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OLS ESTIMATION AND THE "t" TEST REVISITED IN RANK-SIZE RULE REGRESSION

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Author Info

  • Yoshihiko Nishiyama
  • Susumu Osada
  • Yasuhiro Sato

Abstract

The rank-size rule and Zipf's law for city sizes have been traditionally examined by means of OLS estimation and the "t" test. This paper studies the accurate and approximate properties of the OLS estimator and obtains the distribution of the "t" statistic under the assumption of Zipf's law (i.e., Pareto distribution). Indeed, we show that the "t" statistic explodes asymptotically even under the null, indicating that a mechanical application of the "t" test yields a serious type I error. To overcome this problem, critical regions of the "t" test are constructed to test the Zipf's law. Using these corrected critical regions, we can conclude that our results are in favor of the Zipf's law for many more countries than in the previous researches such as Rosen and Resnick (1980) or Soo (2005). By using the same database as that used in Soo (2005), we demonstrate that the Zipf law is rejected for only one of 24 countries under our test whereas it is rejected for 23 of 24 countries under the usual "t" test. We also propose a more efficient estimation procedure and provide empirical applications of the theory for some countries. Copyright (c) 2008, Wiley Periodicals, Inc.

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Bibliographic Info

Article provided by Wiley Blackwell in its journal Journal of Regional Science.

Volume (Year): 48 (2008)
Issue (Month): 4 ()
Pages: 691-716

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Handle: RePEc:bla:jregsc:v:48:y:2008:i:4:p:691-716

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Web page: http://www.blackwellpublishing.com/journal.asp?ref=0022-4146

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Cited by:
  1. L. Benguigui & E. Blumenfeld-Lieberthal, 2011. "The end of a paradigm: is Zipf’s law universal?," Journal of Geographical Systems, Springer, vol. 13(1), pages 87-100, March.
  2. Tomoya Mori & Tony E. Smith, 2009. "A Reconsideration of the NAS Rule from an Industrial Agglomeration Perspective," KIER Working Papers 669, Kyoto University, Institute of Economic Research.
  3. González-Val, Rafael, 2010. "A Nonparametric Estimation of the Local Zipf Exponent for all US Cities," MPRA Paper 26720, University Library of Munich, Germany.
  4. Rafael GONZÀLEZ-VAL, 2012. "Zipf’S Law: Main Issues In Empirical Work," Region et Developpement, Region et Developpement, LEAD, Universite du Sud - Toulon Var, vol. 36, pages 147-164.

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