moral authority

Definition:

moral authority

(of a person, institution, or written work) 

"The quality or characteristic of being respected for having good character or knowledge, especially as a source of guidance or an exemplar of proper conduct."

http://www.yourdictionary.com/moral-authority

example: Moral authority is what the Catholic church doesn't have because of its numerous scandals; and, failures of church hierarchy to address them adequately, e.g., coverups.