The Matching Function and Nonlinear Business Cycles

The Cobb-Douglas matching function is ubiquitous in labor search and matching models, even though it imposes a constant matching elasticity that is unlikely to hold empirically. To examine the implications of this discrepancy, this paper uses a general constant returns to scale matching function to derive conditions that show how the cyclicality of the matching elasticity affects the shape of the job finding rate as a function of productivity and amplifies or dampens nonlinear labor market dynamics. It then shows that modest variation in the matching elasticity, consistent with recent estimates, significantly affects higher order moments and optimal policy. This motivates research that can provide greater clarity on the matching function specification.