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Tails of the unexpected
June 9, 2012 3:06 PM   Subscribe

Tails of the Unexpected: "Normality has been an accepted wisdom in economics and finance for a century or more. Yet in real-world systems, nothing could be less normal than normality. Tails should not be unexpected, for they are the rule." An eminently human-readable explanation of why normal models fail to describe the uncertainties of our abnormal world.

Statistics makes my brain hurt: A gentle introduction to the normal distribution. An intuitive demonstration. A more extensive video from Khan Academy. An intuitive explanation of power laws. A familiar example of power laws.

Further reading: "The Fourth Quadrant", "The Pretence of Knowledge"

Previously: Visualizing randomness, modeling uncertainty, tail probabilities, anti-fragility, Black Swans, complex systems, power law distributions, fake power law distributions, prediction and prophecy in the social sciences, network formation, subjective expectations, the limits of statistics.
posted by ecmendenhall (19 comments total) 42 users marked this as a favorite

 
A very personal reflection on some implications of statistical distributions by Stephen Jay Gould.
posted by cromagnon at 3:51 PM on June 9, 2012 [7 favorites]


Outside of controlled experiments, mutual independence is malarky. Assumptions fall apart, the Center(al Limit Theorem) cannot hold.
posted by persona at 4:17 PM on June 9, 2012 [1 favorite]


A Gaussian tongue licks smooth the spikes of accident.
posted by 0rison at 4:22 PM on June 9, 2012 [6 favorites]


From the Tails of the Unexpected link : "But as Nassim Taleb reminded us, it is possible to be Fooled by Randomness".

Fuck me, this is all fairly basic applied stats stuff - shouldn't the economic & financial elite of the world have understood & been across this years ago?

And so, having been fooled for so long by the appearance of randomness, you've woken up to this and are now turning to power laws. Oh lordy, that'll make things better!

(Short version of the power law, even simpler than the "fake power law distributions" link above : wherever you look, if you squint the right way almost everything appears to follow a power law. Very rarely is an actual power law relationship involved...)
posted by Pinback at 4:52 PM on June 9, 2012 [9 favorites]


shouldn't the economic & financial elite of the world have understood & been across this years ago?

Just think about the kind of person who would want to become an economist. These are people for whom money is so important that's what they chose to spend their lives on. These people aren't mathematicians, they're people who think that money is real in a sense beyond a social game.

I'm sure there exist socialist economists wholly concerned with the logistics of wealth redistribution for the purpose of raising the proletariat, but these are not the people in control of institutions like the Bank of England or the National Treasury.
posted by cmoj at 5:22 PM on June 9, 2012 [3 favorites]


The mathematics of greed...
posted by blue shadows at 5:47 PM on June 9, 2012


A lot of talks and books from financial professionals about the "failure" of normal theory statistics (most especially Talib's The Black Swan) bother the heck out of me. I imagine it is what it would be like to walk in to find your kid playing with a loaded handgun, and then later having to read your kids awful book about how handguns are ineffective toys, and the book continues that someone should invent "toys" that aren't guns.

This talk wasn't as bad as others. Still, I'm not sure what we're hoping to accomplish. Models that are too expensive to calculate so that they're never wrong? Tail densities so large that even the mean doesn't exist? Like George Box said, all models are wrong, but some are useful.
posted by ehassler at 5:51 PM on June 9, 2012 [4 favorites]


cmoj: Economists are mathematicians, and that's just the problem! Formalism in economics abstracts away from real, uncertain, unpredictable behavior in favor of nicely optimized systems of equations. All these models are wrong, some of them are useful, and none of them have any scientific value unless they make testable predictions. Economics is too much like physics and should be much more like medicine: an area where the smartest people are willing to admit they don't know how everything works but keep experimenting anyways.
posted by ecmendenhall at 6:40 PM on June 9, 2012 [6 favorites]


Sorry, the initial part of my last comment was driven more by utter surprise than anything else - this stuff is not new (well, it's been well-enough understood to have been practically applicable for 50 years or more in other, more complex domains), and yet the author's big point is that economics and finance has had an almost pathological death-grip on assumptions of stochasticity and normality.

I started off in electronics 30 years ago. More recently, I've become an ecologist*. In both those fields, it's long been recognised that normality ain't the norm for all but the simplest of systems, and that models that assume normality are at best "broken, but OK for a first approximation**". Both have graduated from assumptions of normality, been through power laws and pareto distributions, and have learned a lot about the attractive pitfalls of each.

The second part of my comment was based on the feeling I got from reading the paper - that they're then suggesting that, instead of assuming normality & a gaussian distribution, economic models would benefit from taking up power-law models. The danger there is that, as well as the same basic mistake (that you should choose a distribution that fits your observations, rather than fitting a model to reality - a subtle difference), power laws are particularly susceptible to being mis-recognised and mis-applied. Given the history as outlined in the article, they seem likely just to substitute a death-grip on normality with a death-grip on power laws. Just because the distribution you observe has a tail doesn't mean you've got a power law relationship happening - in fact, in most real-world cases that's probably the last thing you should be looking at!

Economics is a complex field, and from reading the paper there seems to be too much of a reliance on ignoring the complexity in order to simplify the model components & make them manageable. There's a fine line between under-fitting and over-fitting your model to your system, with the former often due to a reluctance or inability to deal with the inherent complexity. I do kinda like their conclusion, though - public policy should be one step ahead in understanding the system, or at least the risks involved, and "putting in place robust fail-safes to stop chaos emerging". I suspect, though, that the industry wouldn't particularly like the necessary intrusions and restrictions.

(* Still raw enough, though, that I'm uncomfortable in describing myself as one. The more you know, the more you know you don't know, etc…
** Gotta be careful how I say that, seeing as it's often all-too-necessary to gloss over it ;-)

posted by Pinback at 7:39 PM on June 9, 2012 [3 favorites]


Just think about the kind of person who would want to become an economist. These are people for whom money is so important that's what they chose to spend their lives on. These people aren't mathematicians, they're people who think that money is real in a sense beyond a social game.

I think you've confused economists with financiers. I reqlly love economics and wish more people appreciated that it is not about money. Money is just society's way of quantifying people's preferences, so it gets used a lot as a proxy for utility, which is what economists care about.
posted by anigbrowl at 8:17 PM on June 9, 2012 [7 favorites]


they're then suggesting that, instead of assuming normality & a gaussian distribution, economic models would benefit from taking up power-law models.

Wait, is that what they're saying?

This is one of the only times I've really missed the IMG tag, because I think we all need to look at a picture of Charlie Brown saying "AAUUUUGGHH!" right now.
posted by escabeche at 8:21 PM on June 9, 2012 [2 favorites]


Taleb is a horrible writer but he actually makes a good point: we tend to reward managers as if financial outcomes followed a normal distribution. If managers do better than the mean they get greater rewards; if they do much better than the mean they get a great deal more. The problem isn't just that this doesn't reflect real financial outcomes, which tend to be characterised by normal growth punctuated by intermittent catastrophes: the problem is that the robustness necessary to deal with catastrophes imposes a cost which causes lower growth, and consequently we are punish managers who attempt to create robust systems. Managers tend to act as if unpredictable catastrophes never occur. If they happen to be lucky during their tenure they get rewarded for the higher growth; if they're unlucky and a catastrophe does occur they can plausibly say it was unpredictable and move on to their next position.
posted by Joe in Australia at 8:30 PM on June 9, 2012 [7 favorites]


I should add that I think Taleb was only using fractals and power laws as an example of non-normal distributions: he's very clear that he doesn't think there's actually a way to usefully quantify expected financial outcomes. He's all about robustness and flexibility, not finding secret laws of statistics.
posted by Joe in Australia at 8:33 PM on June 9, 2012


I will say, though, that the linked .pdf will do much good if it induces people to read Ian Hacking's marvelous intellectual history of statistics, The Taming of Chance.
posted by escabeche at 8:52 PM on June 9, 2012 [1 favorite]


Economists are mathematicians,

You're right, I should have chosen my words more carefully. They are mathematicians... trying to do sociology with math.
posted by cmoj at 9:12 PM on June 9, 2012


Meanwhile everyone's retirement money is getting funneled via 401k funds into the stock and bond markets, causing the mother of all bubbles.

Some day they'll change the rules about withdrawing in some small (but broken) way, and the whole thing will fall like a broken dam.

This is what happens when people don't understand the difference between money, currency, and debt.

Money never looses all its value, and isn't subject to inflation. (Money in the USA disappeared in 1965)
Currency sometimes goes to zero, and is debased by inflation. (It's a promise of money, usually written on paper)
Debts aren't always repaid, even in the best of times, but trade that risk for interest.
posted by MikeWarot at 9:15 PM on June 9, 2012


escabeche: "Wait, is that what they're saying?"

Well, they're economists, so (as per the old joke) they're not definitively stating anything. But the whole thing starts off talking about normal distributions, how they're not really "normal" (in the sense of "commonplace"), then say "In its place, natural and social scientists have often unearthed behaviour consistent with an alternative distribution, the so-called power law distribution."

They then glossingly generalise that to fat-tailed distributions, spend most of the time talking about fat-tails & how they need to be accounted for, swing back to generic non-normality in economics / finance / risk management (including more talk of fat tails), and finish up with:

"Normality has been an accepted wisdom in economics and finance for a century or more. Yet in real-world systems, nothing could be less normal than normality. Tails should not be unexpected, for they are the rule. As the world becomes increasingly integrated – financially, economically, socially – interactions among the moving parts may make for potentially fatter tails. Catastrophe risk may be on the rise.

If public policy treats economic and financial systems as though they behave like a lottery – random, normal – then public policy risks itself becoming a lottery. Preventing public policy catastrophe requires that we better understand and plot the contours of systemic risk, fat tails and all."


Overall, it leaves you with the impression that (a) power law distributions are more "normal" than the normal distribution, (b) fat-tailed distributions are power law distributions, and (c) the effects of such distributions need to be included in models & regulation.

It'd be a much, much better presentation if they had simply given 1 or 2 other examples of non-normal distributions that are also commonly found recognised observed in real-world systems. Hell, throw in a Beta distribution - you can make that approximate lots of cool-looking curves; from a power law to normal and beyond! Parameter estimation can be a bitch though…
posted by Pinback at 10:07 PM on June 9, 2012 [1 favorite]


And a funny fact: with all this rigour and methodological attention and mathematical approach, nothing beats ordinary well disguised fraud (in terms of cost effectiveness) see MF Global.

Anyway, there's nothing to see there the invisible hand of the marker misquote from Smith bla bla...
posted by elpapacito at 3:35 AM on June 10, 2012 [1 favorite]


MikeWarot: "Meanwhile everyone's retirement money is getting funneled via 401k funds into the stock and bond markets, causing the mother of all bubbles.

Some day they'll change the rules about withdrawing in some small (but broken) way, and the whole thing will fall like a broken dam.
"

OK, that sounds reasonable... lots of people putting their money in, and they'll take it out at some point, and so on... Let's see if the data support your hypothesis.

Can you take a look at this graph that approximately correlates to the value of the entire US stock market, derated for inflation, and point out where the bubble began? BTW, 401ks have been around since 1978.

Frankly, I can't see any support at all for your theory in the data. There was a bubble that began circa 1995, but no one believes that bubble was caused by too much 401k investment.
posted by IAmBroom at 9:32 PM on June 10, 2012


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