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

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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.

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Bibliographic Info

Paper provided by Singapore Management University, School of Economics in its series Working Papers with number 02-2009.

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Length: 55 pages
Date of creation: Jan 2009
Date of revision:
Publication status: Published in SMU Economics and Statistics Working Paper Series
Handle: RePEc:siu:wpaper:02-2009

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Keywords: Spatial Concentration; Population Concentration; Capital Cities; Gravity; CRRA; Harmonic Functions; Axiomatics.;

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References

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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. Campante, Filipe Robin & Chor, Davin & Do, Quoc-Anh, 2009. "Instability and the Incentives for Corruption," Scholarly Articles 4778510, Harvard Kennedy School of Government.
  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. 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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Cited by:
  1. Campante, Filipe R. & Do, Quoc-Anh, 2012. "Isolated Capital Cities, Accountability and Corruption: Evidence from US States," Working Paper Series rwp12-016, Harvard University, John F. Kennedy School of Government.
  2. Guimaraes, Bernardo & CAMPANTE, FILIPE R. & DO, Quoc-Anh, 2013. "Isolated capital cities and misgovernance: Theory and evidence," Textos para discussão 323, Escola de Economia de São Paulo, Getulio Vargas Foundation (Brazil).
  3. Quoc-Anh Do & Yen-Teik Lee & Bang Dang Nguyen & Kieu-Trang Nguyen, 2012. "Out of Sight, Out of Mind: The Value of Political Connections in Social Networks," Working Papers 22-2012, Singapore Management University, School of Economics.
  4. Filipe R Campante & Quoc-Anh Do, 2013. "Isolated Capital Cities, Accountability and Corruption Evidence from US States: Evidence from US States," Sciences Po publications 2013-01, Sciences Po.
  5. 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.
  6. 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.
  7. 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.
  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.

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