Income Distribution: Inequalities, Impacts and Incentives : Inequalities, Impacts and Incentives [1 ed.] 9781614700838, 9781606922026

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Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved. Income Distribution: Inequalities, Impacts and Incentives : Inequalities, Impacts and Incentives, Nova Science Publishers, Incorporated, 2008. ProQuest

Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved. Income Distribution: Inequalities, Impacts and Incentives : Inequalities, Impacts and Incentives, Nova Science Publishers, Incorporated, 2008. ProQuest

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INCOME DISTRIBUTION: INEQUALITIES, IMPACTS AND INCENTIVES

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Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved. Income Distribution: Inequalities, Impacts and Incentives : Inequalities, Impacts and Incentives, Nova Science Publishers, Incorporated, 2008.

INCOME DISTRIBUTION: INEQUALITIES, IMPACTS AND INCENTIVES

IRVING H. WADELL Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

EDITORS

Nova Science Publishers, Inc. New York

Income Distribution: Inequalities, Impacts and Incentives : Inequalities, Impacts and Incentives, Nova Science Publishers, Incorporated, 2008.

Copyright © 2009 by Nova Science Publishers, Inc. All rights reserved. No part of this book may be reproduced, stored in a retrieval system or transmitted in any form or by any means: electronic, electrostatic, magnetic, tape, mechanical photocopying, recording or otherwise without the written permission of the Publisher. For permission to use material from this book please contact us: Telephone 631-231-7269; Fax 631-231-8175 Web Site: http://www.novapublishers.com NOTICE TO THE READER The Publisher has taken reasonable care in the preparation of this book, but makes no expressed or implied warranty of any kind and assumes no responsibility for any errors or omissions. No liability is assumed for incidental or consequential damages in connection with or arising out of information contained in this book. The Publisher shall not be liable for any special, consequential, or exemplary damages resulting, in whole or in part, from the readers’ use of, or reliance upon, this material. Any parts of this book based on government reports are so indicated and copyright is claimed for those parts to the extent applicable to compilations of such works.

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CONTENTS

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Preface

vii

Chapter 1

Equity of Access to Public Parks in Birmingham (UK) Andrew P. Jones, Julii Brainard, Ian J. Bateman and Andrew A. Lovett

Chapter 2

Growth, Inequality and Poverty in Jamaica: 1990 – 2003 John Gafar

37

Chapter 3

Income Distribution and Inequality in Some Major Industrialized Countries Fabio Clementi

55

Chapter 4

Inequalities Reduce Overall Learning and Widen Learning Gaps: Inequality Mechanisms and Mitigation Strategies Ming Ming Chiu

79

Chapter 5

Neoliberalism’s Triumph? Falling Union Density, Falling Minimum Wages, and Rising Wage Inequality in the United States, 1980-2000 Thomas W. Volscho

99

Chapter 6

The Rank-Size Representation of the Income Distributions L. Benguigui and E. Blumenfeld-Lieberthal

117

Chapter 7

Probabilistic Foundations of Economic Distributions and Inequality Indicators J. Rosenblatt and K. Martinás

147

Chapter 8

Analysis of the International Inequality in CO2 Emissions. The Contribution of Income Inequality and Other Factors Emilio Padilla and Juan Antonio Duro

169

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1

vi

Contents

Short Communication Modeling and Forecasting Income Tax Revenue: The Case of Uzbekistan Marat Ibragimov, Rustam Ibragimov and Nishanbay Sirajiddinov

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Index

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183 185

201

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PREFACE Income distribution has always been a central concern of economic theory and economic policy. Classical economists such as Adam Smith, Thomas Malthus and David Ricardo were mainly concerned with factor income distribution, that is, the distribution of income between the main factors of production, land, labour and capital. Modern economists have also addressed this issue, but have been more concerned with the distribution of income across individuals and households. Important theoretical and policy concerns include the relationship between income inequality and economic growth. The article economic inequality discusses the social and policy aspects of income distribution questions. This new book presents significant and recent research developments. Provision of public parks has long been advocated as an equalizing measure between different elements of society. However, in practice, parks have usually been sited with little regard for the geography of where different social groups live. Chapter 1 assesses equity of park provision for different income-status and ethnic populations in the urban area of Birmingham in western England. The analysis was undertaken using different geographical units, and with different (but correlated) deprivation measures, to test the sensitivity of the results to methodological choices. Parks were categorized as being all of one type, or one of two types: pleasant green areas suited for more solitary and passive activities (amenity) or open spaces designed more for informal sports or other physical and group activities (recreational). Distance-weighted access scores were calculated and compared for five groups sorted by relative social deprivation, and for five ethnic groups: Bangladeshis, blacks, Indians, Pakistanis and whites. Visual analysis suggested that both poor, mostly non-white inner city areas and relatively affluent and white outer suburbs would tend to be disadvantaged (compared to the city average) with regard to parks. Statistical analysis found the greatest disparities between deprivation groups, with the most deprived 25% and 10% of the population consistently having the worst access to all park categories, but especially the recreational park category. There was weaker evidence of disparities on the basis of ethnicity and with regard to the amenity parks category. The authors found evidence to suggest that even within the most deprived areas, whites have better access to park areas than non-whites. Economic growth, as measured by real GDP, was modest during 1990-2003, but it could have been underestimated due to the large underground economy. The evidence shows that income of the poor rose proportionately with economic growth, and there exists little or no correlation between economic growth and inequality. There exists no evidence to support the

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viii

Irving H. Wadell

Kuznets hypothesis. The distribution of income was stable during 1990-2003, as Chapter 2 presents. The econometric evidence shows that economic growth reduces poverty in Jamaica. Close to a third of the rural population are poor, and one in three children in Jamaica live in poverty. Chapter 3 analyzes four sets of income data: the US Panel Study of Income Dynamics (PSID), the British Household Panel Survey (BHPS), the German Socio-Economic Panel (GSOEP) and the Italian Survey on Household Income and Wealth (SHIW). It is firstly shown that a two-parameter lognormal distribution can give very accurate fits to the lowmedium income range (98%–99% of the population), whereas the high income range (1%– 2% of the population) is well fitted by a Pareto’s (power-law) function. This combination of two qualitatively different distributions seems stable over the years covered by the datasets, although the indexes specifying them fluctuate over time. These fluctuations are quantified by establishing some links with the country specific business cycle phases, and show how the separation between the two regimes of the income distributions may be due to different income dynamics. In particular, it is found that for the top percentiles of the distributions returns on capital account for a significant share of the total income, so that their contribution to the latter may be responsible for the observed power-law behavior in the tail. Secondly, to assess the contribution of the individual factors and their relative importance to the overall inequality, the authors investigate income inequality using a decomposition analysis by income sources. The results suggest that capital income makes a significant contribution to overall inequality, confirming in this way its role in determining the Pareto’s tail. Country inequality yields greater inequality across families, across schools, and within schools, which widens the achievement gap between rich and poor and reduces overall student learning. Market economies increase individual effort, productivity, and unequal incomes. Governments can exacerbate inequalities through regressive taxes or favorable policies for special interests. Furthermore, weak legal systems that do not redress wrongs harm poor people disproportionately. Meanwhile, hierarchical cultures expect individuals to obey authority, encouraging deference to higher status people and undervaluing lower status people (status effects). At the local level, privileged parents often use their superior resources to give their children more educational resources (family inequality), sending them to schools with more resources and richer schoolmates (school inequality and schoolmate inequality). Within a school, staff can give richer students more resources, assign them to higher ability classes (tracking), or support their status effects in steep status hierarchies. As explained in Chapter 4, inequality can widen the achievement gap through disadvantaged students’ fewer learning opportunities and worse discipline. Meanwhile, six inequality mechanisms reduce both privileged and disadvantaged students’ learning. First, richer parents benefit less than poorer parents from public resources and advocate less public education spending. Second, teachers and students in less equal societies view one another as less similar, feel less solidarity, and share fewer educational resources. Third, less solidarity reduces trust and fosters corruption, which siphons off educational resources. Fourth, less equal countries have higher crime rates, more conflict, and worse student discipline. Fifth, steep status hierarchies distort perceptions of one another’s competencies and needs. Lastly, the effects of diminishing marginal returns are larger in less equal countries. National and school strategies can mitigate these harmful effects. Political coalitions can support welfare, progressive taxes, transparency, minimum standards, or mixing students.

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Preface

ix

School leaders can allocate school resources equally, diversify teaching duties, eliminate tracking, support a caring school community, express clear goals and standards, align school goals and incentives, and enhance transparency of information and decision-making. Contemporary observers contend that neoliberal economic policies are attempts to restore the political-economic power of the capitalist class. Chapter 5 examines the effects of unions and the minimum wage on wage inequality over a twenty year period using state data. The response variable in this study is residual wage inequality among full-time year round nonagricultural workers age 18 to 64 within the lower 48 states over the period 1980 to 2000. Consistent with institutionalist theorists, unions and the minimum wage are inversely associated with residual wage inequality. However, the effect of union density is found to shift from inverse to positive for earners closer to the left tail of the wage distribution by the late 1990s. The shift in the effect is interpreted as potentially the result of neoliberal economic policies intended to weaken labor unions in an attempt to restore class power. Recently, the authors proposed a general framework for classifying distributions of entities which can be categorized by their "sizes". Income distribution is a classic case of such a distribution, thus the authors used their framework in this case. The classification is made with the help of a positive index α which can be smaller than 1, equal to 1 or larger than 1. In each of the three classes, the distributions demonstrate particular properties. The case α =1 corresponds to a Pareto distribution (i.e. a power law). The case α < 1 is characterized by an absence of divergence of the probability density distribution toward small incomes or even by a maximum. It corresponds to all the known cases of real income distributions. In their framework, a distribution is characterized by two parameters: the exponent α and another parameter which the authors call m. With the help of computer simulations the authors found that the Lorenz curve and the Gini coefficient G are related directly to the parameters α and m. Thus, in Chapter 6 the authors propose an explicit relationship between G, α and m. The authors determined the distribution parameters (α, m) for several real income distributions and used them to calculate G. The results suggest that the proposed equation is well verified for real income distributions. Inequality indicators raise the question of how to define and measure inequalities, incomes in particular, in an assembly of individuals. The indicator depends naturally on the probability for a given income to have a beneficiary. It concerns therefore fundamental statistical properties of money and individuals, particularly their distinguishability. The authors postulate that (i) monetary units are indistinguishable from one another, they can in principle form incomes with no a priori limit, in the same way as particles called bosons, described by Bose-Einstein statistics in physics, can cluster without limit in the same state; (ii) no more than one indistinguishable individual can occupy a job or position in society, which makes individuals similar to particles called fermions: no two identical particles ever share the same state. This is the basis of Fermi-Dirac statistics. It allows us to obtain occupation numbers, that is, the number of individuals per job. The actual equilibrium distribution is the most probable one, characterized by the maximum distributional entropy. Society determines the distribution of resources over available positions and thereby the level of inequality. The latter becomes a constraint on the optimal distribution of individuals over existing positions. The model involves the optimisation of the job or position occupation numbers through the maximisation of their associated entropy. This is performed under three constraints: the number of individuals involved, the number of available monetary units and

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Irving H. Wadell

last but not least, the value of actual inequality in society. Occupation numbers depend on incomes through an analytical function containing three adjustable parameters: λ, associated with the position of the peak in the distribution, β, similar to an inverse temperature, giving the width under the peak and thereby the gap between rich and poor, and µ, related to the extrapolation of the distribution towards zero income, and therefore to the relative weight of poverty in society. In Chapter 7, the authors apply the model to available data on incomes in France, U. S. A. and Hungary. The authors obtain very good fits for the whole distribution. A power law provides a fit of about the same quality when restricted to a few points in the upper tail of the distribution. Electricity being something that can be spent like money, they apply the same model to its per capita consumption in the world. The model works for about four orders of magnitude in both directions provided different parameters β and μ are chosen for lowconsumption and high-consumption countries. Chapter 8 analyzes the inequality in per capita CO2 emissions across countries and studies the relationship of this inequality with the international inequality in per capita income. In order to analyze the driving forces of emissions inequality the authors apply the methodology developed by Duro and Padilla (2006) for decomposing this inequality into different components. This will allow us to show the importance of income, energy intensity and carbon intensity of energy (carbonization index) inequalities and two interaction terms in determining the inequality in emissions. The authors also undertake the analysis for different groups of countries, classified according to their GNI per capita, studying the contribution of income inequality and the other components to between and within group inequality. The results confirm the main relevance of income inequality in explaining inequality in CO2 emissions across countries, and that the reductions in emissions inequality experienced in the period analyzed are mainly attributable to the reductions in income inequality. However, the other factors also make a significant contribution—especially to the within-groups inequality. Income tax revenue crucially depends on the wage distribution across and within the industries. However, many transition economies present a challenge for a sound econometric analysis due to data unavailability. The Short Communication presents an approach to modeling and forecasting income tax revenues in an economy under missing data on individual wages within the industries. The authors consider the situations where only the aggregate industry-level data and sample observations for a few industries are available. Using the example of the Uzbek economy in 1995-2005, the authors show how the econometric analysis of wage distributions and the implied tax revenues can be conducted in such settings. One of the main conclusions of the paper is that the distributions of wages and the implied tax revenues in the economy are well approximated by Gamma distributions with semi-heavy tails that decay slower than those of Gaussian variables.

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In: Income Distribution: Inequalities, Impacts and Incentives ISBN: 978-1-60692-202-6 Editor: Irving H. Wadell, pp. 1-36 © 2009 Nova Science Publishers, Inc.

Chapter 1

EQUITY OF ACCESS TO PUBLIC PARKS IN BIRMINGHAM (UK) Andrew P. Jones1,2,*, Julii Brainard1,2, Ian J. Bateman1,2 and Andrew A. Lovett1,2 1

The Centre For Social And Economic Research On The Global Environment 2 The School of Environmental Sciences University Of East Anglia, Norwich, Norfolk, UK

Abstract

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Provision of public parks has long been advocated as an equalizing measure between different elements of society. However, in practice, parks have usually been sited with little regard for the geography of where different social groups live. This study assesses equity of park provision for different income-status and ethnic populations in the urban area of Birmingham in western England. The analysis was undertaken using different geographical units, and with different (but correlated) deprivation measures, to test the sensitivity of the results to methodological choices. Parks were categorized as being all of one type, or one of two types: pleasant green areas suited for more solitary and passive activities (amenity) or open spaces designed more for informal sports or other physical and group activities (recreational). Distance-weighted access scores were calculated and compared for five groups sorted by relative social deprivation, and for five ethnic groups: Bangladeshis, blacks, Indians, Pakistanis and whites. Visual analysis suggested that both poor, mostly non-white inner city areas and relatively affluent and white outer suburbs would tend to be disadvantaged (compared to the city average) with regard to parks. Statistical analysis found the greatest disparities between deprivation groups, with the most deprived 25% and 10% of the population consistently having the worst access to all park categories, but especially the recreational park category. There was weaker evidence of disparities on the basis of ethnicity and with regard to the amenity parks category. We found evidence to suggest that even within the most deprived areas, whites have better access to park areas than non-whites.

*

E-mail address: [email protected]. Tel.: 0044(0)1603 593127. Fax.: 0044(0)1603 507719. Dr Andy Jones, School of Environmental Sciences, University of East Anglia, Norwich, Norfolk, NR4 7TJ.

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2

Andrew P. Jones, Julii Brainard, Ian J. Bateman et al.

Keywords: Environmental Equity, Birmingham UK, Ethnic Minority, Public parks, Deprivation, Geographical Information Systems

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1. Introduction The establishment of urban public parks has its origins in the social ideal of providing pleasant open space that is free at the point of access. These places have always been intended to be equally accessible for different social groups. Public urban parks were originally established, in part, to provide a place where rich and poor could meet on an equal footing (Young 1996). It is therefore somewhat surprising that relatively few studies concerned with environmental social justice have examined the provision and accessibility of open public space for different social groups. Exactly how to define equity of access is debatable, and often context specific. Extended discussion of the general concept of equity is given by Harding and Holdren (1993). Crompton and Wicks (1988), Wicks and Backman (1994) and Marsh and Schilling (1994) discuss different approaches to defining or ensuring equity in a planning context. Crompton and Lue (1992) and Nicholls (2001) consider how equity may be defined with relation to urban park usage, and which definitions are likely to be practicable and preferred by the public. We define equity simply as equal opportunity between social groups. Previous research in this area is very limited, and no studies seem to exist for a large city. Talen (1997) considered ethnic differences in access to public parks in two US towns. She noted the total park acreage within set distances (one or two miles, along the road network) of distinct populations (located by Census tract centre points). Inequities were considered in relation to race, age, overcrowded housing, single-adult households, median house value and vacant or owner-occupied housing. In one town (Macon, Georgia; popn.=96,757) Talen found that low access corresponded with white, high-income suburban locations. In the other town (Pueblo, Colorado; popn.=93,686) there was little evidence of relationships between race or wealth and park access. Nicholls (2001) looked at equity of access to public parks in another US town (Bryan, Texas; popn.=55,002). She considered the population characteristics and location (again denoted by Census tract centre points) within 800m along the road network of park entrances. Equity was investigated with respect to race, housing value, housing status (renting or owning), population density, and age (over 64 or under 18) within or outside this zone. Using a variety of equity tests, Nicholls found no evidence of inequities between racial or economic groups. In a small US city (popn.=133,046) Estabrooks et al. (2003) identified what they described as physical activity resources, including 112 public parks, leisure centres, walking trails and other facilities. It was concluded that communities with lower socioeconomic status had inferior access to such resources, and that this was likely to have detrimental effects on their physical health. Many studies in the USA (e.g. Payne et al. 2002; Tinsley et al. 2002) have reported that ethnic minorities tend to travel further to surveyed parks. In the UK, DTLR (2001) comment that ethnic minorities tend to visit urban parks less often than white people. One may ask whether this is partly because non-white communities find it more difficult (especially in terms of sheer distance) to travel to urban parks. Separate from ethnic effects, it is worthwhile to ask whether access to parks is reduced for economically or socially deprived populations. The Greater London Authority acknowledge (GLA 2001) that socially deprived areas in

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Equity of Access to Public Parks in Birmingham (UK)

3

London often have relatively poor access to green spaces, while GLA (2003) observed that London areas with less green space seemed to have more benefit claimants and overcrowded households. It is perhaps surprising that work on the issue of access to urban parks is uncommon, considering how much this is a very visible and publicly-owned environmental good. In July 2003 the British Government (ODPM, 2003) announced the allocation of £89 million to regenerate public parks and green spaces. Local authorities were invited to apply for funding in their area, and the intention was to select 27 pilot schemes to be distributed evenly throughout England and Wales. A small number of criteria were laid out for how the schemes might be selected. Tackling differentials in public parks provision between different social groups is an important issue to address if similar funding should become available in the future. This analysis focuses on differential access between ethnic minorities and socioeconomic groups with respect to urban parks. Our study area is the city of Birmingham, where we had detailed map information on parks, demographic statistics and the transport network. Birmingham is located in western England (see Figure 1) and is the second largest city in the UK with just under 1 million residents in the 1991 Census. It is a highly mixed area in terms of ethnic groups and incomes.

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2. Methodology We are primarily concerned with local access (less than 4km from home address) in this research. A brief summary of the methodology developed follows, with more details supplied in the subsequent data and analysis sections. On foot surveys were undertaken to collect relevant data on park usage. These survey data were used to model the distance decay relationship between frequency of visits and distance to park entrances. A street atlas was consulted to locate parks, green spaces and other publicly accessible open spaces in Birmingham. Based on the description in the street atlas, parks were placed into one of four categories, similar to other published open space typologies. Park boundaries and entrances were identified using high resolution Ordnance Survey digital map data. From boundary information we calculated each park’s area in hectares. The distance decay function was applied to model the relative availability of park open space from sample origins across Birmingham, with the raw (distance-decay) access score weighted by park size (in ha, using a transformation published by others). From these data, a potential surface was derived that suggested relative park accessibility. Potential access scores were then mapped in relation to social variables to assess the park accessibility for different ethnic and deprivation groups. Most previous equity studies have been undertaken in the United States, and typically tested for on the basis of racial or income distinctions. In the British context, the most feasible divisions are by ethnicity and relative deprivation (household income data are not available for small area geographies in the UK). Ethnicity is available from self-identified replies in the 2001 UK Census. Deprivation indices have been extensively developed in the UK, and can either be obtained for specific geographic areas or calculated directly from Census data according to published formulae. Our study considers five ethnic groups

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(Bangladeshi, Indian, Pakistani, black and white) and two different deprivation indictors (the income domain of the IMD2004 and a modified version of the Townsend Deprivation Index). Both Output Areas (OAs, the smallest areal unit of the 2001 Census) and Lower-layer Super Output Areas (LSOAs, groups of 4-6 OAs with similar social profiles) in Birmingham were used as study area units. OAs and LSOAs were sorted by potential access score, and placed into 50 groups of equal size population (approximately 19,542 persons each). The percentage of each ethnic or deprivation group (within the city) with the given range of access scores was calculated. Cumulative frequency lines were constructed, showing any variations between percentages of people in each social group with specified access scores. Any disparities between the cumulative frequency lines were assessed statistically using Kolmogorov-Smirnov tests. The larger these disparities the more likely it is that some social groups are relatively advantaged or disadvantaged with regard to access to public parks in Birmingham.

3. Data Sources

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The boundaries of the city of Birmingham in central England defined the study area. There were 977,087 residents in the city, according to the 2001 national Census. From the Census, details were extracted of population totals and indicators of social deprivation for Census survey areas. The project benefited from an existing database of Ordnance Survey (OS) digital data encompassing the city of Birmingham (see Figure 1) and extending up to about 500m beyond the city boundaries. These data included property boundary features (OS Landline) and a detailed road network (OSCAR). In addition, we undertook field interviews to collect data on factors influencing visitor patterns.

3.1. Birmingham Road Network Park access was presumed to be effected via links along the city’s road network. The Ordnance Survey OSCAR database was used to extract road centre-lines for the entire city and immediately adjacent areas. The data are nominally correct to early 2000, although it is probable that some recent, relatively minor, alterations in the road network were not recorded accurately. Limited access was noted and recorded for some road junctions (primarily at motorways) and incorporated into subsequent route modeling. The limited extent of digital data coverage, only to about 500m outside the city boundaries, caused the analysis to focus on local rather than regional parks provision. Ideally, the transport network would have incorporated pedestrian pathways as well, but such a source was not available. Nonetheless, as the vast majority of footpaths run alongside roads, the road network should serve as an acceptable proxy for the pedestrian network.

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Equity of Access to Public Parks in Birmingham (UK)

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3.2. Parks in Birmingham Parks and other green spaces within Birmingham and up to 500m outside of the city boundaries were located with the use of a city atlas (Geographers’ A-Z Map Co., 2000). Precise boundaries for each park area were located and extracted from the Ordnance Survey digital Landline database. Following the labeling in the A-Z atlas, four categories of park or green space were distinguished: •

•

•

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•

Amenity parks refers to leisure gardens, country parks, wildlife centers, woods, fish ponds, public greens and commons, areas labeled as simply as ‘park’, and green spaces not allocated for other specific undeveloped purposes (such as canal banks, paved public squares or allotments). Recreational parks are those designated as ‘recreation grounds’, ‘playgrounds’, ‘sports grounds’ and ‘playing fields’ not attached to any specific school or institution. Specialist sports grounds denotes areas labeled as used for a specific sport, such as tennis courts, hockey pitches, cricket grounds and golf courses. Other category was used for cemeteries, school grounds and college or university grounds.

Table 1 gives summary statistics for each type of park. Amenity and recreational parks provide the bulk of park provision in the city, and unlike the specialist or “Other” park categories, it is reasonable to assume that they are usually available for use by all sections of the community. We therefore focus the rest of our analysis 1 on access to these two types of green space. Figure 1 shows amenity and recreational parks in the study area. We consulted both the Birmingham Open Spaces Forum and Birmingham 2 City Council in devising this typology, but we do not pretend that this is a perfect method of categorizing park provision in the city. Therefore, partly to control for any bias imposed by the typology chosen, we also consider a “combined” category of park provision, which is both amenity and recreational park areas together. The large scale of the OS data made it necessary to locate park entrances precisely. The A-Z map and the Landline database were jointly consulted for this purpose. These sources indicate where parks border roads, and where breaks in surrounding buildings exist to apparently allow pedestrian access to the parks, but they do not depict the presence of fencing. Moreover, we have no easy way of detecting informal access routes and points (i.e., cut-throughs over rough ground, or holes in fencing). The presence of overlooked entrances is particularly an issue for the largest parks, but not one we could solve without an extensive programme of field visits.

1

What qualifies as a “park” is a subjective judgement. We relied on the likely activities/visit reasons suggested by information in the Birmingham A-to-Z volume. A broader definition of “parks” might include any open space, no matter how undeveloped the area, or how low the public usage, including allotments, canal banks or public squares. Alternative typologies of green and public open spaces are in Kit Campbell Associates, 2001 and DTLR, 2002a and 2002b. 2 We are grateful to Emma Woolf (BOSF) and Valerie Edwards (BCC) for taking the time to give feedback.

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Andrew P. Jones, Julii Brainard, Ian J. Bateman et al.

Figure 1. Amenity and recreational parks in the study area, with survey parks SF=Summerfield, PHPF=Perry Hall Playing Fields, KHRG=Kinghurst Recreation Grounds.

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Equity of Access to Public Parks in Birmingham (UK)

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Table 1. Main types of park included in each park category General Category Amenity

Including: Public open space/commons/greens Ponds and reservoirs Nature reserves/woods Country parks Park farms Leisure gardens Public playgrounds School rough Other parks not specifically labeled as sporting areas

General Recreation

Recreation grounds Playing fields Sports grounds Paddling pool

105 98 36 1

Specialist Recreation

Golf courses Bowling greens/pavillions Cricket grounds Stadia Tennis courts Football grounds Rugby grounds Hockey pitch Leisure centre

24 20 13 8 7 4 3 1 1

Other

Churchyards School/College grounds Cemeteries

20 18 13

Amenity: General Recreation: Specialist Recreation: Other:

Minimum Area (ha) 0.014 0.280 0.064 .0004

Median Area (ha) 3.24 3.84 2.15 1.93

Number 59 50 31 5 3 2 2 1 89

Maximum Area (ha) 757 100 160 73

Total Area (ha) 2821 1308 1175 382

3.3. Census area Boundaries and 2001 Population The Office of National Statistics (ONS) supplied data on population totals, populationadjusted areal centroids, and areal boundaries of Output Areas (OA), which are the smallest areal units in the 2001 Census. There were 3127 OAs within Birmingham city boundaries, containing an average of 312 persons or 125 households each. OAs are intended by design to all have a relatively constant number of households (Martin et al. 2001). OA centroids and

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Andrew P. Jones, Julii Brainard, Ian J. Bateman et al.

population sums within them were input to the SurfaceBuilder computer programme (Martin 1996). From Census statistics on resident persons and population-weighted centroids, SurfaceBuilder generates a surface depicting the number of persons predicted as resident in regularly spaced square-shaped areas, or cells. Because these data are based upon an interpolation of Census centroid data, they do not reflect genuine survey records, but in our experience they are generally reliable and accurate when calculating area statistics. Due to the generally high resolution of most of the digital map data, the population surface has a resolution of 20x20m cells. We use the population surface only to undertake population weighting for the park access scores (Section 4.2). When calculating totals of each ethnic group in Census areas, we use the actual count data (ONS key statistics) provided for that same area.

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3.4. Deprivation Indicators and Census Data The main geographic units of analysis in this chapter are OAs and Lower Layer Super Output Areas (LSOAs), which are comprised of small groups (typically 4-6 OAs) of contiguous OAs with similar social profiles. There are 641 LSOAs in Birmingham. We worked at both OA and LSOA levels to partially test the sensitivity of the analysis to biases associated with the modifiable areal unit problem (MAUP) (Openshaw and Alvanides 1999). The OA level is appealing because it is the smallest unit area (finest resolution possible) for which data were available in the 2001 Census. LSOA level is appealing because of the availability of the Index of Multiple Deprivation scores (IMD2004) (ODPM 2004) for this geography. The IMD2004 is comprised of seven domains describing different types of deprivation including income, access to housing and services, education, employment, health and disability, skills and training, living environment, and crime. We consider only the income domain of the IMD2004 (which we abbreviate as Inc-IMD2004) here. The income domain relates to data collected in 2001 and 2002 on the proportion of people in the area receiving various types of means-tested income support, including benefits and tax credits. The Inc-IMD2004 reflects the percentage of households in a given area that are reliant on means-tested benefits, and thus the greater the Inc-IMD2004, the lower incomes are generally believed to be in the area. The IMD2004 applies only at LSOA level; there is no IMD equivalent at Output Area level. To measure relative social deprivation between OAs we consulted the 2001 UK Census of Population for relevant indicators, such as domestic overcrowding, unemployment, lack of car ownership and housing tenure. From 2001 OA-level Census data we calculated a deprivation index which is very similar to the Townsend deprivation index (TDI), but using a different input count on the overcrowding element of the TDI (2001 Census data were not available to calculate the TDI exactly as Townsend et al. (1988) had done for 1991 Census data). We refer to the OA-level deprivation indicator as we calculated it, as a Pseudo-TDI. From 2001 Census data, we also derived statistics relating to percentage composition of various ethnic groups. The ethnic categorizations that we use (white, Bangladeshi, black, etc.) were standard categories in the 2001 Census and self-identified by respondents. The following ethnicities/national origins are particularly represented in Birmingham: white, Bangladeshi, Indian, Pakistani and black. For our purposes, we combine both persons of Caribbean and African heritage who identified themselves as “black” in the 2001 Census, as

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Equity of Access to Public Parks in Birmingham (UK)

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well as persons of mixed white and black heritage. Table 2 summarizes the ethnic and social deprivation variables. Table 2. Variables extracted or derived from the 2001 Census or the IMD2004. Variable name BANG INDN PAK BLK WHITE

Description Bangladeshi ethnicity Indian ethnicity Pakistani ethnicity black (African, Caribbean and mixed black/white) white ethnicity

Housing tenure Unemployment Car ownership Overcrowding

Renting from local authority (council housing) Economically active persons seeking work Households not having regular access to at least one car the ratio of total persons in households to the average number of habitable rooms per household

Pseudo-TDI

Calculated from preceding four variables at OA-level, this is similar to the Townsend Deprivation Index

Inc-IMD2004

Income domain, Index of Multiple Deprivation, 2004.

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3.5. Survey of Visitors to Urban Parks A number of variables are likely to impact upon the decision to visit a park. Principal among these is likely to be travel distance. Purpose of visit is also likely to shape decisions regarding which park a person might visit. Furthermore, both seasonality and time of day can influence visit patterns (Scott, 1997; DTLR, 2002a). We were unable to locate previous research indicating the distances persons in Britain travel to visit urban parks. We therefore conducted our own survey to collect data on relevant variables. Visitors to three parks in Birmingham were interviewed during the summer of 2001. Survey parks were chosen by considering deprivation levels in the area around each park. 1991 Census wards were categorized according to their Townsend Deprivation Index 3 (TDI) score (Townsend et al. 1988; calculated from 1991 Census data, as 2001 Census data were not yet available) into three deprivation groups: 33% most deprived, 33% least deprived, or 33% of middle deprivation levels. One relatively medium-size park was selected for survey in an area dominated by each deprivation tercile: Summerfield Park (most deprived), Perry Hall Playing Fields (least deprived) and Kingshurst Recreation Grounds (middle). In total, 117 individuals were interviewed (minimum 35 at each park) and asked for their mode of travel, the full postcode of their outset point, estimated one-way travel time to reach the park, the number of persons in their visitor party, and reasons for being in the park that day. Five interviews had to be excluded from subsequent analysis due to incomplete 3

The TDI was standardised with reference to other TDI values in Birmingham; thus it indicated relative deprivation levels locally, not compared to national levels.

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Andrew P. Jones, Julii Brainard, Ian J. Bateman et al.

information (such as invalid postcode). The outset origin postcode supplied by each survey respondent was linked to a grid reference (on the national grid system) using the Central Postcode Directory. The road network distance between this origin and the nearest park entrance was subsequently calculated within a geographical information system (Arc/Info). Table 3 summarizes survey results for each park. Included are socio-economic statistics for the OAs and LSOAs from which visitors came. The median Inc-IMD2004 score in the West Midlands is 0.23, the median in the city of Birmingham is 0.19. The median IncIMD2004 scores for origin areas of surveyed visitors were respectively 0.39 (Summerfield, relatively high), 0.13 (Perry Hall, relatively low), and 0.27 (Kinghurst, typical of the region but higher than the city median). However, there is considerable overlap if we examine the range of the majority (the tenth to ninetieth percentiles) of deprivation scores for visitors to each park. Therefore it might be better to state that there is a trend for Summerfield visitors to be the most deprived, and Perry Hall park users to be the least deprived, but the social profiles of visitors to each park are far from entirely distinct. Otherwise, the most striking feature of the three parks was the much higher proportion of white visitors to Kinghurst, and an apparent negative relationship between the proportion of visitors travelling by car and the expected deprivation levels at each park.

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4. Analysis The survey data were used to model the relationship between travel distances and frequency of visits. Generalised models of the decay relationship between proximity and visit frequency were generated for all parks. This distance decay relationship was used to create data suggesting the level of park accessiblity from any single origin point in Birmingham. Statistical tests were undertaken to compare park access for specific ethnic communities and deprivation groups. These comparisons suggested inequities on the basis of both social deprivation and ethnicity at both LSOA and OA level. Table 3. Visitors to Birmingham parks, survey results.

Park size, ha: No. of motorists (+cyclists): No. of pedestrians:

Summerfield

Perry Hall

Kinghurst

15.7

62.9

116

7 (+0)

15 (+3)

11 (+2)

28

21

25

Median (mean) one-way journey distance to reach park (m): All visitors: 311 (705) 1420 (2194) Pedestrians only: 225 (395) 717 (923) Median (mean) party size (No. of individuals): 2 (3.37)

2 (2.36)

420 (1232) 288 (814) 1 (2.26)

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Table 3. Continued Summerfield Perry Hall Kinghurst Max. stated travel time in minutes (and modelled km) amongst non-motorists: 22 (1.1 km) 53 (3.1 km) 150 (9.6 km) Primary visit reasons

En-route elsewhere; Bringing children to play; Team sports

Team sports Walks/Dog-Walking; Bringing children to play; En-route elsewhere;

Fishing; Walks; Dog-walking; Team sports

Socio-economic statistics from origin OAs (or LSOAs in the case of Inc-IMD2004) (from 2001 Census/ODPM 2004). 10th-90th percentile (median) % WHITE 17.9-51.7 (42.0) 11.5-95.7 (36.7) 83.2-97.4 (94.1) % BANG

0-2.3 (1.1)

0-10.2 (1.01)

All zero

% INDN

9.9-32.2 (19.2)

0-39.5 (16.7)

0-2.2 (0)

% PAK

2.7-35.0 (13.9)

0-42.3 (6.5)

0-3.12 (0.5)

% BLACK

10.8-28.5 (18.6)

3.2-30.8 (12.1)

1.1-9.4 (4.5)

Inc-IMD2004 score

0.23-0.45 (0.39)

0.08-0.47 (0.13)

0.14-0.40 (0.27)

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4.1. Distance Decay Function for Park Visitors There are many possible ways to derive an accessibility index for an environmental amenity and facility such as public parks. Haynes et al. (2003) argued the case for a function to measure relative accessibility taking the form: P = C * exp(Decay_coefficient * Impedance) where P=Potential or accessibility index C=Constant Decay_coefficient = the rate at which accessibility declines per unit of impedance Impedance = usually measured in terms of travel time or distance A common way to calculate potential would be to predict the number of visitor parties from origin zones as a visitor rate such as observed visitor parties per head (or household) of population. We could take this approach for an individual park, but not for the pooled data, as we did not know what percentage of the total number of visitors we surveyed at each park. This makes it impossible to compare observed visitor rates at different parks.

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Andrew P. Jones, Julii Brainard, Ian J. Bateman et al.

180 Number of visits in previous four weeks, on distance to park

No. visits/last 4 weeks

160 140 120 100 80 60 40 20 0 0

1000

2000

3000 4000 Distance to park

5000

6000

Figure 2. Stated number of visits in preceding four weeks plotted on distance to park: all Birmingham responses.

No. visits in last 4 weeks

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40

Average Number Of Visits in preceding four weeks

35 30 25 20 15 10 5 0 0

500

1000

1500

2000

2500

3000

3500

Distance (m) Figure 3. Average number of visits in preceding four weeks plotted on average distance to park.

Instead we use the number of visits, as reported by surveyees, made in the preceding four weeks. Using these data as intensity of use indicators has the advantage of not depending on population density, or information (otherwise unavailable and often difficult to collect) about the total number of visitors to the park in any given period. But visit frequency can plausibly be expected to decline with decreasing distance, and to reflect, in large part, ease of access. A distance decay relationship between journey origins and parks in Birmingham was derived by comparing the average number of visits in the preceding four weeks (as reported by respondents) and their travel distance (on the road network, as calculated by the GIS).

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Equity of Access to Public Parks in Birmingham (UK)

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Figure 2 plots the stated number of visits in previous four weeks on the calculated distance to each park, for visitors traveling less than six km. The relationship can be generalised by grouping visitors into seven distance bands: 0-250m, 251-500m, 501-750m, 751-1000m, 1001-1500m, 1500-2500m and 2500-3500m. Survey respondents who were only in a park because they were en-route to another location were excluded from this and further analysis. The average number of visits in the preceding four weeks for each distance band has been plotted against the average (calculated) travel distance in Figure 3. Using the functional form recommended by Haynes et al. (2003), the average number of visits was regressed against travel distance for Birmingham parks visitors, to produce Model 1: Avg_vis_4_wks (P) = 32.0085 * exp(-0.0006398 * distance) R2=.9223

(1)

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4.2. Surfaces Depicting Accessibility to Birmingham Parks In order to assess possible inequities, it was necessary to create a comparative measure of park accessibility for different Birmingham communities. To this end we generated 'potential' surfaces, which yielded index scores on the accessibility of either recreational, amenity or combined park areas. To generate potential surfaces required identification of both designated outset and destination points. Sample journey origins were generated on a regular grid every 400 m, initially. Points that actually fell within an existing park were then excluded. The remaining potential origins (1420 points) were moved to the nearest road junction. Destination points were taken to be park entrances, as described in Section 3.2. Visits are known to increase with park size, but the relationship between visit frequency and park size may not be linear. GilesCorti et al. (2005) found empirically (in a study of 516 urban parks in Perth, Australia) that visit frequency was best predicted when they weighted their distance decay function by the natural logarithm of park size (in ha) raised to the power of 0.85, or Attractiveness=Distance_Decay_Function * log(size0.85) We therefore allocated to each entrance a supply weighting which is equal to the area (in ha) of that park, raised to a power of 0.85 and then transformed by natural logarithm. For instance, Phoenix Park to the south of the city centre, measures 1.58 hectares, and is classified as entirely amenity park area. Phoenix has two entrances, each of which was given a supply weighting of 0.388811 (=log(1.580.85)). Very small parks (less than 1 ha) were given a supply weighting of 0.01. Three potential surfaces were generated, one each for amenity, recreational 4 and combined parks.

4

There are many different defensible ways that we might have formulated our access score. Talen and Anselin (1998) undertook an empirical sensitivity analysis to compare the most popular accessibility indices (with respect to urban parks access), and discuss strategies for their appropriate use in equity studies.

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Figures 4a-4b. Access to amenity (4a, left) and recreational (4b, right) parks in Birmingham.

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Equity of Access to Public Parks in Birmingham (UK)

15

Figure 4c. Access to combined amenity and recreational parks.

Within the Arc/Info GIS we calculated the distance (in m) between each pair of origin and destination points. Distances below 110 m were reset to a value of 110, to prevent spuriously high potential being predicted very close to parks. This distance was chosen because of a natural break in the original Birmingham parks survey data. Then Model 2 was used to derive an interaction score between each origin and destination, according to this formula, from Model 1:

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16

Andrew P. Jones, Julii Brainard, Ian J. Bateman et al. SCORE = HECTARES * [32.0085 – exp(-0.0006398 * DISTANCE)]

(2)

Subsequently, scores were summed by origin, to yield a single value indicative of park accessibility for that origin. A triangulated irregular network (TIN) (Peuker et al. 1976) was generated to estimate access scores for locations between origin points. The TIN data were sampled on a regular 20 x 20m grid to create potential surfaces (see Figures 4a-4b). To facilitate interpretation, the Potential values were converted to Z-scores with a mean value of zero and a standard deviation of one. The greater the index value, the greater the access to parks for persons travelling from that location. Negative values denote access below the grid average, positive values suggest better access than most of the grid. On Figure 4a, a northernmiddle area and the southwest of the city are well-endowed with amenity type parks. Areas east of the city centre are particularly devoid of amenity-type parks. On Figure 4b there is a ring of high provision of recreational type parks around the city centre, whilst the city centre itself and the furthest suburbs, especially in the north, are relatively poorly provided for with respect to recreational type parks. Combing the two types of park (Figure 4c) the north eastern suburbs and the city centre itself are most disadvantaged in parks provision. The next step was to overlay these surfaces with OA and LSOA boundaries and the population surface (described in Section 3.3). This enabled us to calculate a populationweighted park access score for each individual OA or LSOA.

5. Results

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Equality of parks access for different communities in Birmingham was examined with respect to both income deprivation and ethnic composition. In order to determine how the estimates of exposure were distributed across different populations, tests that compare the distributions of access scores were undertaken.

5.1. Ethnicity and Equity of Access to Public Parks The population of Birmingham was 70.35% white, 20.16% Asian/mixed Asian and 7.87% black/mixed black in the 2001 Census. To compare park access between these populations, the percentage of the total Birmingham population in each ethnic group was determined for each LSOA. For example, the LSOA labelled E01009276 had 166 persons recorded as black. This equates to 0.216% of the total 76,930 black persons residing inside the Birmingham city boundaries in 2001. Calculating this percentage of the total for each LSOA allowed us to determine what proportion of each ethnic group had stated parks access scores. Table 6 shows the median access scores for each ethnic group with respect to recreational, amenity or combined recreational and amenity park areas. 50% of the relevant ethnic group has an access score at or below the given values, which are relative and derived from our calculated park access scores (Section 3.2). Recall that the raw score values were standardised to have (at LSOA level) a mean of zero and a standard deviation of one. Lower values therefore suggest relatively low access, higher values indicate better access. The group

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Equity of Access to Public Parks in Birmingham (UK)

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median values are generally above zero because the access scores were standardised over the geographic area of the city without population weighting. Table 6. Median parks access indices for ethnic groups in Birmingham. Median access scores for each ethnic group and park type LSOA level Amenity Recreational Combined

BANG -0.027 -0.010 0.060

BLK -0.003 0.118 0.191

INDN -0.027 0.096 0.180

PAK 0.124 0.116 0.206

WHITE 0.064 0.215 0.213

BANG -0.076 -0.184 0.009

BLK -0.005 0.060 0.216

INDN -0.025 -0.052 0.108

PAK 0.141 0.047 0.195

WHITE 0.056 0.326 0.301

OA level Amenity Recreational Combined

In Table 6, there are not striking differences between ethnic groups for amenity parks access. Median scores only range from -0.076 (Bangladeshi) to 0.064 (white). However, with respect to recreational or combined parks access, whites seem to be much better off than the other groups, especially Bangladeshis.

80 70 60 50 40 30

White Indian Pakistani Bangladeshi Black

20 10

Amenity park access index

0 -1 .4 6 -1 .0 9 -0 .8 6 -0 .6 8 -0 .4 9 -0 .3 1 -0 .1 5 -0 .0 3 0. 04 0. 17 0. 37 0. 49 0. 68 0. 82 1. 02 1. 28 1. 77

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90

Cumulative frequency (%)

100

a. Ethnicity and Access to amenity parks. Figure 5. Continued on next page.

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Andrew P. Jones, Julii Brainard, Ian J. Bateman et al.

100 Cumulative frequency (%)

90 80 70 60 50 40 30

White Indian Pakistani Bangladeshi

20

Black

10

2. 04

1. 38

1. 01

0. 85

0. 70

0. 57

0. 45

0. 31

0. 17

0. 03

.0 3

-0

-0

.3 0

.4 6

-0

-0

.6 4

.8 9

-0

-0

.6 2 -1

.1 8

Recreational parks access index

0

b. Ethnicity and access to recreational parks. 100 Cumulative frequency (%)

90

70 60 50 40 30

White Indian

20

Pakistani Bangladeshi

10

1. 66

1. 18

0. 94

0. 81

Black 0. 67

0. 52

0. 43

0. 34

0. 24

0. 13

0. 00

-0

.2 0

-0

.3 6

-0

.5 2

-0

.8 0

-0

.5 9

.0 8

Combined parks access index

0 -1

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80

c. Ethnicity and access to combined (amenity and recreational) parks. Figures 5a-5c. Cumulative frequency plots of park access scores and ethnic populations, LSOA level.

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Equity of Access to Public Parks in Birmingham (UK)

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We further compared the distribution of park access scores for different ethnic groups by plotting cumulative frequency distributions (see Figures 5a-5c) against access scores. On Figures 5a-5c, park access scores for LSOAs were divided into fifty classes. These each contain two percent of Birmingham’s total population. The horizontal axes show the upper limit of amenity or recreational access scores in each class. The vertical axes plot cumulative percentages. A perfectly straight diagonal line on the plots would indicate that the given range of potential scores occurred equally often across that ethnic group. Lines that deviate from a perfect diagonal suggest a population displacement towards higher or lower access scores. Percentile lines bulging to the left of a perfect diagonal indicate a population with relatively lower than average access, lines pushed to the right suggest superior access. The greater the vertical gaps between the cumulative percentile lines, the more likely that an inequality is occurring between groups. It is readily apparent that, at LSOA level, there are only small differences between the ethnic groups with regard to either amenity, recreational or combined parks. We reproduce the cumulative frequency curves at OA level, to see if any discrepancies appear when looking at a higher resolution geographic area (Figures 6a-6c). At OA level, there is still no obvious difference between parks access for the different social groups with respect to the amenity park group (Figure 6a). However, it does seem that some social groups have inferior recreational and combined park access (Figures 6b-6c). Bangladeshis and possibly blacks as well, both appear to be worse off than other ethnic groups.

90 80 60 50 40 30

White Indian Pakistani Bangladeshi

20 10

Black Amenity park access index

0 -1 .4 6 -1 .0 9 -0 .8 6 -0 .6 8 -0 .4 9 -0 .3 1 -0 .1 5 -0 .0 3 0. 04 0. 17 0. 37 0. 49 0. 68 0. 82 1. 02 1. 28 1. 77

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70

Cumulative frequency (%)

100

a. Ethnicity and Access to amenity parks. Figure 6. Continued on next page.

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Andrew P. Jones, Julii Brainard, Ian J. Bateman et al.

100 Cumulative frequency (%)

90 80 70 60 50 40 30

White Indian Pakistani Bangladeshi

20

Black

10

2. 34

1. 60

1. 14

0. 90

0. 73

0. 61

0. 49

0. 36

0. 22

0. 07

-0

.1 4

-0

.2 9

.4 6

-0

-0

.6 4

.9 3

-0

-0

.5 9 -1

.0 2

Recreational parks access index

0

b. Ethnicity and access to recreational parks. 100 Cumulative frequency (%)

90

70 60 50 40 30

White Indian Pakistani

20

Bangladeshi

10

2. 12

1. 34

0. 85

0. 72

0. 58

0. 46

0. 35

0. 25

0. 15

0. 02

.1 0

-0

.2 1

-0

.3 7

-0

.5 5

-0

.8 3

-0

.6 7

1. 04

Black

Combined parks access index

0 -1

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80

c. Ethnicity and access to combined (amenity and recreational) parks. Figures 6a-6c. Cumulative frequency plots of park access scores and ethnic populations, OA level.

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Equity of Access to Public Parks in Birmingham (UK)

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Previous research has often employed regression analysis to quantitatively measure environmental inequity. Thus, one might attempt to predict park access scores from a variety of other LSOA-level variables, including percentage ethnic minorities, local income levels, access to other services, etc. We have found regression analysis to be very awkward to apply in equity studies (e.g., see Brainard et al. 2002). There tends to be strong multi-collinearity between candidate predictor variables. For instance, deprivation is strongly linked to ethnicity. This makes the coefficient estimates derived from ordinary least squares regression unreliable, as it is difficult to disentangle the distinct impacts of highly collinear variables. One way to address this problem is to use more sophisticated but controversial regression techniques (e.g., ridge regression). Else, one could try Analysis of Variance (AoV) to compare the populations, but this requires datasets to have equal variances, which our subgroups generally lack. The non-parametric alternatives to AoV (Kruskal-Wallis or Friedman tests) examine differences in group medians, whereas we are interested in the differences between the entire distributions. A simple yet robust quantitative way to analyse the data in Figures 5a-6c is to use the Kolmogorov-Smirnov test (KS; Connover, 1999). This test assesses the significance of the relative distance between the cumulative frequency lines shown on Figures 5a-5c. Rather than a k-sample test a two-sample KS test was chosen to closely examine the differences in population distribution between the various subgroups1. Table 7a and 7b give results, with the critical values at p=0.1, 0.05 and 0.01 levels. Table 7a. Kolmogorov-Smirnov statistics for two-sample tests comparing cumulative probability distributions for ethnic groups and parks access, LSOA level.

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Amenity White Indian Pakistani Black

Indian 0.0673

Pakistani 0.0675 0.0972

Black 0.0612 0.0442 0.1183

Bangladeshi 0.1033 0.0492 0.1313 0.0721

Indian 0.0715

Pakistani 0.0679 0.0439

Black 0.1010 0.0521 0.0504

Bangladeshi 0.1396 0.0841 0.1104 0.1108

Pakistani 0.0641 0.0600

Black 0.0754 0.0690 0.0465

Bangladeshi 0.1442 0.0776 0.1068 0.1101

Recreational White Indian Pakistani Black

Combined Amenity and Recreational Indian White 0.0709 Indian Pakistani Black Note: Critical KS values for p=0.1 is 0.1725. 1

How we measure inequity (maximum distance between groups) is just one of many possible valid approaches. Marsh and Schilling (1994) describe at length the strengths and weaknesses of different ways to test for inequity using accessibility scores.

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Andrew P. Jones, Julii Brainard, Ian J. Bateman et al.

The KS statistics confirm the visual impression (from Figures 5a-6a) that at LSOA level there is no significant inequity between ethnic groups and their relative access to different categories of park area. The greatest differences occur between whites and Bangladeshis, but these are not significant at p≤.1 (KS value=0.1725). However, using OA geography, there are significant differences (p≤0.05) between ethnic groups for the recreational and combined park categories (bottom two thirds of Table 7b). Working at OA level, whites are especially better off than Bangladeshis (p≤0.01), Pakistanis and blacks (p≤0.05). Table 7b. Kolmogorov-Smirnov statistics for two-sample tests comparing cumulative probability distributions for ethnic groups and parks access, OA level. Amenity White Indian Pakistani Black

Indian 0.0673

Pakistani 0.0675 0.0972

Black 0.0612 0.0423 0.1183

Bangladeshi 0.1033 0.0492 0.1313 0.0721

Indian *0.1879

Pakistani 0.1424 0.1250

Black 0.1474 0.1318 0.0306

Bangladeshi 0.3038 0.1342 **0.2206 **0.2128

Black 0.1610 0.1395 0.1140

Bangladeshi 0.2777 0.1681 **0.2058 **0.1811

Recreational

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White Indian Pakistani Black

Combined Amenity and Recreational Indian Pakistani White 0.1211 0.0933 Indian 0.0732 Pakistani Black

Notes: Critical KS values for p=0.1, 0.05 and 0.01 are respectively 0.1725 (*), 0.1923 (**) and 0.2305 (bold in table).

5.2. Deprivation and Equity of Access to Public Parks Table 8 gives the median park access score for each deprivation group, by type of park and by geography. Quartile groups are indicated by number (IncDepr1-IncDepr10) with the top (most deprived) decile designated IncDepr10. Figures 7a-7c plot, at LSOA level, the cumulative percentiles of population in each Inc-IMD2004 quartile (plus the top decile) against amenity/recreational/combined parks access scores. Figures 8a-8c are equivalent plots for deprivation and parks access, but at OA level and using the pseudo-TDI measure of deprivation (PTDI-1 to PTDI-10). Tables 9a-9b presents KS statistics for the data in Figures 7a-8c.

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Equity of Access to Public Parks in Birmingham (UK)

23

100 90

Cumulative frequenc

80 70 60 50 40

IncDepr1 IncDepr2 IncDepr3 IncDepr4 IncDepr10

30 20 10

1.77

1.38

1.15

1.02

0.87

0.75

0.68

0.57

0.45

0.37

0.25

0.12

0.04

-0.08

-0.15

-0.26

-0.37

-0.49

-0.62

-0.73

-0.86

-1.04

-1.13

-1.46

0.00

Amenity park access index

0

a. Deprivation and Access to amenity parks.

100 80 60 50 40 30 20 10 0

IncDepr1 IncDepr2 IncDepr3 IncDepr4 IncDepr10

Recreational park access index

-1 .6 2 -0 .8 0 -0 .5 3 -0 .3 0 -0 .1 2 0. 00 0. 17 0. 35 0. 54 0. 70 0. 89 1. 25 2. 04

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70

Cumulative frequency (%)

90

b. Deprivation and access to recreational parks. Figure 7. Continued on next page.

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24

Andrew P. Jones, Julii Brainard, Ian J. Bateman et al.

90 80 70 60 50 40 30 20

Cumulative frequency (%)

100

IncDepr1 IncDepr2 IncDepr3 IncDepr4

10

IncDepr10

Combined park access index

-1 .5 9 -0 .7 0 -0 .3 9 -0 .2 0 -0 .0 6 0. 08 0. 24 0. 37 0. 50 0. 67 0. 83 1. 08 1. 66

0

c. Deprivation and access to combined amenity and recreational parks. Figures 7a-7c. Cumulative frequency plots of park access scores and relative deprivation, LSOA level.

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Table 8. Median access scores for each deprivation group, by park type and geography. LSOA level IncDepr1

IncDepr2

IncDepr3

IncDepr4

IncDepr10

Amenity

0.020

0.282

-0.010

0.003

-0.087

Recreational

0.013

0.469

0.337

-0.150

-0.391

Combined

0.238

0.371

0.285

0.033

-0.273

PTDI-1

PTDI-2

PTDI-3

PTDI-4

PTDI-10

Amenity

0.008

0.245

0.035

0.049

0.178

Recreational

0.045

0.512

0.347

-0.105

-0.239

Combined

0.256

0.443

0.360

0.050

0.021

OA level

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Equity of Access to Public Parks in Birmingham (UK)

25

100 80 70 60 50 40 30 20

Cumulative frequency (%)

90

10

Amenity park access index

PTDI-1 PTDI-2 PTDI-3 PTDI-4 PTDI-10

-1 .6 0 -1 .1 3 -0 .8 8 -0 .6 8 -0 .4 7 -0 .3 0 -0 .1 5 -0 .0 3 0. 07 0. 23 0. 39 0. 55 0. 72 0. 90 1. 12 1. 47 2. 14

0

100 90 80 60 50 40 30

PTDI-1 PTDI-2 PTDI-3 PTDI-4 PTDI-10

20 10 0

Recreational park access index

-1 .5 9 -0 .8 0 -0 .5 2 -0 .2 9 -0 .1 0 0. 03 0. 22 0. 40 0. 57 0. 73 0. 97 1. 39 2. 34

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70

Cumulative frequency (%) .

a. Deprivation and Access to amenity parks.

b. Deprivation and access to recreational parks. Figure 8. Continued on next page.

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Andrew P. Jones, Julii Brainard, Ian J. Bateman et al.

Cumulative frequency (%) .

90 80 70 60 50 40 30

PTDI-1 PTDI-2 PTDI-3 PTDI-4 PTDI-10

20 10

22 1.

91 0.

72 0.

53 0.

38 0.

25 0.

11 0.

-0 .

21

-0 .

43

-0 .

73

-0 .

67 -1 .

05

Combined park access index

0

12

100

2.

26

c. Deprivation and access to combined amenity and recreational parks.

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Figures 8a-8c. Cumulative frequency plots of park access scores and relative deprivation, OA level.

For Amenity parks, there is some indication of statistically significant disparity at LSOA level (Figure 7a, top of Table 9a), but not OA level, (Figure 8a, top of Table 9a). At LSOA level the least deprived quartile has better access to amenity parks, but this finding has not held using OA geography. These mixed results make it hard to draw firm conclusions about any possible relative advantage that the least deprived quartile may have with relation to amenity parks. For recreational and combined parks, the middle deprivation groups (IncDepr2-IncDepr3, or PTDI-2 and PTDI-3) have higher scores than the other deprivation groups (Table 8, Figures 7b and 8b/Figures 7c and 8c). This trend is consistent despite changes in geography and deprivation indicator. The KS tests (lower two thirds of Tables 9a-9b) are consistent in confirming the initial impression that the highest deprivation quartile (or decile) is worst off. Interestingly, relatively affluent areas (IncDepr1 lines), also tend to have inferior recreational/combined park access at LSOA and OA level, something we surmised earlier from Figures 4b-4c. However, there are three reasons why we tend to discount the importance of the affluent suburban lack of recreational park areas. First, more residents in these areas are car owners and have relatively superior ability to travel to more distant parks to mitigate local poor provision. Second, local streets are very important as children’s play spaces (Kit Campbell Associates, 2001), and suburban locations are more likely to have quiet streets that are relatively safer for children to play in; thus lack of public recreational space is compensated for in suburban locations by more private and informal recreational space. Third, lower suburban population density that in itself implies that fewer local parks should be needed, compared to an area with many more people.

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Equity of Access to Public Parks in Birmingham (UK)

27

Table 9a. Kolmogorov-Smirnov statistics for two-sample tests comparing cumulative probability distributions for Inc-IMD2004 and parks access, LSOA level. Amenity IncDepr1 IncDepr2 IncDepr3 IncDepr4

IncDepr2 0.1111

IncDepr3 0.1202 0.1602

IncDepr4 *0.1884 **0.2171 0.1022

IncDepr10 **0.2141 0.2316 0.1630 0.0769

IncDepr2 0.2868

IncDepr3 0.2361 0.1119

IncDepr4 **0.2143 0.3909 0.3320

IncDepr10 0.3670 0.6417 0.5467 0.2812

IncDepr4 0.1824 0.2693 **0.1956

IncDepr10 0.3970 0.4956 0.4063 **0.2301

Recreational IncDepr1 IncDepr2 IncDepr3 IncDepr4

Combined Amenity and Recreational IncDepr2 IncDepr3 IncDepr1 **0.2236 0.1705 IncDepr2 0.1127 IncDepr3 IncDepr4

Notes: Critical KS values for p=0.1, 0.05 and 0.01 are respectively 0.1725 (*), 0.1923 (**) and 0.2305 (bold in table).

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5.3. The Most Deprived OAs To what extent are the disparities between ethnic groups at OA level (Table 7b) due to economic factors? For instance, 43.4% of Birmingham’s Bangladeshis and 40% of the city’s Pakistani population live in the most deprived 25% of LSOAs in the city. This compares to 33.6% of blacks, 29% of Indians, and 18.5% of whites. Do some ethnic groups have low access to parks because they tend to live in generally deprived areas, or can race compound disadvantages due to social deprivation (a point argued by Pulido, 2000)? We calculated Kolmogorov-Smirnov tests for parks access in the highest (top decile) deprivation OAs (n=313, population = 98,705, or 10.1% of Birmingham’s total population). The average Pseudo TDI value in these areas is 4.99. Again, there are 50 quantiles, with about six OAs in each quantile. By looking just at the most deprived areas, we attempt to separate ethnic differences from deprivation. Figures 9a-9c show cumulative percentiles of park accessibility scores for just the individuals living in these most deprived areas of Birmingham, divided by ethnic group. Table 10 lists the population totals for each ethnic group in the top deprivation decile. These totals demonstrate that small sample sizes are unlikely to bias the results. Table 10 also gives the median park access scores for each ethnic group. Table 11 shows the KS statistics for differences between the populations in these most deprived OAs.

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28

Andrew P. Jones, Julii Brainard, Ian J. Bateman et al.

Table 9b.Kolmogorov-Smirnov statistics for two-sample tests comparing cumulative probability distributions for pseudo-TDI and parks access, OA level. Amenity PTDI-1 PTDI-2 PTDI-3 PTDI-4

PTDI-2 0.0807

PTDI-3 0.0660 0.1348

PTDI-4 0.1109 0.1579 0.1090

PTDI-10 0.1574 0.1500 0.1536 0.0898

PTDI-2 0.2341

PTDI-3 **0.2305 0.0779

PTDI-4 0.1543 0.3598 0.3325

PTDI-10 0.2914 0.5096 0.4959 0.1667

PTDI-4 *0.1746 0.3068 0.2459

PTDI-10 0.2416 0.3826 0.3210 0.0773

Recreational PTDI-1 PTDI-2 PTDI-3 PTDI-4

Combined Amenity and Recreational PTDI-2 PTDI-3 PTDI-1 **0.2014 *0.1797 PTDI-2 0.0733 PTDI-3 PTDI-4

Notes: Critical KS values for p=0.1, 0.05 and 0.01 are respectively 0.1725 (*), 0.1923 (**) and 0.2305 (bold in table).

Cumulative frequency (%)

90 80 70 60 50 40

White Indian Pakistani

30

Bangladeshi

20

Black

10

a. Access to amenity parks. Figure 9. Continued on next page. Income Distribution: Inequalities, Impacts and Incentives : Inequalities, Impacts and Incentives, Nova Science Publishers, Incorporated, 2008.

1. 81

1. 11

0. 87

0. 74

0. 54

0. 43

0. 36

0. 26

0. 15

0. 04

-0

.1 6

-0

.2 7

-0

.3 6

-0

.5 7

-0

.7 3

-0

.1 8

.0 4

Amenity park access index

0 -1

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100

Equity of Access to Public Parks in Birmingham (UK)

29

Cumulative frequency (%)

100 90 80 70 60 50 40

White Indian Pakistani

30

Bangladeshi

20

Black

10

Recreational park access index 2. 51

0. 91

0. 51

0. 31

0. 08

.0 4

.1 2

-0

-0

.1 9

-0

.2 3

-0

.3 0

.3 7

-0

.4 4

-0

-0

.5 1

-0

.5 9

-0

.7 0

-0

.8 6

-0

-1

.1 5

0

b. Access to recreational parks.

Cumulative frequency (%)

100 90

70 60 50 40

White Indian Pakistani

30

Bangladeshi

20

Black

10

Combined park access index 1. 48

0. 80

0. 48

0. 34

0. 27

0. 21

0. 14

0. 06

0. 02

.0 5

.2 1

-0

-0

.3 0

-0

.4 1

-0

.5 5

-0

.6 8

-0

.8 7

-0

.3 4

0

-1

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80

c. Access to combined parks. Figures 9a-9c. Cumulative frequency plots of park access scores by ethnicity in the 10% most deprived OAs.

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30

Andrew P. Jones, Julii Brainard, Ian J. Bateman et al. Table 10. Population totals by ethnicity and median park access scores in 10% most deprived OAs in Birmingham. BANG

BLACK

INDN

PAK

WHITE

Population total

9808

17412

4806

27018

39660

Median Amenity parks score: Median Recreat’l parks score: Median Combined parks score:

0.085

0.097

0.310

0.252

0.154

-0.391

-0.435

-0.227

-0.203

-0.188

-0.147

-0.218

0.029

0.052

0.058

Table 11. Kolmogorov-Smirnov statistics for two-sample tests comparing cumulative probability distributions for ethnic groups and park access scores, for the 313 most deprived OAs. Amenity parks White Indian Pakistani Black

Indian *0.1805

Pakistani 0.1206 0.1269

Black 0.0889 **0.2146 0.1122

Bangladeshi *0.1859 **0.2170 0.1445 0.1090

Indian **0.2113

Pakistani *0.1874 0.0794

Black 0.2596 0.2366 0.2678

Bangladeshi 0.2436 **0.1953 **0.2117 0.0726

Indian 0.1437

Pakistani **0.2004 0.0597

Black *0.1839 0.2495 0.2456

Bangladeshi 0.2738 **0.2186 **0.2205 0.0980

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Recreational parks White Indian Pakistani Black Combined parks White Indian Pakistani Black

Notes: Critical KS values for p=0.1, 0.05 and 0.01 are respectively 0.1725 (*), 0.1923 (**) and 0.2305 (bold in table).

Differences between median access scores in Table 10 are not obviously great. There is a rather consistent ordering of scores, with Whites and Pakistanis having the highest median access scores, while Bangladeshis and blacks have the lowest scores. The cumulative percentage lines on Figure 9a (amenity parks) seem to closely coincide. There is more apparent disparity between the lines on Figures 9b-9c (recreational and combined parks). In Table 11, KS tests reveal highly significant differences between the ethnic groups in this most deprived cohort.

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Equity of Access to Public Parks in Birmingham (UK)

31

For amenity parks, Indians tend to be significantly better off (KS statistic has p≤0.1) than all other groups except Pakistanis. Whites are better off (p≤0.1) than Bangladeshis. The findings for amenity parks are weak enough that we prefer to treat them cautiously; we know that altering aspects of our methodology might easily cause the KS statistics to fall below the critical thresholds for p=.1. Differences for recreational and combined parks are stronger, with blacks and Bangladeshis being especially disadvantaged compared to the other social groups. These differences are usually significant at a p≤0.05. It seems unlikely that small changes in our methodology would substantially alter the general trends of these results. From our findings we tend to conclude that there is weak evidence of disparity (with regard to ethnicity or income-status) in access to our amenity parks, and strong evidence of inequality with regard to recreational or combined park categories. These findings are most evident for the smallest geographical units (OA level). The results strongly suggest that race and deprivation are, at least for some groups (blacks, Bangladeshis and whites), separate factors in their relative access to park areas.

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6. Conclusion Hopefully this multi-geography analysis is more than just a reminder of the existence of the modifiable areal unit problem (MAUP, Openshaw and Alvanides 1999). It is important to remember that at present the best practical solution for addressing MAUP is to conduct sensitivity analyses, and to work at the smallest geographic units possible. However, few empirical equity studies (our own previous research included) actually test for results at multiple levels of geography. At the moment there will be much impetus for studies to be conduced at LSOA or greater level, due to the availability of the IMD2004 and the difficulties of working at a spatial level smaller than LSOA (e.g., there are 165,925 OAs in England and Wales, compared to just 34,482 LSOAs). We found statistically significant indications of unequal access to public parks with regard to both ethnicity and social deprivation. This general conclusion applies regardless of which geography (LSOA or OA) or park categorisation scheme (amenity, recreational or combined) that we use. The evidence is strongest using the smallest geographic units (OA rather than LSOA), and for our recreational parks category. We acknowledge that our results may be biased by aspects of our methodology, category descriptions, data resolution and formulation of the park access score indicator. Nevertheless, this paper generates a consistent trend of results (that whites and middle- and upper-income groups have superior access to public parks), despite variations in some of the variables (geography, deprivation indicator, park typology). We have experimented (e.g., Brainard et al. 2003) with altering specification of the parks access score in many ways: 1) calculating the distance from an origin to each park entrance and summing this as the access score, rather than distance to the nearest entrance of each park; 2) weighting these distances by a proportion of the total park area, rather than the total park area; 3) using slightly different exponents in the distance decay function; 4) all of 1), 2) and 3). These variations changed some of our results, but not dramatically; the final conclusions for this chapter were broadly the same. The biggest differences seemed to be with respect to the relative position of blacks and Bangladeshis, with blacks coming out somewhat worse in the results presented here.

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32

Andrew P. Jones, Julii Brainard, Ian J. Bateman et al.

There are other methodological assumptions in this research that may well have influenced results. We assume that the distribution of ethnic households within each LSOA/OA is uniform; this is highly unlikely to be true in reality. More precise information about households, especially with regard to ethnic composition and deprivation levels, might alter the final KS statistics. Also, our comparisons between ethnic groups are dependent upon the Census categorisation scheme. Consideration of ethnicity identified on a different basis might change results. However, where the KS statistic is significant at p 0. This suggests a distribution with a survival function proportional to x−α , nowadays known as the Pareto’s distribution.1 Pareto was well aware of the imperfections of statistical data, insufficient reliability of the sources, and lack of veracity of income tax statements; nonetheless, he boldly analyzed the data for widely diverse economies and, based on the fitting of his original function, concluded that empirically the values of parameter α remain “stable” if not constant. Very recently, considerable investigations with modern data in capitalist economies revealed that the upper tail of the income distribution (generally less than the 5% of the individuals) indeed follows the above mentioned behavior, and the variation of the slopes both from time to time and from country to country is large enough not to be negligible. Hence, characterization and understanding of the income distribution is still an open problem. The interesting problem that remains to be answered is the functional form more adequate for the majority of population not belonging to the power-law part of the income distribution. Using data coming from several parts of the world,2 a number of recent studies debate whether the low-middle income range of the income distribution may be fitted by an exponential or lognormal decreasing function.3 In order to add some empirical investigation to the ongoing debate on the shape of income distribution, in this chapter we analyze four datasets relating to a pool of major industrialized countries for several years. When fits are performed, a two-parameter lognormal distribution is used for the low-middle part of the distribution (98%–99% of the population), while the upper high-end tail (1%–2% of the population) is found to be consistent with a power-law type distribution. Our results show that the parameters of the income distributions change in time; therefore, we look at the country-specific growth and business cycle phases to propose some potential explanations for this behavior. In addition, we claim that for the very top of the population returns on capital rather than labor earnings account for a significant share of total income. To confirm our conjecture, a decomposition analysis of the level and trend of total inequality for assessing the contribution of a set of individual income sources is performed. The results obtained lead us to the conclusion that the capital gains contribution to total income may be responsible for the observed power-law behavior 1

The Pareto’s and related heavy-tailed distributions are discussed in great detail in Arnold (1983). The available data are coming from the US (Montroll & Shlesinger, 1982, 1983; Dr˘agulescu & Yakovenko, 2001a,b; Dr˘agulescu, 2003; Willis & Mimkes, 2004; Silva, 2005; Silva & Yakovenko, 2005; Nirei & Souma, 2007), Europe (Dr˘agulescu & Yakovenko, 2001b; Dr˘agulescu, 2003; Willis & Mimkes, 2004; Clementi & Gallegati, 2005a,b; Clementi et al., 2006), Australia (Di Matteo et al., 2004; Banerjee et al., 2006; Clementi et al., 2006) and Asia (Souma, 2001, 2002; Yoon & Kim, 2005; Sinha, 2006; Nirei & Souma, 2007), and are mainly based on the income tax returns of the population. However, there are some other datasets obtained from different sources and spanning so long in time, like for instance the area of the houses in ancient Egypt (Abul-Magd, 2002) or the number of serf families belonging to a noble in the Hungarian medieval aristocratic society (Hegyi et al., 2007). For a recent detailed review of the subject see Richmond et al. (2006). 3 Recently, a distribution proposed by Clementi et al. (2007), Clementi, Di Matteo, et al. (2008), Clementi, Gallegati, & Kaniadakis (2008a,b) and Clementi et al. (2009) has the form of a deformed exponential, i.e. q 1 κ F¯ (x|α, β, κ) = expκ [− (x/β)α ] = , 1 + κ2 (x/β)2α − κ (x/β)α 2

which seems to capture well the behavior of the income distribution at the low-middle range as well as the power-law tail. Income Distribution: Inequalities, Impacts and Incentives : Inequalities, Impacts and Incentives, Nova Science Publishers, Incorporated, 2008.

Income Distribution and Inequality in Some Major Industrialized Countries

57

in the tail of the income distributions. The chapter is structured as follows. §2. describes the data used in our study. §3. presents and analyzes the shape of the income distributions and their time development over the years covered by our datasets. §4. uses decomposition analysis to study the impact of the income constituent parts on the overall inequality and its changes in time, with particular attention to the issue of top capital incomes. §5. concludes.

2.

The Data In this paragraph we describe briefly the data used in this study.

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2.1.

The Cross-National Equivalent File (1980-2002)

We use income data from the US Panel Study of Income Dynamics (PSID), the British Household Panel Survey (BHPS) and the German Socio-Economic Panel (GSOEP) as released in a cross-nationally comparable format in the Cross-National Equivalent File (CNEF). The CNEF brings together multiple waves of longitudinal data from the surveys above, and therefore provides relatively long panels of information. The release of the CNEF we use includes data from 1980 to 2001 for the PSID, from 1991 to 2001 for the BHPS and from 1984 to 2002 for the GSOEP. Our data refer to the period 1980–2001 for the United States and to the period 1991–2001 for the United Kingdom. As the eastern states of Germany were reunited with the western ones of the Federal Republic of Germany in November 1990, the sample of families in the Eastern Germany was merged with the existing data only at the beginning of the 1990s; therefore, in order to perform analyses that represent the population of reunited Germany, we choose to refer to the subperiod 1990–2002 for the GSOEP. A key advantage of the CNEF is that it provides reliable estimates of annual income variables defined in a similar manner for all the countries that are not directly available in the original datasets.4 It includes pre- and post-government household income, estimates of annual labor income, assets, private and public transfers, and taxes paid at household level. In this work, the household pre-government income variable (equal to the sum of household labor income, household asset income, household private transfers, and household private retirement income) serves as the basis for all calculations.5 Following a generally accepted methodology (e.g. Deaton, 1996), the concept of equivalent income will serve as a substitute for personal income. Equivalent income x is calculated as follows. In a first step, household income h is adjusted for by household type θ using an equivalence scale e (θ). This adjusted household income x = h/e (θ) is then attributed to every member of the given household, which implies that income is distributed equally within households. Here 4

Burkhauser et al. (2001, 2004) offers a detailed description of the CNEF. See also the CNEF web site for details: http://www.human.cornell.edu/che/PAM/Research/Centers-Programs/ German-Panel/cnef.cfm. 5 Although annual income measures are available in the original CNEF surveys, household tax burdens are not. Therefore, to construct post-government income using the existing original survey variables, household tax burdens must first be estimated. This leads to a constructed variable which can not be directly and fully compared across nations without significant effort on the part of individual users.

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58

Fabio Clementi

we apply a simple equivalence scale, in which total household income is divided by the square root of the number of household members. The average sample size varies from about 7,300 households, containing approximately 20,200 respondent individuals for the PSID-CNEF, to 6,500 households with approximately 16,000 respondent individuals for the BHPS-CNEF; for the GSOEP-CNEF data from 1990 to 2002, we have about 7,800 households containing approximately 20,400 respondent individuals. All the variables are in current year currency; therefore, we convert into constant figures using the Consumer Price Index (CPI) reported by the OECD.6 The base year is 1995.7

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2.2.

The Survey on Household Income and Wealth (1987-2002)

The Historical Archive (HA) of the Survey on Household Income and Wealth (SHIW), made publicly available by the Bank of Italy, is a sample survey of around 10,300 individuals drawn from the population of Italian households during the years 1977-2002.8 The survey was carried out yearly until 1987 (except for 1985), and every two years thereafter (the survey for 1997 was shifted to 1998). In 1989 a panel section consisting of units already interviewed in the previous survey was introduced in order to allow for better comparison over time.9 Since the incomes from financial assets started to be recorded only in 1987, our data refer to the subperiod 1987–2002. The basic definition of income provided by the SHIW-HA is net of taxation and social security contributions. It is the sum of four main components: compensation of employees (including net wages and salaries and fringe benefits); net income from self-employment (including income from self-employment, depreciation, and entrepreneurial income); pensions and net transfers (including pensions and arrears and other transfers); property income (including income from buildings and income from financial assets). The following components of net disposable income are used in this study: labor income (equal to the sum of compensation of employees and net income from self-employment), pensions and net transfers, and property income. All the amounts are expressed in ITL, except for 2002, where the income variables are reported in EUR. For longitudinal consistency, we report all the data in 1995 prices using the CPI and convert them to EUR (ITL/1, 936.27 = EUR).

3.

Empirical Findings

In what follows we describe the shape of the income distribution for all the countries of our concern. From the analysis we get the result that the indexes specifying it change in time; therefore, we try to look for some factors which might be responsible for this behavior. 6

Available for all the countries and years included in this study from http://www.sourceoecd.org. For longitudinal consistency, all German CNEF income variables are expressed in EUR (DEM/1.95583 = EUR). 8 The 2004 and 2006 waves of the SHIW have been recently made available by the Bank of Italy. Nonetheless, in order to allow matching of the SHIW database temporal length with that of the CNEF data at their right endpoint we have decided not to include these waves in the analysis. 9 See Brandolini (1999) for a detailed description of the data. To download them, go to the following web site: http://www.bancaditalia.it/statistiche/indcamp/bilfait. 7

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Income Distribution and Inequality in Some Major Industrialized Countries 0

0

10

10 Empirical Lognormal Power−law

Empirical Lognormal Power−law

−1

−1

10

Cumulative probability

10

Cumulative probability

59

−2

10

−2

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Figure 1. The complementary cumulative probability distribution of the equivalent personal income in the double logarithmic scale along with the lognormal and Pareto’s fits for some years: (a) United States (1996); (b) United Kingdom (1998); (c) Germany (2002); (d) Italy (2000).

3.1.

The Shape of the Distributions

In Figure 1(a)–(d) we plot the binned complementary cumulative distribution of the equivalent personal income from our datasets for some years in the double logarithmic scale.10 We observe that the lognormal distribution   log x − µ F¯ (x|µ, σ) = 1 − Φ , (1) σ with 0 ≤ x < ∞, −∞ < µ < ∞ and σ > 0, gives a very accurate fit until the 98th –99th percentile of the distribution for all the countries, whereas the upper income tail follows a 10

We eliminated the entries with negative and zero income, grouped the remaining entries into 100 equally spaced bins, and counted the number of entries inside each bin. We also returned the position of the bin centers, which is plotted on the horizontal axis versus the cumulative count of elements in each container (vertical axis). Income Distribution: Inequalities, Impacts and Incentives : Inequalities, Impacts and Incentives, Nova Science Publishers, Incorporated, 2008.

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(c) Germany (1990–2002) Copyright © 2008. Nova Science Publishers, Incorporated. All rights reserved.

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Figure 2. Time development of the income distribution for all the countries and years: (a) United States (1980–2001); (b) United Kingdom (1991–2001); (c) Germany (1990–2002); (d) Italy (1987–2002). Pareto’s or power-law distribution  x α min , F¯ (x|xmin , α) = x

(2)

where xmin , α > 0 and xmin ≤ x < ∞. In the figure, the fit to equation (1) is shown by the solid line, while the dashed line is the fit to equation (2).

3.2.

Temporal Change of the Distributions

The two-part strucure of the income distributions expressed as the lognormal with power-law tails seems to hold all over the time span covered by our datasets. The distributions for all the years and countries are shown in Figure 2(a)–(d). However, as one can easily recognize from the figure, the indexes specifying the distributions differ from year to year.

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First, we observe that the distributions shift over the years covered by our datasets. It is conceivable to assume that the origin of this shift consists in the growth of the countries. To confirm this assumption, we study the distribution of Gross Domestic Product (GDP) and Personal Income (PI) growth rates, and try to show that the evolution of both these quantities is governed by similar mechanisms, pointing in this way to the existence of correlation between them as one would expect. We calculate the growth rates using the data from the OECD for the GDP and connecting individual respondents’ incomes over time for the PI, and express them in terms of their logarithm.11 The chosen base year for calculations is 1995. We find that the distributions of both GDP and PI growth rates display a “tent-shaped” form; hence, they are remarkably well approximated by a Laplace or double exponential distribution   |g − g¯| 1 f (g|¯ g , σ) = √ exp − , (3) σ σ 2 where −∞ < g < ∞, −∞ < g¯ < ∞ and σ > 0. As shown by Figure 3(a)–(d), all the points representing both GDP and PI growth rates “collapse” relatively well close to the peak upon the solid lines, representing the function given by equation (3).12 This leads us to the conclusion that the data are consistent with the assumption that a common empirical law might describe the growth dynamics of both GDP and PI.13 Second, we observe that the power-law slope and the curvature of the lognormal fit are different both in different countries, as well as in different periods for the same country.
−0.5 , and Pareto’s This fact means that Gibrat’s (1931) index, measured as β = 2σ 2 14 index change in time. From the numerical fits of the distributions we obtain Figure 4(a)–

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11

The data collected by the OECD are available at http://www.sourceoecd.org. To consider almost the same number of data points relating to units with different sizes, we drew random samples of the data we have for individuals and standardized them together with the data we have for GDP growth rates. 12 In implementation, the single curve given by equation (3) that we compare to the scaled distributions of GDP and PI growth rate is generated by using the “inverse method”; i.e.: a random variable R ∼ U [0, 1] is firstly generated, and then we specify the inverse cumulative distribution function g = F −1 (r), which give us Laplace-distributed random values; we have: g = F −1 (r) = g¯ + σ log 2r for the negative growth rates, and g = F −1 (r) = g¯ − σ log 2 (1 − r) for the positive growth rates. Finally, we use these random variates to compute the Laplace cumulative distribution: F (g) = 0.5 exp [(g − g¯) /σ] if g ≤ g¯, and F¯ (g) = 1 − 0.5 exp [(g − g¯) /σ] if g > g¯. 13 These findings are reminiscent of the concept of “universality” found in statistical physics, where different systems can be characterized by the same fundamental laws, independent of microscopic details. The appearance of universal mechanisms has raised the question of whether the concepts and methods of statistical physics may be at work in the economic settings. In particular, several statistical physics research groups have recently shown a considerable interest in developing a richer theory of the fluctuations in economics. The objective of these studies is to uncover scaling empirical regularities about the fluctuations which are been shown to give important information regarding the underlying processes responsible for the observed macroscopic behavior, and also lead to a better understanding of the mechanisms responsible for the observed dynamics. The main findings are: (i) the distribution of the logarithm of the growth rates for GDP and firms with approximatively the same size displays an exponential form, and (ii) the fluctuations in the growth rates—as measured by the standard deviation of this distribution—scale as a power-law with size of firms and countries. For analyses and questions raised by these empirical results, see e.g. Amaral, Buldyrev, Havlin, Leschhorn, et al. (1997); see also Amaral, Buldyrev, Havlin, Maass, et al. (1997), Stanley et al. (1996), Lee et al. (1998), Bottazzi et al. (2001, 2002), Sutton (2002), Castaldi & Dosi (2004) and Teitelbaum & Axtell (2005). 14 While the Pareto’s index provides a measure of the income inequality for the tail, the Gibrat’s index provides a measure of the income inequality corresponding to the body of the distribution, and like the former is an inverse index of concentration: i.e., if β has low values (large variance of the global distribution), the per-

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Figure 3. The probability distribution of GDP and PI (logarithmic) growth rates for all the countries and years: (a) United States (1980–2001); (b) United Kingdom (1991–2001); (c) Germany (1990–2002); (d) Italy (1987–2002). The solid lines, representing the Laplace probability density function (3), are guides for the eye. The GDP growth rate is calculated on a quarterly basis. (d). In this figure, squares represent the change of Gibrat’s index and circles represent that of Pareto’s index. It is recognized that Gibrat’s index stays almost the same value over the years covered by our datasets; therefore, the variance of the low-middle income is slowly changing. By contrast, the Pareto’s index is a strongly changing index. From these behaviors we consider that there are some factors causing no correlation between the sonal income is unevenly distributed; clearly, the reverse is true if β has high values. However, a point worth considering is that the measured values of Gibrat’s index and Pareto’s exponent are not consistent with the most widely used measures of income inequality (e.g. the Gini’s coefficient) if one associates lower values of these indexes with increased inequality. In fact, if income follows either a lognormal or a Pareto’s distribution throughout, then a clear correspondence can be found between the two measures and the preferred inequality index; however, observed distributions are not only lognormal and show a power-law only over a very limited range; hence, the correspondence breaks down (see e.g. Persky, 1992).

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Figure 4. The time series of Gibrat’s and Pareto’s indexes over the years covered by our datasets: (a) United States (1980–2001); (b) United Kingdom (1991–2001); (c) Germany (1990–2002); (d) Italy (1987–2002). Gibrat’s and Pareto’s indexes, mainly affecting the latter. To study the origin of the temporal change of Pareto’s index in more detail, we consider its correlation with the asset price, such as the stock price and the housing price. As shown by Figure 5(a)–(d), there was a slight downward trend in the stock markets during the early 1990s, followed by a rise in the mid-1990s which dropped at the end of the decade after the bursting of the speculative bubble. A similar behavior is found in the temporal path of real housing prices (Borio & McGuire, 2004). By comparison with the temporal change of the power-law index α shown in Figure 4(a)–(d), we conclude that both stock market and housing market dynamics have a considerable effect on the upper income tail. These results lead us to check the possibility that non-labor income sources are responsible for the Pareto’s functional form of the observed empirical income distributions at the high-income range. To this end, we look at the composition of total income within the two regimes of the income distributions. Figures 6(a)–(d) and 7(a)–(d) show the share of each income component in the lognormal and power-law sections of the distributions for

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Figure 5. Fluctuations of the stock market indexes and the housing prices for the countries and years of our concern: (a) New York Stock Exchange (NYSE) index and CPI Housing (1980–2001); (b) London Stock Exchange FTSE (Financial Times Stock Exchange) index and CPI Housing (1991–2001); (c) German Stock Exchange Composite DAX (CDAX) index and CPI Housing (1990–2002); (d) Milano Borsa Italia (MIB) index and CPI Housing (1987–2002). The data source is the OECD (http://www.sourceoecd.org); all the data are deflated and normalized to 1 in 1995.

all the countries and years.15 As expected, individuals in the low-middle income ranges (98%–99% of the population) rely mostly on labor income, while individuals in the top percentiles (1%–2% of the population) derive a significant share of their income in the form of capital income, even if labor income (i.e., wage and salary income and self-employment income) still plays an important role at the very top of the income composition pattern. This

15

The share of each income component is calculated as πj µjk /µ, where πj is the fraction of the population in the lognormal and Pareto’s regimes of the distributions, µjk is the mean of the kth source of income of these groups, and µ is the average income of the whole population. Income Distribution: Inequalities, Impacts and Incentives : Inequalities, Impacts and Incentives, Nova Science Publishers, Incorporated, 2008.

Income Distribution and Inequality in Some Major Industrialized Countries 140

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result seems consistent with the decreased importance of capital income at the top of the income distribution documented by Piketty & Saez (2003), Atkinson & Leigh (2004) and Dell (2005) who suggest that the rentier class of the early century hurt by the major shock of World War II never recovered afterwards (possibly because of the rise in progressive taxation, which reduced the rate of wealth accumulation), and has been overtaken by the working riches in the last few decades. This difference we find in the composition of total income adds additional empirical evidence to the conjecture that labor income is mainly responsible for the observed lognormal distribution in the low to middle income range, while returns on capital gains play an important role in determining the power-law behavior in high income region (see e.g. Levy, 2003, 2005).

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Figure 7. The composition of total income in the upper tail of the income distribution: (a) United States (1980–2001); (b) United Kingdom (1991–2001); (c) Germany (1990–2002); (d) Italy (1987–2002).

4.

Inequality Decomposition by Income Source

In this paragraph we perform a decomposition of inequality for assessing the contribution of a set of individual income sources to total inequality.16 Following the methodology of Shorrocks (1982), we express total inequality I as the sum of the contributions of each source of income S, i.e. X Sk , I= k

where Sk depends on incomes from source k, and represents its absolute contribution to total inequality. If Sk > 0, the k th source of income provides a disequalizing effect, and an 16

See Lerman (1999) for a review of alternative methods for source decompositions of income, examples of their applications, and the range of interpretations they permit concerning the contribution of income sources to overall inequality. Income Distribution: Inequalities, Impacts and Incentives : Inequalities, Impacts and Incentives, Nova Science Publishers, Incorporated, 2008.

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equalizing effect if Sk < 0. In practice, the easiest inequality measure to decompose in this way is GE (2), which is a member of the Generalized Entropy (GE) class of inequality measures (Cowell, 1980a,b; Cowell & Kuga, 1981a,b) having the general formula " n   # 1 1 X xi θ −1 , GE (θ) = 2 θ −θ n µ i=1

where n is the number of individuals in the sample, xi is the income of individual i ∈ [1, n] and µ the mean income. The value of GE ranges from 0 to ∞, with zero representing an equal distribution (all incomes identical) and higher values representing higher levels of inequality. The parameter θ represents the weight given to distances between incomes at different parts of the income distribution, and can take any real value. For lower values of θ, GE is more sensitive to changes in the lower tail of the distribution, whereas for higher values is more sensitive to changes that affect the upper tail. With θ = 2, the GE measure becomes 1 GE (2) = CV 2 , 2 where CV is the coefficient of variation given by #1 " n 2 1 1X σ CV = = . (yi − µ)2 µ n µ

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i=1

When the GE (2) inequality measure is used, the absolute contribution of each source to total inequality can be written as q (4) Sk = sk GE (2) = ρk χk GE (2) GE (2)k ,

where sk = Sk /I is the proportional contribution of income component k to total inequality,17 ρk is the correlation between source k and total income, χk = µk /µ is the share of source k in total income and GE (2) and GE (2)k are one-half the squared coefficient of variation of total income and source k, respectively. A large value of Sk suggests that income source k is an important source of total inequality. We also attempt to account for the impact of individual income sources on changes in inequality.18 Using GE (2) as the inequality index, our decomposition of changes in overall inequality builds on the following formula  q X  X ∆ ρk χk GE (2) GE (2)k . (5) ∆Sk = ∆GE (2) = GE (2)t+1 − GE (2)t = k

k

In this decomposition, the changing impact of a source depends on changes in the correlation with total income, changes in the share of total income, and changes in inequality of the source. Therefore, a large value of ∆Sk suggests that changes in factor k have a large influence in changes in total inequality. 17

P Of course, we have k sk = 1. 18 See Jenkins (1995) for the complete methodology and an application to the United Kingdom. Income Distribution: Inequalities, Impacts and Incentives : Inequalities, Impacts and Incentives, Nova Science Publishers, Incorporated, 2008.

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Figure 8. Total inequality, GE (2), and income source contribution to total inequality, Sk = sk GE (2), for the lognormal region of the income distribution: (a) United States (1980–2001); (b) United Kingdom (1991–2001); (c) Germany (1990–2002); (d) Italy (1987–2002). Figures 8(a)–(d) and 9(a)–(d) summarize the contribution to total inequality of each income component in the lognormal and power-law sections of the income distribution for all the countries and years.19 Some important differences need to be emphasized here. First, as one can note by inspecting panels (a) and (b) of the figures, while there is little difference between the US and the UK in overall levels of low-middle income inequality, US income dispersion is higher in the high classes of the income distribution, mostly due to large differences in financial wealth between the two countries at the top of the distributions. A potential explanation for these differences, and possibly for higher accumulations of financial wealth in America compared to most of Europe more generally, involves differences in attitudes toward capitalist financial institutions (Banks et al., 2002). Especially 19

In the figures the total height of each bar represents total inequality as measured by half the squared coefficient of variation GE (2). Each portion of the bar represents the contribution of one of the factors: in terms of equation (4), each portion shows Sk = sk GE (2) for each factor k. Income Distribution: Inequalities, Impacts and Incentives : Inequalities, Impacts and Incentives, Nova Science Publishers, Incorporated, 2008.

Income Distribution and Inequality in Some Major Industrialized Countries 0.8

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Figure 9. Total inequality, GE (2), and income source contribution to total inequality, Sk = sk GE (2), for the power-law region of the income distribution: (a) United States (1980–2001); (b) United Kingdom (1991–2001); (c) Germany (1990–2002); (d) Italy (1987–2002).

during the 1970s and early 1980s, there was more distrust of the fairness of capitalism as an economic system, at least among significant segments of the European population. The stock market is one of most vivid capitalist symbols, so this distrust may have resulted in lower average participation in equity markets among Europeans. This could be one reason why relative exposure to the benefits from equity booms that eventually occurred in a similar manner in the two countries was very different and affected fewer households in the UK. In Germany, panel (c), income inequality for the great majority of the population lowered in the early post-reunification period, mainly because of the massive public transfers from western to eastern states which narrowed the East-West income gap (Schwarze, 1996), and then considerably rose afterward, as a consequence of increasing inequality in East Germany due to a redistribution of mean income from every individual below the median to every individual above the median (Biewen, 2000). Referring to the level and the overall

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trend of income inequality in the top few percents of the distribution, we can corroborate a starting tendency of decreasing inequality until the mid-1990s, and a subsequent reversed trend afterward, which seem to track not only the performance of the stock market but also the contribution that asset flows make to overall inequality, affected by political decisions like a reduction of the highest marginal tax rate, a permanent abolition of the former wealth tax, a further loosing of the taxation of the returns of capital and a reduction of the inheritance tax (Hauser & Stein, 2004). Finally, on the basis of the SHIW-HA evidence, income inequality in Italy, panel (d), showed some modest fluctuations around a flattened trend in the low-middle income range from 1993 to 2002, after the sharp increase between 1991 and 1993 at the time of the most severe recession experienced by the country after the World War II.20 On the other hand, income inequality at the very top of the distribution rose sharply by the mid-1990s, driven by large gains coming from investment in risky assets, which grew considerably during the 1990s in parallel with the stock market boom and the rapid privatization of state-owned corporations and public utilities. Furthermore, the fall in inequality among the very wealthy in the last couple of years can be explained by the changing portfolio composition, which has moved towards tangible assets following the fall in share prices and the modest rise in house prices.21 This evidence suggests that the stock market fluctuations of the 1990s were an important factor behind the recent trend of income inequality among the richest. Next, we turn to the study of changes in income inequality in the two regimes of the distributions. In Figures 10(a)–(d) and 11(a)–(d) the changes over time in the aggregate value of GE (2) derived from our datasets are decomposed according to equation (5). The height of each vertical bar equals the year-on-year change in aggregate amount of inequality, whereas each segment represents the changing impact of one of the individual income sources. As one can easily recognize, labor income is an important contributor to changes in total inequality for the great majority of populations, whereas in the highend tail of the distributions capital income makes by far the most significant contribution to overall changes in inequality, especially from the mid-1990s, as a consequence of the increasing personal ownership of equities. Once again, in the case of UK the contribution of income from capital was somewhat smaller throughout the distribution. On the other hand, as suggested by Jenkins (1999), self-employment income plays an important role in 20 As outlined by Boeri & Brandolini (2004), the rise in inequality in the mid-1990s should be understood as a worsening of the actual economic condition of households in the low-middle income class. Some potential explanations suggested for this “puzzle” are the following: (i) the strong deceleration of income growth in the 1993–2003 period with respect to the previous decade forced Italians to drastically revise downwards expectations of income growth; (ii) employees suffered a market deterioration of their incomes with respect to the self-employees, and this reflected into changes in the distribution of income across social groups; (iii) under stagnating incomes, the increasing income instability because of the volatility of employment and the fluctuations associated with the holding of risky assets is likely to have reduced the well-being of individuals; (iv) the Italian social protection system failed to provide insurance against the greater uncertainty and risk aversion, displaying very poor targeting properties in comparison with the other European countries. 21 As one can note by inspecting Figure 8(d), a significant amount of income inequality in the low-middle income range reflects inequality of property income. This reflects the composition of wealth distribution in Italy, where tangible assets such as consumer durables and real estate (particularly the principal residence) account for the largest fraction of net worth at the bottom and in middle classes of wealth distribution, while businesses and risky financial assets are most frequent among the richest. See Brandolini et al. (2006) for a description of the distribution of wealth in Italy.

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Income Distribution and Inequality in Some Major Industrialized Countries 0.05

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0.05 ∆SLabor income ∆S

Income from asset flows

Changes in overall inequality and source contributions

Changes in overall inequality and source contributions

0.04

0.03

0.02

0.01

0

−0.01

−0.02 ∆SLabor income

−0.03

∆S

∆SPrivate transfers

0.04

∆SPrivate retirement income 0.03

0.02

0.01

0

−0.01

Income from asset flows

∆SPrivate transfers

−0.04

∆S

Private retirement income

−0.05

81/80

83/82

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94/93

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0.06

0.1

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∆SLabor income

∆SLabor income

∆SIncome from asset flows

∆SPensions and net transfers

∆S

∆S

Private transfers

Changes in overall inequality and source contributions

Changes in overall inequality and source contributions

92/91

∆SPrivate retirement income 0.04

0.03

0.02

0.01

Property income

0.05

0

0

−0.01

91/90

93/92

95/94

97/96 Year

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(c) Germany (1990–2002)

01/00

−0.05

89/87

93/91

98/95

02/00

Year

(d) Italy (1987–2002)

Figure 10. One-year dynamic decomposition of GE (2) inequality measure by income source for the lognormal region of the income distribution: (a) United States (1980–2001); (b) United Kingdom (1991–2001); (c) Germany (1990–2002); (d) Italy (1987–2002). the story explaining UK inequality episodes. In fact, reflecting the increased variety of individuals who became self-employed over the period covered by our datasets, there was increasing concentration of people at both the low-middle and high income range of the distribution. Since this income source is well known as being more unequally distributed, the combination of the rising share and rising inequality of self-employment income is likely to have had a significant disequalizing effect. In sum, the decompositions by income source point to the contributory influences of labor earnings and capital income in explaining the level and trend of aggregate inequality at the low-middle and high end of the distributions respectively.

5.

Conclusion

Our analysis of the data for the US, the UK, Germany and Italy shows that there are two regimes in the income distribution. For the low-middle classes up to approximately 98%– Income Distribution: Inequalities, Impacts and Incentives : Inequalities, Impacts and Incentives, Nova Science Publishers, Incorporated, 2008.

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Fabio Clementi 0.6

0.15

∆SLabor income ∆SIncome from asset flows ∆S

Private transfers

0.4

∆SPrivate retirement income

0.3 0.2 0.1 0 −0.1 −0.2 −0.3

Changes in overall inequality and source contributions

Changes in overall inequality and source contributions

0.5

0.1

0.05

0

0.05

∆SLabor income

−0.1

∆S

Income from asset flows

∆SPrivate transfers

−0.4

∆SPrivate retirement income

−0.5

81/80

83/82

85/84

87/86

89/88 91/90 Year

93/92

95/94

97/96

−0.15

01/99

(a) United States (1980–2001)

92/91

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96/95 Year

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(b) United Kingdom (1991–2001)

0.2

0.1 ∆S

Labor income

0.08

∆S

Private transfers

0.15

Changes in overall inequality and source contributions

Changes in overall inequality and source contributions

∆SIncome from asset flows ∆SPrivate retirement income

0.1

0.05

0

−0.05

0.06

0.04

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0

−0.02 ∆S −0.04

Labor income

∆S

Pensions and net transfers

∆SProperty income −0.1

91/90

93/92

95/94

97/96 Year

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(c) Germany (1990–2002)

01/00

−0.06

89/87

93/91

98/95

02/00

Year

(d) Italy (1987–2002)

Figure 11. One-year dynamic decomposition of GE (2) inequality measure by income source for the power-law region of the income distribution: (a) United States (1980–2001); (b) United Kingdom (1991–2001); (c) Germany (1990–2002); (d) Italy (1987–2002). 99% of the total population the incomes are well described by a two-parameter lognormal distribution, whereas the incomes of the top 1%–2% are described by a Pareto’s (power-law) distribution. This structure have been observed in the analysis for different years. However, the indexes specifying the distribution change in time. Thus we studied the temporal change of the distribution. Firstly, we analyzed the gross domestic product and individual income growth rate distributions and noticed that after scaling the resulting empirical probability density functions appear similar for observations coming from different populations. This effect, which is quantitatively the same for countries and individuals, raises the intriguing possibility that a common mechanism might characterize the growth dynamics of gross domestic product and individual income, pointing in this way to the existence of correlation between these quantities. Secondly, from the analysis of the change of Gibrat’s and Pareto’s indexes, we confirmed that these quantities should not necessarily correlate each other. This means that different mechanisms are at working in the distribution of the low-middle

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income range and that of the high income range. One possible origin of no correlation is the change of the asset price, such as the stock price and the housing price, which mainly affects the high income distribution. These results led us to check the possibility that non-labor income sources are responsible for the Pareto’s functional form of the observed empirical income distributions at the very top of them. To this end, we disaggregated the level and time trend of aggregate income inequality into contributory influences from various income sources. Comparison between the low-middle and high income sections of the distributions suggests that the former comprises almost entirely of labor income, while earnings from financial or other assets play an important role in the latter. We conclude that this difference in the composition and inequality of the income is likely to be responsible for the lognormal nature of the former and the power-law behavior in the latter region of the distributions.

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Lee, Y., Amaral, L. A. N., Canning, D., Meyer, M., & Stanley, H. E. (1998). Universal features in the growth dynamics of complex organizations. Physical Review Letters, 81, 3275–3278. Lerman, R. I. (1999). How do income sources affect income inequality? In J. Silber (Ed.), Handbook of Income Inequality Measurement (pp. 341–362). Dordrecht and London: Kluwer Academic. Levy, M. (2003). Are rich people smarter? Journal of Economic Theory, 110, 42–64. Levy, M. (2005). Is risk-aversion hereditary? Journal of Mathematical Economics, 41, 157–168. Montroll, E. W., & Shlesinger, M. F. (1982). On 1/f noise and other distributions with long tails. Proceedings of the National Academy of Sciences USA, 79, 3380–3383. Montroll, E. W., & Shlesinger, M. F. (1983). Maximum entropy formalism, fractals, scaling phenomena, and 1/f noise: A tale of tails. Journal of Statistical Physics, 32, 209–230. Nirei, M., & Souma, W. (2007). A two factor model of income distribution dynamics. Review of Income and Wealth, 53, 440–459. Persky, J. (1992). Retrospectives: Pareto’s law. The Journal of Economic Perspectives, 6, 181–192. Piketty, T., & Saez, E. (2003). Income inequality in the United States, 1913–1998. Quarterly Journal of Economics, 118, 1–39. Income Distribution: Inequalities, Impacts and Incentives : Inequalities, Impacts and Incentives, Nova Science Publishers, Incorporated, 2008.

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Souma, W. (2002). Physics of personal income. In H. Takayasu (Ed.), Empirical Science of Financial Fluctuations: The Advent of Econophysics (pp. 343–352). Tokyo: SpringerVerlag. Stanley, M. H. R., Amaral, L. A. N., Buldyrev, S. V., Havlin, S., Leschhorn, H., Maass, P., et al. (1996). Scaling behavior in the growth of companies. Nature, 379, 804–806. Sutton, J. (2002). The variance of firm growth rates: The ‘scaling’ puzzle. Physica A: Statistical Mechanics and its Applications, 312, 577–590. Teitelbaum, D., & Axtell, R. (2005). Firm Size Dynamics of Industries: Stochastic Growth Processes, Large Fluctuations, and the Population of Firms as a Complex System (Economic Research Working Papers). Washington, DC: US Small Business Administration’s Office of Advocacy. (Available from http://www.sba.gov/advo/research/ rs247tot.pdf) Willis, G., & Mimkes, J. (2004). Evidence for the Independence of Waged and Unwaged Income, Evidence for Boltzmann Distributions in Waged Income, and the Outlines of a Coherent Theory of Income Distribution (EconWPA No. 0408001). Storrs Mansfield, CT: University of Connecticut. (Available from http://ideas.repec.org/p/ wpa/wuwpmi/0408001.html) Yoon, S.-M., & Kim, K. (2005). Distributions of Korean household incomes. Journal of the Korean Physical Society, 46, 1037–1039. Income Distribution: Inequalities, Impacts and Incentives : Inequalities, Impacts and Incentives, Nova Science Publishers, Incorporated, 2008.

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In: Income Distribution: Inequalities, Impacts and Incentives ISBN: 978-1-60692-202-6 Editor: Irving H. Wadell, pp. 79-98 © 2009 Nova Science Publishers, Inc.

Chapter 4

INEQUALITIES REDUCE OVERALL LEARNING AND WIDEN LEARNING GAPS: INEQUALITY MECHANISMS AND MITIGATION STRATEGIES Ming Ming Chiu State University of New York –Buffalo, NY, USA

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Abstract Country inequality yields greater inequality across families, across schools, and within schools, which widens the achievement gap between rich and poor and reduces overall student learning. Market economies increase individual effort, productivity, and unequal incomes. Governments can exacerbate inequalities through regressive taxes or favorable policies for special interests. Furthermore, weak legal systems that do not redress wrongs harm poor people disproportionately. Meanwhile, hierarchical cultures expect individuals to obey authority, encouraging deference to higher status people and undervaluing lower status people (status effects). At the local level, privileged parents often use their superior resources to give their children more educational resources (family inequality), sending them to schools with more resources and richer schoolmates (school inequality and schoolmate inequality). Within a school, staff can give richer students more resources, assign them to higher ability classes (tracking), or support their status effects in steep status hierarchies. Inequality can widen the achievement gap through disadvantaged students’ fewer learning opportunities and worse discipline. Meanwhile, six inequality mechanisms reduce both privileged and disadvantaged students’ learning. First, richer parents benefit less than poorer parents from public resources and advocate less public education spending. Second, teachers and students in less equal societies view one another as less similar, feel less solidarity, and share fewer educational resources. Third, less solidarity reduces trust and fosters corruption, which siphons off educational resources. Fourth, less equal countries have higher crime rates, more conflict, and worse student discipline. Fifth, steep status hierarchies distort perceptions of one another’s competencies and needs. Lastly, the effects of diminishing marginal returns are larger in less equal countries. National and school strategies can mitigate these harmful effects. Political coalitions can support welfare, progressive taxes, transparency, minimum standards, or mixing students. School leaders can allocate school resources equally, diversify teaching duties, eliminate

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Ming Ming Chiu tracking, support a caring school community, express clear goals and standards, align school goals and incentives, and enhance transparency of information and decision-making.

Greater inequality not only widens the achievement gap between the privileged and the disadvantaged but also reduces overall student achievement (Coleman et al., 1966; Jencks, Smith, Acland, & Bane, 1972; Micklewright & Schnepf, 2007). The effect of inequality on student learning is an important policy issue because it suggests that proper re-allocation of existing resources is a low-cost method of improving student learning, in contrast to interventions requiring extra resources that tight school budgets cannot afford. Hence, understanding the link between inequality and overall achievement can help a society optimally allocate its limited resources to maximize the achievement of her students. In this chapter, I examine how country, family, and school inequalities affect student learning and possible strategies for addressing them. These inequalities can widen the achievement gap through differences in educational resources and learning opportunities. Furthermore, these inequalities can reduce overall student learning through less sharing, fewer educational resources, worse student discipline, status effects, and diminishing marginal returns. Lastly, these country, family, and school inequality mechanisms suggest several national and school strategies that might reduce their harmful effects on student learning.

Country, Family, and School Inequalities

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Country Inequalities Country inequality reduces student learning and widens the achievement gap through its economy, government policies, legal system, and cultural values. When country inequality (e.g., Gini) is 10% higher than average, students score 2% lower in science, 1% lower in mathematics, and 1% lower in reading than other students, controlling for total resources in a study of fifteen-year-olds in 41 countries (Chiu & Khoo, 2005). In countries with greater inequality, the lowest SES students suffer more than the highest SES students (–2% vs. –1% respectively when inequality is 10% higher than average; Chiu, in press). (Greater inequality showed similar negative effects on students at all levels of academic achievement; Chiu, in press). A country’s inequality is linked to its economy (see Figure 1). In a market economy, financial incentives encourage individuals to exert more effort to increase productivity. As a result, individual incomes differ according to the demands for their labor or capital. Furthermore, country wealth is related to inequality, though in a complex manner. Inequality often follows an inverted U-shaped relationship; as a country develops, income inequality will often rise, peak, and eventually decline (Kuznets, 1955). In the Organization for Economic Cooperation and Development (OECD) countries for example, richer countries often show greater equality (World Bank, 2007).

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Inequalities Reduce Learning

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Figure 1. Sources of inequality that affect student achievement.

Governments can exacerbate these inequalities through regressive taxes or favorable policies for specific interests. A regressive tax system (e.g., general sales tax instead of property taxes) forces poorer people to pay proportionately more than richer people (Schenk & Oldman, 2007). Favors for special interests can include unequal allocation of public assets, industry subsidies, and entry barriers. Countries with substantial resources (oil, gold, timber, minerals, etc.) often sell these vital resources below cost (or simply give them away) to elites at the expense of poorer citizens (Schubert, 2006). Furthermore, governments often subsidize specific firms or industries (e.g., paying firms not to grow food) in exchange for financial and/or political support (Anderson, Martin, & Valenzuela, 2006). Through legislation, regulation, or licensing, government-created entry barriers (e.g., trade tariffs) reduce competition, thereby enabling favored firms (especially monopolies) to earn higher profits at the expense of consumers (Mankiw, 2004).

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Weak legal systems also increase inequality and facilitate corruption. For people who have been wronged by others and seek redress, a weak legal system offers little protection or recourse (Merryman & Perez-Perdomo, 2007). Although the wealthy or privileged can seek redress through payment or political means, the poor and weak cannot, so they suffer more under weaker legal systems (Pepys, 2007). Weak legal systems also facilitate corruption. When people steal from the school system, they take away educational resources from students (often poorer ones), resulting in fewer educational opportunities and less learning (Segal, 2005; Williams, 2005). A country’s cultural values can also affect inequality. Cultures range from egalitarian to hierarchical. Whereas egalitarian cultures expect individuals to respect and treat one another as equals, hierarchical cultures expect individuals to follow hierarchical roles and to obey authority (Hofstede, 2003). In hierarchical cultures, individuals often defer to higher status people while discouraging, undervaluing, or ignoring those with lower status (status effects; Chiu, in press; Chiu & Khoo, 2005; Chiu & Khoo, in press).

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Family Characteristics The above country inequalities contribute to family inequalities. A student’s family members can provide extra resources or compete for them (see Figure 1). Families with more parents (two vs. one vs. none) typically have higher socio-economic status (SES), more educational resources at home (e.g., books), and more parent-time to spend with their children (greater parent communication and involvement, Amato, 2001; Entwisle & Alexander, 1995, Horvat, Weininger, & Lareau, 2003). Among fifteen-year-olds in 41 countries for example, those with two parents scored 6% higher in science achievement than those living without parents and 2% higher than those with single parents (Chiu, 2007). According to Sirin's (2005) meta-analysis, when a student's family SES is 10% higher than average, he or she averages 3% higher academic achievement than other students. Specifically, family conversations often help children acquire cognitive and social skills, and social and cultural norms more effectively (Ochs, Taylor, Rudolph, & Smith, 1992). In contrast, divorced or separated parents have fewer resources and face more challenges in caring for their children, who might receive less attention (e.g., from step-parents). Children who witness conflicts between their separated parents might suffer emotionally, have lower academic motivation, and learn less (Amato, 2001). Among fifteen-year-olds in 41 countries, those with two parents scored 2% higher in mathematics than those in blended families (parent and step-parent, Chiu & Zeng, 2008). Meanwhile, immigrant parents, especially those that speak a foreign language, often have less cultural capital to share with their children (Portes & MacLeod, 1996). For example, native born students outscored first and second generation immigrants in science achievement by 10% and 6%, respectively (Chiu, 2007). Family members who primarily compete for family resources (such as grandparents and siblings) reduce a child’s access to family resources (resource dilution theory; Downey, 2001). Some students might benefit from their grandparents' physical, informational, social, and emotional resources (DeLeire & Kalil, 2002). However, students who live with poor or ill grandparents compete with them for limited family resources (Patillo-McCoy, Kalil, & Payne, 2003). Furthermore, many countries only recently instituted universal education; so, many

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grandparents received little schooling. As the academic achievements of resident grandparents and grandchildren are linked, students living with grandparents scored 4% less in mathematics than other students (Chiu & Zeng, 2008). Siblings can also compete for family resources (Downey, 2001). As younger siblings compete for family resources only after their births, older siblings initially have more family resources (Powell & Steelman, 1993). Students average 1% lower in science for each extra sibling and an extra 1% lower for each older sibling (Chiu, 2007).

School Inequality

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Unequal school systems yield disparities both across schools and within schools. While differences across schools include unequal schoolmates and unequal educational resources, within school inequality includes unequal resource allocation, tracking, and steep status hierarchies. School system. School systems based on open markets or cronyism yield greater inequality across schools than those based on random allocation (see Figure 1). In open markets, elite private schools charge high tuitions to cater to rich students, using the money to hire skilled staff (principals, teachers, etc.) and buy advanced educational resources (computers, labs, etc.; Darling-Hammond & Post, 2000; Rothstein, 2000). Similarly, locallyfunded public schools (e.g., via neighborhood taxes) serve as indirect open markets, in which richer families move to richer neighborhoods with better funded schools (Hoxby, 2001). In the United States for example, funding per student in one school can be 25 times higher than in another as a result of government preferential funding, private school alumni donations, and local tax-funding of schools (Rothstein, 2000). In other public school systems, cronyism concentrates skilled staff and educational resources in elite schools, to which families with more social capital (e.g., government officials) send their children (Lloyd & Blanc, 1996). In less equal school systems, privileged parents have more incentives to use their financial and/or social capital to enroll their children into better schools. School inequality is substantially greater in poorer countries (specifically, those with less than $16,000 GDP per capita in 1990 US Dollars, Gamoran & Long, 2006; see also Baker, Goesling, & LeTendre 2002; Heyneman & Loxley, 1983). Across school inequality. These unequal school systems yield schools with unequal schoolmates and unequal school resources (see Figure 1). Open markets and cronyism tend to cluster elite housing together in elite neighborhoods in many countries (e.g., Chile, Germany, Indonesia). As a result, high SES students often live together in the same neighborhoods and attend the same schools, separating them from low SES students who cluster together in poorer neighborhoods (schoolmate inequality, Chiu & Khoo, 2005). Through interacting with privileged schoolmates, a student can benefit from their parental capital, material resources, diverse experiences, and higher academic expectations (Pritchett, 2001; Coleman et al., 1966; Jencks et al., 1972; Pong, 1997, 1998). Privileged classmates tend to help a student understand and appreciate the societal and cultural value of schooling, thereby contributing to a class or school culture of higher academic achievement and better discipline (Chiu & McBride-Chang, 2006; Davalos, Chavez, & Guardiola, 2005; Willms, 1999). As a result, low

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SES students often benefit from high SES classmates' greater learning resources (Coleman et al., 1966; Jencks et al., 1972). In countries with greater schoolmate inequality however, low SES students are less likely to have high SES schoolmates. Thus, when schoolmate inequality was 10% higher than average, low SES students scored 1% lower than other students did in mathematics and science (Chiu & Khoo, 2005). Unequal school systems yield schools with unequal resources (see Figure 1). Better schools often have better physical conditions, more educational materials (books, computers) and better teachers than other schools (Berner, 1993; Comber & Keeves, 1973; Fuller, 1987; Fuller & Clarke, 1994). These schools often have higher teacher-to-student ratios and betterqualified teachers (e.g., university degrees; Fuller & Clarke, 1994; Greenwald, Hedges, & Laine, 1996; Rivkin, Hanushek, & Cain, 2005). Superior teachers also show better teaching processes and maintain better student discipline and relationships with their students (e.g., Ma & Willms, 2004; Rowan, Correnti, & Miller, 2002; Willm & Somer, 2001). Hence, students in superior schools often have greater learning opportunities and capitalize on them to learn more (Greenwald, Hedges, & Laine, 1996). Higher SES families in school systems dominated by open markets or cronyism often send their children to these superior schools. Thus, low SES students often attend the worst schools. As high SES students are more likely to have these education resources at home, school resources tend to benefit low SES students more than high SES students (Coleman et al, 1966). Thus, unequal schools tend to result in worse schools for lower SES students and lower academic achievement overall. In countries whose inequality of resources across schools exceeded the mean by 10%, students scored 1% lower than other students (Chiu, in press). Within school inequality. In addition to inequality across schools, students can also suffer from inequality within a school (see Figure 1). Students whose within-school inequality was 10% higher than average scored lower than other students in reading, mathematics, and science by 3%, 3% and 2%, respectively (Chiu & Khoo, 2005). Within school inequality includes unequal resource allocation, tracking, and steep status hierarchies. Privileged parents can leverage their superior resources to direct more educational resources for their children, leaving fewer resources for disadvantaged children. These methods might include explicit bribes of teachers (e.g., Hani, 2005), special favors through social connections with the school staff (cronyism, Lloyd & Blanc, 1996), greater affinity with teachers due to similar social norms or cultural capital (Bourdieu, 1993; Heath, 1983; Roscigno & Ainsworth-Darnell's, 1999 "cultural gatekeeping"). For example, after a lesson that a student liked, a parent with more social skills and cultural capital might send the teacher a thank you note and ask for study tips. As a result, the teacher might pay more attention to this student. Furthermore, some schools (or school systems) assign students with similar past achievement scores together in a class (or a school, or a group within a class, also known as tracking, ability grouping, or streaming). Although tracking does not raise overall learning, it sharply increases the variance in learning (studies show non-significant or slightly negative effects on learning, while variance in achievement averages 25% higher in each country that tracks, Hanushek & Wöbmann, 2006; Ireson & Hallam, 1999; Opdenakker & Van Damme, 2001; Slavin, 1990). Tracking is often accompanied by unequal allocation of other educational resources. Higher tracks often have richer students, better teachers, and more/better educational

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materials. As ability-grouping creates elite schools or classes, privileged parents often advocate ability grouping, and their children are often placed in high track schools, classes, or groups within a class (Opdenakker & Van Damme, 2001). Hence, high-track classes have proportionately more high SES students (Gamoran, 1987; Opdenakker & Van Damme, 2001). Like students with higher SES schoolmates, those with higher SES classmates often enjoy their classmates' greater economic, social, and cultural resources. Such clustering of students by SES also facilitates targeting of school resources to richer students (Chiu & Khoo, 2005). Teachers are often attracted to the smarter students in higher tracks. Not surprisingly, teachers teaching higher tracks often have better academic qualifications, more years of schooling, and more teaching experience than other teachers (Darling-Hammond & Post, 2000; Oakes, 1985). These positive teacher characteristics are linked to more effective instructional practices in higher tracks. Compared to teachers in lower tracks, teachers in higher tracks often have better prepared lessons, teach more enthusiastically, use more complex teaching materials, teach at a faster pace, and lead more stimulating discussions (Gamoran, 1987; Grossen, 1996; Oakes, 1985, 1990;Vanfossen, Jones & Spady, 1987). In contrast, lower-track students receive fewer explanations and directions regarding teacher expectations and goals, reducing learning opportunities (Evertson, 1982; Goodlad, 1984; Oakes, 1985). These distinct instructional practices might explain the differences in academic performance across tracks (Gamoran, 1989; Grossen, 1996; Van Houtte, 2004). Allocation of school resources also interacts with a school’s status hierarchy to increase inequality. According to status characteristics theory, people with higher status receive more attention and other social rewards (Cohen, 1994). Cohen (p. 23) states that schools, like most institutions, have “an agreed-on rank order where it is generally felt to be better to be high than low rank” or a status hierarchy. In schools with “steep pyramid” status hierarchies, a small group of elite staff and students receive extra resources and social rewards, separating them from others. In contrast, schools with “gentle hill” status hierarchies share resources and social rewards more equally, so people view one another as more equal. Steep status hierarchies sharpen the differences among staff and students, tightly aligning people’s behaviours with their expectations based on perceived status differences. According to expectation states theory, status is linked to the expectation of competencies for the current activity (Berger, Cohen, & Zelditch, 1972; Dembo & McAuliffe, 1987). High status is conferred on people who are expected to contribute positively to a desired outcome. These expectations create different opportunities to perform and receive rewards. Members can selectively invite and defer to high status members' views while discouraging, undervaluing, or outright ignoring those of lower status members. By doing so, members enact their expectations of high status members dominating the interaction. Through their human capital, privileged parents can also teach their children social norms and cultural capital to create greater affinity with teachers (Bourdieu, 1993; Heath, 1983). Teachers view these students as higher status, have higher expectations of these students, and often give them more attention and assistance (Roscigno & Ainsworth-Darnell's "cultural gatekeeping", 1999). According to Hallinan and Kubitschek (1999), higher teacher expectations also tend to boost student confidence, resulting in greater goal attainment. In contrast, teachers with low expectations tend to give lower status students tasks that do not sufficiently challenge them, often resulting in both lower motivation and less learning. Likewise, students can also enact these status expectations to favour high status classmates

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over low status classmates during academic discussions or social interactions, either inside or outside of class (Cohen, 1994; Dembo & McAuliffe, 1987; Kircher & Davis, 1986).

Inequality Mechanisms Inequality can harm disadvantaged students through fewer learning opportunities and worse discipline, thereby widening the achievement gap. In addition, inequality can operate through mechanisms that harm both privileged and disadvantaged students to reduce overall achievement.

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Inequality Mechanisms that Harm Low SES Students Inequality can reduce disadvantaged student’s learning opportunities and discipline. First, students with fewer educational resources (books, teachers, etc.) have fewer learning opportunities on which to capitalize to learn. These resources can be physical (e.g., books, computers) or intangible (e.g., schoolmate motivation, teacher explanations). Second, lower status students are more likely to be disrespected and react violently, showing worse student discipline. In less equal schools, low-status students lack the social standing and self-esteem that teachers and peers value (Cohen, 1994). Thus, low-status students typically have fewer friends and weaker social relationships than high-status students (social capital, Putnam, Leonardi, & Nanetti, 1993). As peer judgments often affect a student's self-esteem, low-status people often feel both socially and psychologically insecure (Wilkinson, 2004). Low-status students' lack of self-esteem often makes them more vulnerable to feeling disrespected or losing face (Gilligan, 1996). Thus, they often react to disrespectful comments with physical violence more often than do higher status students (Gilligan, 1996; Tracy & Tracy's [1998] face attacks). Likewise, schools that give privileged students more resources (better equipment, better teachers, and so on) can fuel disadvantaged students' resentment of privileged students (Goldsmith, 2004). This inequity undermines the legitimacy of the school's authority (Henze, Katz, & Norte, 2000). As disadvantaged students become less likely to respect school authority or rules, they are more likely to violate school rules, yielding poorer student discipline (Arum, 2003).

Inequality Mechanisms that Harm Both High and Low SES Students Inequality harms all students, not only low SES students. Students achieve less in countries with greater family inequality due to several mechanisms: (a) less sharing, (b) less educational investment, (c) corruption, (d) poorer student discipline, (e) status distortions, and (g) diminishing marginal returns (See Figure 2). First, people prefer to befriend and interact with others of similar gender, age, status, and so on (homophily, McPherson, Smith-Lovin, & Cook, 2001). Within a steeper status hierarchy, teachers and students differ more and feel less social solidarity with one another. As a result, they are less likely to befriend one another, share resources, or help one another, thereby yielding less learning (Chiu, 2007).

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Figure 2. Processes through which inequality mechanisms might affect all students.

Second, countries or neighborhoods with greater family inequality invest in fewer educational resources. For example, countries with 10% more inequality than average had 2% fewer school resources (Chiu, in press). Elite families often have many more books and other resources at home than others, so their children need fewer resources at school. As a result, elites might argue that families should pay for more of their own children’s schooling, resulting in fewer public school resources (Benabou, 1996). When students' families pay for much of their education however, poorer parents cannot afford the optimal amount for their children, resulting in fewer educational resources overall (Benabou, 1996). Third, in less equal schools and societies, people feel less social solidarity, trust one another less, and are more willing to pursue selfish gains at the expense of others, so staff and students tend to be more corrupt (Uslaner, 2004). When people steal from the school system, they take away educational resources from all students, resulting in fewer learning opportunities and less learning (Segal, 2005; Williams, 2005). Corruption can also reallocate more educational resources within the school system, often to the rich at the expense of others (Uslaner, 2004). Fourth, less equal countries (e.g. USA) often have higher crime rates and more conflict (Freeman, 1995; Wilkinson, 2004; Persson & Tabellini, 1994), which might yield poorer student discipline, distract student attention away from academic study, and reduce student learning (see Figure 2; DeBaryshe, Patterson & Capaldi, 1993). Not only do less equal countries have higher crime rates, teenagers also generally commit disproportionately more crimes, so students in these countries steal more and engage in more physical violence (e.g., Freeman, 1995; Mocan & Rees, 2005; Wilkinson, 2004). Consider economic crime first. A

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low-skilled person often earns less after taxes from the same job in a less equal country (with wider pay ranges and less taxation) than in a more equal country (with narrower pay ranges and more taxation). Thus, for a low-skilled person, crime pays relatively more (crime pay – legal pay) in a less equal country than in a more equal country (Krueger, 2002). For lowachieving students in less equal countries, their futures hold few promising job opportunities, so they have less incentive to study or work for future gains and more incentive to commit economic crimes for immediate gains. Likewise, violence is more prevalent in less equal societies, especially among teenagers (Mocan & Rees, 2005; Wilkinson, 2004). In less equal societies, there are more low-status students who lack the status symbols (e.g., jewelry, expensive clothes, etc.) that peers value and seek in their friends (Frank, 1999). In the less trustful milieu of less equal countries or schools that favor privileged students, lower status students are more likely to be disrespected and react violently, showing worse student discipline (Arum, 2003; Gilligan, 1996; Tracy & Tracy, 1998; Uslaner, 2004; Wilkinson, 2004). The poorer discipline of disadvantaged students can spill over into the general student population. Furthermore, these greater student discipline problems can heighten all students' concerns over their physical and emotional safety. Distracted from their studies by safety concerns, students often have lower academic achievement (e.g., DeBaryshe, Patterson, & Capaldi, 1993). Fifth, a steep status hierarchy can also distort perceptions of one another’s competencies and needs. When teachers and students enact their status expectations, they tend to be less aware of all students’ actual competencies and needs (Ferguson, 2003). For example, teachers might tend to overlook high track students’ weaknesses or underestimate low-track students’ strengths. Furthermore, students might likewise reduce lower status students’ participation opportunities and distort evaluations of one another’s ideas through the greater influence of high status students (Dembo & McAuliffe, 1987; Kircher & Davis, 1986). These distorted perceptions can cause inefficient allocation of resources and reduce student learning (Cohen, 1994). Lastly, inequality lowers overall student achievement due to diminishing marginal returns. Consider a thirsty woman and two glasses of water. She greatly values the first glass of water and drinks it all. Her thirst quenched, she does not finish the second glass of water, showing its lower value (diminishing marginal returns, Mankiw, 2004, p. 273). Likewise, rich students have more educational resources than poor students do. Hence, poorer students typically benefit more from an extra book than richer students do. With greater inequality, richer students benefit less from their extra resources, resulting in lower education outcomes overall (Chiu & Khoo, 2005). Thus, schools that allocate more resources to richer students exacerbate the effect of existing family inequalities through diminishing marginal returns. In sum, students who receive more family, school or schoolmate resources have more learning opportunities on which they can capitalize to learn more. Privileged students with higher status receive more attention and other social rewards from other students and school staff. In contrast, low status students are more likely to have disciplinary problems, especially in schools that favour higher status students. Lastly, greater inequality can hurt all students through fewer public educational resources, less social solidarity more corruption, more student discipline problems, status-distorted assessments, and diminishing marginal returns.

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Policy Implications As these inequality sources and mechanisms reduce student learning and achievement, several strategies might mitigate these harmful effects. At the country level, political coalitions can support systemic changes to reduce the harmful effects of national inequality. Within each school, educational leaders can modify school structures and processes to reduce the effects of students’ unequal economic backgrounds.

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Country Level Strategies Nations can increase family equality through welfare, progressive taxes, transparency, minimum standards, or mixing students (see Figure 3). Welfare redistributes tax revenue from the rich to the poor by targeting resources to the disadvantaged (e.g., food stamps, unemployment benefits, subsidized student lunches, and so on). As school resources overlap with family resources, extra school resources typically benefit poorer students more than they benefit richer students, due to diminishing marginal returns. Hence, governments might also mitigate disparities in family wealth by giving more resources to poorer schools or to schools with poorer students. Similarly, governments can collect proportionately more tax revenue from richer people than poorer people through progressive taxation (graduated income tax, estate tax, taxes on luxury items, tax exemptions on necessities [food, clothing], and so on). Transparent decision making provides valuable information and reduces bias (both actual and perceived). For example, publicizing the school criteria for acceptance of student applicants (exam scores, residence, etc.) helps families and their children prepare appropriately for their preferred schools. Furthermore, it reduces the potential for cronyism to influence assignment of students to schools. Moreover, transparency reduces the perception of bias and enhances respect for educational authorities. Minimum standards benefit everyone by providing valuable information (e.g., nutrition or safety standards) or free products and services (universal schooling, emergency health care, court-appointed lawyers). Still, the poorest families benefit the most as they are the least likely to obtain this information independently and to afford the products and services with their own income. As common standards benefit everyone, they tend to have more political support than welfare. For example, universal and mandatory schooling has reduced the inequality in student achievement due to family SES by over 40% (Hanushek & Wöbmann, 2006; see also Blossfeld & Shavit, 1993). Many countries (e.g., Japan) give schools the same level of funding for each student from general taxes (e.g., income tax), which do not distort tax revenues unlike equal funding mechanisms based on local property taxes (Hoxby, 2001). Likewise, many countries (e.g., Korea) require minimum training and certification programs for all teachers (Wang, Coleman, Coley, & Phelps, 2003). Furthermore, mandatory teacher certification programs can help persuade teachers to devote attention to all students, not only the rich ones. This standardized distribution of resources within a school can also enhance the legitimacy of the school's authority (Henze, Katz, & Norte, 2000). If students accept the legitimacy of school rules and have more selfdiscipline, they can foster an environment that supports academic achievement (Arum, 2003).

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Figure 3. Possible strategies for addressing inequality effects on student achievement.

In large cities with low transportation costs (e.g., Seoul), school systems can mix students with different family SES together in the same school with minimal travel time. By mixing students of different economic strata, they are more likely to share resources and learn more. Due to diminishing marginal returns, mixing students benefits poorer students more than it benefits richer students (Coleman et al., 1966; Jencks et al., 1972). Mixing students also hinders the targeting of extra resources to richer students and hence hinders unequal allocation processes.

School Level Strategies Principals and school leaders can reduce the harmful effects of inequality on student learning by: allocating resources equally, assigning each teacher diverse teaching duties, eliminating tracking, promoting a caring school community, articulating clear goals and

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standards, aligning school goals and incentives, and enhancing transparency (see Figure 3). First, leaders can allocate students, teachers and physical resources more equally. Principals can randomize the allocation of students across courses and multiple classes rather than grouping students by ability. The random allocation of students also prevents assignment of the best teachers to the highest achieving or most privileged students and hinders unequal allocation of resources to students (Chiu & Khoo, 2005). Second, principals can assign capable teachers to a variety of grade levels and subjects. Even if principals cannot randomize student allocation, the reallocation of teachers reduces the likelihood that the best teachers only teach the best students in the highest grades (Darling-Hammond & Post, 2000). By teaching multiple grades and courses, teachers also instruct the same students in different classes across different years. Thus, teachers have fewer students under their charge over time and can devote more time to each student, yielding closer teacher-student relationships (Darling-Hammond, 1997). Third, eliminating tracking increases contact time among students of different SES levels. This fosters diverse friendships, aids sharing of schoolmate resources, and can flatten the status hierarchy (Hallinan & Williams, 1989; Joyner & Kao, 2000; Quillian & Campbell, 2003). Fourth, closer teacher-student relationships are the building blocks for a caring community (Darling-Hammond, 1997). Similarly, joint activities among students with suitable teacher guidance (e.g., cooperative learning during lessons, extra-curricular teams, etc.) increase student contact with one another which can help foster a culture of cooperation (Gutierrez, Baquedano-Lopez, Alvarez, & Chiu, 1999). Care for students can encompass their cognitive, social, and moral development. Fifth, regularly articulating clear, shared goals and standards (e.g., student learning and mutual respect) helps students and teachers understand and develop pragmatic strategies to achieve these common goals (Bransford, Brown, & Cocking/NRC, 2000). Clear, shared goals focus the school community on understanding central issues and help everyone concentrate effort, time, organization, and strategies on redressing student inequalities (Ames & Archer, 1988). Clear standards also provide important measures of progress and can help identify short-term goals (Ames & Archer, 1988). Sixth, principals can review their schools’ incentive structures in order to better align teacher and student efforts with the latter’s cognitive and social goals. For example, teachers or students who improve academic achievement or self-discipline from year to year can receive greater rewards (for example, public recognition or school privileges [Wöbmann, 2000]). A broad range of rewards can be given each year, commensurate with the degree of improvement. As students (and teachers) often work together to achieve greater improvements, group rather than individually rewards can also encourage cooperation (Johnson & Johnson, 1999). Suitably rewarding more people can help flatten the status hierarchy among both staff and students. Seventh, principals can enhance transparency to aid information flow and reduce bias. Greater transparency provides administrators, teachers, and parents with more information about their students and children to improve their learning and well-being (e.g., a database with customized access). Furthermore, administrators can transparently explain school decisions to reduce both actual and perceived bias. Increased transparency may involve consciously explaining major decisions and how they are made, consulting staff, and using reasoned persuasion rather than dictating orders. As information asymmetry creates

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greater inequality; increased transparency and information flow can flatten status hierarchies and help build more equal communities. Note that this set of strategies is not comprehensive. Other strategies might focus, for example, on curriculum structures, appropriate pedagogies, professional development, or deeper community connections, to name a few. However, given the structural stratification in an unequal school system, reconsidering resource allocation and addressing status differentiation might be good starting points.

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Conclusion Country, family, and school inequalities widen the achievement gap between rich and poor and reduce student learning. A country’s economy, government policies, legal system, and cultural values can influence inequality in a country. Family inequalities yield school and schoolmate inequalities as privileged parents use their superior resources to send their children to schools with more resources and richer schoolmates. Within a school, school staff can give richer students more resources, assign richer students to higher ability classes, or support steep status hierarchies whose status effects benefit richer students. Inequality can widen the achievement gap through disadvantaged students’ fewer educational resources, fewer learning opportunities, or worse discipline. Meanwhile, inequality can operate through six mechanisms that harm both privileged and disadvantaged students to reduce overall achievement. First, richer parents advocate less public education spending. Second, teachers and students in less equal countries feel less solidarity and share fewer educational resources. Third, less solidarity yields less trust and fosters greater corruption which leeches educational resources away from students. Fourth, less equal countries’ higher crime rates and greater conflict yield worse student discipline. Fifth, steep status hierarchies distort perceptions of one another’s competencies and needs, resulting in inefficient misallocation of resources. Lastly, inequality yields larger effects of diminishing marginal returns. As these inequality sources and mechanisms reduce student learning and achievement, several national or school-level strategies might mitigate these harmful effects. Nationally, political coalitions can increase family equality through welfare, progressive taxes, transparency, minimum standards, or mixing students. At the school level, principals and school leaders can reduce the harmful effects of inequality by allocating school resources equally, assigning diverse teaching duties, eliminating tracking, promoting a caring school community, articulating clear goals and standards, aligning school goals and incentives, and enhancing transparency.

Acknowledgements I appreciate the helpful comments by Sze Wing KUO and Xiaorui HUANG.

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In: Income Distribution: Inequalities, Impacts and Incentives ISBN: 978-1-60692-202-6 Editor: Irving H. Wadell, pp. 99-115 © 2009 Nova Science Publishers, Inc.

Chapter 5

NEOLIBERALISM’S TRIUMPH? FALLING UNION DENSITY, FALLING MINIMUM WAGES, AND RISING WAGE INEQUALITY IN THE UNITED STATES, 1980-2000 Thomas W. Volscho Department of Sociology, University of Connecticut, CT, USA

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Abstract Contemporary observers contend that neoliberal economic policies are attempts to restore the political-economic power of the capitalist class. This study examines the effects of unions and the minimum wage on wage inequality over a twenty year period using state data. The response variable in this study is residual wage inequality among full-time year round nonagricultural workers age 18 to 64 within the lower 48 states over the period 1980 to 2000. Consistent with institutionalist theorists, unions and the minimum wage are inversely associated with residual wage inequality. However, the effect of union density is found to shift from inverse to positive for earners closer to the left tail of the wage distribution by the late 1990s. The shift in the effect is interpreted as potentially the result of neoliberal economic policies intended to weaken labor unions in an attempt to restore class power.

Introduction Neoliberalism is a set of political and economic practices that emphasize the role of markets in economic outcomes (Harvey, 2005). While on its face, the project is construed as a neutral process of achieving “efficient markets,” scholars and others have argued that from its inception neoliberalism was designed to restore ruling class power (Duménil & Lévy, 2004; Harvey, 2005) Recently, social scientists have looked toward neoliberal economic policies as a potential cause of rising economic inequality (Lobao, Rulli, & Brown, 1999; Lobao & Hooks, 2003; Volscho, 2007). In this chapter, I examine two institutional arrangements that have been attacked by neoliberal policies: unions and minimum wages.

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To examine the effects of these policies on the restoration of class power (reflected by increasing wage inequality), I study the effect of unions and minimum wages on residual wage inequality using panel data from the lower 48 continental United States. Part of the impetus of the study reported in this chapter is to test for change in how these institutional factors affect wage inequality. Any declining significance of these institutional arrangements is consistent with the arguments posed by scholars critical of the neoliberal project. In the next section, I review the neoclassical textbook arguments against unions and minimum wages that neoliberal ideology uses to justify the dismantlement of these institutional arrangements.

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Neoclassical Theories of Union and Minimum Wage Effects on Wage Dispersion Many institutional economists argue that minimum wages and unions lessen wage inequality (Freeman & Medoff, 1984; Freeman, 1996; Galbraith, 2000; Hirsch & Addison, 1986). However, a long-standing hypothesis from neoclassical economics is that unions and minimum wages produce more unemployment and more inequality. Because a union contract or minimum wage sets a non market-determined wage, it artificially raises the price of labor (Stigler, 1946). Due to the increase in price, demand for labor will decline and unemployment of workers whose marginal productivity falls below the new wage will increase. This follows standard price theory in that labor supplied and labor demanded are both functions of the wage rate. Labor supplied increases as a function of the wage rate (w), while labor demanded decreases as a function of w. The intersection of these functions results in the pure market equilibrium wage rate (w*). Unions and the minimum wage can achieve w > w*, but the demand for labor will decrease and some workers may flow into industries and/or occupations not covered by union contracts or the minimum wage (where w’ < w* < w). Other workers may end up unemployed. The labor supply in the uncovered sector will increase and it is likely that within the uncovered sector, wage inequality will increase, but also that the average w’ will decline relative to both w* and w generating greater within and between sector wage inequality (see Brown, Gilroy, & Kohen, 1982; Freeman & Medoff, 1984). Thus, neoclassical reasoning makes a specific theoretical prediction that greater union density and higher minimum wages may actually increase wage inequality. Over fifty years ago, Stigler stated, in reference to the minimum wage that “The manipulation of individual prices is neither an efficient nor an equitable device for changing the distribution of personal income,” (Stigler, 1946) Neoliberal economic reasoning relies on the competitive textbook model outlined above to make a case against unions and the minimum wage. Two prominent neoliberal economists, Milton and Rose Friedman, argued that “…the gains that strong unions win for their members are primarily at the expense of other workers…Union leaders always talk about getting higher wages at the expense of profits. That is impossible: profits simply aren’t big enough,” (Friedman & Friedman, 1980: 233-4). This view suggests that unions do not shift the relative income shares between capital and labor, but that unions redistribute income among wage earners. If this theory is true, then unions simply make some workers better off at the expense

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of other workers. Thus, neoliberal economists often make the case that unions and minimum wage will raise inequality rather than reduce it.

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Institutionalist Theories of Union and Minimum Wage Effects While the neoclassical theoretical model of the labor market has reigned dominant in policy discussions of the minimum wage, the argument that higher minimum wages and unions automatically cause disemployment is not uniformly consistent with empirical studies of labor markets (Card & Krueger, 1995; Card, 2001; Freeman & Medoff, 1984). Card and Krueger’s (1995) reported the results of quasi-experimental research that estimated fast-food employment before and after a minimum wage increase and also re-analyzed econometric evidence from several prior studies. While some subsequent research has focused on the response of hours of work instead of employment (Couch & Wittenburg, 2001), Card and Kruger’s research raises a lot of doubt about the conventional textbook model. Many institutional economists have argued that unions and the minimum wage may actually operate to reduce wage inequality (Freeman & Medoff, 1984; Freeman, 1996; Koeniger, Leonardi, & Nunzjata, 2007; Lester, 1947; Volscho, 2005; Volscho, 2007; Webb, 1912). A minimum wage may function to increase wage rates of low-paid workers by reducing profits (Levitan & Belous, 1979). Other analysts have suggested that a minimum wage may create incentives for a firm to minimize reliance on supervisors and pass some of the savings off as higher wages to low-wage workers (Calvo & Wellisz, 1979)--noted as early as (1912) by Webb. Card and Kruger (1995) have argued that increased minimum wages may have a “ripple effect” on the wage distribution thereby lessening inequality. Institutional economists have argued that through various mechanisms unions can reduce the variance in pay. Union contracts may specify the standardization of rates of pay (Hirsch & Addison, 1986). By standardizing rates of pay, unions can minimize variance in wages (Freeman & Medoff, 1984). Unions operate within an ideology of egalitarianism and as such must work to maximize wages of all members which would likely have the effect of reducing wage inequality. One recent cross-national study of France, the United States, and the United Kingdom demonstrated that in France where union membership and minimum wages increased wage inequality decreased whereas the opposite occurred in the U.K. and U.S. (Koeniger et al., 2007; Mosher, 2007). The declines in U.S. union membership have been suggested to have partially caused rising inequality. Some studies have found that declining union density explains a significant portion of increasing wage inequality in the 1980s (Freeman, 1993) while some cross-sectional research suggests that higher levels of union density are associated with lower levels of earnings inequality across MSAs in the late 1990s (Volscho & Fullerton, 2005). In this paper, I will test the institutionalist hypothesis that unions and the minimum wage reduce wage inequality. Thus, we can expect higher levels of union density and the minimum wage to be associated with lower levels of wage inequality in the states. Furthermore, I will test for potential shifts in the effect of these factors as neoliberal economic ideologies have increasingly informed policies since the early 1980s (Duménil & Lévy, 2004; Harvey, 2005; Lobao et al., 1999; Lobao & Hooks, 2003) and potentially weakened the efficacy of unions and minimum wages. In the next section, I detail the methods and data used in this study.

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Methods

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Dependent Variable: Residual Wage Inequality The dependent variable in this study is residual wage inequality. The units of analysis are the 48 contiguous United States observed at three points in time: 1980, 1990, and 2000. Thus, the final sample for the aggregate pooled time-series analysis of state wage inequality is 144 observations. Following recent practice, wage inequality is defined as the inequality of the residuals from a log wage regression after controlling for observable worker characteristics (Bernard & Jensen, 2000; Juhn, Murphy, & Pierce, 1991; McCall, 2000). Data used for these computations comes from the 5-percent Integrated Public Use Microdata Samples (IPUMS) of the 1980, 1990, and 2000 decennial Censuses (Ruggles et al. 2004). The samples were restricted to workers age 18 through 64 who worked full-time and year round (FTYR, 48 or more weeks at 35 or more hours per week) in the previous year and whose weekly wages were $50 or more in 2000 adjusted dollars. Military, agricultural, self-employed, and unpaid family workers are removed from the samples. This sample restriction allows for a test of the hypotheses on the prime-age working population employed full-time and consistently throughout the year. To estimate wage inequality, I created a variable for estimated weekly wage: annual income divided by weeks worked. This dollar value was converted using factors of 2.34, 1.39, and 1.03 respectively to convert from 1979, 1989, and 1999 into 2000 dollar values using the Bureau of Labor Statistics’ inflation calculator. As noted above, workers with estimated weekly wages of $50 or more were retained for the analysis. Following others, I estimate a standard log hourly wage function to obtain residuals (Bernard & Jensen, 2000; Juhn et al., 1991; Wheeler, 2007). The log wage regression was estimated 144 times—once within each of the 48 states at three points in time (1980, 1990, and 2000) with workers matched to their place of work state. While past researchers have used the residual standard deviation (McCall, 2000) or percentile differences (Bernard & Jensen, 2000), I utilize a slightly different procedure. I do not rely on the residual standard deviation as it is the square root transformation of the residual variance from a log wage regression and may fail the Dalton-Pigou principle of transfers (Osberg, 1984). To measure residual wage inequality, I instead use three generalized entropy measures of inequality which satisfy the Dalton-Pigou transfers principle, make use of all information in the wage distribution, and vary in their sensitivity to changes in different parts of the distribution: one-half the squared Coefficient of Variation (CV), Theil’s Index, and the Mean Log Deviation. To obtain an estimate of residual wage inequality, a standard log wage regression is specified and run for each state-year: lnwage = F(human capital, demographic characteristics, and industry) Where ln wage is the natural log of estimated weekly wages, human capital is specified as three dummies for educational attainment, a quartic for age, a dummy for female workers, a dummy for married workers, seven dummies for ‘race’ and ethnicity, and twelve industry dummies. As noted above, the equation is estimated once within each state per each of the

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three census years. The 1980 sample consisted of 1.18 million cases, the 1990 sample 3.10 million, and 3.54 million cases in the 2000 sample. Next, the residual from the earnings function is taken as the observed ln wage minus the predicted ln wage: Residual = lnwage - E(lnwage) where the residual is the difference between an individual’s actual ln wage and the ln wage expected from the regression function. This result is then exponentiated: z = expResidual so that generalized entropy measures of inequality can be computed. The Theil index is computed as: Theil = (1/N) ∑ (zi/zµ)*ln(zi/zµ)  where zi is the exponentiated residual of the estimated log weekly wage of the ith worker and µ is the average z of all workers within the state and ln is the natural log. This measure will be more sensitive to changes in the middle of the distribution as opposed to the Mean Logarithmic Deviation: MLD = (1/N) ∑ ln(zµ/zi) which is more sensitive to changes at the bottom of the distribution. Still more sensitive to changes at the higher end (more sensitive to the higher end than Theil) of the distribution is one-half the squared coefficient of variation:

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CV = 0.5*(zsd/zµ)2 where CV is one-half the squared ratio of the standard deviation of z to the mean of z for each state-year. While this technique introduces some degree of bias as the mean of the residuals are defined on the geometric scale1, I contend that the gains from the use of Theil’s entropy based inequality measures outweigh the limitations and biases introduced by reliance on the residual standard deviation as the sole metric of residualized wage inequality. Analysts have advanced different interpretations of the distribution of the residuals. Blau and Kahn (1996) and Juhn et al. (1991) argue that the residual distribution is a measure of unobserved market prices for labor (Blau & Kahn, 1996; Juhn et al., 1991). McCall (2000) interprets the distribution of the residuals “…as a measure of variation in the earnings of workers with the same observed characteristics, some unknown portion of which is due to differences in the distribution of, and return to, observed characteristics,” (McCall, 2000). Importantly, the use of the residual distribution allows us to parcel out the effects of measured human capital and demographic characteristics so as to yield a measure that can be used to test how structural factors (such as union density and minimum wages) operate to influence wage inequality.

1

I thank Bruce Western for pointing this out to me.

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Thomas W. Volscho

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Independent Variables Used in the Analysis The main independent variables of interest are union density and the state minimum wage. Union Density (%Union), the percentage of wage and salary workers age 16 and above comes from Hirsch and Macpherson’s database on unions (Hirsch & Macpherson, 2003). The measure is estimated for the year 1999 since Census income data is for the previous year and not the survey year. Information on the state minimum wage (State MW) was obtained from Neumark and Wascher (1992) for 1979 and 1989 and from The Book of the States for 1999 (Council of State Governments, 2001; Neumark & Wascher, 1992). The years 1979, 1989, and 1999 are used to measure the state minimum wage because, as noted above, the Census Bureau asks people about their earnings during the previous year. The minimum wage is adjusted into 2000 dollars and scored as $0 for states without a minimum wage (e.g., Mississippi) and ranges up to $6.90 (Connecticut in 1980). Past research and experimentation with functional form indicated that the state minimum wage should be specified as a piecewise variable (Volscho, 2005). The best fit was found for a node set at $4.25. Thus, the minimum wage variable is scored as 0 for all values less than or equal to $4.25 and then as (MW-4.25) for all values above $4.25. In 2000, for example, Indiana’s real minimum wage was $3.45 and thus scored as 0 whereas Kentucky’s was $4.38 such that the piecewise variable is scored as $0.13 (i.e., 4.38 - 4.25). Also included in the model are controls for percent employed in manufacturing (%Mfg. Emp.) obtained from Census data with the expectation that it will be inversely related to wage inequality (Bernard & Jensen, 2000; Chevan & Stokes, 2000). Dispersion in establishment size is also likely to impact inequality and is controlled with the CV of establishment size (CV Est. Size) owing to the expectation that greater inequality in size of employing establishments will increase wage inequality (Jacobs, 1985). Consistent with recent research (Blanchflower & Oswald, 2005) the log of unemployment is controlled for to estimate the impact of labor market instability with the expectation that higher levels of (ln Unemp.) unemployment are associated with greater wage inequality. The percent of the state age 25 and older who are college educated, (%College) obtained from Census data, is entered as a control in the wage inequality regressions with the expectation that higher inequality will be associated with a more highly educated population (Wheeler, 2005). Percent foreign born (%Immigrant) is entered as a control with the expectation that it may have a positive impact on wage inequality given a bi-modal distribution of education among foreign born workers (Borjas, Freeman, & Katz, 1996). A control for the percent of the population “black” (%”Black”) is included to parcel out the aggregate effects of institutionalized racism on wage inequality. Lastly, control variables for three broad Census regions (Northeast, Midwest, and West) are included to control for regional variation and shocks. Descriptive statistics and data sources are reported in Table 1.

Panel Data Estimation Methods The state dataset represents a balanced and evenly spaced panel of 48 states observed at three time points resulting in 144 observations. Ordinary Least Squares (OLS) estimation applied to such data is theoretically problematic because of potential autocorrelation and un-

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105

estimated unit-specific effects (Halaby, 2004; Wooldridge, 2002). Two approaches are often used to treat unit-effects as Random Effects (REM) or as Fixed Effects (FEM). I estimated both REM and FEM models and the Hausman specification test suggested REM over FEM. Furthermore, I carried out the Breusch-Pagan Lagrangian Multiplier test for random effects and did not find evidence against the null hypothesis indicating that pooled OLS estimation is appropriate. Following Beck and Katz (1995) OLS estimation is carried out with panelcorrected standard errors (Beck & Katz, 1995) in STATA 10.

Analysis of Results Looking at the descriptive statistics presented in Table 1, we can chart the rise of wage inequality because each measure of residual wage inequality increases over the period 19802000. For instance the mean of one-half the squared CV increases by about 106 percent, the Theil by about 55 percent, and the MLD by approximately 31 percent over the twenty year period. Table 1. Descriptive Statistics for Lower 48 States, 1980-2000

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All

1980

1990

2000

mean

sd

mean

sd

mean

sd

mean

sd

1/2 CV2

15.7

(5.4)

10.8

(2.1)

14.0

(1.7)

22.3

(3.4)

Theil

11.7

(2.6)

9.4

(1.2)

11.0

(1.1)

14.6

(1.8)

MLD

11.2

(1.8)

9.9

(1.1)

10.7

(1.0)

13.0

(1.6)

State MW (k=$4.25)

0.8

(0.8)

1.1

(1.0)

0.4

(0.4)

0.7

(0.5)

%Union

16.3

(7.4)

21.5

(7.7)

14.7

(5.9)

12.7

(5.4)

%College

19.7

(4.9)

15.9

(2.9)

19.6

(3.7)

23.7

(4.4)

%Immigrant

5.2

(4.7)

4.1

(3.4)

4.7

(4.4)

6.9

(5.6)

%Mfg. Emp

17.0

(6.6)

20.5

(7.8)

16.8

(5.4)

13.8

(4.6)

CV Est. Size

4.4

(0.4)

4.5

(0.4)

4.4

(0.3)

4.3

(0.3)

ln Unemp

1.6

(0.3)

1.8

(0.2)

1.8

(0.2)

1.3

(0.1)

%"Black"

9.8

(9.4)

9.4

(9.3)

9.8

(9.4)

10.1

(9.6)

Notes: Means and standard deviation for data on lower 48 states. Inequality measures are for residual wage inequality and are all scaled by 100. State MW is a piecewise variable with the knot set at $4.25. Region variables are categorical variables and therefore proportions.

Such means may mask variation. States with the highest growth in residual inequality between 1980 and 2000 were Connecticut, New York, Massachusetts, Washington, and California. States with the lowest growth in residual wage inequality were Florida, South Dakota, Idaho, Vermont, and Delaware. Looking at the variables of theoretical interest we see that average union density and the state minimum wage have decreased over this time period. Note that the State MW is a piecewise variable scored as $0 if the minimum wage is less than or equal to $4.25 in constant

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106

Thomas W. Volscho

2000 dollars and for values greater than $4.25 the variable is (State MW - $4.25). The mean for the piecewise variable is $1.10 in 1979, $0.40 in 1989, and $0.72 in 1999. Thirty percent of the observations have a value of $0 on the piecewise variable. 12.5 percent have a score of about 0.40 ($4.67), another 17.4 percent have a score of $1.05 ($5.31), 8.3 percent at $1.20 ($5.46), and 6.94 percent at $2.62 ($6.88) with the remaining 25 percent of data points falling in between.

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Figure 1. Unions and Wage Inequality, 1980.

Figure 2. Unions and Wage Inequality, 1990. Income Distribution: Inequalities, Impacts and Incentives : Inequalities, Impacts and Incentives, Nova Science Publishers, Incorporated, 2008.

Neoliberalism’s Triumph?

107

Theil Index 12 10 8

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14

16

Figure 3. Unions and Wage Inequality, 2000.

0

.5

1

1.5 Minimum Wage

Theil Index

2

2.5

Fitted values

Figure 4. Minimum Wage and Wage Inequality, 1980.

Figures 1 through 6 provide a view over time of the cross-sectional link between residual inequality (using Theil’s index) and union density and the minimum wage. Looking at figures 1 through 3 we see that in 1980 and 1990 the slope from the bivariate regression seems to weaken. By 2000, the regression slope is slightly positive indicating that states with higher union density have somewhat higher levels of wage inequality than states with lower levels. The slope for the piecewise minimum wage variable is roughly constant across time. Note

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Thomas W. Volscho

8

10

Theil Index

12

14

that by 2000, many states minimum wages were clustered around 1, which is about the value of the federal minimum wage.

0

.5

1 Minimum Wage Theil Index

1.5

2

Fitted values

20 Theil Index 16 18 14 12

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22

Figure 5. Minimum Wage and Wage Inequality, 1990.

0

.5

1 Minimum Wage Theil Index

1.5

Fitted values

Figure 6. Minimum Wage and Wage Inequality, 2000.

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2

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109

Table 2. Effects of State Minimum Wage and Union Density on Residual Wage Inequality in the States, 1980-2000 (1) CV -0.179*** (-3.69)

(2) CV -0.132** (-3.07)

(3) Theil -0.051 (-1.47)

(4) Theil -0.023 (-0.67)

(5) MLD -0.020 (-0.67)

(6) MLD 0.004 (0.13)

%Immigrant

0.256*** (5.99)

0.283*** (9.15)

0.170*** (6.57)

0.185*** (10.45)

0.148*** (6.48)

0.159*** (10.66)

%Mfg. Emp.

-0.129*** (-6.25)

-0.105*** (-5.10)

-0.081*** (-4.32)

-0.066*** (-3.70)

-0.077*** (-4.55)

-0.064*** (-4.06)

CV Est. Size

0.927*** (4.82)

1.225*** (5.71)

0.557*** (3.56)

0.719*** (4.74)

0.475*** (3.40)

0.597*** (4.41)

ln Unemp.

-0.288 (-0.20)

0.913 (0.73)

0.222 (0.34)

0.859 (1.62)

0.540 (0.98)

0.997* (2.21)

% 'Black'

0.089*** (8.08)

0.069*** (5.74)

0.053*** (11.78)

0.041*** (6.75)

0.045*** (12.47)

0.034*** (7.55)

Northeast

-0.979*** (-3.71)

-0.378 (-1.51)

-0.738*** (-5.38)

-0.393** (-2.90)

-0.766*** (-4.40)

-0.485*** (-6.92)

Midwest

-1.343** (-2.81)

-0.889 (-1.68)

-0.627* (-2.52)

-0.410 (-1.70)

-0.466 (-1.91)

-0.339 (-1.59)

West

-0.998* (-2.21)

-0.832* (-2.22)

-0.649* (-2.54)

-0.570** (-2.66)

-0.504* (-2.00)

-0.458* (-2.20)

1990

3.274*** (15.94)

2.215*** (9.00)

1.465*** (10.34)

0.854*** (4.82)

0.487*** (3.91)

-0.014 (-0.09)

2000

11.182*** (23.66)

10.755*** (27.31)

4.748*** (17.97)

4.502*** (19.57)

2.639*** (10.64)

2.438*** (11.26)

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%College

State MW

-0.807*** (-3.60)

-0.524*** (-3.56)

-0.494*** (-3.63)

%Union

-0.062*** (-3.31)

-0.030* (-2.32)

-0.017 (-1.62)

Constant Observations R2 BIC’

11.545*** (3.65) 144 0.902 -279.6

8.868** (3.06) 144 0.913 -286.7

8.208*** (4.36) 144 0.889 -262.1

6.733*** (3.79) 144 0.907 -276.8

8.052*** (5.01) 144 0.841 -210.2

6.923*** (4.45) 144 0.869 -228.3

Note: Panel-corrected t-statistics in parentheses * p