“The Matching Function and Nonlinear Business Cycles“
with Joshua Bernstein and Alex Richter
Journal of Money, Credit and Banking, March 2025, Volume 57(2-3), Pages 349-376
FRB Dallas Working Paper 2201, February 2022
Online Appendix

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.