2005): Testing for Non-nested Conditional Moment Retrictions via Conditional Empirical Likelihood, Cowles Foundation Discussion Paper No

We propose non-nested tests for competing conditional moment resctriction models us-ing 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 Gi-jbels (2003). By using the conditional implied probabilities, we develop three non-nested tests: the moment encompassing, Cox-type, and effcient score encompassing tests. Com-pared 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