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From Gibrat’s law to Zipf’s law through cointegration?

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  • Aurélie, Lalanne
  • Martin, Zumpe

Abstract

This article investigates the role of cointegration in the context of urban growth processes. It proposes the use of cointegration tests to distinguish between two versions of Gibrat’s law: a standard formalization with growth shocks that are iid across time and cities, and an alternative one with shocks that are only iid over time. It then shows that city-size distributions converge to Zipf’s law under the standard version of Gibrat’s law; in contrast, they are perfectly preserved under the alternative formalization. An empirical application to French data provides support for non-cointegrated city growth, and thus for the standard formalization.

Suggested Citation

  • Aurélie, Lalanne & Martin, Zumpe, 2020. "From Gibrat’s law to Zipf’s law through cointegration?," Economics Letters, Elsevier, vol. 192(C).
    • Handle: RePEc:eee:ecolet:v:192:y:2020:i:c:s0165176520301531
    DOI: 10.1016/j.econlet.2020.109211
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    1. Chen, Zhihong & Fu, Shihe & Zhang, Dayong, 2010. "Searching for the parallel growth of cities," MPRA Paper 21528, University Library of Munich, Germany.
    2. Jan Eeckhout, 2004. "Gibrat's Law for (All) Cities," American Economic Review, American Economic Association, vol. 94(5), pages 1429-1451, December.
    3. Sharma, Shalini, 2003. "Persistence and stability in city growth," Journal of Urban Economics, Elsevier, vol. 53(2), pages 300-320, March.
    4. 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.
    5. Krugman, Paul, 1996. "Confronting the Mystery of Urban Hierarchy," Journal of the Japanese and International Economies, Elsevier, vol. 10(4), pages 399-418, December.
    6. Rafael González-Val & Luis Lanaspa & Fernando Sanz-Gracia, 2014. "New Evidence on Gibrat’s Law for Cities," Urban Studies, Urban Studies Journal Limited, vol. 51(1), pages 93-115, January.
    7. repec:wyi:journl:002175 is not listed on IDEAS
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    More about this item

    Keywords

    Gibrat’s law; Zipf’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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