Consistent Tests for Conditional Treatment Effects

We construct a Kolmogorov-Smirnov test for the null hypothesis that the average treatment effect is non-negative conditional on all possible values of the covariates. The null hypothesis of our interest can be characterized as a conditional moment inequality under the unconfoundedness assumption, and we employ the instrumental variable method to convert the conditional moment inequality into unconditional ones without information loss. The Kolmogorov-Smirnov test is constructed based on these unconditional moment inequalities. It is shown that our test can control the size asymptotically, is consistent against fixed alternatives, and is unbiased against some N−1/2 local alternatives. Furthermore, our test is more powerful than Lee and Whang’s (2009) against a broad set of N−1/2 local alternatives. Monte-Carlo simulation results confirm our theoretical findings. Several interesting extensions are discussed too. JEL classification: C01, C12, C21