Decomposition of Rank-Dependent Measures of Inequality by Subgroups

Summary - The purpose of additive subgroup decomposition is to study the relationship\nbetween overall inequality and inequality within and between population\nsubgroups defined by variables like gender, age, education and region of residence.\nAs opposed to the inequality measures that are additively decomposable, the so-called\ngeneralized entropy family of inequality measures, the Gini coefficient does not admit\ndecomposition into within- and between-group components but does also require an\ninteraction (overlapping) term. The purpose of this paper is to introduce an alternative\ndecomposition method that can be considered to be a parallel to Lerman and\nYitzhaki’s (1985) elasticity approach for decomposing the Gini coefficient by income\nsources, which means that the elasticity of the Gini coefficient with respect to various\nincome components is treated as the basic quantities of the decomposition method.\nThus, rather than decomposing the Gini coefficient or any other inequality measure\ninto a within-inequality term, a between-inequality term and eventually an interaction\nterm, the basic quantities of the introduced method are the effects of marginal changes\nin variables that are used to specify the population subgroups.\nKey Words - The Gini coefficient; The Bonferroni coefficient; Rank-dependent measures\nof inequality; Decomposition by subgroups.