Gender inequalities in pensions: different components similar levels of dispersion

While the average gender gap in pensions is quite well documented, gender differences in the distribution of pensions have rarely been explored. We show in this paper that pension dispersion is very similar for men and women within the French pension system of a given sector (public or private). Gender differences are less marked among retired civil servants than among former private sector employees. However, the determinants of these inequalities are not the same for men and women. Using a regression-based decomposition of the Gini coefficient, we find that pension dispersion is mostly due to dispersion of the reference wage for all retirees but gender differences exist. For women, in particular, pension dispersion is also due to the dispersion in contribution periods. We also decompose the Gini coefficient by source of pension to measure the impact of institutional rules (minimum pensions, survivor’s pension) on the extent of pension inequality. Unexpectedly, we find that the impact of minimum pensions is limited, although slightly larger for civil servants than for private-sector employees. Survivor’s pension schemes, on the other hand, contribute positively to pension dispersion among retired women.     

Intersecting generalized Lorenz curves and the Gini index

As is well known, the use of the Gini coefficient in comparisons is inconsistent with an utilitarian approach. This paper analyzes the Gini coefficient's normative significance in welfare comparisons evaluating income distributions according to Yaari dual social welfare function. When generalized Lorenz curves cross once, the Gini coefficient is decisive in determining welfare rankings if we strengthen the Principle of Transfers applying a Positional version of the Principle of Transfer Sensitivity. This result can also be extended to the case of multiple crossings. Received: 28 August 1996 / Accepted: 22 October 1997     

A Family of Correlation Coefficients Based on the Extended Gini Index

The extended Gini is a family of measures of variability which is mainly used in the areas of finance and income distribution. Each index in the family is defined by specifying one parameter, which reflects the social evaluation of the marginal utility of income. The higher the parameter, the more weight is attached to the lower portion of the cumulative distribution, reflecting higher concern for poverty. In this paper we list and investigate the properties of the equivalents of the correlation coefficient that are associated with the extended Gini family. In addition, we show that the extended Gini of a linear combination of random variables can be decomposed, in a way which is equivalent to the decomposition of the variance, with, in addition, terms that reflect additional properties of the random variables. The implication of these properties is that any decomposition that is performed with the coefficient of variation can be replicated by an infinite number of indices that are based on the Extended Gini coefficient.     

Inequality and deprivation within and between groups: An illustration of European union countries

This paper broadens the approach of Hey and Lambert (Q. J. Econ. 95,567–573 1980) regarding relative deprivation to the case in which individuals compare themselves with individuals belonging not only to their own group, but also to other groups. In this way, we obtain the average deprivation of a population in relation to another. This allows us to establish a correspondence between the decomposition of the Gini coefficient based on a partition of the population, and the decomposition of deprivation into two components. One quantifies deprivation within the subpopulation and the other deprivation between populations. An empirical illustration is given, based on the European Community Household Panel (ECHP). The authors acknowledge the financial support of the Spanish Government–MCYT, (SEC2001-1668) and would like to thank Jacques Silber and two anonymous referees for their suggestions.     

The impact of unionization,right-to-work laws,and female labor force participation on earnings inequality across states

This study examines the effect of unionization, right-to-work laws, and participation of women in the labor force on income inequality. Two distinct models are developed using 1970 and 1980 census data on the 50 states in the U.S. First, an income inequality model is specified as a beta distribution of the second kind to estimate Gini measures of income inequality. Second, these Gini estimates are used in a simultaneous equations model. The 1970 results indicate that higher unionization rates decreased inequality while right-to-work laws increased inequality. In 1980, the measure of inequality was lower in states with higher female labor force participation. We thank an unknown referee and the editor for comments and criticisms that greatly improved the paper. The usual caveat applies.     

Spatial approaches to measure subnational inequality: Implications for Sustainable Development Goals

The United Nations expressed an interest in reducing subnational (i.e., province and state level) inequality. We propose using a spatial decomposition of the Gini coefficient (SDGC) to track changes in subnational inequality. Typically, agencies do not track summary measures of subnational clustering of development indicators. Tracking changes in the SDGC can help measure and reduce regional inequality. To illustrate the use of the SDGC, we first present data for 93 nations to obtain cross‐sectional variation. Next, to illustrate how the SDGC trends over time, changes in the Human Development Index in Mongolia are compared to Russia and China. The SDGC can show improvement, decline and persistent clustering of subnational level inequality. The SDGC is a useful measure for the United Nations' Sustainable Development Goals.     

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.     

A multivariate extension of the Lorenz curve based on copulas and a related multivariate Gini coefficient

The Journal of Economic Inequality - We propose an extension of the univariate Lorenz curve and of the Gini coefficient to the multivariate case, i.e., to simultaneously measure inequality in more...     

MEASURING AND ANALYZING CLASS INEQUALITY WITH THE GINI INDEX INFORMED BY MODEL-BASED CLUSTERING

The most widely used measure for studying social, economic, and health inequality is the Gini index/ratio. Whereas other measures of inequality possess certain useful characteristics, such as the straightforward decomposability of the generalized entropy measures, the Gini index has remained the most popular, at least in part due to its ease of interpretation. However, the Gini index has a limitation in measuring inequality. It is less sensitive to how the population is stratified than how individual values differ. The twin purposes of this paper are to explain the limitation and to propose a model-based method—latent class/clustering analysis for understanding and measuring inequality. The latent cluster approach has the major advantage of being able to identify potential "classes" of individuals who share similar levels of income or one or more other attributes and to assess the fit of the model-based classes to the empirical data, based on different cluster distributional assumptions and the number of latent classes. This paper distinguishes class inequality from individual inequality, the type that is better captured by the Gini. Once the classes are estimated, the membership of estimated classes obtained from the best fitting model facilitates the decomposition of the Gini index into individual and class inequality. Class inequality is then measured by two relative stratification indices based on either the relative size of the Gini between-class components or the relative number of stratified individuals. Therefore, the Gini index is extended and assisted by model-based clustering to measure class inequality, thereby realizing its great potential for studying inequality. Income data from France and Hungary are used to illustrate the application of the method.     

基于千户调查的广州城乡居民基尼系数分析

根据广州统计年鉴资料和课题组千户调查数据,运用洛伦兹曲线的函数关系式模型,并借助回归方法估计模型参数,分别计算连续收入分布的基尼系数。研究发现：根据千户调查数据计算的广州市农村居民收入基尼系数为0.4170;广州市2011年城乡居民收入基尼系数为0.3495。这一计算结果优于根据统计年鉴计算的结果,并更符合实践和更具有解释能力。     

Nash Implementation with Lottery Mechanisms

Consider the problem of exact Nash Implementation of social choice correspondences. Define a lottery mechanism as a mechanism in which the planner can randomize on alternatives out of equilibrium while pure alternatives are always chosen in equilibrium. When preferences over alternatives are strict, we show that Maskin monotonicity (Maskin in Rev Econ stud 66: 23–38, 1999) is both necessary and sufficient for a social choice correspondence to be Nash implementable. We discuss how to relax the assumption of strict preferences. Next, we examine social choice correspondences with private components. Finally, we apply our method to the issue of voluntary implementation (Jackon and Palfrey in J Econ Theory 98: 1–25, 2001).I thank Toyo Sakai for his comments on a previous draft. I also thank two anonymous referees and an editor of this journal for helpful comments that improved this paper. A previous version circulated as “A note on Maskin monotonicity”. After the results presented here were obtained, I became aware of a new unpublished paper by Benoit and Ok (2004). The result of Theorem 2 and the discussion that follows is partially similar to their Theorem 1.     

Beyond Oaxaca–Blinder: Accounting for differences in household income distributions

This paper develops a method to decompose differences across distributions of household income, based on counterfactual distributions that ‘lie between’ the actually observed distributions. Our approach decomposes differences between any two income distributions (or functionals such as inequality or poverty measures) into shares due to price effects; occupational structure effects; and endowment effects. Comparing the household income distributions of the USA and Brazil in 1999, we find that most of Brazil’s excess inequality (of 13 Gini points) is accounted for by underlying inequalities in the distributions of education and of non-labor income, notably pensions (between four and six Gini points each). Steeper returns to education in Brazil also make an important contribution (of two to five points). Differences in occupational structure and in racial and demographic composition are much less important. An erratum to this article can be found at     

On probabilistic rationalizability

This paper examines the problem of rationalizability of a choice system without imposing restrictions on the universal set of alternatives and the family of feasible sets. A choice system is the probabilistic counterpart of a choice function which is basic to much of the theory of individual choice behaviour in economics. We provide a necessary and sufficient condition for a choice system to be induced by a probability measure on a set of utility functions. I would like to thank the editor and two anonymous referees for helpful comments.     

Decomposition of gini and multivariate gini indices

A new type of decomposition by population subgroup is proposed for the Gini inequality index. The decomposition satisfies the completely identical distribution (CID) condition, whereby the between-group inequality is null if and only if the distribution within each subgroup is identical to all the others. Thus, this decomposition contrasts strikingly with the subgroup decomposition of the generalized entropy measures, which satisfy the condition that the between-group inequality is null if the mean within each subgroup equals those of all the others. The new decomposition can be generalized to the distance-Gini index and the volume-Gini index, two multivariate Gini indices introduced by Koshevoy and Mosler, with some modification of the index definition and a somewhat loosened CID condition in the latter case. The source decomposition is also generalized to these multi-dimensional indices. Interaction terms appear among sources of different attributes in the decomposition for the modified volume–Gini index.

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.     

Inequality and the time structure of earnings: evidence from Germany

This paper studies the relationships between annual and subannual inequality and mobility during the course of the year. We apply an exact decomposition framework as outlined in Wodon and Yitzhaki (Econ Bull 4:1–8, 2003), and in Yitzhaki and Wodon (Research on Economic Inequality 12:179–199, 2004). Earnings records of pension insurants in Germany serve as the database. The long time horizon of our database allows us to investigate the stability and robustness of the parameters of the decomposition over time. Specifically, we show that the mobility component of the decomposition, as measured by Gini correlation coefficients, changes over the observation period. This makes it difficult to predict the impact of the income accounting period on inequality in a more general context. Thus, it is of paramount importance to use income data from a uniform accounting period in distributional analyses.     

Measuring inequality of opportunity through between-group inequality components

Opportunity egalitarians support rich-to-poor redistribution whenever this allows for the compensation of income disparities due to non-responsible choices (circumstances). In this paper we focus on the measurement of opportunity inequality within Roemer’s (Philos Public Aff 22:146–166, 1993) pragmatic theory where a disjoint and exhaustive partition rule is assumed such that individuals within the same population can be grouped depending on the sole circumstances. Given entropy-based, deprivation-based and welfaristic inequality decomposition procedures, we show that the between-group Gini component from Dagum’s decomposition is the only well known between-group inequality index satisfying the Pigou-Dalton principle of transfer as reformulated for opportunity egalitarianism.     

Distribution of coalitional power in randomized multi-valued social choice

This paper considers the distribution of coalitional influence under probabilistic social choice functions which are randomized social choice rules that allow social indifference by mapping each combination of a preference profile and a feasible set to a social choice lottery over all possible choice sets from the feasible set. When there are at least four alternatives in the universal set and ex-post Pareto optimality, independence of irrelevant alternatives and regularity are imposed, we show that: (i) there is a system of additive coalitional weights such that the weight of each coalition is its power to be decisive in every two-alternative feasble set; and (ii) for each combination of a feasible proper subset of the universal set and a preference profile, the society can be partioned in such a way that for each coalition in this partition, the probability of society's choice set being contained in the union of the best sets of its members is equal to the coalition's power or weight. It is further shown that, for feasible proper subsets of the universal set, the probability of society's choice set containing a pair of alternatives that are not jointly present in anyone's best set is zero. Our results remain valid even when the universal set itself becomes feasible provided some additional conditions hold. Received: 10 May 1999/Accepted: 18 June 2000 I would like to thank Professor Prasanta Pattanaik for suggesting to me the line of investigation carried out in this paper. I am solely responsible for any remaining errors and omissions.     

Multilevel interterritorial convergence and additive multidimensional inequality decomposition

In this paper we justify the use of the between-groups S-convex relative inequality indices to measure interterritorial convergence. In addition, we provide two appealing extensions to the use of the additive decomposable General Entropy inequality indices. First, multilevel decomposition along several subpartitions is satisfied and a natural application to convergence decomposition along different territorial level arises. Second, further general inequality decomposition along several dimensions is also satisfied. Thus, this framework provides a better explanation of the determinants of convergence (and inequality) when it is decomposed into different dimensions in comparison with other indices available in the literature. Received: 21 May 1999/Accepted: 21 September 2000     

Entropy Measures of Inequality*

Although sociologists have long been interested in the analysis of inequality, there have been relatively few systematic attempts to measure it. Most measurement has utilized popular existing measures such as the Gini coefficient, which unfortunately is relatively difficult to compute and interpret. This article presents a new measure of inequality (B) that is based upon the concept of entropy. The B measure is used for categorical data and complements Theil's (T) entropy measure for continuous data. The B measure is illustrated for both income and wealth data and successfully meets several criteria for evaluating measures of inequality. These include the criteria of scale invariance, sensitivity to transfers, and adequate upper bounds. A further advantage of sociological entropy measures of inequality is that they facilitate interdisciplinary comparison of work on inequality between sociology and other disciplines (such as economics) which use entropy measures of inequality.