TY  - JOUR
AU  - Gabaix,Xavier
AU  - Ibragimov,Rustam
TI  - Rank-1/2: A Simple Way to Improve the OLS Estimation of Tail Exponents
JF  - National Bureau of Economic Research Technical Working Paper Series
VL  - No. 342
PY  - 2007
Y2  - September 2007
UR  - http://www.nber.org/papers/t0342
L1  - http://www.nber.org/papers/t0342.pdf
N1  - Author contact info:
Xavier Gabaix
New York University
Finance Department
Stern School of Business
44 West 4th Street, 9th floor
New York, NY 10012
Tel: 212-998-0257
Fax: 212-995-4233
E-Mail: xgabaix@stern.nyu.edu

Rustam Ibragimov
Harvard University
Department of Economics
Littauer Center
1805 Cambridge St.
Cambridge, MA 02138
E-Mail: ribragim@fas.harvard.edu
AB  - 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.
ER  -