Path Independent Inequality Measures

Abstract

This paper explores a natural decomposition property motivated by Shorrocks (1980, Econometrica48, 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.