Carolina Caetano, Gregorio Caetano, Brantly Callaway, Derek Dyal
arXiv 28 Jun 2025 · Econometrics
arXiv:2506.22885 · PDF · DOI · OpenAlex · Extracted main text
In this paper, we study causal inference when the treatment variable is an aggregation of multiple sub-treatment variables. Researchers often report marginal causal effects for the aggregated treatment, implicitly assuming that the target parameter corresponds to a well-defined average of sub-treatment effects. We show that, even in an ideal scenario for causal inference such as random assignment, the weights underlying this average have some key undesirable properties: they are not unique, they can be negative, and, holding all else constant, these issues become exponentially more likely to occur as the number of sub-treatments increases and the support of each sub-treatment grows. We propose approaches to avoid these problems, depending on whether or not the sub-treatment variables are observed.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Caetano, Carolina, Caetano, Gregorio, Nielsen, Eric (2024) Are children spending too much time on enrichment activities? self | 0.874 | 6 | 2 | 100% |
| 2 | D'Haultfoeuille, Xavier (2020) Two-way fixed effects estimators with heterogeneous treatment effects | 0.843 | 4 | 3 | 75% |
| 3 | Rubin, Donald (1980) Randomization analysis of experimental data: The Fisher randomization test comment | 0.737 | 3 | 2 | 100% |
| 4 | VanderWeele, Tyler, Hernán, Miguel (2013) Causal inference under multiple versions of treatment | 0.737 | 3 | 2 | 100% |
| 5 | Imbens, Guido, Rubin, Donald (2015) Causal Inference in Statistics, Social, and Biomedical Sciences | 0.737 | 3 | 2 | 100% |
| 6 | Hernán, Miguel (2016) Does water kill? A call for less casual causal inferences. | 0.644 | 3 | 2 | 67% |
| 7 | Yitzhaki, Shlomo (1996) On using linear regressions in welfare economics | 0.644 | 3 | 2 | 67% |
| 8 | Hernán, Miguel, VanderWeele, Tyler (2011) Compound treatments and transportability of causal inference | 0.644 | 2 | 2 | 100% |
| 9 | Mejia, Daniel, Restrepo, Pascual (2016) Crime and conspicuous consumption | 0.644 | 2 | 2 | 100% |
| 10 | (2009) Brief report: Concerning the consistency assumption in causal inference | 0.644 | 2 | 2 | 100% |
Showing the top 10 of 59 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Heterogeneity Analysis with Heterogeneous Treatments | 0.644 | 2 | 2 |
| 2 | Finite Population Identification and Design-Based Sensitivity Analysis | 0.405 | 1 | 1 |