Estimation of counterfactual distributions using quantile regression

This paper proposes estimators of unconditional distribution functions in the presence of covariates. The methods are based on the estimation of the conditional distribution by (parametric or nonparametric) quantile regression. The conditional distribution is then integrated over the range of the covariates, allowing for the estimation of counterfactual distributions. In the parametric settings, we propose an extension of the Oaxaca (1973) / Blinder (1973) 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 root 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.