Empirical Bayes Counterfactuals in Poisson Regression with an Application to Police Use of Deadly Force

This paper uses an Empirical Bayes approach to estimate the conditional mean function of a Poisson regression model, evaluated at counterfactual values of time-invariant unobserved covariates. The application that motivates and illustrates the methods developed herein is the use of deadly force by police officers in the United States. We construct a yearly panel of lethal encounters covering the period 2013-2018, focusing on law enforcement agencies, rather than cities or states. We estimate counterfactuals for the nation's ten largest police departments by population served, and show that feasible changes in both observed and unobserved characteristics could result in a significant reduction in lethal encounters