Monday, July 6, 2009
How is Finance like a Sand Pile?
Why is it that nobody in the mainstream media seems to know anything about economic theory or the dynamics of financial markets? This morning's Washington Post contained yet another column asking why it is that economists failed to predict last fall's financial crash. The title lays the blame squarely at economist's feet: "Economists out to Lunch."
As if these economists were sitting at the controls of a machine they fully and completely understand. As if something like the crash we experienced could be predicted. As if the financial system had levers to pull or buttons to push that would yield predictable outcomes.
This all seems quite ludicrous to me. Even though I am not an economist, it seems clear that our economic and financial system is a complex system, with all the ramifications that has for predictability--or lack of predictability. It is a system comprised of multiple, nested feedback loops. These types of systems self-organize and display dynamic behavior that is well-understood from complex systems theory.
Not that you would ever know that from reading the newspapers.
One type of self-organized behavior that has been considered by those seeking to describe the dynamics of financial markets is exemplified by a sand pile fed from the top by a stream of sand grains. The dynamics of this sand pile exhibit what is known as self-organized criticality, or SOC.
The grains tumble slowly down the sides of the sand pile, coming to rest at various points along the slope. The pile slowly grows as sand is dribbled onto the top until, suddenly, the system becomes unstable and a small avalanche occurs. A rush of sand tumbles to the bottom, returning the remaining pile to a situation where additional sand can be added--but only for awhile. Small avalanches occur at random intervals and it is never entirely predictable when they will happen.
The sand pile's SOC dynamics exist because this system has an attractor that is simultaneously stable and unstable. This type of attractor is known as a critical point. It is essentially a mountain pass in the hilly terrain that characterizes the dynamic landscape for the system.
This mountain pass is a saddle point: if we stand at the point and look in one direction, the mountain slopes upward. Turn ninety degrees, though, and the mountain slopes down. Another ninety and it slopes up again. Completing the circular spin as we stand at our saddle point, we see the mountain sloping downward again. Sand grains roll down the mountain slopes toward this saddle point but when the resulting sand pile becomes too big, it collapses and rushes away into the surrounding valleys.
SOC has been suggested as the explanation for a variety of phenomena: forest fires, earthquakes, and, yes, financial markets. The common feature in systems that are governed by SOC is that they are driven by a persistent external force. In the case of the sand pile, it is the stream of sand. In the forest fire example, it is thought to be the slow accumulation of dry fuel. In the earthquake example, it is the constant pressure from colliding tectonic plates pushing on a fault line that will, at a random and unpredictable time, slip, causing a quake.
I would love to see a thoughtful discussion of the possible role of SOC in economics and financial systems. Nobelist Paul Krugman's ideas come close, but he seems to shy away from precise scientific language that would make it clear to me that he agrees with the idea that economic systems are complex, self-organizing and, thus, subject to the natural laws for these fascinating types of systems. I will keep looking, but please post links if you know of any relevant work.