IDEAS home Printed from https://ideas.repec.org/p/kyo/wpaper/882.html
   My bibliography  Save this paper

Spatial Patterns and Size Distributions of Cities

Author

Listed:
  • Wen-Tai Hsu

    () (School of Economics, Singapore Management University)

  • Tomoya Mori

    () (Institute of Economic Research, Kyoto University)

  • Tony E. Smith

    () (Department of Electrical and Systems Engineering, University of Pennsylvania)

Abstract

City size distributions are known to be well approximated by power laws across many countries. One popular explanation for such power-law regularities is in terms of random growth processes, where power laws arise asymptotically from the assumption of iid growth rates among all cities within a given country. But this assumption has additional consequences. Since all subsets of cities have the same statistical properties, each subset must exhibit essentially the same power law. Moreover, this common power law (CPL) property must hold regardless of the spatial relations among cities. Using data from the US, this paper shows first that spatial partitions of cities based on geographical proximity are significantly more consistent with the CPL property than are random partitions. It is then shown that this significance becomes even stronger when proximity among cities is measured in terms of trade linkages rather than simple geographical distance. These results provide compelling evidence that spatial relations between cities do indeed matter for city-size distributions. Further analysis shows that these results hinge on the natural “spacing out” property of city patterns in which larger cities tend to be widely spaced apart with smaller cities organized around them.

Suggested Citation

  • 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.
  • Handle: RePEc:kyo:wpaper:882
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    References listed on IDEAS

    as
    1. Eaton, Jonathan & Eckstein, Zvi, 1997. "Cities and growth: Theory and evidence from France and Japan," Regional Science and Urban Economics, Elsevier, vol. 27(4-5), pages 443-474, August.
    2. Kristian Giesen & Jens Südekum, 2011. "Zipf's law for cities in the regions and the country," Journal of Economic Geography, Oxford University Press, vol. 11(4), pages 667-686, July.
    3. Yannis M. Ioannides & Henry G. Overman, 2004. "Spatial evolution of the US urban system," Journal of Economic Geography, Oxford University Press, vol. 4(2), pages 131-156, April.
    4. Esteban Rossi-Hansberg & Mark L. J. Wright, 2007. "Urban Structure and Growth," Review of Economic Studies, Oxford University Press, vol. 74(2), pages 597-624.
    5. Daniel P. McMillen & Christian L. Redfearn, 2010. "Estimation And Hypothesis Testing For Nonparametric Hedonic House Price Functions," Journal of Regional Science, Wiley Blackwell, vol. 50(3), pages 712-733.
    6. Henderson, J V, 1974. "The Sizes and Types of Cities," American Economic Review, American Economic Association, vol. 64(4), pages 640-656, September.
    7. Jan Eeckhout, 2004. "Gibrat's Law for (All) Cities," American Economic Review, American Economic Association, vol. 94(5), pages 1429-1451, December.
    8. Laura Hering & Sandra Poncet, 2010. "Market Access and Individual Wages: Evidence from China," The Review of Economics and Statistics, MIT Press, pages 145-159.
    9. Hernán D. Rozenfeld & Diego Rybski & Xavier Gabaix & Hernán A. Makse, 2011. "The Area and Population of Cities: New Insights from a Different Perspective on Cities," American Economic Review, American Economic Association, vol. 101(5), pages 2205-2225, August.
    10. Ioannides, Yannis M. & Overman, Henry G., 2003. "Zipf's law for cities: an empirical examination," Regional Science and Urban Economics, Elsevier, vol. 33(2), pages 127-137, March.
    11. Xavier Gabaix & Rustam Ibragimov, 2011. "Rank - 1 / 2: A Simple Way to Improve the OLS Estimation of Tail Exponents," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 29(1), pages 24-39, January.
    12. Ioannides, Yannis & Skouras, Spyros, 2013. "US city size distribution: Robustly Pareto, but only in the tail," Journal of Urban Economics, Elsevier, vol. 73(1), pages 18-29.
    13. Behrens, Kristian & Mion, Giordano & Murata, Yasusada & Suedekum, Jens, 2017. "Spatial frictions," Journal of Urban Economics, Elsevier, vol. 97(C), pages 40-70.
    14. Ait-Sahalia, Yacine & Duarte, Jefferson, 2003. "Nonparametric option pricing under shape restrictions," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 9-47.
    15. Tabuchi, Takatoshi & Thisse, Jacques-François, 2011. "A new economic geography model of central places," Journal of Urban Economics, Elsevier, vol. 69(2), pages 240-252, March.
    16. Gilles Duranton & Peter M. Morrow & Matthew A. Turner, 2014. "Roads and Trade: Evidence from the US," Review of Economic Studies, Oxford University Press, vol. 81(2), pages 681-724.
    17. Yoshihiko Nishiyama & Susumu Osada & Yasuhiro Sato, 2008. "OLS ESTIMATION AND THE "t" TEST REVISITED IN RANK-SIZE RULE REGRESSION," Journal of Regional Science, Wiley Blackwell, vol. 48(4), pages 691-716.
    18. Thomas J. Holmes & Sanghoon Lee, 2010. "Cities as Six-by-Six-Mile Squares: Zipf's Law?," NBER Chapters,in: Agglomeration Economics, pages 105-131 National Bureau of Economic Research, Inc.
    19. Guy Michaels, 2008. "The Effect of Trade on the Demand for Skill: Evidence from the Interstate Highway System," The Review of Economics and Statistics, MIT Press, vol. 90(4), pages 683-701, November.
    20. Xavier Gabaix, 2009. "Power Laws in Economics and Finance," Annual Review of Economics, Annual Reviews, vol. 1(1), pages 255-294, May.
    21. Krugman, Paul, 1993. "On the number and location of cities," European Economic Review, Elsevier, vol. 37(2-3), pages 293-298, April.
    22. Fujita, Masahisa & Krugman, Paul & Mori, Tomoya, 1999. "On the evolution of hierarchical urban systems1," European Economic Review, Elsevier, vol. 43(2), pages 209-251, February.
    23. Xavier Gabaix, 1999. "Zipf's Law for Cities: An Explanation," The Quarterly Journal of Economics, Oxford University Press, vol. 114(3), pages 739-767.
    24. Yuichi Kitamura & Gautam Tripathi & Hyungtaik Ahn, 2004. "Empirical Likelihood-Based Inference in Conditional Moment Restriction Models," Econometrica, Econometric Society, vol. 72(6), pages 1667-1714, November.
    25. Berliant, Marcus & Peng, Shin-Kun & Wang, Ping, 2002. "Production Externalities and Urban Configuration," Journal of Economic Theory, Elsevier, pages 275-303.
    26. Duranton, Gilles, 2006. "Some foundations for Zipf's law: Product proliferation and local spillovers," Regional Science and Urban Economics, Elsevier, vol. 36(4), pages 542-563, July.
    27. Quinzii, Martine & Thisse, Jacques-Francois, 1990. "On the Optimality of Central Places," Econometrica, Econometric Society, pages 1101-1119.
    28. Guy Michaels & Ferdinand Rauch & Stephen J. Redding, 2012. "Urbanization and Structural Transformation," The Quarterly Journal of Economics, Oxford University Press, vol. 127(2), pages 535-586.
    29. Soo, Kwok Tong, 2005. "Zipf's Law for cities: a cross-country investigation," Regional Science and Urban Economics, Elsevier, vol. 35(3), pages 239-263, May.
    30. Robert E. Lucas & Esteban Rossi-Hansberg, 2002. "On the Internal Structure of Cities," Econometrica, Econometric Society, vol. 70(4), pages 1445-1476, July.
    31. Xavier Gabaix & Rustam Ibragimov, 2006. "Log(Rank-1/2): A Simple Way to Improve the OLS Estimation of Tail Exponents," Harvard Institute of Economic Research Working Papers 2106, Harvard - Institute of Economic Research.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Takao Asano & Takuma Kunieda & Akihisa Shibata, 2015. "Overconfidence, Underconfidence, and Welfare," Journal of Institutional and Theoretical Economics (JITE), Mohr Siebeck, Tübingen, pages 372-384.
    2. Mori, Tomoya & Smith, Tony E., 2015. "On the spatial scale of industrial agglomerations," Journal of Urban Economics, Elsevier, vol. 89(C), pages 1-20.
    3. Marcus Berliant & Tomoya Mori, 2017. "Beyond urban form: How Masahisa Fujita shapes us," International Journal of Economic Theory, The International Society for Economic Theory, vol. 13(1), pages 5-28, March.
    4. Giesen, Kristian & Suedekum, Jens, 2014. "City age and city size," European Economic Review, Elsevier, pages 193-208.
    5. Ikeda, Kiyohrio & Onda, Mikihisa & Takayama, Yuki, 2017. "Bifurcation theory of a square lattice economy: Racetrack economy analogy in an economic geography model," MPRA Paper 78120, University Library of Munich, Germany.
    6. Ramos, Arturo & Sanz-Gracia, Fernando, 2015. "US city size distribution revisited: Theory and empirical evidence," MPRA Paper 64051, University Library of Munich, Germany.

    More about this item

    Keywords

    power law; Zipf’s law; random growth; space; geography; Voronoi partition; economic region;

    JEL classification:

    • C49 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Other
    • L60 - Industrial Organization - - Industry Studies: Manufacturing - - - General
    • R12 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General Regional Economics - - - Size and Spatial Distributions of Regional Economic Activity; Interregional Trade (economic geography)
    • R14 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General Regional Economics - - - Land Use Patterns

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:kyo:wpaper:882. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Ryo Okui). General contact details of provider: http://edirc.repec.org/data/iekyojp.html .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.