A Note on Between-Group Inequality with an Application to Households

This Note belongs to the recent literature emphasizing that the residual in the traditional Gini index decomposition reveals more than what is commonly believed. We show that the residual reveals the so far unexplored contribution of stratification to between-group inequality, and this suggests that the between-group inequality measure should be modified accordingly. We propose a measure of between-group inequality which is a function of stratification. This is our first result. Moreover, we show that this measure is numerically equivalent to the one suggested by Yitzhaki and Lerman (1991), yet, contrary to the latter, we are able to define precisely its range of variation. This is our second result. Both results are illustrated by analysing between-group inequality and stratification among Italian households.