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Main Authors: Song, Yilin, Guo, F. Richard, Chan, K. C. Gary, Richardson, Thomas S.
Format: Preprint
Published: 2024
Subjects:
Online Access:https://arxiv.org/abs/2405.09510
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author Song, Yilin
Guo, F. Richard
Chan, K. C. Gary
Richardson, Thomas S.
author_facet Song, Yilin
Guo, F. Richard
Chan, K. C. Gary
Richardson, Thomas S.
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2405_09510
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle The Categorical Instrumental Variable Model: Characterization, Partial Identification, and Statistical Inference
Song, Yilin
Guo, F. Richard
Chan, K. C. Gary
Richardson, Thomas S.
Statistics Theory
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.
title The Categorical Instrumental Variable Model: Characterization, Partial Identification, and Statistical Inference
topic Statistics Theory
url https://arxiv.org/abs/2405.09510