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Log-growth distributions of US city sizes and non-Lévy processes

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  • Ramos, Arturo

Abstract

We study whether the hypothesis that the log-population of US cities follows a Lévy process can be rejected or not. The result seems to be rejection. As a consequence, the cited process seems not to be described by a standard Brownian motion with drift (with a Yule process), thus explaining in another way the rejection of the lognormal and double Pareto lognormal distributions for US city size in recent studies. The datasets employed are that of US incorporated places on the period 1890-2000. However, we recall a way of obtaining a family of stochastic Itô differential equations whose sample paths are associated to the time-dependent probability density functions for city size that in principle could be observed empirically

Suggested Citation

  • Ramos, Arturo, 2015. "Log-growth distributions of US city sizes and non-Lévy processes," MPRA Paper 66561, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:66561
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    References listed on IDEAS

    as
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    13. 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.
    14. 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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    More about this item

    Keywords

    Lévy process; Brownian motion with drift; Yule process; stochastic Itô differential equation; US city size;
    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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