Revisiting the model of credit cycles with Good and Bad projects

We revisit the model of endogenous credit cycles by Matsuyama (2013, Sections 2–4). First, we show that the same dynamical system that generates the equilibrium trajectory is obtained under a much simpler setting. Such a streamlined presentation should help to highlight the mechanism through which financial frictions cause instability and recurrent fluctuations. Then, we discuss the nature of fluctuations in greater detail when the final goods production function is Cobb–Douglas. For example, the unique steady state possesses corridor stability (locally stable but globally unstable) for empirically relevant parameter values. This also means that, when a parameter change causes the steady state to lose its local stability, its effects are catastrophic and irreversible so that even a small, temporary change in the financial friction could have large, permanent effects on volatility. Other features of the dynamics include an immediate transition from the stable steady state to a stable asymmetric cycle   of period n≥3n≥3, along which n−1≥2n−1≥2 consecutive periods of gradual expansion are followed by one period of sharp downturn, as well as to a robust chaotic attractor. These results demonstrate the power of the skew-tent map as a tool for analyzing a regime-switching dynamic economic model.