In the movie Harvey from 1950 in the ending it is made clear that Harvey actually exists and is a Pooka, some sort of fairy from the celtic mythology.
Apparently he has chosen Elwood P. Dowd as some sort of medium to make people aware of him and contact them in bars every evening. But what is his actual intention?
And has the death of Elwoods mother anything to do with the whole story? If I recall correctly, Elwoods sister said that Harvey appeared after their mother died.