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

Author

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  • Filipe R. Campante

    (John F. Kennedy School of Government, Harvard University)

  • Quoc-Anh Do

    (School of Economics, Singapore Management University)

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

  • Filipe R. Campante & Quoc-Anh Do, 2009. "A Centered Index of Spatial Concentration: Axiomatic Approach with an Application to Population and Capital Cities," Working Papers 02-2009, Singapore Management University, School of Economics.
    • Handle: RePEc:siu:wpaper:02-2009
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    References listed on IDEAS

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    1. 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.
    2. 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.
    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.
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    6. Alberto F. Ades & Edward L. Glaeser, 1995. "Trade and Circuses: Explaining Urban Giants," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 110(1), pages 195-227.
    7. Campante, Filipe & Do, Quoc-Anh, 2007. "Inequality, Redistribution, and Population," Working Paper Series rwp07-046, Harvard University, John F. Kennedy School of Government.
    8. repec:hal:spmain:info:hdl:2441/o45fqtltm960r11iq437ski90 is not listed on IDEAS
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    Cited by:

    1. Filipe Campante & Edward L. Glaeser, 2018. "Yet another tale of two cities: Buenos Aires and Chicago," Latin American Economic Review, Springer;Centro de Investigaciòn y Docencia Económica (CIDE), vol. 27(1), pages 1-33, December.
    2. 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.
    3. Karina Simone Sass & Alexandre Alves Porsse, 2021. "Urban sprawl and the cost of providing local public services: Empirical evidence for Brazilian municipalities," Regional Science Policy & Practice, Wiley Blackwell, vol. 13(4), pages 1371-1387, August.
    4. repec:hal:spmain:info:hdl:2441/6ggbvnr6munghes9ocq36eaai is not listed on IDEAS
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. repec:spo:wpmain:info:hdl:2441/6ggbvnr6munghes9ocq36eaai is not listed on IDEAS
    10. Elisa Muzzini & Beatriz Eraso Puig & Sebastian Anapolsky & Tara Lonnberg & Viviana Mora, 2016. "Leveraging the Potential of Argentine Cities," World Bank Publications - Books, The World Bank Group, number 24185.
    11. repec:spo:wpecon:info:hdl:2441/dambferfb7dfprc9lj6bo200k is not listed on IDEAS
    12. Paul Maarek & Michael T. Dorsch, 2015. "Rent seeking, revolutionary threat and coups in non-democracies," THEMA Working Papers 2015-13, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    13. Arbia, Giuseppe & Piras, Gianfranco, 2009. "A new class of spatial concentration measures," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4471-4481, October.
    14. Dorsch, Michael T. & Maarek, Paul, 2018. "Rent extraction, revolutionary threat, and coups in non-democracies," Journal of Comparative Economics, Elsevier, vol. 46(4), pages 1082-1103.
    15. repec:hal:wpspec:info:hdl:2441/dambferfb7dfprc9lj6bo200k is not listed on IDEAS

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    More about this item

    Keywords

    Spatial Concentration; Population Concentration; Capital Cities; Gravity; CRRA; Harmonic Functions; Axiomatics.;
    All these keywords.

    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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