Rank-1/2: A Simple Way to Improve the OLS Estimation of Tail Exponents

Xavier Gabaix () and Rustam Ibragimov

No 342, NBER Technical Working Papers from National Bureau of Economic Research, Inc

Abstract: 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.

JEL-codes: C13 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-ecm
Date: 2007-09
Note: TWP
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