Expect the Unexpected

David Warsh at Economic Principles reports on black swans, fat tails, questions about rational expectations, what to do about global warming, and other matters:

In Which Those Troublesome "Black Swans" Find a Champion in Economics, by David Warsh, Economic Principles: ...Nassim Nicholas Taleb burst upon the scene with a 2001 best-seller, Fooled by Randomness: The Hidden Role of Chance in Life and in the Markets. ... The book was a highly-engaging guide to common mistakes that the statistically unsophisticated make in persuading themselves that patterns exist where there are none, especially in financial markets. After a few years seeking to turn his insights into cash with a hedge fund, Empirica Capital, without pronounced effect ..., Taleb is back with The Black Swan: The Impact of the Highly Improbable. The new book is an even greater success.

The title derives from a line of the eighteenth-century philosopher David Hume: "No amount of observations of white swans can allow the inference that all swans are white, but the observation of a single black swan is sufficient to refute that conclusion." When, a few decades later, black swans were discovered in Australia not only to exist but to be relatively abundant, Hume's observation took on additional significance. Taleb classifies as "black swans" all highly unlikely, unexpected and very disruptive events that afterwards are quickly rationalized so as to have seemed predictable all along: market crashes, technological surprises, acts of God, acts of terrorism and the like. We spend our lives assuring each other that each day will be pretty much like the last, he says, but in fact "the world is dominated by the extreme, the unknown and the very improbable."

Although Taleb has a PhD in mathematics from the University of Paris, he is no economist. He is a "quant," or, rather, a scribe of quants, those who invent and build financial markets, as opposed to those who seek to understand them. .. Taleb has a cult following on Wall Street, and a fan in former Secretary of Defense Donald Rumsfeld (remember his much-mocked distinction between "known unknowns" in Iraq and the completely unforeseen surprises he called "unknown unknowns"?). Taleb is "suspicious of theories (particularly those concocted by economists)" and contemptuous of forecasters. He is very big on the lecture circuit.

Meanwhile, however, a pair of papers that make roughly the same case -- a disturbing one in the closely-reasoned world of technical economics -- will appear this month in leading economic journals.  In "Subjective Expectations and the Asset-Return Puzzles" in the September issue of the American Economic Review, Martin Weitzman, professor of economics at Harvard University, contends that the standard treatment of rational expectations equilibrium conceals a hidden assumption, which, if unwarranted, means that economists confront a future permanently more uncertain than previously believed -- a "thick tail" of probabilities, in the language of the bell curve, instead of the comforting thin tail of a normal distribution of probabilities, which describes possibilities that are evermore small. 

And in an essay in the Journal of Economic Literature, Weitzman locates his "nonergodic, Bayesian learning perspective" -- meaning an evolutionary view of both the economy itself and of the possibilities of learning about it -- in the context of the biggest problem of the age, the debate over greenhouse gases. Reviewing the 700-page Stern Review of the Economics of Climate Change, he notes that the report ... has been criticized by several leading economists for its alarmist tone. He, too, indicts it for the very low discount rate the study employs to justify immediate and very expensive measures to cut greenhouse gas emissions.

But Stern may have been right for the wrong reasons, says Weitzman. It wouldn't be right to ignore "the enormously unsettling uncertainty of a very small, but essentially unknown (and perhaps unknowable) probability of a planet Earth that in hindsight we allowed to get wrecked on our watch." A responsible policy approach, then, "neither dismisses the horror stories just because they are two standard deviations away from what is likely not gets stampeded into overemphasizing false dichotomies as if we must make costly all-or-nothing decision right now to avoid theoretically possible horrible outcomes in the distant future." Follow a middle course, he urges: gradually increase emission controls, and commission serious research into the worst possibilities, while conducting plenty of public discussion. "The overarching problem is that we lack a commonly-accepted usable economic framework for dealing withÉ thick-tailed disasters," he writes.

(Both papers may be found on Weitzman's Harvard website, along with a third, "Structural Uncertainty and the Value of Statistical Life in the Economics of Catastrophic Climate Change," which is presumably headed Economica.) ...

When it comes to thinking about the way that people think about the future, macroeconomics economics has been dominated for thirty years or so by a convention known as "rational expectations".... Robert Lucas explained it this way many years ago (to Michel Parkin), "[Rational expectations] doesn't describe the actual process people use trying to figure out the future. Our behavior is adaptive. We try some mode of behavior. If it's successful, we do it again. If not, we try something else. Rational expectations describes the situation when you've got it right."

Rational expectations ... was useful to theorists, but it produced some troubling puzzles, too, about why markets behave the way they do. The biggest of them was posed forcefully in 1985 by a high priest of rational expectations model, Edward Prescott, writing with Rajnish Mehra. If everybody knew what to expect, they asked, how come stocks did so much better than bonds, returning an average of six percent more over time? How come the "risk-free" rate of interest on the best government bonds was so much more than the model indicated it should be? Why were stocks so volatile, when the underlying fundamentals driving them changed so little? 

Three years later Thomas Rietz of the University of Iowa postulated that this equity premium was no puzzle at all if you figured that investors might be worried that a low-probability event, another Great Depression, might occur some time in the future. The generic possibility of a "hidden" event, one that hasn't occurred but which might be a source of legitimate worry, was quickly dubbed "the peso problem" in the early 1990s, after the "puzzle" of high yields on Mexican bonds (at a time the peso was pegged to the US dollar) was suddenly solved -- when the value of the peso collapsed. Investors, it dawned on theorists, had foreseen the possibility of devaluation all along.

Enter Weitzman, 65, a senior figure in the profession... Weitzman became ... curious about in the implications of unknown hidden randomness that might not be evident in the data. A couple of years later, he had concluded that: "the strong force of evolutionary-structural uncertainty is empirically a far more powerful determinant of asset prices and returns than the weak forces of known-fixed-structure [rational expectations equilibrium]-type pure risk."  (Gernot Wagner, late of the Financial Times, boils down the issues here in a lucid explanation of Bayesian asset pricing.) Humankind simply hadn't had enough experience to be confident about its expectations of the future, and Weitzman could prove it. ...

[T]he appearance of "Subjective Expectations" was complicated by the presence of his Harvard colleague Robert Barro, who seemed to hop in front of Weitzman with an extension of the Rietz paper, "Rare Disasters and Asset Markets in the Twentieth Century," published last year in the Quarterly Journal of Economics...

But the authority of Weitzman's insights was reinforced by the recognition that John Geweke, of the University of Iowa, had made a similar argument in a five-page communication to Economic Letters in 2001. Weitzman himself made the rounds of seminars at the top universities with his paper last year, accelerating the assessment process. ... And a tough-minded and accelerated refereeing process brought acceptance earlier this year of the key paper at the AER.

The controversy has yet to be joined by the progenitors of the standard model -- Prescott, Lucas, Thomas Sargent and their seconds. Presumably, they will weigh in before long. Behavioral economists will have their say, as well. Geweke says, "I think Marty is doing what senior people ought to do, bringing it all back together, showing why it matters. If he can get a [new] line of thought going on global warming, attract students, so much the better." For Weitzman, that means beginning with a deep discussion of the characteristics of the standard rational expectations equilibrium model.

Of course, one of the reasons that Donald Rumsfeld admires Nassim Taleb is their shared contempt for the conventional wisdom, whatever it happens to be. Those black swan events come out of nowhere. ...  For all the clarity and precision, his argument about "the inherently-thickened left tail of the reduced-form posterior-predictive probability" of our rates of growth and consumption of the natural world boils down to the injunction to continue to "Expect the unexpected," and to send out probes.