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Groundbreaking contributions to effects of chaos and bifurcation in economics chronicled in new book
LAWRENCE — Chaos. The word suggests disorder, confusion, malevolence.
“Yet nature is chaotic. Human brain waves are chaotic. Chaos is actually good,” said William Barnett, the Oswald Distinguished Professor of Macroeconomics at the University of Kansas.
The professor has published a new book titled “Economic Bifurcation and Chaos.” It provides a unified presentation of Barnett’s (with co-authors’) contributions to the literature on chaos, economic bifurcation and nonlinear dynamics. It’s published by World Scientific.
With assistance in production by Ruoning Han of Whitman College, who received a doctorate in economics from KU, the span of the book’s research begins in 1988 with Barnett’s initial finding of chaos in economic data. It continues with subsequent findings of bifurcation, but not necessarily chaos, in all dynamical macroeconomic models tested by the professor and his co-authors.
Barnett said that chaos theory should not be confused with catastrophe theory.
“In mathematics, catastrophe theory is about a discontinuous break in the solution path. Then the solution can be moving along, and suddenly it jumps down. There’s a discontinuous break in the solution. That’s bad,” he said.
“Chaos just means the solution jiggles around so fast that it looks stochastic without discontinuities. But the stochasticity then has a deterministic explanation, so it doesn’t come from shocks outside the universe or white noise. It’s coming from the system itself.”
He cites how the weather is chaotic, as is the nature of meteorology and climatology.
“The temperature variations never stop. They just keep fluctuating in a stochastic way. That’s actually a plus because stochasticity that has deterministic origins from chaos is informative. It tells you something about the underlying system that’s causing this phenomenon,” he said.
While mathematicians have long known of this theory and its applications, many economists lack expertise in it. As James Heckman, a Nobel laureate in economics, wrote in the book’s front matter, Barnett’s work “analyzes how systems with many interacting parts behave as a whole. … It is a guide to understanding the deep structural features of modern economics and how to account for them in policy analysis.”
The research covered in “Economic Bifurcation and Chaos” extends over three decades to Barnett’s recent findings of Shilnikov chaos (named for Russian mathematician Leonid Shilnikov) in New Keynesian models of the U.S. and U.K. economies. This research discovered what could have caused interest rates to drift downward inadvertently for three decades, eventually entering the zero lower bound, even when not intended by the Federal Reserve.
The initial impetus for some of this research came 50 years ago when Barnett was working as a rocket scientist during the U.S. space race. He recalls testing rocket engines at Edwards Air Force Base.
“Odd things would happen in the engine’s thrust chamber, and we weren’t quite sure why,” he said.
“We weren’t sure what to think about it. We would just keep running tests trying to figure out how to stop the puzzling behavior. But we did have a small number of brilliant mathematicians who basically consulted for us. These were not engineers. I would go talk to them sometimes, and they would explain to me that such occurrences don’t mean there’s necessarily something wrong with the rocket engine. It’s just a normal part of dynamics. But we needed to know how to control it to avoid bad outcomes.”
A half-century later, does Barnett feel like he’s grasped these seemingly impenetrable concepts better?
“Oh yes. I understand them much more now, especially since meeting Belgian physicist Viscount Ilya Prigogine at the University of Texas many years ago,” he said of the Noble laureate and author of 1984’s “Order Out of Chaos.”
A native of Boston, Barnett was originally employed as a scientist at Rocketdyne, a Los Angeles company that created the F-1 and J-2 rocket engines for the Apollo program. He then spent eight years on the staff of the Federal Reserve Board in Washington, D.C.
Barnett has worked at KU for the past 23 years as an expert in econometrics and macroeconomics. He is founder and editor of the Cambridge University Press journal “Macroeconomic Dynamics” and the Emerald Press monograph series “International Symposia in Economic Theory and Econometrics.” Barnett also founded the Society for Economic Measurement and served as its first president. Additionally, he is director at the Center for Financial Stability in New York City.
Now at the age of 83, Barnett said he admits he has no intention of stepping away from writing books at KU, editing journals or learning even more about his chosen field.
Of course, that is unless something chaotic happens.
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