02171cam a22002537 4500001000600000003000500006005001700011008004100028100002000069245013500089260006600224490005100290500002000341520109400361530006101455538007201516538003601588690006901624700002301693710004201716830008601758856003701844856003601881t0342NBER20160827014558.0160827s2007 mau||||fs|||| 000 0 eng d1 aGabaix, Xavier.10aRank-1/2h[electronic resource]:bA Simple Way to Improve the OLS Estimation of Tail Exponents /cXavier Gabaix, Rustam Ibragimov. aCambridge, Mass.bNational Bureau of Economic Researchc2007.1 aNBER technical working paper seriesvno. t0342 aSeptember 2007.3 aDespite 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. aHardcopy version available to institutional subscribers. aSystem requirements: Adobe [Acrobat] Reader required for PDF files. aMode of access: World Wide Web. 7aC13 - Estimation: General2Journal of Economic Literature class.1 aIbragimov, Rustam.2 aNational Bureau of Economic Research. 0aTechnical Working Paper Series (National Bureau of Economic Research)vno. t0342.4 uhttp://www.nber.org/papers/t034241uhttp://dx.doi.org/10.3386/t0342