Causal Inference for Aggregated Treatment

TL;DR

This paper examines the challenges of causal inference with aggregated treatments, highlighting issues with the weights used in marginal effects, and proposes methods to address these problems based on sub-treatment observability.

Contribution

It reveals fundamental issues with marginal causal effects in aggregated treatments and offers solutions tailored to whether sub-treatments are observed or not.

Findings

Weights are non-unique and can be negative in aggregated causal effects.

Problems increase exponentially with more sub-treatments and larger support.

Proposed approaches mitigate issues depending on sub-treatment observability.

Abstract

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.