# Shrill

Robert Waldmann

I usually try to be semi polite. I especially don’t usually deliberately write rude things about smart economists. However, here goes. Evidently Tyler Cowen* wrote

In a strict rational expectations model, we might expect some people to overtrust others and one view of rational expectations is that investorsâ€™ errors will cancel one another out in each market period. Another view of rational expectations is that investorsâ€™ errors will cancel one another out over longer stretches of time but that the aggregate weight of the forecasts in any particular period can be quite biased owing to common entrepreneurial misunderstandings of observed recent history. In the latter case, entrepreneurial errors magnify one another rather than cancel one another out. That is one simple way to account for a widespread financial crisis without doing violence to the rational expectations assumption or denying the mathematical elegance of the law of large numbers.

After the jump an argument which might be of some interest (added as an update) and a rant.

* Update: spelling error corrected.

Update: I just noticed something odd about the paragraph by Cowen. Like many economists he has decided to call “The Efficient Markets Hypothesis”, “Rational Expectations.” So before his redefinition (which I think must be absolutely condemned as I do below) he wrote “one view of rational expectations is that investorsâ€™ errors will cancel one another out in each market period.” If by “errors” he means avoidable errors, then that would be the efficient markets hypothesis. However, it would not amount to rational expectations.

When the rational expectations assumption is used, it is used to mean “the things we care about have the same values they would have if everyone were rational.” In particular, inferences about welfare which some people actually take seriously, are derived from models including the rational expectations hypothesis.

Then somehow, when it is tested it changes to a quite different hypothesis. “aggregate variables which we can measure have the same values they would have if everyone were rational.” So, in finance, it becomes a statement about asset prices. However, for the use of the assumption in contributions to the policy debate to be defensible, one would need a model in which welfare is what it would be if everyone were rational. I am fairly confident that you can’t do this unless you assume people are risk neutral, that is make an assumption which is overwhelmingly rejected by the data.

If aggregates act as if people are rational and they make irrational mistakes which cancel out then they will bear more risk than they would if they were rational. Welfare will be lower. The amount of irrational risk bearing can be influenced by policy. The optimal policy is laissez faire *if* people are rational. If they are not rational yet aggregates behave as if they were rational, then the optimal policy will not be laissez faire.

Before moving on to discuss Cowen’s effort to dodge data by redefining terms,

I note that it does *not* become a statement about asset prices and trading volume for the simple reason that no one can write down a model with the rational expectations hypothesis which isn’t overwhelmingly rejected by the data. I believe that there are simply no models of trading volume including the rational expectations assumption in the literature. For more than 20 years agents who trade with no motive described in the model have been present in (as far as I know) all models of market microstructure. Now it may be hinted that there might be some rational reason for noise traders to trade as they do. However, no one (as far as I know and I am ignorant) has presented such a model, because the volume of trading that could be rationalized is a tiny tiny tiny fraction of observed trading volume.

My original rant is below. 5 minutes after posting, I stand by it, but I think the objection above is actually of some potential interest, while the shrillness below is, of course, something that has been said and written many many times.

Cowen has chosen to redefine the rational expectations hypothesis. He has also defined it so that it is meaningless, unfalsifiable, and not a hypothesis.

His intellectual accomplishment can be reproduced in other fields. If I redefine “The Ptolomaic model” to mean “The hypothesis that the earth orbits the sun” then I can save it from its recent difficulties.

I think he could have made his point more clearly if he decided to redefine “the rational expectations hypothesis” to be the hypothesis that 2+2=4. Oh and while he’s at it he could define “the law of large numbers” to mean large numbers are larger than small numbers.”

His use of the phrase “law of large numbers” shows that he is absolutely unwilling to consider the actual statement of any actual theorem. Oh and that he doesn’t know the difference between mathematics and science.

I think a refutation of Cowen’s argument which is just as valid as his argument is “I am Tyler Cowen and I retract abjure and reject my argument”. Technically, I am not Tyeler Cowen, but if he can redefine the rational expectations hypothesis as he pleases then why can’t I redefine “Tyler Cowen” to mean “Robert Waldmann.”