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An improvement over the normal distribution for log-growth rates of city sizes: Empirical evidence for France, Germany, Italy and Spain

Listed author(s):
  • Puente-Ajovin, Miguel
  • Ramos, Arturo

We study the decennial log-growth population rate distributions of France (1990-2009), Germany (1996-2006), Italy (1951-1961, 2001-2011) and Spain (1950-1960, 2001-2010). It is obtained an excellent parametric description of these log-growth rates by means of a modification of the normal distribution in that the tails are mixed by means of convex linear combinations with exponential distributions, giving rise to the so called “double mixture exponential normal”. The normal distribution is not the one empirically observed for the same datasets.

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File URL: https://mpra.ub.uni-muenchen.de/67471/1/MPRA_paper_67471.pdf
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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 67471.

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Date of creation: 27 Oct 2015
Handle: RePEc:pra:mprapa:67471
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  2. McDonald, James B, 1984. "Some Generalized Functions for the Size Distribution of Income," Econometrica, Econometric Society, vol. 52(3), pages 647-663, May.
  3. 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.
  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. 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.
  6. Giulio Bottazzi & Angelo Secchi, 2011. "A new class of asymmetric exponential power densities with applications to economics and finance," Industrial and Corporate Change, Oxford University Press, vol. 20(4), pages 991-1030, August.
  7. Ramos, Arturo & Sanz-Gracia, Fernando, 2015. "US city size distribution revisited: Theory and empirical evidence," MPRA Paper 64051, University Library of Munich, Germany.
  8. 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.
  9. Glaeser, Edward L & Hedi D. Kallal & Jose A. Scheinkman & Andrei Shleifer, 1992. "Growth in Cities," Journal of Political Economy, University of Chicago Press, vol. 100(6), pages 1126-1152, December.
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    • Glaeser, Edward Ludwig & Kallal, Hedi D. & Scheinkman, Jose A. & Shleifer, Andrei, 1992. "Growth in Cities," Scholarly Articles 3451309, Harvard University Department of Economics.
  10. McDonald, James B. & Xu, Yexiao J., 1995. "A generalization of the beta distribution with applications," Journal of Econometrics, Elsevier, vol. 69(2), pages 427-428, October.
  11. Ole Eiler Barndorff-Nielsen & Robert Stelzer, 2005. "Absolute Moments of Generalized Hyperbolic Distributions and Approximate Scaling of Normal Inverse Gaussian Lévy Processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 32(4), pages 617-637.
  12. Manas, Arnaud, 2009. "French butchers don't do quantum physics," Economics Letters, Elsevier, vol. 103(2), pages 101-106, May.
  13. Edward L. Glaeser & Joseph Gyourko & Raven E. Saks, 2006. "Urban growth and housing supply," Journal of Economic Geography, Oxford University Press, vol. 6(1), pages 71-89, January.
  14. 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.
  15. B. D. McCullough & H. D. Vinod, 2003. "Verifying the Solution from a Nonlinear Solver: A Case Study," American Economic Review, American Economic Association, vol. 93(3), pages 873-892, June.
  16. Gaffeo, Edoardo, 2011. "The distribution of sectoral TFP growth rates: International evidence," Economics Letters, Elsevier, vol. 113(3), pages 252-255.
  17. Edward L. Glaeser & Charles Redlick, 2009. "Social Capital and Urban Growth," International Regional Science Review, , vol. 32(3), pages 264-299, July.
  18. Bottazzi, Giulio & Secchi, Angelo, 2003. "Why are distributions of firm growth rates tent-shaped?," Economics Letters, Elsevier, vol. 80(3), pages 415-420, September.
  19. Christian Schluter & Mark Trede, 2013. "Gibrat, Zipf, Fisher and Tippett: City Size and Growth Distributions Reconsidered," CQE Working Papers 2713, Center for Quantitative Economics (CQE), University of Muenster.
  20. Edward L Glaeser & Jesse M Shapiro, 2003. "Urban Growth in the 1990s: Is City Living Back?," Journal of Regional Science, Wiley Blackwell, vol. 43(1), pages 139-165.
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