The Atkinson Inequality Measure and Inequality Aversion

Abstract

This paper examines the precise way in which the Atkinson inequality measures varies as inequality aversion increases. The aim is to investigate whether precise conditions can be obtained under which a tax reform might be judged to be inequality reducing for one range of aversion parameters, and inequality increasing for another range. A number of elasticities, with respect to inequality aversion, are derived and shown to have convenient interpretations. Specific conditions cannot be produced because the Atkinson measure can take the same value for a range of alternative distributions. Nevertheless, intersecting profiles of Atkinson measures plotted against inequality aversion can arise without the need for pathological assumptions about changes in the income distribution. The analysis shows the need to consider a range of aversion parameters when examining changes to the tax and transfer system. By considering only one or two values, it could be concluded incorrectly that a tax reform is progressive, when a higher degree of inequality aversion would judge a change to be regressive.