Decision Theory for Treatment Choice Problems with Partial Identification

• 成果类型: Article; Early Access
• 署名作者: Montiel Olea, Jose Luis; Qiu, Chen; Stoye, Jorg
• 署名单位: Cornell University
• 刊物名称: REVIEW OF ECONOMIC STUDIES
• ISSN/ISSBN: 0034-6527
• DOI: 10.1093/restud/rdag015
• 发表日期: 2026
• 关键词: regret treatment choice; instrumental variables; treatment rules; Minimax; inference

摘要

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.