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
DO - 10.3386/t0342
UR - http://www.nber.org/papers/t0342
L1 - http://www.nber.org/papers/t0342.pdf
N1 - Author contact info:
Xavier Gabaix
Department of Economics
Harvard University
Littauer Center
1805 Cambridge St
Cambridge, MA 02138
E-Mail: xgabaix@fas.harvard.edu
Rustam Ibragimov
Harvard University
Department of Economics
Littauer Center
1805 Cambridge St.
Cambridge, MA 02138
E-Mail: irustam@imperial.ac.uk
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 -