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A new framework for the US city size distribution: Empirical evidence and theory

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  • Ramos, Arturo
  • Sanz-Gracia, Fernando
  • González-Val, Rafael

Abstract

We study the US city size distribution using the Census places data, without size restriction, for the period (1900-2010). Also, we use the recently introduced US City Clustering Algorithm (CCA) data for 1991 and 2000. We compare the lognormal, two distributions named after Ioannides and Skouras (2013) and the double Pareto lognormal with two newly introduced distributions. The empirical results are overwhelming: One of the new distributions widely outperform any of the previously used density functions for each type of data. We also develop a theory which generates the new distributions based on the standard geometric Brownian motion for the population in the short term. We propose some extensions of the theory in order to deal with the long term empirical features.

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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 52190.

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Date of creation: 13 Dec 2013
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Handle: RePEc:pra:mprapa:52190
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Keywords: US city size distribution; population thresholds; lower and upper tail; new statistical distributions;

Find related papers by JEL classification:

  • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
  • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions
  • R00 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General - - - General

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  1. Rafael González-Val & Arturo Ramos & Fernando Sanz-Gracia, 2013. "The accuracy of graphs to describe size distributions," Applied Economics Letters, Taylor & Francis Journals, vol. 20(17), pages 1580-1585, November.
  2. Xavier Gabaix, 2009. "Power Laws in Economics and Finance," Annual Review of Economics, Annual Reviews, vol. 1(1), pages 255-294, 05.
  3. Combes, Pierre-Philippe & Duranton, Gilles & Gobillon, Laurent & Puga, Diego & Roux, Sébastien, 2012. "The Productivity Advantages of Large Cities: Distinguishing Agglomeration from Firm Selection," IZA Discussion Papers 6502, Institute for the Study of Labor (IZA).
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  6. Y Ioannides & Henry Overman, 2000. "Zipfs Law for Cities: An Empirical Examination," CEP Discussion Papers dp0484, Centre for Economic Performance, LSE.
  7. 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 2205-25, August.
  8. Donald R. Davis & David E. Weinstein, 2001. "Bones, Bombs and Break Points: The Geography of Economic Activity," NBER Working Papers 8517, National Bureau of Economic Research, Inc.
  9. Rafael González-Val & Arturo Ramos & Fernando Sanz-Gracia & María Vera-Cabello, 2015. "Size distributions for all cities: Which one is best?," Papers in Regional Science, Wiley Blackwell, vol. 94(1), pages 177-196, 03.
  10. Rafael González‐Val, 2010. "The Evolution Of U.S. City Size Distribution From A Long‐Term Perspective (1900–2000)," Journal of Regional Science, Wiley Blackwell, vol. 50(5), pages 952-972, December.
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  15. 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.
  16. Giesen, Kristian & Suedekum, Jens, 2014. "City age and city size," European Economic Review, Elsevier, vol. 71(C), pages 193-208.
  17. Anderson, Gordon & Ge, Ying, 2005. "The size distribution of Chinese cities," Regional Science and Urban Economics, Elsevier, vol. 35(6), pages 756-776, November.
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  20. Steven Brakman & Harry Garretsen & Marc Schramm, 2002. "The Strategic Bombing of German Cities during World War II and its Impact on City Growth," CESifo Working Paper Series 808, CESifo Group Munich.
  21. Marco Bee, 2012. "Statistical analysis of the Lognormal-Pareto distribution using Probability Weighted Moments and Maximum Likelihood," Department of Economics Working Papers 1208, Department of Economics, University of Trento, Italia.
  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.
  23. Reed, William J., 2001. "The Pareto, Zipf and other power laws," Economics Letters, Elsevier, vol. 74(1), pages 15-19, December.
  24. William J. Reed, 2002. "On the Rank-Size Distribution for Human Settlements," Journal of Regional Science, Wiley Blackwell, vol. 42(1), pages 1-17.
  25. 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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  28. Gabaix, Xavier & Ibragimov, Rustam, 2011. "Rank − 1 / 2: A Simple Way to Improve the OLS Estimation of Tail Exponents," Journal of Business & Economic Statistics, American Statistical Association, vol. 29(1), pages 24-39.
  29. Kristian GIESEN & Jens SÜDEKUM, 2012. "The French Overall City Size Distribution," Region et Developpement, Region et Developpement, LEAD, Universite du Sud - Toulon Var, vol. 36, pages 107-126.
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Cited by:

  1. 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.
  2. Giesen, Kristian & Suedekum, Jens, 2013. "City age and city size," DICE Discussion Papers 120, Düsseldorf Institute for Competition Economics (DICE), University of Düsseldorf.

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