Bayesian Causal Interence with Some Invalid Instrumental Variables

Abstract: In observational studies, instrumental variables estimation is greatly utilized to identify causal effects. The instrumental variables estimator is consistent only if instruments do not directly effect the outcome variable of interest, often referred to as the exclusion restriction condition. We propose a Bayesian generalized method of moments approach to obtain consistent estimators when there are some invalid instruments in a way that they violate the exclusion restriction condition.