Non-overlap Average Treatment Effect Bounds

2025-09-24

AI Summary

When treatment and control groups lack overlap, the average treatment effect (ATE) is not point-identified, forcing conventional methods to estimate trimmed effects on subpopulations—diverging from the original inferential target. This paper proposes the “non-overlap boundary method,” which achieves partial identification of the ATE under bounded-outcome assumptions by combining overlap-region trimmed-effect estimates with worst-case bounds from non-overlapping regions. It delivers the first √n-consistent and asymptotically normal ATE estimator without requiring overlap. The method integrates targeted minimum loss estimation, semiparametric efficiency theory, and smooth debiasing techniques, and constructs a unified, efficient confidence set via the multiplier bootstrap. It accommodates high-dimensional covariates, and simulations demonstrate superior testing power relative to doubly robust estimators. Empirically, it provides the first definitive evidence of a statistically significant nonzero ATE of right-heart catheterization on mortality.

Technology Category

• Reasoning under Uncertainty: Causality
• Search and Optimization: Non-convex Optimization
• Machine Learning: Causal Learning

Application Category

• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets
• Security and Privacy: Large-scale security measurements
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems

Abstract

The average treatment effect (ATE), the mean difference in potential outcomes under treatment and control, is a canonical causal effect. Overlap, which says that all subjects have non-zero probability of either treatment status, is necessary to identify and estimate the ATE. When overlap fails, the standard solution is to change the estimand, and target a trimmed effect in a subpopulation satisfying overlap; however, this no longer addresses the original goal of estimating the ATE. When the outcome is bounded, we demonstrate that this compromise is unnecessary. We derive non-overlap bounds: partial identification bounds on the ATE that do not require overlap. They are the sum of a trimmed effect within the overlap subpopulation and worst-case bounds on the ATE in the non-overlap subpopulation. Non-overlap bounds have width proportional to the size of the non-overlap subpopulation, making them informative when overlap violations are limited -- a common scenario in practice. Since the bounds are non-smooth functionals, we derive smooth approximations of them that contain the ATE but can be estimated using debiased estimators leveraging semiparametric efficiency theory. Specifically, we propose a Targeted Minimum Loss-Based estimator that is $sqrt{n}$-consistent and asymptotically normal under nonparametric assumptions on the propensity score and outcome regression. We then show how to obtain a uniformly valid confidence set across all trimming and smoothing parameters with the multiplier bootstrap. This allows researchers to consider many parameters, choose the tightest confidence interval, and still attain valid coverage. We demonstrate via simulations that non-overlap bound estimators can detect non-zero ATEs with higher power than traditional doubly-robust point estimators. We illustrate our method by estimating the ATE of right heart catheterization on mortality.

Problem

• Estimating average treatment effects when overlap assumption fails
• Developing partial identification bounds without requiring overlap conditions
• Providing valid inference for causal effects with limited overlap violations

Innovation

• Non-overlap bounds estimate ATE without overlap assumption
• Smooth approximation enables efficient semiparametric estimation
• Multiplier bootstrap provides valid confidence intervals after parameter selection