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Zipf’s law, Gibrat’s law and Cointegration

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  • Aurélie LALANNE
  • Martin ZUMPE

Abstract

This paper examines the methods to detect the nature of the urban growth processes. It seems that cointegration testing enables to disentangle two versions of Gibrat’s law: a first one with growth shocks that are iid across time and cities (implying convergence of the city-size distribution towards Zipf’s law), and an alternative one with growth shocks that are only iid over time (implying conservation of the initial structure of the city size distribution).

Suggested Citation

  • Aurélie LALANNE & Martin ZUMPE, 2015. "Zipf’s law, Gibrat’s law and Cointegration," Cahiers du GREThA (2007-2019) 2015-27, Groupe de Recherche en Economie Théorique et Appliquée (GREThA).
    • Handle: RePEc:grt:wpegrt:2015-27
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    File URL: http://cahiersdugretha.u-bordeaux.fr/2015/2015-27.pdf
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    References listed on IDEAS

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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. Chen, Zhihong & Fu, Shihe & Zhang, Dayong, 2010. "Searching for the parallel growth of cities," MPRA Paper 21528, University Library of Munich, Germany.
    3. Jan Eeckhout, 2004. "Gibrat's Law for (All) Cities," American Economic Review, American Economic Association, vol. 94(5), pages 1429-1451, December.
    4. Kwiatkowski, Denis & Phillips, Peter C. B. & Schmidt, Peter & Shin, Yongcheol, 1992. "Testing the null hypothesis of stationarity against the alternative of a unit root : How sure are we that economic time series have a unit root?," Journal of Econometrics, Elsevier, vol. 54(1-3), pages 159-178.
    5. Sharma, Shalini, 2003. "Persistence and stability in city growth," Journal of Urban Economics, Elsevier, vol. 53(2), pages 300-320, March.
    6. Im, Kyung So & Pesaran, M. Hashem & Shin, Yongcheol, 2003. "Testing for unit roots in heterogeneous panels," Journal of Econometrics, Elsevier, vol. 115(1), pages 53-74, July.
    7. Xavier Gabaix, 1999. "Zipf's Law for Cities: An Explanation," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 114(3), pages 739-767.
    8. Zhihong Chen & Shihe Fu & Dayong Zhang, 2013. "Searching for the Parallel Growth of Cities in China," Urban Studies, Urban Studies Journal Limited, vol. 50(10), pages 2118-2135, August.
    9. Krugman, Paul, 1996. "Confronting the Mystery of Urban Hierarchy," Journal of the Japanese and International Economies, Elsevier, vol. 10(4), pages 399-418, December.
    10. González-Val, Rafael & Lanaspa, Luis & Sanz-Gracia, Fernando, 2013. "Gibrat’s law for cities, growth regressions and sample size," Economics Letters, Elsevier, vol. 118(2), pages 367-369.
    11. repec:wyi:journl:002175 is not listed on IDEAS
    12. Levin, Andrew & Lin, Chien-Fu & James Chu, Chia-Shang, 2002. "Unit root tests in panel data: asymptotic and finite-sample properties," Journal of Econometrics, Elsevier, vol. 108(1), pages 1-24, May.
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    Cited by:

    1. Aurélie Lalanne & Martin Zumpe, 2020. "Time-Series Based Empirical Assessment of Random Urban Growth: New Evidence from France," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 18(4), pages 911-926, December.

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    More about this item

    Keywords

    Zipf’s law; Gibrat’s law; Cointegration tests; unit root tests; urban growth; urban system;
    All these keywords.

    JEL classification:

    • R00 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General - - - General
    • R11 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General Regional Economics - - - Regional Economic Activity: Growth, Development, Environmental Issues, and Changes
    • C41 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Duration Analysis; Optimal Timing Strategies
    • O40 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - General

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