Ranking Income Distributions: A Rank-Dependent and Needs-Based Approach

Abstract

This paper provides a normative framework to assess social welfare within a rank-dependent and bidimensional setting where individuals are characterized by income and needs. In line with the growing interest in top incomes and inequalities concerning the upper part of the income distribution (see Atkinson and Piketty, 2007; 2010; Aaberge, Havnes and Mogstad, 2013), we propose a complete framework to rank bidimensional distributions, by focussing on inequalities among the poorest as well as the richest individuals, both in the monetary and non-monetary dimension. To this end, we develop third degree inverse stochastic dominance conditions for classes of social welfare functions satisfying: i) downside inequality aversion with respect to income and upside inequality aversion with respect to needs; ii) upside inequality aversion with respect to income and downside inequality aversion with respect to needs; iii) upside inequality aversion both with respect to income and needs. Our results emerge along with the existing one, formulated by Zoli (2000), supporting downside inequality aversion both with respect to income and needs.