Many instruments, sample selection and treatment effects in econometrics

This dissertation presents research undertaken in three distinct areas of econometrics. In chapter one I construct new variance adjustments for the Two-Stage Least Squares and Maximum Likelihood estimators of a linear structural equation, in which the regressors are endogenous. Variance estimates based on standard large sample analysis are often too small, which may result in unreliable inference. I derive the variance adjustments by considering a more general asymptotic approximation. The limiting distributions are valid under weak assumptions about the errors. The usefulness of the approximations is assessed in a simulation experiment.; In chapter two I develop Markov Chain Monte Carlo sampling algorithms for the parameters of the sample selection and two-part models. Both models can be used to describe an outcome variable with a limited range. The sample selection model focuses on potential outcomes that are only partially observed. The two-part model focuses on the observed outcomes. I analyze both models from a Bayesian perspective and develop several Gibbs sampling algorithms that can be used to approximate the posterior distribution of the model parameters. The output of the algorithms forms a basis, through the Bayes factor, for determining which model is more effective in describing the data. The different techniques are evaluated and compared in a simulation experiment.; In chapter three I consider the problem of conducting a hypothesis test on the coefficient of a binary endogenous variable. Binary variables are used to capture the effect of different regimes or treatments on the outcome variable of interest. When the assignment of individuals to treatments is nonrandom, an endogeneity problem may occur. To overcome this problem, I consider likelihood and instrumental variables based methods that can be used to test whether the treatment has a significant impact on the outcome. A simulation experiment shows that as the instruments become less relevant, most commonly used testing procedures either become size distorted or lose power.