IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2311.08958.html
   My bibliography  Save this paper

Locally Asymptotically Minimax Statistical Treatment Rules Under Partial Identification

Author

Listed:
  • Daido Kido

Abstract

Policymakers often desire a statistical treatment rule (STR) that determines a treatment assignment rule deployed in a future population from available data. With the true knowledge of the data generating process, the average treatment effect (ATE) is the key quantity characterizing the optimal treatment rule. Unfortunately, the ATE is often not point identified but partially identified. Presuming the partial identification of the ATE, this study conducts a local asymptotic analysis and develops the locally asymptotically minimax (LAM) STR. The analysis does not assume the full differentiability but the directional differentiability of the boundary functions of the identification region of the ATE. Accordingly, the study shows that the LAM STR differs from the plug-in STR. A simulation study also demonstrates that the LAM STR outperforms the plug-in STR.

Suggested Citation

  • Daido Kido, 2023. "Locally Asymptotically Minimax Statistical Treatment Rules Under Partial Identification," Papers 2311.08958, arXiv.org.
    • Handle: RePEc:arx:papers:2311.08958
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2311.08958
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Toru Kitagawa & Aleksey Tetenov, 2018. "Who Should Be Treated? Empirical Welfare Maximization Methods for Treatment Choice," Econometrica, Econometric Society, vol. 86(2), pages 591-616, March.
    2. Eric Mbakop & Max Tabord‐Meehan, 2021. "Model Selection for Treatment Choice: Penalized Welfare Maximization," Econometrica, Econometric Society, vol. 89(2), pages 825-848, March.
    3. Keisuke Hirano & Jack R. Porter, 2012. "Impossibility Results for Nondifferentiable Functionals," Econometrica, Econometric Society, vol. 80(4), pages 1769-1790, July.
    4. 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.
    5. Charles F. Manski, 1989. "Anatomy of the Selection Problem," Journal of Human Resources, University of Wisconsin Press, vol. 24(3), pages 343-360.
    6. Stoye, Jörg, 2009. "Minimax regret treatment choice with finite samples," Journal of Econometrics, Elsevier, vol. 151(1), pages 70-81, July.
    7. Keisuke Hirano & Jack R. Porter, 2009. "Asymptotics for Statistical Treatment Rules," Econometrica, Econometric Society, vol. 77(5), pages 1683-1701, September.
    8. Song, Kyungchul, 2014. "Local asymptotic minimax estimation of nonregular parameters with translation-scale equivariant maps," Journal of Multivariate Analysis, Elsevier, vol. 125(C), pages 136-158.
    9. Charles F. Manski, 2009. "The 2009 Lawrence R. Klein Lecture: Diversified Treatment Under Ambiguity," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 50(4), pages 1013-1041, November.
    10. Hong, Han & Li, Jessie, 2018. "The numerical delta method," Journal of Econometrics, Elsevier, vol. 206(2), pages 379-394.
    11. Stoye, Jörg, 2012. "Minimax regret treatment choice with covariates or with limited validity of experiments," Journal of Econometrics, Elsevier, vol. 166(1), pages 138-156.
    12. Song, Kyungchul, 2014. "Point Decisions For Interval–Identified Parameters," Econometric Theory, Cambridge University Press, vol. 30(2), pages 334-356, April.
    13. Manski, Charles F, 1990. "Nonparametric Bounds on Treatment Effects," American Economic Review, American Economic Association, vol. 80(2), pages 319-323, May.
    14. Tetenov, Aleksey, 2012. "Statistical treatment choice based on asymmetric minimax regret criteria," Journal of Econometrics, Elsevier, vol. 166(1), pages 157-165.
    15. Charles F. Manski, 2004. "Statistical Treatment Rules for Heterogeneous Populations," Econometrica, Econometric Society, vol. 72(4), pages 1221-1246, July.
    16. Manski, Charles F., 2007. "Minimax-regret treatment choice with missing outcome data," Journal of Econometrics, Elsevier, vol. 139(1), pages 105-115, July.
    17. Charles F. Manski & John V. Pepper, 2000. "Monotone Instrumental Variables, with an Application to the Returns to Schooling," Econometrica, Econometric Society, vol. 68(4), pages 997-1012, July.
    18. 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.
    19. 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.
    20. Takuya Ishihara & Toru Kitagawa, 2021. "Evidence Aggregation for Treatment Choice," Papers 2108.06473, arXiv.org.
    Full references (including those not matched with items on IDEAS)

    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. Manski, Charles F., 2023. "Probabilistic prediction for binary treatment choice: With focus on personalized medicine," Journal of Econometrics, Elsevier, vol. 234(2), pages 647-663.
    2. Toru Kitagawa & Sokbae Lee & Chen Qiu, 2022. "Treatment Choice with Nonlinear Regret," Papers 2205.08586, arXiv.org, revised Feb 2024.
    3. Charles F. Manski, 2021. "Econometrics for Decision Making: Building Foundations Sketched by Haavelmo and Wald," Econometrica, Econometric Society, vol. 89(6), pages 2827-2853, November.
    4. Daido Kido, 2022. "Distributionally Robust Policy Learning with Wasserstein Distance," Papers 2205.04637, arXiv.org, revised Aug 2022.
    5. Susan Athey & Stefan Wager, 2021. "Policy Learning With Observational Data," Econometrica, Econometric Society, vol. 89(1), pages 133-161, January.
    6. Kohei Yata, 2021. "Optimal Decision Rules Under Partial Identification," Papers 2111.04926, arXiv.org, revised Aug 2023.
    7. Eric Mbakop & Max Tabord‐Meehan, 2021. "Model Selection for Treatment Choice: Penalized Welfare Maximization," Econometrica, Econometric Society, vol. 89(2), pages 825-848, March.
    8. Thomas M. Russell, 2020. "Policy Transforms and Learning Optimal Policies," Papers 2012.11046, arXiv.org.
    9. Kitagawa, Toru & Wang, Guanyi, 2023. "Who should get vaccinated? Individualized allocation of vaccines over SIR network," Journal of Econometrics, Elsevier, vol. 232(1), pages 109-131.
    10. Davide Viviano, 2019. "Policy Targeting under Network Interference," Papers 1906.10258, arXiv.org, revised Apr 2024.
    11. Chunrong Ai & Yue Fang & Haitian Xie, 2024. "Data-driven Policy Learning for a Continuous Treatment," Papers 2402.02535, arXiv.org.
    12. Firpo, Sergio & Galvao, Antonio F. & Kobus, Martyna & Parker, Thomas & Rosa-Dias, Pedro, 2020. "Loss Aversion and the Welfare Ranking of Policy Interventions," IZA Discussion Papers 13176, Institute of Labor Economics (IZA).
    13. Shosei Sakaguchi, 2021. "Estimation of Optimal Dynamic Treatment Assignment Rules under Policy Constraints," Papers 2106.05031, arXiv.org, revised Apr 2024.
    14. Keisuke Hirano & Jack R. Porter, 2016. "Panel Asymptotics and Statistical Decision Theory," The Japanese Economic Review, Japanese Economic Association, vol. 67(1), pages 33-49, March.
    15. Timothy Christensen & Hyungsik Roger Moon & Frank Schorfheide, 2020. "Robust Forecasting," Papers 2011.03153, arXiv.org, revised Dec 2020.
    16. Stoye, Jörg, 2012. "Minimax regret treatment choice with covariates or with limited validity of experiments," Journal of Econometrics, Elsevier, vol. 166(1), pages 138-156.
    17. Vira Semenova, 2023. "Adaptive Estimation of Intersection Bounds: a Classification Approach," Papers 2303.00982, arXiv.org.
    18. Yuya Sasaki & Takuya Ura, 2020. "Welfare Analysis via Marginal Treatment Effects," Papers 2012.07624, arXiv.org.
    19. Timothy Christensen & Hyungsik Roger Moon & Frank Schorfheide, 2022. "Optimal Decision Rules when Payoffs are Partially Identified," Papers 2204.11748, arXiv.org, revised May 2023.
    20. Davide Viviano & Jelena Bradic, 2020. "Fair Policy Targeting," Papers 2005.12395, arXiv.org, revised Jun 2022.

    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:2311.08958. 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.