  We propose a doubly robust inference method for causal effects of continuous
treatment variables, under unconfoundedness and with nonparametric or
high-dimensional nuisance functions. Our 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 non-parametric
convergence rates. The first-step estimators for the nuisance conditional
expectation function and the conditional density can be nonparametric or ML
methods. Utilizing a kernel-based doubly robust moment function and
cross-fitting, we give high-level conditions under which the nuisance function
estimators do not affect the first-order large sample distribution of the DML
estimators. We provide sufficient low-level conditions for kernel, series, and
deep neural networks. We justify the use of kernel to localize the continuous
treatment at a given value by the Gateaux derivative. We implement various ML
methods in Monte Carlo simulations and an empirical application on a job
training program evaluation
