Here are comments on Xavier Gabaix' "A Behavioral new-Keynesian model." Xavier presented at the October 21 NBER Economic Fluctuations and growth meeting , and I was the discussant. Slides here
Short summary: It's a really important paper. I think it's too important to be true.
Gabaix' irrationality fixes the pathologies of the standard model by making a stable model unstable , and hence locally determinate. Gabaix' irrationality parameter M in [0 ,1] can thus substitute for the usual Taylor principle that interest rates move more than one for one with inflation.
Gabaix imagines -- after three papers worth of careful math -- that people pay less attention to future income when deciding on consumption than they should. Making today's consumption less sensitive to future income , means expectations of future income are larger for any amount of today's consumption. Thus , it makes model dynamics unstable.
But just a little irrationality won't do. If you move a stable eigenvalue , say 0.8 , by a bit , say 0.85 , it's still stable. You have to move it all the way past 1 before it does any good at all.
Thus , Gabaix puts irrationality right in the middle of monetary policy. If Gabaix is right , you simply cannot explain monetary policy in simple terms with money supply and money demand , or interest rate rises lower investment and inflation via a Phillips curve , as simple approximations that more complex models , perhaps involving some irrationality , improve on. Monetary policy is centrally about the Fed exploiting irrationality , full stop , and cannot be explained or understood at all without that feature.
More in the comments. There are too many equations and figures to mirror it here , so you have to get the pdf if you're interested. This is for academics anyway.