Measuring Urban Agglomeration. A Refoundation of the mean City-Population Size Index

In this paper, we put forth the view that the potential for urbanisation economies increases with interaction opportunities. On the basis of that premise, three properties are key to an agglomeration index, which should: (i) increase with the concentration of population and conform to the Pigou-Dalton transfer principle; (ii) increase with the absolute size of constituent population interaction zones; and (iii) be consistent in aggregation. Confining our attention to pairwise interactions, and invoking the space-analytic foundations of local labour market area (LLMA) delineation, we develop an index of agglomeration based on the number of interaction opportunities per capita in a geographical area. This leads to Arriaga's mean city-population size, which is the mathematical expectation of the size of the LLMA in which a randomly chosen individual lives. The index has other important properties. It does not require an arbitrary population threshold to separate urban from non-urban areas. It adapts readily to situations where an LLMA lies partly outside the geographical area for which agglomeration is measured. Finally, it can be satisfactorily approximated when data are truncated or aggregated into size classes. We apply the index to the Spanish NUTS III regions, and evaluate its performance by examining its correlation with the location quotients of several knowledge-intensive business services (KIBS) known to be highly sensitive to urbanisation economies. The Arriaga index correlations are clearly stronger than those of either the classical degree of urbanisation or the Hirshman-Herfindahl concentration index