Paul Krugman posted the graph above on his New York Times blog the other day. It charts change in GDP against austerity as % of GDP in European countries. Krugman claims that this proves that austerity is directly related to GDP contractions, making the basis error of confusing a correlation for a causation.
The big problem is that Krugman assumes that spending cuts have taken place independent of lower or negative GDP growth, and then tries to prove that austerity has caused lower GDP growth by showing a correlation between more austerity and less growth. But, obviously, you could make the reverse claim – the countries (like Greece and Ireland) implementing the harshest austerity packages are doing so precisely because they have had shrinking economies. Greece is cutting back expenditure more quickly and deeply than Germany is. Greece has to, Germany doesn't.
There is a relationship between GDP contraction and austerity, but it could run either or both ways. It would be interesting to see some time series that tried to see whether austerity has followed or lead economic recessions. That might tell us something interesting, but this doesn't. I don't know whether to assume Krugman's being silly or deceptive by pretending this graph is "proof" of anything significant at all.