The sizes and powers of some stochastic dominance tests: A Monte Carlo study for correlated and heteroskedastic distributions

Abstract

Testing for stochastic dominance among distributions is an important issue in the study of asset management, income inequality, and market efficiency. This paper conducts Monte Carlo simulations to examine the sizes and powers of several commonly used stochastic dominance tests when the underlying distributions are correlated or heteroskedastic. Our Monte Carlo study shows that the test developed by Davidson and Duclos [R. Davidson, J.Y. Duclos, Statistical inference for stochastic dominance and for the measurement of poverty and inequality, Econometrica 68 (6) (2000) 1435-1464] has better size and power performances than two alternative tests developed by Kaur et al. [A. Kaur, B.L.S.P. Rao, H. Singh, Testing for second order stochastic dominance of two distributions, Econ. Theory 10 (1994) 849-866] and Anderson [G. Anderson, Nonparametric tests of stochastic dominance in income distributions, Econometrica 64 (1996) 1183-1193]. In addition, we find that when the underlying distributions are heteroskedastic, both the size and power of the test developed by Davidson and Duclos [R. Davidson, J.Y. Duclos, Statistical inference for stochastic dominance and for the measurement of poverty and inequality, Econometrica 68 (6) (2000) 1435-1464] are superior to those of the two alternative tests. © 2007 IMACS.