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Covariate Balancing and the Equivalence of Weighting and Doubly Robust Estimators of Average Treatment Effects

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  • Tymon S{l}oczy'nski
  • S. Derya Uysal
  • Jeffrey M. Wooldridge

Abstract

How should researchers adjust for covariates? We show that if the propensity score is estimated using a specific covariate balancing approach, inverse probability weighting (IPW), augmented inverse probability weighting (AIPW), and inverse probability weighted regression adjustment (IPWRA) estimators are numerically equivalent for the average treatment effect (ATE), and likewise for the average treatment effect on the treated (ATT). The resulting weights are inherently normalized, making normalized and unnormalized IPW and AIPW identical. We discuss implications for instrumental variables and difference-in-differences estimators and illustrate with two applications how these numerical equivalences simplify analysis and interpretation.

Suggested Citation

  • Tymon S{l}oczy'nski & S. Derya Uysal & Jeffrey M. Wooldridge, 2023. "Covariate Balancing and the Equivalence of Weighting and Doubly Robust Estimators of Average Treatment Effects," Papers 2310.18563, arXiv.org, revised Sep 2025.
    • Handle: RePEc:arx:papers:2310.18563
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    1. Tymon Sloczynski & S. Derya Uysal & Jeffrey M. Wooldridge & Tymon Słoczyński & Derya Uysal, 2022. "Doubly Robust Estimation of Local Average Treatment Effects Using Inverse Probability Weighted Regression Adjustment," CESifo Working Paper Series 10105, CESifo.
    2. Sant’Anna, Pedro H.C. & Zhao, Jun, 2020. "Doubly robust difference-in-differences estimators," Journal of Econometrics, Elsevier, vol. 219(1), pages 101-122.
    3. Słoczyński, Tymon & Wooldridge, Jeffrey M., 2018. "A General Double Robustness Result For Estimating Average Treatment Effects," Econometric Theory, Cambridge University Press, vol. 34(1), pages 112-133, February.
    4. Bryan S. Graham & Cristine Campos De Xavier Pinto & Daniel Egel, 2012. "Inverse Probability Tilting for Moment Condition Models with Missing Data," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 79(3), pages 1053-1079.
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    1. repec:ags:aaea22:344219 is not listed on IDEAS
    2. Michael C. Knaus, 2024. "Treatment Effect Estimators as Weighted Outcomes," Papers 2411.11559, arXiv.org, revised Dec 2024.

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    More about this item

    JEL classification:

    • C20 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models
    • C26 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Instrumental Variables (IV) Estimation

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