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The size distribution of income, or income inequality, has long been a concern to scholars in many disciplines tor different reasons. Statisticians have approached the distribution of income among individuals as a stochastic process. Economists have sought to explain income distribution by means, of economic and institutional factors. More recently, economists have been interested in the effects of economic growth and government policies on income distribution. Sociologists and political scientists have thought of income inequality as a major source of social revolt or political violence.

This paper examines the notion of intermediate inequality and its measurement. Specifically, we investigate whether the intermediateness of an intermediate measure can be preserved through repeated (affine) inequality-neutral income transformation. For all existent intermediate measures of inequality, we show that the intermediateness cannot be preserved through the transformation; each intermediate measure tends to either a relative measure or an absolute measure. This observation is then generalized to the class of unit-consistent inequality measures. An inequality measure is unit-consistent if inequality rankings by the measure are not affected by the measuring units in which incomes are expressed. We show that the unit-consistent class of intermediate measure of inequality consists of generalizations of an existent intermediate measure and, hence, the intermediateness also cannot be retained in the limit through transformations.

A number of multidimensional poverty measures that respect the ordinal nature of dimensions have recently been proposed within the counting approach framework. Besides ensuring a reduction in poverty, however, it is important to monitor distributional changes to ensure that poverty reduction has been inclusive in reaching the poorest. Distributional issues are typically captured by adjusting a poverty measure to be sensitive to inequality among the poor. This approach, however, has certain practical and conceptual limitations. It conflicts, for example, with some policy-relevant measurement features, such as the ability to decompose a measure into dimensions post-identification and does not create an appropriate framework for assessing disparity in poverty across population subgroups. In this chapter, we propose and justify the use of a separate decomposable inequality measure – a positive multiple of “variance” – to capture the distribution of deprivations among the poor and to assess disparity in poverty across population subgroups. We demonstrate the applicability of our approach through two contrasting inter-temporal illustrations using Demographic Health Survey data sets for Haiti and India.

Purpose: Most of the characterizations of inequality or poverty indices assume some invariance condition, be that scale, translation, or intermediate, which imposes value judgments on the measurement. In the unidimensional approach, Zheng (2007a, 2007b) suggests replacing all these properties with the unit-consistency axiom, which requires that the inequality or poverty rankings, rather than their cardinal values, are not altered when income is measured in different monetary units. The aim of this paper is to introduce a multidimensional generalization of this axiom and characterize classes of multidimensional inequality and poverty measures that are unit consistent.

Design/methodology/approach: Zheng (2007a, 2007b) characterizes families of inequality and poverty measures that fulfil the unit-consistency axiom. Tsui (1999, 2002), in turn, derives families of the multidimensional relative inequality and poverty measures. Both of these contributions are the background taken to achieve our characterization results.

Findings: This paper merges these two generalizations to identify the canonical forms of all the multidimensional subgroup- and unit-consistent inequality and poverty measures. The inequality families we derive are generalizations of both the Zheng and Tsui inequality families. The poverty indices presented are generalizations of Tsui's relative poverty families as well as the families identified by Zheng.

Originality/value: The inequality and poverty families characterized in this paper are unit and subgroup consistent, both of them being appropriate requirements in empirical applications in which inequality or poverty in a population split into groups is measured. Then, in empirical applications, it makes sense to choose measures from the families we derive.

We present a comparison of coverage and values for five inequality data sets that have worldwide or major international coverage and independent measurements that are intended to present consistent coefficients that can be compared directly across countries and time. The comparison data sets are those published by the Luxembourg Income Studies (LIS), the OECD, the European Union’s Statistics on Incomes and Living Conditions (EU-SILC), and the World Bank’s World Development Indicators (WDI). The baseline comparison is with our own Estimated Household Income Inequality (EHII) data set of the University of Texas Inequality Project. The comparison shows the historical depth and range of EHII and its broad compatibility with LIS, OECD, and EU-SILC, as well as problems with using the WDI for any cross-country comparative purpose. The comparison excludes the large World Incomes Inequality Database (WIID) of UNU-WIDER and the Standardized World Income Inequality Database (SWIID) of Frederick Solt; the former is a bibliographic collection and the latter is based on imputations drawn, in part, from EHII and the other sources used here.

We use Cross-National Equivalent File (CNEF) data from the United States and Great Britain to investigate the association between adults’ health and the income inequality they experienced as children up to 80 years earlier. Our inequality data track shares of national income held by top income percentiles from the early 20th century. We average those data over the same early-life years and merge them to CNEF data from both countries that measure self-reported health of individuals between 1991 and 2007. Observationally, adult men and women in the United States and Great Britain less often report being in better health if inequality was higher in their first five years of life. Although the trend in inequality is similar in both countries over the past century, the empirical association between health and inequality in the United States differs substantially from the estimated relationship in Great Britain. When we control for demographic characteristics, measures of permanent income, and early-life socio-economic status, the health–inequality association remains robust only in the U.S. sample. For the British sample, the added controls drive the coefficient on inequality toward zero and statistical insignificance.

In the literature on the relationship between class of origin and educational attainment, the typical conclusion is that class inequality was stable over the last century, and the attempts at egalitarian reform thus proven ineffective. The conclusion turns out to depend on the choice of statistical measure, in this case loglinear measures of association. Also linear measures of association give similar results. If instead, measures of inequality are used, the contrasting conclusion of a strong reduction in the class bias in recruitment to higher education emerges.

As the provision of higher education has increased over time, the trends in the results of these three measures differ. It is argued that it is measures of inequality that capture inequality in the allocation of higher education or bias in the allocation mechanisms. The argument in favor of using loglinear measures has been the special property of “margin insensitivity” attributed to them. It has also been suggested that they capture bias in the allocation mechanism, which may develop in a way different from the trend in the inequality of the allocation outcome. It is argued that neither claim is tenable.

Using decomposable measures of inequality, the implications of household structure are investigated by examining inequality between and within household groups based on the number of exemptions, which correlates with household size, and the filing status, which correlates with the common forms of household structure, i.e. married, single, head of household. Detailed household income data are used to measure income inequality for both pre-tax/transfer and post-tax/transfer definitions of income. These decompositions provide information about the degree of inequality, both before and after taxes and transfers, which is due to household size and filing status. The bootstrap is employed to construct standard errors for the inequality measures and their decompositions, and hypothesis tests are conducted to determine whether the observed changes in the distribution of income are statistically significant.

Purpose – We propose the Information Theory of Segregation, which holds that all measures of segregation and of inequality are united within a single conceptual framework. Accepting this framework implies that all measures of inequality can also be used to measure segregation and that all measures of segregation are fundamentally based on measures of inequality.

Methodology – We state several propositions that follow from the information theory perspective, and show mathematically that many common measures of inequality and segregation satisfy the propositions.

Findings – We show that all common measures of inequality can be used to form measures of segregation and that the resulting measures can be applied to binary, polytomous, and continuous variables. Further, we develop several new measures, including a Gini Segregation Index (GS) for continuous variables and Income Dissimilarity Index (ID), a version of the Index of Dissimilarity suitable for measuring economic segregation. We show that segregation measures can easily be adapted to handle persons of mixed race, and describe the Non-Exclusive Index of Dissimilarity (NED) and the Non-Exclusive Entropy Index of Segregation (NEH). We also develop a correction for structural constraints on the value of segregation measures, comparable to capacity constraints in a communications channel, which prevent them from reaching their theoretical maximum or minimum value.

Originality – Placing inequality and segregation measures in a common framework is useful for several reasons. It highlights a common mathematical structure shared by many different segregation measures, and it suggests certain useful variants of these measures that have not been recognized previously.

When health is measured by a bounded variable, differences in health can be presented as levels of attainment or shortfall. Measurement of heath inequality then usually involves the choice of either the attainment or the shortfall distribution, and this choice may affect comparisons of inequality across populations. A number of indices have been introduced to overcome this problem. This chapter proposes a framework in which attainment and shortfall distributions can be jointly analyzed. Joint distributions of attainments and shortfalls are defined from points of view consistent with concerns for relative, absolute or intermediate inequality. Inequality measures invariant according to the corresponding ethical criterion are then applied. A dominance criterion that guarantees unanimous rankings of the joint distributions is also proposed.