Driving the School Bus Blindfolded

Alas, at the time of writing, the economics establishment is still ignorant of the presence of complexity, which degrades predictability. I will not get too involved in my outrage—instead of doing a second deserto, Mark Spitznagel and I are designing another risk management program to robustify portfolios against model error, error mostly stemming from the government’s error in the projection of deficits, leading to excessive borrowing and possible hyperinflation.

I was once at the World Economic Forum in Davos; at one of my sessions, I illustrated interdependence in a complex system and the degradation of forecasting, with the following scheme: unemployment in New York triggered by Wall Street losses, percolating and generating unemployment in, say, China, then percolating back into unemployment in New York, is not analyzable analytically, because the feedback loops produced monstrous estimation errors. I used the notion of “convexity,” a disproportionate nonlinear response stemming from a variation in input (as the tools for measuring error rates go out of the window in the presence of convexity). Stanley Fischer, the head of the central bank of Israel, former IMF hotshot, co-author of a classic macroeconomics textbook, came to talk to me after the session to critique my point about such feedback loops causing unpredictability. He explained that we had input-output matrices that were good at calculating such feedbacks, and he cited work honored by the “Nobel” in economics. The economist in question was one Vassili Leontieff, I presume. I looked at him with the look “He is arrogant, but does not know enough to understand that he is not even wrong” (needless to say, Fischer was one of those who did not see the crisis coming). It was hard to get the message across that, even if econometric methods could track the effects of feedback loops in normal times (natural, since errors are small), such models said nothing about large disturbances. And I will repeat, large disturbances are everything in Extremistan.

The problem is that if I am right, Fischer’s textbook, and his colleagues’ textbooks, should be dispensed with. As should almost every prediction method that uses mathematical equations.

I tried to explain the problems of errors in monetary policy under nonlinearities: you keep adding money with no result … until there is hyperinflation. Or nothing. Governments should not be given toys they do not understand.

VI

The Fourth Quadrant, the Solution to That Most Useful of Problems

Taleb’s map distinguishes the tail behavior of events from the sensitivity of a decision’s payoff to their magnitude. The Fourth Quadrant combines fat-tailed uncertainty with complex payoffs: rare, very large outcomes can dominate the consequences of a decision. In that setting, the absence of damaging events in a sample provides weak reassurance about exposure to them.

This is more specific than saying that all decisions in Extremistan are equally unpredictable or dangerous. What matters is both the uncertainty and what an extreme outcome would do to you. A model that tracks small fluctuations may still be a poor basis for estimating losses during a large disturbance.

Taleb describes a more constructive way to introduce this limit. Rather than begin with “This is what you don’t know,” begin with “This is where your methods work beautifully” and then identify the conditions under which those methods become unreliable. His example of an event that can cause a “war” makes the distinction concrete: knowing that war may occur tells us little about whether it will kill three people or a billion.

His argument also concerns uncertainty about the model itself. Variance describes a distribution’s spread; it is not by itself a measure of ignorance about the average. With fat tails, however, estimates of averages, variance, and higher moments can be highly sensitive to rare observations and to assumptions about events not yet observed. Adding another estimated parameter does not necessarily resolve that uncertainty.

For a decision in the Fourth Quadrant, examine the consequences of the model being wrong. Which losses could you absorb, and which could threaten survival? Reducing exposure to a catastrophic error may be more useful than reporting a precise probability that the available evidence cannot support.