Rankings of income distributions: a note on intermediate inequality indices

Abstract

The purpose of this paper is to analyze the advantages and disadvantages of several intermediate inequality measures, paying special attention to the unit-consistency axiom proposed by Zheng (2007). First, we demonstrate why one of the most referenced intermediate indices, proposed by Bossert and Pfingsten (1990), is not unit-consistent. Second, we explain why the invariance criterion proposed by Del Río and Ruiz-Castillo (2000), recently generalized by Del Río and Alonso-Villar (2008), leads instead to inequality measures that are unaffected by the currency unit. Third, we show that the intermediate measures proposed by Kolm (1976) may also violate unit-consistency. Finally, we reflect on the concept of intermediateness behind the above notions together with that proposed by Krtscha (1994). Special attention is paid to the geometric interpretations of our results.

Citation

del Río, C. and Alonso-Villar, O. (2008), "Rankings of income distributions: a note on intermediate inequality indices", Bishop, J. and Zheng, B. (Ed.) Inequality and Opportunity: Papers from the Second ECINEQ Society Meeting (Research on Economic Inequality, Vol. 16), Emerald Group Publishing Limited, Leeds, pp. 213-229. https://doi.org/10.1016/S1049-2585(08)16010-0