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.
I sometimes think that the real issue, especially in economic forecasting, aren’t fat tails but unanticipated structural breaks in deterministic parameters.
That could be, but how often do structural breaks occur? What sort of errors do these breaks produce? I don’t really see these as competing hypotheses.
I am not sure I get the connection between normal distributions and stability. If people assume normal distributions, rare events are still “expected” every once in a while. Rare events are expected over just about any probability distribution. Randomness is everywhere.
I agree with your conclusion, though. Additionally, underestimating the volitility of the market is not necessarily a problem of the market per say, but of the individuals doing the underestimating. In any long period of time, we should see “Great Moderations” in just about any distribution just by chance. And, we should see big shocks every now and then too. I agree with Taleb in the sense that people are often “fooled by randomness,” and to your point, in both directions.
Scott, it’s true that rare events are expected even under a normal distribution, but with fat tails, events that you would otherwise expect to be very rare happen more frequently. That is why I associate volatility with fat tails and stability with a normal distribution.
Well, I think these might be alternative hypotheses. The world which you seem to describe is a strictly stationary one, only with fat tails.
The one which I’m suggesting is one with normal distributions, but with ones that undergo locational shifts. In fact, I believe that the normality assumptions are usually quite plausible (more so than a world with infinite/undefined moments). These shifts are essentially unmodelled, hence we do not know what is driving them but there are methods of identifying them if they occur.
Most fundamentally, the methods which enable to identify structural breaks are not the same ones as those which we would deploy in presence of fat-tailed distributions (and vice-versa). So there might be a choice to be made.
http://www.sciencedirect.com/science/article/B7P5J-4JSMTWJ-H/2/e17d009c73049240317e03f537ebebdd
I understand that strictly speaking there is a difference between those two worlds. I am not wedded to a stationary model, so I’m happy to think also in terms of structural breaks. Nevertheless, I think that even in the world you describe, ex post we would observe that ordinary economic agents make fat-tailed errors. Am I wrong about this?
By the way, we need not posit an error distribution with infinite or undefined moments, such as the Cauchy distribution. Just because it’s my favorite distribution does not mean that it describes reality. I’d settle for a t-distribution with some (but not infinite) degrees of freedom (this is what I meant by “more like a Cauchy distribution than like a normal distribution”—as you know, but some other readers may not, a Cauchy distribution coincides with a t-distribution with 1 degree of freedom, and a normal distribution coincides with a t-distribution with infinite degrees of freedom.).