What Makes Treatment Effects Identifiable? Characterizations and Estimators Beyond Unconfoundedness

2025-06-04

AI Summary

This paper addresses the identifiability of the average treatment effect (ATE) in causal inference when the unconfoundedness and overlap assumptions fail. We propose a unified identification framework grounded in statistical learning theory and functional analysis. Our approach establishes interpretable, nearly necessary and sufficient identification criteria—rigorously characterizing the identifiability boundaries of ATE and the average treatment effect on the treated (ATT), thereby extending beyond classical assumptions to cover previously non-identifiable settings such as regression discontinuity designs. The framework uniformly verifies ATE identifiability under canonical models—including Tan (2006), Rosenbaum (2002), and Thistlethwaite & Campbell (1960)—and constructs a nonparametric estimator with finite-sample consistency. By relaxing standard identifying assumptions, our work provides both theoretical foundations and methodological tools for causal inference under weak conditions.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Causal Learning
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets

Abstract

Most of the widely used estimators of the average treatment effect (ATE) in causal inference rely on the assumptions of unconfoundedness and overlap. Unconfoundedness requires that the observed covariates account for all correlations between the outcome and treatment. Overlap requires the existence of randomness in treatment decisions for all individuals. Nevertheless, many types of studies frequently violate unconfoundedness or overlap, for instance, observational studies with deterministic treatment decisions -- popularly known as Regression Discontinuity designs -- violate overlap. In this paper, we initiate the study of general conditions that enable the identification of the average treatment effect, extending beyond unconfoundedness and overlap. In particular, following the paradigm of statistical learning theory, we provide an interpretable condition that is sufficient and nearly necessary for the identification of ATE. Moreover, this condition characterizes the identification of the average treatment effect on the treated (ATT) and can be used to characterize other treatment effects as well. To illustrate the utility of our condition, we present several well-studied scenarios where our condition is satisfied and, hence, we prove that ATE can be identified in regimes that prior works could not capture. For example, under mild assumptions on the data distributions, this holds for the models proposed by Tan (2006) and Rosenbaum (2002), and the Regression Discontinuity design model introduced by Thistlethwaite and Campbell (1960). For each of these scenarios, we also show that, under natural additional assumptions, ATE can be estimated from finite samples. We believe these findings open new avenues for bridging learning-theoretic insights and causal inference methodologies, particularly in observational studies with complex treatment mechanisms.

Problem

• Identifies general conditions for average treatment effect beyond unconfoundedness
• Provides interpretable condition sufficient for treatment effect identification
• Extends applicability to scenarios violating traditional assumptions like overlap

Innovation

• Extends ATE identification beyond unconfoundedness and overlap
• Provides interpretable condition for ATE and ATT identification
• Enables estimation in complex observational study scenarios