Extremal quantile regressions for selection models and the black-white wage gap

We consider the estimation of a semiparametric sample selection model without instrument or large support regressor. Identification relies on the independence between the covariates and selection, for arbitrarily large values of the outcome. We propose a simple estimator based on extremal quantile regression and establish its asymptotic normality by extending previous results on extremal quantile regressions to allow for selection. Finally, we apply our method to estimate the black-white wage gap among males from the NLSY79 and NLSY97. We find that premarket factors such as AFQT and family background play a key role in explaining the black-white wage gap.