EconPapers    
Economics at your fingertips  
 

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

Xavier Gabaix and Rustam Ibragimov

No 2106, Harvard Institute of Economic Research Working Papers from Harvard - Institute of Economic Research

Abstract: A popular way to estimate a Pareto exponent is to run an OLS regression: log (Rank) = c - blog (Size), and take b as an estimate of the Pareto exponent. Unfortunately, this procedure is strongly biased in small samples. We provide a simple practical remedy for this bias, and argue that, if one wants to use an OLS regression, one should use the Rank -1/2, and run log (Rank- 1/2) = c-b log (Size). The shift of 1/2 is optimal, and cancels the bias to a leading order. The standard error on the Pareto exponent is not the OLS standard error, but is asymptotically (2/n)^{1/2}b. To obtain this result, we provide asymptotic expansions for the OLS estimate in such log-log rank-size regression with arbitrary shifts in the ranks. The arguments for the asymptotic expansions rely on strong approximations to martingales with the optimal rate and demonstrate that martingale convergence methods provide a natural and conceptually simple framework for deriving the asymptotics of the tail index estimates using the log-log rank-size regressions.

Date: 2006
References: Add references at CitEc
Citations: View citations in EconPapers (16) Track citations by RSS feed

Downloads: (external link)
http://www.economics.harvard.edu/pub/hier/2006/HIER2106.pdf (application/pdf)
Our link check indicates that this URL is bad, the error code is: 404 Not Found (http://www.economics.harvard.edu/pub/hier/2006/HIER2106.pdf [301 Moved Permanently]--> https://www.economics.harvard.edu/pub/hier/2006/HIER2106.pdf [301 Moved Permanently]--> https://economics.harvard.edu/pub/hier/2006/HIER2106.pdf)

Related works:
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:fth:harver:2106

Access Statistics for this paper

More papers in Harvard Institute of Economic Research Working Papers from Harvard - Institute of Economic Research Contact information at EDIRC.
Bibliographic data for series maintained by Thomas Krichel ().

 
Page updated 2020-09-22
Handle: RePEc:fth:harver:2106