The Hamilton Project, an initiative at the Brookings Institution, will begin awarding a new prize, "The Hamilton Project Economic Policy Innovation Prize," to select graduate and undergraduate students for innovative economic policy proposals....The top undergraduate student will be awarded $10,000 and the top graduate student $15,000.
Update: Here, from the Independent Institute, is an essay contest for students and junior faculty on the topic, “Is foreign aid the solution to global poverty?”
Update 2: And here is an Economic Communicators Contest aimed at assistant professors, graduate students, and high school teachers.