Testing Conditional Moment Restrictions Using a Smoothed Empirical Likelihood

University Of Wisconsin-Madison, Madison WI

Investigators

Abstract

In this project the methodology developed by Tripathi and Kitamura (2000) is extended to test the validity of conditional moment restrictions. This approach, referred to as the ``smoothed empirical likelihood (SEL)'' approach, is an extension of the empirical likelihood (EL) technique developed elsewhere in the statistical literature. An extension is necessary because the conventional EL approach fails when dealing with conditional moment restrictions where the conditioning variables are continuously distributed. It is demonstrated that a likelihood ratio type test based on the SEL procedure is easy to construct and straightforward to implement. It is asymptotically normal under the null hypothesis and is able to detect local alternatives which converge to the null at rates only slightly slower than the parametric rate. A distinguishing feature of the proposed test is that it is asymptotically optimal in terms of an average power criterion used by Wald to demonstrate the large sample optimality of the parametric likelihood ratio statistic.