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Size Distributions for All Cities: Which One is Best?

  • González-Val, Rafael
  • Ramos, Arturo
  • Sanz, Fernando
  • Vera-Cabello, María

This paper analyses in detail the features offered by three distributions used in urban economics to describe city size distributions: lognormal, q-exponential and double Pareto lognormal, and another one of use in other areas of economics: the log-logistic. We use a large database which covers all cities with no size restriction in the US, Spain and Italy from 1900 until 2010, and, in addition, the last available year for the rest of the countries of the OECD. We estimate the previous four density functions by maximum likelihood. To check the goodness of the fit in all periods and for the thirty-four countries we use the Kolmogorov-Smirnov and Cramér-von Mises tests, and compute the Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC). The results show that the distribution which best fits the data in most of the cases (86.76%) is the double Pareto lognormal.

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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 44314.

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Date of creation: 09 Feb 2013
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Handle: RePEc:pra:mprapa:44314
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  1. 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.
  2. Hsing, Yu, 1990. "A note on functional forms and the urban size distribution," Journal of Urban Economics, Elsevier, vol. 27(1), pages 73-79, January.
  3. Kristian Giesen & Jens Suedekum, 2012. "The size distribution across all 'cities': A unifying approach," ERSA conference papers ersa12p106, European Regional Science Association.
  4. Guy Michaels & Ferdinand Rauch & Stephen J. Redding, 2012. "Urbanization and Structural Transformation," The Quarterly Journal of Economics, Oxford University Press, vol. 127(2), pages 535-586.
  5. 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.
  6. Jan Eeckhout, 2004. "Gibrat's Law for (All) Cities," American Economic Review, American Economic Association, vol. 94(5), pages 1429-1451, December.
  7. 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.
  8. Giesen, Kristian & Suedekum, Jens, 2009. "Zipf's Law for Cities in the Regions and the Country," IZA Discussion Papers 3928, Institute for the Study of Labor (IZA).
  9. Yannis Menelaos Ioannides & Henry G. Overman, 2003. "Zipf’s law for cities : an empirical examination," LSE Research Online Documents on Economics 583, London School of Economics and Political Science, LSE Library.
  10. Paul Cheshire & Stefano Magrini, 2005. "Population Growth in European Cities: weather matters – but only nationally," Urban/Regional 0506009, EconWPA.
  11. Soo, Kwok Tong, 2005. "Zipf's Law for cities: a cross-country investigation," Regional Science and Urban Economics, Elsevier, vol. 35(3), pages 239-263, May.
  12. Anderson, Gordon & Ge, Ying, 2005. "The size distribution of Chinese cities," Regional Science and Urban Economics, Elsevier, vol. 35(6), pages 756-776, November.
  13. Reed, William J., 2001. "The Pareto, Zipf and other power laws," Economics Letters, Elsevier, vol. 74(1), pages 15-19, December.
  14. Rafael González-Val & Luis Lanaspa & Fernando Sanz, 2012. "New evidence on Gibrat’s law for cities," Working Papers 2012/18, Institut d'Economia de Barcelona (IEB).
  15. Wen‐Tai Hsu, 2012. "Central Place Theory and City Size Distribution," Economic Journal, Royal Economic Society, vol. 122(563), pages 903-932, 09.
  16. 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.
  17. 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.
  18. Maarten Bosker & Steven Brakman & Harry Garretsen & Marc Schramm, 2006. "A Century of Shocks: The Evolution of the German City Size Distribution 1925 – 1999," CESifo Working Paper Series 1728, CESifo Group Munich.
  19. Rosen, Kenneth T. & Resnick, Mitchel, 1980. "The size distribution of cities: An examination of the Pareto law and primacy," Journal of Urban Economics, Elsevier, vol. 8(2), pages 165-186, September.
  20. 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.
  21. Cameron, Trudy Ann, 1990. "One-stage structural models to explain city size," Journal of Urban Economics, Elsevier, vol. 27(3), pages 294-307, May.
  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. Kamecke, Ulrich, 1990. "Testing the rank size rule hypothesis with an efficient estimator," Journal of Urban Economics, Elsevier, vol. 27(2), pages 222-231, March.
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