Doubly Robust Estimation of Direct and Indirect Quantile Treatment Effects with Machine Learning

Abstract: We suggest double/debiased machine learning estimators of direct and indirect quantile treatment effects under a selection-on-observables assumption. This permits disentangling the causal effect of a binary treatment at a specific outcome rank into an indirect component that operates through an intermediate variable called mediator and an (unmediated) direct impact. The proposed method is based on the efficient score functions of the cumulative distribution functions of potential outcomes, which are robust to certain misspecifications of the nuisance parameters, i.e., the outcome, treatment, and mediator models. We estimate these nuisance parameters by machine learning and use cross-fitting to reduce overfitting bias in the estimation of direct and indirect quantile treatment effects. We establish uniform consistency and asymptotic normality of our effect estimators. We also propose a multiplier bootstrap for statistical inference and show the validity of the multiplier bootstrap. Finally, we investigate the finite sample performance of our method in a simulation study and apply it to empirical data from the National Job Corp Study to assess the direct and indirect earnings effects of training.