Rational expectations do not prevent us understanding sustained periods of deficient demand when an inflation targeting central bank hits a lower bound. Indeed they help, because with rational expectations inflation targeting prevents inflation expectations delivering the real interest rate we need, as I have argued here.
The traditional Phillips curve has always seemed to me to be an advertisement for the dangers of not doing microfoundations. It seems plausible enough, which is why it was used routinely before the rational expectations revolution. But it contains the serious flaw noted above, which almost destroyed Keynesian economics.
I wrote two very rude comments (in anti chronological order)
You write (suspected typo elided) "inflation targeting ... delivering the real interest rate we need." I note that the ECB has consistently targetted inflation (at least you are willing to give inflation targetting credit for events in 2005 and 2006. You must conclude that the Eurozone has the real interest rate we need.
But the Eurozone suffered a severe recession, currently has extremely high unemployment and appears to be headed for a second dip.
I think you meant to qualify the claim with "with the right inflation target, assuming (for some reason) that the target is credible ..."
I too have semi defended the rational expectations assumption recently. However, the basic advantage I see is that the assumption of rational expectations makes it more difficult (not impossible) for people to tell stories about how their preferred policies are good, because (it is assumed rather than argued) they will influence expectations in a desirable way.
Briefly, I think the point is to exorcise the confidence fairy. Less briefly, my reasoning was that, if one is not required to assume rational expectations, one can argue that cutting spending will cause increased growth by increasing business confidence. A model in which businessmen with rational expectations increase investment and production because of a spending cut is not easy to write. My guess is that it would be a model with sunspot equilibria, so anything can change investment. If so the case for expansionary austerity would be identical to the case that what we need is to burn incense to the flying spaghetti monster (which claim is consistent with the rational expectations assumption on models where sunspots can matter).
The key question, I think, is not rational vs irrational. It isn't even rational vs adaptive. It is whether we should treat expectations as a policy variable imagining that policy makers can control them as they control, say, the federal funds rate.
Then I thought "same for the people who think that expected inflation is just like the federal funds rate" and here we are. I might add, I also thought "this time I won't be very rude in comment" really honestly. But, as I see it, you leave me no choice.
Look why not just talk about a monetary authority which targets real yearly GDP. To a million pounds per capital You are simply assuming that a central bank can get the inflation expectations it wants. That rational people will believe its dynamically inconsistent promises.
Oddly the last time I remember defending rational expectations was when I tried to explain (to Matthew Yglesias) why Paul Krugman was skeptical about the effectiveness of monetary policy right now.
I note again that you have not identified one advance new Keynesians have made beyond Keynes. The alleged examples include speculation about UK consumption some of which, you note, is not incorporated into new Keynesian models yet and none of which has yielded an improved prediction and, of course, the old Phillips curve. The only connection between the old Phillips curve and Keynes is that he warned against believing in it as clearly as anyone could writing before Phillips.
You contest Krugman's claim that those who seek microfoundations have had no successes since the critique of the old Phillips curve yet you go back to that again and again. I see no trace of a justification for your disagreement with Krugman in this post or in any other post of yours which I have read.