To support continued progress toward maximum employment and price stability, the Committee expects that a highly accommodative stance of monetary policy will remain appropriate for a considerable time after the economic recovery strengthens.The FOMC is telling us that, in circumstances under which it would otherwise tighten, it doesn't expect to be doing that.
You can find the motivation for that element of the Fed policy in Woodford's work. It's in his Jackson Hole paper, but the key reference is this 2003 paper by Eggertsson and Woodford. The logic is fairly simple. In New Keynesian models, the central bank sets the nominal interest rate so as to achieve the "correct" real interest rate, but sometimes the zero lower bound gets in the way, and the real interest rate will be too high relative to the "Wicksellian natural rate," with the nominal interest rate at zero. But, according to Eggertsson and Woodford, all is not lost. The central bank can promise a period of high inflation when the nominal interest rate "lifts off" the zero lower bound and/or a longer period over which the nominal interest rate will be zero. Then, given higher expected future inflation, inflation is higher in the present, and the real interest rate falls, in spite of the fact that the nominal interest rate is zero and can't go lower.
Key to making the policy work is commitment. A Taylor-rule policymaker acting with complete discretion will not choose the high inflation policy in the future.
The FOMC appears to have bought the Eggertsson/Woodford argument. It's reflected both in the sentence quoted above, and in the extension of "expected liftoff" to mid-2015. What's wrong with that?
1. Do we think that Eggertsson/Woodford provides a good description of what is currently going on in the world? We have to buy the idea that the key problem we face is that the real rate of interest is too high. Real rates of interest - for all maturities - are historically very low. We need to think that the "Wicksellian rate" is even lower. Why should that be? In the Eggertsson/Woodford model, central bankers hit the zero lower bound because there are exogenous shocks to the optimal real interest rate. Just what drives those shocks is unclear, and it is also unclear what a low Wicksellian real rate has to do with the recent financial crisis. If anything, we can think of the financial crisis, and the European sovereign debt crisis, as having produced a shortage of safe assets, which makes real rates of return too low rather than too high.
2. Eggertsson Woodford does not tell us anything about quantitative easing (QE). How does the FOMC know that the model which has all the effects in it that they want - effects on inflation and real activity from various kinds of asset swaps and forward guidance - is actually going to have the Eggertsson/Woodford effect in it? Note that Eggertsson/Woodford work out a neutrality theorem - QE does not matter in their model. But of course Eggertsson/Woodford don't have a serious theory of the term structure of interest rates, and neither does anyone else, including the economists at the Fed. If we put together a monetary policy motivated by results from model x, model y, and model z, we might want to make sure that x, y, and z are mutually consistent.
3. The Eggerstsson/Woodford analysis relies on log-linearized solutions. This work by Toni Braun and coauthors shows how this can lead us astray.