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Zipf's Law for Cities and Beyond: The Case of Denmark

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  • Thorbjørn Knudsen

Abstract

Zipf's law for cities is one of the most conspicuous and robust empirical facts in the social sciences. It says that for most countries, the size distribution of cities must fit the power law: the number of cities with populations greater than S is inversely proportional to S. The present paper answers three questions related to Zipf's law: (1) does the Danish case refute Zipf's law for cities?, (2) what are the implications of Zipf's law for models of local growth?, and (3) do we have a Zipf's law for firms? Based on empirical data on the 61 largest Danish cities for year 2000, the answer to (1) is NO—the Danish case is not the exception which refutes Zipf's law. The consideration of (2) then leads to an empirical test of (3). The question of the existence of Zipf's law for firms is tested on a sample of 14,541 Danish production companies (the total population for 1997 with 10 employees or more). Based on the empirical evidence, the answer to (3) is YES in the sense that the growth pattern of Danish production companies follows a clean rank‐size distribution consistent with Zipf's law.

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  • Thorbjørn Knudsen, 2001. "Zipf's Law for Cities and Beyond: The Case of Denmark," American Journal of Economics and Sociology, Wiley Blackwell, vol. 60(1), pages 123-146, January.
    • Handle: RePEc:bla:ajecsc:v:60:y:2001:i:1:p:123-146
    DOI: 10.1111/1536-7150.00057
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    Cited by:

    1. Piotr Gabrielczak & Tomasz Serwach, 2019. "Firm-size distribution in Poland – is power law applicable?," Lodz Economics Working Papers 3/2019, University of Lodz, Faculty of Economics and Sociology.
    2. Duje Bonacci, 2004. "Towards quantitative tools for analysing qualitative properties of virtual communities," Interdisciplinary Description of Complex Systems - scientific journal, Croatian Interdisciplinary Society Provider Homepage: http://indecs.eu, vol. 2(2), pages 126-135.
    3. Gaffeo, Edoardo & Gallegati, Mauro & Palestrini, Antonio, 2003. "On the size distribution of firms: additional evidence from the G7 countries," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(1), pages 117-123.
    4. Sokołowski Dariusz & Jażdżewska Iwona, 2021. "Zipf's Law for cities: estimation of regression function parameters based on the weight of American urban areas and Polish towns," Bulletin of Geography. Socio-economic Series, Sciendo, vol. 53(53), pages 147-156, September.
    5. Qi Li & Patrick Paul Walsh, 2009. "The Firm Size Distribution in a Small Open Economy: Theory and Evidence," Working Papers 200920, Geary Institute, University College Dublin.

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