Does the Fed think QEIII will produce higher inflation?
The short answer is, not really.
The longer answer can be found in these charts which were released on September 13th, the same day that QEIII was announced:
The bottom panel shows that no one on the FOMC is predicting a surge in inflation from QEIII. The highest individual prediction in 2014 is 2.2% and in 2015 it's 2.3%. The "central tendencies" for those years are 1.8% - 2% in 2014 and 1.9% - 2% in 2015. You can read these numbers from the first table in the link provided above.
I just don't see that the Fed views their language in the QEIII statement or the minutes as seriously committing to higher than equilibrium (i.e. 2%) inflation in the future.
The FOMC is bullish on growth in 2014 and 2015 as can be seen from the top panel of the embedded chart, with a "central tendency" of their forecasts reported as 3.2% - 3.8%. Their long run forecast central tendency is 2.2% - 3%.
There is nothing in these forecasts that indicates the Fed expects NGDP to get back on anything resembling its pre-crash trend.
People, believe me when I tell you that I want the economy to recover. I want lots of new jobs created. I want there to be good times in America for all.
But I think people are projecting their own views onto Fed actions. The FOMC just isn't playing the game that the Woodfordians want them to play.
It's my view that it is impossible for the Fed to play and win the Woodfordian game, but I'd love to be proven wrong.