Rank - 1 / 2: A Simple Way to Improve the OLS Estimation of Tail Exponents

Xavier Gabaix and Rustam Ibragimov

Journal of Business & Economic Statistics, 2011, vol. 29, issue 1, 24-39

Abstract: 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 )-super-1 / 2 ζ . 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.

Date: 2011
References: Add references at CitEc
Citations: View citations in EconPapers (360)

Downloads: (external link)
http://hdl.handle.net/10.1198/jbes.2009.06157 (text/html)
Access to full text is restricted to subscribers.

Related works:
Working Paper: Rank-1/2: A Simple Way to Improve the OLS Estimation of Tail Exponents (2007)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:taf:jnlbes:v:29:y:2011:i:1:p:24-39

Ordering information: This journal article can be ordered from
http://www.tandfonline.com/pricing/journal/UBES20

DOI: 10.1198/jbes.2009.06157

Access Statistics for this article

Journal of Business & Economic Statistics is currently edited by Eric Sampson, Rong Chen and Shakeeb Khan

More articles in Journal of Business & Economic Statistics from Taylor & Francis Journals
Bibliographic data for series maintained by Chris Longhurst ().