Not Keen on more Chaos in the Future of Macroeconomics

Steve Keen argues that we should use chaos theory as a future foundation for macroeconomics. We tried that thirty-five years ago and rejected it. Here’s why.  

In response to Olivier Blanchard’s recent attempt to move towards a consensus in macroeconomics, Steve Keen has launched a blistering attack on the DSGE approach. His thesis is that the economy is best modeled as a complex adaptive system. I am, or at least was, very receptive to that idea. But in contrast to Steve, I believe that DSGE models are here to stay, just not New Keynesian DSGE models.

Complexity theory is not a new idea in economics. In June of 1985, Jean-Michel Grandmont and Pierre Malgrange organized a conference in Paris. The conference was dedicated to the idea that the economy is inherently non-linear and that the applications that Steve Keen cites as successful examples of non-linear theory in the physical sciences could be extended to economics.  I was privileged to attend that conference and to present a paper on non-linear business cycles. Many of the conference papers were published in the Journal of Economic Theory.

Among the highlights at the 1985 conference were an important paper by Michele Boldrin and Luigi Montruchio which demonstrated that the representative agent growth model can display chaotic dynamics. Michael Woodford presented a paper entitled “Stationary Sunspot Equilibria in a Finance Constrained Economy”. Roger Guesnerie, Jean Michel Grandmont, Donald Saari, Steven R. Williams, Roes-Anne Danna, Guy Laroque, Raymond Deneckere, Steve Pelikam and Pietro Recclin all presented papers that appeared in the conference volume. Frank Hahn attended and was his usual perceptive and boisterous self. Karl Shell presented a paper that Grandmont later rejected for JET (a somewhat ballsy decision since Karl was editor of JET at the time).  This was also the first time I met Jess Benhabib. We went on to write our classic paper on indeterminacy.

The attendees were a relative who’s who of European and American mathematical economists and the agenda was clear. Can we translate the success of chaos theory and non-linear dynamics from the physical sciences into economics? The answer was very clear. Non!

For me, and I believe for many others, the highlight of the conference was a paper by the American economist William (Buzz) Brock with the title “Distinguishing Random and Deterministic Systems”.  This is a wonderful paper and I recommend you read it. In his conference presentation, Buzz described an experiment that changed the world of fluid dynamics. At one time, physicists described the motion of turbulence in fluids with a high dimensional linear system hit by random shocks. It turns out, the world is not like that. And physicists can prove it.

Buzz described an experiment, conducted by physicists, in which they take two cylinders and put a colored fluid between them. As they rotate the inner cylinder, the motion of the fluid moves from calm motion through cycles to chaos. To measure this transition, they shine a strobe light through the fluid and record a sequence of dots. As the speed of rotation increases, there comes a point where the sequence of dots is well described by a three dimensional differential equation system with a chaotic attracting set. The path of any given sequence is completely deterministic but any given path is sensitive to initial conditions. Paths that initially start close together begin to diverge. This is the ‘butterfly wings’ phenomenon. A butterfly flapping its wings in Brazil can cause a hurricane in the Caribbean.

The obvious question that Buzz asked was: are economic systems like this? The answer is: we have no way of knowing given current data limitations. Physicists can generate potentially infinite amounts of data by experiment. Macroeconomists have a few hundred data points at most. In finance we have daily data and potentially very large data sets, but the evidence there is disappointing. It’s been a while since I looked at that literature, but as I recall, there is no evidence of low dimensional chaos in financial data.

Where does that leave non-linear theory and chaos theory in economics? Is the economic world chaotic? Perhaps. But there is currently not enough data to tell a low dimensional chaotic system apart from a linear model hit by random shocks. Until we have better data, Occam’s razor argues for the linear stochastic model.

If someone can write down a three equation model that describes economic data as well as the Lorentz equations describe physical systems: I'm all on board. But in the absence of experimental data, lots and lots of experimental data, how would we know if the theory was correct?