Optimal Policy Choices Under Uncertainty

Sarah Moon

Papers from arXiv.org

Abstract: Policymakers often make changes to policies whose benefits and costs are unknown and must be inferred from statistical estimates in empirical studies. In this paper I consider the problem of a planner who changes upfront spending on a set of policies to maximize social welfare but faces statistical uncertainty about the impact of those changes. I set up a local optimization problem that is tractable under statistical uncertainty and solve for the local change in spending that maximizes the posterior expected rate of increase in welfare. I propose an empirical Bayes approach to approximating the optimal local spending rule, which solves the planner's local problem with posterior mean estimates of benefits and net costs. I show theoretically that the empirical Bayes approach performs well by deriving rates of convergence for the rate of increase in welfare. These rates converge for a large class of decision problems, including those where rates from a sample plug-in approach do not.

Date: 2025-03, Revised 2025-08
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