Posterior Average Effects (joint with Martin Weidner)

Abstract:

The applied economist is often interested in computing an average with respect to a distribution of unobservables. Common examples are average partial effects in discrete choice, moments of individual fixed-effects in panel data, or counterfactual policy simulations based on a structural model. We consider empirical Bayes (EB) estimators of such effects, where the average is computed conditional on the observation sample. While EB estimators are sometimes used to “shrink” individual estimates – e.g., of teacher value-added or hospital quality – toward a common mean and reduce estimation noise, a study of their frequentist properties is still lacking. We establish two robustness properties of EB estimators under misspecification of the assumed distribution of unobservables: EB estimators are optimal in terms of local (worst-case) bias, and their global bias is no larger than twice the minimum bias that can be achieved within a large class of estimators of average effects. These results provide a rationale for the use of empirical Bayes estimators, beyond the settings to which they have been applied so far.