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

TL;DR

This paper develops a comprehensive framework for categorical instrumental variable models, providing a simple characterization of potential outcomes, unifying various assumptions, and offering methods for statistical inference with finite-sample guarantees.

Contribution

It introduces a closed-form inequality-based characterization of potential outcomes in categorical IV models and constructs confidence intervals for linear functionals with finite-sample coverage.

Findings

Unified inequalities for potential outcomes in categorical IV models

Confidence intervals for treatment effects with finite-sample guarantees

Application to real data demonstrating practical utility

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 set of inequalities. These inequalities unify several different IV models defined by versions of the independence and exclusion restriction assumptions and are shown to be non-redundant. Finally, given a set of linear functionals of the joint counterfactual distribution, such as pairwise average treatment effects, 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.