A Sharp Test for the Judge Leniency Design

We propose sharp testable implications and tests to jointly assess the random assignment, exclusion, and monotonicity assumptions in judge leniency designs. Our procedures accommodate various data scenarios in which the number of defendants handled by a judge may be either small or large, and allow for discrete or continuous instrumental variables. When the validity of the design is rejected, a variant of the marginal treatment effect can be identified under weaker assumptions. We apply our test to the Philadelphia court data studied by Stevenson (2018) and demonstrate that it outperforms non-sharp joint tests by significant margins in simulation studies