On a family of achievement and shortfall inequality indices

Working Paper 2013-300

Abstract

This paper identifies a family of absolute consistent inequality indices using a weakly decomposable postulate suggested by Ebert (2010). Since one member employs an Atkinson (1970) type aggregation we refer to it as the Atkinson index of consistent inequality. A second member of this family parallels the Kolm (1976) index of inequality while a third member of the family can be regarded as the normalized Theil (1972) consistent mean logarithmic deviation index. Two innovative features of these indices are that no specific structure is imposed on the form of the index at the outset and no transformation of any existing index is considered to ensure consistency. Each of them regards an achievement distribution as equally unequal as the corresponding shortfall distribution. We apply these indices to study inequality in mental health in Britain between 1991 and 2008.

Authors: Satya R. Chakravarty, Nachiketa Chattopadhyay, Conchita D’Ambrosio.