Lost in Aggregation: The Causal Interpretation of the IV Estimand

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.