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Making Sense of Chaos with the Windy-Boat

Roger Farmer

Last week my Rebuild Macro colleague Doyne Farmer, asked “Are Business Cycles Chaotic?” Doyne’s answer is that economies are complex chaotic systems. He draws an analogy with meteorology and he compares the mathematics of business cycles to the science of the weather. I agree with Doyne on this point. But why do we care?

I wrote a piece on this topic, Not Keen on more Chaos in the Future of Macroeconomics, on my personal blog, Roger Farmer’s Economic Window. Although I agree that economies are chaotic systems, I do not agree with the way that Doyne proposes to address that issue.

Doyne uses the rocking horse metaphor that I discussed in depth in my book How the Economy Works. According to this metaphor, which dates back to Wicksell in the late nineteenth century, the economy is like a rocking horse shocked repeatedly and randomly by a child with a club.  The behaviour of the rocking horse is nothing like the dynamics of the shocks; which are random blows with no intertemporal pattern. Nor is it like the behaviour of the rocker, which displays a smooth cyclical return to its rest point after any single shock. Instead, the rocking horse moves randomly through time in predictable ways. This is the way most conventional economists see the world.

Why is Doyne unhappy with the way most conventional economists see the world?  In his own work, Doyne models complex systems with millions of interacting agents. He sees a parallel between his economic models and meteorological models of the weather. Chaotic systems never return to a single point: they keep moving in ways that, although deterministic, are nevertheless unpredictable.

“Chaotic systems never return to a single point: they keep moving in ways that, although deterministic, are nevertheless unpredictable”

In How the Economy Works, I argued that the rocking horse metaphor is a very bad approximation to a chaotic system because it makes a strong prediction that is contradicted by data. The rocking horse, if struck just once, always returns to the same point. The data do not. The US unemployment rate has wandered randomly between 3% and 25% but it does not return to a single point. Central Bank economists construct rocking horse models in which the unemployment rate fluctuates around a unique rate that they call the natural rate of unemployment. The natural rate of unemployment is a myth that does not, and has never, existed in the data.

The rocking horse is the wrong way to approximate a complex dynamical system. Is there a better one?  I believe so. In my book How the Economy Works I provide an alternative narrative that I call the windy-boat metaphor. In this narrative, the economy is a sailboat on the ocean with a broken rudder. The wind blows the boat here and there and after a strong gust it never returns to the same point. The windy-boat metaphor leads to approximations to complex systems that, although simple, do not predict that the system is self-stabilizing. Instead it leads to models that display what mathematicians call hysteresis. Perhaps we will eventually have good models of the non-linear dynamics of real world economies. In the meantime, our simple models should provide good approximations to those dynamics that are not obviously contradicted by the facts.

Conventional macroeconomists approximate the world with the rocking horse model. That is one way of cutting the Gordian knot of complexity theory. But, as Doyne points out, it leads to some pretty silly conclusions. In my work, I replace the rocking horse model with a simple alternative. The windy-boat metaphor makes sense of chaos. It predicts many of the simple correlations we see in data and it provides a viable model of real-world economies that fits the facts.

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