Possibilistic Instrumental Variable Regression with Potentially Invalid Instruments

2025/11/20 by Steiner, Gregor, Houssineau, Jeremie, Steel, Mark F. J.
Mathematics · Computer Science · #Advanced Causal Inference Techniques #Bayesian Modeling and Causal Inference #Statistical Methods and Inference

paper · doi:10.48550/arxiv.2511.16029

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/χ² approximations. Simulation experiments and real-data applications indicate strong performance of the proposed approach.

Citations

• Possibilistic inferential models: a review
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• Plausibly Exogenous
• Fuzzy sets as a basis for a theory of possibility

Related

• BudgetIV: Optimal Partial Identification of Causal Effects with Mostly Invalid Instruments
• Necessary and Probably Sufficient Test for Finding Valid Instrumental\n Variables
• A Synthetic Instrumental Variable Method: Using the Dual Tendency Condition for Coplanar Instruments
• Identification and Robust Inference for Multiple Treatment Effects with Possibly Invalid Instruments
• Semi-Instrumental Variables: A Test for Instrument Admissibility