I think I have written this post many times. I am daring to side with Peter Diamond in his debate on economics with Matthew Yglesias.
Yglesias thinks it is absurd to argue that the Fed can't achieve 4% expected inflation soon after time t if it wants 4% expected inflation at time t. I stress that "wants" is in the present tense. I am quite sure that he doesn't implicitly add the qualifier "and will still want 4% inflation when the unemployment rate is 5%" or (and this is the relevant one) "and economic agents believe it will still want 4% inflation when the unemployment rate is 5%."
IIRC his argument is that the Fed has a monopoly on generation of dollars and so can clearly determine the relative price of dollars and other things, and he has claimed that it can do so through expectations before changing anything. In any case his argument was that it can achieve this through expectations even if the Fed couldn't change real interest rates, real GDP or employment without changing expected inflation.
I think this has been fair so far. Now I will consider a special case. t is January 20 2001. The Fed sure wanted 4% inflation then. It achieved 4% inflation but not soon after. And before it got to 4% inflation it caused extremely high short term safe real interest rates, high medium term real interest rates and an unbroken post WWII unemployment rate.
I don't recall anything in the argument which implies that time t inflation rate is less than 4% . It seems to work equally well for shifts in either direction.
But those of us who remember 1981 and 1982 believe that it is very hard to cause a change in inflation or expected inflation. That a declared goal is not enough. That demonstrated extreme determination is not enough -- inflation above 4% and extremely high unemployment lasted long after Volker (and over on this side of the pond) Thatcher made their absolute determination and utter relentlessness clear.
I also think that people who followed monetary policy well before 2008 have a very clear sense of just how vastly more massive the Bernanke Fed's stimulus efforts have been than all previous efforts (put together really).
As always this doesn't mean I think the monetary authority shouldn't declare a higher target inflation rate (4% better than 2% and 6% better than 4%). But I don't think it will make a big difference.