Title: Rank-1/2
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.