Bipolarisation measurement

Working Paper 2023-653

Abstract

This paper introduces and axiomatically characterises new classes of bipolarisation indices based on the equivalent representation of observed distributions with the help of two-income distributions. This representation makes it possible to interpret the suggested indices either as I) the representative income gap between individuals from the top part of the distribution and those from the bottom part, orii) the excess representative income share of the top part compared against its population share.The proposed bipolarisation indices show additional appealing features. First, they can handle any population partition between the p percent poorest individuals and the (1-p) richest individuals (including the popular p=50% choice). Secondly, they can be easily decomposed into spread and clustering contributions toward total bipolarisation. Finally, they relate to familiar inequality indices so that bipolarisation levels can easily be connected to the average income and inequality levels relating to each part of the income distribution. The new classes include some prominent rank-dependent bipolarisation indices from the literature as special cases, together with numerous novel proposals for both absolute and relative approaches to bipolarisation. An illustration is given using consumption data from nine Sub-Saharan African countries.

Authors: Florent Bresson, Marek Kosny, Gaston Yalonetzky.