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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.

The purpose of this paper is to measure the unidimensional and multidimensional inequality in the case of Pakistan and compare their results at the provincial as well as regional (urban and rural areas) level. The authors collected data from Pakistan Social and Living Standard Measurement and Household Integrated Economic Survey for fiscal years of 1998–1999 and 2013–2014.

The authors used Gini coefficient for unidimensional inequality and multidimensional indexing approach of Araar (2009) for multidimensional inequality.

The findings predicted that unidimensional inequality is relatively high in the urban area due to uneven dissemination of income, but multidimensional inequality is quite high in rural areas because of higher disparities among all dimensions. At the provincial level, Punjab has relatively high-income inequality followed by Sindh, KPK and Baluchistan.

This study is a pioneering effort to compare two time periods to explore unidimensional and multidimensional inequality in all provinces of Pakistan and their representative rural-urban regions by applying Araar and Duclos’s (2009) approach. Further, this study opens some new insights for policy makers.

Recent decades have witnessed a rising interest in the measurement of inequality from a multidimensional perspective. This literature has however remained largely theoretical. This chapter presents an empirical application of a recent methodology and in doing so offers practical insights on how multidimensional inequality can be measured over two attributes (wealth and health) in the developing country context. Following Abul Naga and Geoffard (2006), a methodological framework allowing the decomposition of multidimensional inequality into two univariate Atkinson–Kolm–Sen equality indices and a third term measuring the association between the attributes is implemented. The methodology is then illustrated using data from the World Health Surveys 2002–2003. Specifically, this study presents the first comparative analysis on multidimensional inequality for a set of Middle East and North African (MENA) countries. Results reveal that the multidimensional (in-)equality indices tend to mimic the (in-)equality ordering of the wealth distributions as the latter are always less equally distributed than health. An empirical conclusion that emerges is that reducing the correlation between the attributes may help to reduce overall welfare inequality, specifically when socioeconomic inequality in health is pro-poor. The finding that the correlation between attributes has a significant contribution in the quantification of inequality has important policy implications since it reveals that it is not only wealth and health inequalities per se that matter in the measurement of welfare inequality but also the associations between them.

The paper examines several measures of multidimensional inequality, analysing their properties and majorisation criteria. Moreover, it presents a new measure which generalises Bourguignon (1999) and includes Tsui measures (1999), while preserving the advantages of Maasoumi's method (1986) of explicitly acknowledging the role of parameters relevant to multivariate settings. Finally, an application to Argentine data is provided in order to illustrate the decisions involved in the process of applying these measures and the usefulness of having appropriate criteria when making those decisions.

Health outcomes are often described according to two dimensions: quality of life and quantity of life. We analyze the measurement of inequality of health distributions referring to these two dimensions. Our analysis relies on a novel treatment of the quality-of-life dimension, which might not have a standard mathematical structure. We single out two families of (absolute and relative) multidimensional health inequality indices, inspired by the classical normative approach to income inequality measurement. We also discuss how to extend the analysis to deal with the related problem of health deprivation measurement in this setting.

The purpose of this paper is to combine multidimensional welfare analysis and entropy metrics to derive not only the best relative weights but also substitution degree among different attributes to construct multidimensional indices of well-being with Chinese Household Income Project Survey 2002 data.

The authors follow Maasoumi’s two-step measures of multivariate inequality to calculate the inequality for three social groups in China, urban residents, migrants, and rural residents. The two-step approach provides an aggregation formula which is numerically identified in this paper based on a metric entropy distance measure between the distribution of the aggregate well-being functions, on the one hand, and the distribution of the self-reported “happiness” indicator. The authors compare the differences in relative weights and substitution degree for the three groups, and link them to some institutional factors.

The authors find that incorporating substitution among attributes, and taking into consideration group heterogeneity are very important in multidimensional analysis of well-being.

The two-step approach provides an aggregation formula which is numerically identified in this paper based on a metric entropy distance measure between the distribution of the aggregate well-being functions, on the one hand, and the distribution of the self-reported “happiness” indicator.

Looking at the Jewish population in Israel in 1995 this paper compares three multidimensional approaches to poverty measurement and checks to what extent they identify the same households as poor. Logit regressions are then estimated to understand which variables have an impact on poverty. Finally, the so-called Shapley decomposition is introduced to estimate the exact marginal impact of these determinants of poverty.

Of particular interest to this study was the combined effect of the generation to which the head of the household belongs and his/her place of birth. It turns out that the ethnic origin has a significant impact on multidimensional poverty in Israel insofar as being a head of household born in Asia or Africa, whatever the generation to which one belongs, increases, ceteris paribus, the probability of being poor.

In the unidimensional poverty field, a number of axioms capture the distribution sensitivity among the poor. One of them is the monotonicity sensitivity axiom that demands that a poverty measure should be more sensitive to a reduction in the income of a poor person, the poorer that person is. On the other hand, the minimal transfer axiom requires poverty to decrease when a transfer of income is made from a poor person to a poorer one. These axioms turn out to be identical, but they provide different and interesting interpretations. Both of them rely deeply on the income-ranking of the poor.

Some generalizations of the minimal transfer axiom and its variations have been proposed in the multidimensional framework. In none of them the partial ordering of the poor is taken into account. No counterpart of the monotonicity sensitivity axiom exists.

This note introduces multidimensional generalizations of the two mentioned axioms, keeping the crucial assumption that only when the poor involved are unambiguously ranked are the axioms uncontroversial. We show that the two generalizations proposed are also identical in the multidimensional setting although offering different interpretations. Relationships between the new properties and those existing in the literature are analyzed.

We propose a framework for the measurement of income mobility over several time periods, based on the notion that multi-period mobility amounts to measuring the degree of association between the individuals and the time periods. More precisely we compare the actual income share of individuals at a given time in the total income of all individuals over the whole period analyzed, with their “expected” share, assumed to be equal to the hypothetical income share in the total income of society over the whole accounting period that an individual would have had at a given time, had there been complete independence between the individuals and the time periods. We then show that an appropriate way of consistently measuring multi-period mobility should focus on the absolute rather than the traditional (relative) Lorenz curve and that the relevant variable to be accumulated should be the difference between the “a priori” and “a posteriori” shares previously defined. Moving from an ordinal to a cardinal approach to measuring multi-period mobility, we then propose classes of mobility indices based on absolute inequality indices. We illustrate our approach with an empirical application using the EU-SILC rotating panel dataset. Our empirical analysis seems to vindicate our approach because it clearly shows that income mobility was higher in the new EU countries (those that joined the EU in 2004 and later). We also observe that income mobility after 2008 was higher in three countries that were particularly affected by the financial crisis: Greece, Portugal, and Spain.