Scott Sumner asked me to take another look at this. I've graphed the relationships again, categorized according to Euro membership. The Euro group includes Denmark, per Mark Sadowski's comment at TheMoneyIllusion. For my graphs, the entire set consists of the OECD countries, from IMF data. (ex. Estonia because of incomplete data)
The results look to me like they fit Scott's expectations.
On the consolidation vs. growth relationship, the R-squared for non-Euro countries is .0175. The four non-Euro countries in the lower right quadrant are Great Britain, Iceland, Hungary, and the Czech Republic.
On the initial structural balance and growth, there is a similar positive relationship with both Euro and non-Euro countries. The correlation is much stronger for the Euro countries.
On both relationships, the intercept growth rate for the Euro countries is 2% lower than for the non-Euro countries. This is the average growth rate over 4 years, so after accounting for either consolidation or structural balance, the Euro countries have lost 8% in economic activity compared to the rest of the developed world.
Fiscal policy does not have a statistically significant correlation with growth in the non-Euro countries. The annual growth coefficient of -.1422 for the Euro countries implies a multiplier of .56.
This appears to confirm Scott's point of view:
2) The Euro countries could individually experience a relationship between fiscal policy and growth because they share a monetary policy, which doesn't allow monetary policy to counteract each country's fiscal policy. This is also what we find here, although the coefficient (ex. Greece) is only .56 (.14 x 4), which is quite weak. If we include Greece, then both fiscal consolidation and the initial structural balance have strong correlations with economic growth, with p-values well under .01.
3) Tighter monetary policy regarding the Euro would lead to lower NGDP growth. That is also what we find across the board here. The Euro area has lower growth across these comparisons of about 2% per year over 4 years - presumably, at least in part, due to tighter monetary policy.
It is also interesting to revisit the relationship between the starting structural balance and the subsequent fiscal consolidation. For the entire set of countries, R-squared is .60 while the coefficient is -.63. When we separate the data by Euro affiliation, we see that the relationship comes mostly from the Euro countries. And, here, the removal of the Greece outlier doesn't affect the relationship very much.
This looks like strong evidence to me of the primary power of monetary policy during the crisis years. For countries with independent monetary policy, there are very weak relationships between fiscal policy and economic growth during 2008-2012. Countries with positive structural balances before the crisis tended to have less fiscal consolidation (p value = .045) and higher growth (p value = .065), but, interestingly, fiscal consolidation itself does not have a statistically significant correlation with economic growth for these countries. This suggests that fiscal policy could be managed for its own sake in these countries, and was largely overshadowed by other factors, monetary policy presumably being a large and controllable one.
For the Euro countries, there was a very strong correlation between the 2008 structural balance and subsequent consolidation (p value ~0, even ex Greece). The 2008 structural balance had a weaker correlation with subsequent growth (p value = .12, ex Greece), but consolidation had a stronger negative correlation with growth (p value = .085, ex Greece). European policies forced countries to correct their structural imbalances, and their lack of control over monetary policy meant that fiscal consolidation was felt in lower growth.
In addition, annual NGDP growth across the Euro countries was about 2% lower over these years. As Scott would say, this is the measure of monetary policy. Looser monetary policy would have raised NGDP across the Euro countries. They would have still shared a unique susceptibility to fiscal policy, but positive effects of looser money might have reduced the need for consolidation.