A dissimilarity index of multidimensional inequality of opportunity

A recent literature on inequality of opportunity offers quantitative tools for comparisons and measurement based on stochastic dominance criteria and traditional inequality indices. In this paper I suggest an additional way of assessing inequality of opportunity with two indices of dissimilarity across distributions. The indices are based on a traditional homogeneity test of multinomial distributions and are similar to the square coefficient of variation (Reardon and Firebaugh, Sociol Method 32:33?C67, 2002). Their properties are studied, as well as their usefulness and limitations in applications when both circumstances and advantages/outcomes are multidimensional. An empirical application measures changes in inequality of opportunity from an old to a young cohort in Peru. The importance of assessing the sensitivity of the results to group definitions and group proportions is highlighted.     

Multidimensional inequality and multidimensional generalized entropy measures: An axiomatic derivation

This paper generalizes the axiomatic approach to the design of income inequality measures to the multiattribute context. While the extension of most axioms considered desirable for inequality indices is straightforward, it is not entirely clear when a situation is more unequal than another when each person is characterised by a vector of attributes of well-being. We explore two majorization criteria which are partial orders ranking distributions of attributes by their degree of inequality. The two criteria are motivated by the Pigou-Dalton Transfer Principle in the unidimensional context and its equivalent formulation. These criteria gauge inequality loosely speaking with respect to the dispersion of the multidimensional distribution of the attributes. They, however, fail to address a different dimension of multivariate inequality pertaining to an increase in the correlation of the attributes. In this connection, this paper introduces a correlation-increasing majorization criterion proposed by Boland and Proschan (1988). Finally, in conjunction with other axioms commonly invoked in the literature on inequality, the majorization criteria lead inexorably to the class of multidimensional generalized entropy measures. Received: 15 June 1995 / Accepted: 30 September 1997     

Axiomatic measurement of multidimensional well-being inequality: Some distributional questions

This paper focuses on two main issues which are crucial for improving on the analysis of multidimensional inequality: the effect of both the dispersion of well-being attributes across individuals and the interaction among attributes on the measurement of multidimensional well-being. To approach these distributional questions we rely on the Atkinson, Kolm, Sen (hereafter AKS) methodology, which defines a multidimensional inequality index consistent with the Pigou–Dalton principle. This index can be decomposed into univariate indexes belonging to the class of AKS indexes, and a residual term accounting for the interaction across dimensions. The empirical application investigates the evolution of inequality in well-being across some EU countries between 1994 and 2001.Since the multidimensional index depends on the values assigned to the parameters, we test the sensitivity of the trend in well-being to the degree of inequality aversion on each dimension. Our empirical results summarize the evolution of inequality for the indicators of well-being considered both separately and jointly, over time and across countries.     

Geographic decomposition of inequality in health and wealth: evidence from Cambodia

Applying the small-area estimation methods to Cambodia data, we decompose the total inequality in wealth (consumption) and health (child undernutrition) indicators into within-location and between-location components. Because the knowledge of the pattern of spatial disparity in poverty and undernutrition is important for the geographic targeting of resources, we conduct a geographic decomposition of the variance of the Foster-Greere-Thorbecke index in addition to the standard decomposition exercise based on the generalized entropy measures. We find that a sizable proportion of wealth inequality is due to between-location inequality, whereas health inequality is mainly due to within-location inequality.     

Allowing for heterogeneity in the decomposition of measures of inequality in health*

This paper shows how recently developed regression-based methods for the decomposition of health inequality can be extended to incorporate heterogeneity in the responses of health to the explanatory variables. We illustrate our method with an application to the GHQ measure of psychological well-being taken from the British Household Panel Survey. The results suggest that there is an important degree of heterogeneity in the association of health to explanatory variables across birth cohorts and genders which, in turn, accounts for a substantial percentage of the inequality in observed health.*Data from the British Household Panel Survey (BHPS) were supplied by the ESRC Data Archive. Neither the original collectors of the data nor the Archive bear any responsibility for the analysis or interpretations presented here. This chapter derives from the project “The dynamics of income, health and inequality over the lifecycle” (known as the ECuity III Project), which is funded in part by the European Community's Quality of Life and Management of Living Resources programme (contract QLK6-CT-2002-02297) and the project “La dinámica del estado de salud y los factores socieconómicos a lo largo del ciclo vital. Implicaciones para las políticas públicas”, which is supported by the Fundación BBVA.     

Source decomposition of changes in income inequality: the integral-based approach and its approximation by the chained Shapley-value approach

This paper proposes source decomposition of the change in income inequality between two time points using the integral-based approach (IBA) and the (chained) Shapley-value approach as its approximation. In comparison to static Shapley-value decompositions and traditional decompositions for the square of the coefficient of variation and the Gini index, the new dynamic Shapley-value approach is intuitively appealing as a decomposition procedure for changes in inequality. It is expected to yield relatively small differences among various inequality measures, essentially maintaining consistency with income source classification. Path dependency, a possible drawback of the new decompositions, is not expected to be a particular problem in the usual cases. The properties are illustrated for application to the increase in US family income inequality during 1979–1996. In this empirical study, the new decompositions showed a tendency that was clearly different from those of the existing decompositions, indicating that the proposed procedures shed new light on analysis of the causes of inequality changes. An extension to incorporate other factors such as family structure is also successful without loss of the desirable properties.     

Complaints and inequality

Temkin (1986, 1993) set out a philosophical basis for the analysis of income inequality that provides an important alternative to the mainstream welfarist approach. We show that the Temkin principles can be characterised by a parsimonious axiomatic structure and we use this structure to derive a new class of inequality indices and an inequality ordering. This class of indices has a family relationship to well-known measures of inequality, deprivation and poverty. The ordering is shown to have properties analogous to second-order dominance results.We would like to acknowledge financial support by the Training and Mobility of Researchers Programme of the European Communities, grant #ERBFMRXC T980248 (Living Standards, Inequality and Taxation), and to thank STICERD for hosting Ebert in order to facilitate our collaboration. Ralph Bayer helped greatly in preparation of the figures. We are grateful for comments from Yoram Amiel, Kurt Devooght and Alain Trannoy and from participants at workshops in Warwick, Bocconi, the LSE and Venice. We also wish to acknowledge the helpful comments of the referees of this journal.     

Intermediate inequality and welfare

We introduce a new centrist or intermediate inequality concept, between the usual relative and absolute notions, which is shown to be a variant of the α-ray invariant inequality measures in Pfingsten and Seidl (1997). We say that distributions x and y have the same (x, π)-inequality if the total income difference between them is allocated among the individuals as follows: 100π% preserving income shares in x, and 100(1−π)% in equal absolute amounts. This notion can be made as operational as current standard methods in Shorrocks (1983). Received: 13 May 1998/Accepted: 25 January 1999     

Unions and wage inequality

Summary and Conclusions The impact of unions on the structure of wages has recently attracted renewed interest as analysts have struggled to explain the rise in earnings inequality in several industrialized countries. Canada, the United Kingdom, and the United States provide a potentially valuable set of countries for examining this question. All three countries now collect comparable data on wages and union status in their regular labor force surveys. Several features of the collective bargaining institutions of these countries make them suitable for studying the relationship between unions and wage inequality. Bargaining is highly decentralized; there are no general mechanisms for extending collective bargaining provisions beyond the “organized” sector; and the fraction of the work force covered by collective bargaining is relatively modest. Thus it is possible to compare the structure of wages for workers covered by union contracts to those who are not covered, and potentially infer the effect of unions on overall wage inequality.     

Child labour and inequality

This paper focuses on the role that inequality plays in shaping political support for child labour regulation policies. We provide a model of the evolution of child labour, fertility and human capital where the heterogeneity between low- and high-skilled workers allows for an endogenous analysis of inequality generated by child labour. Depending on the initial level of inequality, child labour regulation policies can affect the welfare of low- and high-skilled workers in different ways and therefore can have an impact on political support for their introduction. The possible conflicts of interest that may arise between the two groups can help explain the difficulties that many governments have when dealing with the issue of child labour.     

Social isolation and inequality

There is an increasing interest in the concept of social exclusion and the related concept of social isolation and their potential role in understanding inequality. We examine the degree to which voluntary separation from social activities during adolescence affects adult wages. It is well-known that participation in high school athletic programs leads to higher adult wages. We present empirical evidence that this premium is not primarily due to selection on predetermined characteristics valued in the labor market. This is a revised version of a paper presented at a conference on Theoretical Perspectives on Identity, Community and Economic Policy, Barcelona, February 2004 sponsered by The Pew Charitable Trusts.     

The effect of education,income inequality and merit on inequality acceptance

A large number of observational and experimental studies have explored the determinants of individual preferences for redistribution. In general, inequalities are more likely to be accepted by people of higher socioeconomic status, in richer societies and when inequalities are perceived as justifiable owing to differences in productivity. Almås et al. (2020) show that in a relatively unequal society (the United States), the highly educated accept inequality significantly more than the less educated, whereas, in a relatively equal society (Norway), the less educated accept inequality more, but not significantly more, than the highly educated. Here, we replicate this finding using data from experiments conducted in four locations across three countries all distinct from the ones studied by Almås et al. However, a closer look at the data indicates that the origin of the interaction effect varies depending on which societies one compares. Data for Norway and the United States indicate that meritocratic values among the highly educated are less prevalent in more equal societies and that this is the driver of the triple interaction effect. In contrast, in our data the interaction effects have multiple drivers.     

The empirical assessment of multidimensional welfare,inequality and poverty: Sample weighted multivariate generalizations of the Kolmogorov–Smirnov two sample tests for stochastic dominance

Sample weighted multidimensional extensions to existing stochastic dominance, inequality and polarization comparison techniques are introduced and employed to examine whether or not ignoring multidimensional and sample weighting aspects result in misleading inferences. The techniques are employed in the context of a sample of nations, in essence each country in the sample is represented by an agent characterized by the per capita GNP of that country, the GNP growth rate of that country and the average life expectancy in that country. In essence the inequality that is being examined is that between the representative agents in these countries, intra country inequality is not being measured. The results suggest that multidimensional techniques lead to substantially different conclusions from those drawn from the use of unidimensional measures and that sample weighting also has a profound effect on the empirical outcomes. An erratum to this article can be found at     

Social inequality and art institutions

Our objective is to examine how several aspects of the class structure influence the prevalence of artistic institutions. The analysis is based on quantitative comparisons of the 125 largest metropolitan areas in the United States. Most of the literature on the history of art concludes that artistic developments depend on the patronage of an elite—as noble patrons, as rich donors, or even as affluent bourgeois donors and audiences. Whereas these conclusions imply that class inequalities further the growth of the arts, our empirical findings indicate the opposite. Both lesser inequality and reductions of inequality in a metropolis increase a variety of artistic institutions, and these influences persist when other influences on these institutions are controlled.     

Income inequality and self-reported values

What is the relationship between income inequality and the values people endorse? Using survey data from all thirty-four OECD countries over a period of almost thirty years, we investigate the following dimensions of value systems: work ethic, civism, obedience, honesty, altruism, and tolerance. In most cases, no robust relation to income inequality is detected. However, we find some evidence that larger income disparities are associated with a stronger work ethic. This suggests that income inequality might spur hard work not only through pecuniary incentives but also because it makes people attach a symbolic value to being laborious.     

Compensation systems and earnings inequality

We develop a wage-structure determination model in which a firm with incomplete information offers an optimal sequence of contracts for its heterogeneous employees. The model integrating the principal-agent framework and monitoring mechanism is characterized by endogeneity of the selection of two compensation methods: performance-pay and non-performance-pay schemes. The model is used to examine the switching of pay schemes and its inequality effect. We point out that the growth of performance-pay jobs is accompanied by a downward adjustment of the rewards for performance, which brings forth a countervailing effect on wage inequality. The simulation analysis of a case of uniform-distributed ability reveals that the net effect of the growth of performance-pay jobs on wage inequality depends on the driving force behind the switch.     

Income inequality and income segregation

This article investigates how the growth in income inequality from 1970 to 2000 affected patterns of income segregation along three dimensions: the spatial segregation of poverty and affluence, race-specific patterns of income segregation, and the geographic scale of income segregation. The evidence reveals a robust relationship between income inequality and income segregation, an effect that is larger for black families than for white families. In addition, income inequality affects income segregation primarily through its effect on the large-scale spatial segregation of affluence rather than by affecting the spatial segregation of poverty or by altering small-scale patterns of income segregation.     

Envy,inequality and fertility

Review of Economics of the Household - This study seeks to examine the consequences of “keeping up with the Joneses” on household fertility outcomes. “Envy” is introduced in...