Instrumental variables (IVs) are a popular and powerful tool for estimating causal effects in the presence of unobserved confounding. However, classical approaches rely on strong assumptions such as the $\textit{exclusion criterion}$, which states that instrumental effects must be entirely mediated by treatments. This assumption often fails in practice. When IV methods are improperly applied to data that do not meet the exclusion criterion, estimated causal effects may be badly biased. In this work, we propose a novel solution that provides $\textit{partial}$ identification in linear models given a set of $\textit{leaky instruments}$, which are allowed to violate the exclusion criterion to some limited degree. We derive a convex optimization objective that provides provably sharp bounds on the average treatment effect under some common forms of information leakage, and implement inference procedures to quantify the uncertainty of resulting estimates. We demonstrate our method in a set of experiments with simulated data, where it performs favorably against the state of the art.

翻译：工具变量（IV）是存在未观测混杂因素时估计因果效应的常用且强大的工具。然而，经典方法依赖于严格假设，例如$\textit{排除准则}$，该准则要求工具变量的效应必须完全由处理变量中介。这一假设在实践中常不成立。当IV方法被不恰当地应用于不满足排除准则的数据时，估计的因果效应可能出现严重偏差。在本工作中，我们提出一种新颖的解决方案，在给定一组$\textit{泄漏工具变量}$的条件下在线性模型中实现$\textit{部分}$识别，这些工具变量允许在有限程度上违反排除准则。我们推导出一个凸优化目标，该目标在某些常见的信息泄漏形式下能够提供平均处理效应的可证明的紧凑界限，并实现推断程序以量化估计结果的不确定性。我们通过一系列模拟数据实验展示了该方法，其表现优于当前最先进的方法。