Instrumental variables are a popular tool to infer causal effects under unobserved confounding, but choosing suitable instruments is challenging in practice. We propose gIVBMA, a Bayesian model averaging procedure that addresses this challenge by averaging across different sets of instrumental variables and covariates in a structural equation model. This allows for data-driven selection of valid and relevant instruments and provides additional robustness against invalid instruments. Our approach extends previous work through a scale-invariant prior structure and accommodates non-Gaussian outcomes and treatments, offering greater flexibility than existing methods. The computational strategy uses conditional Bayes factors to update models separately for the outcome and treatments. We prove that this model selection procedure is consistent. In simulation experiments, gIVBMA outperforms current state-of-the-art methods. We demonstrate its usefulness in two empirical applications: the effects of malaria and institutions on income per capita and the returns to schooling. A software implementation of gIVBMA is available in Julia.

翻译：工具变量是在未观测混杂因素下推断因果效应的常用工具，但在实践中选择合适的工具变量具有挑战性。我们提出gIVBMA——一种贝叶斯模型平均方法，通过在结构方程模型中跨不同工具变量集和协变量集进行平均来应对这一挑战。该方法支持基于数据的有效且相关工具变量选择，并对无效工具变量提供额外的稳健性。我们的方法通过尺度不变先验结构扩展了先前工作，并兼容非高斯分布的结果变量和处理变量，相比现有方法具有更高的灵活性。计算策略采用条件贝叶斯因子分别更新结果变量和处理变量的模型。我们证明了该模型选择过程具有一致性。在模拟实验中，gIVBMA的表现优于当前最先进的方法。我们通过两个实证应用展示了其有效性：疟疾与制度对人均收入的影响，以及教育回报率。gIVBMA的软件实现已在Julia语言中提供。