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June 2021 A causal bootstrap
Guido Imbens, Konrad Menzel
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Ann. Statist. 49(3): 1460-1488 (June 2021). DOI: 10.1214/20-AOS2009

Abstract

The bootstrap, introduced by The Jackknife, the Bootstrap and Other Resampling Plans ((1982), SIAM), has become a very popular method for estimating variances and constructing confidence intervals. A key insight is that one can approximate the properties of estimators by using the empirical distribution function of the sample as an approximation for the true distribution function. This approach views the uncertainty in the estimator as coming exclusively from sampling uncertainty. We argue that for causal estimands the uncertainty arises entirely, or partially, from a different source, corresponding to the stochastic nature of the treatment received. We develop a bootstrap procedure for inference regarding the average treatment effect that accounts for this uncertainty, and compare its properties to that of the classical bootstrap. We consider completely randomized and observational designs as well as designs with imperfect compliance.

Funding Statement

Guido Imbens acknowledges financial support under ONR grant N00014-17-1-2131.

Acknowledgments

March 2018—this version July 2020. We thank Alberto Abadie, Alfred Galichon, and Parker Zhao for useful comments and discussions.

Citation

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Guido Imbens. Konrad Menzel. "A causal bootstrap." Ann. Statist. 49 (3) 1460 - 1488, June 2021. https://doi.org/10.1214/20-AOS2009

Information

Received: 1 November 2019; Revised: 1 July 2020; Published: June 2021
First available in Project Euclid: 9 August 2021

Digital Object Identifier: 10.1214/20-AOS2009

Subjects:
Primary: 62D05 , 62D20

Keywords: bootstrap , Causal inference , partial identification

Rights: Copyright © 2021 Institute of Mathematical Statistics

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Vol.49 • No. 3 • June 2021
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