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.
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Paper provided by Singapore Management University, School of Economics in its series Working Papers with number
02-2009.
Length: 55 pages Date of creation: Date of revision: Publication status: Published in SMU Economics and Statistics Working Paper Series Handle: RePEc:siu:wpaper:02-2009
Find related papers by JEL classification: C43 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Index Numbers and Aggregation F10 - International Economics - - Trade - - - General R23 - Urban, Rural, and Regional Economics - - Household Analysis - - - Regional Migration; Regional Labor Markets; Population
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