IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2205.08586.html
   My bibliography  Save this paper

Treatment Choice with Nonlinear Regret

Author

Listed:
  • Toru Kitagawa
  • Sokbae Lee
  • Chen Qiu

Abstract

The literature focuses on the mean of welfare regret, which can lead to undesirable treatment choice due to sensitivity to sampling uncertainty. We propose to minimize the mean of a nonlinear transformation of regret and show that singleton rules are not essentially complete for nonlinear regret. Focusing on mean square regret, we derive closed-form fractions for finite-sample Bayes and minimax optimal rules. Our approach is grounded in decision theory and extends to limit experiments. The treatment fractions can be viewed as the strength of evidence favoring treatment. We apply our framework to a normal regression model and sample size calculation.

Suggested Citation

  • Toru Kitagawa & Sokbae Lee & Chen Qiu, 2022. "Treatment Choice with Nonlinear Regret," Papers 2205.08586, arXiv.org, revised Oct 2024.
    • Handle: RePEc:arx:papers:2205.08586
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2205.08586
    File Function: Latest version
    Download Restriction: no
    ---><---

    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. Manski, Charles F., 1986. "Ordinal Utility Models Of Decision Making Under Uncertainty," SSRI Workshop Series 292682, University of Wisconsin-Madison, Social Systems Research Institute.
    3. Peter Klibanoff & Massimo Marinacci & Sujoy Mukerji, 2005. "A Smooth Model of Decision Making under Ambiguity," Econometrica, Econometric Society, vol. 73(6), pages 1849-1892, November.
    4. Stoye, Jörg, 2009. "Minimax regret treatment choice with finite samples," Journal of Econometrics, Elsevier, vol. 151(1), pages 70-81, July.
    5. Rachel Cassidy & Charles F. Manski, 2019. "Tuberculosis diagnosis and treatment under uncertainty," Proceedings of the National Academy of Sciences, Proceedings of the National Academy of Sciences, vol. 116(46), pages 22990-22997, November.
    6. Toru Kitagawa & Aleksey Tetenov, 2021. "Equality-Minded Treatment Choice," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 39(2), pages 561-574, March.
    7. Keisuke Hirano & Jack R. Porter, 2009. "Asymptotics for Statistical Treatment Rules," Econometrica, Econometric Society, vol. 77(5), pages 1683-1701, September.
    8. Dehejia, Rajeev H., 2005. "Program evaluation as a decision problem," Journal of Econometrics, Elsevier, vol. 125(1-2), pages 141-173.
    9. Eric Mbakop & Max Tabord‐Meehan, 2021. "Model Selection for Treatment Choice: Penalized Welfare Maximization," Econometrica, Econometric Society, vol. 89(2), pages 825-848, March.
    10. 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.
    11. 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.
    12. Manski, Charles F., 2013. "Public Policy in an Uncertain World: Analysis and Decisions," Economics Books, Harvard University Press, number 9780674066892, Spring.
    13. Bhattacharya, Debopam & Dupas, Pascaline, 2012. "Inferring welfare maximizing treatment assignment under budget constraints," Journal of Econometrics, Elsevier, vol. 167(1), pages 168-196.
    14. Karl Schlag, 2006. "ELEVEN - Tests needed for a Recommendation," Economics Working Papers ECO2006/2, European University Institute.
    15. Charles F. Manski, 2004. "Statistical Treatment Rules for Heterogeneous Populations," Econometrica, Econometric Society, vol. 72(4), pages 1221-1246, July.
    16. Tetenov, Aleksey, 2012. "Statistical treatment choice based on asymmetric minimax regret criteria," Journal of Econometrics, Elsevier, vol. 166(1), pages 157-165.
    17. Charles F. Manski & Aleksey Tetenov, 2014. "The Quantile Performance of Statistical Treatment Rules Using Hypothesis Tests to Allocate a Population to Two Treatments," CeMMAP working papers 44/14, Institute for Fiscal Studies.
    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. Tommaso Denti & Luciano Pomatto, 2022. "Model and Predictive Uncertainty: A Foundation for Smooth Ambiguity Preferences," Econometrica, Econometric Society, vol. 90(2), pages 551-584, March.
    20. Takuya Ishihara & Toru Kitagawa, 2021. "Evidence Aggregation for Treatment Choice," Papers 2108.06473, arXiv.org, revised Jul 2024.
    21. 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.
    22. Susan Athey & Stefan Wager, 2021. "Policy Learning With Observational Data," Econometrica, Econometric Society, vol. 89(1), pages 133-161, January.
    23. 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.
    24. Raffaella Giacomini & Toru Kitagawa & Matthew Read, 2021. "Robust Bayesian Analysis for Econometrics," Working Paper Series WP-2021-11, Federal Reserve Bank of Chicago.
    25. Manski, Charles F., 2007. "Minimax-regret treatment choice with missing outcome data," Journal of Econometrics, Elsevier, vol. 139(1), pages 105-115, July.
    26. Charles F. Manski, 2022. "Identification and Statistical Decision Theory," Papers 2204.11318, arXiv.org, revised Mar 2024.
    27. 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.
    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. Susan Athey & Stefan Wager, 2021. "Policy Learning With Observational Data," Econometrica, Econometric Society, vol. 89(1), pages 133-161, January.
    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, 2023. "Locally Asymptotically Minimax Statistical Treatment Rules Under Partial Identification," Papers 2311.08958, arXiv.org.
    5. 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.
    6. Davide Viviano, 2019. "Policy Targeting under Network Interference," Papers 1906.10258, arXiv.org, revised Apr 2024.
    7. Chunrong Ai & Yue Fang & Haitian Xie, 2024. "Data-driven Policy Learning for Continuous Treatments," Papers 2402.02535, arXiv.org, revised Nov 2024.
    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. 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).
    10. Toru Kitagawa & Hugo Lopez & Jeff Rowley, 2022. "Stochastic Treatment Choice with Empirical Welfare Updating," Papers 2211.01537, arXiv.org, revised Feb 2023.
    11. Kock, Anders Bredahl & Preinerstorfer, David & Veliyev, Bezirgen, 2023. "Treatment recommendation with distributional targets," Journal of Econometrics, Elsevier, vol. 234(2), pages 624-646.
    12. Shosei Sakaguchi, 2021. "Estimation of Optimal Dynamic Treatment Assignment Rules under Policy Constraints," Papers 2106.05031, arXiv.org, revised Aug 2024.
    13. Toru Kitagawa & Weining Wang & Mengshan Xu, 2022. "Policy Choice in Time Series by Empirical Welfare Maximization," Papers 2205.03970, arXiv.org, revised Dec 2024.
    14. Thomas M. Russell, 2020. "Policy Transforms and Learning Optimal Policies," Papers 2012.11046, arXiv.org.
    15. Takanori Ida & Takunori Ishihara & Koichiro Ito & Daido Kido & Toru Kitagawa & Shosei Sakaguchi & Shusaku Sasaki, 2022. "Choosing Who Chooses: Selection-Driven Targeting in Energy Rebate Programs," NBER Working Papers 30469, National Bureau of Economic Research, Inc.
    16. Yuya Sasaki & Takuya Ura, 2020. "Welfare Analysis via Marginal Treatment Effects," Papers 2012.07624, arXiv.org.
    17. Takanori Ida & Takunori Ishihara & Koichiro Ito & Daido Kido & Toru Kitagawa & Shosei Sakaguchi & Shusaku Sasaki, 2021. "Paternalism, Autonomy, or Both? Experimental Evidence from Energy Saving Programs," Papers 2112.09850, arXiv.org.
    18. 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.
    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 & 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:2205.08586. 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.