# Lost in Aggregation: The Causal Interpretation of the IV Estimand

arXiv: https://arxiv.org/abs/2601.12120 · HTML: https://mlsanity.com/paper/2601.12120/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 47 references that are in the map.
- First posted on arXiv 17 Jan 2026.

## Builds on (most cited first, 4 of 4)

- [Meaningful Causal Aggregation and Paradoxical Confounding](https://mlsanity.com/paper/2304.11625/) (2023)
- [How Much Should We Trust Instrumental Variable Estimates in Political Science? Practical Advice Based on Over 60 Replicated Studies](https://mlsanity.com/paper/2303.11399/) (2023)
- [A Latent Mixture Model for Heterogeneous Causal Mechanisms in Mendelian Randomization](https://mlsanity.com/paper/2007.06476/) (2020)
- [The impact of coarsening an exposure on partial identifiability in instrumental variable settings](https://mlsanity.com/paper/2401.17735/) (2024)

## Abstract (arXiv)

Instrumental variable estimation has emerged as a standard approach to mitigating confounding bias in the social sciences and epidemiology, where conducting randomized experiments can be too costly or infeasible. However, justifying the validity of the instrument is frequently challenging. 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, unobserved components that each may have a different effect on the outcome. While the aggregation problem itself is general, our focus is on instrumental variable estimation in a linear setting, the regime underlying much of applied IV practice. We show that the causal effect of an aggregate treatment is generally ambiguous, as it depends on how an intervention on the aggregate is instantiated at the component level. We formalize this relation using the aggregate-constrained component intervention distribution (ACID). We then identify two key conditions 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.