UCLA

This dissertation studies econometric questions in the context of three different methods that are frequently used by empirical economists.

Chapter 1 provides a short introduction to the contexts, questions, methods and results studied in Chapter 2 to Chapter 4.

Chapter 2 studies a nonparametric hedonic equilibrium model in which certain product characteristics are unobserved. Unlike most previously studied hedonic models, both the observed and unobserved agent heterogeneities enter the structural functions nonparametrically. Prices are endogenously determined in equilibrium. Using both within-market and cross-market price variation, I show that all the structural functions of the model are nonparametrically identified up to normalization. In particular, the unobserved product quality function is identified if the relative prices of the agent characteristics differ in at least two markets. Following the constructive identification strategy, I provide easy-to-implement series minimum distance estimators of the structural functions and derive their uniform rates of convergence. To illustrate the estimation procedure, I estimate the unobserved efficiency of American full-time workers as a function of age and unobserved ability.

Chapter 3 studies the averaging GMM estimator that combines a conservative GMM estimator based on valid moment conditions and an aggressive GMM estimator based on both valid and possibly misspecified moment conditions, where the weight is the sample analog of an infeasible optimal weight. We establish asymptotic theory on uniform approximation of the upper and lower bounds of the finite-sample risk difference between two estimators, which is used to show that the averaging estimator uniformly dominates the conservative estimator by reducing the risk under any degree of misspecification. Extending seminal results on the James-Stein estimator, the uniform dominance is established in non-Gaussian semiparametric nonlinear models. The simulation results support our theoretical findings.

Chapter 4 examines properties of permutation tests in the context of synthetic control. Permutation tests are frequently used method of inference for synthetic control when the number of potential control units is small. We show that the size of permutation tests may be distorted. Several alternative methods are discussed.