Monotonicity among Judges : Evidence from Judicial Panels and Consequences for Judge IV Designs

Judge IV designs rely on monotonicity—each judge being weakly stricter than more lenient judges in all cases. I directly measure monotonicity in judicial panels in four different settings and find that it is violated in up to fifty percent of cases. The monotonicity violations are not detected by conventional tests. A recent relaxation of monotonicity—under which 2SLS identifies a positively weighted average of treatment effects—is violated in only around ten percent of cases. I further propose a new monotonicity condition—violated in less than five percent of cases—under which an equally weighted local average treatment effect (LATE) is identified by standard marginal treatment effect (MTE) analysis. Since MTE estimates are hard to interpret when monotonicity is violated, I also show how to identify LATE under the same condition without relying on MTEs. Similar results are provided for the (local) average treatment effects on the treated and on the untreated. Overall, my results indicate that the bias in judge IV estimates due to monotonicity violations is small. Judge IV designs with many judges per randomization unit are especially robust to monotonicity violations