Bifurcation analysis of New Keynesian models

Grandmont (1985) found that the parameter space of even the simplest, most classical models are stratified into bifurcation regions. Barnett and He (1999,2002) subsequently found transcritical, codimension-two, and Hopf bifurcation boundaries within the parameter space of the policy-relevant Bergstrom and Wymer continuous-time Keynesian macroeconometric model of the UK economy. Barnett and He (2005) continued their investigation of policy-relevant bifurcation with the Leeper and Sims (1994) Euler equations macroeconometric model and found the existence of a singularity bifurcation boundary within the model's parameter space. Singularity bifurcation had not previously been encountered in economics. In this paper we study bifurcation within the class of new Keynesian models. The first model is the simplest linear 3-equation model, consisting of IS curve, Phillips curve, and monetary policy rule, which in our case is the Taylor rule. We find the possibility of Hopf bifurcation, with the setting of the policy parameters influencing the existence and location of the bifurcation boundary. We further study forward looking, backward looking, and hybrid models having both forward and backwards looking features. We also investigate different monetary policy rules relative to bifurcation. In each case, we solve numerically for the location and properties of the bifurcation boundary and its dependency upon policy rule parameter settings