IDEAS home Printed from https://ideas.repec.org/a/bla/jregsc/v48y2008i1p165-211.html
   My bibliography  Save this article

The Number-Average Size Rule: A New Empirical Relationship Between Industrial Location And City Size

Author

Listed:
  • Tomoya Mori
  • Koji Nishikimi
  • Tony E. Smith

Abstract

The spatial intensities of both industries and population are highly uneven across space. Moreover, these intensities differ not only across industries, but also change through time. Nevertheless, we show using Japanese data for metropolitan areas in two time periods that the location intensities of both industries and population are linked by surprisingly simple and persistent patterns. In particular, we identify a strong negative log-linear relation between the number and the average (population) size of metro areas in which a given industry is found. This relation, which we designate as the Number-Average Size (NAS) Rule, is also shown to be intimately connected to both the Rank-Size Rule and Christaller's (1966) Hierarchy Principle applied to metropolitan areas. In particular, we show mathematically that in the presence of the Hierarchy Principle (which holds quite well in Japan) this NAS Rule is essentially equivalent to the Rank Size Rule. Copyright Blackwell Publishing, Inc. 2008

Suggested Citation

  • Tomoya Mori & Koji Nishikimi & Tony E. Smith, 2008. "The Number-Average Size Rule: A New Empirical Relationship Between Industrial Location And City Size," Journal of Regional Science, Wiley Blackwell, vol. 48(1), pages 165-211.
  • Handle: RePEc:bla:jregsc:v:48:y:2008:i:1:p:165-211
    as

    Download full text from publisher

    File URL: http://www.blackwell-synergy.com/doi/abs/10.1111/j.1467-9787.2008.00550.x
    File Function: link to full text
    Download Restriction: Access to full text is restricted to subscribers.

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

    References listed on IDEAS

    as
    1. Overman, Henry G. & Ioannides, Yannis M., 2001. "Cross-Sectional Evolution of the U.S. City Size Distribution," Journal of Urban Economics, Elsevier, vol. 49(3), pages 543-566, May.
    2. 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.
    3. 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.
    4. Gilles Duranton & Henry G. Overman, 2008. "Exploring The Detailed Location Patterns Of U.K. Manufacturing Industries Using Microgeographic Data," Journal of Regional Science, Wiley Blackwell, vol. 48(1), pages 213-243.
    5. Henderson, J V, 1974. "The Sizes and Types of Cities," American Economic Review, American Economic Association, vol. 64(4), pages 640-656, September.
    6. Guy Dumais & Glenn Ellison & Edward L. Glaeser, 2002. "Geographic Concentration As A Dynamic Process," The Review of Economics and Statistics, MIT Press, vol. 84(2), pages 193-204, May.
    7. Jan Eeckhout, 2004. "Gibrat's Law for (All) Cities," American Economic Review, American Economic Association, vol. 94(5), pages 1429-1451, December.
    8. Takatoshi Tabuchi & Jacques-François Thisse, 2006. "Regional Specialization, Urban Hierarchy, And Commuting Costs," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 47(4), pages 1295-1317, November.
    9. Fujita, Masahisa & Tabuchi, Takatoshi, 1997. "Regional growth in postwar Japan," Regional Science and Urban Economics, Elsevier, vol. 27(6), pages 643-670, November.
    10. Henderson, Vernon, 1997. "Medium size cities," Regional Science and Urban Economics, Elsevier, vol. 27(6), pages 583-612, November.
    11. Gilles Duranton & Diego Puga, 2000. "Diversity and Specialisation in Cities: Why, Where and When Does it Matter?," Urban Studies, Urban Studies Journal Limited, vol. 37(3), pages 533-555, March.
    12. 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.
    13. Gilles Duranton & Henry G. Overman, 2005. "Testing for Localization Using Micro-Geographic Data," Review of Economic Studies, Oxford University Press, vol. 72(4), pages 1077-1106.
    14. Duranton, Gilles & Puga, Diego, 2005. "From sectoral to functional urban specialisation," Journal of Urban Economics, Elsevier, vol. 57(2), pages 343-370, March.
    15. 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.
    16. 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.
    17. Nagel, Kai & Shubik, Martin & Paczuski, Maya & Bak, Per, 2000. "Spatial competition and price formation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 287(3), pages 546-562.
    18. Henderson, Vernon & Kuncoro, Ari & Turner, Matt, 1995. "Industrial Development in Cities," Journal of Political Economy, University of Chicago Press, vol. 103(5), pages 1067-1090, October.
    19. Duncan Black & Vernon Henderson, 2003. "Urban evolution in the USA," Journal of Economic Geography, Oxford University Press, vol. 3(4), pages 343-372, October.
    20. Tomoya Mori & Koji Nishikimi & Tony E. Smith, 2005. "A Divergence Statistic for Industrial Localization," The Review of Economics and Statistics, MIT Press, vol. 87(4), pages 635-651, November.
    21. 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.
    22. Xavier Gabaix, 1999. "Zipf's Law for Cities: An Explanation," The Quarterly Journal of Economics, Oxford University Press, vol. 114(3), pages 739-767.
    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. 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.
    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. 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. Xavier Gabaix, 2009. "Power Laws in Economics and Finance," Annual Review of Economics, Annual Reviews, vol. 1(1), pages 255-294, May.
    5. Hsu, Wen-Tai & Zhang, Hongliang, 2014. "The fundamental law of highway congestion revisited: Evidence from national expressways in Japan," Journal of Urban Economics, Elsevier, vol. 81(C), pages 65-76.
    6. Behrens, Kristian & Robert-Nicoud, Frédéric, 2015. "Agglomeration Theory with Heterogeneous Agents," Handbook of Regional and Urban Economics, Elsevier.
    7. 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.
    8. MORI Tomoya, 2017. "Evolution of Sizes and Industrial Structure of Cities in Japan from 1980 to 2010: Constant churning and persistent regularity," Discussion papers 17013, Research Institute of Economy, Trade and Industry (RIETI).
    9. Tomoya Mori, 2017. "Central Place Analysis," KIER Working Papers 959, Kyoto University, Institute of Economic Research.
    10. Kim, Ho Yeon, 2012. "Shrinking population and the urban hierarchy," IDE Discussion Papers 360, Institute of Developing Economies, Japan External Trade Organization(JETRO).
    11. Wen-Tai Hsu & Thomas J. Holmes, 2009. "Optimal City Hierarchy: A Dynamic Programming Approach to Central Place Theory," 2009 Meeting Papers 342, Society for Economic Dynamics.
    12. Gordon Mulligan & Mark Partridge & John Carruthers, 2012. "Central place theory and its reemergence in regional science," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 48(2), pages 405-431, April.
    13. Ricardo Hausmann & César Hidalgo, 2011. "The network structure of economic output," Journal of Economic Growth, Springer, vol. 16(4), pages 309-342, December.
    14. Dobis, Elizabeth A. & Delgado, Michael S. & Florax, Raymond J.G.M & Mulder, Peter, 2015. "The Significance of Urban Hierarchy in Explaining Population Dynamics in the United States," 2015 AAEA & WAEA Joint Annual Meeting, July 26-28, San Francisco, California 205869, Agricultural and Applied Economics Association;Western Agricultural Economics Association.
    15. Tomoya Mori & Tony E. Smith, 2011. "An Industrial Agglomeration Approach To Central Place And City Size Regularities," Journal of Regional Science, Wiley Blackwell, vol. 51(4), pages 694-731, October.
    16. Hsu, Wen-Tai & Holmes, Thomas J. & Morgan, Frank, 2014. "Optimal city hierarchy: A dynamic programming approach to central place theory," Journal of Economic Theory, Elsevier, vol. 154(C), pages 245-273.
    17. Giorgio Fazio & Marco Modica, 2015. "Pareto Or Log-Normal? Best Fit And Truncation In The Distribution Of All Cities," Journal of Regional Science, Wiley Blackwell, vol. 55(5), pages 736-756, November.
    18. Hyejin Youn & Lu'is M. A. Bettencourt & Jos'e Lobo & Deborah Strumsky & Horacio Samaniego & Geoffrey B. West, 2014. "The systematic structure and predictability of urban business diversity," Papers 1405.3202, arXiv.org.
    19. Xu, Hangtian, 2016. "Multiple Equilibria in the Urban Spatial Structure: Evidence from the Hanshin Earthquake," MPRA Paper 75219, University Library of Munich, Germany.
    20. repec:bla:rgscpp:v:9:y:2017:i:1:p:39-59 is not listed on IDEAS
    21. Tomoya Mori & Tony E. Smith, 2009. "A Reconsideration of the NAS Rule from an Industrial Agglomeration Perspective," KIER Working Papers 669, Kyoto University, Institute of Economic Research.

    More about this item

    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:bla:jregsc:v:48:y:2008:i:1:p:165-211. 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: (Wiley-Blackwell Digital Licensing) or (Christopher F. Baum). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0022-4146 .

    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.