We tackle two limitations of standard instrumental variable regression in experimental and observational studies: restricted estimation to the conditional mean of the outcome and the assumption of a linear relationship between regressors and outcome. More flexible regression approaches that solve these limitations have already been developed but have not yet been adopted in causality analysis. The paper develops an instrumental variable estimation procedure building on the framework of generalized additive models for location, scale and shape. This enables modelling all distributional parameters of potentially complex response distributions and non‐linear relationships between the explanatory variables, instrument and outcome. The approach shows good performance in simulations and is applied to a study that estimates the effect of rural electrification on the employment of females and males in the South African province of KwaZulu‐Natal. We find positive marginal effects for the mean for employment of females rates, negative effects for employment of males and a reduced conditional standard deviation for both, indicating homogenization in employment rates due to the electrification programme. Although none of the effects are statistically significant, the application demonstrates the potentials of using generalized additive models for location, scale and shape in instrumental variable regression for both to account for endogeneity and to estimate treatment effects beyond the mean.

中文翻译：

---

灵活的工具变量分布回归

我们在实验和观察研究中解决了标准工具变量回归的两个局限性：将估计限制在结果的条件均值上，并假设回归变量与结果之间存在线性关系。解决这些局限性的更灵活的回归方法已经开发出来，但因果关系分析尚未采用。本文基于位置，比例和形状的通用加性模型的框架，开发了一种工具变量估计程序。这样就可以对潜在复杂响应分布的所有分布参数以及解释变量，工具和结果之间的非线性关系进行建模。该方法在模拟中显示出良好的性能，并应用于估计南非电气化对南非夸祖鲁-纳塔尔省农村劳动力电气化对就业的影响的研究。我们发现女性就业率的平均值具有正的边际效应，男性就业率具有负面影响，并且两者的条件标准偏差均减小，这表明由于电气化计划，就业率趋于均一。尽管这些影响在统计学上均不显着，但该应用程序证明了在工具变量回归中使用广义加性模型确定位置，比例和形状的可能性，既可以考虑内生性，也可以评估超出均值的治疗效果。我们发现女性就业率的平均值具有正的边际效应，男性就业率具有负面影响，并且两者的条件标准偏差均减小，这表明由于电气化计划，就业率趋于均一。尽管这些影响在统计学上均不显着，但该应用程序证明了在工具变量回归中使用广义加性模型确定位置，比例和形状的可能性，既可以考虑内生性，也可以评估超出均值的治疗效果。我们发现女性就业率的平均值具有正的边际效应，男性就业率具有负面影响，并且两者的条件标准偏差均减小，这表明由于电气化计划，就业率趋于均一。尽管这些影响均无统计学意义，但该应用程序证明了在工具变量回归中使用广义加性模型确定位置，比例和形状的潜力，既可以解释内生性，也可以估算超出均值的治疗效果。