Too Much Good News is Bad News

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2024-12-28 16:00:05

In each of these cases I think it’s because the noise has a fatter-tailed distribution than the signal. As a consequence when you see a very-high observation you conclude it’s mostly noise, which implies that after a certain point an increase in the observed outcome becomes bad news instead of good news.

This is a related but slightly different point. Scott Sumner argued “extreme events generally have multiple causes”, with a few examples:

I think Sumner is wrong in his generalization: extreme events typically have a single cause, not multiple causes. Formally (following Nair, Weierman and Zwart below), extreme draws from a sum of thin-tailed influences tend to have many causes, but extreme draws from a sum of fat-tailed influences tend to have one cause.

We often cannot observe the distributions of the individual components but we can observe the distribution of the final aggregate outcome, and if the final outcome is fat-tailed then at least some of the components must be fat-tailed.