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Are the log-growth rates of city sizes normally distributed? Empirical evidence for the US

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  • Ramos, Arturo

Abstract

We study the decennial log-growth population rate distributions of the US incorporated places (resp., all places) for the period 1990-2000 (resp. 2000-2010) and the recently constructed US City Clustering Algorithm (CCA) population data in the period 1991-2000. It is obtained an excellent parametric description of these log-growth rates by means of a newly introduced distribution called “double mixture exponential Generalized Beta 2”. The normal distribution is not the one empirically observed for the same datasets.

Suggested Citation

  • Ramos, Arturo, 2015. "Are the log-growth rates of city sizes normally distributed? Empirical evidence for the US," MPRA Paper 65584, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:65584
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    References listed on IDEAS

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    1. 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.
    2. Cirillo, Pasquale, 2013. "Are your data really Pareto distributed?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(23), pages 5947-5962.
    3. 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.
    4. 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, March.
    5. Rafael Gonz�lez-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.
    6. 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.
    7. Rafael González-Val & Luis Lanaspa & Fernando Sanz-Gracia, 2014. "New Evidence on Gibrat’s Law for Cities," Urban Studies, Urban Studies Journal Limited, vol. 51(1), pages 93-115, January.
    8. Jan Eeckhout, 2009. "Gibrat's Law for (All) Cities: Reply," American Economic Review, American Economic Association, vol. 99(4), pages 1676-1683, September.
    9. 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.
    10. Giesen, Kristian & Suedekum, Jens, 2014. "City age and city size," European Economic Review, Elsevier, vol. 71(C), pages 193-208.
    11. 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 and the Associazione ICC, vol. 20(4), pages 991-1030, August.
    12. Lee, Sanghoon & Li, Qiang, 2013. "Uneven landscapes and city size distributions," Journal of Urban Economics, Elsevier, vol. 78(C), pages 19-29.
    13. James B. McDonald, 2008. "Some Generalized Functions for the Size Distribution of Income," Economic Studies in Inequality, Social Exclusion, and Well-Being, in: Duangkamon Chotikapanich (ed.), Modeling Income Distributions and Lorenz Curves, chapter 3, pages 37-55, Springer.
    14. Jan Eeckhout, 2004. "Gibrat's Law for (All) Cities," American Economic Review, American Economic Association, vol. 94(5), pages 1429-1451, December.
    15. John Sutton, 1997. "Gibrat's Legacy," Journal of Economic Literature, American Economic Association, vol. 35(1), pages 40-59, March.
    16. Gilles Duranton, 2007. "Urban Evolutions: The Fast, the Slow, and the Still," American Economic Review, American Economic Association, vol. 97(1), pages 197-221, March.
    17. Ramos, Arturo & Sanz-Gracia, Fernando, 2015. "US city size distribution revisited: Theory and empirical evidence," MPRA Paper 64051, University Library of Munich, Germany.
    18. 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.
    19. Parker, Simon C, 1999. "The Beta as a Model for the Distribution of Earnings," Bulletin of Economic Research, Wiley Blackwell, vol. 51(3), pages 243-251, July.
    20. 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.
    21. Moshe Levy, 2009. "Gibrat's Law for (All) Cities: Comment," American Economic Review, American Economic Association, vol. 99(4), pages 1672-1675, September.
    22. 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, December.
    23. Parker, Simon C., 1999. "The generalised beta as a model for the distribution of earnings," Economics Letters, Elsevier, vol. 62(2), pages 197-200, February.
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    Cited by:

    1. Ramos, Arturo, 2015. "Log-growth distributions of US city sizes and non-Lévy processes," MPRA Paper 66561, University Library of Munich, Germany.
    2. Puente-Ajovin, Miguel & Ramos, Arturo, 2015. "An improvement over the normal distribution for log-growth rates of city sizes: Empirical evidence for France, Germany, Italy and Spain," MPRA Paper 67471, University Library of Munich, Germany.
    3. Luckstead, Jeff & Devadoss, Stephen & Danforth, Diana, 2017. "The size distributions of all Indian cities," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 474(C), pages 237-249.

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    More about this item

    Keywords

    urban log-growth rates distribution; exponential distribution; exponential Generalized Beta 2 distribution; US population log-growth rates;
    All these keywords.

    JEL classification:

    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions
    • R11 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General Regional Economics - - - Regional Economic Activity: Growth, Development, Environmental Issues, and Changes
    • R12 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General Regional Economics - - - Size and Spatial Distributions of Regional Economic Activity; Interregional Trade (economic geography)

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