A Centered Index of Spatial Concentration: Axiomatic Approach with an Application to Population and Capital Cities

55 Pages Posted: 3 Aug 2010

See all articles by Filipe R. Campante

Filipe R. Campante

Harvard University - Harvard Kennedy School (HKS)

Quoc-Anh Do

Sciences Po - Department of Economics; Centre for Economic Policy Research (CEPR)

Multiple version iconThere are 2 versions of this paper

Date Written: December 2008

Abstract

We construct an axiomatic index of spatial concentration around a center or capital point of interest, a concept with wide applicability from urban economics, economic geography and trade, to political economy and industrial organization. We propose basic axioms (decomposability and monotonicity) and refinement axioms (order preservation, convexity, and local monotonicity) for how the index should respond to changes in the underlying distribution. We obtain a unique class of functions satisfying all these properties, defined over any n-dimensional Euclidian space: the sum of a decreasing, isoelastic function of individual distances to the capital point of interest, with specific boundaries for the elasticity coefficient that depend on n. We apply our index to measure the concentration of population around capital cities across countries and US states, and also in US metropolitan areas. We show its advantages over alternative measures, and explore its correlations with many economic and political variables of interest.

Keywords: Spatial Concentration, Population Concentration, Capital Cities, Gravity, CRRA, Harmonic Functions, Axiomatics

JEL Classification: C43, F10, R23

Suggested Citation

Campante, Filipe R. and Do, Quoc-Anh, A Centered Index of Spatial Concentration: Axiomatic Approach with an Application to Population and Capital Cities (December 2008). Available at SSRN: https://ssrn.com/abstract=1362349 or http://dx.doi.org/10.2139/ssrn.1362349

Filipe R. Campante

Harvard University - Harvard Kennedy School (HKS) ( email )

79 John F. Kennedy Street
Cambridge, MA 02138
United States
617-384-7958 (Phone)

Quoc-Anh Do (Contact Author)

Sciences Po - Department of Economics ( email )

28 rue des Saints-Pères
Paris, 75007
France

Centre for Economic Policy Research (CEPR) ( email )

London
United Kingdom

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