Measuring Group Disadvantage with Inter-distributional Inequality Indices: A Critical Review and Some Amendments to Existing Indices

Gaston Yalonetzky

doi:10.5018/economics-ejournal.ja.2012-9

Abstract

AbstractA long literature on inter-distributional inequality (IDI) has developed statistical tools for measuring the extent of inequality between two groups (e.g. men versus women). The paper reviews some of the most prominent IDI indices proposed in the last four decades. The assessment focuses on how these indices react to inequalities that are disadvantageous to different groups, using two operationalizations of a concept of group-specific disadvantage focus (GDF). Relying on a complementary set of properties, the review also assesses whether these indices are informative about other interesting features related to IDI comparisons, chiefly distributional equality, but also absence of distributional overlap and presence of firstorder stochastic dominance. The author proposes amendments to several of these indices in order to render them in fulfillment of GDF properties and more informative on the mentioned distributional features.

Highlights

The concern for differences in the distribution of wellbeing characteristics among groups within societies has earned a long-standing interest in the Social Sciences and Political Philosophy
In this paper I rst propose a property of a(n index's) sensitivity to inequality that is detrimental exclusively to one speci c group and that is applicable to indices of inter-distributional inequality that deal with populations of different size
I take the opportunity to extend this review of existing indices in order to evalute whether these indices are informative, or not, regarding other interesting features related to inter-distributional inequality (IDI) comparisons

Summary

Introduction

In this paper I rst propose a property of a(n index's) sensitivity to inequality that is detrimental exclusively to one speci c group and that is applicable to indices of inter-distributional inequality that deal with populations of different size. When α = 1; both PROBY1 (Y X) and PROBY1 (X Y ) are sensitive to changes in the percentile gaps, and they are helpful to detect absence of distributional overlap because: PROBY1 (X Y ) = 1 $ FX zYmax = 0: When α = 1 the following relationship holds: 2PROB = PROBY1 (Y X) PROBY1 (X Y ) + 1 Since these indices map from probability space, it is easy to show that they ful ll properties of population replication invariance and ratio scale invariance. As for other distributional features, C does not distinguish between distributional

Likewise

Concluding remarks