Essays on Model Selection and Semi-Nonparametric Instrumental Variable Estimation

This dissertation provides model selection and estimation methods for semi-nonparametric models under the existence of endogeneity. A central concept throughout the dissertation is that models are simplifications or approximations of reality and therefore are potentially misspecified. In particular, nonparametric methods acknowledge that finite dimensional fitted models are inherently misspecified. Once we view models as approximations, then the goal of model selection is to select a best approximating model rather than identifying a correct model.;In the 1970s, seminal model selection procedures were advocated in the statistical literature, including Akaike information criterion (AIC; Akaike (1973)), Mallows criterion (Mallows (1973)), cross-validation (Stone (1974)), Takeuchi information criterion (TIC; Takeuchi (1976)) and Bayesian information criterion (BIC; Schwarz (1978)). This dissertation combines prominent ideas of the traditional methods with recently developed statistical techniques to obtain a new perspective on model selection.;The first chapter proposes model selection criteria for moment restriction models. The criteria are natural extensions of the AIC and TIC. In the spirit of Akaike (1973), we derive asymptotically unbiased estimators for the expected value of the Cressie-Read discrepancy from the fitted model to the data generating process. The resulting criteria are penalized empirical Cressie-Read statistics. A relationship to the cross-validation criterion is also discussed.;The second chapter proposes a model selection criterion for nonparametric instrumental variable models. The criterion is similar to the Mallows criterion in the regression model. Under certain conditions, the criterion is asymptotically equivalent to the AIC criterion proposed in Chapter 1. The main result of this chapter is an extension of Li (1987) to the case of two stage least squares estimation. The criterion is asymptotically optimal in the sense of selecting the pair of model and instrument which achieves the lowest loss.;The third chapter considers an empirical likelihood-based estimation method for semiparametric instrumental variable models. Unknown functions are approximated by a sieve method. Consistency of the estimator is established. Also, the estimator of the finite dimensional parameters is n -consistent, asymptotically normally distributed and asymptotically efficient.