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Consistent Nonparametric Tests for Bivariate Stochastic Dominance with Applications to Labor Market Econometrics
Abstract
In this paper, we develop fully consistent nonparametric tests for bivariate stochastic dominance, generalizing the weak convergence approach. We overcome known problems with multivariate Kolmogorov-Smirnov statistics using empirical processes theory and bootstrap techniques to obtain fully consistent non parametric tests for bivariate 1st and 2nd order stochastic dominance over several modularity classes of test functions. We introduce theorems showing the weak convergence of our test statistics to appropriate transformations of Brownian bridge processes and use this to obtain data depending p-values. We also make a bootstrap power assessment of the tests, showing them to be in line with top standards in the statistical literature. As we don’t assume absolute continuity our approach is useful even for discrete distributions. We finally apply our tests to construct bivariat e economic welfare rankings for Argentina in the aftermath of the 2001 crisis.
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