Stability Analysis of Continuous-Time Macroeconometic Systems

Abstract

There has been increasing interest in continuous-time macroeconometric models. This research investigates stability of the Bergstrom, Nowman, and Wymer continuous-time model of the U.K. when system parameters change. This particularly well-regarded continuous-time macroeconometric model is chosen to assure the empirical and potential policy relevance of the results. Stability analysis is 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. The main objective of this paper is to determine the boundaries of parameters at which instability occurs. Two types of boundaries are found: the transcritical bifurcation boundary and the Hopf bifurcation boundary, corresponding to two different ways that instability occurs when parameter values cross the bifurcation boundary.The existence of the Hopf bifurcation boundary is particularly useful, since Hopf bifurcation may provide explanations for some cyclical phenomena in macroeconomy. Numerical algorithms are designed to locate the stability boundaries, which are displayed in three-dimensional diagrams. A notable and perhaps surprising fact is that both types of bifurcations can coexist with this well-regarded U.K. model--in the same neighborhood of the parameter space.