The rise and fall of urban concentration in Britain: Zipf, Gibrat and Gini across two centuries

City size and growth are the subject of a substantial literature in economic geography and urban economics, but consensus remains elusive on the extent to which key regularities such as Zipf's Law or Gibrat's Law holds across space and time. We contribute to this literature by examining city size, rank and growth in Britain 1801-2011, the first country in the world to urbanize. Across Zipf, Gibrat and Gini analyses, we find that urban concentration in Britain peaked in the mid-nineteenth century before falling 1861-1911 and again 1951-1991. The evolving relationship between city size, rank and growth in Britain since 1801 strongly suggests that drivers mentioned in the literature, such as random growth, increasing returns to scale and the importance of location fundamentals, are not constant over time. There is some evidence of increasing returns to scale 1801-1861, then offset by factors favouring smaller cities, possibly related to new transport technologies. Further, we show that conclusions about both Zipf's and Gibrat's Law would change if weaker city definitions, sample cutoffs and regression methods were used, a likely factor in understanding the often contradictory results in the literature on city dynamics.