Can price inflation fix a lagging economy?

Recently, a number of Keynesians, including of course Paul Krugman, have argued that the key to a quick economic recovery is higher price inflation. Just how high they want it go depends on which one you ask but Krugman for example argued that sustained inflation at 3-4% would "almost surely help the economy".

Now, it should be conceded that higher monetary inflation can stimulate short-term economic growth to the extent the new money enters the economy according to the scenario described by the Austrian business cycle theory. The recent slight acceleration of growth in the United States does reflect this. But this will only pave the way for future problems, as Greenspan's "successful" attempt to revive the economy after the "dot com bubble" by creating a housing bubble illustrated.

Moreover, if inflation happens in other ways it will not revive real economic growth. It will boost nominal growth but the higher price inflation will mean that real economic growth won't increase. An example of this is Britain, who have had sustained inflation of 3-4% (though VAT changes have sometimes pushed it below or above that range, but the average has been about 3.5%) for the latest 5 years, yet have seen unemployment rise and real average pay for people with jobs drop by a total of 10%.

But perhaps Krugman was too timid in his recommendation for inflation of 3-4%. How about 9.2%? That is in fact what they've had in Iceland on average between 2008 and 2011. If higher inflation was a miracle cure, then surely 9.2% would be good enough.

Yet though Iceland's economy recovered slightly in 2011, by 1.5% adjusted for terms of trade changes, it remained a full 9.7% below its 2008 level. And that's assuming an average inflation rate of "only" 6.7% (for some reason the domestic demand and private consumption deflators in the GDP numbers have increased significantly less than the harmonized consumer price index for Iceland).

Some point to how Iceland still has relatively low (7%) unemployment but that overlooks first of all that Iceland had extraordinarily low (just 2%) unemployment before the crisis, and secondly that "hidden" unemployment has increased strongly as there has been a big drop in the participation rate and thirdly that there has been a 9% drop in real wages for people who still have jobs.