Essays on estimation of discrete choice models with endogeneity

This dissertation presents new estimation methods for econometric models with binary endogenous regressors. The first essay focuses on a triangular system of equations where both the equation for the binary outcome and the equation for the dummy endogenous variable have the linear index, threshold crossing form, and presents a computationally simple estimation method that does not rely on distributional assumptions on the unobservables or on the presence of any regressors with unbounded support, and that yields root-n consistent and asymptotically normal estimators. In outlining this new estimation method, two contributions are made. The first one is proposing a novel "matching" estimator for the coefficient on the binary endogenous variable in the outcome equation. Second, in order to establish the asymptotic properties of the proposed estimators for the coefficients of the exogenous regressors in the outcome equation, the results of Powell, Stock and Stoker (1989) are extended to cover the case where the weighted average derivative estimation requires a first step semi-parametric procedure. The second chapter consists of results of joint work with Edward Vytlacil, and considers the estimation of the average effect of a dummy endogenous variable in models where the error term is weakly but not additively separable from the regressors. An imputation based estimator for the average effect of the binary endogenous variable is proposed, and conditions under which the proposed estimator is root-n consistent and asymptotically normal are established here. The analysis in the second chapter includes the case of a dummy endogenous variable in a discrete choice model as a special case. As a result, the estimators given in these two chapters are related. Nevertheless, the extension of the estimation method presented in the first chapter to the estimation of average treatment effect yields an estimator which is different from the one presented in the second chapter. The third chapter of the manuscript investigates the small sample behavior of the proposed estimators under different specifications using Monte Carlo analysis.