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

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  • Sloczynski, Tymon

    (Brandeis University)

  • Uysal, Derya

    (LMU Munich)

  • Wooldridge, Jeffrey M.

    (Michigan State University)

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

  • Sloczynski, Tymon & Uysal, Derya & Wooldridge, Jeffrey M., 2025. "Covariate Balancing and the Equivalence of Weighting and Doubly Robust Estimators of Average Treatment Effects," IZA Discussion Papers 18147, Institute of Labor Economics (IZA).
    • Handle: RePEc:iza:izadps:dp18147
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    References listed on IDEAS

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    1. 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.
    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.
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    Keywords

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    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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