Decomposing the Gini Inequality Index

Abstract

The aim of this article is to propose a new breakdown of the Gini inequality ratio into three components ( within-group inequality, between-group inequality, and intensity of transvariation between groups to the total inequality index). The between-group inequality concept computes all the differences in salaries between men and women. The main contribution is to show this relationship when dealing with noninteger frequency data appearing on survey data. This article also proves the relationship between the very intuitive Gini concentration ratio and the very commonly used Gini index in the case of discrete distributions with a finite number of observations. The former refers to the relationship between the cumulative proportion of population and income, while the latter is the absolute mean difference divided by twice the arithmetic mean. This article complements the inequality decomposition literature that has stemmed from Gini’s work. The research is applied to analyze gender income inequality in a Spanish region using Spanish Structure of Earnings Survey data from 2010.