This paper proposes a search-and-matching model of unemployment in which jobs are rationed: the labor market does not clear in the absence of matching frictions. This job shortage arises in an economic equilibrium from the combination of some wage rigidity and diminishing marginal returns to labor. In recessions, job rationing is acute, driving the rise in unemployment, whereas matching frictions contribute little to unemployment. Intuitively in recessions, jobs are lacking, the labor market is slack, and recruiting is easy and inexpensive, so matching frictions do not matter much. In a calibrated model, cyclical fluctuations in the composition of unemployment are large.
Figure 5: Rationing and frictional unemployment in the United States, 1964–2009
Michaillat, Pascal. 2012. “Do Matching Frictions Explain Unemployment? Not in Bad Times.” American Economic Review 102 (4): 1721–1750. https://doi.org/10.1257/aer.102.4.1721 .