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Did Zipf Anticipate Socio-Economic Spatial Networks?

  • P. Nijkamp
  • A. Reggiani

An avalanche of empirical studies has addressed the validity of the rank-size rule (or Zipf’s law) in a multi-city context in many countries. City size in most countries seems to obey Zipf’s law, but the question under which conditions (e.g. sample size, spatial scale) this ‘law’ holds remained largely underinvestigated. Another complementary question is whether socio-economic networks in space also show a similar hierarchical pattern. Against this background, the present paper investigates – from a methodological viewpoint – the relationship between network connectivity and the rank-size rule (or Zipf’s law) in an urban-economic network constellation. After a review of the literature, we address in particular the following methodological issues: (i) the (aggregate) behavioural foundation underlying the rank-size rule/Zipf’s law in the light of spatial-economic network theories (e.g. entropy maximization, spatial interaction theory, etc.); (ii) the nature of the analytical relationship between social-spatial network analysis and the rank-size rule/Zipf’s law. We argue that the rank size rule is compatible with conventional economic foundations of spatial network models. Consequently, a spatial-economic interpretation – as well as a network connectivity interpretation – of the rank-size rule coefficient is provided. Our methodological contribution forms the foundation for the subsequent empirical analysis applied to spatial networks in a socio-economic context. The aim here is to test the sensitivity of empirical findings for changes in scale, functional forms, time periods, and network structures. Our application is concerned with an extensive spatio-temporal panel database related to the evolution of urban population in Germany. We test the relevance of the rank-size rule/Zipf’s law, and its evolution over the years, and – in parallel – the related ‘socio-economic’ connectivity in these urban networks. In particular, we will show that Zipf’s law (i.e., with the rank-size coefficient equal to 1) is only valid under particular conditions of the sample size. The paper concludes with some retrospective and prospective remarks.

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Paper provided by Dipartimento Scienze Economiche, Universita' di Bologna in its series Working Papers with number wp816.

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Date of creation: Mar 2012
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Handle: RePEc:bol:bodewp:wp816
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  1. Nitsch, Volker, 2004. "Zipf zipped," Discussion Papers 2004/16, Free University Berlin, School of Business & Economics.
  2. Marcus Berliant & Hiroki Watanabe, 2012. "A Scale-Free Transportation Network Explains the City-Size Distribution," ERSA conference papers ersa12p601, European Regional Science Association.
  3. Fungisai Nota & Shunfeng Song, 2008. "Further Analysis of the Zipf Law: Does the Rank-Size Rule Really Exist?," Working Papers 08-005, University of Nevada, Reno, Department of Economics;University of Nevada, Reno , Department of Resource Economics.
  4. J W Weibull, 1980. "On the numerical measurement of accessibility," Environment and Planning A, Pion Ltd, London, vol. 12(1), pages 53-67, January.
  5. Giesen, Kristian & Zimmermann, Arndt & Suedekum, Jens, 2010. "The size distribution across all cities - Double Pareto lognormal strikes," Journal of Urban Economics, Elsevier, vol. 68(2), pages 129-137, September.
  6. Nijkamp, Peter, 1975. "Reflections on gravity and entropy models," Regional Science and Urban Economics, Elsevier, vol. 5(2), pages 203-225, May.
  7. Xavier Gabaix & Rustam Ibragimov, 2007. "Rank-1/2: A Simple Way to Improve the OLS Estimation of Tail Exponents," NBER Technical Working Papers 0342, National Bureau of Economic Research, Inc.
  8. Edward L. Glaeser & Jose A. Scheinkman & Andrei Shleifer, 1995. "Economic Growth in a Cross-Section of Cities," NBER Working Papers 5013, National Bureau of Economic Research, Inc.
  9. Xavier Gabaix & Yannis M. Ioannides, 2003. "The Evolution of City Size Distributions," Discussion Papers Series, Department of Economics, Tufts University 0310, Department of Economics, Tufts University.
  10. Sebastien TERRA, 2009. "Zipf's Law for Cities: On a New Testing Procedure," Working Papers 200920, CERDI.
  11. Xavier Gabaix, 1999. "Zipf'S Law For Cities: An Explanation," The Quarterly Journal of Economics, MIT Press, vol. 114(3), pages 739-767, August.
  12. Jan Eeckhout, 2004. "Gibrat's Law for (All) Cities," American Economic Review, American Economic Association, vol. 94(5), pages 1429-1451, December.
  13. Francesca Lotti & Enrico Santarelli & Marco Vivarelli, 2009. "Defending Gibrat’s Law as a long-run regularity," Small Business Economics, Springer, vol. 32(1), pages 31-44, January.
  14. Valente J. Matlaba & Mark Holmes & Philip McCann & Jacques Poot, 2011. "A Century of the Evolution of the Urban System in Brazil," Working Papers in Economics 11/12, University of Waikato, Department of Economics.
  15. Aura Reggiani & Pietro Bucci & Giovanni Russo, 2011. "Accessibility and Impedance Forms: Empirical Applications to the German Commuting Network," International Regional Science Review, , vol. 34(2), pages 230-252, April.
  16. Gan, Li & Li, Dong & Song, Shunfeng, 2006. "Is the Zipf law spurious in explaining city-size distributions?," Economics Letters, Elsevier, vol. 92(2), pages 256-262, August.
  17. repec:cup:cbooks:9780521857406 is not listed on IDEAS
  18. Aura Reggiani & Peter Nijkamp (ed.), 2006. "Spatial Dynamics, Networks and Modelling," Books, Edward Elgar, number 3887.
  19. 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.
  20. repec:dgr:uvatin:20110104 is not listed on IDEAS
  21. repec:cup:cbooks:9780521674096 is not listed on IDEAS
  22. repec:dgr:uvatin:20060100 is not listed on IDEAS
  23. Giesen, Kristian & Suedekum, Jens, 2009. "Zipf's Law for Cities in the Regions and the Country," IZA Discussion Papers 3928, Institute for the Study of Labor (IZA).
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