We study identification and estimation of the average partial effect in an instrumental variable correlated random coefficients model with continuously distributed endogenous regressors. This model allows treatment effects to be correlated with the level of treatment. The main result shows that the average partial effect is identified by averaging coefficients obtained from a collection of ordinary linear regressions that condition on different realizations of a control function. These control functions can be constructed from binary or discrete instruments, which may affect the endogenous variables heterogeneously. Our results suggest a simple estimator that can be implemented with a companion Stata module.

中文翻译：

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工具变量相关随机系数模型的辨识

我们研究具有连续分布的内生回归变量的工具变量相关随机系数模型中平均部分效应的识别和估计。该模型使治疗效果与治疗水平相关。主要结果表明，平均局部效果是通过对从一组普通线性回归中获得的系数进行平均来确定的，这些线性回归的条件是控制函数的不同实现。这些控制功能可以从二进制或离散的仪器中构建，这可能会异质地影响内生变量。我们的结果提出了一个简单的估算器，可以与配套的Stata模块一起实现。