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.

翻译：连续处理效应的因果推断是实践中的常见问题，例如在研究剂量-反应函数时。经典分析通常假设所有混杂因素均被完全观测，而在实际应用中，未观测混杂往往持续存在。本文提出了一种利用工具变量局部识别剂量-反应函数的新框架，从而减轻由未观测混杂引起的偏差。我们引入了均匀正则加权函数的概念，并考虑用有限个开集覆盖处理空间。在每个开集上，这样的加权函数存在，使我们能够在相应区域内局部识别剂量-反应函数。对于估计问题，我们在带有工具变量的去偏机器学习框架下，为连续处理开发了一种增广逆概率加权评分。当通过核回归或经验风险最小化估计剂量-反应函数时，我们进一步建立了其渐近性质。最后，我们通过模拟和实证研究评估了所提方法在有限样本下的表现。