Randomness and the Black Swan

15 November 2006 at 4:16 pm 6 comments

| Peter Klein |

I’m on a private discussion list where the subject of resampling/bootstrapping techniques, and their application to empirical social science research, is being discussed. A commentator pointed to a 1988 New York Times article in which Stanford’s Jerome Friedman calls bootstrapping “the most important new idea in statistics in the last 20 years, and probably the last 50.” Murray Rothbard invoked bootstrapping, indirectly, in a 1989 article criticizing empirical methods in economics:

As improbable as this may seem now, I was at one time in college a statistics major. After taking all the undergraduate courses in statistics, I enrolled in a graduate course in mathematical statistics at Columbia with the eminent Harold Hotelling, one of the founders of modern mathematical economics. After listening to several lectures of Hotelling, I experienced an epiphany: the sudden realization that the entire “science” of statistical inference rests on one crucial assumption, and that that assumption is utterly groundless. I walked out of the Hotelling course, and out of the world of statistics, never to return.

The “crucial assumption” to which Rothbard refers is the assumption of normality. Of course, it is possible to do statistical inference without assuming data are normally distributed, and the central limit theorem tells us not to worry about distributional properties as samples become “large.” But how large is large?

Some resampling enthusiasts (e.g., the late Julian Simon, better known for his controversial work on natural resources) argue that regardless of the asymptotic properties of a particular distribution, we should pay more attention to the rate at which it approaches the normal. It may take far more than N=30 observations, or even N=300 or N=3,000. Rothbard goes on to cite Friedman and bootstrapping pioneer Bradley Efron, arguing that the newer techniques constitute a fundamental challenge to the standard practices in empirical social-science research.

Anothter commentator pointed to mathematician/investor Nassim Nicholas Taleb, a co-author of Benoit Mandelbrot. In a recent lecture series, Taleb

emphatically rejected the [central limit theorem], and the entire “Gaussian” approach as applicable to social and economic reality. . . . He pointed out — as Rothbard also pointed out in [the article quoted above] — that the fractal approach, which does not give precise probabilities, is much more applicable to social reality because it does not arbitrarily dismiss inconvenient events as “outliers.” For example, according to Taleb, the Crash of 1987, the proverbial Black Swan to Gaussians, “is not an outlier if you use a fractal with an exponent of 3.” (In the Gaussian world the Crash of 1987 was 20 standard deviations from the mean, an episode that would occur “every several billion lifetimes of the universe.”) Taleb went on to argue that Mandelbrot’s fractals allow us to account for a few Black Swans, although by no means all, and transform them into Gray Swans or “known unknowns.” Taleb also produced a startling graph showing that in the last 50 years the ten most extreme days in the financial markets represent half the returns. And yet these Black Swans are dismissed by Gaussians. Taleb concluded that those using sigmas (standard deviations) as a measure of risk and randomness in the world of finance were practicing “phony mathematics” and were “charlatans.”

I haven’t read Taleb’s 2004 book Fooled by Randomness, but hope to do so soon. His newest book, The Black Swan, is scheduled for publication in April 2007.

So, does the rise of resampling/boostrapping methods, and/or fractal approaches, pose a fundamental challenge to conventional models in empirical social science?

Entry filed under: - Klein -, Management Theory, Methods/Methodology/Theory of Science, Strategic Management.

The Intellectuals and Socialism Taleb on Mathematical Economics

6 Comments Add your own

  • 1. Mark E Hoffer  |  16 November 2006 at 9:05 am

    Is this: “So, does the rise of resampling/boostrapping methods, and/or fractal approaches, pose a fundamental challenge to conventional models in empirical social science?”

    -a rhetorical Q: ?

  • 2. Peter Klein  |  16 November 2006 at 10:00 am

    Didn’t mean it that way. Read “fundamental” as “meaningful,” “of lasting importance,” “needing to be taken seriously,” etc.

  • 3. Mark E Hoffer  |  17 November 2006 at 12:11 am

    Dr. Klein,

    Succinctly, Yes.

    Interestingly enough, I find the subsequent O&M post, “Taleb on Mathematical Economics”, to add additional insight into the answer.

    excerpt: “without considering the fact that either the class of mathematics they were using was too restrictive for the class of problems they were dealing with, or that perhaps they should be aware that the precision of the language of mathematics could lead people to believe that they had solutions when in fact they had none. . .” would seem to address: “conventional models in empirical social science”, as well.

  • 4. C. Grammich  |  17 November 2006 at 9:50 am

    Being the somewhat frivolous sort, I must say whenever I hear of the assumptions of normality in statistical inference, I think of R. C. Lewontin’s 1995 review, in the New York Review of Books, of the work by Laumann et al. with surveys on sexual practices. Unfortunately, I can’t remember an exact quote, but I do recall Lewontin saying something like his own sex life, if Laumann et al. were to be believed, was quite “normal,” even conservative, but that there was likely no way Laumann and his colleagues could have paid him enough money to discuss it in any detail. Which, of course, raises, among other questions, the one of whom, exactly, were Laumann et al. able to get to divulge such details, and why they were willing to do so . . .

    More seriously, I recommend Lewontin’s review, and the subsequent exchanges, particularly that with Richard Sennett, to anybody interested in these issues in sociology. In fact, in trying to find Lewontin’s original review on-line, I saw that this “series” is on the syllabi for some introductory courses on social research.

    Jonathan Cohn also had a good article on similar issues in political science, asking “When Did Political Science Forget About Politics?,” a critical review of the influence of “rational choice” theory in the study of politics, published in The New Republic in 1999.

  • 5. Alison Kemper  |  17 November 2006 at 12:17 pm

    Looked up the reference to Cohn.

    Title Irrational exuberance.

    Author Cohn, Jonathan S

    Source The New Republic, vol. 221, no. 17, pp. 25-31, October 25 1999

    ISSN 0028-6583

  • 6. Peter Klein  |  17 November 2006 at 12:20 pm

    Thanks, see also this post.

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