Instrumental variable based estimation of a causal effect has emerged as a standard approach to mitigate confounding bias in the social sciences and epidemiology, where conducting randomized experiments can be too costly or impossible. However, justifying the validity of the instrument often poses a significant challenge. In this work, we highlight a problem generally neglected in arguments for instrumental variable validity: the presence of an ''aggregate treatment variable'', where the treatment (e.g., education, GDP, caloric intake) is composed of finer-grained components that each may have a different effect on the outcome. We show that the causal effect of an aggregate treatment is generally ambiguous, as it depends on how interventions on the aggregate are instantiated at the component level, formalized through the aggregate-constrained component intervention distribution. We then characterize conditions on the interventional distribution and the aggregate setting under which standard instrumental variable estimators identify the aggregate effect. The contrived nature of these conditions implies major limitations on the interpretation of instrumental variable estimates based on aggregate treatments and highlights the need for a broader justificatory base for the exclusion restriction in such settings.

翻译：基于工具变量的因果效应估计已成为社会科学和流行病学中缓解混杂偏倚的标准方法，在这些领域进行随机实验可能成本过高或无法实施。然而，论证工具变量的有效性常常构成重大挑战。本研究聚焦于工具变量有效性论证中普遍被忽视的一个问题：即"聚合处理变量"的存在——当处理变量（如教育水平、GDP、热量摄入）由更细粒度的组分构成，且各组分对结果可能具有不同影响时。我们证明，聚合处理的因果效应通常具有模糊性，因为它取决于聚合层面的干预如何通过组分层面的干预具体实现，这一关系通过聚合约束的组分干预分布形式化表述。随后，我们刻画了在何种干预分布条件与聚合设定下，标准工具变量估计量能够识别聚合效应。这些条件的非自然特性表明，基于聚合处理的工具变量估计在解释上存在根本局限，并凸显了在此类情境中为排除限制假设构建更广泛论证基础的必要性。