Paul Krugman notes work by my colleague George Evans relating to the recent debate over the stability of GE models:
God Didn’t Make Little Green Arrows: Actually, they’re little blue arrows here. In any case George Evans reminds me of paper (pdf) he and co-authors published in 2008 about stability and the liquidity trap, which he later used to explain what was wrong with the Kocherlakota notion (now discarded, but still apparently defended by Williamson) that low rates cause deflation.
The issue is the stability of the deflation steady state ("on the importance of little arrows"). This is precisely the issue George studied in his 2008 European Economic Review paper with E. Guse and S. Honkapohja. The following figure from that paper has the relevant little arrows:
This is the 2-dimensional figure (click on it for a larger version) showing the phase diagram for inflation and consumption expectations under adaptive learning (in the New Keynesian model both consumption or output expectations and inflation expectations are central). The intended steady state (marked by a star) is locally stable under learning but the deflation steady state (given by the other intersection of black curves) is not locally stable and there are nearby divergent paths with falling inflation and falling output. There is also a two page summary in George's 2009 Annual Review of Economics paper.
The relevant policy issue came up in 2010 in connection with Kocherlakota's comments about interest rates, and I got George to make a video in Sept. 2010 that makes the implied monetary policy point.
I think it would be a step forward if the EER paper helped Williamson and others who have not understood the disequilibrium stability point. The full EER reference is Evans, George; Guse, Eran and Honkapohja, Seppo, "Liquidity Traps, Learning and Stagnation" European Economic Review, Vol. 52, 2008, 1438 – 1463.