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A Centered Index of Spatial Concentration: Expected Influence Approach

Author

Listed:
  • Filipe Campante

    (Harvard University)

  • Quoc-Anh Do

    (Singapore Management University)

Abstract

We construct a general axiomatic approach to measuring 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. By analogy with expected utility theory, we propose a basic axiom of independence (sub-group consistency) and continuity for a concentration order that ranks any two distributions relative to the capital point. We show that this axiom implies an expected influence representation of that order, conceptualizing concentration as an aggregation of the expected influence exerted by the capital on all points in the relevant space (or vice-versa). We then propose two axioms (monotonicity and rank invariance) and prove that they imply that the associated influence function must be a decreasing isoelastic function of the distance to the capital. 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 Campante & Quoc-Anh Do, 2010. "A Centered Index of Spatial Concentration: Expected Influence Approach," Sciences Po publications info:hdl:2441/7t0dp4mp828, Sciences Po.
  • Handle: RePEc:spo:wpmain:info:hdl:2441/7t0dp4mp8288lr2u6l7j8uk4li
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    File URL: https://spire.sciencespo.fr/hdl:/2441/7t0dp4mp8288lr2u6l7j8uk4li/resources/centered-index.pdf
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    References listed on IDEAS

    as
    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. 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.
    4. Campante, Filipe & Do, Quoc-Anh, 2007. "Inequality, Redistribution, and Population," Working Paper Series rwp07-046, Harvard University, John F. Kennedy School of Government.
    5. Roland G. Fryer Jr. & Richard Holden, 2011. "Measuring the Compactness of Political Districting Plans," Journal of Law and Economics, University of Chicago Press, vol. 54(3), pages 493-535.
    6. Peter C. Fishburn, 1976. "Unbounded Utility Functions in Expected Utility Theory," The Quarterly Journal of Economics, Oxford University Press, vol. 90(1), pages 163-168.
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    Citations

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    Cited by:

    1. 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.
    2. 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.
    3. Toke S. Aidt & Gabriel Leon, 2014. "The Democratic Window of Opportunity: Evidence from Riots in sub-Saharan Africa," Cambridge Working Papers in Economics 1417, Faculty of Economics, University of Cambridge.
    4. Toke Aidt & Gabriel Leon, 2014. "The Democratic Window of Opportunity: Evidence from Riots in Sub-Saharan Africa," CESifo Working Paper Series 4884, CESifo Group Munich.
    5. Per G. Fredriksson & Eric Neumayer, 2016. "Corruption and Climate Change Policies: Do the Bad Old Days Matter?," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 63(2), pages 451-469, February.
    6. Filipe Campante & Quoc-Anh Do & Bernardo Guimaraes, 2014. "Capital Cities, Conflict, and Misgovernance: Theory and Evidence," Sciences Po Economics Discussion Papers 2014-13, Sciences Po Departement of Economics.
    7. Filipe 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.
    8. 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.
    9. 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.

    More about this item

    Keywords

    Spatial Concentration; Expected Influence; Expected Utility; Population Concentration; Capital Cities; Gravity; CRRA; Harmonic Functions; Axiomatics;

    JEL classification:

    • C43 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Index Numbers and Aggregation
    • D78 - Microeconomics - - Analysis of Collective Decision-Making - - - Positive Analysis of Policy Formulation and Implementation
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • R23 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - Household Analysis - - - Regional Migration; Regional Labor Markets; Population

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