Working Paper

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


Richard Smith

Published Date

31 October 2005


Working Paper (CWP13/05)

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 forthe discussion. By defining an appropriate set of nonlinear moment conditions, GEL estimationyields objects which mirror in an asymptotic sense those which form the basis of the exact theory inAS allowing the definition of asymptotically pivotal test statistics appropriate for weakly identifiedmodels, 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 approachof 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 sameasymptotic bias properties of EL and possess a well-defined limit distribution under misspecification.