Essays on moment conditions models econometrics

Over the last two decades, econometric models characterized in terms of moment restrictions have gained a prominent role in economics. Moment conditions arise naturally in economic models of optimizing behavior where the Euler equation from the optimal control problem implies restrictions on the correlations between economic quantities. Generalized Method of Moments (GMM) is one of the most popular techniques for estimating and conducting inference on models that are specified through restrictions on the moments of economic variables. This work extends the literature on alternative on GMM. The first chapter is dedicated to the introduction of GMM methods. Chapter 2 presents a generalization of Empirical Likelihood. In the same chapter it is proved that the alternatives to EL may be preferable because they provide estimator that are third order efficient and yet have bounded influence function. Using this generalization a rich framework for inference is laid out in Chapter 3. Test statistics can be constructed for testing hypotheses on the parameters or on the specification of the model. The statistics can be based on the estimates of the parameter vector, on the Lagrange multipliers or on the weights of the MD problem. A small Monte Carlo experiment shows that test statistics based on the Lagrange multiplier of a MD problem defined in terms of divergences that deliver estimators with bounded influence function performs well in terms of both size and power. The last chapter of the dissertation deals with the possibility of carrying Bayesian inference when the only available information is given by restrictions on the moments. Two are the main findings of Chapter 4. First, it is shown that---by using a Bayesian procedure that puts priors on the space of distributions---posterior can be obtained that are related to the MD methods discussed in Chapter 2. Second, the validity of the MD posteriors and the posterior that uses the GMM objective function as likelihood is discussed and analyzed. Although it is found that the GMM-based posterior is invalid for Bayesian inference, MD-based likelihood tend to give valid Bayesian posterior.