Tuesday, June 17, 2008

Why I Don't Appreciate Fat Tails

I think on any issue, there is a big difference between apostates and everyone else. Those who believed X when young, learn not-X when older, and then vociferously argue that X is an abomination. For example, Andrew Sullivan hypothesized that ex-New York Times editor Howell Raines's obsession with race was because Raines noted that as a child raised in the south, he considered blacks inferior at one time (he won a Pulitzer for a NYTMagazine article on his family's black housekeeper). Sullivan called it the Guilty Southern White Boy syndrome, the need to assert, as if one is discovering a new planet, that black people are people too. Thus, Raines supports affirmative action as a penance of sorts.

I was born to liberal parents, and so I have no guilt about prior racism. I have never considered black Americans inferior, so I'm not defensive about not supporting affirmative action, or criticizing the race hucksters.

In a similar way, I always considered the Normal or Gaussian distribution an approximation of reality. Reality generally has fatter tails, but the gist of the normal distribution is pretty good, and has lots of neat properties: the sum of normal random variables is normally distributed, the expectation of e^x has a closed form if x is normally distributed. This makes it useful for exposition. People like Taleb and Haug, I bet, learned about the normal distribution and took it as gospel. then, when they discovered actual distributions were not exactly normal, they figured they had discovered something really novel, true and important. True, yes. Important, sometimes. Novel, not to me.

I just think it comes from the way people learn things. Some like to move in a sequence of true-believer modes, and clearly, the popularity of Taleb suggests he strikes a nerve with many people who also feel betrayed by the actual inexactitude of the normal distribution. I never thought the normal distribution was perfect, so this observation leaves me flat.

1 comment:

Pete Sattler said...

Doesn't the Central Limit Theorem
state that all means are normal? I honestly don't remember the assumptions to prove the CLT, but if we abandon the central limit theory then everything we know about statistics and econometrics can't be used.

Anycase, all models are wrong. The only question is how wrong, and if they can still be a useful approximation.