Estimation of marginal effects in semiparametric selection models with binary outcomes

This paper addresses the estimation of a semiparametric sample selection index model where both the selection rule and the outcome variable are binary. Since the marginal effects are often of primary interest and are difficult to recover in a semiparametric setting, we focus on developing an estimator for the marginal effects. This marginal effect estimator uses only observations where the selection probability is above a certain threshold. A key innovation is that this high probability set is adaptive to the data. We establish the large sample properties of the marginal effect estimator as well as those for an index estimator upon which it depends. Monte Carlo studies show that these estimators perform well in finite samples.