Noise-induced transitions in a stochastic Goodwin-type business cycle model

Abstract

We motivate and specify a stochastic Goodwin-type business cycle model. Our analysis focusses on a subset of the parameter space where several attractors coexist. Applying a semi-numerical approach based on the stochastic sensitivity function and confidence domains due to Milstein and Ryashko (1995), we study random transitions between stable attractors in the context of the Goodwin-type economy embedded in an uncertain environment. Relying on a mix of analytical considerations and simulations we demonstrate that under weak noise levels regime switching is a prominent feature in the presence of low saving rates. Moreover, we explain how increased uncertainty can induce an essentially unpredictable income process out of an apparently stable high-income level situation. All dynamic phenomena are explained in terms of key concepts constituting the stochastic sensitivity function method.