The Rank-Size Rule in Europe: testing Zipf’s law using European data

The large literature on the rank-size rule of city sizes has received rather inconsistent treatment in the European continent. Part of the problem has been the fact that (unlike the U.S.) there are inconsistent Census dates and no uniform definition of what is meant by a functional urban area. This paper uses data from a French research project which provides physical urban area data for a number of European countries, down to quite small minimum urban sizes. This allows international comparison of the usual Pareto estimation parameters, and also some examination of whether square or cubic terms are significant. The nature and economic basis of such non-linearities in the logarithmic rank-size relationship are of interest. The paper examines the possibility of measuring the primacy of the urban size distribution using the second or third order polynomial fit in OLS estimations, and focuses on the way in which the slope of the Log(Rank) / Log (Size) relationship may differ within the estimated fit. As a result, the crude Zipf law estimate using the linear functional form may produce quite misleading results. We find that certain countries with strong regional governance or a history of regional city-states have `anti-primate ’ distributions, at least at the top end of the size distribution. 1