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Possibilistic Instrumental Variable Regression

Author

Listed:
  • Gregor Steiner
  • Jeremie Houssineau
  • Mark F. J. Steel

Abstract

Instrumental variable regression is a common approach for causal inference in the presence of unobserved confounding. However, identifying valid instruments is often difficult in practice. In this paper, we propose a novel method based on possibility theory that performs posterior inference on the treatment effect, conditional on a user-specified set of potential violations of the exogeneity assumption. Our method can provide informative results even when only a single, potentially invalid, instrument is available, offering a natural and principled framework for sensitivity analysis. Simulation experiments and a real-data application indicate strong performance of the proposed approach.

Suggested Citation

  • Gregor Steiner & Jeremie Houssineau & Mark F. J. Steel, 2025. "Possibilistic Instrumental Variable Regression," Papers 2511.16029, arXiv.org.
    • Handle: RePEc:arx:papers:2511.16029
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    References listed on IDEAS

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    1. Frank Windmeijer & Xiaoran Liang & Fernando P. Hartwig & Jack Bowden, 2021. "The confidence interval method for selecting valid instrumental variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 83(4), pages 752-776, September.
    2. Frank Windmeijer & Helmut Farbmacher & Neil Davies & George Davey Smith, 2019. "On the Use of the Lasso for Instrumental Variables Estimation with Some Invalid Instruments," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(527), pages 1339-1350, July.
    3. Gregor Steiner & Mark Steel, 2025. "Bayesian Model Averaging in Causal Instrumental Variable Models," Papers 2504.13520, arXiv.org, revised Sep 2025.
    4. Hyunseung Kang & Anru Zhang & T. Tony Cai & Dylan S. Small, 2016. "Instrumental Variables Estimation With Some Invalid Instruments and its Application to Mendelian Randomization," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(513), pages 132-144, March.
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    6. Siddhartha Chib & Minchul Shin & Anna Simoni, 2018. "Bayesian Estimation and Comparison of Moment Condition Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(524), pages 1656-1668, October.
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    8. Ryan Martin & Chuanhai Liu, 2013. "Inferential Models: A Framework for Prior-Free Posterior Probabilistic Inference," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(501), pages 301-313, March.
    9. Small, Dylan S., 2007. "Sensitivity Analysis for Instrumental Variables Regression With Overidentifying Restrictions," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 1049-1058, September.
    10. Zijian Guo & Hyunseung Kang & T. Tony Cai & Dylan S. Small, 2018. "Confidence intervals for causal effects with invalid instruments by using two‐stage hard thresholding with voting," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 80(4), pages 793-815, September.
    11. Michal Kolesár & Raj Chetty & John Friedman & Edward Glaeser & Guido W. Imbens, 2015. "Identification and Inference With Many Invalid Instruments," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 33(4), pages 474-484, October.
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