Causal Inference for Aggregated Treatment

2025-06-28

AI Summary

This paper addresses a fundamental bias in interpreting marginal causal effects when the treatment variable is an aggregate of multiple sub-treatments. Under randomization, conventional approaches interpret the aggregate effect as a weighted average of sub-treatment effects—but the implied weights are non-unique, potentially negative, and deteriorate exponentially as the number and support size of sub-treatments grow. Building on the potential outcomes framework, the paper systematically identifies the structural origins of this problem and proposes novel, identifiable, unbiased, and robust estimators—separately for settings where sub-treatments are observable or unobservable. Key contributions include: (i) the first formal characterization of the ill-posedness of implicit weights in aggregated treatments, challenging the “natural averaging” assumption; (ii) the construction of alternative causal parameters that ensure valid interpretation; and (iii) substantial improvements in accuracy and interpretability of causal inference under multi-level, high-dimensional discrete treatment structures.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Causal Learning
• Multiagent Systems: Mechanism Design

Application Category

• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

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.

Problem

• Analyzing causal effects of aggregated treatment variables
• Addressing undesirable properties in sub-treatment effect averaging
• Proposing solutions for observed and unobserved sub-treatments

Innovation

• Aggregated treatment causal inference analysis
• Identifies undesirable weights in averaging effects
• Proposes solutions for observed sub-treatments