Misspecification and Heterogeneity in Binary Choice Models

We address function misspecification and model heterogeneity, two critical issues in empirical work. A nonparametric approach is proposed for single-index, binary-choice models when parametric models such as Probit and Logit are potentially misspecified. The new approach involves two steps: first, we estimate index coefficients using sliced inverse regression without knowing the conditional probability function of the binary choice model; second, we estimate the unknown conditional probability function using kernel regression. Moreover, we consider model heterogeneity associated with categorical explanatory variables. The merits of the new method are demonstrated for treatment evaluation using both simulated and labor market data.