New Tests for Poorness, Richness, and Middle Class Welfare: Stochastic Dominance Analysis for Different Types of Social Welfare Functions

Abstract

Chow, et al. (2016) use the theory of ascending stochastic dominance (ASD), descending stochastic dominance (DSD) to develop stochastic dominance (SD) tests for richness and poorness. In this paper, we extend their work by applying Markowitz stochastic dominance (MSD) and prospect stochastic dominance (PSD) to develop SD tests for the poor (test for poorness), the rich (test for richness), and for the middle class (we call it test for middle class) to achieve a more robust analysis of relative welfare levels in the study of income distributions. The findings of these tests can be used to draw preference for different types of increasing social welfare functions; namely, concave social welfare functions, convex social welfare functions, and S-shaped and reverse S-shaped social welfare functions. The feasibility of the proposed approach and the new tests of richness, poorness, AND the middle class developed for it are demonstrated using distributions of incomes in Hong Kong.