Maybe the classical hypothesis worked in the UK

See The economic recovery in the United Kingdom by Tyler Cowen:

There is an excellent Chris Giles FT article on this topic, here is the bit of greatest interest to some recent debates:

The latest IMF fiscal monitor shows a cyclically-adjusted deficit of 5.9 per cent of national income in 2011, falling only to 5.7 per cent in 2012. This 0.2 percentage point drop in the cyclically-adjusted deficit appears tiny compared with the 2010 vintage of the same IMF document, which shows plans for a 1.4 percentage point decline over the same two years.

That’s not my favorite measure of fiscal stance, but it is the one most commonly cited.  What we see is that “austerity didn’t get much worse,” to borrow the language of many of the Keynesians.  It remains a mystery to me how this could account for the British recovery, as for instance expressed by Krugman:

Finally, Britain is growing much faster right now than I expected. Fundamental model flaw? I don’t think so. As Simon Wren-Lewis has pointed out repeatedly, the Cameron government essentially stopped tightening fiscal policy before the upturn, which means in effect that the “x” in my equation didn’t do what I thought it would. On top of that, there was a drop in private savings, which is one of those things that happens now and then.The point is that the deviation of British growth from what a standard Keynesian model would have predicted, while real, wasn’t out of line with the normal range of variation-due-to-stuff-happening; nothing there that warranted a major revision of framework.

I would say the fiscal stance of the British government stayed more or less the same, and a rapid recovery came, because the labor market was flexible and market economies have a natural (though in my view not universal) tendency to mean-revert and put unemployed resources back to work.  Furthermore the UK had a relatively loose monetary policy, which sustained nominal values, even in light of a supposed liquidity trap.  (The hypothesis that the relatively high inflation rate came from a VAT hike didn’t last long.)
I took the Keynesian position on Britain to be “they are in a liquidity trap, and possibly secular stagnation, so they will just sit there and not experience any natural tendency toward major recovery, at least not for a long time.”  If the current Keynesian position (would it now be the New New Old Keynesian view?) is “in the absence of additional negative shocks, even in a liquidity trap market economies have a natural tendency to mean-revert and put unemployed resources back to work pretty quickly,”…well, I guess I am more of a Keynesian than I used to think.
Addendum: The article also offers this:

UK officials have no time for such comparisons, based on “spurious cyclical adjustment”. The Treasury said: “It’s interesting how the people who have started saying that we eased up on austerity are the very same people who just a few months earlier were accusing us of doggedly sticking to it. We have been consistent and stuck to the plans we set out.”
The independent Office for Budget Responsibility provides data with which to arbitrate this dispute. On the public spending side, there is no evidence of a secret stimulus. Public expenditure in 2012 and 2013 was a little lower than the level planned in 2010.
Its data also show there were no significant changes to the UK tax system in 2012-13, so no deliberate stimulus. Tax revenues, by contrast, were much weaker than expected as the economy stagnated, showing the strength of the automatic stabilisers in Britain.
Measures of the degree of fiscal tightening that do not rely on tax revenues, but changes in the tax system, such as those from the OBR or the independent Institute for Fiscal Studies, still show as much austerity in 2012 and 2013 as they did in 2010.

Sorry guys, but I have to call this one for some version of the classical hypothesis.  And by the way, I still think the UK recovery is relatively fragile, but not for reasons which have much to do with traditional Keynesianism.
- See more at: http://marginalrevolution.com/marginalrevolution/2014/06/the-economic-recovery-in-the-united-kingdom.html#sthash.u5ff6Gk0.dpuf

"There is an excellent Chris Giles FT article on this topic, here is the bit of greatest interest to some recent debates:

The latest IMF fiscal monitor shows a cyclically-adjusted deficit of 5.9 per cent of national income in 2011, falling only to 5.7 per cent in 2012. This 0.2 percentage point drop in the cyclically-adjusted deficit appears tiny compared with the 2010 vintage of the same IMF document, which shows plans for a 1.4 percentage point decline over the same two years.

 That’s not my favorite measure of fiscal stance, but it is the one most commonly cited.  What we see is that “austerity didn’t get much worse,” to borrow the language of many of the Keynesians.  It remains a mystery to me how this could account for the British recovery, as for instance expressed by Krugman:

Finally, Britain is growing much faster right now than I expected. Fundamental model flaw? I don’t think so. As Simon Wren-Lewis has pointed out repeatedly, the Cameron government essentially stopped tightening fiscal policy before the upturn, which means in effect that the “x” in my equation didn’t do what I thought it would. On top of that, there was a drop in private savings, which is one of those things that happens now and then.The point is that the deviation of British growth from what a standard Keynesian model would have predicted, while real, wasn’t out of line with the normal range of variation-due-to-stuff-happening; nothing there that warranted a major revision of framework.

 I would say the fiscal stance of the British government stayed more or less the same, and a rapid recovery came, because the labor market was flexible and market economies have a natural (though in my view not universal) tendency to mean-revert and put unemployed resources back to work.  Furthermore the UK had a relatively loose monetary policy, which sustained nominal values, even in light of a supposed liquidity trap.  (The hypothesis that the relatively high inflation rate came from a VAT hike didn’t last long.)

 

I took the Keynesian position on Britain to be “they are in a liquidity trap, and possibly secular stagnation, so they will just sit there and not experience any natural tendency toward major recovery, at least not for a long time.”  If the current Keynesian position (would it now be the New New Old Keynesian view?) is “in the absence of additional negative shocks, even in a liquidity trap market economies have a natural tendency to mean-revert and put unemployed resources back to work pretty quickly,”…well, I guess I am more of a Keynesian than I used to think.

Addendum: The article also offers this:

UK officials have no time for such comparisons, based on “spurious cyclical adjustment”. The Treasury said: “It’s interesting how the people who have started saying that we eased up on austerity are the very same people who just a few months earlier were accusing us of doggedly sticking to it. We have been consistent and stuck to the plans we set out.”

The independent Office for Budget Responsibility provides data with which to arbitrate this dispute. On the public spending side, there is no evidence of a secret stimulus. Public expenditure in 2012 and 2013 was a little lower than the level planned in 2010.

Its data also show there were no significant changes to the UK tax system in 2012-13, so no deliberate stimulus. Tax revenues, by contrast, were much weaker than expected as the economy stagnated, showing the strength of the automatic stabilisers in Britain.

Measures of the degree of fiscal tightening that do not rely on tax revenues, but changes in the tax system, such as those from the OBR or the independent Institute for Fiscal Studies, still show as much austerity in 2012 and 2013 as they did in 2010.

Sorry guys, but I have to call this one for some version of the classical hypothesis.  And by the way, I still think the UK recovery is relatively fragile, but not for reasons which have much to do with traditional Keynesianism."