Abstract
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.
Highlights
IntroductionLogarithmic-Harmonic PotentialAsymmetric behaviour has been documented in postwar US unemployment rates, suggesting that they increase quickly in recessions but decline slowly during expansions.Consider a scenario in which the economy is in a recession: in response to this negative shock, job vacancies (demand for labour) drop on impact, leading to a rise in unemployment.consider the response to an -sized positive shock
We developed an equilibrium model in which the behaviour of the labour market and government interventions form an aggregate fundamental following the Rayleigh process in a logarithmic–harmonic potential
The solution of the model equation illustrates that the unemployment rate rises faster with a 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
Summary
Logarithmic-Harmonic PotentialAsymmetric behaviour has been documented in postwar US unemployment rates, suggesting that they increase quickly in recessions but decline slowly during expansions.Consider a scenario in which the economy is in a recession: in response to this negative shock, job vacancies (demand for labour) drop on impact, leading to a rise in unemployment.consider the response to an -sized positive shock. Consider a scenario in which the economy is in a recession: in response to this negative shock, job vacancies (demand for labour) drop on impact, leading to a rise in unemployment. While the adjustment in response to such positive shock is qualitatively similar, because of the different dynamics of demand for labour under the shocks, the unemployment rate increases by more in response to a negative shock than it drops in response to a positive one. The importance of this issue has been stressed by many papers in the both theoretical and empirical literature [1–7]
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