Possibilistic Instrumental Variable Regression with Potentially Invalid Instruments

Gregor Steiner; Jeremie Houssineau; Mark F. J. Steel

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arXiv · 2511.16029

Possibilistic Instrumental Variable Regression with Potentially Invalid Instruments

Gregor Steiner·Jeremie Houssineau·Mark F. J. Steel

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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 instrument exogeneity assumption. Our method can provide valid results even when only a single, potentially invalid, instrument is available. Crucially, and in contrast with existing methods, we prove a finite-sample coverage guarantee for the exactly calibrated (validified) uncertainty intervals when the violation set contains the true value, and we provide practical MC/$\chi^2$ approximations. Simulation experiments and real-data applications indicate strong performance of the proposed approach.

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Gregor Steiner, Jeremie Houssineau, Mark F. J. Steel. 2025-11-20. Possibilistic Instrumental Variable Regression with Potentially Invalid Instruments. https://arxiv.org/abs/2511.16029

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