With regards to its interest-rate policy, the Federal Reserve has followed the advice from theory by committing to deflation and to keep interest rates at zero for the foreseeable future. It has deviated from the theoretical recommendations by not making a clear commitment to have higher-than-average inflation in the future, and especially by not providing a clear signal that it will keep nominal interest rates low for some time even after the crisis is over.
Scott Sumner might feel a bit less lonely reading this. Thanks to Mark Thoma for the pointer. Reis also tries to explain the Fed's non-standard balance sheet moves.
Rather than try to come up with an economic theory to explain Fed policy, I would suggest a more cynical approach. The goal has been to transfer wealth to banks and to the holders of mortgage securities. The thinking is that those constituents are more important to the economy than taxpayers.
Suppose that in 2013 President Palin meets with Ben Bernanke and says, "I want you to sell your entire portfolio of mortgage securities, by close of business today." I don't think that Bernanke could argue that she was interfering with the conduct of monetary policy.
The Fed has changed from a central bank to a piggy bank. Any economist who tries to interpret Fed policy from the standpoint of economic theory is playing a fool's game.