# The Variance as a subgroup decomposable measure of inequality

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## Abstract

An inequality index is called subgroup decomposable if it can be expressed as a weighted sum of inequality values calculated for population subgroups plus the contribution arising out of differences among subgroup means. Theil (1967) and Shorrocks (1980) pointed out two important requirements for subgroup decomposable inequality indices. Shorrocks (1980) has shown that Theil's mean logarithmic deviation, for which the weights of subgroup terms are respective population shares, is the only relative inequality index that fulfils these two properties. In this paper we show that the variance is the only absolute inequality index to satisfy the population share weighted subgroup decomposability property, which in turn implies that it also meets the two properties suggested by Theil and Shorrocks. A numerical illustration of several inequality indices in also presented in the paper. JEL classification numbers:D31, D63.

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