one based solely upon the earnings from labor—the earnings test—and one based solely upon investment (interest and dividend) income. Here, I provide a very brief survey of some of the main means-tested age pension schemes employed by various countries. Means tests have been applied for many types of public benefits in many countries. However, the following discussion concentrates mainly on means tests that are explicitly related to social security or age pensions. The UK age pension is subject to an earnings test. Brewer et al. (2010) has a detailed account and discussion of means testing in this context as part of the fairly recent Mirrlees review of taxation in the UK contained in Adam et al. (2010). Details may also be found in the studies of the implications of the UK means test undertaken by Sefton et al. (2008) and Sefton et al. (2005), which compares the UK and Danish means test schemes. In the USA, the Supplementary Security Income (SSI) scheme is subject to earnings, income, and resources tests. Earlier reviews of this scheme, including its means-tested aspects, are provided by Moffitt (1992) and Daly and Burkhauser (2003). An overview of means testing in a range of transfer programs in the USA is provided by Moffitt (2003a), which appears in Moffitt (2003b). Piggott et al. (2009) also has a discussion of the US Supplemental Security Income Program, along with discussions of the Chilean minimum pension guarantee and assistance pension, the Brazilian rural pension and South Africa’s means-tested age pension. Canada’s Old Age Security Pension has a “clawback” based on income, currently at a rate of 15% of income in excess of an income threshold (Service Canada, 2016). In Europe, there are numerous countries that have means test for various benefit programs. For a review and discussion of these, see, for example, Sainsbury and Morissens (2002). For developing countries, targeting has been reviewed by van de Walle (1998), while Nelson (2007) undertakes analysis of the vulnerability of social insurance in the presence of means tests in 18 countries. Chomik et al. (2015) provide a review of means testing of the age pension for selected OECD countries and report results for variations in implementation for Australia. More detail on national pension systems for OECD countries, including means testing, is available in OECD (2015). 4.2.2.1 Australia’s Age Pension—Subject to Income and Assets Tests

The Australian age pension is provided to all residents (with appropriate residency) who have reached the eligibility age (currently increasing gradually from 65 to 67 years) and who satisfy the means test. The means test comprises two separate tests—an income test and an assets test—and the binding test applies, meaning that both tests must be satisfied to be eligible for the age pension. The income test specifies the definition of the testable income, the maximum pension that is paid provided that the testable income does not exceed a specified income threshold, and the taper rate by which the pension payment is linearly reduced as income exceeds the threshold. Accordingly, there is an income above which the pension payment is zero. The assets test has an analogous

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structure: a definition of assessable assets, a threshold asset below which the full pension applies, and a taper rate by which the pension payment is reduced linearly as assessable assets exceed the threshold.k The income test and assets test combine to yield the following means-tested pension payment Pðy,aÞ ¼ min fP y ðyÞ,P a ðaÞg, where Py(y) is the pension payment under the income test and Pa(a) is the pension payment under the asset test. The pension payment is thus determined by the binding means test. The income test may be expressed as 8 m 0  y  y1