Now, why should people, rationally, expect their income to revert to trend? What's the fundamental re-equilibrating force that ends recessions in a New Keynesian model? The short answer is that there isn't one. Mathematicians will recognise that my solution 3 is just one of many possible solutions. Y(t) = A - BM(t), where A is any positive or negative number, also works. We just assume that people trust the central bank will do whatever it takes to bring income back to trend eventually, and work backwards from there. We assume there's a confidence fairy, in other words.
and the data doesn't look good.
And now we have empirical evidence that the New Keynesian confidence fairy isn't working.
And it appears that this assumption is key to making the 'new Keynesian' multipliers much less than the 'Old Keynesian multipliers'. And those lower multipliers are one of the arguments against government action (whether cutting taxes or spending).
This period of economic activity is like a pinch point in biological evolution. The data coming out of it should be killing off economic models that are simply non-predictive, or at the very least causing them to adapt rapidly. I can't say I'm seeing a lot of that at present.