Optimal Estimation when Researcher and Social Preferences are Misaligned

Econometric analysis typically focuses on the statistical properties of fixed estimators. In practice, however, researchers may have preferences over estimates and engage in specification searches. In this paper, I approach the analysis of experimental data as a mechanism-design problem. Specifically, I focus on covariate adjustments, which can increase precision, but open the door to bias when researchers search through specifications. First, I derive a justification for unbiasedness as a mini-max optimal requirement on estimation that aligns researchers’ preferences with the minimization of the mean-squared error relative to the true treatment effect. Second, I provide a constructive characterization of all unbiased estimators as sample-splitting procedures. Third, I show that a researcher restricted to the class of unbiased estimators will solve a prediction problem. The duality between unbiased