The Categorical Instrumental Variable Model: Characterization, Partial Identification, and Statistical Inference
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866912702537924608 |
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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 |