Essays on Panel Data and System of Equations under Model Uncertainty
This dissertation consists of four chapters that study estimation and inference in systemof equations and panel data under model uncertainty. In Chapter 2, I consider model uncertainty in a panel data model, and introduce a Stein-like shrinkage estimator that is a weighted average of an unrestricted estimator and a restricted estimator. The restricted estimator represents a belief about where the parameters of the model are likely to be close. Chapter 3 considers the estimation uncertainty from choosing different number of lagged dependent variables as instruments in dynamic panel data models. Generalized method of moments (GMM), the typical estimation method, can produce efficient estimators when all lagged dependent variables are used as instruments. However, estimation using all instruments can cause substantial bias. Conversely, the GMM estimators that use one lag as instrument are asymptotically unbiased under forward demeaning transformation, but at the cost of losing efficiency. Therefore, I introduce an averaging estimator which is a weighted average of the two GMM estimators where the averaging weight is proportional to a quadratic loss function that minimizes the asymptotic risk. In Chapter 4, I consider simultaneous equations models (SEM), and develop an estimator to deal with the model uncertainty about the magnitude of endogeneity. Ordinary least squares (OLS) estimators are the most efficient estimators, however, may suffer from substantial bias when the degree of endogeneity is substantial. On the contrary, two-stage least squares (2SLS) estimators are consistent but not efficient. Therefore, I consider a Stein-like shrinkage estimator which is a weighted average of the OLS and 2SLS estimators, where the weight is inversely related to a Wu-Hausman statistic that measures the magnitude of the endogeneity. Chapter 5 considers latent group structures to model uncertainty resulting from unobserved heterogeneity in panel data models. Basically, I consider a panel data model where the slope parameters are heterogenous across groups but homogenous within a group, and the group identity is unknown. I provide a framework for estimation and identification of the latent group structure using a pairwise fusion penalized approach.