Title: Optimal decision rules under partial identification
Authors: Kohei Yata - University of Wisconsin-Madison (United States) [presenting]
Abstract: A class of statistical decision problems is considered in which the policymaker must decide between two alternative policies to maximize social welfare (e.g., the population mean of an outcome) based on a finite sample. The central assumption is that the underlying, possibly infinite-dimensional parameter, lies in a known convex set, potentially leading to partial identification of the welfare effect. An example of such restrictions is the smoothness of counterfactual outcome functions. As the main theoretical result, we obtain a finite-sample decision rule (i.e., a function that maps data to a decision) that is optimal under the minimax regret criterion. This rule is easy to compute, yet achieves optimality among all decision rules; no ad hoc restrictions are imposed on the class of decision rules. We apply the results to the problem of whether to change a policy eligibility cutoff in a regression discontinuity setup. We illustrate the approach in an empirical application to the BRIGHT school construction program in Burkina Faso, where villages were selected to receive schools based on scores computed from their characteristics. Under reasonable restrictions on the smoothness of the counterfactual outcome function, the optimal decision rule implies that it is not cost-effective to expand the program.