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Local concentrations

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  • François Bavaud

Abstract

Most global indices of concentrations are obtained as weighted averages of convex functions of distributions ratios, such as the per capita income. We seek to define local indices of concentrations, comparing the wealth of a region to its neighbours, where the spatial weights defining neighbourhood are formally equivalent to the components of a reversible Markov transition matrix. Second-order local concentrations are shown to generalize Moran or Geary autocorrelation indices, while first-order local concentrations can be constructed so as to not exceed their ordinary or global counterpart. Behaviour under aggregation and the Pigou-Dalton principle are further discussed within the proposed formalism, which is exemplified on wealth distribution among the Swiss cantons under the neighbourhood structure induced by inter-regional migrations. Copyright (c) 2008 the author(s). Journal compilation (c) 2008 RSAI.

Suggested Citation

  • François Bavaud, 2008. "Local concentrations," Papers in Regional Science, Wiley Blackwell, vol. 87(3), pages 357-370, August.
  • Handle: RePEc:bla:presci:v:87:y:2008:i:3:p:357-370
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    References listed on IDEAS

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    1. Bourguignon, Francois, 1979. "Decomposable Income Inequality Measures," Econometrica, Econometric Society, vol. 47(4), pages 901-920, July.
    2. François Bavaud, 2002. "The Quasi-Symmetric Side of Gravity Modelling," Environment and Planning A, , vol. 34(1), pages 61-79, January.
    3. Cowell, Frank A., 1980. "Generalized entropy and the measurement of distributional change," European Economic Review, Elsevier, vol. 13(1), pages 147-159, January.
    4. Shorrocks, Anthony F, 1984. "Inequality Decomposition by Population Subgroups," Econometrica, Econometric Society, vol. 52(6), pages 1369-1385, November.
    5. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
    6. Dagum, Camilo, 1980. "Inequality Measures between Income Distributions with Applications," Econometrica, Econometric Society, vol. 48(7), pages 1791-1803, November.
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