Conditional Stochastic Dominance Testing

This article proposes bootstrap-based stochastic dominance tests for nonparametric conditional distributions and their moments. We exploit the fact that a conditional distribution dominates the other if and only if the difference between the marginal joint distributions is monotonic in the explanatory variable at each value of the dependent variable. The proposed test statistic compares restricted and unrestricted estimators of the difference between the joint distributions, and it can be implemented under minimal smoothness requirements on the underlying nonparametric curves and without resorting to smooth estimation. The finite sample properties of the proposed test are examined by means of a Monte Carlo study. We illustrate the test by studying the impact on postintervention earnings of the National Supported Work Demonstration, a randomized labor training program carried out in the 1970s.