Optimal Estimation When Researcher and Social Preferences Are Misaligned

Econometric analysis typically focuses on the statistical properties of fixed estimators and ignores researcher choices. In this article, I instead approach the analysis of experimental data as a mechanism-design problem that acknowledges that researchers choose between estimators, sometimes based on the data and often according to their own preferences. Specifically, I focus on covariate adjustments, which can increase the precision of a treatment-effect estimate, but open the door to bias when researchers engage in specification searches. First, I establish that unbiasedness as a requirement on the estimation of the average treatment effect can align researchers' preferences with the minimization of the mean-squared error relative to the truth, and that fixing the bias can yield an optimal restriction in a minimax sense. Second, I provide a constructive characterization of treatment-effect estimators with fixed bias as sample-splitting procedures. Third, I discuss the implementation of second-best estimators that leave room for beneficial specification searches.