Economic Analysis: Theory and Practice

The Zipf's law: A cross-country analysis

Vol. 17, Iss. 7, JULY 2018

Received: 14 March 2018

Received in revised form: 25 April 2018

Accepted: 14 May 2018

Available online: 27 July 2018


JEL Classification: R13

Pages: 1337–1351

Manaeva I.V. Belgorod National Research University, Belgorod, Russian Federation

Kanishcheva A.V. Belgorod National Research University, Belgorod, Russian Federation

Importance The article addresses the modern settlement system in cities of the world, being a topical problem of spatial economy. It presents empirical studies of the Zipf's law in foreign and domestic literature. To assess the conformity of the modern settlement system with the rank-size distribution, we chose the following countries: Belarus, Brazil, Great Britain, Egypt, Norway, Poland, Russia, Turkey, USA, France, Japan.
Objectives The aim is to analyze the feasibility of the Zipf's law at the cross-country level.
Methods We apply the least square method to analyze the feasibility of the Zipf's law for the sample of countries.
Results The closest to the ideal Zipf's curve are settlement systems in cities of developing countries (Turkey, Poland, Brazil) and developed countries (USA, Japan). The gap between the main 'primate city' and subsequent rank cities is very significant.
Conclusions Traditionally, the sample of 'primate city' countries is a capital. Large centers will continue to grow at a faster pace and attract more and more migrants. This trend is negative, as overpopulation of large cities will be accompanied by a change in the ethnic and social composition of residents, as well as by suburbanization, which can lead to social and economic stagnation.

Keywords: Zipf's law, rank-size distribution, population size, cross-country level


  1. Eaton J., Eckstein Z. Cities and growth: Theory and evidence from France and Japan. Regional Science and Urban Economics, 1997, vol. 27, iss. 4-5, рр. 443–474.
  2. Auerbach F. Das Gesetz der Bevölkerungskonzentration. Petermanns Geographische Mitteilungen, 1913, no. 59, рр. 74–76.
  3. Gabaix X. Zipf's law for cities: An explanation. The Quarterly Journal of Economics, 1999, vol. 114, iss. 3, рр. 739–767. URL:
  4. Rossi‐Hansberg E., Wright M.L.J. Urban Structure and Growth. Review of Economic Studies, 2007, no. 74, рр. 597–624.
  5. Duranton G. Urban evolutions: The fast, the slow, and the still. The American Economic Review, 2007, vol. 97, iss. 1, рр. 197–221.
  6. Wen‐Tai Hsu. Central place theory and city size distribution. The Economic Journal, 2012, vol. 122, iss. 563, рр. 903–932. URL:
  7. Mansury Y., Gulyás L. The Emergence of Zipf's Law in a System of Cities: An Agent‐based Simulation Approach. Journal of Economic Dynamics and Control, 2007, vol. 31, iss. 7, рр. 2438–2460. URL:
  8. Krugman P. Confronting the Mystery of Urban Hierarchy. Journal of the Japanese and International Economies, 1996, vol. 10, iss. 4, рр. 399–418. URL:
  9. Ioannides Y.M., Overman H.G. Zipf’s law for cities: An empirical examination. Regional Science and Urban Economics, 2003, vol. 33, iss. 2, рр. 127–137. URL:
  10. Berry B.J., Okulicz‐Kozaryn A. The city size distribution debate: Resolution for US urban regions and megalopolitan areas. Cities, 2012, vol. 29, suppl. 1, рр. S17–S23, URL:
  11. Ziqin W. Zipf Law Analysis of Urban Scale in China. Asian Journal of Social Science Studies, 2016, vol. 1, iss. 1, рр. 53–58. URL:
  12. Black D., Henderson V. Urban evolution in the USA. Journal of Economic Geography, 2003, vol. 3, iss. 4, рр. 343–372.
  13. Eeckhout J. Gibrat's Law for (All) Cities: Reply. The American Economic Review, 2009, vol. 99, iss. 4, рр. 1676–1683. URL:
  14. Levy M. Gibrat's Law for (All) Cities: Comment. The American Economic Review, 2009, vol. 99, iss. 4, рр. 1672–1675. URL:
  15. Bee M., Riccaboni M., Schiavo S. The size distribution of US cities: Not Pareto, even in the tail. Economics Letters, 2013, vol. 120, iss. 2, рр. 232–237. URL:
  16. Soo K.T. Zipf's Law and Urban Growth in Malaysia. Urban Studies, 2007, vol. 44, iss. 1, рр. 1–14. URL:
  17. Pérez‐Campuzano E., Guzmán‐Vargas L., Angulo‐Brown F. Distributions of city sizes in Mexico during the 20th century. Chaos, Solitons & Fractals, 2015, vol. 73, рр. 64–70.
  18. Duran H.E., Ozkan S.P. Trade Openness, Urban Concentration And City‐Size Growth In Turkey. Regional Science Inquiry, 2015, vol. 7, iss. 1, рр. 35–46.
  19. Kolomak E.A. [Development of Russian urban system: Tendencies and Determinants]. Voprosy Ekonomiki, 2014, no. 10, pp. 82–96. (In Russ.)
  20. Andreev V.V., Lukiyanova V.Yu., Kadyshev E.N. [Analysis of people territorial distribution in regions of the Volga Federal District on the base of Zipf and Gibrat laws]. Prikladnaya ekonometrika = Applied Econometrics, 2017, vol. 48, pp. 97–121. (In Russ.)

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