We propose a nonparametric inference method for causal eﬀects of continuous treatment variables, under unconfoundedness and in the presence of high-dimensional or nonparametric nuisance parameters. Our simple kernel-based double debiased machine learning (DML) estimators for the average dose-response function (or the average structural function) and the partial eﬀects are asymptotically normal with nonparametric convergence rates. The nuisance estimators for the conditional expectation function and the conditional density can be nonparametric kernel or series estimators or ML methods. Using doubly robust inﬂuence function and cross-ﬁtting, we give tractable primitive conditions under which the nuisance estimators do not aﬀect the ﬁrst-order large sample distribution of the DML estimators. We implement various ML methods in Monte Carlo simulations and an empirical application on a job training program evaluation to support the theoretical results and demonstrate the usefulness of our DML estimator in practice.
Double debiased machine learning nonparametric inference with continuous treatments
17 December 2019
Working Paper (CWP72/19)