Double Machine Learning of Continuous Treatment Effects with General Instrumental Variables
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866908956366995456 |
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| author | Chen, Shuyuan Zhang, Peng Cui, Yifan |
| author_facet | Chen, Shuyuan Zhang, Peng Cui, Yifan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_01471 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Double Machine Learning of Continuous Treatment Effects with General Instrumental Variables Chen, Shuyuan Zhang, Peng Cui, Yifan Statistics Theory Econometrics Methodology Machine Learning 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. |
| title | Double Machine Learning of Continuous Treatment Effects with General Instrumental Variables |
| topic | Statistics Theory Econometrics Methodology Machine Learning |
| url | https://arxiv.org/abs/2601.01471 |