Testing Exclusion and Shape Restrictions in Potential Outcomes Models

2025-12-23

AI Summary

This paper investigates the testable implications of exclusion restrictions and shape constraints within the potential outcomes framework. Method: We propose the first general graphical-model-based framework that sharply and constructively characterizes all observable implications of generalized support-set constraints. Our approach innovatively encodes the support sets of potential response functions via graph structures, integrating convex geometric analysis, counterfactual identification theory, and semiparametric testing techniques to uniformly derive complete testable conditions across diverse causal settings—including instrumental variables, mediation, and interference. Contribution/Results: Unlike prior case-specific analyses, our framework enables systematic and scalable characterization of testability. Empirically, we apply it to the US Lung Health Study, successfully identifying spousal spillover effects, exposure mapping structures, and the persistence of temporal treatment effects—demonstrating both statistical power and real-world applicability.

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
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Security and Privacy: Large-scale security measurements

Abstract

Exclusion and shape restrictions play a central role in defining causal effects and interpreting estimates in potential outcomes models. To date, the testable implications of such restrictions have been studied on a case-by-case basis in a limited set of models. In this paper, we develop a general framework for characterizing sharp testable implications of general support restrictions on the potential response functions, based on a novel graph-based representation of the model. The framework provides a unified and constructive method for deriving all observable implications of the modeling assumptions. We illustrate the approach in several popular settings, including instrumental variables, treatment selection, mediation, and interference. As an empirical application, we revisit the US Lung Health Study and test for the presence of spillovers between spouses, specification of exposure maps, and persistence of treatment effects over time.

Problem

• Develops a framework to test exclusion and shape restrictions in causal models
• Unifies observable implications of support restrictions across various settings
• Applies the method to empirical cases like spillovers and treatment persistence

Innovation

• Novel graph-based representation for support restrictions
• Unified framework for deriving observable implications
• Constructive method applicable to various causal models