Noise-Induced Phenomena in the Kaldor Business Cycle Model

Abstract

The periodic behavior of macroeconomic indicators or business cycles is a common observation in the economic system. In the past, business cycle modeling often involved the use of non-linear economic dynamic theory, general equilibrium theory, and methods to analyze complex systems, such as agent-based modeling and complex network theory. Several studies have shown that crisis and synchronization in business cycles can be modeled using threshold characteristics in the economic systems. In a non-linear system, it is well known that additive noise leads to qualitative transformations in system behavior, such as coherence resonance, stochastic resonance, and noise-induced transitions (referred to as noise-induced phenomena in this study). Recent studies have shown that noise-induced transitions arise in the non-linear economic business cycle model with multiple attractors around the sub-critical Hopf bifurcation. However, the relationship between the threshold characteristics in the economic dynamics and noise-induced phenomena has not been studied. In this study, we focus on the threshold characteristic of the Kaldor business cycle model under the bias of income, and show that coherence resonance and stochastic resonance can be produced as an effect of this threshold characteristic.