Black Swans and Endogenous Uncertainty
Ubiquity, Complexity Theory, and Sandpiles
Fingers of Instability
A Stable Disequilibrium
General Equilibrium with Endogenous Uncertainty
John is in Florida and feeling a bit under the weather, so this week we’re bringing back one of his most popular letters, from December 2007. In the letter he discusses the work of Professor Graciela Chichilnisky of Columbia University, one of whose key insights is that the greater the number of connections within an economic network, the more the system is at risk. Given the current macroeconomic environment, it is important to remind ourselves of how complacent we were back in 2007 and how it all fell apart so quickly, just as John outlined in this rather prescient piece.
This is a theme to which John has returned again and again, pointing out that reforms such as Dodd-Frank (the Dodd–Frank Wall Street Reform and Consumer Protection Act of 2010) fell well short of solving the problem of excessive interconnectedness among global financial players. It shored up the big “sandpile” rather than breaking it up into smaller, more manageable sandpiles. Now, if the Chinese, Japanese, and/or European sides of the sandpile should avalanche, the whole US side is likely to go, too.
John will be back next week with a report from Washington DC and the next installment of his series on income inequality.
How does the risk of default in California or Thailand get spread throughout the world, causing problem in money market funds in Europe and Florida? Yes, we can trace the linkages now, but was it possible to predict the crisis beforehand? And can we use what we learn to predict and hopefully hedge ourselves from the next crisis? Why do these things seem to be happening with more frequency? This week we are going to look at some economic theories that will give us some insight into the above questions. As it turns out, the more that individuals hedge their risk in economic markets – the larger and more interconnected the network – the more the entire system is put at risk. There is a lot of ground to cover, so we will jump right in.
Before we get to the economic theory, let’s review part of a letter I wrote in April of 2006 discussing chaos theory, as it will give us a useful mind picture to understand the latter part of the letter. This was part of a letter in which I laid out my thought that we would indeed experience a future crisis along the lines we are now seeing.
We are going to start our explorations with excerpts from a very important book by Mark Buchanan called Ubiquity, Why Catastrophes Happen. I HIGHLY recommend it to those of you who, like me, are trying to understand the complexity of the markets. Not directly about investing, although he touches on it, it is about chaos theory, complexity theory, and critical states. It is written in a manner any layman can understand. There are no equations, just easy-to-grasp, well-written stories and analogies.
We have all had the fun as kids of going to the beach and playing in the sand. Remember taking your plastic bucket and making sand piles? Slowly pouring the sand into ever bigger piles, until one side of the pile started an avalanche?
Imagine, Buchanan says, dropping one grain of sand after another onto a table. A pile soon develops. Eventually, just one grain starts an avalanche. Most of the time it’s a small one, but sometimes it builds up and it seems like one whole side of the pile slides down to the bottom.
Well, in 1987 three physicists, named Per Bak, Chao Tang and Kurt Weisenfeld, began to play the sandpile game in their lab at Brookhaven National Laboratory in New York. Now, actually piling up one grain of sand at a time is a slow process, so they wrote a computer program to do it. Not as much fun but a whole lot faster. Not that they really cared about sandpiles. They were more interested in what are called nonequilibrium systems.
They learned some interesting things. What is the typical size of an avalanche? After a huge number of tests with millions of grains of sounds, they found out that there is no typical number: “Some involved a single grain; others, ten, a hundred or a thousand. Still others were pile-wide cataclysms involving millions that brought nearly the whole mountain down. At any time, literally anything, it seemed, might be just about to occur.”
The pile was indeed completely chaotic in its unpredictability. Now, let’s read this next paragraph slowly. It is important, as it creates a mental image that helps me understand the organization of the financial markets and the world economy. (emphasis mine)
To find out why [such unpredictability] should show up in their sandpile game, Bak and colleagues next played a trick with their computer. Imagine peering down on the pile from above, and coloring it in according to its steepness. Where it is relatively flat and stable, color it green; where steep and, in avalanche terms, “ready to go,” color it red. What do you see? They found that at the outset the pile looked mostly green, but that, as the pile grew, the green became infiltrated with ever more red. With more grains, the scattering of red danger spots grew until a dense skeleton of instability ran through the pile. Here then was a clue to its peculiar behavior: a grain falling on a red spot can, by domino-like action, cause sliding at other nearby red spots. If the red network was sparse, and all trouble spots were well isolated one from the other, then a single grain could have only limited repercussions. But when the red spots come to riddle the pile, the consequences of the next grain become fiendishly unpredictable. It might trigger only a few tumblings, or it might instead set off a cataclysmic chain reaction involving millions. The sandpile seemed to have configured itself into a hypersensitive and peculiarly unstable condition in which the next falling grain could trigger a response of any size whatsoever.
Something only a math nerd could love? Scientists refer to this as a critical state. The term critical state can mean the point at which water would go to ice or steam, or the moment that critical mass induces a nuclear reaction, etc. It is the point at which something triggers a change in the basic nature or character of the object or group. Thus, (and very casually, for all you physicists) we refer to something being in a critical state (or us the term critical mass) when there is the opportunity for significant change.
But to physicists, [the critical state] has always been seen as a kind of theoretical freak and sideshow, a devilishly unstable and unusual condition that arises only under the most exceptional circumstances [in highly controlled experiments]…. In the sandpile game, however, a critical state seemed to arise naturally through the mindless sprinkling of grains.
Thus, they asked themselves, could this phenomena show up elsewhere? In the earth’s crust, triggering earthquakes; in wholesale changes in an ecosystem; or in a stock market crash? “Could the special organization of the critical state explain why the world at large seems so susceptible to unpredictable upheavals?” Buchanan asks. Could it help us understand not just earthquakes but why a cartoon in a third-rate paper in Denmark could cause worldwide riots?
Buchanan concludes in his opening chapter:
There are many subtleties and twists in the story … but the basic message, roughly speaking, is simple: The peculiar and exceptionally unstable organization of the critical state does indeed seem to be ubiquitous in our world. Researchers in the past few years have found its mathematical fingerprints in the workings of all the upheavals I’ve mentioned so far [earthquakes, eco-disasters, market crashes], as well as in the spreading of epidemics, the flaring of traffic jams, the patterns by which instructions trickle down from managers to workers in the office, and in many other things. At the heart of our story, then, lies the discovery that networks of things of all kinds – atoms, molecules, species, people, and even ideas – have a marked tendency to organize themselves along similar lines. On the basis of this insight, scientists are finally beginning to fathom what lies behind tumultuous events of all sorts, and to see patterns at work where they have never seen them before.
Now, let’s think about this for a moment. Going back to the sandpile game, you find that as you double the number of grains of sand involved in an avalanche, the likelihood of an avalanche becomes 2.14 times as unlikely. We find something similar in earthquakes. In terms of energy, the data indicate that quakes become four times less likely each time you double the energy they release. Mathematicians refer to this as a “power law,” or a special mathematical pattern that stands