Double debiased machine learning nonparametric inference with continuous treatments

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 a nonparametric convergence rate. The nuisance estimators for the conditional expectation function and the generalized propensity score 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.