"The parents who gave more process-praise had children who believe their intelligence and social qualities could be developed and they were more eager for challenges" — according to Stanford researcher Carol Dweck, quoted in this essay by Jenny Anderson.
I haven't delved through Dweck's study, but I wonder whether correlation is causation here. Maybe less intelligent parents are the ones who make "person-based" comments like "You're so smart!" and more intelligent parents figure out that it is better not to tell the child what he is but to talk about the specifics of the thing that he is attempting to do. If so, the difference in intelligence may be simply inborn.