Population and Economic Change in Developing Countries 9780226180250

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Population and Economic Change in Developing Countries

A Conference Report Universities-National Bureau Committee for Economic Research Number 30

National Bureau of Economic Research

Population and Economic Change in Developing Countries Edited by

Richard A. Easterlin

The University of Chicago Press

Chicago and London

The University of Chicago Press, Chicago 60637 The University of Chicago Press, Ltd., London © 1980 by the National Bureau of Economic Research All rights reserved. Published 1980 Midway Reprint edition 1987 Printed in the United States of America

ISBN 0-226-18027-1

National Bureau of Economic Research Arthur F. Burns, honorary chairman James J. O'Leary, chairman Eli Shapiro, vice-chairman Martin Feldstein, president

Charles E. McLure, Jr., vice-president Charles A. Walworth, treasurer Sam Parker, director of finance and administration

Directors at Large Moses Abramovitz Atherton Bean Andrew F. Brimmer Otis F. Brubaker Arthur F. Burns George T. Conklin, Jr. Solomon Fabricant Martin Feldstein

Eugene P. Foley Edward L. Ginzton David L. Grove WaIter W. Heller Walter E. Hoadley Roy E. Moor Geoffrey H. Moore James J. O'Leary

Peter G. Peterson Robert V. Roosa Richard N. Rosett Bert Seidman Eli Shapiro Arnold M. Soloway Stephen Stamas Lazare Teper

Directors by University Appointment Gardner Ackley, Michigan G. L. Bach, Stanford Charles H. Berry, Princeton Otto Eckstein, Harvard Walter D. Fisher, Northwestem John H. Kareken, Minnesota J. C. LaForce, California, Los Angeles Robert J. Lampman, Wisconsin

Maurice W. Lee, North Carolina James L. Pierce, California, Berkeley Almarin Phillips, Pennsylvania Lloyd G. Reynolds, Yale Robert M. Solow, Massachusetts Institute of Technology Henri Theil, Chicago William S. Vickrey, Columbia

Directors by Appointment of Other Organizations Eugene A. Birnbaum, American Management Associations Carl F. Christ, American Economic Association Robert G. Dederick, National Association of Business Economists Stephan F. Kaliski, Canadian Economics Association Franklin A. Lindsay, Committee for Economic Development Paul W. McCracken, American Statistical A ssociation

Douglass C. North, Economic History Association Rudolph A. Oswald, American Federation of Labor and Congress of Industrial Organizations Charles A. Walworth, American Institute of Certified Public Accountants G. Edward Schuh, American Agricultural Economics Associatic 11 James C. Van Horne, American Finance Association

Directors Emeriti Percival F. Brundage Emilio G. Collado Frank W. Fetter Thomas D. Flynn

Gottfried Haberler Albert J. Hettinger, Jr. George B. Roberts Murray Shields

Boris Shishkin Willard L. Thorp Joseph H. Willits Theodore O. Yntema

Since this volume is a record of conference proceedings, it has been exempted from the rules governing critical review of manuscripts by the Board of Directors of the National Bureau (resolution adopted 6 July 1948, as revised 21 November 1949 and 20 April 1968).

Universities-National Bureau Committee for Economic Research This committee is a cooperative venture of universities and the National Bureau. Its guiding objective is the encouragement of economic research on problems susceptible of objective treatment and of sufficiently broad scope to merit attention by institutions serving a scientific and public interest.

Participating Universities and Their Representatives Brown, Jerome L. Stein California (Berkeley), Daniel McFadden California (Los Angeles), J. C. La Force California (San Diego), Robert E. Engle Carnegie-Mellon, Edward C. Prescott Chicago, Lester G. Telser Columbia, Robert Mundell Cornell, S. C. Tsiang Duke, T. Dudley Wallace Harvard, John V. Lintner Illinois, Robert Resek Indiana, Franz Gehrels Iowa State, Dudley G. Luckett Johns Hopkins, Carl F. Christ Maryland, Barbara Bergman Massachusetts Institute of Technology, Richard S. Eckaus McGill, Alex G. Vicas Michigan, Harold T. Shapiro Michigan State, Victor Smith Minnesota, James M. Henderson

New School for Social Research, Thomas Vietorisz New York, M. Ishaq Nadiri New York State (Buffalo), Daniel Hamberg North Carolina, Henry A. Latane Northwestern, Robert Eisner Ohio State, Donald O. Parsons Pennsylvania, Jere R. Behrman Pittsburgh, S. H. Chou Princeton, Edwin S. Mills Purdue, Patric H. Hendershott Queen's, Martin F. J. Prachowny Rochester, Walter Y. Oi Stanford, Moses Abramovitz Texas, Samuel L. Myers, Jr. Toronto, Richard Bird Vanderbilt, Anthony M. Tang Virginia, Richard T. Selden Washington (Saint Louis), Hyman Minsky Washington (Seattle), Richard W. Parks Wisconsin, Leonard W. Weiss Yale, Richard Ruggles

National Bureau of Economic Research Representative Robert E. Lipsey

Members at Large Irma Adelman Bela A. Balassa Carl E. Beigie

Daniel Creamer Frank de Leeuw

Walter S. Salant George J. Stigler

The officers of the Universities-National Bureau Committee are: Edwin S. Mills, chairman; Leonard W. Weiss, vice-chairman; and Christine Mortensen, secretary. The members of the Executive Committee are: Irma Adelman, Richard Bird, Robert Eisner, Robert E. Lipsey, Dudley G. Luckett, Edwin S. Mills, and Leonard W. Weiss.

Contents

Prefatory Note Introduction

ix

Richard A. Easterlin

1.

Child Costs and Economic Development Peter H. Lindert Comment: Eva Mueller

2.

Toward a More General Economic Model of Fertility Determination: Endogenous Preferences and Natural Fertility Richard A. Easterlin, Robert A. Pollak, and Michael L. Wachter Comment: Harvey Leibenstein Comment: Warren Sanderson

3.

4.

vii

Child Mortality and Fertility: Issues in the Demographic Transition of a Migrant Population Yoram Ben-Porath Comment: Etienne van de Walle Comment: Anne D. Williams

1 5

81

151

An Economic Interpretation of the Decline in Fertility in a Rapidly Developing Country: Conse209 quences of Development and Family Planning T. Paul Schultz Comment: Ronald Freedman Comment: Riad Tabbarah

viii

5.

6.

7.

8.

9.

Contents Causes and Consequences of Mortality Declines in Less Developed Countries during the Twentieth Century Samuel H. Preston Comment: John Durand Comment: Victor R. Fuchs Comment: Richard W. Parks Internal Migration in Developing Countries: A Survey Michael P. Todaro Comment: Gary S. Fields Comment: Robert J. Willis Interactions of Economic and Demographic Household Behavior Allen C. Kelley Comment: Warren C. Robinson Comment: Julian L. Simon Comment: Paul Demeny Recent Population Trends in Less Developed Countries and Implications for Internal Income Inequality Simon Kuznets Comment: Albert Fishlow A Historical Perspective on Economic Aspects of the Population Explosion: The Case of Preindustrial England Ronald Demos Lee Comment: Nathan Keyfitz Comment: Marc Nerlove

289

361

403

471

517

List of Contributors

567

A uthor Index

571

Subject Index

574

Prefatory Note

This volume contains the papers presented at the Conference on Population and Economic Change in Less Developed Countries held in Philadelphia 30 September to 2 October 1976, sponsored by the UniversitiesNational Bureau Committee for Economic Research. Funds for the conference were provided by the National Science Foundation; we are indebted for its support. We also thank Richard A. Easterlin, who served as chairman of the conference and editor of this volume.

Executive Committee, October 1976 Edwin S. Mills, chairman Irma Adelman Richard Bird Robert Eisner Dudley G. Luckett Leonard W. Weiss Robert E. Lipsey, NBER representative

ix

Introduction Richard A. Easterlin

The concerns behind the papers in this volume are as old as economics itself. Like the present authors, the classical economists wrestled with the causes and consequences of population change in the course of economic development. What is different here is the absence of simple answers. To some this will be a disappointment, but to others it will seem a mark of progress. In the study of population, as in many other areas of economic inquiry, growing awareness of the variety of human experience has had a chastening effect. What is common to the papers assembled here-as befits an NBER volume-is a respect for facts and an effort to match theory with reality. Peter Lindert's study "Child Costs and Economic Development" provides an appropriate point of departure. It starts with the most challenging subject in the whole field of population, which appears and reappears throughout this volume, the "demographic transition"-the shift from high to low mortality and fertility repeatedly observed in the history of developing areas. It focuses on the possible role in this transition of the variable most natural to an economist's viewpoint, the cost of children. Lindert utilizes the sophisticated theoretical notion of cost that has emerged particularly from recent advances in what has been called "the new home economics." Unlike most of this work, however, Lindert's paper takes seriously the problem of measuring costs, thus fusing theory and measurement. Lindert's paper, in its stress on cost considerations in fertility determination, conforms to economic orthodoxy. The paper by Easterlin, Pollak, and Wachter, while not rejecting the possible relevance of costs, Richard A. Easterlin is associated with the Population Studies Center, University of Pennsylvania.

1

2

Richard A. Easterlin

advances, so far as economists are concerned, some less orthodox views -the need in the study of fertility behavior for fuller attention to determinants of preferences, and to factors relating to the fecundity or reproductive capacity of women. A broader framework encompassing such factors is presented. This framework, the authors claim, makes more tractable such problems as the postwar American baby boom and the variability of fertility in less developed countries. Perhaps most disturbing to orthodox economic precepts is the argument and evidence advanced that in many times and places, observed fertility is not a product of deliberate choice. In the standard formulation of the demographic transition, the decline in mortality leads that in fertility. Causal inferences have frequently been drawn from this pattern-for example, that if, in a regime of high mortality, parents view high fertility as necessary to compensate for child deaths, a reduction in child mortality will reduce the fertility required for replacement purposes. Yoram Ben-Porath's paper makes it clear that the possible analytical links between child mortality and fertility are much more complicated than this simple replacement notion suggests. The Israeli immigration experience, providing a dramatic change in the environment of different population groups, offers an unusual opportunity to explore some of the issues, drawing on both cross-sectional and time-series data. Of special interest is the comparison between immigrants of Afro-Asian origin and those of European origin. Most empirical research on the economics of fertility in the last decade has focused on developed countries. The paper by T. Paul Schultz seeks to adapt a widely used "value of time" model to the experience of a less developed country undergoing the demographic transition. Schultz sets himself a more ambitious goal than the usual cross-sectional explanation-he seeks to account for the actual declines over time in age-specific fertility rates. Supporters of this model will be pleased at the consistency of his results with prior research on the relation of fertility to husband's and wife's education. As Schultz carefully notes, however, interpreting education's effect solely in terms of the "price of time" is questionable, and we need to get directly at the mechanisms by which education influences fertility. The central issue in the first four papers is the determinants of human fertility. Although the revival of economic research on this topic is new -dating only from the 1950s-economic research on mortality is even newer. Samuel Preston's paper is one of a few recent attempts to apply economic analysis to the study of mortality. The result is impressive. In the subject of economic growth a standard conceptual approach is to partition the growth in productivity into movements along a "production function" and shifts in the "production function" itself, these shifts often being identified with technological change. Preston utilizes an analogous

3

Introduction

framework to derive a quantitative answer to an issue that has long beguiled students of mortality-the comparative roles in life expectancy improvement of higher per capita income (movement along a function) and improvements in public health and medicine (shifts in the function due to "technological change" in the biomedical area). Whether or not Preston's specific answer stands up to future scrutiny, his paper represents an important breakthrough from qualitative speculation to quantitative analysis of this problem. Michael Todaro's study shifts attention to the remaining component of population change, migration. Here the volume enters terrain more customary for economists. Todaro provides a major service in distilling the extensive migration-model literature, summarizing the results of empirical tests, and, on the basis of this, identifying major priorities for research on internal migration. With the paper by Allen Kelley, the volume turns its primary focus from the causes of population change to its effects. Kelley's paper deals specifically with the effects of alternative family sizes and structures on saving and income in urban Kenya. One might suppose that investigation of such effects of demographic variables would require no more than -harvesting the results of earlier work, for there is a long history of economic speculation on such topics. But that is the catch-economic speculation, yes; systematic empirical study, no. Whereas econometric study has become the hallmark of most areas of economic research, questions of the effects of population change have heretofore been left largely to a priori theorizing. Kelley's paper represents an important departure-a rejection of preconceived answers and an attempt to match theory to the facts. This includes an attempt to recognize the possible interdependence between household decisions about saving and fertility. As with Preston's paper, Kelley's contribution lies not only in the specific answers he obtains, but in the approach he suggests for future research on the subject. In contrast to Kelley's paper, where the approach is new but the problem is old, Simon Kuznets's paper takes up a subject that economists (the classical economists aside) have seriously neglected-the distributive implications of demographic change. That developing nations experience a demographic transition is well established; surprisingly little thought, however, has been given to the effects of this transition on income inequality within a country. Kuznets's concern is whether the size and incidence by class of the dramatic mortality and fertility declines during the demographic transition tend to heighten or reduce income inequality. As befits a pioneering venture on this topic, his paper is particularly concerned with establishing the facts, and in so doing it identifies important gaps in empirical knowledge. It also offers some suggestive speculations on the subject, some of which challenge one's initial predilections.

4

Richard A. Easterlin

Ronald Lee's paper is perhaps the most ambitious one in the volume, for it seeks to bring together causes and effects of population change in an econometric model of economic-demographic interrelations. The empirical focus is premodern England, and the question is whether there may have been a self-regulating mechanism that made for a balance between population and economic resources. If, for example, an exogenous decline in mortality set in motion more rapid population growth, did the economic effects of this growth feed back on fertility or mortality in a way that brought population growth to a halt? Although his results are not necessarily definitive, Lee shows how theory and data may be used to move such questions from speculation to serious analysis. He notes that international economic interdependence and rapid technological change in the contemporary world caution against automatically extending his results to today's less developed areas. In the original conference plan, each paper was to be written by an economist and commented on by both an economist and a demographer (the two categories, of course, are not wholly mutually exclusive). The intent was to retain in some degree the interdisciplinary flavor of a predecessor U-NBER conference on population and economic change (in developed countries) some two decades ago. As it turns out, there is less representation of demographers' views in this volume than was hoped for, but the distinctive flavor of their contribution is well illustrated in several comments. To speed publication, the editorial committee precluded authors' replies. This committee, the same as the conference planning committee, consisted of Allen Kelley, T. Paul Schultz, Robert Willis, and Richard A. Easterlin, chairman. Christine Mortensen provided extensive help in organizing the conference, which was held at the University of Pennsylvania Population Studies Center, 30 September through 2 October 1976. As a whole the papers and accompanying comments demonstrate what economics brings to the study of population-new theoretical ideas, greater logical consistency, fuller perception of interrelations, more precise specification of problems, and a methodology that fosters confrontation of theory and the quantitative record. If one takes the earlier conference volume as a benchmark, the papers show that economic research on population has moved from fledgling status to become full grown. One may note, too, a growing sensitivity of economic research to the value and importance of demographers' contributions.

1

Child Costs and Economic Development Peter H. Lindert

1.1

The Delayed Fertility Transition

Many who are concerned about rapid population growth in developing countries have hoped and expected that economic development would be an effective contraceptive. If it is, then population policy can confine itself to the libertarian stance of subsidizing family-planning propaganda and contraceptive means. While experience has shown that family-planning programs achieve only very modest fertility reductions when large families are desired, the task of reducing desired family size might be left to policies aimed at economic development. By fostering education, industrialization, income growth, and female employment outside the home, general development policies may be a prompt and efficient way to cut fertility. But if economic development fails to bring prompt and sustained fertility reductions, developing countries will have more reason to consider tougher antinatal measures, such as Singapore's stiff birth disincentives of 1972-73 or, beyond them, compulsory sterilization. The social costs of these measures would have to be weighed against the perceived social-insurance benefits of faster fertility reduction as a means of lessening congestion and income inequality. Peter H. Lindert is Professor of Economics at the University of California at Davis. The author wishes to thank Michael R. Haines, Allen C. Kelley, Barry M. Popkin, Bryan Boulier, Dov Chernichovsky, and Kathryn E. Walker for their help in making available several sets of survey data for this study. Also gratefully acknowledged is the financial support of the Rockefeller Foundation, the Population Council (with funds from the United States Agency for International Development), the Institute for Research on Poverty at the University of Wisconsin (United States Office of Economic Opportunity), and the University of Wisconsin Graduate School for the earlier United States-related portions of this research.

5

6

Peter H. Lindert

There is a consensus that economic development ultimately prevents births, both by improving the supply of contraceptive means and by raising the perceived costliness of extra children. Ignoring George Stigler's lemma that "there are not ten good reasons for anything," we rattle off long lists of well-known reasons why economic development makes children seem more costly and less of an economic asset.! Economic development pulls women out of the home, giving them a greater sense of control over their lives, greater access to contraceptive information, and a heightened sense of the earnings they stand to lose by having children. Economic development pulls older children out of jobs and into school, thus cutting their direct economic contribution to their parents' households. It also raises couples' awareness that social mobility depends on per capita family expenditures that would be dragged down by the arrival of extra children. Their "consumer aspirations" are raised, both by income growth itself and by greater exposure to new luxury goods. This exposure is fostered by the migration from farm to city, by industrialization, and by education. Children become less valuable as insurance of old-age support as the development of asset markets and social security gives parents cheaper ways to assure themselves that support. Greater geographic mobility replaces the extended family with the nuclear family, raising the cost and difficulty of arranging for supplementary child care. Meanwhile, reductions in infant and child mortality cut the number of births necessary to achieve any desired number of surviving children. The individual arguments linking fertility decline to economic development through child costs are not always well spelled out, or documented, or logically aligned with each other-a shortcoming that will be partly remedied here. But they are at least well agreed upon. Indeed, "economic" as these links may sound to some, their importance in explaining the secular fertility decline is not a subject that divides the disciplines. Much less resolved is the explanation of the earlier part of the fertility transition that most directly worries antinatal scholars and policy-makers in developing countries today. The secular fertility decline often begins rather late in the "development" or "modernization" process. Just how late depends on how one defines development and modernization. If the onset of development is signaled by a sustained drop in mortality, then the lag of the fertility decline behind the start of development is often long and highly variable. Figure 1.1 and table 1.1 remind us of this by returning to the varied chronologies of crude birthrates and death rates, the most available proxies for fertility and mortality rates across wide stretches of time and space. Among the early-developing countries, some had no lag between the onset of death rate decline and that of birthrate decline, whereas others

/

Fig. 1.1

o

/

/

/

Japan 1973

10

USA 1973

40

50

Crude birthrate per 1,000

1/

o

/

/

10

/

20,

30

/

/

/

Crude death rate per 1,000

40

/

/

/

Taiwan 1973

/

/

/

/

/

/

/

/

20

/

/

/

/

/

/

/

/

/

/

/

/

/

/

/

/

/

/

Taiwan 1920-24 /

/

/

Mexico / 1895-99 /

Crude birthrates and death rates in eight countries. Selected peacetime dates.

30

/

~\;) '"-

o be!) implies the existence of "excess" or "unwanted" fertility, as the term is used in the demographic literature. We utilize our generalized fertility model and the associated concepts of natural and desired fertility to classify societies or populations within societies into several categories. The categorization is useful in that it implies restrictions on the coefficients of the variables that appear in the optimal solution functions. Some groups, especially in less developed countries, may be at or close to their natural fertility levels. These groups can be divided into two subcategories. First there are those that lack the motivation to practice fertility regulation because desired fertility is greater than or equal to the optimal solution. Second, there are those, again largely in less developed countries, where the economic costs or preference drawbacks of fertility regulation outweigh the potential gains. In both these cases, the determinants of fertility are largely independe,nt of the preferences for children. "Demand models," with their emphasis on income and substitution effects, are not relevant. Although income might be a significant determinant of completed family size, its influence would be unintended and would work through improved nutrition and health, which would lead to increased fecundity and decreased infant mortality. Demand models tell a different story, typically suggesting that increases in income lead to an increase in the number of children demanded. For natural fertility societies, demand variables-correctly measured and interpreted-are insignificant. At the other extreme are groups, largely in developed countries, that can be approximated by the perfect contraceptive society. In this case, births and infant mortality technology functions are not quantitatively important determinants of the level of fertility. The properly specified optimal solution function now contains the preference parameters related to children and may reflect endogenous tastes and household technology, including those aspects concerning child-rearing, as well as the budget constraint. The general fertility model, which includes endogenous tastes and the births production function, has implications for a number of important demographic questions. We have already indicated its significance

8S

Toward a More General Model of Fertility Determination

for specifying the optimal solution function in different societies for different' time periods. It is of particular importance that the parameters of this function vary systematically in quantitative importance as one moves along the continuum from less to more developed economies and/or lower to higher socioeconomic classes within a society. Hence, elasticities of births and completed family size with respect to their arguments will vary systematically both across and within societies. We shall also indicate the model's implications for the analysis of the "demographic transition," long-run fertility swings, secular trends in fertility in both less developed countries and developed countries, and the welfare benefits of various types of fertility-control programs in different societies. At various points we contrast our analysis with the "Chicago-Columbia" approach, by which we mean the line of inquiry exemplified in two recent special issues of the Journal of Political Economy, since published as an NBER volume. 1 That there is a distinctive Chicago-Columbia approach to the economics of fertility hardly requires demonstration. In a review of the volume that brings together the JPE work, Allen Kelley observes that "the papers are ... largely of one voice, showing a common perspective to the analysis of economic problems and to a certain extent a mild intolerance of other approaches to viewing the world of social and economic behavior" (Kelley 1976, p. 517). As examples of spokesmen for the approach, one may cite T. W. Schultz (in his editor's introduction to the JPE volume), Michael Keeley (in a reply to a critique by Leibenstein), and T. P. Schultz (in several survey articles) .2 We shall draw particularly on the last two in comparing our framework with the Chicago-Columbia approach, because these articles provide valuable general discussions of that viewpoint. 3 The Chicago-Columbia approach is most simply characterized by what it emphasizes and deemphasizes. Particular emphasis is placed on cost factors and on the opportunity cost of a wife's time; little or no attention is given to taste factors and to the births production function (the latter relates to what T. P. Schultz calls "supply" factors). T. P. Schultz asserts that "cross-sectional studies of individual countries at all levels of development have confirmed the qualitative predictions of this rudimentary demand theory of fertility" (T. P. Schultz 1976, p. 98).4 Our main reservation about this line of work is that its deemphasis of tastes and "supply" factors severely limits its empirical relevance. For developed countries the model is of limited application because it ignores preference variables. This is most strikingly illustrated by the failure of the Chicago-Columbia approach to advance an explanation for the recent fertility swing in the United States. 5 For less developed countries, fitting a "demand" model to data for households whose fertility is largely uncontrolled leads to unwarranted inferences about "demand" elasticities.

86

Richard A. Easterlin/Robert A. Pollak/Michael L. Wachter

Furthermore, the subordination of taste considerations lends itself to dubious conclusions about economic welfare and public policy. Minimizing the importance of tastes makes it easier to draw unambiguous inferences about the desirability of policies aimed at reducing "unwanted" fertility, but the lack of attention to tastes make such inferences questionable. At the same time, the approach is unlikely to be helpful to those directing family planning programs, who must make choices between attempting to alter preferences (for example, by allocating resources to advertising the benefits of small families) and simply providing contraceptive information or cheaper services. Hence, we believe that both the analysis of fertility behavior and of the welfare effect of government programs requires a more balanced approach, one in which economic research on preferences and natural fertility takes equal place with the usual concerns of the Chicago-Columbia approach.

2.2

The Formal Model

In this section we develop a formal framework for analyzing marital fertility. We begin by summarizing the household production model, which provides the starting point for our analysis. In the three subsequent subsections we modify the household production model to incorporate a number of additional variables related to the determination of marital fertility and completed family size. In section 2.2.2 we incorporate the basic variables related to fertility into the household production model by adding two new "production" relations, a "births production function" and an infant mortality or "deaths function," and then describe two extensions of this model, one incorporating unperceived jointness (section 2.2.3) and the other interdependent preferences (section 2.2.4). By unperceived jointness we mean a situation in which the family does not correctly recognize the relationship between its fecundity and its consumption or life-style decisions. For example, an increase in nonlabor income might cause an unintended and unanticipated increase in births through the following chain of causation: the increase in nonlabor income causes an increase in consumption of health care services or food, which leads to an improvement in health or nutrition; these in turn cause an increase in fecundity. The essence of unperceived jointness is that the decision to devote additional resources to improved health or nutrition rather than shelter or recreation is made without awareness of its implications for fertility. By interdependent preferences we mean that the family's tastes are influenced by the consumption and family-sizt" decisions of other families. In the "socialization" version of the interdependent preferences

87

Toward a More General Model of Fertility Determination

model the family's tastes are influenced by the observed behavior of other families in the society, perhaps those in a suitably restricted socioeconomic group. In the "intrafamily" version, a family's aspirations for both commodity consumption and family size are influenced by the consumption and family-size patterns the husband and the wife experienced in childhood and adolescence. Our model provides a framework for analyzing a number of important aspects of fertility behavior, but it neglects a number of others. First, we deal exclusively with marital fertility. Second, we do not attempt to explain the determination of age at marriage. Third, our analysis is based on a single-period planning model in which the family makes a once-and-for-all decision about its consumption and fertility at the time of marriage. Those aspects of fertility behavior that are best understood in terms of a sequential decision-making model-for example, the timing and spacing of children-are beyond the scope of the analysis, although in principle it could be extended this way. Fourth, our model treats average fertility outcomes as if they were certain to be realized by the "representative family." That is, we ignore both the discreteness of children and the randomness of the births and deaths functions and focus on the mean experience of a group of identical families. In general, randomness and discreteness have implications for the average fertility of families who are not risk-neutral and whose behavior is therefore sensitive to the variance as well as to the mean outcome. Finally, we ignore the fact that children come in two sexes and that parents may have preferences for the sex composition of their families. Such preferences could be incorporated into a sequential model of fertility that recognized the role of uncertainty. In such a model one would expect sex preferences to influence family size, but such preferences cannot be incorporated into a one-period planning model in any straightforward way.G 2.2.1

The Household Production Model

In this section we introduce the standard household production model that serves as the basis for our subsequent discussion of fertility. The model is one in which the household purchases "goods" on the market and combines them with time in a "household production function" to produce "commodities.'" These commodities, rather than the goods, are the arguments of the household's preference ordering; market goods and time are desired not for their own sake, but only as inputs into the production of "commodities." The n market goods are denoted by X = (Xl> . . . X n ), and the m commodities by Z = (ZI, ... ZIIl), and the time allocation vector by t; the vector t records how much time each family member devotes to market work and to each household activity. Let R

88

Richard A. Easterlin/Robert A. Pollak/Michael L. Wachter

denote the household's preference ordering over commodity vectors, and U(Z) the corresponding utility function. s We represent the household's technology by a production set, T. Thus, the "input-output" vector (Z,X,t) belongs to the set T, (Z,X,t) E T, if and only if the commodity collection Z is producible from the goods collection X and the time-allocation vector t. We could distinguish those uses of time devoted to household production activities from those devoted to market work and include only the former as arguments of the household's technology, but it is harmless to include the entire vector, and we do so for notational convenience. Unless explicitly stated to the contrary, constant returns to scale and/or the absence of joint production are not assumed. If the household derives satisfaction or dissatisfaction from time spent at various household or market activities, the times devoted to these activities will appear as components of the vector Z as well as the vector t. Technically, this is a case of joint production, since, for example, time devoted to the activity "cooking" is both an input into the production of a "home cooked meal" and is itself one of the outputs of the activity "cooking"-an output that may yield a utility or disutility quite distinct from that associated with eating the meal itself. Because we have not ruled out joint production, there need not be a one-to-one correspondence between activities and commodities. We let tIt denote the total time available to household member h, and t"8 the time which he (or she) allocates to activity s. Thus, the family's time constraint may be written as s

_

~ t".

=

h= 1, ... ,H

tIl

.... =1

where S is the total number of market and nonmarket activities and H the number of household members. We distinguish between the set of market activities (M) and the set of household production or nonmarket activities (T). Thus, if Wit denotes the market wage rate of household member h, his earnings are H

given by

~ WIt

t"8 and the household's total earnings by

Nf.![

~

~

11 _-= 1

sf..1!

w" t"".

We let Jh denote the household's nonlabor income, and write its budget constraint in the form Jl

~ k=l

Pk Xk


0; F' (W) > 0 and F' (2) ~ o.

Holding Wand 2 constant, the function F can be simplified to read: (5)

F(~:,W, 2) = f (~:), where l'

2:: 0 for all values of E L between zero and one. " U

Substituting equations 4 and 5 into equation 2 yields the basic differential equation for urban labor force growth in the Todaro model, namely,

(6)

L" =

L II

r

+ LLn f ( LE,,). II

u

By then comparing the time path of this equation with the growth rate of urban employment, we can analyze the dynamic process of ruralurban migration and urban unemployment under differing assumptions about population and employment growth rates (see Todaro 1969 and 1971b, appendix). The main attribute of this mathematical model, however, is its rigorous demonstration that migration in excess of the growth of urban job opportunities not only is privately rational from the point of view of maximizing individual income but will continue to exist so long as the "expected" urban-rural real income differential remains positive. For any given relative real wage differential (W > I), there will exist some urban unemployment rate that will finally equilibrate urban and rural "expected" incomes. But if the relative wage differential continues to grow (as it has in most developing nations), and if real urban wages

371

Internal Migration in Developing Countries

are inflexible downward (as they have proved to be throughout the Third World), the rising rates of urban unemployment may never actually be able to exert their ultimate equilibrating influence on migration streams. On the contrary, continued and even accelerated rates of ruralurban migration will continue to exist simultaneously with these everhigher levels of urban unemployment. In summary, there are four essential features of the basic Todaro migration model: 1. migration is stimulated primarily by rational economic considerations of relative benefits and costs, mostly financial, but also psychological; 2. the decision to migrate depends on "expected" rather than actual urban-rural real wage differentials where the "expected" differential is determined by the interaction of two variables-the actual urban-rural wage differential and the probability of successfully obtaining employment in the urban modern sector; 3. the probability of obtaining an urban job is inversely related to the urban unemployment rate; and 4. migration rates in excess of urban job opportunity growth rates are not only possible but rational and likely in the face of continued positive urban-rural expected income differentials. High rates of urban unemployment are therefore inevitable outcomes of the serious imbalances of economic opportunities between urban and rural areas of most underdeveloped countries. 6.2.3

Modifications of the Basic Todaro Model

There have been a number of important modifications of the basic Todaro migration model since it first appeared as a Ph.D. dissertation in 1967. Many of these modifications were designed to introduce certain elements of reality into the migration process, elements that were assumed away or not taken into explicit account in the original Todaro model. But the basic features of the model remain intact, and they provide the framework for most contemporary econometric migration studies (see section 6.3 below). Among the major modifications of the original model, the following are perhaps among the most significant.

Harris and Todaro (1970) First, I and my colleague John Harris utilized and extended the basic Todaro framework to construct a two-sector internal trade model of migration and unemployment that permitted explicit attention to the impact of migration on rural incomes, urban and rural output, and total social welfare (Harris and Todaro 1970). The two sectors are the permanent urban and the rural; for analytical purposes they are distinguished from the viewpoint of production and incomes. Thus it is

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Michael P. Todaro

assumed that the rural sector specializes in the production of agricultural goods, part of which are traded to the urban sector in return for the manufactured goods in which that sector specializes. It is assumed further that the rural sector has a choice of using all available labor to produce agricultural goods, some of which are traded for urban manufactured goods, or using only part of its labor to produce food while "exporting" the remaining labor to the urban sector (through migration) in return for wages paid in the form of manufactured goods. Thus it is assumed that the typical migrant retains his ties to the rural sector. The income he earns is assumed for analytical purposes to accrue to the rural sector. Such an assumption is clearly more valid for most African countries than it is for Asia or Latin America, where migrant ties to the rural sector are less pronounced. Although these assumptions about intersectoral linkages enable Harris and Todaro to assess the welfare and distributional consequences of migration, they are not necessary for demonstrating the private rationality of continued migration in the face of rising urban unemployment. The crucial assumption for this proposition is once again my hypothesis that rural-urban migration will continue so long as the "expected" urban real income (the wage times the probability of finding a job) exceeds real agricultural income at the margin-that is, potential rural migrants behave as maximizers of expected utility. The complete Harris-Todaro model, then, represents a simple extension of traditional two-sector neoclassical trade models. Thus there are variable proportions agricultural and manufacturing production technologies for the rural and urban sectors, neoclassical behavioral rules for the determination of levels of factor use and output in each sector, and a traditional trade-theory mechanism for determining the terms of trade between agricultural and manufactured goods. But it is the migration equation that represents the unique, most innovative feature of the overall model. Harris and Todaro then utilize their internal trade with migration model to draw out a number of policy implications for developing countries. First, they evaluate the welfare effects (in terms of lost or gained output in each sector) of alternative urban employment policies -for example, uniform or sector-specific wage subsidies, urban demand expansion, and migration restriction (see Bhagwati and Srinivasan 1974, below, for a critique of some of this analysis). Second, and more important, they draw attention to the critical importance of urban wage determination, commodity pricing policies, and rural development programs on relative output levels, the terms of trade, and intersectoral labor allocation between sectors as a result of induced migration. Perhaps most important, the Harris-Todaro model shows that accelerated urban employment creation may actually increase levels of unemployment (see

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Internal Migration in Developing Countries

Todaro 1976b and below for a new theoretical specification and empirical formulation of this concept of induced migration). Finally, they demonstrate the conditions under which coercive restraints on migration can actually reduce the level of rural welfare. The mathematics of the Harris-Todaro model can be written as follows. Letting W Rand W" respectively represent nominal agricultural and urban wage rates, E u the number of urban jobs, and L" the urban labor force, expected urban income, E(W,,), can be written as:

(7)

E(W,,) = W"

~:.

Expected rural income, E (W R), is simply W R. The amount of ruralurban migration, M = L,,, is once again a function of the urban-rural expected wage differential, that is, (8)

The rural-urban equilibrium expected wage condition is then

(9) which becomes (10)

W W " XEll L- = R,

"

so that the Harris-Todaro model predicts as a first approximation an "equilibrium" urban unemployment rate given by: (11 )

1

-

E" -1 WR L" - W,,'

This prediction should not be taken literally; it is intended only to illustrate an inverse relationship between equilibrium unemployment rates and urban-rural expected wage differentials. While the combined Todaro/Harris-Todaro theoretical model does capture many of the most important labor market interactions between rural and urban sectors from the viewpoint of internal migration analysis, from an empirical or econometric estimation viewpoint the basic model clearly requires further modification and extension. The following are examples of such modifications and extensions. 7 Johnson (1971)

Johnson (1971) was one of the first to modify theoretically the basic Todaro/Harris-Todaro model by explicitly introducing variables for the rate of labor turnover and the possibility of the urban employed sharing their income with the unemployed through some form of extended family network. Thus Johnson defines the actual income in urban areas as

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Michael P. Todaro

+

(1 - a) W" aW"n for the employed and aW"n for the unemployed, where Wit is the urban wage rate, n is the urban employment rate, and a( < 1) is the proportion of the total wage bill that is shared with the unemployed (Johnson 1971, p. 22). Therefore, if p is the probability that an individual will be employed at a point in time, urban expected income at that time can be represented as: (12) Johnson also introduces into Todaro's basic job probability formulation a variable to reflect the rate of labor turnover in the urban modern sector. Rather than new job creation being simple g X EI/ (which assumes no labor turnover), the rate of new urban "hires" can be represented by

E" = g X E" + f3E where f3 is the rate of job turnover. Although f3 is probably much lower in developing nations than in de(13)

ll ,

veloped countries owing to the scarcity of urban-sector job opportunities and the fact that most people who quit do so only with the knowledge that another job awaits them, Johnson's introduction of a labor turnover variable does bring the probability formula of the simple Todaro model a bit closer to reality.

Bhagwati and Srinivasan (1974) Bhagwati and Srinivasan (1974) provide an extensive yet, on the whole, positive critique of the Harris-Todaro model, identifying some of its major policy conclusions, especially those relating to the migration and employment effect of various wage and production subsidy programs in both rural and urban areas. In particular, they point out that the Harris-Todaro conclusion that a (second-best) combination of an urban wage subsidy with physical migration restriction would be necessary to achieve economywide production efficiency is not correct since a best solution can be realized by a variety of different tax or subsidy schemes, without the necessity of physical restrictions on internal migration.

Cordon and Findlay (1975) Cordon and Findlay (1975) further extend the Harris-Todaro model by introducing intersectoral capital mobility between the rural and urban sectors in response to differentials in the return on capital. They also examine the comparative static effects of economic growth in both the original Harris-Todaro model and the modified model with perfect capital mobility and with commodity prices determined externally in an open economy framework. They then explore the policy implications of the

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Internal Migration in Developing Countries

modified model and reach a number of conclusions that both support and modify those derived by Harris and Todaro.

Fields (1975) One of the most extensive and useful modifications of the basic HarrisTodaro framework is that provided by Fields (1975). Fields uses the Harris-Todaro framework of quantity rather than wage adjustments as the principal equilibrating force in urban labor markets to consider four additional factors in the determination of equilibrium levels of urban unemployment in developing countries: (1) a more generalized description of the urban job search process in which a rural resident may have some positive probability of finding an urban job without first migrating to the city; (2) the existence of underemployment in the urban traditional or "informal" sector in which workers are not barred from searching for a modern sector job although their probability of success is lower than that of an unemployed worker who engages in full-time job search; (3) the likelihood that educated workers will be given preferential treatment in modern-sector job hiring; and (4) the recognition of labor turnover in a multi period urban framework and the likelihood of differential attitudes toward risk aversion among different migrants. He shows that each of these realistic extensions implies a lower equilibrium urban unemployment rate than that "predicted" by the simple Harris-Todaro expected wage gap model. On the basis of his analysis, Fields suggests three additional policy variables beyond those suggested by Harris and Todaro and Bhagwati and Srinivasan that may have an important effect on the volume of unemployment and underemployment in LDCs (p. 185). These include (1) the establishment of rural and urban labor exchanges designed to minimize the need for migrants to engage in costly (private and social) job search and thus to reduce the size of the urban informal sector, lower open unemployment, and raise national output; and (2) the (somewhat curious) recommendation that "overeducation of the labour force might have the beneficial effect of both lessening urban unemployment and increasing national income in both the rural and the urban areas" (p. 185). This paradox arises because more highly educated workers are selected first, thus reducing the probability that less-educated workers will successfully secure a modern sector job and thereby, through lower induced migration, reducing the number of potential migrants by more than the number of jobs taken by the better educated (via the Todaro induced-migration multiplier). Unfortunately, Fields does not take into account the "social costs" of overeducation, especially in terms of foregone job opportunities. The variables also include (3) the suggestion that it is job hiring rather than number of jobs that primarily influence worker's locational decisions. Fields shows, therefore,

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Michael P. Todaro

that "a small increase in the number of jobs has a much larger proportional effect on job hiring and induces substantial rural-urban migration and increases the rate of unemployment. Thus migration can be stemmed simply by not growing so fast" (p. 186). This last policy conclusion echoes the one in my original 1969 article but does not emphasize, as that article did, the concomitant importance of generating a more rapid rate of rural employment and output growth. Conclusions In spite of many significant modifications of the basic Todaro/HarrisTodaro model, it remains that its fundamental contribution-the idea that migration proceeds primarily in response to differences in "expected" urban and rural real incomes and that as a result of this the observed accelerated rates of internal LDC migration in the context of rising urban unemployment are not only a plausible phenomenon but in fact are entirely rational from the private "expected" income-maximization viewpoint of individual migrants-remains widely accepted as the "received theory" in the literature on migration and economic development (Fields 1975, p. 167; Jolly et al. 1973, pp. 13-16; Meier 1976, IV.C.1 ). This general acceptance at the "theoretical" level is reflected at the empirical level also by the widespread utilization of econometric migration functions that give explicit recognition to the "expected" income differential as one of the most important explanatory variables in the migration decision-making process. In the next section we look at this growing body of quantitative migration literature for a wide range of developing nations. 6.3

A Summary Review of Quantitative Migration Studies

Having set forth the general theoretical framework, we can now review and summarize the results of some completed migration studies. My main objective in this section is to determine what now seems to be known about migrant characteristics and the migration process in developing nations. This will allow us in the final section to delineate questions and issues that remain unanswered and therefore to suggest the most promising areas for future migration research. 6.3.1

Summary Results of the Nonrigorous Descriptive Literature

Our best sources of information on the range of descriptive migration literature for developing countries are the earlier comprehensive surveys by Brigg (1971,1973), Carynnyk-Sinclair (1974), and, most recently, those of Connell et al. (1975) and Lipton (1976). Descriptive literature on economic, sociological, and demographic migration for a wide range of countries in Latin America, Asia, and Africa was examined by Brigg,

377

Internal Migration in Developing Countries

Carynnyk-Sinclair, Connell, and Lipton, and on the basis of these and other surveys (e.g., Byerlee 1974) the following generalizations can be made. Who Migrates?

As I pointed out earlier, migrants typically do not represent a random sample of the overall population. On the contrary, they tend to be disproportionately young, better educated, less risk-averse, and more achievement-oriented and to have better personal contacts in destination areas than the general population in the region of out-migration. 8 In Africa, the problem of migrant "school leavers" is widespread (Byerlee 1974; Caldwell 1969; Rempel 1971). Although many migrants are unskilled, landless peasants, especially in Asia (Lipton 1976), many others possess job-transferable skills, have increasingly more years of schooling, and have some regular source of financial support for the period immediately following migration (Todaro 1971a; Barnum and Sabot 1975b; Schultz 1975). Although single men still appear to dominate the migration streams in Africa and Asia (Connell et a1. 1975), married men (many accompanied by their families) and single women are now more prevalent in Latin American migration patterns (Brigg 1971; Herrick 1971) . Why Do People Migrate?

The overwhelming conclusion of almost all migration studies, both descriptive and econometric, is that people migrate primarily for economic reasons. The greater the difference in economic opportunities between urban and rural regions, the greater the flow of migrants from rural to urban areas. While distance is usually a significant intervening obstacle, its negative influence can be largely offset by sizable income differentials, especially for the more educated migrants (Barnum and Sabot 1975b; Schultz 1975; Lipton 1976). In addition to the primary economic motive, people migrate (1) to improve their education or skill level (also ultimately an economic motive); (2) to escape social and cultural imprisonment in homogeneous rural areas; (3) to escape rural violence (Colombia) and political instability; and (4) to join family and friends who have previously migrated to urban areas. Few studies seem to support the often-heard hypothesis that migrants are attracted to cities in search of better entertainment or "bright lights." What Are the Economic Effects of Migration on Source and Destination Areas?

The quantitative evidence necessary to begin to answer this most crucial of all questions is almost nonexistent in both the descriptive lit-

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Michael P. Todaro

erature and most econometric studies. It is thus a major pnonty for future research. While there is no absence of hypotheses and conjectures about the relationship between migration and, say, rural development, such hypotheses are yet to be supported by anything more than casual empirical evidence (e.g., see Lipton 1976). As I pointed out earlier, internal migration was traditionally viewed as socially beneficent. Workers were shifted from low-productivity, labor-surplus source regions to high-productivity, labor-scarce destination areas. Seasonal migrants were able to supplement their incomes by short-term "circular" migration in accordance with seasonal variations in labor requirements (Elkan 1960, 1967). If real wages were imbalanced between two locations, the neoclassical price-adjustment model dictated that in-migration would work to restore the balance by raising rural average incomes and lowering urban wages. More recently, internal migration has been viewed less sanguinely, especially with regard to its effects on rural productivity and income distribution (Lipton 1976). Rural-urban migration also appears to be accelerating in spite of rising levels of urban unemployment and growing numbers of "urban surplus" workers (Sabot 1975b). Rather than adjusting downward to rising unemployment, however, urban wage levels continue to rise, mostly as a result of institutional rather than competitive economic forces (see, for example, House and Rempel 1976 for evidence from Kenya). While most studies show that individual migrants appear to be behaving in a privately rational manner, many observers now believe that internal migration adversely affects the welfare of source areas (primarily rural) (see Lipton 1976; Connell et al. 1975; Schultz 1976; for a counterargument, however, see Griffen 1976). On the other hand, such migration seems to be contributing little, if anything, to expanded social welfare in destination areas (mostly urban) (Harris and Sabot 1976; Todaro 1976c). But, in spite of the growing acceptance of this "new view" of the contemporary relationship between internal migration and rural and urban development, little empirical evidence to convincingly support or refute this view can be gleaned from the descriptive migration studies reviewed in the Brigg, SincLair, Connell, and Lipton surveys or in other descriptive studies. Clearly, more carefully designed econometric studies are required to test alternative hypotheses about the "net" social effects of internal migration on both source and destination areas. We turn finally to the limited but growing number of technically sophisticated econometric migration studies that have recently begun to emerge to see if anything more can be learned. 6.3.2

A Survey of Recent Econometric Migration Literature

Yap (1975) has provided one of the most extensive reviews of the limited but growing econometric literature on internal migration in de-

379

Internal Migration in Developing Countries

veloping countries. The econometric studies examined by Yap cover Ghana (Beals, Levy, and Moses 1967), Kenya (Huntington 1974), and Tanzania (Barnum and Sabot 1975b) in Africa; Colombia (Schultz 1971), Brazil (Sahota 1968), and Venezuela (Levy and Wadycki 1972, 1973, 1974) in Latin America; Taiwan (Speare 1971) and India (Greenwood 1971a,b) in Asia; and Egypt (Greenwood 1969) in the Near East. More recently, the following studies (not included in the Yap survey) have been completed: Kenya (Knowles and Anker 1975; House and Rempel 1976); Tunisia (Hay 1974); Venezuela (Schultz 1975); Costa Rica (Carvajal and Geithman 1974); and Peru (Falaris 1976). All the above are cross-sectional studies, although Barnum and Sabot utilize both cross-sectional and time-series data. Most explain point-topoint migration, usually between states or regions, although the studies by Barnum and Sabot, Huntington, Knowles and Anker, and House and Rempel deal specifically with rural-urban migration. All except the Taiwan and Tunisia studies consider aggregate flows between areas, and most utilized census data (again with the notable exceptions of Barnum and Sabot, Huntington, Knowles and Anker, and Hay). Most deal with male migration only. With the exception of Hay's microprobability function for Tunisia explained earlier, all are "macro" migration functions. They typically are specified in logarithmic form, the basic general formulation being:

i = 1,

;=l,

,n ,n

where, as before,

M ij

p; = Y

rate of migration from i to j expressed in terms of the population in i

= wage or income levels

V = unemployment rates Z = degree of urbanization dij

= distance between i and ;, and

Cij

= friends and relatives of residents of i in destination,

j.

A capsule description including regression results for the studies of Tanzania, Venezuela, India, and Kenya is given in table 6.1. The following is a summary of the major findings of these studies. The Importance of Income and Employment Differentials

As might be expected, all of the above-cited econometric work demonstrates once again the overwhelming importance of economic variables in explaining migratory movements. Differences in average income or

380

Michael P. Todaro

Table 6.1

Partial Income Elasticities, Migration Functions for Men: Selected LDCs

Dependent variable a

Tanzania Kenya Barnum Huntington and Sabot (1975a)b (1974)

Venezuela Venezuela Levy and India Wadycki Greenwood Schultz (1975)d ( 1971a)e (1972)

M ij

M ij

PiP j

Destination wage (W j ) +6.79* (4.61 ) Wage (W j ) -1.15* (2.69)

Origin wage

M ij

M ij

Pij

p;-

Pi

+ 1.26*

+0.94* (2.59 )

+0.56* (2.02)

1.83* (4.33 )

-0.56

-0.85* (2.32)

-1.24* (4.48 )

-.857* (1.96 )

P ii

Sources: Schultz (1975, table Sa); Yap (1975, table 3). *p ::; .05. aDefinitions: M ij : Migration from place i to j. P., P j : Population in place i, k, respectively.

bBarnum and Sabot estimated a linear function, using lifetime earnings, undiscounted. The elasticities are calculated at the mean of the variables, using the income coefficients, .0024 (destination income), and - .0070 (origin income). eGreenwood's dependent variable is M 29

Urbanization

Percentage in Indicated Categories 36.2

/IV

12.8 .2

17.4 .2

*Significant at least at the .05 level.

Consumer durables are considered as current consumption. There is no feasible way to estimate the rate of depreciation of the household's stock of consumer durables. The treatment of consumer durables as current consumption, while not entirely satisfactory, is widely employed in these types of household studies, given the above-mentioned data constraints. 50 Total Saving (S*), which combines financial saving with human capital investments in education (school fees, school uniforms, books), broadens the concept of household capital accumulation and is justified by considering educational expenditures as in part an investment in a producer durable. While the analytical distinction between education as current or future consumption and as investment in an income-earning asset has been clearly delineated by Theodore Schultz and others, empirical estimates of the share of education which is consumption and that which is investment have been meager. This study will therefore examine the two extreme cases: one in which education is entirely a consumption good (whether current or future consumption); and one in which education is entirely a producer durable. In advanced countries, the consumer durable motivation plausibly dominates. In lower-income countries, educational expenditures are also likely to be influenced by investment motivations. Education, especially more advanced levels such as high school and college, is a luxury good, given the closeness of many households to a subsistence level of consumption. Moreover, the rate of return on education is high, making it an attractive form of investment. 51 Measured financial saving in Kenya is small, 7 shillings per household per period, or about 1% of average household income. As in most household surveys of this type, saving is likely to be underestimated. When human capital investments are added, the saving figure rises to 36 shillings, or 5% of average household income. In both measures the variation is large. This variation is explained in part by real factors and in part by notable measurement errors common both to the measurement of saving and to any measure formed as a residual of two large elements.

420

Allen C. Kelley

Education (Eip , E iS ) is classified into three categories: less than completed primary education, completed primary education (EiP ) ' and some secondary or university education (E iS )' Kenyan education is divided into three levels: primary (standards 1-8), secondary (forms I-VI), and university. There is at present an insufficient supply of secondary and university facilities, given the fee schedule. As a result, students can advance to higher education levels solely by passing various standardized examinations. Only a small fraction of college-age students are admitted to the university. Because there were only seven households in our sample that had a member with any university education, considerations of statistical estimation reliability dictated that we collapse the secondary and university levels into a single category. 52

7.4

Econometric Considerations

The models considered in this study are interactive in nature; that is, they represent a household paradigm where key decisions are simultaneously made. 53 Two-stage least-squares regression analysis is therefore employed throughout. 7.4.1

Nonlinear Estimation

The basic disaggregated model of household behavior summarized in equations 1-3 is nonlinear in the parameters. This results from the nonlinear association between the variables children ever born and age of mother. To estimate this model, nonlinear regression procedures were employed. After some experience with these procedures, it was decided that the benefits of the precision of nonlinear estimation were far outweighed by the costs, especially by comparison with a simpler and almost as satisfactory estimation method whereby the nonlinear relationship was linearly transformed into two straight-line segments. 54 Our a priori expectations with respect to the nonlinear association between children ever born and age of mother are presented by the solid line in figure 7.1. Initial estimates that employed nonlinear regression procedures in fact provided estimates of this relationship that conformed to these expectations. Namely, completed family size is reached rather rapidly after childbearing begins and approaches an upper limit in the middle to later years of life, owing to the onset of female sterility. A linear approximation to this hypothesis is presented by the two broken line segments in the figure. The linear approximation is obtained by defining a dummy variable D that takes on a value of zero below a specified age A *t and a value of unity thereafter. The regression equation represented by figure 7.1 would therefore be written as Ceb = a f3D yA t OAt X D E. The line segment to the left of A *t has an intercept of a and a slope of

+

+

+

+

421

Interactions of Economic and Demographic Household Behavior Ceb=g[A f • D'A f • D], D=O, A f

~

2::

34

•

>-

"c: '" ~ '" 1:3

• 32

•

2 .:;

••

30

o

2

.4

.6

.8

Rate of Change of Population (percentage per year)

Fig. 9.5

Population growth rates and life expectancy of the British aristocracy, by twenty-fIve-year periods 1550-74 to 17001724.

This is strong support for the view that population growth rates varied independently, not primarily in response to changes in wages or the demand for labor (for formal tests of these hypotheses see Lee 1973, 1978a, b). But how then are we to explain the broad historical agreement of economic and demographic trends? In subsequent sections I will discuss in more detail the mechanisms thought to have regulated population in relation to resources in preindustrial Western Europe and attempt to reconcile the dependent and independent aspects of population change. 9.3.2

Fertility and Mortality

The Preventive Check To the extent that European societies controlled population, it was almost entirely through regulation of fertility, not mortality. The conventional view of the mechanism linking fertility to resources in preindustrial Western Europe has not changed in broad outline since Malthus: Marriage required a sufficient livelihood, in the form of property or an adequate wage income. "Sufficiency" was defined by longstanding norms and institutions, which varied from country to country. Thus Malthus thought that the English were more prosperous than other Europeans because they regarded wheat and meat as necessities and would not

537

Perspective on Economic Aspects of the Population Explosion

marry without income enough to provide them for their families. Europeans in general were regarded as more prosperous than other peoples because they required more comfortable circumstances before they were willing to marry. Once married, couples were believed to bear children at a "natural" rate, while making no efforts to control family size. Such a system would relate aggregate fertility rates to per capita income or wealth, and to wage rates. Whereas historical demographers have confirmed the general outline of the natural fertility theory, a number of studies have shown that in the eighteenth and nineteenth centuries, at least, marital fertility as well as nuptiality responded positively to the harvest cycle. There is also some mixed evidence that on balance suggests that wealthier couples may not only have married earlier, but also have had higher fertility within marriage (see Smith 1977). The Cambridge Group's aggregate parish register data set makes it possible to analyze the effect on vital rates of short-run variations in the real wage. It provides series of the annual numbers of baptisms, burials, and marriages in 404 parishes from 1539 to 1839. In theoretical work described elsewhere (Lee 1975, 1978a) I have shown that short-run fluctuations in such series can be interpreted as fluctuations in marital fertility, mortality, and nuptiality. This enables us to draw demographic inferences from changes in the numbers of events without bothering about the size and structure of the population at risk. I have also shown (Lee 1978a) that short-run fluctuations can be used to study the causes of population change without contamination by the simultaneity in the system. I have used cross-spectral analysis to estimate these relations, in part because for compelling reasons the theoretical analysis mentioned above had to be carried out in spectral terms. 12 However, given the theoretical results, the empirical work could have been carried out by regression analysis after suitable "filtering" of the series. Spectral analysis examines the variances and covariances of sets of series by frequency or periodicity. Any detrended series may be examined in this way; there is no presumption that there are cycles in the data. It is convenient, although not entirely accurate, to think of frequency here as distinguishing, say, between long-run (low-frequency) and short-run (high-frequency) components of variation in the series. My previous work has established that for wavelengths of less than fifteen years or so, the population size and age structure, and the duration structure of marriages, have only negligible effects on births, deaths, and marriages. For my purposes, therefore, I will refer to these as "short run. " I will use three basic cross-spectral concepts in this paper. The first is "coherence squared," denoted C'2(A), which is analogous to R2 in

538

Ronald Demos Lee

regression analysis but is specific to wavelength '\. The second is phase shift, cj> ('\), which measures the lag of one series behind the other in radians at each wavelength. The third is "gain squared," G2(,\), which is analogous to the square of a regression coefficient, again specific to wavelength. Estimated cross spectra for births and marriages in relation to wages are presented in figure 9.6. First consider births. For periods of thirteen years or less, C 2 (,\) is typically significantly greater than zero, indicating that wage fluctuations did indeed affect marital fertility, explaining perhaps 25 % of the variance. The phase shift diagram indicates that marital fertility lagged slightly behind the wage rate, by something less than a year. I have not drawn in confidence bands for the phase estimates, but Births by Wages

.6

C>U

U

055',,,,,,,",,

.4

c"o

~

~

~ ~ o a-

' 'I

Marnages by Wages

.6

.2

UUl

6

""~

4

ol:'

~V) ~ ~

","0

.I: '" a..~

2

2

o

o C..J.,..-J-......l-.--'------,-L--L

coL..:2l::0...,1'::-0-:6'-:.7,.---..J4,.----:3~.3::-::'2-=5~2

o Lag

co 2010 6.7

--:

4

3.3 2.5

2

4

3.32.5

2

.6

Wavelength,

Fig. 9.6

I.,

In Years

Wavelength, ;"

In

Years

Cross-spectral estimates of births and marriages by wages for England, 1539-1839. Phase estimates indicated by solid circles correspond to significant estimates of coherence squared and are more accurate than others. Estimates were made using a Parzen window with T = 301, M = 20. Births, marriages, and wages were measured as the residuals from a regression of the lag of the basic series on time.

539

Perspective on Economic Aspects of the Population Explosion

they are very narrow, typically about ±0.3 radians. The estimates of 02(A) can here be interpreted as elasticities,13 suggesting a value of 0.3. I also estimated separate cross spectra for each of the periods 15391638, 1639-1745, and 1746-1839 and found virtually identical results within each subperiod. This establishes the existence of a procyclical response of marital fertility to wages as far back as the sixteenth century, with no noticeable change in the timing or sensitivity of the relationship. The estimated cross spectrum for marriages and wages shows a coherence-squared very similar to that for fertility. The phase diagram shows that nuptiality responded to wages with no lag at all, in contrast to fertility. The gain-squared estimates show that the elasticity for nuptiality was on the order of 0.5, or nearly twice as high as that of fertility. Generally, the association was closer and more sensitive for fluctuations of about ten years' periodicity than it was for very short-run fluctuations. To summarize, these results show that as far back as the sixteenth century, both marital fertility and nuptiality were strongly influenced by short-run variations in the real wage, which explained 20% to 30% of their short-run variance. Without making any judgment on whether the association of marital fertility with wage variations was due to voluntary limitation of fertility, these results provide some support for the existence of an aggregate relation between general fertility and wages. 14

The Positive Check While the role of exogenous mortality decline in the current LDCs' rapid population growth is widely acknowledged, it is less well known that large exogenous changes in mortality occurred in the past, leading to major population swings in Europe from the thirteenth through the eighteenth centuries. And I refer not to catastrophic mortality associated with periodic harvest failure or epidemic, but rather to long-run changes persisting for decades or centuries. The causes of these shifts are obscure; they may have been climatic, or the by-product of independent epidemiological and ecological changes, or the result of voyages of exploration. But that these changes occurred is clear; their magnitude is suggested by the life expectancy series for upper-class Englishmen shown in figure 9.1. Other confirming evidence is found both for England and for the Continent in reconstitution studies based on parish registers, in data from religious orders and the professions, and in the analysis of wills and death taxes. The exogeneity of the changes is clear from their temporal relation to changes in wages and population size, and from their disregard for class distinctions (see Chambers 1972; Lee 1973, 1978a and 1978b). I do not mean to suggest that mortality was completely independent of income; but the importance of this endogenous component has been greatly exaggerated. The extent to which mortality was associated with

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wages in the short-run can be studied with the Cambridge Group's parish data; figure 9.7 shows the relevant cross-spectral estimates. The coherence-squared indicates that only about 10% of the variance is explained, less than half the amount explained for nuptiality and marital fertility. The phase diagram is somewhat erratic but suggests that mortality and wages were negatively related, with mortality lagging by from zero to one year. The squared gain, not shown here, suggests an elasticity of about -0.5. (For an analysis of wages and mortality by cause of death in sixteenth- and seventeenth-century London, see Mirowski 1976.) I have also analyzed the relation of wages to the rate of natural increase; these results are also shown in figure 9.7. The coherence-squared averages about 0.15, with a very small lag of growth behind wages. The elasticity is not a useful measure of sensitivity in this case. It is more helpful to note that a doubling of the real wage would increase the population growth rate by about 1.25% per year, ceteris paribus. Direct Links of Fertility to Mortality

I have so far discussed the relations of fertility and mortality to wages. Now I will briefly consider the possibility that there were direct links of fertility to mortality, such that fertility would adjust to changes in mortality. Several such links have been suggested in the literature. One is that, through inheritance, high mortality resulted in the transfer of assets to the nubile, thus increasing nuptiality, then fertility (Ohlin 1961). The cross spectrum of marriages and deaths lends some support to this hypothesis. However, it is only the redistributive effect that should be counted here; changes in the population/wealth ratio are an indirect influence of mortality on fertility, already reflected in the wage rate. Another suggested link is that couples may have attempted to replace unexpected infant and child deaths and that, when mortality changed, they would eventually revise their mortality expectations and adjust their fertility accordingly. This argument requires the assumption that couples controlled their fertility and strove for some number of surviving children, in contrast to the natural-fertility hypothesis. Knodel (1975) has shown that this "replacement hypothesis" is false for a sample of preindustrial European parish populations. My own studies of the short-run relation of fertility to mortality show a very strong negative relation. Perhaps the most convincing evidence that fertility did not strongly compensate for mortality changes even over the long run is given by figure 9.5, which shows a very close correlation of mortality and population growth rates over a period of 175 years. To sum up section 9.3, I have shown that, at least in the short-run, there was an endogenous component to population change, operating through nuptiality, marital fertility, and mortality. Presumably these

Perspective on Economic Aspects of the Population Explosion

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Deaths by Wages

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Rate of Natural Increase by Wages

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