A comparison between the Pearson-based dissimilarity index and the multiple-group overlap index

Working paper

The Overlap Index has received renewed attention as a measure of inequality between two distributions (e.g. Anderson, Ge, and Leo, 2010). In this paper I propose a straightforward extension of the Overlap index to comparisons of multinomial, multivariate distributions of wellbeing over several groups. I also compare its properties against those of a dissimilarity index based on Pearson's goodness of fit statistic. The comparison highlights that both indices are similar in declaring perfect between-group equality if and only if the distributions are identical. They are different in their sensitivity to most migrations of individuals from one wellbeing state to another (with meaningful exceptions), and to different population invariance axioms. They also differ in the situations under which they attain its value of maximum inequality. The comparison illustrates the importance of both group size and concepts of minimum and maximum inequality in between-group inequality analysis. An empirical application of both indices, to a cohort history of between-group inequality in educational attainment in India, shows that such inequality across gender and caste increased toward independence and then, after the 1950s, it started to decline.

Authors: Yalonetzky, G

• Publication status: Published
• Peer review status: Reviewed (other)
• Publisher: Oxford Poverty & Human Development Initiative (OPHI)
• Series: OPHI research in progress
• Publication date: 2010-01-01
• Edition: Publisher's version
• Paper number: 16a
• Language: English
• Keywords: ophi; between-group inequality