Double Debiased Machine Learning Nonparametric Inference with Continuous Treatments

• Main Authors: Colangelo, Kyle, Lee, Ying-Ying
• Format: Article in Journal/Newspaper
• Language: unknown
• Published: arXiv 2020
• Subjects: Econometrics econ.EM; FOS Economics and business; DML
• Online Access: https://dx.doi.org/10.48550/arxiv.2004.03036; https://arxiv.org/abs/2004.03036

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 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 or ML methods. Utilizing a kernel-based doubly robust moment function and cross-fitting, we give high-level conditions under which the nuisance estimators do not affect the first-order large sample distribution of the DML estimators. We further provide sufficient low-level conditions for kernel and series estimators, as well as modern ML methods - generalized random forests 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.