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

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  • 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.

Suggested Citation

  • Yoshihiko Nishiyama & Susumu Osada & Yasuhiro Sato, 2008. "OLS ESTIMATION AND THE "t" TEST REVISITED IN RANK-SIZE RULE REGRESSION," Journal of Regional Science, Wiley Blackwell, vol. 48(4), pages 691-716.
  • Handle: RePEc:bla:jregsc:v:48:y:2008:i:4:p:691-716
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    References listed on IDEAS

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    Cited by:

    1. Kuninori Nakagawa, 2014. "Municipal sizes and municipal restructuring in Japan," ERSA conference papers ersa14p416, European Regional Science Association.
    2. Rafael González-Val, 2016. "Historical urban growth in Europe (1300–1800)," Working Papers 2016/8, Institut d'Economia de Barcelona (IEB).
    3. Sueli Moro & Reginaldo J. Santos, 2013. "The characteristics and evolution of the Brazilian spatial urban system: empirical evidences for the long-run, 1970-2010," Textos para Discussão Cedeplar-UFMG 474, Cedeplar, Universidade Federal de Minas Gerais.
    4. Wen-Tai Hsu & Tomoya Mori & Tony E. Smith, 2014. "Spatial Patterns and Size Distributions of Cities," KIER Working Papers 882, Kyoto University, Institute of Economic Research.
    5. Zengwang Xu & Robert Harriss, 2010. "A Spatial and Temporal Autocorrelated Growth Model for City Rank—Size Distribution," Urban Studies, Urban Studies Journal Limited, vol. 47(2), pages 321-335, February.
    6. João Nicolau & Paulo M.M. Rodrigues, 2015. "A New Regression-Based Tail Index Estimator: An Application to Exchange Rates," Working Papers w201514, Banco de Portugal, Economics and Research Department.
    7. 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.
    8. Rafael González-Val, 2012. "A Nonparametric Estimation of the Local Zipf Exponent for all US Cities," Environment and Planning B, , vol. 39(6), pages 1119-1130, December.
    9. Francisco Goerlich, 2013. "A simple and efficient test for the Pareto law," Empirical Economics, Springer, vol. 45(3), pages 1367-1381, December.
    10. Luckstead, Jeff & Devadoss, Stephen & Danforth, Diana, 2017. "The size distributions of all Indian cities," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 474(C), pages 237-249.
    11. Rafael González‐Val, 2010. "The Evolution Of U.S. City Size Distribution From A Long‐Term Perspective (1900–2000)," Journal of Regional Science, Wiley Blackwell, vol. 50(5), pages 952-972, December.
    12. 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.
    13. Harry P. Bowen & Haris Munandar & Jean-Marie Viaene, 2008. "On the Extent of Economic Integration: A Comparison of E.U. Countries and U.S. States," Discussion Paper Series 2008-01, McColl School of Business, Queens University of Charlotte.
    14. 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.
    15. Kuninori Nakagawa, 2016. "Municipal sizes and municipal restructuring in Japan," Letters in Spatial and Resource Sciences, Springer, vol. 9(1), pages 27-41, March.
    16. Konishi, Yoko & Nishiyama, Yoshihiko, 2009. "Hypothesis testing in rank-size rule regression," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(9), pages 2869-2878.
    17. repec:wiw:wiwrsa:ersa14p34 is not listed on IDEAS

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