Two classical decompositions of the Gini index by income sources

Working Paper 2022-618

Abstract

Natural Gini decomposition (Rao, V. M., 1969, J R Stat Soc Ser A, 132:418–425) and marginal Gini decomposition (Lerman, R. I., and Yitzhaki, S., 1985, Rev Econ Stat 67:151–156) are the most popular and widely used methods to reveal the contributions of various income sources to total income inequality. Their acceptance and highly spread empirical application have persisted in the face of criticism of the former method. This paper aims to “liberate” the natural Gini decomposition from two major critiques: that the method should be abolished because a uniformly distributed income source obtains zero contribution and that contribution terms lack a meaningful interpretation. Regarding the latter critique, it is shown that the contribution of a certain income source expresses inequality reduction due to the replacement of this source by a marginal uniformly distributed counterfactual income. Concerning the former critique, the argument is as follows: natural Gini decomposition belongs to the absolute inequality view, which commands that equal additions of income leave inequality unchanged. In this sense, it is perfectly normal that the natural Gini decomposition obtains zero contribution of the uniformly distributed income.

Authors: Ivica Urban.