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Zipf's Law for Cities in the Regions and the Country

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  • Giesen, Kristian

    ()
    (University of Duisburg-Essen)

  • Suedekum, Jens

    ()
    (Heinrich Heine University Düsseldorf)

Abstract

The salient rank-size rule known as Zipf's law is not only satisfied for Germany's national urban hierarchy, but also for the city size distributions in single German regions. To analyze this phenomenon, we build on the insights by Gabaix (1999) that Zipf's law follows from a stochastic growth process. In particular, Gabaix shows that if the regions follow Gibrat's law, we should observe Zipf at both the regional and the national level. This theory has never been addressed empirically. Using non-parametric techniques we find that Gibrat's law holds in each German region, irrespective of how "regions" are defined. In other words, Gibrat's law and therefore Zipf's law tend to hold everywhere in space.

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Bibliographic Info

Paper provided by Institute for the Study of Labor (IZA) in its series IZA Discussion Papers with number 3928.

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Length: 24 pages
Date of creation: Jan 2009
Date of revision:
Publication status: published in: Journal of Economic Geography, 2011, 11 (4), 667-686
Handle: RePEc:iza:izadps:dp3928

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Keywords: rank-size rule; Gibrat's law; city size distributions; city growth; Zipf's law;

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Cited by:
  1. Sánchez-Vidal, María & González-Val, Rafael & Viladecans-Marsal, Elisabet, 2014. "Sequential city growth in the US: Does age matter?," Regional Science and Urban Economics, Elsevier, vol. 44(C), pages 29-37.
  2. 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.
  3. Valente J. Matlaba & Mark J. Holmes & Philip McCann & Jacques Poot, 2013. "A Century Of The Evolution Of The Urban System In Brazil," Review of Urban & Regional Development Studies, Wiley Blackwell, vol. 25(3), pages 129-151, November.
  4. Boris Portnov, 2011. "Does Zipf’s law hold for primate cities? Some evidence from a discriminant analysis of world countries," Jahrbuch für Regionalwissenschaft, Springer, vol. 31(2), pages 113-129, October.
  5. Aloysius Gunadi Brata & Henri L.F. de Groot & Piet Rietveld, 2013. "Dynamics in Aceh and North Sumatera after the Twin Disasters: An Investigation into the Relevance of the Locational Fundamental Theory," Tinbergen Institute Discussion Papers 13-115/VIII, Tinbergen Institute.
  6. Ferdinand Rauch, 2013. "Cities as Spatial Clusters," Economics Series Working Papers 656, University of Oxford, Department of Economics.
  7. Rafael González-Val & Luis Lanaspa & Fernando Sanz, 2012. "New evidence on Gibrat’s law for cities," Working Papers 2012/18, Institut d'Economia de Barcelona (IEB).
  8. Xinyue Ye & Yichun Xie, 2012. "Re-examination of Zipf’s law and urban dynamic in China: a regional approach," The Annals of Regional Science, Springer, vol. 49(1), pages 135-156, August.
  9. González-Val, Rafael & Ramos, Arturo & Sanz, Fernando & Vera-Cabello, María, 2013. "Size Distributions for All Cities: Which One is Best?," MPRA Paper 44314, University Library of Munich, Germany.
  10. Gerson Javier Pérez & Adolfo Meisel Roca, 2013. "Ley de Zipf y de Gibrat para Colombia y sus regiones: 1835-2005," DOCUMENTOS DE TRABAJO SOBRE ECONOMÍA REGIONAL 011539, BANCO DE LA REPÚBLICA - ECONOMÍA REGIONAL.
  11. 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.
  12. P. Nijkamp & A. Reggiani, 2012. "Did Zipf Anticipate Socio-Economic Spatial Networks?," Working Papers wp816, Dipartimento Scienze Economiche, Universita' di Bologna.

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