Nonstationary response of a nonlinear economic cycle model under random disturbance

Abstract

Stochastic mechanics is widely applied in the field of economics and econometrics. One important application is to study economic fluctuations in economic cycle theory. However, nonstationary response of nonlinear economic cycles with random disturbance is less investigated. This paper is devoted to studying the nonstationary response of a nonlinear economic cycle model. First, a nonlinear economic cycle model is developed according to the Goodwin model and the Puu nonlinear economic cycle model. Gaussian white noise is regarded as a spontaneous function in the developed nonlinear economic cycle model. Then, a path integration method is adopted based on Gauss–Legendre scheme and short-time Gaussian approximation for obtaining the nonstationary probability density function (PDF) of the nonlinear economic cycle model. The obtained results are verified by the simulation result. Finally, the evolution of the nonstationary PDF is studied in detail in the numerical analysis. The effects of system parameters are compared and discussed. The results show that the addition of the quadratic term of income velocity leads to the nonzero means of the PDFs of income and income velocity. Due to the presence of the quadratic and cubic terms, these PDFs have non-Gaussian distributions.