Essays on empirical likelihood

This thesis consists of three research chapters on the theory of empirical likelihood (EL), which is a class of inferential methods widely used in econometrics. In Chapter 2, we focus on estimation and testing of moment restriction models with weakly dependent stationary time series data using blockwise empirical likelihood method. Empirical likelihood based methods often encounters the finite sample problem that the constraint set of the profiling step becomes empty. This issue undermines the validity of EL-based methods in empirical applications. We first show first-order validity of Chen, Variyath and Abraham (2008)'s pseudo observation adjustment, which is used to overcome this shortcoming. Under regularity conditions, key higher-order properties are found. The first property is that blockwise EL ratio statistics admit higher-order refinement and this refinement can be implemented via either mean adjustment to the EL ratio statistic or creating a pseudo observation with specific level of adjustment. By the latter approach, we address both the empty-constraint-set issue and low precision of chi-square approximation. We also find that for testing problems, the optimal block length choice that minimizes the higher-order approximation error has an order of magnitude the sample size to the power of 2/5. In Chapter 3, we focus on parameter hypothesis testing problems for moment restriction models using EL ratio tests. We substantially extend existing theorems on Bartlet correctability of EL ratio tests for parameter testing problems in Chen and Cui (2007) and Chen and Cui (2006.a). We consider tests of general nonlinear restrictions on the parameter under the null hypothesis. We show Bartlett correctability of EL ratio tests of such a large family of testing problems, which are potentially useful in many empirical applications. In Chapter 4, we focus on estimation and testing of conditional moment restrictions with i.i.d. data. Following the approach of adjusted empirical likelihood (AEL) proposed by Chen, Variyath and Abraham (2008), this paper develops AEL-based methods for conditional moment restrictions, and establishes that new methods produce semiparametrically efficient estimators and consistent specification tests. This new method shows improved computational efficiency and accuracy in finite samples, as compared to some existing alternatives.Arts, Faculty ofVancouver School of EconomicsGraduat