Counterfactual Treatment Effects: Estimation and Inference

This article proposes statistical methods to evaluate the quantile counterfactual treatment effect (QCTE) if one were to change the composition of the population targeted by a status quo program. QCTE enables a researcher to carry out an ex-ante assessment of the distributional impact of certain policy interventions or to investigate the possible explanations for treatment effect heterogeneity. Assuming unconfoundedness and invariance of the conditional distributions of the potential outcomes, QCTE is identified and can be nonparametrically estimated by a kernel-based method. Viewed as a random function over the continuum of quantile indices, the estimator converges weakly to a zero mean Gaussian process at the parametric rate. We propose a multiplier bootstrap procedure to construct uniform confidence bands, and provide similar results for average effects and for the counterfactually treated subpopulation. We also present Monte Carlo simulations and two counterfactual exercises that provide insight into the heterogeneous earnings effects of the Job Corps training program in the United States.