Association and causation: Attributes and effects of judges in equal employment opportunity commission litigation outcomes

Abstract

A large literature on judicial decision making asks if judges with different features of an attribute (e.g, sex, race) adjudicate cases differently. Researchers estimate models for case outcomes, interpreting coefficients associated with attributes as effects. But attributes are not treatments. While these coefficients indicate how judges with different features adjudicate the different cases they are assigned, ideally, different judges should be compared on a common set of cases. We construct a general methodology for making such comparisons, using it to study whether monetary relief in discrimination cases brought by the Equal Employment Opportunity Commission differs by judges’ race. For all federal judges (treatments) eligible to hear a case (unit), we define potential outcomes, using unit treatment effects between judges with different features to define a unit feature comparison (UFC), then using these to define new population estimands: the average (AFC) and quantile (QFC) feature comparisons. We estimate these quantities by combining observed case outcomes with missing potential outcomes imputed from the posterior predictive distribution of a two-part Bayesian hierarchical model. A case initially assigned to a non-white or African American judge is more likely to result in monetary relief than were that case initially assigned to an eligible white or non-African American judge. For the amount of relief, the 95% posterior interval for the AFC covers 0, while the upper endpoint of the 95% posterior interval for the median QFC is negative.