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A Model of Unemployment with Matching Frictions and Job Rationing


This dissertation proposes a model of the labor market that integrates two important sources of unemployment. The first source is a matching friction, which is a friction in matching unemployed workers to recruiting firms. The second source is job rationing, which is a possible shortage of jobs in the economy. To examine how these two sources interact over the business cycle, I decompose unemployment into a component caused by job rationing---rationing unemployment---and another component caused by matching frictions---frictional unemployment. Formally, I define rationing unemployment as the level of unemployment that would prevail if matching frictions disappeared, and frictional unemployment as additional unemployment due to the matching frictions.

The main theoretical result of this dissertation is that during recessions rationing unemployment increases, driving the rise in total unemployment, whereas frictional unemployment decreases. Intuitively, in bad times, there are too few jobs, the labor market is slack, recruiting is easy, and matching frictions contribute little to unemployment.

I specify a model in which job rationing stems from a small amount of wage rigidity and diminishing marginal returns to labor. In the model calibrated with U.S. data, I find that when unemployment is below 5%, it is only frictional; but when unemployment reaches 9%, frictional unemployment amounts to less than 2% of the labor force, and rationing unemployment to more than 7%.

I then show that in recessions, job rationing generates inefficiently high unemployment, which leaves room for labor market policies to improve social welfare. I evaluate three labor market policies—direct employment, placement services, and a wage subsidy—over the business cycle. First, I compute state-dependent fiscal multipliers (the increase in social welfare obtained by spending one dollar on a policy) to determine the effectiveness of these unemployment-reducing policies. I prove theoretically that placement services are more effective in good times than in bad times. The converse is true of direct employment. Intuitively, in bad times, frictional unemployment is low; placement services aim to further reduce this component and are therefore ineffective. The effectiveness of direct employment is a function of how much it crowds private employment out; in bad times, competition for workers is weak and crowding out is limited; thus, this policy is effective. In the calibrated model, wage subsidies are also more effective in bad times than in good times.

To conclude, I characterize the optimal mix of policies implemented by a benevolent social

planner. The optimal unemployment-reducing policy evolve over the business cycle: its puts more weight on policy instruments reducing matching frictions (placement services) in good times than in bad times; conversely, it puts more weight on policy instruments creating jobs directly (direct employment and a wage subsidy) in bad times than in good times. Intuitively, the optimal unemployment-reducing policy should adapt to the state of the labor market because of the cyclical fluctuations in the sources of unemployment.

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