Instrumental Variable Analysis Without Structural Equations

2026-04-27

AI Summary

Traditional instrumental variable methods rely on the stringent assumption that the structural equation model holds exactly—a condition often violated in practice, leading to invalid inference. This work proposes a novel inference framework based on debiased least squares and inverse problem regularization, which defines a target parameter that coincides with conventional estimands when the structural model is correctly specified yet remains well-defined and inferable even under model misspecification. By relaxing the requirement of exact structural equation validity, the approach ensures robust statistical inference under substantially weaker conditions, thereby significantly enhancing the reliability and applicability of instrumental variable methods in realistic settings.

Technology Category

• Reasoning under Uncertainty: Probabilistic Inference
• Machine Learning: Structured Learning
• Intelligent Robots: State Estimation

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

We consider debiased inference on least-squares solutions to inverse problems as a way to avoid having to assume exact solutions exist. Such assumptions are substantive and not innocuous and their failure may well imperil inference when we impose them on the statistical model. Our approach instead allows us to conduct inference on a quantity that is defined regardless of solutions existing and coincides with the usual estimands when they do. For the case of instrumental variables, this means we can motivate the analysis with structural models but these do not need to hold exactly for the inferential procedure to remain valid.

Problem

• Instrumental Variable
• Inverse Problems
• Structural Equations
• Debiased Inference
• Least-Squares Solutions

Innovation

• Instrumental Variable
• Debiased Inference
• Inverse Problems
• Structural Equations
• Least-Squares Solutions