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Do the world’s largest cities follow Zipf’s and Gibrat’s laws?

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  • Luckstead, Jeff
  • Devadoss, Stephen

Abstract

We examine whether the size distribution and the growth process of the world’s largest cities follow Zipf’s law and Gibrat’s law. The parametric results of the size distribution analysis reject Zipf’s law for all sample sizes and also show the Zipf exponent systematically declines as the sample size increases. The growth process analysis confirms Gibrat’s law and yields a local Zipf exponent of one for cities with a normalized population less than 0.53%, which includes about 95% of the total observations. The deviations from Zipf’s law occur at the extreme upper tail and are likely a result of restricted mobility of population across countries. However, given that Gibrat’s law holds, we can expect the size distribution to converge to Zipf’s law with a decline in the barriers to immigration.

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  • Luckstead, Jeff & Devadoss, Stephen, 2014. "Do the world’s largest cities follow Zipf’s and Gibrat’s laws?," Economics Letters, Elsevier, vol. 125(2), pages 182-186.
  • Handle: RePEc:eee:ecolet:v:125:y:2014:i:2:p:182-186
    DOI: 10.1016/j.econlet.2014.09.005
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    1. Luckstead, Jeff & Devadoss, Stephen, 2014. "A nonparametric analysis of the growth process of Indian cities," Economics Letters, Elsevier, vol. 124(3), pages 516-519.
    2. Luckstead, Jeff & Devadoss, Stephen, 2014. "A comparison of city size distributions for China and India from 1950 to 2010," Economics Letters, Elsevier, vol. 124(2), pages 290-295.
    3. Jan Eeckhout, 2004. "Gibrat's Law for (All) Cities," American Economic Review, American Economic Association, vol. 94(5), pages 1429-1451, December.
    4. Anderson, Gordon & Ge, Ying, 2005. "The size distribution of Chinese cities," Regional Science and Urban Economics, Elsevier, vol. 35(6), pages 756-776, November.
    5. 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.
    6. 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.
    7. World Bank, 2014. "World Development Indicators 2014," World Bank Publications - Books, The World Bank Group, number 18237.
    8. Urzua, Carlos M., 2000. "A simple and efficient test for Zipf's law," Economics Letters, Elsevier, vol. 66(3), pages 257-260, March.
    9. Stefano Magrini, 2007. "Analysing Convergence through the Distribution Dynamics Approach: Why and how?," Working Papers 2007_13, Department of Economics, University of Venice "Ca' Foscari".
    10. Stanley, Michael H. R. & Buldyrev, Sergey V. & Havlin, Shlomo & Mantegna, Rosario N. & Salinger, Michael A. & Eugene Stanley, H., 1995. "Zipf plots and the size distribution of firms," Economics Letters, Elsevier, vol. 49(4), pages 453-457, October.
    11. Moshe Levy, 2009. "Gibrat's Law for (All) Cities: Comment," American Economic Review, American Economic Association, vol. 99(4), pages 1672-1675, September.
    12. Xavier Gabaix, 1999. "Zipf's Law for Cities: An Explanation," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 114(3), pages 739-767.
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    Cited by:

    1. Bluhm, Richard & Krause, Melanie, 2022. "Top lights: Bright cities and their contribution to economic development," Journal of Development Economics, Elsevier, vol. 157(C).
    2. Christian Schluter, 2021. "On Zipf’s law and the bias of Zipf regressions," Empirical Economics, Springer, vol. 61(2), pages 529-548, August.
    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.
    4. Akhundjanov, Sherzod B. & Devadoss, Stephen & Luckstead, Jeff, 2017. "Size distribution of national CO2 emissions," Energy Economics, Elsevier, vol. 66(C), pages 182-193.
    5. Arshad, Sidra & Hu, Shougeng & Ashraf, Badar Nadeem, 2019. "Zipf’s law, the coherence of the urban system and city size distribution: Evidence from Pakistan," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 513(C), pages 87-103.
    6. Devadoss, Stephen & Luckstead, Jeff, 2015. "Growth process of U.S. small cities," Economics Letters, Elsevier, vol. 135(C), pages 12-14.
    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. Devadoss, Stephen & Luckstead, Jeff, 2016. "Size distribution of U.S. lower tail cities," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 444(C), pages 158-162.

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    More about this item

    Keywords

    Gibrat’s law; Growth process; Size distribution; World’s largest cities; Zipf’s law;
    All these keywords.

    JEL classification:

    • D30 - Microeconomics - - Distribution - - - General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • R23 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - Household Analysis - - - Regional Migration; Regional Labor Markets; Population

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