Asymptotics for Treatment Choice with Partial Identification

2026-08-09

AI Summary

This study addresses compound uncertainty arising from both sampling noise and partial identification by developing a unified asymptotic decision framework. The approach centers reduced-form parameters around the least-favorable configuration and introduces a drift sequence that simultaneously attenuates sampling error and identification uncertainty, thereby recasting the original problem as a normal location-shift model with a limiting identified set. This framework provides the first characterization of the asymptotic decision structure under such compound uncertainty and yields theoretically implementable near-optimal decision rules. Applications include treatment selection under contaminated data, robust welfare analysis based on partially identified consumer surplus, and aggregation of experimental estimates to support policy adoption, substantially enhancing the robustness and practicality of statistical decisions.

Abstract

We provide a new asymptotic framework to derive approximately optimal treatment assignments when sampling noise from data is compounded by fundamental uncertainty due to partial identification. We recenter the reduced-form parameter around its \emph{least-favorable} configuration and consider drifting parameter sequences that yield both diminishing levels of sampling uncertainty and of partial identification. We characterize the limiting decision problem as a normal location shift model with a suitable limiting identified set. We apply our results to treatment choice problems with contaminated outcomes, to robust welfare analyses with partially identified consumer surplus, and to the problem of aggregating experimental estimates for policy adoption.

Problem

• treatment choice
• partial identification
• asymptotics
• decision theory
• policy adoption

Innovation

• partial identification
• asymptotic framework
• treatment choice
• least-favorable configuration
• normal location shift model