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

2026-01-28

AI Summary

This study systematically reconstructs Pearl’s causal hierarchy from the potential outcomes framework, mapping causal estimands at each level to distinct features of the potential outcomes distribution and analyzing their identifiability conditions and strategies. By integrating the potential outcomes model, structural causal models, and formal classification methods, this work establishes—for the first time—a comprehensive taxonomy of Pearl’s causal hierarchy from the perspective of potential outcomes. The analysis not only clarifies the identification challenges inherent to estimands at each level but also deepens understanding of Level 3 (counterfactual) estimands. Furthermore, it reveals that higher-level estimands rely on stronger identification assumptions and correspond to richer information in the potential outcomes distribution, thereby offering a novel theoretical and practical perspective for causal inference.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Causal Learning
• Knowledge Representation and Reasoning: Action, Change, and Causality

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

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.

Problem

• causal hierarchy
• potential outcomes
• identifiability
• causal estimands
• structural causal models

Innovation

• causal hierarchy
• potential outcomes
• identifiability
• causal estimands
• structural causal models