Essays in Econometrics

This dissertation consists of two chapters, both contributing to the field of econometrics. The contributions are mostly in the areas of estimation theory, as both chapters develop new estimators and study their properties. They are also both developed for semi-parametric models: models containing both a finite dimensional parameter of interest, as well as infinite dimensional nuisance parameters. In both chapters, we show the estimators' consistency, asymptotic normality and characterize their asymptotic variance. The second chapter is co-authored with professors Jinyong Hahn, Bryan S. Graham and James L. Powell./nIn the first chapter, we focus on estimation in a cross-sectional model with independence restrictions, because unconditional or conditional independence restrictions are used in many econometric models to identify their parameters. However, there are few results about efficient estimation procedures for finite-dimensional parameters under these independence restrictions. In this chapter, we compute the efficiency bound for finite-dimensional parameters under independence restrictions, and propose an estimator that is consistent, asymptotically normal and achieves the efficiency bound. The estimator is based on a growing number of zero-covariance conditions that are asymptotically equivalent to the independence restriction. The results are illustrated with four examples: a linear instrumental variables regression model, a semilinear regression model, a semiparametric discrete response model and an instrumental variables regression model with an unknown link function. A Monte-Carlo study is performed to investigate the estimator's small sample properties and give some guidance on when substantial efficiency gains can be made by using the proposed efficient estimator./nIn the second chapter, we focus on estimation in a panel data model with correlated random effects and focus on the identification and estimation of various functionals of the random coefficient's distributions. In particular, we design estimators for the conditional and unconditional quantiles of the random coefficient's distribution. This model allows for irregularly identified panel data models, as in Graham and Powell (2012), where quantiles of the effect are identified by using two subpopulations of "movers" and "stayers", i.e. those for whom the covariates change by a large amount from one period to another, and those for whom covariates remain (nearly) unchanged. We also consider an alternative asymptotic framework where the fraction of stayers in the population is shrinking with the sample size. The purpose of this framework is to approximate a continuous distribution of covariates where there is an infinitesimal fraction of exact stayers. We also derive the asymptotic variance of the coefficient's distribution in this framework, and we conjecture the form of the asymptotic variance under a continuous distribution of covariates./nThe main goal of this dissertation is to expand the choice set of estimators available to applied researchers. In chapter one, the proposed estimator attains the efficiency bound and might allow researchers to gain more precision in estimation, by getting smaller standard errors. In the second chapter, the new estimator allows researchers to estimate quantile effects in a just-identified panel data model, a contribution to the literature.

Advisor: Powell, James L.