A Computational Implementation of GMM

In this paper we study a statistical method of implementing quasi-Bayes estimators for nonlinear and nonseparable GMM models, that is motivated by the ideas proposed in Chernozhukov and Hong (2003) and Creel and Kristensen (2011) and that combines simulation with nonparametric regression in the computation of GMM models. We provide formal conditions under which frequentist inference is asymptotically valid and demonstrate the validity of the use of posterior quantiles. We also show that in this setting, local linear regression methods have theoretical advantages over kernel methods that are also reflected in finite sample simulation results. Our results also apply to both exactly and over identified models. These estimators do not need to rely on numerical optimization or Markov Chain Monte Carlo simulations. They provide an effective compliment to the classical M-estimators and to MCMC methods, and can be applied to both likelihood based models and method of moment based models.