An Ex-Post View of Inequality of Opportunity in France and its Regions

This paper proposes an ex-post measure of inequality of opportunity in France and its regions by assessing the inequality between individuals exerting the same effort. To this end, we define a fair income that fulfils ex-post equality of opportunity requirements. Unfairness is measured by an unfair Gini based on the distance between the actual income and the fair income. Our findings reveal that the measures of ex-post inequality of opportunity largely vary across regions, and that this is due to differences in reward schemes and in the impact of the non responsibility factors of income. We find that most regions have actual incomes closer to fair incomes than to average income, excepted Ile de France where the actual income looks poorly related to effort variables. Finally, we find that income inequality and inequality of opportunity are positively correlated among regions.     

Income inequality games

The paper explores different applications of the Shapley value for either inequality or poverty measures. We first investigate the problem of source decomposition of inequality measures, the so-called additive income sources inequality games, based on the Shapley value, introduced by Chantreuil and Trannoy (1999) and Shorrocks (1999). We show that multiplicative inequality games provide dual results compared with Chantreuil and Trannoy’s ones. We also investigate the case of multiplicative poverty games for which indices are non additively decomposable in order to capture contributions of sub-indices, which are multiplicatively connected with, as in the Sen-Shorrocks-Thon poverty index. We finally show, in the case of additive poverty indices, that the Shapley value may be equivalent to traditional methods of decomposition such as subgroup consistency and additive decomposition.     

Intersecting Lorenz Curves, the Degree of Downside Inequality Aversion, and Tax Reforms

This paper clarifies the conceptual distinction of downside inequality aversion (or transfer sensitivity) as a normative criterion for judging income distributions from the Pigou-Dalton principle of transfers. We show that when the Lorenz curves of two income distributions intersect, how the change from one distribution to the other is judged by an inequality index exhibiting downside inequality aversion often depends on the relative strengths of its downside inequality aversion and inequality aversion. For additive inequality indices or their monotonic transformations, a measure characterizing the strength of an index’s downside inequality aversion against its inequality aversion is shown to determine the ranking by the index of two distributions whose Lorenz curves cross once. The precise condition under which the same result generalizes to the case of multiple-crossing Lorenz curves is also identified. The results are particularly useful in understanding the distributional impact of tax reforms. I received exceptionally helpful comments from Mike Hoy, Peter Lambert, the Editor, Buhong Zheng, and an anonymous referee. The remaining errors and shortcomings are my own – W.H. Chiu     

Inequality of opportunity in the land of opportunities, 1968–2001

We measure inequality of opportunity for earnings acquisition in the U.S. between 1968 and 2001. Following recent theories of social justice, earnings determinants are divided into two parts: Circumstances, which are characteristics outside individual control and effort representing factors impacting earnings but under individuals’ responsibility. Equality of opportunity requires that inequality of circumstances must be corrected while differences of effort must remain unaltered. Circumstances are represented by parental education and occupation, ethnic origin, place of birth and age. Effort is modeled with schooling choices and labour supply decisions. Using the PSID from 1968 to 2001, we provide two alternative assessments of inequality of opportunity using counterfactual distributions. The statistical framework is semi-parametric and builds on duration models. Finally, we conclude that inequality of opportunity represents between 20 and 43% of earnings inequality, but decreases all over the period reaching around 18% in 2001.     

The effect on inequality of changing one or two incomes

We examine the effect on inequality of increasing one income, and show that for two wide classes of indices a benchmark income level or position exists, dividing upper from lower incomes, such that if a lower income is raised, inequality falls, and if an upper income is raised, inequality rises. We provide a condition on the inequality orderings implicit in two inequality indices under which the one has a lower benchmark than the other for all unequal income distributions. We go on to examine the effect on the same indices of simultaneously increasing one income and decreasing another higher up the distribution, deriving results which quantify the extent of the ‘bucket leak’ which can be tolerated without negating the beneficial inequality effect of the transfer. Our results have implications for the inequality and poverty impacts of different income growth patterns, and of redistributive programmes, leaky or not, which are briefly discussed.     

The measurement of opportunity inequality: a cardinality-based approach

We consider the problem of ranking distributions of opportunity sets on the basis of equality. First, conditional on a given ranking of individual opportunity sets, we define the notion of an equalizing transformation. Then, assuming that the opportunity sets are ranked according to the cardinality ordering, we formulate the analogues of the notions of the Lorenz partial ordering, equalizing (Dalton) transfers, and inequality averse social welfare functions – concepts which play a central role in the literature on income inequality. Our main result is a cardinality-based analogue of the fundamental theorem of inequality measurement: one distribution Lorenz dominates another if and only if the former can be obtained from the latter by a finite sequence of rank preserving equalizations, and if and only if the former is ranked higher than the latter by all inequality averse social welfare functions. In addition, we characterize the smallest monotonic and transitive extension of our cardinality-based Lorenz inequality ordering. Received: 2 May 1995 / Accepted: 11 October 1996     

Inequality in the relative differential sense with continuous distributions

Existing literature has studied the relative differential inequality (RDI) concept as an inequality comparison for discrete distributions, where RDI dominance occurs if there is Lorenz dominance between the distributions for all subsets of individuals of corresponding rank. The paper investigates RDI in the context of continuous distributions, providing continuous counterparts to existing discrete results, and others, including discussion of the uniform, Pareto and log-normal families of continuous distributions. The usefulness of RDI for comparative static analysis in theoretical economic models based on continuous distributions is indicated.      

Lorenz non-consistent welfare and inequality measurement

Typical welfare and inequality measures are required to be Lorenz consistent which guarantees that inequality decreases and welfare increases as a result of a progressive transfer. We explore the implications for welfare and inequality measurement of substituting the weaker absolute differentials and deprivation quasi-orderings for the Lorenz quasi-ordering. Restricting attention to distributions of equal means, we show that the utilitarian model - the so-called expected utility model in the theory of risk - does not permit one to make a distinction between the views embedded in the differentials, deprivation and Lorenz quasi-orderings. In contrast it is possible within the dual model of M. Yaari (Econometrica 55 (1987), 99–115) to derive the restrictions to be placed on the weighting function which guarantee that the corresponding welfare orderings are consistent with the differentials and deprivation quasi-orderings respectively. Finally we drop the equal mean condition and indicate the implications of our approach for the absolute ethical inequality indices.     

Lorenz non-consistent welfare and inequality measurement

Typical welfare and inequality measures are required to be Lorenz consistent which guarantees that inequality decreases and welfare increases as a result of a progressive transfer. We explore the implications for welfare and inequality measurement of substituting the weaker absolute differentials and deprivation quasi-orderings for the Lorenz quasi-ordering. Restricting attention to distributions of equal means, we show that the utilitarian model – the so-called expected utility model in the theory of risk – does not permit one to make a distinction between the views embedded in the differentials, deprivation and Lorenz quasi-orderings. In contrast it is possible within the dual model of M. Yaari (Econometrica 55 (1987), 99–115) to derive the restrictions to be placed on the weighting function which guarantee that the corresponding welfare orderings are consistent with the differentials and deprivation quasi-orderings respectively. Finally we drop the equal mean condition and indicate the implications of our approach for the absolute ethical inequality indices.     

Inequality of opportunity in Italy

In this paper we provide a methodology to measure opportunity inequality and to decompose overall income inequality in an “ethically offensive” and an “ethically acceptable” part. Moreover, we analyze inequality of opportunity in Italy. According to our results, inequality of opportunity accounts for about 20% of overall income inequality in Italy. Moreover, the regions in the South are characterized by a higher degree of opportunity inequality than the regions in the North, especially when considering population subgroups by gender.     

Measuring inequality of opportunity with imperfect data: the case of Turkey

The measurement of inequality of opportunity has hitherto not been attempted in a number of countries because of data limitations. This paper proposes two alternative approaches to circumventing the missing data problems in countries where a demographic and health survey (DHS) and an ancillary household expenditure survey are available. One method relies only on the DHS, and constructs a wealth index as a measure of economic advantage. The alternative method imputes consumption from the ancillary survey into the DHS. In both cases, we compute a lower bound estimator of the share of (ex-ante) inequality of opportunity in total inequality. Parametric and non-parametric estimates are calculated for each method, and the parametric approach is shown to yield preferable lower-bound measures. In an application to the sample of ever-married women aged 30–49 in Turkey, inequality of opportunity accounts for at least 26% (31%) of overall inequality in imputed consumption (the wealth index).     

On the welfare loss caused by inequality of opportunity

Based on the ethical principle of equality of opportunity, this paper presents a measure of the welfare loss that is caused by an unfair distribution of a particular outcome (income, health, education, etc). The key idea is that a fair society should produce outcomes that depend on individuals’ effort and not on their external circumstances such as gender, socioeconomic background, etc. We propose measuring inequality of opportunity as the welfare loss attributed to the outcome differences among individuals who exert a similar level of effort. Our results are in line with those aspects of fairness literature that give priority to the ex post compensation approach to equality of opportunity. Finally, we present an empirical application for the measurement of the welfare loss in the income distribution in Europe. We have observed a high degree of heterogeneity among European countries. The welfare loss due to inequality of opportunity ranges in those, from basically zero to almost one fifth of their potential welfare.     

Constructing indices of multivariate polarization

Multivariate indices of polarization are constructed to measure effects of non-income attributes like wealth and education. Polarization is considered as the presence of groups which are internally homogeneous, externally heterogeneous, and of similar size. We propose a class of polarization indices which is built from measures of relative groups size and from decomposable indices of socio-economic inequality. For the latter, we employ the special inequality indices of Maasoumi (Econometrica 54:991–997, 1986), Tsui (J Econ Theory 67:251–265, 1995; Soc Choice Welf 16:145–157, 1999) and Koshevoy and Mosler (J Multivar Anal 60:252–276, 1997). Then, postulates for multidimensional polarization measurement are stated and discussed. The approach is illustrated by an empirical application to the population of the East and West Germany with polarization defined on income and education.     

Dynastic inequality,mobility and equality of opportunity

One often heard counter to the concern about rising income and wealth inequality is that it is wrong to focus on inequality of outcomes in a “snapshot”. Intergenerational mobility and “equality of opportunity”, so the argument goes, is what matters for normative evaluation. In response to this counter, we ask what pattern of intergenerational mobility leads to lower inequality not between individuals but between the dynasties to which they belong? And how does this pattern in turn relate to commonly held views on what constitutes equality of opportunity? We revive and revisit here our earlier contributions which were in the form of working papers (Kanbur and Stiglitz 1982, 1986) in order to engage with the current debate. Focusing on bistochastic transition matrices in order to hold constant the steady state snapshot income distribution, we develop an explicit partial ordering which ranks matrices on the criterion of inequality between infinitely lived dynasties. A general interpretation of our result is that when comparing two transition matrices, if one matrix is “further away” from the identity matrix then it will lead to lower dynastic inequality. More specifically, the result presents a computational procedure to check if one matrix dominates another on dynastic inequality. We can also assess “equality of opportunity”, defined as identical prospects irrespective of starting position. We find that this is not necessarily the mobility pattern which minimizes dynastic inequality.     

Within inequality characteristics and adaptation of immigrants in the United States

Until recently, in works of literature, the assimilation of immigrants had been viewed as an individualistic rather than a community-based process. However, Hatton and Leigh (2011) showed that immigrants integrate to their host country as communities, not as individuals; hence, group characteristics play as much of a role as individual characteristics in terms of adaptation. This paper introduces another dimension to the immigrant adaptation proxies that reflect community-based characteristics. The fundamental assertion of this paper is that inequality can be used as a proxy of adaptation within immigrant groups. Immigrant groups that exhibit income and education distributions similar to those of the natives can be regarded as well-adapted groups, while those who exhibit vastly different distributions should be considered to be groups with limited adaptation. Using the American Community Survey (ACS) 2010 cohort, this paper presents the initial findings of the within-group inequality of immigrants. Then, a cross-sectional regression analysis is employed to analyze the determinants of inequality across these immigrant groups. The results suggest that immigrant community-based characteristics, such as average income, education, and number of years that the immigrants have spent in the US, can indeed explain most of the variation in inequality.     

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     

Illustrating the Implications of How Inequality is Measured: Decomposing Earnings Inequality by Race and Gender

This paper makes three distinct contributions: it presents a novel modification to an established methodology for assessing inequality using the CPS ASEC data, it illustrates how valuable a multi-metric inequality analysis is by reconciling some open questions regarding the trend in inequality and the role of the composition of income along the distribution, and it provides a baseline assessment of the trend in earnings inequality for four distinct groups of income earners. The evolution of earnings inequality from 1995 to 2010 is compared to increasing inequality in total income as documented by Thomas Piketty and Emmanuel Saez to show that earnings inequality has followed a qualitatively similar, though less extreme trend. In the process, the disconnect between the trend in the Gini coefficient and inequality assessed via the share of income going to the top 1 % of income earners is reconciled through the use of several alternative inequality indices. Finally, the evolution of the earnings distribution for black women, black men, white women, and white men are considered separately, which shows that there are important differences in the experience of inequality. The main findings are that only white men have experienced changes in within-group earnings inequality that parallel the changes in inequality seen in the overall distribution. By contrast, black income earners have seen no notable increase in within-group inequality by any measure, suggesting that they may rightly perceive growing inequality as primarily a between-group phenomena.     

Inequality of opportunity in daycare and preschool services in Brazil

In this paper we measure inequality of opportunity in daycare and preschool services in Brazil. For this purpose, we construct an opportunity index that modifies the Human Opportunity Index proposed in the literature and used in Barros et al. (2009) to measure inequality in basic opportunities in Latin America and the Caribbean. Specifically, we construct an opportunity measure that includes not only attendance but also parental choice not to enroll children in daycare or preschool, using data from a supplementary questionnaire included in the 2006 version of Pesquisa Nacional por Amostra de Domicílios (PNAD). The results show that there are large differences between our opportunity index and the Human Opportunity Index for children aged 0–3 years old and considerably smaller differences for children aged 4–6 years old, which suggests that preschool may be closer to a basic opportunity than daycare.     

The measurement of structural and exchange income mobility

Chakravarty, Dutta and Weymark (1985) present operational axioms for an ethical index of income mobility that are best suited for a two period world. This paper suggests a decomposition of this index into two terms: (i) an index of structural or snapshot mobility, which captures the welfare effect of differences in the inequality of the cross-section income distributions; and (ii) an index of exchange or rerankings mobility, which captures the welfare impact of rank reversals between the first- and the second-period income distributions. Income inequality reductions and rank reversals are always welfare enhancing. The properties of all the income mobility concepts introduced in the paper do not require any new value judgements beyond the traditional ones.     

Deprivation,welfare and inequality

We provide a characterization of the generalised satisfaction—in our terminology non-deprivation—quasi-ordering introduced by S.R. Chakravarty (Keio Econ Stud 34:17–32, (1997)) for making welfare comparisons. The non-deprivation quasi-ordering obeys a weaker version of the principle of transfers: welfare improves only for specific combinations of progressive transfers, which impose that the same amount be taken from richer individuals and allocated to one arbitrary poorer individual. We identify the extended Gini social welfare functions that are consistent with this principle and we show that the unanimity of value judgements among this class is identical to the ranking of distributions implied by the non-deprivation quasi-ordering. We extend the approach to the measurement of inequality by considering the corresponding relative and absolute ethical inequality indices. This is a shortened version of Magdalou and Moyes (2008), which contains the details of the proofs as well as an empirical illustration.