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Double/debiased machine learning for treatment and structural parameters

Author

Listed:
  • Victor Chernozhukov

    () (Institute for Fiscal Studies and MIT)

  • Denis Chetverikov

    () (Institute for Fiscal Studies and UCLA)

  • Mert Demirer

    (Institute for Fiscal Studies)

  • Esther Duflo

    (Institute for Fiscal Studies)

  • Christian Hansen

    (Institute for Fiscal Studies and Chicago GSB)

  • Whitney K. Newey

    () (Institute for Fiscal Studies and MIT)

  • James Robins

    (Institute for Fiscal Studies)

Abstract

We revisit the classic semiparametric problem of inference on a low dimensional parameter ?0 in the presence of high-dimensional nuisance parameters ?0. We depart from the classical setting by allowing for ?0 to be so high-dimensional that the traditional assumptions, such as Donsker properties, that limit complexity of the parameter space for this object break down. To estimate ?0, we consider the use of statistical or machine learning (ML) methods which are particularly well-suited to estimation in modern, very high-dimensional cases. ML methods perform well by employing regularization to reduce variance and trading off regularization bias with overfitting in practice. However, both regularization bias and overfitting in estimating ?0 cause a heavy bias in estimators of ?0 that are obtained by naively plugging ML estimators of ?0 into estimating equations for ?0. This bias results in the naive estimator failing to be N -1/2 consistent, where N is the sample size. We show that the impact of regularization bias and overfitting on estimation of the parameter of interest ?0 can be removed by using two simple, yet critical, ingredients: (1) using Neyman-orthogonal moments/scores that have reduced sensitivity with respect to nuisance parameters to estimate ?0, and (2) making use of cross-fitting which provides an efficient form of data-splitting. We call the resulting set of methods double or debiased ML (DML). We verify that DML delivers point estimators that concentrate in a N -1/2-neighborhood of the true parameter values and are approximately unbiased and normally distributed, which allows construction of valid confidence statements. The generic statistical theory of DML is elementary and simultaneously relies on only weak theoretical requirements which will admit the use of a broad array of modern ML methods for estimating the nuisance parameters such as random forests, lasso, ridge, deep neural nets, boosted trees, and various hybrids and ensembles of these methods. We illustrate the general theory by applying it to provide theoretical properties of DML applied to learn the main regression parameter in a partially linear regression model, DML applied to learn the coefficient on an endogenous variable in a partially linear instrumental variables model, DML applied to learn the average treatment effect and the average treatment effect on the treated under unconfoundedness, and DML applied to learn the local average treatment effect in an instrumental variables setting. In addition to these theoretical applications, we also illustrate the use of DML in three empirical examples.

Suggested Citation

  • Victor Chernozhukov & Denis Chetverikov & Mert Demirer & Esther Duflo & Christian Hansen & Whitney K. Newey & James Robins, 2017. "Double/debiased machine learning for treatment and structural parameters," CeMMAP working papers CWP28/17, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  • Handle: RePEc:ifs:cemmap:28/17
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Whitney K. Newey & James M. Robins, 2017. "Cross-fitting and fast remainder rates for semiparametric estimation," CeMMAP working papers CWP41/17, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    2. Miruna Oprescu & Vasilis Syrgkanis & Zhiwei Steven Wu, 2018. "Orthogonal Random Forest for Heterogeneous Treatment Effect Estimation," Papers 1806.03467, arXiv.org.
    3. Xinkun Nie & Stefan Wager, 2017. "Quasi-Oracle Estimation of Heterogeneous Treatment Effects," Papers 1712.04912, arXiv.org, revised Jun 2018.
    4. Monica Andini & Emanuele Ciani & Guido de Blasio & Alessio D'Ignazio & Viola Salvestrini, 2017. "Targeting policy-compliers with machine learning: an application to a tax rebate programme in Italy," Temi di discussione (Economic working papers) 1158, Bank of Italy, Economic Research and International Relations Area.
    5. Matt Goldman & Brian Quistorff, 2018. "Pricing Engine: Estimating Causal Impacts in Real World Business Settings," Papers 1806.03285, arXiv.org, revised Jun 2018.
    6. Victor Chernozhukov & Mert Demirer & Esther Duflo & Ivan Fernandez-Val, 2017. "Generic machine learning inference on heterogenous treatment effects in randomized experiments," CeMMAP working papers CWP61/17, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    7. Vira Semenova, 2017. "Machine Learning for Partial Identification: Example of Bracketed Data," Papers 1712.10024, arXiv.org.
    8. Susan Athey & Guido W. Imbens & Stefan Wager, 2016. "Approximate Residual Balancing: De-Biased Inference of Average Treatment Effects in High Dimensions," Papers 1604.07125, arXiv.org, revised Jan 2018.
    9. Sven Klaassen & Jannis Kueck & Martin Spindler, 2017. "Transformation Models in High-Dimensions," Papers 1712.07364, arXiv.org.

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    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics

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