1 Estimation of counterfactual distributions using quantile regression

This paper proposes estimators of unconditional distribution functions in the presence of covariates. The conditional distribution is estimated by (parametric or nonparametric) quantile regression. In the parametric setting, we propose an extension of the Oaxaca / Blinder decomposition of means to the full distribution. In the nonparametric setting, we develop an efficient local-linear regression estimator for quantile treatment effects. We show n consistency and asymptotic normality of the estimators and present analytical estimators of their variance. Monte-Carlo simulations show that the procedures perform well in finite samples. An application to the black-white wage gap illustrates the usefulness of the estimators