Haldane’s Tails of the Unexpected

A. Haldane, B. Nelson Tails of the unexpected,  The Credit Crisis Five Years On: Unpacking the Crisis conference, University of Edinburgh Business School, 8-9 June 2012

The credit crisis is blamed on a simplistic belief in ‘the Normal Distribution’ and its ‘thin tails’, understating risk. Complexity and chaos theories point to greater risks, as does the work of Taleb.

Modern weather forecasting is pointed to as good relevant practice, where one can spot trouble brewing. Robust and resilient regulatory mechanisms need to be employed. It is no good relying on statistics like VaR (Value at Risk) that assume a normal distribution. The Bank of England is developing an approach based on these ideas.

Comment

Risk arises when the statistical distribution of the future can be calculated or is known. Uncertainty arises when this distribution is incalculable, perhaps unknown.

While the paper acknowledges Keynes’ economics and Knightian uncertainty, it overlooks Keynes’ Treatise on Probability, which underpins his economics.

Much of modern econometric theory is … underpinned by the assumption of randomness in variables and estimated error terms.

Keynes was critical of this assumption, and of this model:

Economics … shift[ed] from models of Classical determinism to statistical laws. … Evgeny Slutsky (1927) and Ragnar Frisch (1933) … divided the dynamics of the economy into two elements: an irregular random element or impulse and a regular systematic element or propagation mechanism. This impulse/propagation paradigm remains the centrepiece of macro-economics to this day.

Keynes pointed out that such assumptions could only be validated empirically and (as the current paper also does) in the Treatise he cited Lexis’s falsification.

The paper cites a game of paper/scissors/stone which Sotheby’s thought was a simple game of chance but which Christie’s saw  as an opportunity for strategizing – and won millions of dollars. Apparently Christie’s consulted some 11 year old girls, but they might equally well have been familiar with Shannon‘s machine for defeating strategy-impaired humans. With this in mind, it is not clear why the paper characterises uncertainty a merly being about unknown probability distributions, as distinct from Keynes’ more radical position, that there is no such distribution. 

The paper is critical of nerds, who apparently ‘like to show off’.  But to me the problem is not the show-offs, but those who don’t know as much as they think they know. They pay too little attention to the theory, not too much. The girls and Shannon seem okay to me: it is those nerds who see everything as the product of randomness or a game of chance who are the problem.

If we compare the Slutsky Frisch model with Kuhn’s description of the development of science, then economics is assumed to develop in much the same way as normal science, but without ever undergoing anything like a (systemic) paradigm shift. Thus, while the model may be correct most of the time,  violations, such as in 2007/8, matter.

Attempts to fine-tune risk control may add to the probability of fat-tailed catastrophes. Constraining small bumps in the road may make a system, in particular a social system, more prone to systemic collapse. Why? Because if instead of being released in small bursts pressures are constrained and accumulate beneath the surface, they risk an eventual volcanic eruption.

 One can understand this reasoning by analogy with science: the more dominant a school which protects its core myths, the greater the reaction and impact when the myths are exposed. But in finance it may not be just ‘risk control’ that causes a problem. Any optimisation that is blind to the possibility of systemic change may tend to increase the chance of change (for good or ill) [E.g. Bohr Atomic Physics and Human Knowledge. Ox Bow Press 1958].

See Also

Previous posts on articles by or about Haldane, along similar lines:

My notes on:

Dave Marsay

Which Car?: a puzzle

Here’s a variation on some of my other uncertainty puzzles:

You are thinking of buying a new car. Your chosen model comes in a choice of red or silver. You are about to buy a red one when you learn that red car drivers have twice the accident rate of those who drive silver ones.

Should you switch, and why?

Dave Marsay

Assessing and Communicating Risks and Uncertainty

David Spielgelhalter Assessing and Communicating Risks and Uncertainty Science in Parliament vol 69, no. 2, pp. 21-26. This is part of the IMA’s Mathematics Matters: A Crucial Contribution to the Country’s Economy.

This starts with a Harvard study showing that “a daily portion of red meat was associated with an increase in the annual risk of death by 13% over the period of the study”. Does this mean, as the Daily Express claimed, that “10% of all deaths could be avoided”?

David S uses ‘survival analysis’ to show that “a 40 year-old  man who eats a quarter-pound burger for his working lunch each day can expect, on average, to live to 79, while his mate who avoids the burger can expect to live to 80.” He goes on: “over a lifetime habit, each daily portion of red meat is associated with about 30 minutes off your life expectancy .. ” (my emphasis.)

As a mathematician advising politicians and other decision-makers, I would not be comfortable that policy-makers understood this, and would act appropriately. They might, for example, assume that we should all be discouraged from eating too much red meat.

Even some numerate colleagues with some exposure to statistics might, I think, suppose that their life expectancy was being reduced by eating red meat. But all that is being said is that if a random person were selected from the population as a whole then – knowing nothing about them – a statistician would ‘expect’ them to have a shorter life if they eat red meat. But every actual individual ‘you’ has a family history and many by 40 will have had cholesterol tests. It is not clear what the relevance to them is of the statistician’s ‘averaged’ figures.

Generally speaking, statistics gathered for one set of factors cannot be used to draw precise conclusions about  other sets of factors, much less about individuals. David S’s previous advice at Don’t Know, Can’t Know applies. In my experience, it is not safe to assume that the audience will appreciate these finer points. All that I would take from the Harvard study is that if you eat red meat most days it might be a good idea to consult your doctor. I would also hope that there was research going on into the factors in the apparent dangers.

See Also

I would appreciate a link to the original study.

Dave Marsay