Causal inference for aggregated treatment
Carolina Caetano, Gregorio Caetano, Brantly Callaway, and Derek Dyal (2025)
Abstract
We study causal inference when the treatment variable is an aggregation of multiple sub-treatments. Researchers often report marginal effects for the aggregated treatment, implicitly assuming the target parameter corresponds to a well-defined average of sub-treatment effects. We show that, even under ideal conditions such as random assignment, the weights underlying this average have some key undesirable properties: they are not unique, can be negative, and, all else equal, these issues become exponentially more likely as the number of sub-treatments increases and their support grows. We propose diagnostics to detect these problems and introduce alternative approaches to circumvent them, depending on whether sub-treatments are observed.