Three Essays on Econometrics

This dissertation contains three chapters. In the first chapter, I investigate why there exists considerable variation in estimates of the coefficient of relative risk aversion (CRRA) and the elasticity of intertemporal substitution (EIS) in the consumption-based asset pricing model with Epstein and Zin (1989) preferences. I find the Epstein and Zin (1989) structure collapses to the time-separable structure when returns are within a reasonable range. I also show the choice of parameters might lead to an ill-behaved conditional moment, which might cause either the GMM method to get stuck, or the estimates do not move much from the starting points. The second and third chapters are about the estimation of latent group heterogeneities in panel data. In chapter two, I propose a Mahalanobis metric based k-means algorithm (KMM) for group membership estimation in linear panel data models with time-varying grouped fixed effects by Bonhomme and Manresa (2015). The proposed method improves the accuracy of estimates by taking serial correlation and heteroscedasticity into account. I also derive the optimal beta for group membership estimation and show that it may be different from the true coefficient parameter. Since the optimal beta is not feasible in practice, I propose the data-driven selection method for its implementation. In the third chapter, I develop a novel approach to estimate causal parameters and latent group heterogeneities in two independent steps without an iteration procedure. In the existing literature, the estimation of coefficients depend on the estimation of grouping, and vice versa, which may lead to significant estimation error if any step is misleading. My approach applies to a linear panel data model with either time-varying or interactive group fixed effects