On testing conditional moment restrictions: The canonical case

Let (x, z) be a pair of random vectors. We construct a new smoothed empirical likelihood based test for the hypothesis that E(z|x) a.s. = 0, and show that the test statistic is asymptotically normal under the null. An expression for the asymptotic power of this test under a sequence of local alternatives is also obtained. The test is shown to possess an optimality property in large samples. Simulation evidence suggests that it also behaves well in small samples.