Double Machine Learning of Continuous Treatment Effects with General Instrumental Variables

2026-01-04

AI Summary

This study addresses the bias arising from unobserved confounding in causal effect estimation with continuous treatment variables by proposing a local identification framework based on instrumental variables. The approach achieves local identification of the dose–response function through the construction of uniformly positive regular weighting functions over multiple open subsets of the treatment space. It extends the double machine learning methodology to settings involving continuous treatments and general instrumental variables. By integrating augmented inverse probability weighting, kernel regression, and debiased machine learning techniques, the method yields an estimator whose asymptotic properties are rigorously established. Both simulation studies and empirical analyses demonstrate that the proposed estimator exhibits strong finite-sample performance.

Technology Category

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

Application Category

• Responsible Web: Machine-in-the-loop, human agency and autonomy
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Estimating causal effects of continuous treatments is a common problem in practice, for example, in studying dose-response functions. Classical analyses typically assume that all confounders are fully observed, whereas in real-world applications, unmeasured confounding often persists. In this article, we propose a novel framework for local identification of dose-response functions using instrumental variables, thereby mitigating bias induced by unobserved confounders. We introduce the concept of a uniform regular weighting function and consider covering the treatment space with a finite collection of open sets. On each of these sets, such a weighting function exists, allowing us to identify the dose-response function locally within the corresponding region. For estimation, we develop an augmented inverse probability weighting score for continuous treatments under a debiased machine learning framework with instrumental variables. We further establish the asymptotic properties when the dose-response function is estimated via kernel regression or empirical risk minimization. Finally, we conduct both simulation and empirical studies to assess the finite-sample performance of the proposed methods.

Problem

• continuous treatment effects
• unobserved confounding
• instrumental variables
• dose-response function
• causal inference

Innovation

• Double Machine Learning
• Continuous Treatment Effects
• Instrumental Variables
• Local Identification
• Debiased Machine Learning