Nonparametric tests of conditional treatment effects with an application to single‐sex schooling on academic achievements

We develop a general class of nonparametric tests for treatment effects conditional on covariates. We consider a wide spectrum of null hypotheses regarding conditional treatment effects, including the following: (a) the null hypothesis of the conditional stochastic dominance between treatment and control groups; (b) the null hypothesis that the conditional average treatment effect is nonpositive for each value of covariates; (c) the null hypothesis of no distributional (or average) treatment effect conditional on covariates. The test statistics are based on L-1-type functionals of uniformly consistent nonparametric kernel estimators of conditional expectations that characterize the null hypotheses. We show that our tests using the standard normal critical values have asymptotically correct size. We also show that the proposed nonparametric tests are consistent against general fixed alternatives and have non-negligible powers against some n(-1/2) local alternatives to the null hypothesis with inequality constraints and n(-1/2)h(-d/4) local alternatives to the null hypothesis with equality constraints, where h is a bandwidth, n is the sample size and d is the dimension of continuous covariates. We illustrate the usefulness of our tests by applying them to the effect of single-sex schooling on academic achievements using Korean data.