Economic Bifurcation and Chaos

Economic Bifurcation and Chaos provides a unified presentation of the contributions to the literature on economic bifurcation, nonlinear dynamics, and chaos by William A Barnett and his coauthors. The span of the research begins in 1988 with Barnett's initial finding of chaos in economic data. The book continues with subsequent findings of bifurcation in all dynamical macroeconomic models so far tested by Barnett and his coauthors. The research covered extends over 3 decades to his recent findings of Shilnikov chaos in New Keynesian models of the UK and US economies. While methodology for testing for bifurcation, nonlinear dynamics, and chaos are fundamental to the research, the book's ultimate objectives focus on implications for robustness of dynamical inferences and implications for policy.

Bifurcation subsets are found stratifying the parameter space of all tested macroeconomic models, with confidence regions of parameter estimates crossing the boundaries between those subsets. A robustness problem results from policy simulations conducted only at point estimates of model parameters. Such simulations should be conducted at various locations throughout the confidence region to explore the dynamical implications of such models.

A more dramatic result is acquired in the special case of New Keynesian models during periods of active Taylor rule setting of short-term interest rates. That policy, without the imposition of a long run transversality condition, bifurcates the economy's dynamics to Shilnikov chaos, implying unintended long run downward drift of interest rates within the Shilnikov fractal attractor set. To control the drift, there needs to be a second policy instrument focused on the long run.