Instrumental variable methods are fundamental to causal inference when treatment assignment is confounded by unobserved variables. In this article, we develop a general nonparametric framework for identification and learning with multi-categorical or continuous instrumental variables. Specifically, we propose an additive instrumental variable framework to identify mean potential outcomes and the average treatment effect with a weighting function. Leveraging semiparametric theory, we derive efficient influence functions and construct consistent, asymptotically normal estimators via debiased machine learning. 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：当处理分配受到未观测变量混杂时，工具变量方法是因果推断的基础。本文针对多分类或连续工具变量，提出了一个通用的非参数识别与学习框架。具体而言，我们提出了一个加性工具变量框架，通过加权函数识别平均潜在结果与平均处理效应。基于半参数理论，我们推导了有效影响函数，并通过去偏机器学习构建了一致且渐近正态的估计量。本文进一步将方法拓展至纵向数据、动态处理策略以及乘性工具变量。我们通过模拟研究及分析《职业培训合作法案》项目的真实数据，验证了所提方法的有效性。