We construct tests for the null hypothesis that the conditional average treatment effect is non-negative, conditional on every possible value of a subset of covariates. Testing such a null hypothesis can provide more information than the sign of the average treatment effects parameter. The null hypothesis can be characterized as infinitely many of unconditional moment inequalities. A Kolmogorov–Smirnov test is constructed based on these unconditional moment inequalities, and a simulated critical value is proposed. It is shown that our test can control the size uniformly over a broad set of data-generating processes asymptotically, that it is consistent against fixed alternatives and that it is unbiased against some local alternatives. Several extensions of our test are also considered and we apply our tests to examine the effect of a job-training programme on real earnings.