In fact I much prefer simplest new Keynesian models to standard obscure new Keynesian models. Oh hell, my damn comment was waaay too long. here it is
I understand that hoping to read my name two times on your blog in one day is too optimistic. But really, I much prefer two Keynesian models to new Keynesian models. As you mention from time to time some people think the main purpose of models is to clarify thought. I am another one of those people.
More to the point simple models make clear which assumptions are key. As you mentioned in the New Keynesian ... fiscal policy post there are two key things to say about new Keynesian model dynamics
1) it is assumed that the economy gets back to the steady state (you wrote "a steady state" but it in the work horse models there is only one steady state)
2) there is no reason to think this is realistic. In fact leading new Keynesian OJ Blanchard has written about hysteresis not so long after figuring out how to deal wtih anticipated shocks in a model with a saddle path equilibrium.
I was thinking of commenting on those two points. In (almost all of ?) contemporary macro, it is assumed that there is a unique steady state and saddle dynamics around it. This means it is assumed that, excpet for exogenous shocks, the economy is predictable. That seems to me to be a problem right there given how badly contemporary macroeconomists (including the oversigned) forecast. But it provides a key insight to policy makers (in scare quotes)
"In the long run, macro policy doesn't affect real variables. So the very serious statesman who focuses on the long run should target inflation and ignore unemployment and output. "
The problem is that this policy relevant conclusion is an arbitrary assumption. The fearful plumbing is all analysis of the short run. Since it is not assumed a priori it is complicated. Since there isn't a standard (plainly false) assumption there is a lot of controversy. Since it is fearflul plumbing it makes policy makers queesy.
I think the impact of the analysis on actual policy is all due to the assumption and not the fancy math, clever modelling innovation or well anything whcih wasn't shoved aside as something we don't have to worry about.
What's worse, while, the serious statesman ignores the Keynesian parts of new Keynesian economics, the political hack ignores all of it. The short term political effect of policy proposals is based entirely on economically illiterate conventional wisdom. The case that good policy is good politics is an argument that even politicians who care only about winning elections should consider the medium run impact of policy.
The NK case for Keynesian policy is that it will be politically costly in the short run and won't help the economy in the long run but in the in between run it would be good for the economy and the politicians who implemented it. I can't explain the failure of the not the short run, not the long run, but roughly somewhere in the middle run analysis to convince policy makers.