Primary Submission Category: Instrumental Variables
Categorical Instrumental Variable Models: Characterization, Inference and Computation
Authors: Richard Guo, Yilin Song, K. C. Gary Chan, Thomas Richardson,
Presenting Author: Richard Guo*
The Minneapolis Domestic Violence Experiment, which evaluated police responses to domestic calls, is a classic example of a categorical instrumental variable (IV) model due to non-compliance with random assignment. In this setting, where the instrument, treatment, and outcome all take finitely many values, a general methodological framework for rigorous analysis has remained elusive, despite certain established results for binary IVs in the literature. For any categorical IV model, we derive a simple, closed-form characterization of the set of joint potential outcome distributions compatible with the observed data. We show that this characterization forms a system of non-redundant inequalities that unifies several IV models under varying independence and exclusion restriction assumptions. Building on this partial identification framework, we construct confidence intervals with simultaneous finite-sample coverage for linear functionals of the joint counterfactual distribution, such as pairwise average treatment effects, utilizing a tail bound on the Kullback-Leibler divergence. Finally, we develop specialized, highly efficient optimization algorithms to compute these intervals under the derived constraints. We demonstrate our method with a reanalysis of the Minneapolis data.