Chaotic dynamics of a piecewise linear model of credit cycles

We develop a simple piecewise linear overlapping generations model exhibiting endogenous business cycles, which is based on Matsuyama's (2007) model of credit cycles. Some sort of “noise” representing information imperfection is shown to transform the Matsuyama model into a continuous, eventually expanding, piecewise linear map on the interval, which is tractable enough to investigate the dynamics in depth by using the techniques of the Frobenius–Perron operators to find observable chaos. While, according to the analysis of Asano et al. (2012), the Matsuyama model exhibits periodic cycles of arbitrarily large period, it is essentially not capable of chaotic dynamics. However, our model exhibits ergodic chaos with some robustness.