Alternative estimation methods and specification tests for moment condition models

Abstract

The study of the generalized method of moments (GMM) and alternative estimation methods for models which are defined solely in terms of a set of moment conditions constitutes a recent and increasingly popular research topic in econometrics. In this thesis we focus on the analysis of GMM and generalized empirical likelihood (GEL) estimators and related statistics, providing an up-to-date survey of the existing literature and performing three major contributions to this subject. Our first major investigation concerns the examination of the small sample bias of ten alternative estimators for moment condition models, which may be divided into two classes. The first includes the first-order asymptotically equivalent GMM, continuous-updating GMM, empirical likelihood and empirical information estimators. The second contains six GMM bootstrap estimators, three of which are developed in this thesis. Two extensive Monte Carlo studies reveal that one of the new bootstrap techniques produces the estimators with less bias in most cases. Second, we derive several Pearson-type statistics suitable for testing overidentifying moment conditions and parametric restrictions. In a Monte Carlo study concerning the first class of tests, we find that, in small samples, the size behaviour of one of the new statistics is superior to that of both alternative tests based on their asymptotic distributions and bootstrap forms of the popular Hansen’s (1982) J test. The proposal of a number of new non-nested hypothesis tests that integrate and complement the work of other authors constitute our last major contribution. We derive generalized statistics that include most of the existing tests as particular cases and develop GEL parametric and moment encompassing tests that enlarge substantially the number of tests available to the practitioner to assess non-nested moment condition models. Simulation experiments indicate that GEL-based encompassing tests using a robust estimator for the variance matrix of the moment indicators are particularly efficacious.