The President chooses who will be the Fed Chairman and thereby chooses which economic school of thought will be running the Fed.
The House of Representatives has the final say on all spending bills and the Speaker decides which spending bills come up for a vote and which bills will never be voted on (or do I have that part wrong?).
Obviously each of them has influence over economic matters, but who has the more powerful voice in the day-to-day running of the economy - the President or the Speaker?