Rank-1/2
Subtitle: a simple way to improve the ols estimation of tail exponents
By: Xavier Gabaix, Rustam Ibragimov
Contributors: Ibragimov, Rustam; National Bureau of Economic Research
Series: NBER working paper series -- working paper . 342; Working paper series (National Bureau of Economic Research : Online) -- working paper no. . 342.
Publisher: National Bureau of Economic Research
Published: 2007
Place of publication: Cambridge, MA
Language: eng
Format: [electronic resource] :
Description: "Despite the availability of more sophisticated methods, a popular way to estimate a Pareto exponent is still to run an OLS regression: log(Rank)=a-b log(Size), and take b as an estimate of the Pareto exponent.  The reason for this popularity is arguably the simplicity and robustness of this method.  Unfortunately, this procedure is strongly biased in small samples.  We provide a simple practical remedy for this bias, and propose that, if one wants to use an OLS regression, one should use the Rank-1/2, and run log(Rank-1/2)=a-b log(Size).  The shift of 1/2 is optimal, and reduces the bias to a leading order.  The standard error on the Pareto exponent zeta is not the OLS standard error, but is asymptotically (2/n)^(1/2) zeta.  Numerical results demonstrate the advantage of the proposed approach over the standard OLS estimation procedures and indicate that it performs well under dependent heavy-tailed processes exhibiting deviations from power laws.  The estimation procedures considered are illustrated using an empirical application to Zipf's law for the U.S.  city size distribution"--National Bureau of Economic Research web site.
Notes: Title from PDF file as viewed on 9/21/2007.

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