The Categorical Instrumental Variable Model: Characterization, Partial Identification, and Statistical Inference

Abstract

We study categorical instrumental variable (IV) models with instrument, treatment and outcome taking finitely many values. We derive a simple closed-form characterization of the set of joint distributions of potential outcomes that are compatible with a given observed data distribution in terms of a minimal set of inequalities. These inequalities unify several different IV models defined by versions of the independence and exclusion restriction assumptions. They lead to sharp bounds on causal functionals and provide a sharp criterion for model falsification. For linear functionals of the joint counterfactual distribution, such as pairwise average treatment effects and probabilities of potential outcomes, we construct confidence intervals with simultaneous finite-sample coverage, using a tail bound on the Kullback--Leibler divergence. We illustrate our method using data from the Minneapolis Domestic Violence Experiment.

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