| This dissertation consists of three chapters on econometric models with endogenous regressors. The chapters are concerned with identification and estimation in nonparametric panel data models, instrumental variable models, and a popular demand model, respectively.;In the first chapter, I study nonparametric panel data models with multidimensional, unobserved individual effects and a fixed number of time periods. I focus on models where the unobservables have a factor structure and enter an unknown structural function nonadditively. Key distinguishing features are that the individual effects may impact outcomes differently in different time periods and that I allow for heterogeneous marginal effects. The paper provides conditions for point identification in static and dynamic models with both continuous and discrete outcomes. I then present different estimators and study their finite sample properties in Monte Carlo experiments. Finally, I demonstrate the methods in an empirical application, where I investigate the relationship between teaching practice and student achievement.;The second chapter, which is joint work with Joel Horowitz, deals with inference about a linear functional, L(g), where the function g satisfies the relation Y = g(X) + U; E(U| W) = 0. When X and W are discrete and W has fewer points of support than X, neither g nor L(g) is nonparametrically identified. We explore the use of shape restrictions for achieving partial identification of L(g) and show that they restrict L(g) to an interval whose endpoints are solutions to linear programming problems. Inference can be carried out by using the bootstrap. We illustrate our method in an empirical application.;The last chapter develops asymptotic theory for differentiated product demand systems with a fixed number of products and a large number of markets. I take into account that the predicted and observed market shares are approximated by Monte Carlo integration and a sample of consumers, respectively. These approximations lead to additional variance and bias terms in the asymptotic expansion of the estimator. I propose a bias and a variance correction to control for these terms. Monte Carlo results show that these corrections should be used in applications to avoid severe undercoverage caused by the approximations. |
