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@article{Gabaix:2011:10.1198/jbes.2009.06157,
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 = {http://dx.doi.org/10.1198/jbes.2009.06157},
volume = {29},
year = {2011}
}

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TY  - JOUR
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  - http://dx.doi.org/10.1198/jbes.2009.06157
UR  - http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000286407200003&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=1ba7043ffcc86c417c072aa74d649202
UR  - http://hdl.handle.net/10044/1/67780
VL  - 29
ER  -

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