IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2310.06242.html
   My bibliography  Save this paper

Treatment Choice, Mean Square Regret and Partial Identification

Author

Listed:
  • Toru Kitagawa
  • Sokbae Lee
  • Chen Qiu

Abstract

We consider a decision maker who faces a binary treatment choice when their welfare is only partially identified from data. We contribute to the literature by anchoring our finite-sample analysis on mean square regret, a decision criterion advocated by Kitagawa, Lee, and Qiu (2022). We find that optimal rules are always fractional, irrespective of the width of the identified set and precision of its estimate. The optimal treatment fraction is a simple logistic transformation of the commonly used t-statistic multiplied by a factor calculated by a simple constrained optimization. This treatment fraction gets closer to 0.5 as the width of the identified set becomes wider, implying the decision maker becomes more cautious against the adversarial Nature.

Suggested Citation

  • Toru Kitagawa & Sokbae Lee & Chen Qiu, 2023. "Treatment Choice, Mean Square Regret and Partial Identification," Papers 2310.06242, arXiv.org.
    • Handle: RePEc:arx:papers:2310.06242
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2310.06242
    File Function: Latest version
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Charles F. Manski, 2013. "Response to the Review of ‘Public Policy in an Uncertain World’," Economic Journal, Royal Economic Society, vol. 0, pages 412-415, August.
    2. 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.
    3. Timothy Christensen & Hyungsik Roger Moon & Frank Schorfheide, 2022. "Optimal Decision Rules when Payoffs are Partially Identified," Papers 2204.11748, arXiv.org, revised May 2023.
    4. Susan Athey & Stefan Wager, 2021. "Policy Learning With Observational Data," Econometrica, Econometric Society, vol. 89(1), pages 133-161, January.
    5. Azevedo, Eduardo M. & Mao, David & Montiel Olea, José Luis & Velez, Amilcar, 2023. "The A/B testing problem with Gaussian priors," Journal of Economic Theory, Elsevier, vol. 210(C).
    6. 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.
    7. Lihua Lei & Roshni Sahoo & Stefan Wager, 2023. "Policy Learning under Biased Sample Selection," Papers 2304.11735, arXiv.org.
    8. Eric Mbakop & Max Tabord‐Meehan, 2021. "Model Selection for Treatment Choice: Penalized Welfare Maximization," Econometrica, Econometric Society, vol. 89(2), pages 825-848, March.
    9. Charles F. Manski, 1989. "Anatomy of the Selection Problem," Journal of Human Resources, University of Wisconsin Press, vol. 24(3), pages 343-360.
    10. Stoye, Jörg, 2009. "Minimax regret treatment choice with finite samples," Journal of Econometrics, Elsevier, vol. 151(1), pages 70-81, July.
    11. Toru Kitagawa & Aleksey Tetenov, 2021. "Equality-Minded Treatment Choice," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 39(2), pages 561-574, March.
    12. Aleksey Tetenov, 2008. "Measuring Precision of Statistical Inference on Partially Identified Parameters," Carlo Alberto Notebooks 98, Collegio Carlo Alberto, revised 2012.
    13. Keisuke Hirano & Jack R. Porter, 2009. "Asymptotics for Statistical Treatment Rules," Econometrica, Econometric Society, vol. 77(5), pages 1683-1701, September.
    14. William A. Brock, 2006. "Profiling Problems With Partially Identified Structure," Economic Journal, Royal Economic Society, vol. 116(515), pages 427-440, November.
    15. 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.
    16. Daido Kido, 2022. "Distributionally Robust Policy Learning with Wasserstein Distance," Papers 2205.04637, arXiv.org, revised Aug 2022.
    17. Tetenov, Aleksey, 2012. "Statistical treatment choice based on asymmetric minimax regret criteria," Journal of Econometrics, Elsevier, vol. 166(1), pages 157-165.
    18. Manski, Charles F., 2000. "Identification problems and decisions under ambiguity: Empirical analysis of treatment response and normative analysis of treatment choice," Journal of Econometrics, Elsevier, vol. 95(2), pages 415-442, April.
    19. Charles F. Manski, 2004. "Statistical Treatment Rules for Heterogeneous Populations," Econometrica, Econometric Society, vol. 72(4), pages 1221-1246, July.
    20. Manski, Charles F., 2007. "Minimax-regret treatment choice with missing outcome data," Journal of Econometrics, Elsevier, vol. 139(1), pages 105-115, July.
    21. Hayashi, Takashi, 2008. "Regret aversion and opportunity dependence," Journal of Economic Theory, Elsevier, vol. 139(1), pages 242-268, March.
    22. Bhattacharya, Debopam & Dupas, Pascaline, 2012. "Inferring welfare maximizing treatment assignment under budget constraints," Journal of Econometrics, Elsevier, vol. 167(1), pages 168-196.
    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. Toru Kitagawa & Sokbae Lee & Chen Qiu, 2022. "Treatment Choice with Nonlinear Regret," Papers 2205.08586, arXiv.org, revised Oct 2024.
    2. 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.
    3. Chunrong Ai & Yue Fang & Haitian Xie, 2024. "Data-driven Policy Learning for Continuous Treatments," Papers 2402.02535, arXiv.org, revised Nov 2024.
    4. 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.
    5. Susan Athey & Stefan Wager, 2021. "Policy Learning With Observational Data," Econometrica, Econometric Society, vol. 89(1), pages 133-161, January.
    6. 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.
    7. Daido Kido, 2023. "Locally Asymptotically Minimax Statistical Treatment Rules Under Partial Identification," Papers 2311.08958, arXiv.org.
    8. 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.
    9. Davide Viviano, 2019. "Policy Targeting under Network Interference," Papers 1906.10258, arXiv.org, revised Apr 2024.
    10. Eric Mbakop & Max Tabord‐Meehan, 2021. "Model Selection for Treatment Choice: Penalized Welfare Maximization," Econometrica, Econometric Society, vol. 89(2), pages 825-848, March.
    11. Garbero, Alessandra & Sakos, Grayson & Cerulli, Giovanni, 2023. "Towards data-driven project design: Providing optimal treatment rules for development projects," Socio-Economic Planning Sciences, Elsevier, vol. 89(C).
    12. Kock, Anders Bredahl & Preinerstorfer, David & Veliyev, Bezirgen, 2023. "Treatment recommendation with distributional targets," Journal of Econometrics, Elsevier, vol. 234(2), pages 624-646.
    13. Shosei Sakaguchi, 2021. "Estimation of Optimal Dynamic Treatment Assignment Rules under Policy Constraints," Papers 2106.05031, arXiv.org, revised Aug 2024.
    14. Toru Kitagawa & Weining Wang & Mengshan Xu, 2022. "Policy Choice in Time Series by Empirical Welfare Maximization," Papers 2205.03970, arXiv.org, revised Dec 2024.
    15. Toru Kitagawa & Weining Wang & Mengshan Xu, 2024. "Policy choice in time series by empirical welfare maximization," CeMMAP working papers 27/24, Institute for Fiscal Studies.
    16. Yuya Sasaki & Takuya Ura, 2020. "Welfare Analysis via Marginal Treatment Effects," Papers 2012.07624, arXiv.org.
    17. Timothy B. Armstrong & Shu Shen, 2023. "Inference on optimal treatment assignments," The Japanese Economic Review, Springer, vol. 74(4), pages 471-500, October.
    18. Matthew A. Masten, 2023. "Minimax-regret treatment rules with many treatments," The Japanese Economic Review, Springer, vol. 74(4), pages 501-537, October.
    19. Achim Ahrens & Alessandra Stampi‐Bombelli & Selina Kurer & Dominik Hangartner, 2024. "Optimal multi‐action treatment allocation: A two‐phase field experiment to boost immigrant naturalization," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 39(7), pages 1379-1395, November.
    20. Davide Viviano & Jess Rudder, 2020. "Policy design in experiments with unknown interference," Papers 2011.08174, arXiv.org, revised May 2024.

    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:2310.06242. 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.