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

  • Campante, Filipe Robin
  • Do, Quoc-Anh

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 Harvard Kennedy School of Government in its series Scholarly Articles with number 4481653.

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Date of creation: 2009
Date of revision:
Publication status: Published in HKS Faculty Research Working Paper Series
Handle: RePEc:hrv:hksfac:4481653
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  1. Filipe R. Campante & Davin Chor & Quoc-Anh Do, 2009. "Instability And The Incentives For Corruption," Economics and Politics, Wiley Blackwell, vol. 21(1), pages 42-92, 03.
  2. Jean-Yves Duclos & Joan Esteban & Debraj Ray, 2015. "Polarization: Concepts, Measurement, Estimation," Working Papers 46, Barcelona Graduate School of Economics.
  3. Campante, Filipe & Do, Quoc-Anh, 2007. "Inequality, Redistribution, and Population," Working Paper Series rwp07-046, Harvard University, John F. Kennedy School of Government.
  4. C. A. Hidalgo & B. Klinger & A. -L. Barabasi & R. Hausmann, 2007. "The Product Space Conditions the Development of Nations," Papers 0708.2090,
  5. Glaeser, Edward L. & Kahn, Matthew E., 2004. "Sprawl and urban growth," Handbook of Regional and Urban Economics, in: J. V. Henderson & J. F. Thisse (ed.), Handbook of Regional and Urban Economics, edition 1, volume 4, chapter 56, pages 2481-2527 Elsevier.
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