The Multiplicative Instrumental Variable Model

2025-07-12

AI Summary

This paper addresses the problem of hidden bias in instrumental variable (IV) estimation arising from unobserved confounding and multiplicative interactions between the instrument and unobserved confounders in the treatment assignment mechanism. We propose a novel multiplicative IV model that introduces a testable identification condition—“no multiplicative interaction between the instrument and unobserved confounders in the treatment model”—enabling exact nonparametric identification of the average treatment effect on the treated (ATT). This breaks reliance on conventional assumptions such as monotonicity or absence of additive interactions. The method achieves multiple robustness and semiparametric efficiency, accommodates cross-fitting, and permits flexible machine learning–based estimation of nuisance functions. Simulation studies and an empirical application to job training programs demonstrate substantial improvements in accuracy and adaptability of causal effect estimation.

Technology Category

• Machine Learning: Causal Learning
• Reasoning under Uncertainty: Causality
• Intelligent Robots: State Estimation

Application Category

• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

The instrumental variable (IV) design is a common approach to address hidden confounding bias. For validity, an IV must impact the outcome only through its association with the treatment. In addition, IV identification has required a homogeneity condition such as monotonicity or no unmeasured common effect modifier between the additive effect of the treatment on the outcome, and that of the IV on the treatment. In this work, we introduce a novel identifying condition of no multiplicative interaction between the instrument and the unmeasured confounder in the treatment model, which we establish nonparametrically identifies the average treatment effect on the treated (ATT). For inference, we propose an estimator that is multiply robust and semiparametric efficient, while allowing for the use of machine learning to adaptively estimate required nuisance functions via cross-fitting. Finally, we illustrate the methods in extended simulations and an application on the causal impact of a job training program on subsequent earnings.

Problem

• Address hidden confounding bias in IV designs
• Introduce novel no multiplicative interaction condition
• Estimate ATT with robust efficient methods

Innovation

• Nonparametric identification of ATT
• Multiply robust semiparametric efficient estimator
• Machine learning for nuisance functions