Exponentially Tilted Empirical Likelihood

Newey and Smith (2001) have recently shown that Empirical Likelihood (EL) exhibits desirable higher-order asymptotic properties, namely, that its O ¡ n−1 ¢ bias is particularly small and that biascorrected EL is higher-order efficient. Although EL possesses these properties when the model is correctly specified, this paper shows that the asymptotic variance of EL in the presence of model misspecification may become undefined when the functions defining the moment conditions are unbounded. In contrast, the Exponential Tilting (ET) estimator avoids this problem under mild regularity conditions. Since ET does not share the higher-order asymptotic properties of EL, there is a need for an estimator that combines the qualities of both estimators. This paper introduces a new estimator called Exponentially Tilted Empirical Likelihood (ETEL) that is shown to have the same O ¡ n−1 ¢ bias and the same O ¡ n−2 ¢ variance as EL, while maintaining a well-defined asymptotic variance under model misspecification. ∗The author would like to thank Alberto Abadie, Yuichi Kitamura, and participants at seminars given at University of Michigan, University of Pennsylvania, University of Chicago, and UCLA for helpful comments. This work is made possible through financial support from the National Science Foundation via grant SES-0214068.