IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2310.18563.html

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2310.18563
    File Function: Latest version
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    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. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Mogstad, Magne & Torgovitsky, Alexander, 2024. "Instrumental variables with unobserved heterogeneity in treatment effects," Handbook of Labor Economics,, Elsevier.
    2. Negi Akanksha, 2024. "Doubly weighted M-estimation for nonrandom assignment and missing outcomes," Journal of Causal Inference, De Gruyter, vol. 12(1), pages 1-25.
    3. Pedro H. C. Sant'Anna & Xiaojun Song & Qi Xu, 2022. "Covariate distribution balance via propensity scores," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 37(6), pages 1093-1120, September.
    4. Kalbfuss, Jörg & Odermatt, Reto & Stutzer, Alois, 2024. "Medical marijuana laws and mental health in the United States," Health Economics, Policy and Law, Cambridge University Press, vol. 19(3), pages 307-322, July.
    5. Tymon Słoczyński & S. Derya Uysal & Jeffrey M. Wooldridge, 2025. "Abadie’s Kappa and Weighting Estimators of the Local Average Treatment Effect," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 43(1), pages 164-177, January.
    6. Yukun Ma & Pedro H. C. Sant'Anna & Yuya Sasaki & Takuya Ura, 2023. "Doubly Robust Estimators with Weak Overlap," Papers 2304.08974, arXiv.org, revised Apr 2023.
    7. Jiaqi Chen & Song Xu & Jing Gao, 2020. "The Mixed Effect of China’s New Health Care Reform on Health Insurance Coverage and the Efficiency of Health Service Utilisation: A Longitudinal Approach," IJERPH, MDPI, vol. 17(5), pages 1-13, March.
    8. Lewbel, Arthur & Choi, Jin Young & Zhou, Zhuzhu, 2023. "Over-identified Doubly Robust identification and estimation," Journal of Econometrics, Elsevier, vol. 235(1), pages 25-42.
    9. Difang Huang & Jiti Gao & Tatsushi Oka, 2025. "Semiparametric single-index estimation for average treatment effects," Econometric Reviews, Taylor & Francis Journals, vol. 44(6), pages 843-885, July.
    10. Filippin, Antonio & Mantovani, Marco, 2025. "Moral preferences over health-wealth trade-offs," Journal of Economic Behavior & Organization, Elsevier, vol. 235(C).
    11. Yang Ning & Sida Peng & Jing Tao, 2020. "Doubly Robust Semiparametric Difference-in-Differences Estimators with High-Dimensional Data," Papers 2009.03151, arXiv.org.
    12. Böckerman, Petri & Bryson, Alex & Ilmakunnas, Ilari & Ilmakunnas, Pekka, 2025. "Does high involvement management make you work longer? Insights from linked survey and register data," The Journal of the Economics of Ageing, Elsevier, vol. 30(C).
    13. Gianluca Biggi & Martina Iori & Julia Mazzei & Andrea Mina, 2025. "Green intelligence: the AI content of green technologies," Eurasian Business Review, Springer;Eurasia Business and Economics Society, vol. 15(3), pages 803-840, September.
    14. Jun Hyung Kim & Yu Kyung Koh & Jinseong Park, 2023. "Mental Health Consequences of Working from Home during the Pandemic," Global Economic Review, Taylor & Francis Journals, vol. 52(1), pages 18-50, January.
    15. Arun Advani & Toru Kitagawa & Tymon Słoczyński, 2019. "Mostly harmless simulations? Using Monte Carlo studies for estimator selection," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 34(6), pages 893-910, September.
    16. Nikolic, Jelena & Rubil, Ivica & Tomić, Iva, 2017. "Pre-crisis reforms, austerity measures and the public-private wage gap in two emerging economies," Economic Systems, Elsevier, vol. 41(2), pages 248-265.
    17. Xiangou Deng & Zhaohui Li & Michael J. Seiler & Hua Sun, 2024. "Market Strength and Brokerage Choice in Residential Housing," The Journal of Real Estate Finance and Economics, Springer, vol. 69(4), pages 741-777, November.
    18. Guo, Rui & Zhang, Yujie & Chen, Kaihua & Wang, Yufei & Ning, Lutao, 2025. "Heterogeneous impact of green finance instruments on firms' green innovation novelty: Policy mix or mess?," Energy Economics, Elsevier, vol. 144(C).
    19. Georgios Nalbantis & Tim Pawlowski & Dominik Schreyer, 2023. "Substitution Effects and the Transnational Demand for European Soccer Telecasts," Journal of Sports Economics, , vol. 24(4), pages 407-442, May.
    20. Sasaki, Yuya & Ura, Takuya, 2023. "Estimation and inference for policy relevant treatment effects," Journal of Econometrics, Elsevier, vol. 234(2), pages 394-450.

    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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2310.18563. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.