**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 choi ce, moments of individual fixed-effects in panel data, or counterfactual po licy simulations based on a structural model. We consider empirical Bayes ( EB) estimators of such effects, where the average is computed conditional o n 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 frequen tist properties is still lacking. We establish two robustness properties of EB estimators under misspecification of the assumed distribution of unobse rvables: 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 ach ieved within a large class of estimators of average effects. These results provide a rationale for the use of empirical Bayes estimators, beyond the s ettings to which they have been applied so far.

DTSTAMP:20200815T171617Z DTSTART:20190305T123000Z DTEND:20190305T133000Z SEQUENCE:0 TRANSP:OPAQUE END:VEVENT END:VCALENDAR