Dissertation Idea #3: History
Find an obscure dataset that has been used only by historians who don’t know statistics. See what can be learned from using statistical methods and economic reasoning. The problem being that economists will think most history-type projects irrelevant, while historians may ignore outsiders on general principle and aren’t on your dissertation committee in an case. The other problem being that actually finding a dataset that 1)hasn’t been really examined; and 2)has the potential to shed much light on an area; is likely to be very time consuming.
It has, however, been done successfully as a dissertation.