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

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 km(2) 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.