Numerical analysis on"trap of credit creation" in macroeconomics under zero-interest-rate policy

Protracted recession in Japan for the last twenty years is characterized by persistent deflation and negative output gap. Recently, Inoue et al. presented the concept of "trap of credit creation" which represents mechanism of the persistent deflation based on zero-interest-rate economy. Three new Keynesian DGE models by Inoue et al. explain this type of deflation as a steady state of a system. The DGE models, which are based on optimization for utility function, derive simultaneous nonlinear differential equations. In the present paper, we study dynamical features on the steady states of the three DGE models (i.e. Model I, II, and III), using numerical calculation: i.e. we analyze stability of steady states, using Jacobian matrices. Model I and II correspond to models for positive-interest-rate economy, and Model III suggests mechanism of the recession characterized as trap of credit creation under zero-interest-rate economy. We show each of the models have a stable steady state. This result supports adequacy of the present models, which can shed light on mechanism of the protracted recession.