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Double Debiased Machine Learning Nonparametric Inference with Continuous Treatments

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  • Kyle Colangelo
  • Ying-Ying Lee

Abstract

We propose a nonparametric inference method for causal effects of continuous treatment variables, under unconfoundedness and nonparametric or high-dimensional 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, series, and deep neural networks. We propose a data-driven bandwidth to consistently estimate the optimal bandwidth that minimizes the asymptotic mean squared error. 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.

Suggested Citation

  • Kyle Colangelo & Ying-Ying Lee, 2020. "Double Debiased Machine Learning Nonparametric Inference with Continuous Treatments," Papers 2004.03036, arXiv.org, revised Jul 2022.
  • Handle: RePEc:arx:papers:2004.03036
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    References listed on IDEAS

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    Cited by:

    1. Yu-Chin Hsu & Martin Huber & Ying-Ying Lee & Chu-An Liu, 2021. "Testing Monotonicity of Mean Potential Outcomes in a Continuous Treatment with High-Dimensional Data," Papers 2106.04237, arXiv.org, revised Aug 2022.
    2. Rahul Singh & Liyuan Xu & Arthur Gretton, 2020. "Kernel Methods for Causal Functions: Dose, Heterogeneous, and Incremental Response Curves," Papers 2010.04855, arXiv.org, revised Oct 2022.
    3. Sylvia Klosin, 2021. "Automatic Double Machine Learning for Continuous Treatment Effects," Papers 2104.10334, arXiv.org.
    4. Anna Baiardi & Andrea A. Naghi, 2021. "The Value Added of Machine Learning to Causal Inference: Evidence from Revisited Studies," Tinbergen Institute Discussion Papers 21-001/V, Tinbergen Institute.
    5. Hugo Bodory & Martin Huber & Lukáš Lafférs, 2022. "Evaluating (weighted) dynamic treatment effects by double machine learning [Identification of causal effects using instrumental variables]," The Econometrics Journal, Royal Economic Society, vol. 25(3), pages 628-648.
    6. AmirEmad Ghassami & Numair Sani & Yizhen Xu & Ilya Shpitser, 2021. "Multiply Robust Causal Mediation Analysis with Continuous Treatments," Papers 2105.09254, arXiv.org.
    7. Rahul Singh, 2020. "Kernel Methods for Unobserved Confounding: Negative Controls, Proxies, and Instruments," Papers 2012.10315, arXiv.org, revised Sep 2022.

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