Modelling Asymmetric Unemployment Dynamics: The Logarithmic-Harmonic Potential Approach

Asymmetric behaviour has been documented in unemployment rates which increase quickly in recessions but decline relatively slowly during expansions. To model such asymmetric dynamics, this paper provides a rigorous derivation of the asymmetric mean-reverting fundamental dynamics governing the unemployment rate based on a model of a simple labour supply and demand (fundamental) relationship, and shows that the fundamental dynamics is a unique choice following the Rayleigh process. By analogy, such a fundamental can be considered as a one-dimensional overdamped Brownian particle moving in a logarithmic-harmonic potential well, and a simple prototype of stochastic heat engines. The solution of the model equation illustrates that the unemployment rate rises faster with more flattened potential well of the fundamental, more ample labour supply, and less anchored expectation of the unemployment rate, suggesting asymmetric unemployment rate dynamics in recessions and expansions. We perform explicit calibration of both the unemployment rate and fundamental dynamics, confirming the validity of our model for the fundamental dynamics.