Optimal Estimation when Researcher and Social Preferences are Misaligned

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Econometric analysis typically focuses on the statistical properties of fixed estimators and ignores researcher choices. In this article, I 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 is a requirement on the estimation of the average treatment effect that aligns 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 all treatment-effect estimators with fixed bias as sample-splitting procedures. Third, I show that a researcher restricted specifically to the class of unbiased estimators of the average treatment effect solves a prediction problem. The equivalence of unbiased estimation and prediction across sample splits characterizes all admissible unbiased procedures in finite samples, leaves space for beneficial specification searches, and offers an opportunity to leverage machine learning. As a practical implication, I describe flexible pre-analysis plans for randomized experiments that achieve efficiency without bias.

Last updated on 06/05/2018