Path Independent Inequality Measures

This paper explores a natural decomposition property motivated by Shorrocks (1980, Econometrica 48, 613 625) and Anand (1983, ``Inequality and poverty in Malaysia,'' Oxford University Press) that we call path independent decomposability. Between-group inequality is found by applying the inequality measure to the smoothed distribution, which replaces each income in a subgroup with its representative income. Within-group inequality is the measure applied to the standardized distribution, which rescales subgroup distributions to a common representative income level. Path independence requires overall inequality to be the sum of these two terms. We derive the associated class of relative inequality measures a single parameter family containing both the second Theil measure (the mean logarithmic deviation) and the variance of logarithms. Journal of Economic Literature Classification Numbers: C43, D31, D63, 015. 2000 Academic Press