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

Filipe Campante () and Quoc-Anh Do ()

No 02-2009, Working Papers from Singapore Management University, School of Economics

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. (search for similar items in EconPapers)
JEL-codes: C43 F10 R23 (search for similar items in EconPapers)
Date: 2009-01
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Published in SMU Economics and Statistics Working Paper Series

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https://mercury.smu.edu.sg/rsrchpubupload/14221/CampanteDoDec2008CISC.pdf (application/pdf)

Related works:
Working Paper: A Centered Index of Spatial Concentration: Axiomatic Approach with an Application to Population and Capital Cities (2009) Downloads
Working Paper: A Centered Index of Spatial Concentration: Axiomatic Approach with an Application to Population and Capital Cities (2009) Downloads
Working Paper: A Centered Index of Spatial Concentration: Axiomatic Approach with an Application to Population and Capital Cities (2009) Downloads
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