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

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Listed author(s):
  • 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
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, 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.
  2. Giesen, Kristian & Suedekum, Jens, 2014. "City age and city size," European Economic Review, Elsevier, vol. 71(C), pages 193-208.
  3. Sukkoo Kim, 2000. "Urban Development in the United States, 1690–1990," Southern Economic Journal, Southern Economic Association, vol. 66(4), pages 855-880, April.
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  5. 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.
  6. 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.
  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 2205-2225, August.
  8. Reed, William J., 2001. "The Pareto, Zipf and other power laws," Economics Letters, Elsevier, vol. 74(1), pages 15-19, December.
  9. 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.
  10. 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.
  11. Pierre‐Philippe Combes & Gilles Duranton & Laurent Gobillon & Diego Puga & Sébastien Roux, 2012. "The Productivity Advantages of Large Cities: Distinguishing Agglomeration From Firm Selection," Econometrica, Econometric Society, vol. 80(6), pages 2543-2594, November.
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  15. Reed, William J., 2003. "The Pareto law of incomes—an explanation and an extension," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 319(C), pages 469-486.
  16. Xavier Gabaix, 2009. "Power Laws in Economics and Finance," Annual Review of Economics, Annual Reviews, vol. 1(1), pages 255-294, 05.
  17. Miguel, Edward & Roland, Gérard, 2011. "The long-run impact of bombing Vietnam," Journal of Development Economics, Elsevier, vol. 96(1), pages 1-15, September.
  18. 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.
  19. Vernon Henderson & Duncan Black, 1999. "Spatial Evolution of Population and Industry in the United States," American Economic Review, American Economic Association, vol. 89(2), pages 321-327, May.
  20. Xavier Gabaix, 1999. "Zipf's Law for Cities: An Explanation," The Quarterly Journal of Economics, Oxford University Press, vol. 114(3), pages 739-767.
  21. Donald R. Davis & David E. Weinstein, 2002. "Bones, Bombs, and Break Points: The Geography of Economic Activity," American Economic Review, American Economic Association, vol. 92(5), pages 1269-1289, December.
  22. William J. Reed, 2002. "On the Rank-Size Distribution for Human Settlements," Journal of Regional Science, Wiley Blackwell, vol. 42(1), pages 1-17.
  23. 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.
  24. 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.
  25. Singh, S K & Maddala, G S, 1976. "A Function for Size Distribution of Incomes," Econometrica, Econometric Society, vol. 44(5), pages 963-970, September.
  26. 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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  30. 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.
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Cited by:

  1. Miguel Puente-Ajovín & Arturo Ramos, 2015. "On the parametric description of the French, German, Italian and Spanish city size distributions," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 54(2), pages 489-509, March.
  2. Giesen, Kristian & Suedekum, Jens, 2014. "City age and city size," European Economic Review, Elsevier, vol. 71(C), pages 193-208.

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