Working Paper: NBER ID: w25528
Authors: Brigham R. Frandsen; Lars J. Lefgren; Emily C. Leslie
Abstract: 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.
Keywords: judicial decision-making; pretrial release; causal inference; instrumental variables
JEL Codes: C26; K14
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| judge assignment (K40) | average outcomes (P17) |
| judge propensity (C52) | average outcomes (P17) |
| judge propensity (C52) | marginal treatment effect (C22) |
| average outcomes (P17) | judge propensity (C52) |
| exclusion restriction violation (C24) | alternative assumptions for causal interpretation (C32) |
| monotonicity assumption violation (D11) | alternative assumptions for causal interpretation (C32) |
| rejection of null hypothesis (C12) | violation of exclusion restriction or monotonicity assumption (C24) |