Gini index decomposition for the case of two subgroups

Abstract

Gini inequality index decomposition into within and between inequality components arises since a long time a controversial, wide and interesting discussion. The measurement of inequality between is traditionally obtained in the framework of analysis of variance as a function of only the means of the subgroups. An alternative methodology to measure inequality between states the possibility to take into account all differences between subgroups distributions. By referring to this new approach, the paper introduces a relevant simplification of the measurement of inequality between and of the transvariation contribution for the case of a population divided in two subgroups. Without transvariation, inequality between can be obtained as the difference of the poor share in the population and the poor share in the variable of interest. Also for the case of two overlapping subgroups simple and straightforward expressions for the transvariation contribution and inequality between are derived.