Budget deficits and growth in Europe

There is a lively, ongoing debate in the blogosphere over the relationship between fiscal austerity and economic performance. Jeff Sachs recently penned an article criticising Paul Krugman's predictions as to the impact of austerity on US economic performance, to which Krugman responded on his blog. In the first of his responses, Krugman presents a chart showing that change in government purchases is strongly associated with GDP growth across country-years for European countries between 2010 and 2013. 

To Krugman's credit, he acknowledges the limitations of his analysis, writing, "You can, if you like, argue that it’s a spurious correlation for some reason." Indeed, it is not clear how valid change in government purchases is as a measure of fiscal austerity. The Financial Times Lexicon defines 'austerity' as follows:

Austerity measures refer to official actions taken by the government, during a period of adverse economic conditions, to reduce its budget deficit using a combination of spending cuts or tax rises.

This means that a year in which government purchases go up is not necessarily one of fiscal austerity: if I understand correctly (please tell me if I don't), it is possible for a government to increases purchases whilst simultaneously reducing the budget deficit; e.g., by cutting transfer payments or raising consumption taxes.

An alternative way to examine austerity's impact on economic performance is to simply plot GDP growth between 2010 and 2013 against the average budget deficit over this time period. Using Eurostat (as Krugman does) for budget deficit data, and the World Bank for GDP data, one obtains the scatterplot shown below. The relationship is moderate and positive: r = .44 (p = 0.019). While Greece and Ireland are obvious outliers, their effects on the correlation more-or-less cancel out; after removing them, r = .41 (p = 0.038). 

This analysis is of course also problematic. Most importantly, the denominator of the budget deficit (namely GDP) will tend to be smaller in countries experiencing slower growth, meaning that the deficit itself will be larger. Or in other words, countries that happen to be growing faster can better afford to reduce their budget deficits. Overall, methods more complex than simple scatterplots are needed to rigorously evaluate the impact of fiscal austerity on economic performance.