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Double machine learning for treatment and causal parameters


  • 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)


Most modern supervised statistical/machine learning (ML) methods are explicitly designed to solve prediction problems very well. Achieving this goal does not imply that these methods automatically deliver good estimators of causal parameters. Examples of such parameters include individual regression coffiecients, average treatment e ffects, average lifts, and demand or supply elasticities. In fact, estimators of such causal parameters obtained via naively plugging ML estimators into estimating equations for such parameters can behave very poorly. For example, the resulting estimators may formally have inferior rates of convergence with respect to the sample size n caused by regularization bias. Fortunately, this regularization bias can be removed by solving auxiliary prediction problems via ML tools. Speci ficially, we can form an efficient score for the target low-dimensional parameter by combining auxiliary and main ML predictions. The efficient score may then be used to build an efficient estimator of the target parameter which typically will converge at the fastest possible 1/v n rate and be approximately unbiased and normal, allowing simple construction of valid con fidence intervals for parameters of interest. The resulting method thus could be called a "double ML" method because it relies on estimating primary and auxiliary predictive models. Such double ML estimators achieve the fastest rates of convergence and exhibit robust good behavior with respect to a broader class of probability distributions than naive "single" ML estimators. In order to avoid overfi tting, following [3], our construction also makes use of the K-fold sample splitting, which we call cross- fitting. The use of sample splitting allows us to use a very broad set of ML predictive methods in solving the auxiliary and main prediction problems, such as random forests, lasso, ridge, deep neural nets, boosted trees, as well as various hybrids and aggregates of these methods (e.g. a hybrid of a random forest and lasso). We illustrate the application of the general theory through application to the leading cases of estimation and inference on the main parameter in a partially linear regression model and estimation and inference on average treatment eff ects and average treatment e ffects on the treated under conditional random assignment of the treatment. These applications cover randomized control trials as a special case. We then use the methods in an empirical application which estimates the e ffect of 401(k) eligibility on accumulated financial assets.

Suggested Citation

  • Victor Chernozhukov & Denis Chetverikov & Mert Demirer & Esther Duflo & Christian Hansen & Whitney K. Newey, 2016. "Double machine learning for treatment and causal parameters," CeMMAP working papers CWP49/16, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  • Handle: RePEc:ifs:cemmap:49/16

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    References listed on IDEAS

    1. David A. Wise, 1994. "Studies in the Economics of Aging," NBER Books, National Bureau of Economic Research, Inc, number wise94-1, October.
    2. Victor Chernozhukov & Iván Fernández‐Val & Blaise Melly, 2013. "Inference on Counterfactual Distributions," Econometrica, Econometric Society, vol. 81(6), pages 2205-2268, November.
    3. Ai, Chunrong & Chen, Xiaohong, 2012. "The semiparametric efficiency bound for models of sequential moment restrictions containing unknown functions," Journal of Econometrics, Elsevier, vol. 170(2), pages 442-457.
    4. A. Belloni & V. Chernozhukov & L. Wang, 2011. "Square-root lasso: pivotal recovery of sparse signals via conic programming," Biometrika, Biometrika Trust, vol. 98(4), pages 791-806.
    5. David A. Wise, 1994. "Introduction to "Studies in the Economics of Aging"," NBER Chapters,in: Studies in the Economics of Aging, pages 1-10 National Bureau of Economic Research, Inc.
    6. Andrews, Donald W K, 1994. "Asymptotics for Semiparametric Econometric Models via Stochastic Equicontinuity," Econometrica, Econometric Society, vol. 62(1), pages 43-72, January.
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    8. Leeb, Hannes & P tscher, Benedikt M., 2008. "Can One Estimate The Unconditional Distribution Of Post-Model-Selection Estimators?," Econometric Theory, Cambridge University Press, vol. 24(02), pages 338-376, April.
    9. Newey, Whitney K, 1994. "The Asymptotic Variance of Semiparametric Estimators," Econometrica, Econometric Society, vol. 62(6), pages 1349-1382, November.
    10. Xiaohong Chen & Oliver Linton & Ingrid Van Keilegom, 2003. "Estimation of Semiparametric Models when the Criterion Function Is Not Smooth," Econometrica, Econometric Society, vol. 71(5), pages 1591-1608, September.
    11. Leeb, Hannes & Potscher, Benedikt M., 2008. "Sparse estimators and the oracle property, or the return of Hodges' estimator," Journal of Econometrics, Elsevier, vol. 142(1), pages 201-211, January.
    12. Pötscher, Benedikt M. & Leeb, Hannes, 2009. "On the distribution of penalized maximum likelihood estimators: The LASSO, SCAD, and thresholding," Journal of Multivariate Analysis, Elsevier, vol. 100(9), pages 2065-2082, October.
    13. Victor Chernozhukov & Denis Chetverikov & Kengo Kato, 2014. "Central limit theorems and bootstrap in high dimensions," CeMMAP working papers CWP49/14, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    14. Linton, Oliver, 1996. "Edgeworth Approximation for MINPIN Estimators in Semiparametric Regression Models," Econometric Theory, Cambridge University Press, vol. 12(01), pages 30-60, March.
    15. Victor Chernozhukov & Denis Chetverikov & Kengo Kato, 2012. "Gaussian approximations and multiplier bootstrap for maxima of sums of high-dimensional random vectors," Papers 1212.6906,, revised Jan 2018.
    16. Victor Chernozhukov & Christian Hansen & Martin Spindler, 2015. "Post-Selection and Post-Regularization Inference in Linear Models with Many Controls and Instruments," American Economic Review, American Economic Association, vol. 105(5), pages 486-490, May.
    17. Leeb, Hannes & P tscher, Benedikt M., 2008. "Guest Editors' Editorial: Recent Developments In Model Selection And Related Areas," Econometric Theory, Cambridge University Press, vol. 24(02), pages 319-322, April.
    18. A. Belloni & V. Chernozhukov & K. Kato, 2015. "Uniform post-selection inference for least absolute deviation regression and other Z-estimation problems," Biometrika, Biometrika Trust, vol. 102(1), pages 77-94.
    19. Newey, Whitney K, 1990. "Semiparametric Efficiency Bounds," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 5(2), pages 99-135, April-Jun.
    20. Alexandre Belloni & Victor Chernozhukov & Kengo Kato, 2013. "Robust inference in high-dimensional approximately sparse quantile regression models," CeMMAP working papers CWP70/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    21. Jinyong Hahn, 1998. "On the Role of the Propensity Score in Efficient Semiparametric Estimation of Average Treatment Effects," Econometrica, Econometric Society, vol. 66(2), pages 315-332, March.
    22. Chamberlain, Gary, 1992. "Efficiency Bounds for Semiparametric Regression," Econometrica, Econometric Society, vol. 60(3), pages 567-596, May.
    Full references (including those not matched with items on IDEAS)


    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.

    Cited by:

    1. Zhou, Zhengyuan & Athey, Susan & Wager, Stefan, 2018. "Offline Multi-Action Policy Learning: Generalization and Optimization," Research Papers 3734, Stanford University, Graduate School of Business.
    2. Victor Chernozhukov & Vira Semenova, 2018. "Simultaneous inference for Best Linear Predictor of the Conditional Average Treatment Effect and other structural functions," CeMMAP working papers CWP40/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    3. Christian Hansen & Damian Kozbur & Sanjog Misra, 2016. "Targeted undersmoothing," ECON - Working Papers 282, Department of Economics - University of Zurich, revised Apr 2018.
    4. Lester Mackey & Vasilis Syrgkanis & Ilias Zadik, 2017. "Orthogonal Machine Learning: Power and Limitations," Papers 1711.00342,, revised Aug 2018.
    5. repec:wly:emetrp:v:85:y:2017:i::p:233-298 is not listed on IDEAS
    6. A. Belloni & V. Chernozhukov & I. Fernández‐Val & C. Hansen, 2017. "Program Evaluation and Causal Inference With High‐Dimensional Data," Econometrica, Econometric Society, vol. 85, pages 233-298, January.
    7. Susan Athey & Guido W. Imbens, 2017. "The State of Applied Econometrics: Causality and Policy Evaluation," Journal of Economic Perspectives, American Economic Association, vol. 31(2), pages 3-32, Spring.
    8. Alexei Alexandrov & Russell Pittman & Olga Ukhaneva, 2017. "Pricing of Complements in the U.S. Freight Railroads: Cournot Versus Coase," EAG Discussions Papers 201711, Department of Justice, Antitrust Division.
    9. Victor Chernozhukov & Wolfgang K. Hardle & Chen Huang & Weining Wang, 2018. "LASSO-Driven Inference in Time and Space," Papers 1806.05081,, revised Apr 2019.
    10. Damian Kozbur, 2017. "Testing-Based Forward Model Selection," American Economic Review, American Economic Association, vol. 107(5), pages 266-269, May.
    11. Crane-Droesch, Andrew, 2017. "Semiparametric Panel Data Using Neural Networks," 2017 Annual Meeting, July 30-August 1, Chicago, Illinois 258128, Agricultural and Applied Economics Association.
    12. Alexandrov, Alexei & Pittman, Russell & Ukhaneva, Olga, 2017. "Royalty stacking in the U.S. freight railroads: Cournot vs. Coase," MPRA Paper 78249, University Library of Munich, Germany.
    13. repec:eee:econom:v:206:y:2018:i:2:p:472-514 is not listed on IDEAS


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