I don't know
By my reading of the Constitution and commentary by the Founders, the Fed is specifically forbidden.
The President chooses the head from a list provided to him, confirmed by Congress. And as far as I know, that's the extent of Congressional input into the whole operation.
The Fed is not subject to congressional oversight.
Just recently as a result of the housing collapse Congress finally got a limited audit of what the Fed felt like showing them.
Allowing private banks to establish monetary policy and issue currency is THE definition of appointing the fox to guard the henhouse, IMHO. I know Jefferson was dead set against it.
It doesn't need to be nationalized, it needs to be repatriated, by repeal of the Federal Reserve Act, IMO.
Anyone wondering what I'm talking about start here:
The Psychology of Persuasion
The FED should be put under congressional control. The threat of being voted out of office is a better check on bad behavior than nothing at all.