摘要：
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. In 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. In 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 coefficien
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