Inference on Nonlinear Counterfactual Functionals under a Multiplicative IV Model

2025-07-21

AI Summary

This paper addresses the causal identification of nonlinear counterfactual functionals—such as quantile treatment effects—under unobserved confounding. We propose a moment condition framework grounded in the multiplicative instrumental variable (MIV) model. By constructing a system of nonlinear moment equations that ensures identifiability, we develop an efficient, multiply robust estimator, thereby extending instrumental variable (IV) methods beyond their traditional scope of average treatment effects. Theoretically, our estimator is shown to be asymptotically efficient and doubly robust—consistent if either the outcome or instrument propensity model is correctly specified. Monte Carlo simulations demonstrate its strong finite-sample performance even with moderate sample sizes. This work substantially broadens the applicability of IV methods to complex causal parameters, particularly distributional treatment effects, offering a novel tool for policy evaluation and heterogeneous effect analysis.

Technology Category

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

Application Category

• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Security and Privacy: Large-scale security measurements

Abstract

Instrumental variable (IV) methods play a central role in causal inference, particularly in settings where treatment assignment is confounded by unobserved variables. IV methods have been extensively developed in recent years and applied across diverse domains, from economics to epidemiology. In this work, we study the recently introduced multiplicative IV (MIV) model and demonstrate its utility for causal inference beyond the average treatment effect. In particular, we show that it enables identification and inference for a broad class of counterfactual functionals characterized by moment equations. This includes, for example, inference on quantile treatment effects. We develop methods for efficient and multiply robust estimation of such functionals, and provide inference procedures with asymptotic validity. Experimental results demonstrate that the proposed procedure performs well even with moderate sample sizes.

Problem

• Identify causal effects using multiplicative IV model
• Estimate nonlinear counterfactual functionals robustly
• Infer quantile treatment effects asymptotically

Innovation

• Uses multiplicative IV model for causal inference
• Enables identification of counterfactual functionals
• Develops efficient multiply robust estimation methods