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Explaining the size distribution of cities: x-treme economies

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  • Berliant, Marcus
  • Watanabe, Hiroki

Abstract

We criticize the theories used to explain the size distribution of cities. They take an empirical fact and work backward to obtain assumptions on primitives. The induced theoretical assumptions on consumer behavior, particularly about their inability to insure against the city-level productivity shocks in the model, are untenable. With either self insurance or insurance markets, and either an arbitrarily small cost of moving or the assumption that consumers do not perfectly observe the shocks to firms' technologies, the agents will never move. Even without these frictions, our analysis yields another equilibrium with insurance where consumers never move. Thus, insurance is a substitute for movement. We propose an alternative class of models, involving extreme risk against which consumers will not insure. Instead, they will move, generating a Fréchet distribution of city sizes that is empirically competitive with other models.

Suggested Citation

  • Berliant, Marcus & Watanabe, Hiroki, 2009. "Explaining the size distribution of cities: x-treme economies," MPRA Paper 13671, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:13671
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    References listed on IDEAS

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    1. Kristian Behrens & Gilles Duranton & Frédéric Robert-Nicoud, 2014. "Productive Cities: Sorting, Selection, and Agglomeration," Journal of Political Economy, University of Chicago Press, vol. 122(3), pages 507-553.
    2. 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.
    3. Jan Eeckhout, 2004. "Gibrat's Law for (All) Cities," American Economic Review, American Economic Association, vol. 94(5), pages 1429-1451, December.
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    5. Berliant, Marcus & Kung, Fan-chin, 2006. "Can Information Asymmetry Cause Agglomeration?," MPRA Paper 1278, University Library of Munich, Germany, revised 29 Dec 2006.
    6. Gabaix, Xavier & Ioannides, Yannis M., 2004. "The evolution of city size distributions," Handbook of Regional and Urban Economics,in: J. V. Henderson & J. F. Thisse (ed.), Handbook of Regional and Urban Economics, edition 1, volume 4, chapter 53, pages 2341-2378 Elsevier.
    7. Berliant, Marcus & Kung, Fan-chin, 2010. "Can information asymmetry cause stratification?," Regional Science and Urban Economics, Elsevier, vol. 40(4), pages 196-209, July.
    8. 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.
    9. Starrett, David, 1978. "Market allocations of location choice in a model with free mobility," Journal of Economic Theory, Elsevier, vol. 17(1), pages 21-37, February.
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    11. Fujita, Masahisa & Mori, Tomoya, 1997. "Structural stability and evolution of urban systems," Regional Science and Urban Economics, Elsevier, vol. 27(4-5), pages 399-442, August.
    12. Xavier Gabaix, 2011. "The Granular Origins of Aggregate Fluctuations," Econometrica, Econometric Society, vol. 79(3), pages 733-772, May.
    13. M. Goldstein & S. Morris & G. Yen, 2004. "Problems with fitting to the power-law distribution," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 41(2), pages 255-258, September.
    14. Xavier Gabaix, 1999. "Zipf's Law for Cities: An Explanation," The Quarterly Journal of Economics, Oxford University Press, vol. 114(3), pages 739-767.
    15. Jonathan Eaton & Samuel Kortum, 2002. "Technology, Geography, and Trade," Econometrica, Econometric Society, vol. 70(5), pages 1741-1779, September.
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    Citations

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    Cited by:

    1. OSHIRO Jun & SATO Yasuhiro, 2016. "Industrial Structure in Urban Accounting," Discussion papers 16105, Research Institute of Economy, Trade and Industry (RIETI).
    2. Berliant, Marcus & Watanabe, Hiroki, 2011. "A scale-free transportation network explains the city-size distribution," MPRA Paper 34820, University Library of Munich, Germany.
    3. Ho Yeon KIM & Petra de Jong & Jan Rouwendal & Aleid Brouwer, 2012. "Shrinking population and the urban hierarchy
      [Housing preferences and attribute importance among Dutch older adults: a conjoint choice experiment]
      ," ERSA conference papers ersa12p350, European Regional Science Association.
    4. Duranton, Gilles & Puga, Diego, 2014. "The Growth of Cities," Handbook of Economic Growth,in: Handbook of Economic Growth, edition 1, volume 2, chapter 5, pages 781-853 Elsevier.
    5. Duranton, Gilles & Puga, Diego, 2014. "The Growth of Cities," Handbook of Economic Growth,in: Handbook of Economic Growth, edition 1, volume 2, chapter 5, pages 781-853 Elsevier.
    6. 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.
    7. Kim, Ho Yeon, 2012. "Shrinking population and the urban hierarchy," IDE Discussion Papers 360, Institute of Developing Economies, Japan External Trade Organization(JETRO).
    8. 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.
    9. 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

    Zipf's Law; Gibrat's Law; Size Distribution of Cities; Extreme Value Theory;

    JEL classification:

    • R12 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General Regional Economics - - - Size and Spatial Distributions of Regional Economic Activity; Interregional Trade (economic geography)

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