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

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  • Campante, Filipe Robin
  • Do, Quoc-Anh

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.

Suggested Citation

  • Campante, Filipe Robin & Do, Quoc-Anh, 2009. "A Centered Index of Spatial Concentration: Axiomatic Approach with an Application to Population and Capital Cities," Scholarly Articles 4481653, Harvard Kennedy School of Government.
  • Handle: RePEc:hrv:hksfac:4481653
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    References listed on IDEAS

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    1. Jean-Yves Duclos & Joan Esteban & Debraj Ray, 2004. "Polarization: Concepts, Measurement, Estimation," Econometrica, Econometric Society, vol. 72(6), pages 1737-1772, November.
    2. 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.
    3. C. A. Hidalgo & B. Klinger & A. -L. Barabasi & R. Hausmann, 2007. "The Product Space Conditions the Development of Nations," Papers 0708.2090, arXiv.org.
    4. 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, March.
    5. Alberto F. Ades & Edward L. Glaeser, 1995. "Trade and Circuses: Explaining Urban Giants," The Quarterly Journal of Economics, Oxford University Press, vol. 110(1), pages 195-227.
    6. Campante, Filipe & Do, Quoc-Anh, 2007. "Inequality, Redistribution, and Population," Working Paper Series rwp07-046, Harvard University, John F. Kennedy School of Government.
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    Citations

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    Cited by:

    1. Filipe Campante & Edward L. Glaeser, 2009. "Yet Another Tale of Two Cities: Buenos Aires and Chicago," NBER Working Papers 15104, National Bureau of Economic Research, Inc.
    2. Sebastian Galiani & Sukkoo Kim, 2008. "Political Centralization and Urban Primacy: Evidence from National and Provincial Capitals in the Americas," NBER Chapters,in: Understanding Long-Run Economic Growth: Geography, Institutions, and the Knowledge Economy, pages 121-153 National Bureau of Economic Research, Inc.
    3. Filipe R. Campante & Quoc-Anh Do, 2014. "Isolated Capital Cities, Accountability, and Corruption: Evidence from US States," American Economic Review, American Economic Association, vol. 104(8), pages 2456-2481, August.
    4. Quoc-Anh Do & Filipe R. Campante, 2009. "Keeping Dictators Honest: the Role of Population Concentration," Working Papers 01-2009, Singapore Management University, School of Economics.
    5. Campante, Filipe R. & Do, Quoc-Anh & Guimaraes, Bernardo, 2012. "Isolated Capital Cities and Misgovernance: Theory and Evidence," Working Paper Series rwp12-058, Harvard University, John F. Kennedy School of Government.
    6. Quoc-Anh Doy & Filipe R. Campante, 2009. "Keeping Dictators Honest : the Role of Population Concentration," Governance Working Papers 22076, East Asian Bureau of Economic Research.
    7. Quoc-Anh Do & Bang Dang Nguyen & Yen-Teik Lee & Kieu-Trang Nguyen, 2011. "Out of Sight, Out of Mind:The Value of Political Connections in Social Networks," Working Papers 19-2011, Singapore Management University, School of Economics.
    8. Filipe R Campante & Quoc-Anh Do, 2013. "Isolated Capital Cities, Accountability and Corruption Evidence from US States: Evidence from US States," Sciences Po Economics Discussion Papers 2013-01, Sciences Po Departement of Economics.
    9. Elisa Muzzini & Beatriz Eraso Puig & Sebastian Anapolsky & Tara Lonnberg & Viviana Mora, 2016. "Leveraging the Potential of Argentine Cities," World Bank Publications, The World Bank, number 24185.
    10. Filipe R. Campante & Quoc-Anh Do, 2014. "Isolated Capital Cities, Accountability, and Corruption: Evidence from US States," American Economic Review, American Economic Association, vol. 104(8), pages 2456-2481, August.
    11. Arbia, Giuseppe & Piras, Gianfranco, 2009. "A new class of spatial concentration measures," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4471-4481, October.

    More about this item

    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, Regional, Real Estate, and Transportation Economics - - Household Analysis - - - Regional Migration; Regional Labor Markets; Population

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