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 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).

We survey the literature on global capital allocation. We begin by reviewing the rise of cross-border investment, the shift towards portfolio investment, and the literature focusing on aggregate patterns in multilateral and bilateral positions. We then turn to the recent literature that uses micro-data to document patterns in global capital allocations. We focus on the importance of the currency of denomination of assets in international portfolios and the role that tax havens and offshore financial centers play in intermediating global capital. We conclude with directions for future research in this area.