Aug 16, 2012

Rational Expectations and Assuming the Consequent

Here's John Kay giving an example of something that has always bothered me:
I used to tell students who queried the premise of “rational” behaviour in financial markets – where rational means are based on Bayesian subjective probabilities – that people had to behave in this way because if they did not, people would devise schemes that made money at their expense.
Here's another example from David Levine:
Take an example: how we might predict stock market crashes? Suppose that two behavioral psychologists, call them "Kahneman and Tversky," produce a model of "cognitive biases" that predicts when crashes will occur. The model tells us that the stock market will crash on October 28. Since the model is reliable and has a perfect track record, we naturally believe this prediction. So what would you do? You would sell all your stock on October 27. But of course if enough people do this the stock market will crash on October 27 and not October 28. So this apparently reliable model will be proven wrong.
The idea here is that markets can incorporate expectations about pretty much anything. So if you make a public, reliable predication about something that will happen, people will arbitrage the thing into reality before the predicted time. Hard to deny that scenario.

But all the work in this scenario is being done by "we naturally believe this prediction." Well, suppose "we" don't? Suppose you're an agoraphobic computer programmer living in a basement in Silver Spring, Maryland, and you make a financial model. Your model predicts a crash on October 28th this year. But no one believes you. Maybe you're dismissed as a crank in the lickspittle financial press. (Imagine that.) Or maybe you're really unconvincing in person. But your model is correct, and your prediction comes true, at precisely the time you said.

Being able to predict the precise time of a crisis is not common, of course, but the function of belief in validating this kind of argument for rational expectations is critical. To say that financial crises are unpredictable because people will arbitrage any model, and therefore rational expectations theory obtains, seems perilously close to saying "because rational expectations, therefore rational expectations."

In fact, many people have been in the general situation of our computer programmer. People like Michael Burry, who didn't predict exactly when the financial crisis would happen, but knew that it would happen at some point, and predicted correctly in broad outline and detail how it would happen. And what did people in his little fund do when he told them what was going to happen? They didn't believe him! Even after he made them millions of dollars, they still resented him for it for some reason.

Anyway, the idea that people will take widely accepted models into account seems true in a boring and obvious way. But to derive from that a rational expectations theory seems unjustified.

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