Weak instruments and empirical likelihood: a discussion of the papers by DWK Andrews and JH Stock and Y Kitamura

Initially this discussion briefly reviews the contributions of Andrews and Stock and Kitamura, henceforth A, S and K respectively. Because the breadth of material covered by AS and K is so vast, we concentrate only on a few topics. Generalized empirical likelihood (GEL) provides the focus for the discussion. By defining an appropriate set of nonlinear moment conditions, GEL estimation yields objects which mirror in an asymptotic sense those which form the basis of the exact theory in AS allowing the definition of asymptotically pivotal test statistics appropriate for weakly identified models, the acceptance regions of which may then be inverted to provide asymptotically valid con- fidence interval estimators for the parameters of interest. The general minimum distance approach of Corcoran (1998) which parallels the information theoretic development of EL in K is briefly reviewed. A new class of estimators mirroring Schennach (2004) is suggested which shares the same asymptotic bias properties of EL and possess a well-defined limit distribution under misspecification.