Judging Judge Fixed Effects

We propose a test for the identifying assumptions invoked in designs based on random assignment to one of many "judges.'' We show that standard identifying assumptions imply that the conditional expectation of the outcome given judge assignment is a continuous function with bounded slope of the judge propensity to treat. The implication leads to a two-part test that generalizes the Sargan-Hansen overidentification test and assesses whether implied treatment effects across the range of judge propensities are possible given the domain of the outcome. We show the asymptotic validity of the testing procedure, demonstrate its finite-sample performance in simulations, and apply the test in an empirical setting examining the effects of pre-trial release on defendant outcomes in Miami. When the assumptions are not satisfied, we propose a weaker average monotonicity assumption under which IV still converges to a proper weighted average of treatment effects.