收入随机干扰下非线性经济周期模型随机响应分析

Stochastic Response Analysis of a Nonlinear Business Cycle Model with Random Income Disturbance

经济周期演化具有非常复杂的非线性和随机性特征,对其演化响应研究可以更好地掌握经济周期演化规律.本文首先建立了具有前两个时期收入差的一次方项与三次方项的非线性经济周期动力模型,用于模拟收入对投资的非线性影响,并采用两个互相独立的高斯白噪声随机函数分别模拟不确定因素干扰与收入随机干扰.然后运用基于短时高斯转移概率密度和Gauss-Legendre积分的路径积分法,求解收入与收入变化率的概率密度函数.最后研究了收入随机干扰和补充储蓄率对非线性经济周期演化的影响.研究表明:随机干扰下的收入早期变化波动显著,后期趋于稳定.收入随机干扰增强显著加大了收入的随机性,使得收入更加难于预测与控制.此外,提高补充储蓄率会降低获得高收入的概率.

The evolution of a business cycle has nonlinear and stochastic characteristics,and it is improtant to find its evolution law.Firstly,a nonlinear business cycle dynamic model with first-order and third-order terms of the difference between pre-income and prior income to simulate a generic nonlinear impact of incomes on the investment is established in this paper.Two independent Gaussian white noise random functions are used to simulate the interference of uncertain factors and random income,respectively.Then a path integral method,based on short-term Gaussian transition probability density and Gauss-Legendre integration scheme,is applied to solve the probability density function of income and income change rate.Finally,the effects of income random disturbance and supplementary saving rate on the evolution of the nonlinear business cycle are studied.The results show that the fluctuation of the income in the random interference is significant in the early stage,and it tends to be stable in the later period.The increase of income random interference significantly increases the randomness of income,making income more difficult to be predicted and controlled.In addition,the enhancement of supplementary saving rate decreases the probability of high income.