A Sharp Test for the Judge Leniency Design

TL;DR

This paper develops sharp, testable implications for judge leniency designs, enabling rigorous assessment of key assumptions and improving upon existing non-sharp tests, with practical application to Philadelphia court data.

Contribution

It introduces a novel set of sharp tests for judge leniency assumptions, accommodating various data types and instrumental variables, and offers methods for partial identification when assumptions fail.

Findings

The proposed tests effectively detect violations of key assumptions.

Application to Philadelphia data reveals potential assumption violations.

Simulation studies show the tests outperform existing non-sharp methods.

Abstract

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