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The Evolution of Zipf's Law for U.S. Cities

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  • Angelina Hackmann
  • Torben Klarl

Abstract

Exploiting the cascade structure of cities and based on a dataset for U.S. cities between 1840 and 2016, the aim of this short paper is to answer three important questions: First, do we observe that the U.S. city size distribution exhibits a smooth transition to Zipf's law from the beginning or are there periods showing a pronounced departure from Zipf's law? Second, if we observe periods of departure, which alternative laws instead should be used to accurately describe the city size distribution? Third, employing information from the cascade structure of cities, do we always find evidence for primate cities for a specific period of time? Inter alia, we find that the exact Zipf's law has evolved over time from the more general, so-called three-parameter Zipf's law which can be traced back to Mandelbrot (1982).

Suggested Citation

  • Angelina Hackmann & Torben Klarl, 2018. "The Evolution of Zipf's Law for U.S. Cities," CESifo Working Paper Series 7232, CESifo.
    • Handle: RePEc:ces:ceswps:_7232
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    More about this item

    Keywords

    city size distributions; Zipf’s law; hierachical scaling law; urban systems;
    All these keywords.

    JEL classification:

    • 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)
    • R15 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General Regional Economics - - - Econometric and Input-Output Models; Other Methods

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