Modeling the financial crisis

There is an interesting op-ed piece in the New York Times this week by physicist and science writer Mark Buchanan on predicting the current financial crisis. His argument is that traditional economists were unable to predict or handle the current situation (Nouriel Rubini notwithstanding) since their worldviews are shaped by equilibrium theorems, which unfortunately are either incomplete or wrong. Buchanan writes:

Well, part of the reason is that economists still try to understand markets by using ideas from traditional economics, especially so-called equilibrium theory. This theory views markets as reflecting a balance of forces, and says that market values change only in response to new information — the sudden revelation of problems about a company, for example, or a real change in the housing supply. Markets are otherwise supposed to have no real internal dynamics of their own. Too bad for the theory, things don’t seem to work that way.

Nearly two decades ago, a classic economic study found that of the 50 largest single-day price movements since World War II, most happened on days when there was no significant news, and that news in general seemed to account for only about a third of the overall variance in stock returns. A recent study by some physicists found much the same thing — financial news lacked any clear link with the larger movements of stock values.

Certainly, markets have internal dynamics. They’re self-propelling systems driven in large part by what investors believe other investors believe; participants trade on rumors and gossip, on fears and expectations, and traders speak for good reason of the market’s optimism or pessimism. It’s these internal dynamics that make it possible for billions to evaporate from portfolios in a few short months just because people suddenly begin remembering that housing values do not always go up.

Really understanding what’s going on means going beyond equilibrium thinking and getting some insight into the underlying ecology of beliefs and expectations, perceptions and misperceptions, that drive market swings.

He then goes on to describe the work of some pioneers who are trying to model the actual dynamics of markets. A Yale economist with two physicists (Doyne Farmer being one of them) used an agent-based model to simulate a credit market. They found that as the leverage (amount of money borrowed to amplify gains) increases there is a phase transition or bifurcation from a functioning credit market to an unstable situation that results in a financial meltdown.

I found this article interesting on two points. The first is the attempt to contrast two worldviews: the theorem proving mathematician economist versus the computational physicist modeler. The second is the premise that the collective dynamics of a group of individuals can be simpler than the behavior of a single individual. A thousand brains may have a lower Kolmogorov complexity than a single brain. My guess is that biologists (Jim Bower?) may not buy this. Although, my worldview is more in line with Buchanan’s, in many ways his view is on less stable ground than traditional economics. With an efficient market of rational players, you can at least make some precise statements. Whereas with the agent-based model there is little understanding as to how the models scale and how sensitive the outcomes depend on the rules. Sometimes it is better to be wrong with full knowledge than be accidentally right.

I’ve always been intrigued by agent-based models but have never figured how to use them effectively. My work has tended to rely on differential equation models (deterministic and stochastic) because I generally know what to expect from them. With an agent-based model, I don’t have a feel for how they scale or how sensitive they are to changes in the rules. However, this lack of certainty (which also exists for nonlinear differential equations, just look at Navier-Stokes for example), may be inherent in the systems they describe. It could simply be that some complex problems are so intractable that any models of them will rely on having good prior information (gleened from any and all sources) or plain blind luck.

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