Scientific progress is, it would seem, largely a matter of deciding, in a fairly ad hoc way, when investigations need to ignore outliers and when outliers are the most important facts around. There is no fixed rule that can decide this question, which is surely a big part of the reason why scientific investigation cannot yet be given over to robots.
This point came forcefully to my attention recent when I read, in close conjunction, about epidemiology and about the expectations hypothesis. Let’s start with the latter: EH is the postulate that market expectations about the future of the short-term interest rate drive the rest of the yield curve. In other words, the market’s expectations for the one-year rate next year (and the well-known mathematics of compounding) are together sufficient to explain the two-year rate this year.
This is a venerable theory. As early as 1896, Irving Fisher wrote, “The investor who holds a bond for a long time realizes an interest rate which is an ‘average’ of the oscillating rates of those who speculate during the interim.” That is the gist of it.
Burial and Exhumation
The usual take on the expectation hypothesis is that it has been tested and found wanting. When Lucio Sarno, Daniel Thornton, and Giorgio Valente wrote a paper on the subject in 2005 they put this view squarely in the title, “The Empirical Failure of the Expectations Hypothesis of the Term Structure of Bond Yields.”
But two of those three authors revisited the question, or a microcosm of it, two years later. Sarno and Thornton, now working with Pasquale Della Corte, wrote, “The Expectation Hypothesis of the Term Structure of Very Short-Term Rates.” [For no good reason, sometimes the EH is stated with the plural adjective “Expectations” and sometimes with the singular adjective “Expectation.”] Here Sarno et al. found that EH does quite well in explaining the term structure of U.S. repo rates ranging from overnight to three months.
At any rate, a new paper seeks to resuscitate EH more broadly, and it will bring us back to the question of outliers. Karim M. Abadir and Christina Atanasova argue that if one discards a handful of “extreme observations,” involving such unusual events as the “Volcker experiment” in the U.S. in the early 1980s, EH works quite well in modeling the yield curve.
Yes, I have to agree in principle that if one views financial economics as a real science there is a point to the occasional setting aside of the outliers in the search for a model of normality. Consider the above graph. It doesn’t matter for the purpose of this illustration what X and Y stand for. The graph makes a case for a close correlation between them, and the data point at X=2.2, Y=42, the outlier, should not be allowed to obscure that fact.
Epidemics and Superspreaders
The other half of the bit of synchronicity was a reading of Spillover, a book by science writer David Quammen on epidemiology and in particular about zoonosis, the spread of disease across species barriers, and it intrigued me that Quammen discusses the epidemiological concept of the “superspreader.”
The superspreader is “a patient who, for one reason or another, directly infects far more people than does the typical infected patient.” A superspreader is the fat tail, the outlier, of the mathematics of epidemiology. Public health officials have, it appears, only recently caught on to the fact that population estimates of the average rate of secondary infection (contagion) can obscure the degree of variation, and that success in containing an outbreak depends crucially on identifying and isolating the potential superspreaders.
If you, as a public health official, quarantine 49 infected patients but let one go, and that one is Typhoid Mary, you have failed.
In this context, at least, it is self-defeating to create a model for normalcy when your concern ought precisely to be with a certain sort of outlier.
My own tentative conclusion: leave the EH to the academic economists, who may get some mileage out of throwing away the outliers. Alpha hunters and their risk managers are roughly in the position of public health officials. If you’ve bet the firm on the proposition that whenever X (above) equals 2.2, Y will equal 22, you have failed.