Presented By: Department of Economics
Multimargin Selection in Leniency Designs
Lonjezo Sithole, University of Michigan
Leniency designs use quasi-random assignment to decision makers with different treatment propensities to estimate causal effects. When decision makers weight unobserved case characteristics differently, a higher (lower) overall treatment rate can mask a lower (higher) probability of treating some case types. I develop a model with finitely many latent regimes, each representing a case type with its own potential outcome distributions and treatment probabilities that vary across decision-makers. The main identifying restriction is that, within a regime and conditional on observed characteristics, unobserved factors governing treatment decisions are independent of potential outcomes. Under the model, observed outcome distributions admit a finite mixture representation, and pairwise Wald estimands decompose into regime-specific treatment effects weighted by each regime’s share of the aggregate first stage. I give conditions for identifying the number of regimes, their treatment effects, and their weights using parametric restrictions on outcome distributions or auxiliary pretreatment measurements. I characterize when the weights are nonnegative and when they are constant across decision-maker pairs. I develop bootstrap tests of both restrictions and establish their pointwise asymptotic validity for a fixed number of regimes. Applying the model to Miami-Dade pretrial bail data, I find that some of the more lenient groups of judges release fewer defendants of the case type for whom release most reduces prison time.