Optimal Policy Choices Under Uncertainty

Policymakers often face the decision of how to allocate resources across many different policies using noisy estimates of policy impacts. This paper develops a framework for optimal policy choices under statistical uncertainty. I consider a social planner who must choose upfront spending on a set of policies to maximize expected welfare. I show that, for small policy changes relative to the status quo, the posterior mean benefit and net cost of each policy are sufficient statistics for an oracle social planner who knows the true distribution of policy impacts. Since the true distribution is unknown in practice, I propose an empirical Bayes approach to estimate these posterior means and approximate the oracle planner. I derive finite-sample rates of convergence to the oracle planner's decision and show that, in contrast to empirical Bayes, plug-in methods can fail to converge. In an empirical application to 68 policies from Hendren and Sprung-Keyser (2020), I find welfare gains from the empirical Bayes approach and welfare losses from a plug-in approach, suggesting that careful incorporation of statistical uncertainty into policymaking can qualitatively change welfare conclusions.