Does research show that some drugs are more effective when the patient pays more for them?

I am not aware of such a study, but it wouldn't surprise me. A significant number of people continue to report that they get better effects from the pricier, brand-name medications than they do from generics (which are chemically identical). I've even heard doctors and nurses, who know better, admit to this. However, I doubt you'll see a well-performed study on this -- who would pay for it?