| In the last 20 years, the generalized method of moments (GMM) has become a dominant framework for econometric analysis, particularly in macroeconomics, finance, and panel data analysis. However, recent simulation and empirical results show that the GMM approach can have poor finite sample performance.; Empirical likelihood has drawn the recent attention of researchers as an alternative to GNIM. Theoretical comparisons, such as the higher order and large deviation comparisons, show that empirical likelihood has more desirable properties than GMM. This dissertation is devoted to extensions of the empirical likelihood method in econometrics.; In Chapter 1, I propose new estimation and inference methods for quantile regression models based on the methods of empirical likelihood and its extensions. I consider four concepts of nonparametric likelihood and investigate the statistical properties of the derived estimators and test statistics. My extensions to the empirical likelihood approach effectively deal with several problems of existing quantile regression estimation and inference methods, such as the efficiency of the estimators, variance estimation to construct confidence sets, and higher order refinements of confidence sets.; In Chapter 2, I extend the method of empirical likelihood to semiparametric models. I propose a new general estimation method for conditional moment restriction models with unknown functions, which include partially linear models; single index models, and transformation models as special cases. I call the new estimator the penalized empirical likelihood estimator, which is based on the conditional empirical likelihood estimator and the method of penalization. I show the consistency, convergence rate, asymptotic normality, and efficiency of the proposed estimator.; In Chapter 3, I propose a new inference method for nonlinear and dynamic moment restriction models including weakly identified parameters, which induce the inconsistency and non-standard asymptotic distribution of the conventional GMM estimator. My method is based on generalized empirical likelihood and its extension to time series models. By using "squashed" moment restrictions, the proposed test statistic and confidence set are robust to weak identification and the number of moment restrictions or instrumental variables. |
