In observational studies, instrumental variables estimation is often used to identify causal effects. We propose a quasi-Bayesian approach to make consistent inferences about the causal effect when there are some invalid instruments that violate the exclusion restriction condition. Asymptotic properties of the proposed Bayes estimator, including model selection consistency, are established. A simulation study demonstrates that the proposed Bayesian method produces consistent point estimators and valid credible intervals with correct coverage rates for Gaussian and non-Gaussian data with some invalid instruments. We also demonstrate the proposed method in an application to real data.

中文翻译：

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一些无效工具变量的因果推断：准贝叶斯方法*

在观察性研究中，工具变量估计通常用于识别因果效应。当存在一些违反排除限制条件的无效工具时，我们提出了一种准贝叶斯方法来对因果效应做出一致的推断。建立了所提出的贝叶斯估计器的渐近特性，包括模型选择一致性。一项模拟研究表明，所提出的贝叶斯方法可以产生一致的点估计量和有效的可信区间，并且具有正确覆盖率的高斯和非高斯数据以及一些无效仪器。我们还在真实数据的应用中演示了所提出的方法。