Income inequality measurement: a fresh look at two old issues

The literature on income inequality measurement is split into (1) the ethical approach, from which the Atkinson–Kolm–Sen and Kolm–Pollak classes of indices are derived, and (2) the axiomatic approach, which mainly leads to the generalised entropies. This paper shows how to rationalise, under utilitarianism, the generalised entropies as ethical indices. In this framework a generalised entropy index is consistent with the principle of transfers if and only if the underlying utility function is increasing. This unconventional interpretation explains the strange behaviour of the generalised entropies for some values of the inequality aversion parameter, as identified by Shorrocks (Econometrica 48:613–625, 1980). In that case, the underlying utility function is convex. Then, it provides a solution to escape the so-called Hansson–Sen paradox (Hansson in Foundational problems in the special sciences. Reidel Publishing Company, Dordrecht, 1977; Sen in Personal income distribution. North-Holland, Amsterdam, pp 81–94, 1978) that affects the standard ethical indices and which corresponds to a counterintuitive increase in inequality as a result of a concave transformation of the utility function. A normalised version of the generalised entropies behaves appropriately after such a transformation.