Gini Index Decomposition for the Case of Two Subgroups

Abstract

In the framework of inequality measures decompositions, this article introduces an immediate and straightforward simplification for the Gini index when a population is divided in two subgroups. Since one of the key points in inequality analysis is represented by the role of overlapping units, a simulation study is developed in order to analyze the effects of the overlapping component on inequality decomposition. Simple expressions for the measurement of either overlapping component and inequality between are derived, which allow to correctly evaluate and compare the effects of different factors on total inequality.

Keywords:

• Gini index
• Inequality between
• Inequality decomposition

Mathematics Subject Classification:

• 62P25
• 62P20
• 91B82

Notes

¹See, for example, Bhattacharya and Mahalanobis (1967), Lerman and Yitzhaki (1984), Mehran (1975), Podder (1993, 1997), Pyatt (1976), Rao (1968), Schechtman and Yitzhaki (1987, 1999), Yao (1997), Yitzhaki (1994), and Yitzhaki and Lerman (1991).

²See, for example, Deutsch and Silber (1997), Frick and Goebel (2005), Frick et al. (2006), Yitzhaki (1994), and Yitzhaki and Lerman (1991).