Stochastic perturbations of limit cycles in nonlinear business cycle models: Kaldor's theory revisited

This paper introduces and validates a new approximation method for stochastic perturbations of limit cycles, taking up Kaldor's nonlinear theory of business cycles. This method provides explicit formulas for approximating solutions and probability distributions in stochastic business cycle models. The performance of these formulas is verified through numerical analysis, and time series analysis is used to fit the model to the data. This study attempts to pave the way for synthesizing the “exogenous” and “endogenous” approaches to business cycles.