MLI's Cross comments in the Financial Post on the difficulties that rare but high-impact events pose for the mathematical approach to economics.

Black Swan Economics by Philip Cross, Special to the Financial Post





Nassim Taleb, author of the best sellers The Black Swan and Anti-Fragile, formalized his searing critique of economists and statisticians in 'A Brief Exposition of Violations of Scientific Rigor In Current Economic Modelling,' presented at a conference in France in July. Most of this paper is drawn from a longer treatise on 'Fat Tails and (Anti)Fragility,' available free on the web, which presents 160 pages of the dense mathematics behind the ideas promulgated in his recent books (you've been warned, this isn't light summertime reading).

The crux of his papers is how the occurrence of rare but high-impact events undermines much of the standard statistical theory used in fields ranging from economics to portfolio investment theory. Some of the criticism is well-founded. As a life-long student of business cycles, I have witnessed the consequences of economists both underestimating the risks of booms and busts and overestimating human rationality; the two are related, as shown by the formation of recurring bubbles in financial and housing markets. Economics, like transportation safety (Taleb's analogy, not mine), should first of all be based on avoiding catastrophe.

These 'Black Swan' events are central to his analysis. They lurk unseen in the 'tails' of the probability distribution of what may occur. They cannot be modeled, they distort the measurement of the median, and they result in the underestimation of risk. Risk lies in the future, not in the past, and risk management based on the study of history invariably is erroneous in the long-term. This is because history itself is only one sample from many alternative scenarios that could have happened, which distorts our estimates of the probability that an event may happen. But since we are part of that sample, it is very difficult for people to grasp this concept.

Mathematics has an ambiguous impact on economics. In the words of Robert Heilbroner, the famed popularizer of economics, "Mathematics has given economics rigour, but alas, also mortis." Exposure to its rigour makes some economists formidable debaters in the public arena, cowing other social scientists who lack its logical discipline. However, mathematics is about certainty, the opposite of probability which allows for a range of uncertain outcomes. An over-reliance on abstract mathematical models leads to a view of economics that ignores the risks that exist in the real world.The risks of basing policy on econometrics are on display in the sluggish recovery of Europe and the U.S.

Economists are not always consistent in applying logic. We are all instructed in econometrics class that, when applying standard statistical techniques, you should reflect on whether the data have a normal distribution. For over a decade, it has been a crusade of Taleb's that once you introduce skewness, which applies to almost all economic phenomenon, it is erroneous to assume the data have a normal distribution, on which the most common statistical techniques depend. This may be why econometrics has never been decisive in settling any economic question of consequence, according to Larry Summers, widely-touted as possibly the next head of the Federal Reserve Board.

One reason social scientists are so wedded to the normal distribution is it validates results drawn from small samples. A recent paper on the challenging topic of intergenerational mobility had only 13 sample points to support its main conclusion. But small samples likely don't include the rare events that preoccupy much of Taleb's thinking. By his standards, research based on small samples is little more than anecdotes; "Social scientists need to have a clear idea of the difference between science and journalism, or the one between empiricism and anecdotal statements. Science is not about making claims about a sample, but using a sample to make general claims and discuss properties that apply outside the sample."

Still, society should not dismiss economics any more than it should be in thrall to it. Economics has had great triumphs since the 1970s, wrestling the inflation dragon to the ground in developed countries while lighting the path out of poverty for much of the developing world. It is still notable that the success in controlling inflation and boosting growth in developed countries owed more to heuristics and tinkering than to modelling.

The risks of basing policy on econometrics are on display in the sluggish recovery of Europe and the U.S. In Europe, the IMF recently admitted its estimates of the multiplier effects of fiscal policy were too low, leading it to underestimate the drag on growth from fiscal austerity. In the U.S., quantitative easing by the Federal Reserve Board has had the desired impact of boosting prices for assets such as stocks, bonds and even housing of late, but the stimulus from this wealth on spending has been lower than what models predicted. Having a head of the Federal Reserve who shares this skepticism about models could improve its performance.

Philip Cross is Research Coordinator at the Macdonald-Laurier Institute and former Chief Economic Analyst at Statistics Canada.