Causal inference with some invalid instrumental variables: A quasi‐Bayesian approach*
提出一种准贝叶斯方法，在部分工具变量违反排他性约束时仍能一致估计因果效应，模拟和实际数据验证了其有效性。
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.