Local concentrations

François Bavaud

Papers in Regional Science, 2008, vol. 87, issue 3, 357-370

Abstract: 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. Resumen. La mayoría de índices globales de concentraciones se obtienen como promedios ponderados de funciones convexas de índices de distribución, como la renta per capita. Buscamos definir índices locales de concentraciones, comparando la riqueza de una región con sus vecinas, donde las ponderaciones espaciales que definen la vecindad son formalmente equivalentes a los componentes de una matriz de transición Markov reversible. Se muestran concentraciones locales de segundo orden para generalizar los índices de autocorrelación de Moran o Geary, mientras que las concentraciones locales de primer orden se elaboran de manera que no excedan su contraparte ordinaria o global. Se discuten el comportamiento bajo agregación y el Principio de Pigou‐Dalton dentro del formalismo propuesto, el cual se ejemplifica mediante la distribución de riqueza entre cantones suizos bajo la estructura de vecindad inducida por migraciones regionales.

Date: 2008
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https://doi.org/10.1111/j.1435-5957.2008.00196.x

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Persistent link: https://EconPapers.repec.org/RePEc:bla:presci:v:87:y:2008:i:3:p:357-370

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