Nonparametric Tests for Bivariate Stochastic Dominance without Continuity Assumptions

TL;DR

This paper develops nonparametric tests for bivariate stochastic dominance that do not require the assumption of continuous distributions, extending previous methods to more general cases using empirical process theory and bootstrap techniques.

Contribution

It introduces consistent nonparametric tests for bivariate stochastic dominance without continuity assumptions, broadening applicability in economic inequality analysis.

Findings

Tests are consistent and nonparametric.

Applicable to first and second order stochastic dominance.

Useful in multidimensional economic inequality studies.

Abstract

The use of Kolmogorov-Smirnov-type statistics for testing stochastic dominance goes back to McFadden (1989). In this paper we extend the approach of Barret and Donald (2003) to the bivariate case, without the assumption of absolute continuity for the underlying distributions. Using empirical processes theory and bootstrap techniques we obtain consis- tent nonparametric tests for bivariate first and second order stochastic dominance, over several modularity classes of test functions. This tests are in turn useful tools in applied fields such as multidimensional eco- nomic inequality as shown by Perez (2015).