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The matching function -a key building block in models of labor market frictions-implies that the job …nding rate depends only on labor market tightness. We estimate such a matching function and …nd that the relation, although remarkably stable over 1967-2007, broke down spectacularly after 2007. We argue that labor market heterogeneities are not fully captured by the standard matching function, but that a generalized matching function that explicitly takes into account worker heterogeneity and market segmentation is fully consistent with the behavior of the job …nding rate. The standard matching function can break down when, as in the Great Recession, the average characteristics of the unemployed change too much, or when dispersion in labor market conditions -the extent to which some labor markets fare worse than others-increases too much.JEL classi…cations: J6, E24, E32.