pp 1–18 | Cite as

The size ranking of cities in Germany: caught by a MAUP?

  • Rüdiger Budde
  • Uwe Neumann


A long standing question in urbanisation studies queries whether an empirical regularity known as Zipf's law applies to the size ranking of cities within countries or regions. Part of the debate addresses the statistical attributes of the size distribution. More recently, the definition of the territories assigned to cities has become a matter of concern in this context. Since the shape of administrative boundaries may not represent economic entities, analysis of the size ranking among cities defined by municipal territories may be affected by a considerable modifiable areal unit problem. Following a methodical approach that relates to current research on natural cities, we study the extent to which variation in the territory assigned to urban areas in Germany affects basic features of the size ranking. We define urban areas according to variable thresholds of population density across 1 km2 grids by a clustering algorithm. We find a systematic but moderate deviation from Zipf's law suggesting scale economies among urban agglomerations if peripheral zones are included.


Agglomeration Natural cities Zipf's law MAUP Spatial clustering 

JEL Classification

C38 R12 R14 



We are thankful for helpful comments that significantly improved our paper to Colin Vance and to three anonymous referees. Earlier versions of the paper were presented at the 7th Summer Conference in Regional Science (Marburg, 2014), the Workshop on Neighbourhood Effects (Essen, 2014) and at the SCORUS Conference 2016 (Lisbon). We thank Astrid Schürmann for giving our English a final polish. This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors. It uses data compiled by RWI as part of the project “Neighbourhood effects: Analysis of individual rational behaviour in a social context“, financed by the Leibniz Association (Joint Initiative for Research and Innovation).

Compliance with ethical standards

Conflicts of interest

All authors declare that they have no conflicts of interest.


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Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.RWI - Leibniz Institute for Economic ResearchEssenGermany

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