Three essays on nonlinear panel data models and quantile regression analysis

This dissertation is a collection of three independent essays in theoretical and applied econometrics, organized in the form of three chapters. In the first two chapters, I investigate the properties of parametric and semiparametric fixed effects estimators for nonlinear panel data models. The first chapter focuses on fixed effects maximum likelihood estimators for binary choice models, such as probit, logit, and linear probability model. These models are widely used in economics to analyze decisions such as labor force participation, union membership, migration, purchase of durable goods, marital status, or fertility. The second chapter looks at generalized method of moments estimation in panel data models with individual-specific parameters. An important example of these models is a random coefficients linear model with endogenous regressors. The third chapter (co-authored with Joshua Angrist and Victor Chernozhukov) studies the interpretation of quantile regression estimators when the linear model for the underlying conditional quantile function is possibly misspecified.