Position: A Potential Outcomes Perspective on Pearl's Causal Hierarchy

TL;DR

This paper reinterprets Pearl's causal hierarchy through the potential outcomes framework, providing a systematic classification of estimands, their identifiability challenges, and strategies, thereby deepening understanding of complex causal questions.

Contribution

It offers a formal, systematic mapping of causal estimands to hierarchy layers from a potential outcomes perspective, clarifying identifiability issues and strategies.

Findings

Higher hierarchy layers relate to richer potential outcomes features.

Stronger assumptions are needed for identification at higher layers.

The perspective clarifies challenges and strategies for complex causal estimands.

Abstract

Pearl's causal hierarchy has garnered sustained attention as a foundational lens for formulating and understanding causal questions, and has been extensively discussed within the framework of structural causal models. In this paper, we revisit the hierarchy from a potential outcomes perspective and provide a formal, systematic classification of how various causal estimands are mapped to specific layers. Building on this classification, we summarize key identifiability challenges for estimands at different layers and review general strategies for achieving identification under varying assumptions. Our perspective is both intuitive and theoretically grounded, as higher layers of the hierarchy correspond to progressively richer features of the potential outcomes distribution, which in turn require stronger assumptions for identification. We expect this perspective to help clarify and deepen understanding of various causal estimands, particularly those in the third layer of the causal hierarchy, along with their associated identifiability challenges, identifiability strategies, and application scenarios.