Here are some interesting academic research papers on charity ratings:
Ceren Budak and Justin Rao, Measuring the Efficiency of Charitable Giving with Content Analysis and Crowdsourcing, 2016. This paper shows that the lack of information about charities resulted in 15% of donations being "wasted" by supporting low-performing, inefficient charities. Budak and Rao used Charity Navigator's ratings on US donations.
Jennifer Mayo, Navigating the Notches: Charity Response to Ratings, April 2022. Mayo's University of Michigan PhD paper on charity ratings looks at how changes to a charity's star rating affect donations. Ceren Budak (paper above) is also at University of Michigan. A change in star rating from 3-star to 4-star at Charity Navigator is associated with a 6% rise in donations, with larger effects for small charities. A downgrade in star ratings did not have the same effect as donors hold fast to their beliefs.