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A Comparative Analysis of Gibrat’s and Zipf’s Law on Urban Population

Listed author(s):
  • M. Modica
  • A. Reggiani
  • P. Nijkamp

The regional economics and geography literature on urban population size has in recent years shown interesting conceptual and methodological contributions on the validity of Gibrat’s Law and Zipf’s Law. Despite distinct modeling features, they express similar fundamental characteristics in an equilibrium situation. Zipf’s law is formalized in a static form, while its associated dynamic process is articulated by Gibrat’s Law. Thus, it is likely that both Zipf’s Law and Gibrat’s Law share a common root. Unfortunately, empirical investigations on the direct relationship between Gibrat’s Law and Zipf’s Law are rather rare and not conclusive. The present paper aims to answer the question whether (a generalisation of) Gibrat’s Law allows us to infer Zipf’s Law, and vice versa? In our conceptual and applied framework, particular attention will be paid to the role of the mean and the variance of city population as key indicators for assessing the (non-) validity of the generalised Gibrat’s Law. Our empirical experiments are based on a comparative analysis between the dynamics of the urban population of four countries with entirely mutually contrasting spatial-economic and geographic characteristics: Botswana, Germany, Hungary and Luxembourg. We arrive at the following results: if (i) the mean is independent of city size (first necessary condition of Gibrat’s law) and (ii) the coefficient of the rank-size rule/Zipf’s Law is different from one, then the variance is dependent on city size.

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Paper provided by Dipartimento Scienze Economiche, Universita' di Bologna in its series Working Papers with number wp1008.

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Date of creation: May 2015
Handle: RePEc:bol:bodewp:wp1008
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  1. Kristian Giesen & Jens Südekum, 2011. "Zipf's law for cities in the regions and the country," Journal of Economic Geography, Oxford University Press, vol. 11(4), pages 667-686, July.
  2. 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.
  3. repec:ags:aaea07:384 is not listed on IDEAS
  4. González-Val, Rafael & Lanaspa, Luis & Sanz, Fernando, 2008. "New Evidence on Gibrat’s Law for Cities," MPRA Paper 10411, University Library of Munich, Germany.
  5. Giorgio Fazio & Marco Modica, 2012. "Pareto or log-normal? A recursive-truncation approach to the distribution of (all) cities," Working Papers 2012_10, Business School - Economics, University of Glasgow.
  6. Jan Eeckhout, 2004. "Gibrat's Law for (All) Cities," American Economic Review, American Economic Association, vol. 94(5), pages 1429-1451, December.
  7. Bottazzi, Giulio & Dosi, Giovanni & Lippi, Marco & Pammolli, Fabio & Riccaboni, Massimo, 2001. "Innovation and corporate growth in the evolution of the drug industry," International Journal of Industrial Organization, Elsevier, vol. 19(7), pages 1161-1187, July.
  8. Xavier Gabaix & Rustam Ibragimov, 2011. "Rank - 1 / 2: A Simple Way to Improve the OLS Estimation of Tail Exponents," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 29(1), pages 24-39, January.
  9. Rosen, Kenneth T. & Resnick, Mitchel, 1980. "The size distribution of cities: An examination of the Pareto law and primacy," Journal of Urban Economics, Elsevier, vol. 8(2), pages 165-186, September.
  10. Chesher, Andrew, 1979. "Testing the Law of Proportionate Effect," Journal of Industrial Economics, Wiley Blackwell, vol. 27(4), pages 403-411, June.
  11. Parr, John B., 1985. "A note on the size distribution of cities over time," Journal of Urban Economics, Elsevier, vol. 18(2), pages 199-212, September.
  12. Soo, Kwok Tong, 2005. "Zipf's Law for cities: a cross-country investigation," Regional Science and Urban Economics, Elsevier, vol. 35(3), pages 239-263, May.
  13. Córdoba, Juan-Carlos, 2008. "On the distribution of city sizes," Journal of Urban Economics, Elsevier, vol. 63(1), pages 177-197, January.
  14. Cuberes, David, 2011. "Sequential city growth: Empirical evidence," Journal of Urban Economics, Elsevier, vol. 69(2), pages 229-239, March.
  15. Duncan Black & Vernon Henderson, 2003. "Urban evolution in the USA," Journal of Economic Geography, Oxford University Press, vol. 3(4), pages 343-372, October.
  16. Juan Carlos Córdoba, 2008. "A Generalized Gibrat'S Law," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 49(4), pages 1463-1468, November.
  17. Gabaix, Xavier & Ibragimov, Rustam, 2011. "Rank − 1 / 2: A Simple Way to Improve the OLS Estimation of Tail Exponents," Journal of Business & Economic Statistics, American Statistical Association, vol. 29(1), pages 24-39.
  18. Henderson, J. Vernon & Wang, Hyoung Gun, 2007. "Urbanization and city growth: The role of institutions," Regional Science and Urban Economics, Elsevier, vol. 37(3), pages 283-313, May.
  19. Xavier Gabaix, 1999. "Zipf's Law for Cities: An Explanation," The Quarterly Journal of Economics, Oxford University Press, vol. 114(3), pages 739-767.
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