Eli Dourado

Risk, fat tails, and business cycles

Tyler Cowen offers his non-Keynesian take on the recession, applying the theory he lays out in Risk and Business Cycles (recommended for all economics graduate students, but master Snowdon and Vane first). I agree with his arguments, but I want to add what I think is a missing ingredient in his theory: fat tails.

David Levy is the source of my appreciation for fat tails. His graduate Econometrics 1 class is basically a class on robust estimation. He makes his students do loads of exploratory data analysis—we generated data with different error distributions and then evaluated how various techniques performed at estimating the true parameters, which we knew because we generated the data. My favorite distribution is the Cauchy distribution. It is fascinating because to the naked eye it looks a lot like the normal distribution, but the techniques that work for normally distributed errors are very inefficient for Cauchy-distributed errors.

I think that real-world macroeconomic errors are distributed more like a Cauchy distribution than like a normal distribution. They have fat tails. But humans do not find Cauchy-distributed errors intuitive. Most of the errors we deal with in our ordinary lives are distributed normally. We make a cognitive error when we confront fat tails.

The implication for Cowen’s theory is this. People invest and consume thinking the world is less volatile than it is. There is a series of years in which the errors are in the main part of the distribution. People infer that the world is pretty stable. Then the eight-sigma event happens. People realize that the world is volatile and they have inadvertently been taking more risk than they intended to take; they exit risky investments and move to safer ones. Cowen’s theory takes over.

Risk and Business Cycles explicitly adopts a rational expectations assumption, and I am positing a systematic error. I think that my position is defensible. I think RE can be a useful methodological tool, but one has to recognize its limitations. RE is likely to closely describe reality when feedback is reliable. I have no problem with adopting mean-zero first-order errors in macroeconomics, but I think there is good reason to believe that people’s expectations about the shape of the error distribution is not subject to good feedback. It is entirely possible that 19 out of 20 years, the people who assume a normal distribution will outperform those who assume a fat-tailed distribution. The other years, government intervention may insulate those who feel the pain of their big mistakes.

The past few decades are sometimes called The Great Moderation. My hypothesis supports skepticism that anything significant changed during this period. The world has always been volatile; we just didn’t realize it.