Double Machine Learning of Continuous Treatment Effects with General Instrumental Variables

TL;DR

This paper introduces a novel framework for estimating causal effects of continuous treatments using instrumental variables, addressing unmeasured confounding with a debiased machine learning approach and local identification techniques.

Contribution

It proposes a new identification strategy with uniform regular weighting functions and an augmented inverse probability weighted score for continuous treatments.

Findings

The method effectively mitigates bias from unobserved confounders.

Asymptotic properties are established for kernel and empirical risk minimization estimators.

Simulation and empirical studies demonstrate finite-sample performance.

Abstract

Estimating causal effects of continuous treatments is a common problem in practice, for example, in studying average 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 the identification of average 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 average dose-response function locally within the corresponding region. For estimation, we propose an augmented inverse probability weighted score for continuous treatments with instrumental variables under a debiased machine learning framework, and provide practical guidance to adaptively establish regular weighting functions from the data. We further establish the asymptotic properties when the average 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.