Kernel Weighted Smoothed Maximum Score Estimation for Applied Work

The endogenous binary response model frequently arises in economic applications when a covariate is correlated with the error term in the latent equation due to data limitations. Applied workers generally address endogeneity using the principle of Maximum Likelihood (ML) which imposes stringent paramet- ric assumptions. These ML estimators are inconsistent if the posited parametrization is incorrect which can translate in practice into aberrant results contradicting economic theory. Semiparametric estima- tors have been developed imposing weaker distributional assumptions. Some semiparametric techniques permit inferences from data but restrict heteroscedasticity which may furnish deceptive results. Other semiparametric techniques can accommodate almost any heteroscedasticity but forbid inferences. This article summarizes two new estimation techniques which allow for inferences under general heteroscedas- ticity conditions. Some Monte Carlo experiments are conducted highlighting the robust advantage of these estimators. Finally, these estimation techniques are applied to assess the e ect of education on maternal pregnancy smoking using the 1988 National Health Interview Survey.