Possibilistic Instrumental Variable Regression with Potentially Invalid Instruments

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.