Feb

17

SpecListers occasionally report on novel sightings of Benford's Law — both its utility and its futility.

The latest sighting is from a Journal of the Physics Society, where Mr. T.A. Mir at the Nuclear Research Laboratory, Astrophysical Sciences Division in Kashmir, India evidently had too much time (and yellow cake) on his hands, and set aside his quarks to ponder "The Leading Digit Distribution of the Worldwide Illicit Financial Flows." (sic)

The paper (which I didn't read because of poor grammar in the title) can be found here.

Not to be outdone by a physicist (an EXPERIMENTAL one, no less), I just ran the Benford's Law distribution on the monthly CPI data from both the USA and China for the last umpteen years.

Here's the distribution (using the leading digit to the right of the decimal point, since the digit to the left of the decimal is almost always zero hence I used my poetic license to move the decimal point one place to the right.):

China:

0: 8%

1: 19%

2: 17%

3: 21%

4: 11%

5: 14%

6: 13%

7: 15%

8: 11%

9: 14%

USA:

0: 8%

1: 19%

2: 21%

3: 15%

4: 22%

5: 17%

6: 18%

7: 19%

8: 11%

9: 12% (Percents don't equal 100 due to rounding.)

As any self-respecting THEORETICAL physicist can tell you, the appropriate Benford distribution should be

1: 30.1%

2: 17.6%

3: 12.5%

4: 9.7%

5: 7.9%

6: 6.7%

7: 5.8%

8: 5.1%

9: 4.6%

Alas, Mr. Benford lived in the universe of Natural Numbers and not the more restrictive Whole Number world, (which is a mathematically imprecise way of saying that he ain't got no zeros.) So, I'll take some liberty and add all of the zeros to the ones (since that's allowed using the core principle known as "Close Enough For Government Work." ) But even after I do that, it's not Benford-esque. It's much closer to a uniform distribution. So — there you have it: In 10 minutes on a boring afternoon, based on the inspiration of an EXPERIMENTAL nuclear physicist on the other side of the world, I just proved that both the USA and the Chinese are lying about their respective CPI's. Only one question remains: Will ZEROHEDGE pick up this startling conclusion and run with it?


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3 Comments so far

  1. Mony Saad on February 17, 2012 4:38 pm

    Dear Mr. Niederhoffer,

    Greetings from Portugal. I am contacting you because I came with a foreign exchange formula. I tested it for the years 2011, 2010, 2009. It worked in all the executed simulations. If the formula is proven to be accurate is it of interest to you?

    Kind regards,
    Mony
    E-mail: monyantunes@netcabo.pt
    T: +(351)933 773 741

  2. Adam Braus on February 19, 2012 11:27 am

    This is a fascinating post!

    What are the implications of dropping the first zero though? it seems like on a logarithmic scale, it might still work (since Bedford’s law is supposed to work on various scales and we’re just multiplying by 10!), but I am not certain.

    From your conclusion, is it possible to say in which direction they’re misrepresenting inflation?

    ~Adam

  3. Tim on February 20, 2012 2:31 pm

    My understanding of Benford’s Law is that it works best when the data series spans several orders of magnitude. Although monthly CPI varies more than we would like, it is not dynamic / volatile enough for Benford’s Law to hold true.

    Recommend re-performing your assessment if/when hyper-inflation sets in.

    My $0.02.

    -TR

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