A beautiful theory killed by an inconvenient fact!

There was a good article titled "How Did Economists Get It So Wrong" by Paul Krugman, the economist, in last week's New York Times Magazine. It focuses on the crisis in academic economics created by the inconvenient fact of the economic crisis that began last year. The article holds that economists mistook the beauty of their quantitative models supported by statistical data for truth. The article begins:

It’s hard to believe now, but not long ago economists were congratulating themselves over the success of their field. Those successes — or so they believed — were both theoretical and practical, leading to a golden era for the profession. On the theoretical side, they thought that they had resolved their internal disputes. Thus, in a 2008 paper titled “The State of Macro” (that is, macroeconomics, the study of big-picture issues like recessions), Olivier Blanchard of M.I.T., now the chief economist at the International Monetary Fund, declared that “the state of macro is good.” The battles of yesteryear, he said, were over, and there had been a “broad convergence of vision.” And in the real world, economists believed they had things under control: the “central problem of depression-prevention has been solved,” declared Robert Lucas of the University of Chicago in his 2003 presidential address to the American Economic Association. In 2004, Ben Bernanke, a former Princeton professor who is now the chairman of the Federal Reserve Board, celebrated the Great Moderation in economic performance over the previous two decades, which he attributed in part to improved economic policy making.

Thomas Kuhn described a paradigm shift as that which occurs when the scientists in a specific field find enough discrepencies have built up between what their theory says should happen, and what is measured as actually happening. It sounds like the economists have been forced into a paradigm shift by a single, very large fact -- the economic crisis which they had not predicted which wiped out $13 trillion in American wealth and is driving unemployment up to ten percent of the U.S. workforce. A veritable 800 pound gorilla of an inconvenient fact.

There is a place for beautiful models in theory building. They can illuminate relationships in ways that are clearer than in the confusion of booming buzzing reality. The danger of course is confusing a model that is great for didactic and exploratory purposes with that booming buzzing reality.

A beautiful horse race model

I have thought in the past that it would be interesting to take betting on a simple horse race as a model - a handful of horses with a single winner. Betting on a horse race has the interesting element that betting takes place over a limited period of time, ending when the horses leave the starting gate.

I think it is reasonable to assume that there is a "real" set of probabilities describing the probability that each horse would win the race. There are clearly unpredictable elements in any horse race, but equally clearly, all things being equal, some horses run faster than others.

Betters however don't know the "true probabilities" but can estimate them. Thus a specific better can be regarded as adding or subtracting an increment from the probability that each horse will win. Assuming that the betters are rational, the sum of the increments will be zero. It seems obvious that some betters are better than others at estimating the odds. The worse oddsmen would have larger increments to the real odds than the better ones.

People go to horse races to have fun, and the fun is worth something. Some people enjoy seeing a longshot on which they have bet come in first, and are willing to pay some of the expected value of their bet to get the occassional fun of the winning longshot. One might suggest that some people enjoy winning often, and are willing to pay some of the expected value of their winnings by betting on favorites to see more winners.

One can assume two forms of betting. The pari mutual race track betting where odds are estimated during the betting period, but the bets are paid off according to the final distribution of bets. The bookie, on the other hand, takes a bet at set odds, and those odds change as the time of the race approaches.

This is a really messy problem for analytic models, but would seem quite reasonable for simulation models. I think it would be interesting to see for example how closely the odds achieved in such a system modeled the "true odds" that were assumed. There are known divergences in real horse race betting; would they appear in the models?

I think models like this could help us to understand real financial decisions. They have long been possible with the advent of computers, and it would be relatively easy to simulate several thousand betters for hundreds of repetitions of a given race.