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Doubly robust uniform confidence band for the conditional average treatment effect function


  • Sokbae (Simon) Lee

    () (Institute for Fiscal Studies and Columbia University and IFS)

  • Ryo Okui

    () (Institute for Fiscal Studies and Kyoto University)

  • Yoon-Jae Whang

    () (Institute for Fiscal Studies and SNU)


In this paper, we propose a doubly robust method to present the heterogeneity of the average treatment e ffect with respect to observed covariates of interest. We consider a situation where a large number of covariates are needed for identifying the average treatment eff ect but the covariates of interest for analyzing heterogeneity are of much lower dimension. Our proposed estimator is doubly robust and avoids the curse of dimensionality. We propose a uniform confi dence band that is easy to compute, and we illustrate its usefulness via Monte Carlo experiments and an application to the eff ects of smoking on birth weights.

Suggested Citation

  • Sokbae (Simon) Lee & Ryo Okui & Yoon-Jae Whang, 2016. "Doubly robust uniform confidence band for the conditional average treatment effect function," CeMMAP working papers CWP03/16, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  • Handle: RePEc:ifs:cemmap:03/16

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    References listed on IDEAS

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    Cited by:

    1. Lechner, Michael, 2018. "Modified Causal Forests for Estimating Heterogeneous Causal Effects," IZA Discussion Papers 12040, Institute of Labor Economics (IZA).
    2. Anthony Strittmatter, 2018. "What Is the Value Added by Using Causal Machine Learning Methods in a Welfare Experiment Evaluation?," Papers 1812.06533,, revised Mar 2019.
    3. Knaus, Michael C. & Lechner, Michael & Strittmatter, Anthony, 2018. "Machine Learning Estimation of Heterogeneous Causal Effects: Empirical Monte Carlo Evidence," IZA Discussion Papers 12039, Institute of Labor Economics (IZA).
    4. Pedro H. C. Sant'Anna & Jun B. Zhao, 2018. "Doubly Robust Difference-in-Differences Estimators," Papers 1812.01723,, revised May 2020.
    5. Pedro H. C. Sant'Anna, 2016. "Nonparametric Tests for Treatment Effect Heterogeneity with Duration Outcomes," Papers 1612.02090,, revised Feb 2020.
    6. Michael Zimmert & Michael Lechner, 2019. "Nonparametric estimation of causal heterogeneity under high-dimensional confounding," Papers 1908.08779,
    7. Daniel Jacob, 2019. "Group Average Treatment Effects for Observational Studies," Papers 1911.02688,, revised Mar 2020.
    8. Shengfang Tang & Zongwu Cai & Ying Fang & Ming Lin, 2019. "Testing Unconfoundedness Assumption Using Auxiliary Variables," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 201905, University of Kansas, Department of Economics, revised Mar 2019.
    9. Pedro H. C. Sant'Anna & Xiaojun Song, 2020. "Specification tests for generalized propensity scores using double projections," Papers 2003.13803,
    10. Zongwu Cai & Ying Fang & Ming Lin & Shengfang Tang, 2020. "Inferences for Partially Conditional Quantile Treatment Effect Model," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 202005, University of Kansas, Department of Economics, revised Feb 2020.
    11. Shengfang Tang & Zongwu Cai & Ying Fang & Ming Lin, 2020. "A New Quantile Treatment Effect Model for Studying Smoking Effect on Birth Weight During Mother's Pregnancy," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 202003, University of Kansas, Department of Economics, revised Feb 2020.
    12. Qingliang Fan & Yu-Chin Hsu & Robert P. Lieli & Yichong Zhang, 2019. "Estimation of Conditional Average Treatment Effects with High-Dimensional Data," Papers 1908.02399,, revised Aug 2020.

    More about this item


    Average treatment effect conditional on covariates; uniform confidence band; double robustness; Gaussian approximation.;

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models

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