Possibilistic Instrumental Variable Regression

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.

💡 Research Summary

This paper introduces a novel framework for instrumental variable (IV) regression that leverages possibility theory to handle potential violations of the exogeneity assumption. Traditional IV methods require three core conditions: relevance (the instrument affects the treatment), unconfoundedness (the instrument is not correlated with unobserved confounders), and exclusion (the instrument influences the outcome only through the treatment). While relevance can often be verified, the latter two are frequently doubtful in applied work, leading to biased estimates when invalid instruments are used.

The authors propose to replace the conventional probabilistic prior with a possibility function—a mapping from the parameter space to