This dissertation consists of three essays on estimating average treatment effects (ATE) under counterfactual framework. In Chapter 1, I compare the performances of single-step and two-step estimators for estimating the ATE in a linear model when treatment assignment depends on unobservables. Recent advances in computing technology have enabled the extensive use of single-step estimators, such as Limited Information Maximum Likelihood (LIML), instead of 2SLS. In this study I make clear that there are two kinds of single-step estimators for estimating ATE. LIML-type estimator is the one which uses the control function method, on which the two-step method is also based, whereas FIML-type estimator directly uses the joint distribution of underlying errors or endogenous variables. I find that the relative asymptotic efficiency between two-step Heckit and single-step LIML cannot be determined in general. However, the relative efficiency of single-step LIML with respect to two-step Heckit is decreasing as the sample size increases, implying that if the asymptotic variances are same, then single-step LIML is less efficient in finite samples. On the other hand the FIML estimator tends to have very small finite sample variances, but it is less robust to misspecification. Newey-type series estimators are also considered for correcting the misspecification of error distributions, but it turned out that cost is greater than the benefit. Under weak many instrument cases, the advantage of LIML in terms of median bias was not as strong as in the linear models. Chapter 2 explores the ATE estimator proposed by Terza (2009)'s Nonlinear Full Endogenous Treatment (NFES) model, where count dependent and binary treatment variables are present. When the true conditional mean function takes the form of exponential function, the Heckit-type linear method, while it can be a good approximation, is inconsistent for the true ATE since it is derived under the assumption of linear conditional mean. The asymptotic distribution of nonlinear estimators have additional terms in asymptotic variance of which magnitudes depend on population coefficient. Due to their presence, the asymptotic variances of nonlinear estimators can be either larger or smaller than the linear counterparts depending on the values of coefficients. It turns out that they tend to have small variances when the variance of conditional ATE are small. And Monte Carlo experiments show that they are fairly robust to various distributional misspecifications. In summary, nonlinear ATE estimators are robust and consistent with small variance when the treatment effects are not substantially different across individuals. An application to Botswana fertility is given where the treatment is seven years of education with the dependent variable fertility.Chapter 3 presents a method for estimating ATE for the case that the dependent variable is count variable and the coefficients of covariates are random variables which are correlated with the binary treatment variable. The identifying assumptions are given and the estimating equation based on them is derived. Simulations show that, in large samples, it has usually smaller biases and larger variances than the linear methods have. An application on Botswana fertility is given with same variables as in Chapter 2.
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