{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,9]],"date-time":"2026-10-09T16:08:31Z","timestamp":1791562111678,"version":"4.3.4"},"reference-count":77,"publisher":"Oxford University Press (OUP)","license":[{"start":{"date-parts":[[2026,2,17]],"date-time":"2026-02-17T00:00:00Z","timestamp":1771286400000},"content-version":"am","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/pages\/standard-publication-reuse-rights"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>We apply classical statistical decision theory to a large class of treatment choice problems with partial identification. We show that, in a general class of problems with Gaussian likelihood, all decision rules are admissible; it is maximin-welfare optimal to ignore all data; and, for severe enough partial identification, there are infinitely many minimax-regret optimal decision rules, all of which sometimes randomize the policy recommendation. We uniquely characterize the minimax-regret optimal rule that least frequently randomizes, and show that, in some cases, it can outperform other minimax-regret optimal rules in terms of what we call profiled regret. We analyse the implications of our results in the aggregation of experimental estimates for policy adoption, extrapolation of Local Average Treatment Effects, and policy making in the presence of omitted variable bias.<\/jats:p>","DOI":"10.1093\/restud\/rdag015","type":"journal-article","created":{"date-parts":[[2026,2,14]],"date-time":"2026-02-14T12:43:34Z","timestamp":1771073014000},"source":"Crossref","is-referenced-by-count":4,"title":["Decision Theory for Treatment Choice Problems with Partial Identification"],"prefix":"10.1093","author":[{"given":"Jos\u00e9 Luis","family":"Montiel Olea","sequence":"first","affiliation":[{"name":"Department of Economics, Cornell University ,","place":["USA"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Chen","family":"Qiu","sequence":"additional","affiliation":[{"name":"Department of Economics, Cornell University ,","place":["USA"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"J\u00f6rg","family":"Stoye","sequence":"additional","affiliation":[{"name":"Department of Economics, Cornell University ,","place":["USA"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2026,2,17]]},"reference":[{"key":"2026032603410436300_rdag015-B1","author":"Adjaho","year":"2022"},{"key":"2026032603410436300_rdag015-B2","doi-asserted-by":"crossref","first-page":"46","DOI":"10.1214\/aoms\/1177730090","article-title":"Estimation of the Parameters of a Single Equation in a Complete System of Stochastic Equations","volume":"20","author":"Anderson","year":"1949","journal-title":"The Annals of Mathematical Statistics"},{"key":"2026032603410436300_rdag015-B3","author":"Andrews","year":"2022"},{"key":"2026032603410436300_rdag015-B4","author":"Aradillas Fern\u00e1ndez","year":"2025"},{"key":"2026032603410436300_rdag015-B5","author":"Aradillas Fern\u00e1ndez","year":"2024"},{"key":"2026032603410436300_rdag015-B6","doi-asserted-by":"crossref","first-page":"133","DOI":"10.3982\/ECTA15732","article-title":"Efficient Policy Learning with Observational Data","volume":"89","author":"Athey","year":"2021","journal-title":"Econometrica: Journal of the Econometric Society"},{"key":"2026032603410436300_rdag015-B7","doi-asserted-by":"crossref","first-page":"1386","DOI":"10.1080\/01621459.2025.2489135","article-title":"Safe Policy Learning Through Extrapolation: Application to Pre-Trial Risk Assessment","volume":"120","author":"Ben-Michael","year":"2025","journal-title":"Journal of the American Statistical Association"},{"key":"2026032603410436300_rdag015-B8","doi-asserted-by":"crossref","first-page":"3045","DOI":"10.1080\/01621459.2023.2300507","article-title":"Policy Learning with Asymmetric Utilities","volume":"119","author":"Ben-Michael","year":"2024","journal-title":"Journal of the American Statistical Association"},{"key":"2026032603410436300_rdag015-B9","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-4286-2","volume-title":"Statistical Decision Theory and Bayesian Analysis","author":"Berger","year":"1985"},{"key":"2026032603410436300_rdag015-B10","doi-asserted-by":"crossref","first-page":"168","DOI":"10.1016\/j.jeconom.2011.11.007","article-title":"Inferring Welfare Maximizing Treatment Assignment under Budget Constraints","volume":"167","author":"Bhattacharya","year":"2012","journal-title":"Journal of Econometrics"},{"key":"2026032603410436300_rdag015-B11","doi-asserted-by":"crossref","first-page":"293","DOI":"10.1080\/01621459.1970.10481080","article-title":"Selecting One of Two Treatments When the Responses are Dichotomous","volume":"65","author":"Canner","year":"1970","journal-title":"Journal of the American Statistical Association"},{"key":"2026032603410436300_rdag015-B12","volume-title":"Statistical Inference","author":"Casella","year":"2002"},{"key":"2026032603410436300_rdag015-B13","doi-asserted-by":"crossref","first-page":"625","DOI":"10.1002\/jae.583","article-title":"Econometric Applications of Maxmin Expected Utility","volume":"15","author":"Chamberlain","year":"2000","journal-title":"Journal of Applied Econometrics"},{"key":"2026032603410436300_rdag015-B14","volume-title":"The Oxford Handbook of Bayesian Econometrics","author":"Chamberlain","year":"2011"},{"key":"2026032603410436300_rdag015-B15","article-title":"A Note on Minimax Regret Rules with Multiple Treatments in Finite Samples","author":"Chen","year":"2026","journal-title":"Econometric Theory"},{"key":"2026032603410436300_rdag015-B16","author":"Christensen","year":"2022"},{"key":"2026032603410436300_rdag015-B17","doi-asserted-by":"crossref","DOI":"10.1137\/1.9781611971309","volume-title":"Optimization and Nonsmooth Analysis","author":"Clarke","year":"1990"},{"key":"2026032603410436300_rdag015-B18","author":"D\u2019Adamo","year":"2021"},{"key":"2026032603410436300_rdag015-B19","author":"Daskalakis","year":"2021"},{"key":"2026032603410436300_rdag015-B20","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1016\/j.jeconom.2004.04.006","article-title":"Program Evaluation as a Decision Problem","volume":"125","author":"Dehejia","year":"2005","journal-title":"Journal of Econometrics"},{"key":"2026032603410436300_rdag015-B21","author":"Diegert","year":"2022"},{"key":"2026032603410436300_rdag015-B22","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1214\/aoms\/1177729689","article-title":"Elimination of Randomization in Certain Statistical Decision Procedures and Zero-Sum Two-Person Games","volume":"22","author":"Dvoretzky","year":"1951","journal-title":"The Annals of Mathematical Statistics"},{"key":"2026032603410436300_rdag015-B23","volume-title":"Mathematical Statistics: A Decision Theoretic Approach","author":"Ferguson","year":"1967"},{"key":"2026032603410436300_rdag015-B24","doi-asserted-by":"crossref","first-page":"1519","DOI":"10.3982\/ECTA16773","article-title":"Robust Bayesian Inference for Set-Identified Models","volume":"89","author":"Giacomini","year":"2021","journal-title":"Econometrica: Journal of the Econometric Society"},{"key":"2026032603410436300_rdag015-B25","author":"Guggenberger","year":"2025"},{"key":"2026032603410436300_rdag015-B26","volume-title":"Econometrics","author":"Hansen","year":"2022"},{"key":"2026032603410436300_rdag015-B27","doi-asserted-by":"crossref","first-page":"4730","DOI":"10.1073\/pnas.96.8.4730","article-title":"Local Instrumental Variables and Latent Variable Models for Identifying and Bounding Treatment Effects","volume":"96","author":"Heckman","year":"1999","journal-title":"Proceedings of the National Academy of Sciences"},{"key":"2026032603410436300_rdag015-B28","doi-asserted-by":"crossref","first-page":"669","DOI":"10.1111\/j.1468-0262.2005.00594.x","article-title":"Structural Equations, Treatment Effects, and Econometric Policy Evaluation 1","volume":"73","author":"Heckman","year":"2005","journal-title":"Econometrica: Journal of the Econometric Society"},{"key":"2026032603410436300_rdag015-B29","doi-asserted-by":"crossref","first-page":"1683","DOI":"10.3982\/ECTA6630","article-title":"Asymptotics for Statistical Treatment Rules","volume":"77","author":"Hirano","year":"2009","journal-title":"Econometrica: Journal of the Econometric Society"},{"key":"2026032603410436300_rdag015-B30","first-page":"283","volume-title":"Handbook of Econometrics","author":"Hirano","year":"2020"},{"key":"2026032603410436300_rdag015-B31","author":"Ida","year":"2022"},{"key":"2026032603410436300_rdag015-B32","doi-asserted-by":"crossref","first-page":"467","DOI":"10.2307\/2951620","article-title":"Identification and Estimation of Local Average Treatment Effects","volume":"62","author":"Imbens","year":"1994","journal-title":"Econometrica: Journal of the Econometric Society"},{"key":"2026032603410436300_rdag015-B33","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9781139025751","volume-title":"Causal Inference in Statistics, Social, and Biomedical Sciences","author":"Imbens","year":"2015"},{"key":"2026032603410436300_rdag015-B34","author":"Ishihara","year":"2021"},{"key":"2026032603410436300_rdag015-B35","article-title":"Confounding-robust Policy Improvement","volume":"31","author":"Kallus","year":"2018","journal-title":"Advances in Neural Information Processing Systems"},{"key":"2026032603410436300_rdag015-B36","doi-asserted-by":"crossref","first-page":"272","DOI":"10.1214\/aoms\/1177728259","article-title":"The Theory of Decision Procedures for Distributions with Monotone Likelihood Ratio","volume":"27","author":"Karlin","year":"1956","journal-title":"The Annals of Mathematical Statistics"},{"key":"2026032603410436300_rdag015-B37","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1007\/s00182-005-0004-3","article-title":"The Dvoretzky-Wald-Wolfowitz Theorem and Purification in Atomless Finite-Action Games","volume":"34","author":"Khan","year":"2006","journal-title":"International Journal of Game Theory"},{"key":"2026032603410436300_rdag015-B38","author":"Kido","year":"2022"},{"key":"2026032603410436300_rdag015-B39","author":"Kido","year":"2023"},{"key":"2026032603410436300_rdag015-B40","author":"Kitagawa","year":"2022"},{"key":"2026032603410436300_rdag015-B41","author":"Kitagawa","year":"2021"},{"key":"2026032603410436300_rdag015-B42","doi-asserted-by":"crossref","first-page":"591","DOI":"10.3982\/ECTA13288","article-title":"Who Should be Treated? Empirical Welfare Maximization Methods for Treatment Choice","volume":"86","author":"Kitagawa","year":"2018","journal-title":"Econometrica: Journal of the Econometric Society"},{"key":"2026032603410436300_rdag015-B43","doi-asserted-by":"crossref","first-page":"561","DOI":"10.1080\/07350015.2019.1688664","article-title":"Equality-Minded Treatment Choice","volume":"39","author":"Kitagawa","year":"2021","journal-title":"Journal of Business Economics and Statistics"},{"key":"2026032603410436300_rdag015-B44","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1016\/j.jeconom.2021.09.009","article-title":"Who Should get Vaccinated? Individualized Allocation of Vaccines over SIR Network","volume":"232","author":"Kitagawa","year":"2023","journal-title":"Journal of Econometrics"},{"key":"2026032603410436300_rdag015-B45","volume-title":"Theory of Point Estimation","author":"Lehmann","year":"1998","edition":"2nd edn"},{"key":"2026032603410436300_rdag015-B46","volume-title":"Testing Statistical Hypotheses","author":"Lehmann","year":"2005"},{"key":"2026032603410436300_rdag015-B47","author":"Lei","year":"2023"},{"key":"2026032603410436300_rdag015-B48","doi-asserted-by":"crossref","first-page":"415","DOI":"10.1016\/S0304-4076(99)00045-7","article-title":"Identification Problems and Decisions under Ambiguity: Empirical Analysis of Treatment Response and Normative Analysis of Treatment Choice","volume":"95","author":"Manski","year":"2000","journal-title":"Journal of Econometrics"},{"key":"2026032603410436300_rdag015-B49","doi-asserted-by":"crossref","first-page":"1221","DOI":"10.1111\/j.1468-0262.2004.00530.x","article-title":"Statistical Treatment Rules for Heterogeneous Populations","volume":"72","author":"Manski","year":"2004","journal-title":"Econometrica: Journal of the Econometric Society"},{"key":"2026032603410436300_rdag015-B50","volume-title":"Social Choice with Partial Knowledge of Treatment Response","author":"Manski","year":"2005"},{"key":"2026032603410436300_rdag015-B51","volume-title":"Identification for Prediction and Decision","author":"Manski","year":"2007"},{"key":"2026032603410436300_rdag015-B52","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1016\/j.jeconom.2006.06.006","article-title":"Minimax-regret Treatment Choice with Missing Outcome Data","volume":"139","author":"Manski","year":"2007","journal-title":"Journal of Econometrics"},{"key":"2026032603410436300_rdag015-B53","doi-asserted-by":"crossref","first-page":"345","DOI":"10.1097\/EDE.0000000000001178","article-title":"Towards Credible Patient-Centered Meta-Analysis","volume":"31","author":"Manski","year":"2020","journal-title":"Epidemiology"},{"key":"2026032603410436300_rdag015-B54","doi-asserted-by":"crossref","first-page":"2827","DOI":"10.3982\/ECTA17985","article-title":"Econometrics for Decision Making: Building Foundations Sketched by Haavelmo and Wald","volume":"89","author":"Manski","year":"2021","journal-title":"Econometrica: Journal of the Econometric Society"},{"key":"2026032603410436300_rdag015-B55","first-page":"1","article-title":"Identification and Statistical Decision Theory","volume":"41","author":"Manski","year":"2024","journal-title":"Econometric Theory"},{"key":"2026032603410436300_rdag015-B56","doi-asserted-by":"crossref","first-page":"1998","DOI":"10.1016\/j.jspi.2006.06.037","article-title":"Admissible Treatment Rules for a Risk-Averse Planner with Experimental Data on an Innovation","volume":"137","author":"Manski","year":"2007","journal-title":"Journal of Statistical Planning and Inference"},{"key":"2026032603410436300_rdag015-B57","doi-asserted-by":"crossref","first-page":"2158","DOI":"10.1214\/aos\/1176349416","article-title":"Some Incomplete but Boundedly Complete Location Families","volume":"21","author":"Mattner","year":"1993","journal-title":"Annals of Statistics"},{"key":"2026032603410436300_rdag015-B58","doi-asserted-by":"crossref","first-page":"825","DOI":"10.3982\/ECTA16437","article-title":"Model Selection for Treatment Choice: Penalized Welfare Maximization","volume":"89","author":"Mbakop","year":"2021","journal-title":"Econometrica: Journal of the Econometric Society"},{"key":"2026032603410436300_rdag015-B59","author":"Menzel","year":"2023"},{"key":"2026032603410436300_rdag015-B60","doi-asserted-by":"crossref","first-page":"1589","DOI":"10.3982\/ECTA15463","article-title":"Using Instrumental Variables for Inference about Policy Relevant Treatment Parameters","volume":"86","author":"Mogstad","year":"2018","journal-title":"Econometrica: Journal of the Econometric Society"},{"key":"2026032603410436300_rdag015-B61","doi-asserted-by":"crossref","first-page":"577","DOI":"10.1146\/annurev-economics-101617-041813","article-title":"Identification and Extrapolation of Causal Effects with Instrumental Variables","volume":"10","author":"Mogstad","year":"2018","journal-title":"Annual Review of Economics"},{"key":"2026032603410436300_rdag015-B62","doi-asserted-by":"crossref","first-page":"395","DOI":"10.3982\/ECTA7793","article-title":"Efficient Tests under a Weak Convergence Assumption","volume":"79","author":"M\u00fcller","year":"2011","journal-title":"Econometrica: Journal of the Econometric Society"},{"key":"2026032603410436300_rdag015-B63","doi-asserted-by":"crossref","first-page":"241","DOI":"10.1007\/BF00133643","article-title":"Minimax, Information and Ultrapessimism","volume":"33","author":"Parmigiani","year":"1992","journal-title":"Theory and Decision"},{"key":"2026032603410436300_rdag015-B64","volume-title":"Convex Analysis","author":"Rockafellar","year":"1997"},{"key":"2026032603410436300_rdag015-B65","doi-asserted-by":"crossref","first-page":"575","DOI":"10.1007\/s11238-014-9442-3","article-title":"Minimax and the Value of Information","volume":"78","author":"Sadler","year":"2015","journal-title":"Theory and Decision"},{"key":"2026032603410436300_rdag015-B66","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1080\/01621459.1951.10500768","article-title":"The Theory of Statistical Decision","volume":"46","author":"Savage","year":"1951","journal-title":"Journal of the American Statistical Association"},{"key":"2026032603410436300_rdag015-B67","author":"Schlag","year":"2006"},{"key":"2026032603410436300_rdag015-B68","volume-title":"Integration in Hilbert Space","author":"Skorohod","year":"2012"},{"key":"2026032603410436300_rdag015-B69","doi-asserted-by":"crossref","first-page":"190","DOI":"10.1017\/S0266466607070089","article-title":"Minimax Regret Treatment Choice With Incomplete Data and Many Treatments","volume":"23","author":"Stoye","year":"2007","journal-title":"Econometric Theory"},{"key":"2026032603410436300_rdag015-B70","doi-asserted-by":"crossref","first-page":"70","DOI":"10.1016\/j.jeconom.2009.02.013","article-title":"Minimax Regret Treatment Choice with Finite Samples","volume":"151","author":"Stoye","year":"2009","journal-title":"Journal of Econometrics"},{"key":"2026032603410436300_rdag015-B71","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1080\/15598608.2009.10411923","article-title":"Partial Identification and Robust Treatment Choice: An Application to Young Offenders","volume":"3","author":"Stoye","year":"2009","journal-title":"Journal of Statistical Theory and Practice"},{"key":"2026032603410436300_rdag015-B72","doi-asserted-by":"crossref","first-page":"138","DOI":"10.1016\/j.jeconom.2011.06.012","article-title":"Minimax Regret Treatment Choice with Covariates or with Limited Validity of Experiments","volume":"166","author":"Stoye","year":"2012","journal-title":"Journal of Econometrics"},{"key":"2026032603410436300_rdag015-B73","doi-asserted-by":"crossref","first-page":"257","DOI":"10.1146\/annurev-economics-080511-110959","article-title":"New Perspectives on Statistical Decisions under Ambiguity","volume":"4","author":"Stoye","year":"2012","journal-title":"Annual Review of Economics"},{"key":"2026032603410436300_rdag015-B74","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1016\/j.jeconom.2011.06.013","article-title":"Statistical Treatment Choice Based on Asymmetric Minimax Regret Criteria","volume":"166","author":"Tetenov","year":"2012","journal-title":"Journal of Econometrics"},{"key":"2026032603410436300_rdag015-B75","volume-title":"Statistical Decision Functions","author":"Wald","year":"1950"},{"key":"2026032603410436300_rdag015-B76","author":"Yata","year":"2021"},{"key":"2026032603410436300_rdag015-B77","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1007\/978-1-4613-3557-3_12","volume-title":"Minimax and Applications","author":"Yu","year":"1995"}],"container-title":["Review of Economic Studies"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/academic.oup.com\/restud\/advance-article-pdf\/doi\/10.1093\/restud\/rdag015\/66958101\/rdag015.pdf","content-type":"application\/pdf","content-version":"am","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/restud\/advance-article-pdf\/doi\/10.1093\/restud\/rdag015\/66958101\/rdag015.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,26]],"date-time":"2026-03-26T07:41:14Z","timestamp":1774510874000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/restud\/advance-article\/doi\/10.1093\/restud\/rdag015\/8488610"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,2,17]]},"references-count":77,"URL":"https:\/\/doi.org\/10.1093\/restud\/rdag015","relation":{},"ISSN":["0034-6527","1467-937X"],"issn-type":[{"value":"0034-6527","type":"print"},{"value":"1467-937X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,2,17]]},"article-number":"rdag015"}}