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

36 Pages Posted: 26 Dec 2014

See all articles by Andre Lemelin

Andre Lemelin

INRS-UCS Université du Québec

Fernando Rubiera-Morollon

Universidad de Oviedo

Ana Gómez-Loscos

Banco de España

Date Written: December 26, 2014


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.

Keywords: urban and regional economics, urbanisation, agglomeration economies, indexes and Spain

JEL Classification: R11, R12

Suggested Citation

Lemelin, Andre and Rubiera-Morollon, Fernando and Gómez-Loscos, Ana, Measuring Urban Agglomeration. A Refoundation of the mean City-Population Size Index (December 26, 2014). Banco de Espana Working Paper No. 1430. Available at SSRN: or

Andre Lemelin (Contact Author)

INRS-UCS Université du Québec ( email )

385, rue Sherbrooke est
Montreal, Quebec H2X 1E3

Fernando Rubiera-Morollon

Universidad de Oviedo ( email )

Escuela Universitaria Jovellanos
Francisco Tomas y Valiente 1 33201 Gijon
Oviedo, 33006

Ana Gómez-Loscos

Banco de España ( email )

Alcala 50
Madrid 28014

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