A Kernel Weighted Smoothed Maximum Score Estimator for the Endogenous Binary Choice Model

This dissertation considers a local control function approach for the binary response model under endogeneity. The objective of the Smoothed Maximum Score estimator (SMSE)(Horowitz 1992) is modified by weighting the observations with a kernel. Under some mild regularity conditions similar in nature to those of the SMSE, the consistency of this Kernel Weighted Smoothed Maximum Score estimator (KWSMSE) is established. Also, under some smoothness conditions the KWSMSE's asymptotic normality is established. Furthermore, the covariance of the limiting distribution can be estimated consistently from data permitting convenient inferences. Under stronger regularity conditions a Score Approximation Smoothed Maximum Score Estimator (SASMSE) constructed via sieves is shown to achieve a faster rate of convergence in probability. Some Monte Carlo experiments are conducted highlighting the robust advantage of these estimators. Finally, these estimation techniques are applied to assess the effect of education on maternal pregnancy smoking using the 1988 National Health Interview Survey.