The contribution of this paper is twofold. First, it reformulates the model of endogenous credit cycles by Matsuyama (2013, Sections 2-4). It is shown that the same dynamical system that generates the equilibrium trajectory can be obtained under a much simpler set of assumptions. Such a streamlined presentation should help to highlight the key mechanisms through which financial frictions cause instability and persistent fluctuations. Second, it discusses the nature of fluctuations in greater detail for the case where the production function of the final good sector is Cobb-Douglas. For example, the unique steady state possesses corridor stability (i.e., stable against small shocks but unstable against large shocks) for empirically relevant parameter values. This also means that, when a parameter change causes the steady state to lose its stability, its effects are catastrophic and irreversible so that even a small, temporary shock could have large, permanent effects on volatility. Other notable features of the present model include an immediate transition from the stable steady state to a stable asymmetric cycle of period n ≥ 3, along which n ‒1 ≥ 2 consecutive periods of gradual expansion is followed by one period of sharp downturn, or to robust chaotic attractors.
Keywords: borrower net worth; composition of credit flows; financial instability; corridor stability; asymmetric cycles; regime-switching; bifurcation analysis of a piecewise smooth nonlinear dynamical system
Views expressed in the paper are those of the authors and do not necessarily reflect those of the Bank of Japan or Institute for Monetary and Economic Studies.