Bifurcations in Continuous-Time Macroeconomic Systems

This research investigates bifurcation phenomena in a continuous-time model of the United Kingdom. We use the Bergstrom, Nowman, and Wymer continuous-time dynamic macroeconometric model of the UK economy. We find that bifurcations are important with this model for understanding the dynamic properties of the system and for determining which parameters are the most important to those dynamic properties. We have discovered that both saddle-node bifurcations and Hopf bifurcations indeed exist with this model within the model's region of plausible parameter settings. We find that the existence of Hopf bifurcations is particularly useful, since those bifurcations may provide explanations for some cyclical phenomena in the macroeconomy. We further design numerical algorithms to locate the bifurcation boundaries, which we display in three dimensional color bifurcation diagrams. A notable and perhaps surprising fact is that both types of bifurcation can coexist with this well-regarded UK model---in the same neighborhood of the parameter space.