Firstly, from an expectations perspective, it leaves us seriously vulnerable to a deflation trap, as when if the interest rate hits the lower bound, we lose monetary policy as a vehicle for boosting the economy. Realizing this, consumers expect low core inflation or deflation and so are encouraged to save - reinforcing the deflation trap. Interest rates can't go low enough to move some of these excess savings into investments and so they effectively just lie around doing nothing -perhaps getting parked into treasury bills- when they could be financing small business investment for the credit constrained etc.
An increasing voice seems to be building from the US Policy Community for Nominal GDP Targeting. From what I can make out, this works a lot like a price level target in so far as, when the economy falls from its intended path, the expectations of future loose monetary policy (and hence inflation) encourage spending now leading ultimately to a lessening of the threat of a deflation trap. The Nominal GDP target is being endorsed now by Krugman and Christina Romer, as well as tacitly perhaps by Mankiw and even Jan Hatzius from Goldman Sachs.
I think its clear, from the appalling Unemployment situation on both sides of the pond (8.1% over here, 9.1% over there -and that's not including those withdrawn from the labour pool or of course those in jail- about 1% of America), that governments have to do more. Moreover, there are two clear reasons to prefer solutions to come from central banks and monetary policy over parliaments and fiscal policy - which is that whilst fiscal policy can certainly restore the 'flexible price equilibrium' income, it cannot create the optimal composition of that income. This is because monetary policy can ultimately leave it to consumers and businesses to choose how to spend their money, whilst fiscal policy in the shape of spending (tax cuts in a depression just get saved, afterall, if the Marginal Propensity to spend is falling and interest rates stuck at 0 are not providing sufficient incentives to invest) must be spent on specific 'pet' projects. Those projects may or may not be societally optimal (there's a standard caveat to this point which is public goods provision as well as a less obvious but important counter argument here about dynamic effects and the possibility that government interference might change the optimal outcome but I honestly don't see it as being enormously important, I'm assuming that the flexible price outcome is the preferred one). The second point is the fiscal issue - whilst inflation would tend to reduce the debt burden, expansionary fiscal policy would do the opposite and so lacks 'political support' in both the UK and US (specifically, it lacks the support of necessary numbers of MP's and Congressmen). Whether it ought to do so or not is another issue, but clearly as long as political power remains distributed as it currently is, large fiscal stimulus seems impossibly optimistic.
If you accept these points, then I think the case for Nominal GDP Targeting becomes hard to refute. It will lead to higher core inflation in the short run most likely, but then, the real costs of inflation come from variability and unpredictability, rather than its level per se. Moreover, a bit higher inflation would be no bad thing.
Incidentally, if the BofE or the Fed moved to an NGDP target, then there remain questions about how it would meet its target. To move the UK out of its current doldrums would require enormous monetary stimulus which would probably have to take the shape of QE. QE is growing unpopular politically, being seen as a sort of backdoor bailout. Perhaps the next round could come with stricter lending regulatory requirements for small businesses?
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