We propose non-nested tests for competing conditional moment restriction models using a method of empirical likelihood. Our tests are based on the method of conditional empirical likelihood developed by Kitamura, Tripathi and Ahn (2004) and Zhang and Gijbels (2003). By using the conditional implied probabilities, we develop three non-nested tests: the moment encompassing, Cox-type, and eﬀicient score encompassing tests. Compared to the existing non-nested tests which mainly focus on testing unconditional moment restrictions, our approach directly tests conditional moment restrictions which imply the inﬁnite number of unconditional moment restrictions. We derive the null distributions and power properties of the proposed tests. Simulation experiments show that our tests have reasonable ﬁnite sample properties.
Otsu, Taisuke and Whang, Yoon-Jae, "Testing for Non-nested Conditional Moment Restrictions via Conditional Empirical Likelihood" (2005). Cowles Foundation Discussion Papers. 1820.