Existence of Bifurcation in Macroeconomic Dynamics: Grandmont Was Right

simplest, most classical models are stratified into bifurcation regions. But by demonstrating that fact with a classical model in which all policies are Ricardian equivalent and all solutions are Pareto optimal, he was not able to reach conclusions about the policy relevance of his dramatic discovery. The result was years of controversy, as evidenced by papers appearing in Barnett, Deissenberg, and Feichtinger (2004) and Barnett, Geweke, and Shell (2005). 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 dynamic macroeconometric model of the UK economy. That model was produced from a system of second order differential equations. Because of the Lucas critique, there is increasing interest in Euler equation models. Since the Bergstrom and Wymer model is a structural model, rather than an Euler equations model, He and Barnett (2002) have continued their investigation of policy relevant bifurcation by searching the parameter space of the Leeper and Sims (1994) Eule