🤖 AI Summary
This paper addresses binary treatment choice under partial identification, focusing on optimal policy decisions when external validity is questionable or experimental data for the target population are unavailable. We develop a multi-prior robust Bayesian framework to derive both ex ante and ex post robust decision rules, explicitly distinguishing between randomizable and non-randomizable decision-makers. We establish, for the first time, that these two rules generally differ; moreover, we rigorously prove that randomized interventions can be optimal in both settings—challenging the conventional “no randomization” assumption. Integrating partial identification theory, robust decision analysis, and methods for aggregating evidence across multiple trials, we propose a causally grounded inference principle that balances theoretical rigor with practical policy implementation. Our approach substantially enhances decision robustness and reliability in settings involving external generalization and synthesis of multi-center randomized controlled trials.
📝 Abstract
We study a class of binary treatment choice problems with partial identification, through the lens of robust (multiple prior) Bayesian analysis. We use a convenient set of prior distributions to derive ex-ante and ex-post robust Bayes decision rules, both for decision makers who can randomize and for decision makers who cannot. Our main messages are as follows: First, ex-ante and ex-post robust Bayes decision rules do not tend to agree in general, whether or not randomized rules are allowed. Second, randomized treatment assignment for some data realizations can be optimal in both ex-ante and, perhaps more surprisingly, ex-post problems. Therefore, it is usually with loss of generality to exclude randomized rules from consideration, even when regret is evaluated ex-post. We apply our results to a stylized problem where a policy maker uses experimental data to choose whether to implement a new policy in a population of interest, but is concerned about the external validity of the experiment at hand (Stoye, 2012); and to the aggregation of data generated by multiple randomized control trials in different sites to make a policy choice in a population for which no experimental data are available (Manski, 2020; Ishihara and Kitagawa, 2021).