This is a question that has raged in the blogosphere for some time now. And here is an answer from Prakash Loungani et al. (2011):
We provide cross-country evidence on the relative importance of cyclical and structural factors in explaining unemployment, including the sharp rise in U.S. long-term unemployment during the Great Recession of 2007-09. About 75% of the forecast error variance of unemployment is accounted for by cyclical factors-real GDP changes (Okun‘s Law), monetary and fiscal policies, and the uncertainty effects emphasized by Bloom (2009). Structural factors, which we measure using the dispersion of industry-level stock returns, account for the remaining 25 percent. For U.S. long-term unemployment the split between cyclical and structural factors is closer to 60-40, including during the Great Recession.
This is a little less than Scott Sumner's 70-30 split, but is still far more weighted toward cyclical factors than Arnold Kling's Recalculation theory suggests. Tyler Cowen will also appreciate the light this study sheds on his questions regarding the relative importance of aggregate demand and aggregate supply shocks.