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US city size distribution: Robustly Pareto, but only in the tail

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  • Ioannides, Yannis
  • Skouras, Spyros

Abstract

We establish empirically using three different definitions of US cities that the upper tail obeys a Pareto law and not a lognormal distribution. We emphasize estimation of a switching point between the body of the city size distribution (which includes most cities) and its upper tail (which includes most of the population). For the 2000 Census Places data, in particular, our preferred model suggests that switching from a lognormal to a Pareto law occurs within a narrow confidence interval around population 60,290, with a corresponding Pareto exponent of 1.25. Most cities obey a lognormal; but the upper tail and therefore most of the population obeys a Pareto law. We obtain qualitatively similar results for the upper tail with the Area Clusters data of Rozenfeld et al. (2011), and the US Census combined Metropolitan and Micropolitan Areas data, though the shape of that distribution at smaller sizes is sensitive to the definition used.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Urban Economics.

Volume (Year): 73 (2013)
Issue (Month): 1 ()
Pages: 18-29

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Handle: RePEc:eee:juecon:v:73:y:2013:i:1:p:18-29

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Web page: http://www.elsevier.com/locate/inca/622905

Related research

Keywords: Gibrat’s law; Zipf’s law; Pareto law; Upper tail; Mixture of distributions; Switching regressions; Urban evolution; Urban hierarchy;

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References

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  1. Gilles Duranton & Diego Puga, 2001. "From sectoral to functional urban specialisation," Working Papers dpuga-01-01, University of Toronto, Department of Economics.
  2. 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.
  3. Andrews, Donald W K, 2001. "Testing When a Parameter Is on the Boundary of the Maintained Hypothesis," Econometrica, Econometric Society, vol. 69(3), pages 683-734, May.
  4. Gilles Duranton, 2007. "Urban Evolutions: The Fast, the Slow, and the Still," American Economic Review, American Economic Association, vol. 97(1), pages 197-221, March.
  5. Yannis M. Ioannides & Henry G. Overman & Esteban Rossi-Hansberg & Kurt Schmidheiny, 2007. "The Effect of Information and Communication Technologies on Urban Structure," Discussion Papers Series, Department of Economics, Tufts University 0708, Department of Economics, Tufts University.
  6. William J. Reed, 2002. "On the Rank-Size Distribution for Human Settlements," Journal of Regional Science, Wiley Blackwell, vol. 42(1), pages 1-17.
  7. Xavier Gabaix, 1999. "Zipf'S Law For Cities: An Explanation," The Quarterly Journal of Economics, MIT Press, vol. 114(3), pages 739-767, August.
  8. Yannis M. Ioannides, 2012. "From Neighborhoods to Nations: The Economics of Social Interactions," Economics Books, Princeton University Press, edition 1, volume 1, number 9892.
  9. Hernán D. Rozenfeld & Diego Rybski & Xavier Gabaix & Hernán A. Makse, 2009. "The Area and Population of Cities: New Insights from a Different Perspective on Cities," NBER Working Papers 15409, National Bureau of Economic Research, Inc.
  10. Duncan Black & Vernon Henderson, 2003. "Urban evolution in the USA," Journal of Economic Geography, Oxford University Press, vol. 3(4), pages 343-372, October.
  11. Jan Eeckhout, 2004. "Gibrat's Law for (All) Cities," American Economic Review, American Economic Association, vol. 94(5), pages 1429-1451, December.
  12. J.V. Henderson, 1972. "The Sizes and Types of Cities," Working Papers 75, Queen's University, Department of Economics.
  13. Glaeser, E.L. & Ades, A.F., 1993. "Trade and Circuses: Explaining Urban Giants," Harvard Institute of Economic Research Working Papers 1646, Harvard - Institute of Economic Research.
  14. Yannis M. Ioannides, 2012. "Preface
    [From Neighborhoods to Nations: The Economics of Social Interactions]
    ," Introductory Chapters, Princeton University Press.
  15. Henderson, Vernon, 1997. "Medium size cities," Regional Science and Urban Economics, Elsevier, vol. 27(6), pages 583-612, November.
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Citations

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Cited by:
  1. Südekum, Jens & Giesen, Kristian, 2013. "City Age and City Size," Annual Conference 2013 (Duesseldorf): Competition Policy and Regulation in a Global Economic Order 79996, Verein für Socialpolitik / German Economic Association.
  2. Duranton, Gilles & Puga, Diego, 2013. "The growth of cities," CEPR Discussion Papers 9590, C.E.P.R. Discussion Papers.
  3. González-Val, Rafael & Ramos, Arturo & Sanz, Fernando & Vera-Cabello, María, 2013. "Size Distributions for All Cities: Which One is Best?," MPRA Paper 44314, University Library of Munich, Germany.
  4. Kristian Giesen & Jens Suedekum, 2012. "The size distribution across all 'cities': A unifying approach," ERSA conference papers ersa12p106, European Regional Science Association.
  5. Lee, Sanghoon & Li, Qiang, 2013. "Uneven landscapes and city size distributions," Journal of Urban Economics, Elsevier, vol. 78(C), pages 19-29.
  6. Ramos, Arturo & Sanz-Gracia, Fernando & González-Val, Rafael, 2013. "A new framework for the US city size distribution: Empirical evidence and theory," MPRA Paper 52190, University Library of Munich, Germany.
  7. Bee, Marco & Riccaboni, Massimo & Schiavo, Stefano, 2013. "The size distribution of US cities: Not Pareto, even in the tail," Economics Letters, Elsevier, vol. 120(2), pages 232-237.
  8. 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.
  9. Puente-Ajovin, Miguel & Ramos, Arturo, 2014. "On the parametric description of the French, German, Italian and Spanish city size distributions," MPRA Paper 55285, University Library of Munich, Germany.

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