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When individual or household incomes are collected for administrative or scientific surveys, the accounting period is sometimes a month, sometimes a quarter, and sometimes a year. The accounting period likely affects the shape of the income distribution and the level of measured inequality. The present study systematically explores the sensitivity of inter-temporal and inter-regional inequality comparisons to the length of the accounting period.

This paper develops criteria for an alternative concept of inequality dominance and shows how they relate to criteria for comparing relative poverty. The results warn inter alia against the use of some popular indices of inequality. They do, however, provide an ethical basis for the use of other popular indices of (restricted) inequality as potential relative poverty indices. The results also suggest an interesting extension of the Schutz coefficient as well as a use of Lorenz curves for the analysis of relative poverty and restricted inequality. A graphical illustration shows how the new criteria of restricted inequality dominance extend the ranking power of previously proposed inequality dominance criteria.

Purpose – We propose applying Reardon's approach to the measurement of ordinal segregation to the study of inequality in life chances in the case of ordinal variables. We also propose additional measures of inequality in life chances in such a case.

Methodology – We state the desirable properties of measures of inequality in life chances when the variable under study is ordinal and check which properties are fulfilled by the various indices examined in this chapter.

Findings – All the indices defined in this chapter seem suitable for the analysis of inequality in life chances with ordinal variables but we found some trade-off between indices fulfilling the population composition invariance and those fulfilling the group replication invariance.

Originality – Besides extending the indices suggested by Reardon to the study of inequality of life chances, we propose, to analyze this issue, two additional sets of indices based on the notion of distributional dissimilarity.

Mobility implies initial and final distributions and a transition process linking the observations of these two distributions. An inequality index describes properties of the intitial or final distribution. A mobility index describes the transition. In most cases, mobility indices have been developed using properties of transition matrices independently of the concepts of inequality and equity that may also be used in the analysis. This paper presents a new tool – the Gini index of mobility – that provides an overall consistent framework for the analysis of mobility, inequality, and horizontal equity. The theoretical concepts are illustrated empirically using panel data from rural Mexico.

What change in the distribution of a population’s health preserves the level of inequality? The answer to this analogous question in the context of income inequality lies somewhere between a uniform and a proportional change. These polar positions represent the absolute and relative inequality equivalence criterion (IEC), respectively. A bounded health variable may be presented in terms of both health attainments and shortfalls. As a distributional change cannot simultaneously be proportional to attainments and to shortfalls, relative inequality measures may rank populations differently from the two perspectives. In contrast to the literature that stresses the importance of measuring inequality in attainments and shortfalls consistently using an absolute IEC, this chapter formalizes a new compromise concept for a bounded variable by explicitly considering the two relative IECs, defined with respect to attainments and shortfalls, to represent the polar cases of defensible positions.

We use a surplus-sharing approach to provide new insights on commonly used inequality indices by evaluating the underpinning IECs in terms of how infinitesimal surpluses of health must be successively distributed to preserve the level of inequality. We derive a one-parameter IEC that, unlike those implicit in commonly used indices, assigns constant weights to the polar cases independent of the health distribution.

The data employed to measure income inequality usually come from household surveys, which commonly suffer from atypical observations such as outliers and contamination points. This is of importance since a single atypical observation can make classical inequality indices totally uninformative. To deal with this problem, robust univariate parametric or ad hoc procedures are commonly used; however, neither is fully satisfactory. The purpose of this paper is to propose a methodology to deal with this problem.

The author propose two robust procedures to estimate inequality indices that can use all the information from a data set, and neither of them rely on a parametric distributional assumption. The methodology performs well irrespectively of the size and quality of the data set.

Applying these methods to household data for UK (1979) and Mexico (2006 and 2011), the author find that for UK data the Gini, Coefficient of Variation and Theil Inequality Indices are over estimated by between 0.02 and 0.04, while in the case of Mexico the same indices are over estimated more deeply, between 0.1 and almost 0.4. The relevance of including atypical observations that follow the linear pattern of the data are shown using the data from Mexico (2011).

The methodology has two main limitations: the procedures are not able to identify a bad leverage outlier from a contamination point; and in the case that the data has no atypical observations, the procedures will tag as atypical a very small fraction of observations.

A reduction in the estimate of inequality has important consequences from a policy maker perspective. First, ceteris paribus, the optimal amount of resources destinated to directly address inequality/poverty. Those “extra” resources can be destinated to promote growth. Notice that this is a direct consequence of having a more egalitarian economy than previously thought, this is due to the fact that poor people will actually enjoy a bigger share of any national income increment. This also implies that, in order to reduce poverty, public policies should focus more on economic growth.

To the knowledge, in the inequality literature this is the first methodology that is able to identify outliers and contamination points in more than one direction. That is, not only at the tails of the distribution, but on the whole marginal distribution of income. This is possible via the use of other variables related to income.

The purpose of this paper is to propose the application of Gini, Theil and concentration indices for measuring inequality in water usage.

Gini coefficients and Theil indices have been used to estimate the overall inequality in domestic water use in a sample of 30 countries around the world. Along with Theil’s L (unweighted) index, liters per capita per day and gross national income weighted Theil index have also been estimated. Theil indices have been further disintegrated into within- and between-group inequalities. Concentration curve is also constructed to study the inequality in water use in accordance to the countries’ economic standing.

Domestic water use is high among the well-off countries considered in the study. Also, the Theil indices indicate that between group inequality contributes more to the overall inequality. It is observed that Theil indices, which consider only per capita water usage and can be decomposed, give a better insight into the existing inequality.

Different approaches were used to quantify inequality. The choice of index depends on the context of the study. The proposed approaches can contribute to planning of sustainable water management and development policies.

There is a dearth of metrics for quantifying inequality in water access or use. The study presents the application of indices, widely used in quantifying inequality in access to other resources such as income and energy, in assessing water inequality.

Purpose: This paper studies the Bonferroni (B) and De Vergottini (V) inequality measures, evaluating their differences and similarities, both normatively and statistically.

Design: We highlight the similarities of these two indices with the well-known Gini index (G) and use the AKS [Atkinson (1970), Kolm (1976), Sen (1973)] approach to relate social welfare functions and inequalities indices. In addition, we propose two formulations for relative deprivation, alternative to Yitzhaki (1979) and Hey and Lambert (1980) approach.

Findings: The three indices belong to the same family and introduce different and, in some sense, complementary value judgments in the measurement of inequality and welfare; each of them evaluates in a different way the local inequality in the income distribution. The three indices present inequality aversion (satisfy the Pigou-Dalton Principle of Transfers). But only B satisfies the Principle of Positional Transfer Sensitivity. The three absolute indices are interpreted as measures of the mean social deprivation starting from different definitions of individual deprivation.

Originality: The originality of this paper lies in the joint use of the three indices in the measurement of inequality, welfare, and deprivation. We apply these indices to obtain rankings of the European Union countries, using the European Community Household Panel data (2000). A sensitivity analysis of the rankings to different equivalence scales is also included.

Various indicators of income inequality and social welfare can be obtained simply by using the Gini index and the mean income of the population. This paper reviews existing indicators and presents several new indicators of this kind. While contemporary researchers seem to be preoccupied with relative inequality, this paper advocates for using intermediate inequality views and supplementing inequality rankings of countries with rankings based on social welfare. Empirical analysis, performed for 36 European countries, demonstrates such an approach’s advantages.

Traditional indices of bi-dimensional inequality and polarization were developed for cardinal variables and cannot be used to quantify dispersion in ordinal measures of socioeconomic status and health. This chapter develops two approaches to the measurement of inequality and bi-polarization using only ordinal information. An empirical illustration is given for 24 European Union countries in 2004–2006 and 2011. Results suggest that inequalities and bi-polarization in income and health are especially large in Estonia and Portugal, and that inequalities have significantly increased in recent years in Austria, Belgium, Finland, Germany, and the Netherlands, whereas bi-polarization significantly decreased in France, Portugal, and the United Kingdom.