Benchmark inequality measures

Abstract

The research leading to these results has received funding from the European Research Council (ERC-2014-StG-637768, EQUALIZE project), the CERCA Programme from Generalitat de Catalunya and from the Spanish Ministry of Economy and Competitiveness ìRamÛn y CajalîResearch Grant Program (RYC-2013-14196)

In measuring the variability of a bounded variable such as health status, the use of traditional income inequality measures poses several problems. On the one hand, the bounded nature of the variable generates a strong relationship between its mean and the corresponding inequality levels (i.e. when the mean approaches either the lower or the upper bounds, inequality mechanically goes to zero). On the other hand, the lack of consistency between achievement and shortfall distributions precludes the use of classical measures of relative inequality. In this paper we propose new inequality indices that aim at capturing the intuitions of relative inequality but adapted to the context of bounded variables (the so-called benchmark inequality measures). The benchmark inequality indices proposed here simultaneously solve both problems: they consistently rank achievement and shortfall distributions and take into account the fact that when the mean of a bounded distribution approaches some of its bounds, the scope for potential variability is substantially reduced. Keywords: Inequality measurement, Bounded variables, Attainment, Shortfall, Consistency.