Subgroup decomposability of Theil entropy measure of inequality: Evidence from India

Abstract

Henry Theil published a seminal book ‘Economics and Information Theory’ and introduced the essential functional forms for modelling and understanding inequality, known as the Theil Entropy Measure. The measure has a particular advantage as it is subgroup decomposable and satisfies the additive decomposability criterion developed by Bourguignon. This criterion is intended to establish that we can neatly decompose the inequality measure into within-group inequality and between-group inequality. Nevertheless, researchers like Sudhir Anand, Udo Ebert, and Mishra & Parikh have suggested an alternative method of subgroup decomposition. This method exhibits that the entropy measure fails to be neatly decomposed into within-group inequality and between-group inequality; a residual part is also present. Indeed, we observe that this residual part is an ‘interaction’ of within-group inequality and between-group inequality. For empirical evidence, we decompose the combined (combining rural and urban regions) consumer expenditure inequality into within-region inequality and between-region inequality for all India and its major states from 1983 to 2011-12.