Uncovering Complexities in Horizontal Inequality: A Novel Decomposition of the Gini Index

This study introduces an innovative tool to analyse how various inequality factors, including geography, race, and gender, contribute to overall inequality. Traditional approaches typically partition populations into groups based on a single factor and assess inequality by additively decomposing an inequality measure into within- and between-group components. After discussing the theoretical impossibility of additively decomposing the Gini index into within- and between-group components, in fact, we propose a Gini decomposition into two highly informative within- and between-components, with substantial improvement upon the usual assessment of horizontal inequality. This method represents a significant advancement over the traditional horizontal inequality assessment, which only compares group means and overlooks the complexities of differences between groups. Our approach accurately captures the nuances of group disparities, offering a robust measure of horizontal inequality. Through rigorous simulations and empirical analysis of the OECD Income Distribution Database, we validate the effectiveness of our method in evaluating and understanding inequality. This work enriches the toolkit available to researchers in the field by offering a framework for selecting the most suitable measure of horizontal inequality, along with the code for implementing the proposed decomposition.