Imperial College London


Business School

Professor of Finance and Econometrics



+44 (0)20 7594 9344i.rustam Website CV




40953 Prince's GateSouth Kensington Campus






BibTex format

author = {Gabaix, X and Ibragimov, R},
doi = {10.1198/jbes.2009.06157},
journal = {Journal of Business and Economic Statistics},
pages = {24--39},
title = {Rank-1/2: A simple way to improve the OLS estimation of tail exponents},
url = {},
volume = {29},
year = {2011}

RIS format (EndNote, RefMan)

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 ζ is not the OLS standard error, but is asymptotically (2 / n)1 / 2ζ. 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 United States city size distribution.
AU - Gabaix,X
AU - Ibragimov,R
DO - 10.1198/jbes.2009.06157
EP - 39
PY - 2011///
SN - 0735-0015
SP - 24
TI - Rank-1/2: A simple way to improve the OLS estimation of tail exponents
T2 - Journal of Business and Economic Statistics
UR -
UR -
UR -
VL - 29
ER -