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.

翻译：工具变量回归是存在未观测混杂时进行因果推断的常用方法。然而，在实践中识别有效工具变量往往较为困难。本文提出一种基于可能性理论的新方法，该方法在给定用户指定的外生性假设潜在违背集合条件下，对处理效应进行后验推断。即使仅存在单一且可能无效的工具变量，我们的方法仍能提供信息性结果，为敏感性分析提供了一个自然且原则性的框架。仿真实验与真实数据应用表明，所提方法具有优越的性能。