Instrumental variable methods are fundamental to causal inference when treatment assignment is confounded by unobserved variables. In this article, we develop a general nonparametric causal framework for identification and learning with multi-categorical or continuous instrumental variables. Specifically, the mean potential outcomes and the average treatment effect can be identified via a regular weighting function derived from the proposed framework. Leveraging semiparametric theory, we derive efficient influence functions and construct two consistent, asymptotically normal estimators via debiased machine learning. The first estimator uses a prespecified weighting function, while the second estimator selects the optimal weighting function adaptively. Extensions to longitudinal data, dynamic treatment regimes, and multiplicative instrumental variables are further developed. We demonstrate the proposed method by employing simulation studies and analyzing real data from the Job Training Partnership Act program.

翻译：工具变量方法是处理分配受未观测变量混杂时因果推断的基础。本文针对多分类或连续工具变量，构建了一个通用的非参数因果框架用于识别与学习。具体而言，平均潜在结果与平均处理效应可通过该框架导出的正则化加权函数进行识别。借助半参数理论，我们推导了有效影响函数，并通过去偏机器学习构建了两个具有一致性且渐近正态的估计量。第一个估计量使用预设的加权函数，而第二个估计量则自适应地选择最优加权函数。本文进一步将该方法扩展到纵向数据、动态处理机制以及乘法工具变量的场景。我们通过模拟研究及分析《职业培训伙伴法案》项目的真实数据，对所提方法进行了验证。