IDEAS home Printed from https://ideas.repec.org/a/eee/ecolet/v192y2020ics0165176520301531.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0165176520301531
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.econlet.2020.109211?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    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
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Chengri Ding & Zhi Li, 2019. "Size and urban growth of Chinese cities during the era of transformation toward a market economy," Environment and Planning B, , vol. 46(1), pages 27-46, January.
    2. 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.
    3. Aurélie Lalanne & Martin Zumpe, 2015. "Zipf's law, Gibrat's law and Cointegration," Post-Print hal-02479896, HAL.
    4. Ronan Lyons & Elisa Maria Tirindelli, 2022. "The Rise & Fall of Urban Concentration in Britain: Zipf, Gibrat and Gini across two centuries," Trinity Economics Papers tep0522, Trinity College Dublin, Department of Economics.
    5. 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.
    6. González-Val, Rafael & Ramos, Arturo & Sanz-Gracia, Fernando, 2010. "On the best functions to describe city size distributions," MPRA Paper 21921, University Library of Munich, Germany.
    7. Aurélie Lalanne, 2014. "Zipf’s Law and Canadian Urban Growth," Urban Studies, Urban Studies Journal Limited, vol. 51(8), pages 1725-1740, June.
    8. Wu, Jian-Xin & He, Ling-Yun, 2017. "How do Chinese cities grow? A distribution dynamics approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 470(C), pages 105-118.
    9. Aloysius G. Brata & Henri L. F. de Groot & Piet Rietveld, 2014. "The Impact of the Indian Ocean Tsunami and the Nias Earthquake on the Spatial Distribution of Population in Northern Sumatra," Bulletin of Indonesian Economic Studies, Taylor & Francis Journals, vol. 50(1), pages 101-121, April.
    10. Xin Li & Kyung-Min Nam, 2017. "One country, two “urban” systems: focusing on bimodality in China’s city-size distribution," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 59(2), pages 427-452, September.
    11. Chao Li & John Gibson, 2016. "Pareto's Law and City Size in China: Diverging Patterns in Land and People," Working Papers in Economics 16/09, University of Waikato.
    12. Michel DIMOU & Alexandra SCHAFFAR & Zhihong CHEN & Shihe FU, 2008. "LA CROISSANCE URBAINE CHINOISE RECONSIDeReE," Region et Developpement, Region et Developpement, LEAD, Universite du Sud - Toulon Var, vol. 27, pages 109-131.
    13. Bosker, Maarten & Brakman, Steven & Garretsen, Harry & Schramm, Marc, 2008. "A century of shocks: The evolution of the German city size distribution 1925-1999," Regional Science and Urban Economics, Elsevier, vol. 38(4), pages 330-347, July.
    14. Luc Christiaensen & Ravi Kanbur, 2017. "Secondary Towns and Poverty Reduction: Refocusing the Urbanization Agenda," Annual Review of Resource Economics, Annual Reviews, vol. 9(1), pages 405-419, October.
    15. Stephen J. Redding, 2010. "The Empirics Of New Economic Geography," Journal of Regional Science, Wiley Blackwell, vol. 50(1), pages 297-311, February.
    16. Duranton, Gilles & Puga, Diego, 2014. "The Growth of Cities," Handbook of Economic Growth, in: Philippe Aghion & Steven Durlauf (ed.), Handbook of Economic Growth, edition 1, volume 2, chapter 5, pages 781-853, Elsevier.
    17. Denise PUMAIN, 2012. "Une Théorie Géographique Pour La Loi De Zipf," Region et Developpement, Region et Developpement, LEAD, Universite du Sud - Toulon Var, vol. 36, pages 31-54.
    18. Clémentine Cottineau, 2022. "What do analyses of city size distributions have in common?," Scientometrics, Springer;Akadémiai Kiadó, vol. 127(3), pages 1439-1463, March.
    19. Jovanovic, Franck & Schinckus, Christophe, 2016. "Breaking down the barriers between econophysics and financial economics," International Review of Financial Analysis, Elsevier, vol. 47(C), pages 256-266.
    20. Beltrán Tapia, Francisco J. & Díez-Minguela, Alfonso & Martinez-Galarraga, Julio, 2018. "Tracing the Evolution of Agglomeration Economies: Spain, 1860–1991," The Journal of Economic History, Cambridge University Press, vol. 78(1), pages 81-117, March.

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ecolet:v:192:y:2020:i:c:s0165176520301531. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/ecolet .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.