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

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

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
Date of revision:
Handle: RePEc:pra:mprapa:52190
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  1. Miguel, Edward & Roland, Gérard, 2011. "The long-run impact of bombing Vietnam," Journal of Development Economics, Elsevier, vol. 96(1), pages 1-15, September.
  2. Jan Eeckhout, 2004. "Gibrat's Law for (All) Cities," American Economic Review, American Economic Association, vol. 94(5), pages 1429-1451, December.
  3. Toda, Alexis Akira, 2012. "The double power law in income distribution: Explanations and evidence," Journal of Economic Behavior & Organization, Elsevier, vol. 84(1), pages 364-381.
  4. 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.
  5. 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.
  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, 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.
  8. Steven Brakman & Harry Garretsen & Marc Schramm, 2004. "The strategic bombing of German cities during World War II and its impact on city growth," Journal of Economic Geography, Oxford University Press, vol. 4(2), pages 201-218, April.
  9. Combes, Pierre-Philippe & Duranton, Gilles & Gobillon, Laurent & Puga, Diego & Roux, Sébastien, 2009. "The productivity advantages of large cities: Distinguishing agglomeration from firm selection," CEPR Discussion Papers 7191, C.E.P.R. Discussion Papers.
  10. 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.
  11. Sukkoo Kim, 2000. "Urban Development in the United States, 1690–1990," Southern Economic Journal, Southern Economic Association, vol. 66(4), pages 855-880, April.
  12. Kwok Tong Soo, 2004. "Zipfs Law for Cities: A Cross Country Investigation," CEP Discussion Papers dp0641, Centre for Economic Performance, LSE.
  13. repec:oup:qjecon:v:114:y:1999:i:3:p:739-767 is not listed on IDEAS
  14. 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.
  15. 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.
  16. 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.
  17. Xavier Gabaix, 2009. "Power Laws in Economics and Finance," Annual Review of Economics, Annual Reviews, vol. 1(1), pages 255-294, 05.
  18. 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.
  19. 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.
  20. 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.
  21. William J. Reed, 2002. "On the Rank-Size Distribution for Human Settlements," Journal of Regional Science, Wiley Blackwell, vol. 42(1), pages 1-17.
  22. 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.
  23. 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.
  24. 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.
  25. 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.
  26. Edward L. Glaeser & Jesse M. Shapiro, 2001. "Cities and Warfare: The Impact of Terrorism on Urban Form," Harvard Institute of Economic Research Working Papers 1942, Harvard - Institute of Economic Research.
  27. Singh, S K & Maddala, G S, 1976. "A Function for Size Distribution of Incomes," Econometrica, Econometric Society, vol. 44(5), pages 963-70, September.
  28. Reed, William J., 2001. "The Pareto, Zipf and other power laws," Economics Letters, Elsevier, vol. 74(1), pages 15-19, December.
  29. Duncan Black & Vernon Henderson, 2003. "Urban evolution in the USA," Journal of Economic Geography, Oxford University Press, vol. 3(4), pages 343-372, October.
  30. 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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