One-Step Estimators for Over-Identified Generalized Method of Moments Models

In this paper I discuss alternatives to the GMM estimators proposed by Hansen (1982) and others. These estimators are shown to have a number of advantages. First of all, there is no need to estimate in an initial step a weight matrix as required in the conventional estimation procedure. Second, it is straightforward to derive the distribution of the estimator under general misspecification. Third, some of the alternative estimators have appealing information-theoretic interpretations. In particular, one of the estimators is an empirical likelihood estimator with an interpretation as a discrete support maximum likelihood estimator. Fourth, in an empirical example one of the new estimators is shown to perform better than the conventional estimators. Finally, the new estimators make it easier for the researcher to get better approximations to their distributions using saddlepoint approximations. The main cost is computational: the system of equations that has to be solved is of greater dimension than the number of parameters of interest. In practice this may or may not be a problem in particular applications.