Rank-1/2: A Simple Way to Improve the OLS Estimation of Tail Exponents
Xavier Gabaix and
No 342, NBER Technical Working Papers from National Bureau of Economic Research, Inc
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.
JEL-codes: C13 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-ecm
References: Add references at CitEc
Citations: View citations in EconPapers (91) Track citations by RSS feed
Downloads: (external link)
Journal Article: Rank - 1 / 2: A Simple Way to Improve the OLS Estimation of Tail Exponents (2011)
This item may be available elsewhere in EconPapers: Search for items with the same title.
Export reference: BibTeX
RIS (EndNote, ProCite, RefMan)
Persistent link: https://EconPapers.repec.org/RePEc:nbr:nberte:0342
Ordering information: This working paper can be ordered from
Access Statistics for this paper
More papers in NBER Technical Working Papers from National Bureau of Economic Research, Inc National Bureau of Economic Research, 1050 Massachusetts Avenue Cambridge, MA 02138, U.S.A.. Contact information at EDIRC.
Bibliographic data for series maintained by ().