This is very wonkish, but it's also very important. The issue is whether DSGE models used for policy analysis can properly capture the relative costs of deviations of inflation and output from target. Simon Wren-Lewis argues -- and I very much agree -- that the standard models are not a very good guide to policy because they vastly overstate the cost of inflation relative to the cost of output (and employment) fluctuations (see the original for the full argument and links to source material):
Microfounded Social Welfare Functions, by Simon Wren-Lewis: More on Beauty and Truth for economists
... Woodford’s derivation of social welfare functions from representative agent’s utility ... can tell us some things that are interesting. But can it provide us with a realistic (as opposed to model consistent) social welfare function that should guide many monetary and fiscal policy decisions? Absolutely not. As I noted in that recent post, these derived social welfare functions typically tell you that deviations of inflation from target are much more important than output gaps - ten or twenty times more important. If this was really the case, and given the uncertainties surrounding measurement of the output gap, it would be tempting to make central banks pure (not flexible) inflation targeters - what Mervyn King calls inflation nutters.
Where does this result come from? ... Many DSGE models use sticky prices and not sticky wages, so labour markets clear. They tend, partly as a result, to assume labour supply is elastic. Gaps between the marginal product of labor and the marginal rate of substitution between consumption and leisure become small. Canzoneri and coauthors show here how sticky wages and more inelastic labour supply will increase the cost of output fluctuations... Canzoneri et al argue that labour supply inelasticity is more consistent with micro evidence.
Just as important, I would suggest, is heterogeneity. The labour supply of many agents is largely unaffected by recessions, while others lose their jobs and become unemployed. Now this will matter in ways that models in principle can quantify. Large losses for a few are more costly than the same aggregate loss equally spread. Yet I believe even this would not come near to describing the unhappiness the unemployed actually feel (see Chris Dillow here). For many there is a psychological/social cost to unemployment that our standard models just do not capture. Other evidence tends to corroborate this happiness data.
So there are two general points here. First, simplifications made to ensure DSGE analysis remains tractable tend to diminish the importance of output gap fluctuations. Second, the simple microfoundations we use are not very good at capturing how people feel about being unemployed. What this implies is that conclusions about inflation/output trade-offs, or the cost of business cycles, derived from microfounded social welfare functions in DSGE models will be highly suspect, and almost certainly biased.
Now I do not want to use this as a stick to beat up DSGE models, because often there is a simple and straightforward solution. Just recalculate any results using an alternative social welfare function where the cost of output gaps is equal to the cost of inflation. For many questions addressed by these models results will be robust, which is worth knowing. If they are not, that is worth knowing too. So its a virtually costless thing to do, with clear benefits.
Yet it is rarely done. I suspect the reason why is that a referee would say ‘but that ad hoc (aka more realistic) social welfare function is inconsistent with the rest of your model. Your complete model becomes internally inconsistent, and therefore no longer properly microfounded.’ This is so wrong. It is modelling what we can microfound, rather than modelling what we can see. Let me quote Caballero...“[This suggests a discipline that] has become so mesmerized with its own internal logic that it has begun to confuse the precision it has achieved about its own world with the precision that it has about the real one.”
As I have argued before (post here, article here), those using microfoundations should be pragmatic about the need to sometimes depart from those microfoundations when there are clear reasons for doing so. (For an example of this pragmatic approach to social welfare functions in the context of US monetary policy, see this paper by Chen, Kirsanova and Leith.) The microfoundation purist position is a snake charmer, and has to be faced down.
 Lucas, R. E., 2003, Macroeconomic Priorities, American Economic Review 93(1): 1-14.