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The size ranking of cities in Germany: caught by a MAUP?

  • Rüdiger Budde
  • Uwe Neumann
Article
  • 59 Downloads

Abstract

A long standing question in urbanisation studies queries whether an empirical regularity known as Zipf's law applies to the size ranking of cities within countries or regions. Part of the debate addresses the statistical attributes of the size distribution. More recently, the definition of the territories assigned to cities has become a matter of concern in this context. Since the shape of administrative boundaries may not represent economic entities, analysis of the size ranking among cities defined by municipal territories may be affected by a considerable modifiable areal unit problem. Following a methodical approach that relates to current research on natural cities, we study the extent to which variation in the territory assigned to urban areas in Germany affects basic features of the size ranking. We define urban areas according to variable thresholds of population density across 1 km2 grids by a clustering algorithm. We find a systematic but moderate deviation from Zipf's law suggesting scale economies among urban agglomerations if peripheral zones are included.

Keywords

Agglomeration Natural cities Zipf's law MAUP Spatial clustering 

JEL Classification

C38 R12 R14 

Notes

Acknowledgements

We are thankful for helpful comments that significantly improved our paper to Colin Vance and to three anonymous referees. Earlier versions of the paper were presented at the 7th Summer Conference in Regional Science (Marburg, 2014), the Workshop on Neighbourhood Effects (Essen, 2014) and at the SCORUS Conference 2016 (Lisbon). We thank Astrid Schürmann for giving our English a final polish. This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors. It uses data compiled by RWI as part of the project “Neighbourhood effects: Analysis of individual rational behaviour in a social context“, financed by the Leibniz Association (Joint Initiative for Research and Innovation).

Compliance with ethical standards

Conflicts of interest

All authors declare that they have no conflicts of interest.

References

  1. Arcaute, E., Hatna, E., Ferguson, P., Youn, H., Johansson, A., & Batty, M. (2015). Constructing cities, deconstructing scaling laws. Journal of the Royal Society Interface, 12(101), 20140745.Google Scholar
  2. Arshad, S., Hu, S., & Ashraf, B. N. (2018). Zipf’s law and city size distribution: A survey of the literature and future research agenda. Physica A, 492, 75–92.CrossRefGoogle Scholar
  3. BBSR Bundesinstitut für Bau-, Stadt- und Raumforschung. (2012). Raumordnungsbericht 2011. http://www.bbsr.bund.de/BBSR/DE/Veroeffentlichungen/Sonderveroeffentlichungen/2012/rob-2011.html?nn=391978. Accessed 15 May 2018.
  4. Benguigui, L., & Blumenfeld-Lieberthal, E. (2007). Beyond the power law—a new approach to analyze city size distributions. Computers, Environment and Urban Systems, 31(6), 648–666.CrossRefGoogle Scholar
  5. Bereitschaft, B., & Debbage, K. (2014). Regional variations in urban fragmentation among U.S. metropolitan and megapolitan areas. Applied Spatial Analysis and Policy, 7(2), 119–147.CrossRefGoogle Scholar
  6. Bergs, R. (2018). The detection of natural cities in the Netherlands—Nocturnal satellite imagery and Zipf’s law. Review of Regional Research (forthcoming).Google Scholar
  7. BMVBS Bundesministerium für Verkehr, Bau und Stadtentwicklung, BBR Bundesamt für Bauwesen und Raumordnung (eds.) (2007) Initiativkreis Europäische Metropolregionen in Deutschland. Werkstatt: Praxis 52. Berlin, Bonn.Google Scholar
  8. Bosker, M., Brakman, S., Garretsen, H., & Schramm, M. (2008). A century of shocks: The evolution of the German city size distribution 1925–1999. Regional Science and Urban Economics, 38(4), 330–347.CrossRefGoogle Scholar
  9. Brezzi, M., Piacentini, M., Rosina, K. & Sanchez-Serra, D. (2012). Redefining urban areas in OECD countries. In OECD (Ed.), Redefining “Urban”. A new way to measure metropolitan areas. Paris: OECD.Google Scholar
  10. Calinski, T., & Harabasz, J. (1974). A dendrite method for cluster analysis. Communications in Statistics, 3(1), 1–27.Google Scholar
  11. Chaudhry, O., & Mackaness, W. (2008). Automatic identification of urban settlement boundaries for multiple representation databases. Computers, Environment and Urban Systems, 32(2), 95.CrossRefGoogle Scholar
  12. Clauset, A., Shalizi, C. R., & Newman, M. E. J. (2009). Power-law distributions in empirical data. SIAM Review, 51(4), 661–703.CrossRefGoogle Scholar
  13. Cristelli, M., Batty, M., & Pietronero, L. (2012). There is more than a power law in Zipf. Scientific Reports, 2, 812.CrossRefGoogle Scholar
  14. Das, R. J., & Dutt, A. K. (1993). Rank-size distribution and primate city characteristics in India—a temporal analysis. GeoJournal, 29(2), 125–137.CrossRefGoogle Scholar
  15. Davis, D. R., & Weinstein, D. E. (2002). Bones, bombs and breakpoints: the geography of economic activity. American Economic Review, 92(5), 1269–1289.CrossRefGoogle Scholar
  16. Deutscher Bundestag. (2017). Stadtentwicklungsbericht 2016. DS 18/11975 v. 18.04.2017. http://www.bundestag.de/presse/hib/2017_04/-/504172. Accessed 5 May 2017.
  17. Duranton, G. (2007). Urban evolutions: The fast, the slow, and the still. American Economic Review, 97(1), 197.CrossRefGoogle Scholar
  18. Eekhout, J. (2004). Gibrat's law for (all) cities. American Economic Review, 94(5), 1429–1451.CrossRefGoogle Scholar
  19. Fujita, M., Krugman, P. & Venables, A. J. (1999). The spatial economy. Cities, Regions and International Trade. Cambridge, MA: MIT Press.Google Scholar
  20. Gabaix, X. (1999). Zipf's law for cities: an explanation. Quarterly Journal of Economics, 114(3), 739–767.CrossRefGoogle Scholar
  21. Gabaix, X., & Ibragimov, R. (2011). Rank-1/2: A simple way to improve the OLS estimation of tail exponents. Journal of Business & Economic Statistics, 29(1), 24–39.CrossRefGoogle Scholar
  22. Gabaix, X., & Ioannides, Y. (2004). The evolution of city size distributions. In V. Henderson & J. F. Thisse (Eds.), Handbook of Regional and Urban Economics (Vol. 4). North-Holland: Elsevier Science.Google Scholar
  23. Gibrat, R. (1931). Les inégalités économiques. Paris: Librairie du Recueil Sirey.Google Scholar
  24. Giesen, K., & Südekum, J. (2011). Zipf's law for cities in the regions and the country. Journal of Economic Geography, 11(4), 667–686.CrossRefGoogle Scholar
  25. Gonzáles-Val, R. (2012). Zipf's law: main issues in empirical work. Région et Développement, 36, 148–164.Google Scholar
  26. Huang, Z. (1998). Extensions to the k-Means algorithm for clustering large data sets with categorical values. Data Mining and Knowledge Discovery, 2(3), 283–304.CrossRefGoogle Scholar
  27. INSPIRE Thematic Working Group Coordinate reference systems and Geographical grid sys-tems. (2010). D2.8.I.2 INSPIRE Specification on Geographical Grid Systems—Guidelines. http://inspire.ec.europa.eu/documents/Data_Specifications/INSPIRE_Specification_GGS_v3.0.pdf. Accessed 15 May 2018.
  28. Jiang, B., & Jia, T. (2011). Zipf’s law for all the natural cities in the United States: A geospatial perspective. International Journal of Geographical Information Science, 25(8), 1269–1281.CrossRefGoogle Scholar
  29. Jiang, B., Yin, J., & Liu, Q. (2015). Zipf’s law for all the natural cities around the world. International Journal of Geographical Information Science, 29(3), 498–522.CrossRefGoogle Scholar
  30. Just, T. & Stephan, P. (2009). Die seltsam stabile Größenstruktur deutscher Städte: Das Zipfsche Gesetz und seine Implikationen für urbane Regionen. Research notes working paper series/Deutsche Bank Research 31.DB Research, Frankfurt.Google Scholar
  31. Kaufman, L., & Rousseeuw, P. J. (1990). Finding groups in data. New York: Wiley.CrossRefGoogle Scholar
  32. Krugman, P. (1991). Geography and trade. Cambridge: MIT Press.Google Scholar
  33. Krugman, P. (1996). The self-organizing economy. Oxford: Blackwell Science.Google Scholar
  34. Li, S., & Sui, D. (2012). Pareto’s law and sample size: a case study of China’s urban system 1984–2008. GeoJournal, 78(4), 615–626.CrossRefGoogle Scholar
  35. Malevergne, Y., Pisarenko, V., & Sornette, D. (2011). Testing the Pareto against the lognormal distributions with the uniformly most powerful unbiased test applied to the distribution of cities. Physical Review E, 83(3), 036111.CrossRefGoogle Scholar
  36. Mandelbroth, B. B., & Wheeler, J. A. (1983). The fractal geometry of nature. American Journal of Physics, 51(3), 286.CrossRefGoogle Scholar
  37. microm—Micromarketing-Systeme und Consult GmbH. (2011). microm Datenhandbuch 2011. Neuss: microm GmbH.Google Scholar
  38. Newman, M. E. J. (2005). Power laws, Pareto distributions and Zipf’s law. Contemporary Physics, 46(5), 323–351.CrossRefGoogle Scholar
  39. Openshaw, S. (1984). The modifiable areal unit problem. Norwich: Geo Books.Google Scholar
  40. Prossek, A., Schneider, H., Wessel, H. A., Wetterau, B., & Wiktorin, D. (Eds.). (2009). Atlas der Metropole Ruhr. Vielfalt und Wandel des Ruhrgebiets im Kartenbild. Köln: Emons.Google Scholar
  41. Pumain, D. (2012). Une théorie géographique pour la loi de Zipf. Région et Développement, 36, 31–54.Google Scholar
  42. Pumain, D., & Moriconi-Ebrard, F. (1997). City size distributions and metropolinisation. GeoJournal, 43(4), 307–314.CrossRefGoogle Scholar
  43. Rauch, F. (2013). Cities as spatial clusters. Economics Series Working Papers 656. Department of Economics, University of Oxford.Google Scholar
  44. Redding, S. J. (2009). Economic geography: A review of the theoretical and empirical literature. CEPR Discussion Papers, (p 7126), London.Google Scholar
  45. Reggiani, A & Nijkamp, P. (2012). Did Zipf anticipate socio-economic spatial networks? Working Papers, (p 816), Department of Economics, Università di Bologna.Google Scholar
  46. Rosen, K., & Resnick, M. (1980). The size distribution of cities: An examination of the pareto law and primacy. Journal of Urban Economics, 8(2), 165–186.CrossRefGoogle Scholar
  47. Rozenfeld, H. D., Rybskia, D., Andrade, J. S., Jr., Battyc, M., Stanley, H. E., & Maksea, H. A. (2008). Laws of population growth. Proceedings of the National Academy of Sciences, 105(48), 18702–18707.CrossRefGoogle Scholar
  48. Schmidheiny, K. & Südekum, J. (2015). The pan-European population distribution across consistently defined functional urban areas. IZA DP, 9020. Bonn.Google Scholar
  49. Schweitzer, F., & Steinbrink, J. (1997). Urban cluster growth: Analysis and computer simulation of urban aggregations. In F. Schweitzer (Ed.), Self-organization of complex structures: From individual to collective dynamics. London: Gordon and Breach.Google Scholar
  50. Simón, A. & Leal, M. (2011). Updated UMZs and corresponding methodological documentation. Method based on CLC v16. Universidad de Málaga. http://eea.europa.eu/www/umz/v4f0/RpD_UMZ_Methodology_f3.0.pdf. Accessed 9 May 2017.
  51. Struyf, A., Hubert, M., & Rousseeuw, P. J. (1997). Clustering in an object-oriented environment. Journal of Statistical Software, 1(4), 1–30.Google Scholar
  52. Tannier, C., Thomas, I., Vuidel, G., & Frankhauser, P. (2011). A fractal approach to identifying urban boundaries. Geographical Analysis, 43(2), 211–227.CrossRefGoogle Scholar
  53. Vanneste, D., Thomas, I., & Vanderstraeten, L. (2008). The spatial structure(s) of the Belgian housing stock. Journal of Housing and the Built Environment, 23(3), 173–198.CrossRefGoogle Scholar
  54. Votsis, A. (2017). Exploring the spatiotemporal behavior of Helsinki’s housing prices with fractal geometry and co-integration. Journal of Geographical Systems, 19(2), 133–155.CrossRefGoogle Scholar
  55. Zipf, G. (1949). Human behaviour and the principle of least effort. Cambridge: Addison Wesley.Google Scholar

Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.RWI - Leibniz Institute for Economic ResearchEssenGermany

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