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 systems 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. An accompanying $\texttt{R}$ package, $\texttt{leakyIV}$, is available from $\texttt{CRAN}$.

翻译：工具变量（IVs）是在存在未观测混杂因素时估计因果效应的常用且强大工具。然而，经典方法依赖于诸如$\textit{排除准则}$等强假设，即工具效应必须完全通过治疗变量传递。这一假设在实践中常不成立。当IV方法被错误应用于不满足排除准则的数据时，估计的因果效应可能产生严重偏差。本研究提出一种创新解决方案，针对线性系统，在允许工具变量在有限程度上违反排除准则（即$\textit{泄漏工具变量}$）时，实现因果效应的$\textit{部分}$识别。我们推导出一个凸优化目标函数，可在常见信息泄漏形式下提供平均处理效应的可证明紧致边界，并实施推断程序量化估计结果的不确定性。通过模拟数据集实验验证，该方法相较于现有最优方法表现更优。配套的$\texttt{R}$语言程序包$\texttt{leakyIV}$已发布于$\texttt{CRAN}$。