Tuesday, June 9, 2009

The law of large numbers

Ezra Klein points to this paper (400k pdf file) by Tyler Cowen.

Cowen claims that

... In favored approaches of the 1980s and 1990s, it was common to admit that individual mistakes were possible but that such mistakes would be governed by the “law of large numbers.” ...

with the implication that this meant in the aggregate mistakes would cancel out. This shows a rather serious misunderstanding of the law of large numbers.

Basically the law of large numbers says that under some conditions independent random errors will tend to cancel out. But it is incorrect to expect it to apply to errors made by investors because such errors are not independent in general. For example if the government makes a mistake in computing some economic statistic many investors may make similar errors because they rely on this statistic. Similarly for any other widely circulated error. Additionally because of the human tendency to go along with the crowd, late deciders will tend to adopt the opinions of early deciders another source of dependence.

Modern economics is often criticized for relying on unrealistic models of economic behavior which don't apply to the real economy. I don't know if Cowen has correctly described rational expectations models. If he has, they appear to be seriously flawed.

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