This paper establishes a new fact about the compositional changes in the pool of unemployed over the U.S. business cycle and evaluates a number of theories that can potentially explain it. Using micro-data from the Current Population Survey for the years 1962-2011, it documents that in recessions the pool of unemployed shifts towards workers with high wages in their previous job. Moreover, it shows that these changes in the composition of the unemployed are mainly due to the higher cyclicality of separations for high-wage workers, and not driven by differences in the cyclicality of job-finding rates. A search-matching model with endogenous separations and worker heterogeneity in terms of ability has difficulty in explaining these patterns, but an extension of the model with credit-constraint shocks does much better in accounting for the new facts.