IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2512.12781.html

Distributionally Robust Treatment Effect

Author

Listed:
  • Ruonan Xu
  • Xiye Yang

Abstract

Using only retrospective data, we study the problem of predicting treatment effects for the same treatment/policy implemented in a different location or time period. We propose a distributionally robust estimator that minimizes the worst-case mean squared error for the prediction of treatment effect over a class of distributions defined by a Wasserstein neighborhood around the source distribution. Because the joint distribution of potential outcomes is unidentified, the problem is inherently one of partial identification. We characterize the sharp upper and lower bounds of the minimax optimizer by exploiting the Fr\'echet class of distributions consistent with the marginal distributions of potential outcomes. The resulting predictor preserves the sign of the average treatment effect under the source distribution but is shrunk toward zero, with the degree of shrinkage depending on the extent of treatment effect heterogeneity. We establish consistency and asymptotic normality of the bound estimators, develop a two-step inference procedure, and discuss the choice of the robustness parameter.

Suggested Citation

  • Ruonan Xu & Xiye Yang, 2025. "Distributionally Robust Treatment Effect," Papers 2512.12781, arXiv.org, revised Apr 2026.
    • Handle: RePEc:arx:papers:2512.12781
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2512.12781
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Daido Kido, 2022. "Distributionally Robust Policy Learning with Wasserstein Distance," Papers 2205.04637, arXiv.org, revised Aug 2022.
    2. Timothy Christensen & Benjamin Connault, 2023. "Counterfactual Sensitivity and Robustness," Econometrica, Econometric Society, vol. 91(1), pages 263-298, January.
    3. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
    4. Yanqin Fan & Hyeonseok Park & Gaoqian Xu, 2023. "Quantifying Distributional Model Risk in Marginal Problems via Optimal Transport," Papers 2307.00779, arXiv.org.
    5. Lihua Lei & Roshni Sahoo & Stefan Wager, 2023. "Policy Learning under Biased Sample Selection," Papers 2304.11735, arXiv.org.
    6. Rui Gao & Anton Kleywegt, 2023. "Distributionally Robust Stochastic Optimization with Wasserstein Distance," Mathematics of Operations Research, INFORMS, vol. 48(2), pages 603-655, May.
    7. Weibin Mo & Zhengling Qi & Yufeng Liu, 2021. "Learning Optimal Distributionally Robust Individualized Treatment Rules," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(534), pages 659-674, April.
    8. Hunt Allcott, 2015. "Site Selection Bias in Program Evaluation," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 130(3), pages 1117-1165.
    9. James J. Heckman & Jeffrey Smith & Nancy Clements, 1997. "Making The Most Out Of Programme Evaluations and Social Experiments: Accounting For Heterogeneity in Programme Impacts," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 64(4), pages 487-535.
    10. Zhaonan Qu & Yongchan Kwon, 2024. "Distributionally Robust Instrumental Variables Estimation," Papers 2410.15634, arXiv.org, revised Dec 2024.
    11. Fan, Yanqin & Park, Sang Soo, 2010. "Sharp Bounds On The Distribution Of Treatment Effects And Their Statistical Inference," Econometric Theory, Cambridge University Press, vol. 26(3), pages 931-951, June.
    12. McCloskey, Adam, 2017. "Bonferroni-based size-correction for nonstandard testing problems," Journal of Econometrics, Elsevier, vol. 200(1), pages 17-35.
    13. Weibin Mo & Zhengling Qi & Yufeng Liu, 2021. "Rejoinder: Learning Optimal Distributionally Robust Individualized Treatment Rules," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(534), pages 699-707, April.
    14. Jose Blanchet & Karthyek Murthy, 2019. "Quantifying Distributional Model Risk via Optimal Transport," Mathematics of Operations Research, INFORMS, vol. 44(2), pages 565-600, May.
    15. Athey, Susan & Imbens, Guido W. & Metzger, Jonas & Munro, Evan, 2024. "Using Wasserstein Generative Adversarial Networks for the design of Monte Carlo simulations," Journal of Econometrics, Elsevier, vol. 240(2).
    16. Chen, Xiaohong & Hansen, Lars Peter & Hansen, Peter G., 2024. "Robust inference for moment condition models without rational expectations," Journal of Econometrics, Elsevier, vol. 243(1).
    17. Joseph Hotz, V. & Imbens, Guido W. & Mortimer, Julie H., 2005. "Predicting the efficacy of future training programs using past experiences at other locations," Journal of Econometrics, Elsevier, vol. 125(1-2), pages 241-270.
    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. Alfred Galichon & Marc Henry, 2026. "An econometrician's guide to optimal transport," Papers 2604.04227, arXiv.org.

    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. Alfred Galichon & Marc Henry, 2026. "An econometrician's guide to optimal transport," Papers 2604.04227, arXiv.org.
    2. Daido Kido, 2022. "Distributionally Robust Policy Learning with Wasserstein Distance," Papers 2205.04637, arXiv.org, revised Aug 2022.
    3. Florian F Gunsilius, 2025. "A primer on optimal transport for causal inference with observational data," Papers 2503.07811, arXiv.org, revised Mar 2025.
    4. Zhaonan Qu & Yongchan Kwon, 2024. "Distributionally Robust Instrumental Variables Estimation," Papers 2410.15634, arXiv.org, revised Dec 2024.
    5. Christopher Adjaho & Timothy Christensen, 2022. "Externally Valid Policy Choice," Papers 2205.05561, arXiv.org, revised Nov 2025.
    6. Buhl-Wiggers, Julie & Kerwin, Jason T. & Muñoz-Morales, Juan & Smith, Jeffrey & Thornton, Rebecca, 2024. "Some children left behind: Variation in the effects of an educational intervention," Journal of Econometrics, Elsevier, vol. 243(1).
    7. Daido Kido, 2023. "Locally Asymptotically Minimax Statistical Treatment Rules Under Partial Identification," Papers 2311.08958, arXiv.org.
    8. Tadao Hoshino, 2025. "Evaluating Policy Effects under Network Interference without Network Information: A Transfer Learning Approach," Papers 2510.14415, arXiv.org.
    9. Larry L. Orr, 2026. "Do “Evidence‐Based Policy” Clearinghouses Provide Good Advice for Local Policymakers?," Journal of Policy Analysis and Management, John Wiley & Sons, Ltd., vol. 45(1), January.
    10. Ertian Chen, 2025. "Robust Structural Estimation under Misspecified Latent-State Dynamics," Papers 2510.22347, arXiv.org, revised Nov 2025.
    11. Yanqin Fan & Yuan Qi & Gaoqian Xu, 2025. "Policy Learning with $\alpha$-Expected Welfare," Papers 2505.00256, arXiv.org.
    12. Evan Munro, 2025. "Treatment Allocation with Strategic Agents," Management Science, INFORMS, vol. 71(1), pages 123-145, January.
    13. Ismaël Mourifié & Marc Henry & Romuald Méango, 2020. "Sharp Bounds and Testability of a Roy Model of STEM Major Choices," Journal of Political Economy, University of Chicago Press, vol. 128(8), pages 3220-3283.
    14. Burt S. Barnow & Jeffrey Smith, 2015. "Employment and Training Programs," NBER Chapters, in: Economics of Means-Tested Transfer Programs in the United States, Volume 2, pages 127-234, National Bureau of Economic Research, Inc.
    15. Pablo Lavado & Gonzalo Rivera, 2016. "Identifying Treatment Effects with Data Combination and Unobserved Heterogeneity," Working Papers 79, Peruvian Economic Association.
    16. John A. List, 2024. "Optimally generate policy-based evidence before scaling," Nature, Nature, vol. 626(7999), pages 491-499, February.
    17. Jiannan Lu & Peng Ding & Tirthankar Dasgupta, 2018. "Treatment Effects on Ordinal Outcomes: Causal Estimands and Sharp Bounds," Journal of Educational and Behavioral Statistics, , vol. 43(5), pages 540-567, October.
    18. Firpo, Sergio & Galvao, Antonio F. & Kobus, Martyna & Parker, Thomas & Rosa-Dias, Pedro, 2025. "Loss aversion and the welfare ranking of policy interventions," Journal of Econometrics, Elsevier, vol. 252(PB).
    19. Andor, Mark A. & Gerster, Andreas & Peters, Jörg & Schmidt, Christoph M., 2020. "Social Norms and Energy Conservation Beyond the US," Journal of Environmental Economics and Management, Elsevier, vol. 103(C).
    20. Benjamin Lu & Eli Ben-Michael & Avi Feller & Luke Miratrix, 2023. "Is It Who You Are or Where You Are? Accounting for Compositional Differences in Cross-Site Treatment Effect Variation," Journal of Educational and Behavioral Statistics, , vol. 48(4), pages 420-453, August.

    More about this item

    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:2512.12781. 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.