@techreport{NBERt0342,
title = "Rank-1/2: A Simple Way to Improve the OLS Estimation of Tail Exponents",
author = "Xavier Gabaix and Rustam Ibragimov",
institution = "National Bureau of Economic Research",
type = "Working Paper",
series = "Technical Working Paper Series",
number = "342",
year = "2007",
month = "September",
doi = {10.3386/t0342},
URL = "http://www.nber.org/papers/t0342",
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.},
}