Menzie Chinn directs us to a paper by Christopher Neely that shows (1) the Fed is far from powerless when it policy rate is at the zero bound and (2) the Fed is a monetary superpower:
The Federal Reserve’s large scale asset purchases (LSAP) of agency debt, MBS and long-term U.S. Treasuries not only reduced long-term U.S. bond yields but also significantly reduced long-term foreign bond yields and the spot value of the dollar. These changes were much too large to have been generated by chance and they closely followed LSAP announcement times. These changes in U.S. and foreign bond yields are roughly consistent with a simple portfolio choice model. Likewise, the exchange rate responses to LSAP announcements are roughly consistent with a UIP-PPP based model. The success of the LSAP in reducing longterm interest rates and the value of the dollar shows that central banks are not toothless when short rates hit the zero bound.This means the Fed is still capable of influencing domestic and global demand. The question, then, is whether the Fed wants to stabilize demand. Unfortunately, there is no consensus on this issue in the Fed.