NEW YORK – Mathematics can be beguilingly elegant. It can also be dangerous when people mistake its elegance for truth.
Albert Einstein’s theory of general relativity might be the best example of elegant math, capturing a wide range of subtle and surprising phenomena with remarkable simplicity. Step toward the practical, though, and physics moves quickly away from elegance to makeshift usefulness. There’s no pretty expression for the operation of a nuclear reactor, or for how air flows past the swept wings of an aircraft. Understanding demands ugly approximations, or brute-force simulation on a large computer.
In one very practical and consequential area, though, the allure of elegance has exercised a perverse and lasting influence. For several decades, economists have sought to express the way millions of people and companies interact in a handful of pretty equations.
The resulting mathematical structures, known as dynamic stochastic general equilibrium models, seek to reflect our messy reality without making too much actual contact with it. They assume that economic trends emerge from the decisions of only a few “representative” agents — one for households, one for firms, and so on. The agents are supposed to plan and act in a rational way, considering the probabilities of all possible futures and responding in an optimal way to unexpected shocks.
Surreal as such models might seem, they have played a significant role in informing policy at the world’s largest central banks. Unfortunately they don’t work very well, and they proved spectacularly incapable of accommodating the way markets and the economy acted before, during and after the recent crisis.
Now, some economists are beginning to pursue a rather obvious, but uglier, alternative. Recognizing that an economy consists of the actions of millions of individuals and firms thinking, planning and perceiving things differently, they are trying to model all this messy behavior in considerable detail. Known as agent-based computational economics, the approach is showing promise.
Take, for example, a 2012 (and still somewhat preliminary) study by a group of economists, social scientists, mathematicians and physicists examining the causes of the housing boom and subsequent collapse from 2000 to 2006.
Starting with data for the Washington D.C. area, the study’s authors built up a computational model mimicking the behavior of more than 2 million potential homeowners over more than a decade. The model included individual details such as race, income, wealth, age and marital status, and on how these characteristics correlate with home buying behavior.
Led by further empirical data, the model makes some simple, yet plausible, assumptions about the way people behave. For example, homebuyers try to spend about a third of their annual income on housing, and treat any expected house-price appreciation as income. Within those constraints, they borrow as much money as lenders’ credit standards allow, and bid on the highest-value houses they can. Sellers put their houses on the market at about 10 percent above fair market value, and reduce the price gradually until they find a buyer.
The model captures things that dynamic stochastic general equilibrium models do not, such as how rising prices and the possibility of refinancing entice some people to speculate, buying more-expensive houses than they otherwise would. The model accurately fits data on the housing market over the period from 1997 to 2010 (not surprisingly, as it was designed to do so). More interesting, it can be used to probe the deeper causes of what happened.
Consider, for example, the assertion of some prominent economists, such as Stanford University’s John Taylor, that the low-interest-rate policies of the Federal Reserve were to blame for the housing bubble. Some dynamic stochastic general equilibrium models can be used to support this view. The agent-based model, however, suggests that interest rates weren’t the primary driver: If you keep rates at higher levels, the boom and bust do become smaller, but only marginally.
A much more important driver might have been leverage — that is, the amount of money a homebuyer could borrow for a given down payment. In the heady days of the housing boom, people were able to borrow as much as 100 percent of the value of a house — a form of easy credit that had a big effect on housing demand.
In the model, freezing leverage at historically normal levels completely eliminates both the housing boom and the subsequent bust.
Does this mean leverage was the culprit behind the subprime debacle and the related global financial crisis?
Not necessarily. The model is only a start and might turn out to be wrong in important ways. That said, it makes the most convincing case to date, and it seems likely that any stronger case will have to be based on an even deeper plunge into the messy details of how people behaved. It will entail more data, more agents, more computation and less elegance.
If economists jettisoned elegance and got to work developing more realistic models, we might gain a better understanding of how crises happen, and learn how to anticipate similarly unstable episodes in the future. The theories won’t be pretty, and probably won’t show off any clever mathematics. But we ought to prefer ugly realism to beautiful fantasy.
Mark Buchanan, a theoretical physicist and the author of “The Social Atom: Why the Rich Get Richer, Cheaters Get Caught and Your Neighbor Usually Looks Like You,” is a Bloomberg View columnist. The opinions expressed here are his own. Email: firstname.lastname@example.org