In my last post, I found no relation between spending growth (2007-9) and economic growth (2009-11) using data from the International Monetary Fund. I tried the same thing with data from the Organisation for Economic Cooperation and Development. More precisely, I looked at the relation between "general government final consumption expenditure" (P3S13) and "gross domestic product, expenditure approach" (B1_GE). "Final consumption expenditure" is government spending on goods and services; it does not include transfers of money (like social security payments). In principle, this kind of spending should be more relevant to stimulus, since individuals who receive transfers might save them rather than spend them.
The first figure shows the relation between change in government consumption expenditure from 2007-9 and GDP growth in 2009-10 (2010 was the most recent data available for most countries). The IMF figures on GDP go to 2011, so the second figure shows the relation between change in government consumption and the IMF numbers on GDP change in 2009-11. Both ways, there is a positive relationship--countries that increased spending in 2007-9 had higher growth in later years. The ranking of countries on change in government consumption seems to correspond pretty well to the conventional impressions about which countries followed stimulus or austerity.
Of course, this is a quick and dirty analysis, but it suggests that stimulus worked. For example, the difference in 2009-11 economic growth between the US and UK (1.8% vs. 0%) is almost exactly what would be predicted from the 2007-9 difference in spending growth (4.6% vs. 2.4%).