The Cyclical Behavior of Equilibrium Unemployment and Vacancies: Evidence and Theory

This paper argues that a broad class of search models cannot generate the observed business-cycle-frequency fluctuations in unemployment and job vacancies in response to shocks of a plausible magnitude. In the U.S., the vacancy-unemployment ratio is 20 times as volatile as average labor productivity, while under weak assumptions, search models predict that the vacancy-unemployment ratio and labor productivity have nearly the same variance. I establish this claim both using analytical comparative statics in a very general deterministic search model and using simulations of a stochastic version of the model. I show that a shock that changes average labor productivity primarily alters the present value of wages, generating only a small movement along a downward sloping Beveridge curve (unemployment-vacancy locus). A shock to the job destruction rate generates a counterfactually positive correlation between unemployment and vacancies. In both cases, the shock is only slightly amplified and the model exhibits virtually no propagation. I reconcile these findings with an existing literature and argue that the source of the model's failure is lack of wage rigidity, a consequence of the assumption that wages are determined by Nash bargaining.