Nonparametric Tests of Conditional Treatment Effects

We develop a general class of nonparametric tests for treatment effects conditional on covariates. We consider a wide spectrum of null and alternative hypotheses regarding conditional treatment effects, including (i) the null hypothesis of the conditional stochastic dominance between treatment and control groups; (ii) the null hypothesis that the conditional average treatment effect is positive for each value of covariates; and (iii) the null hypothesis of no distributional (or average) treatment effect conditional on covariates against a one-sided (or two-sided) alternative hypothesis. The test statistics are based on L_{1}-type functionals of uniformly consistent nonparametric kernel estimators of conditional expectations that characterize the null hypotheses. Using the Poissionization technique of Gine et al. (2003), we show that suitably studentized versions of our test statistics are asymptotically standard normal under the null hypotheses and also show that the proposed nonparametric tests are consistent against general fixed alternatives. Furthermore, it turns out that our tests have non-negligible powers against some local alternatives that are n^{-1/2} different from the null hypotheses, where n is the sample size. We provide a more powerful test for the case when the null hypothesis may be binding only on a strict subset of the support and also consider an extension to testing for quantile treatment effects. We illustrate the usefulness of our tests by applying them to data from a randomized, job training program (LaLonde (1986)) and by carrying out Monte Carlo experiments based on this dataset