Concentration of Economic Activity: An Analytical Framework

Abstract

Alonso-Villar O. and del Río C. Concentration of economic activity: an analytical framework, Regional Studies. The goal of this paper is to offer an analytical framework within which relative concentration, including both the concentration of each sector and aggregate concentration, can be analysed. By borrowing properties from the literature on income inequality and segregation and adapting them to a location context, this paper characterizes the generalized entropy family of concentration indexes and shows the properties of the L-index. In addition, it offers other measures taken from the segregation literature. All these tools are used to analyse the spatial patterns of manufacturing industries in Spain from 1977 to 2008, paying special attention to their technological intensity.

Alonso-Villar O. and del Río C. 经济活动的密集度：分析框架， 区域研究。本文旨在提出分析框架以对相对密集度，包括各部门及总密集度，进行分析。借用收入差异及隔离的相关研究，并将其应用于特定的地理背景，本文对广义熵浓度指标进行了特征化，同时展示了L系数的特征。除此之外，文章提供了基于隔离研究的其他测评方法。我们将工具用于分析西班牙从 1977 到 2008 年间制造业的空间模式，特别关注了技术强度。

地理密集 非均衡测评

Alonso-Villar O. et del Río C. La concentration de l'activité économique: un cadre analytique, Regional Studies. Cet article cherche à fournir un cadre analytique au sein duquel on peut analyser la concentration relative, y compris à la fois la concentration de chaque secteur et la concentration globale. En empruntant des notions à la documentation sur les inégalités de revenus et la ségrégation, et en les adaptant en fonction du lieu, cet article caractérise la famille entropique généralisée des indices de la concentration et montre les propriétés de l'indice-L. Qui plus est, on fournit d'autres mesures empruntées à la documentation sur la ségrégation. On se sert de tous ces outils afin d'analyser la distribution géographique des industries manufacturières en Espagne de 1977 à 2008, en prêtant une attention particulière à leur intensité technologique.

Concentration géographique Mesures d'inégalité

Alonso-Villar O. und del Río C. Konzentration der Wirtschaftstätigkeit: ein analytischer Rahmen, Regional Studies. Ziel dieses Beitrags ist die Bereitstellung eines analytischen Rahmens zur Analyse der relativen Konzentration, zu der die Konzentration in jedem Sektor sowie die Gesamtkonzentration gehören. Durch das Ausborgen von Merkmalen aus der Literatur über Einkommensungleichgewichte und Segregation sowie durch eine Anpassung dieser Merkmale an einen Standortkontext charakterisieren wir in diesem Beitrag die generalisierte Entropiefamilie der Konzentrationsindizes und verdeutlichen die Eigenschaften des L-Indexes. Darüber hinaus kommen weitere Maßstäbe aus der Literatur über Segregation zum Einsatz. Anhand sämtlicher dieser Instrumente werden die räumlichen Muster von produzierenden Branchen in Spanien im Zeitraum von 1977 bis 2008 unter besonderer Berücksichtigung ihrer technischen Intensität analysiert.

Geografische Konzentration Maßstäbe von Ungleichgewicht

Alonso-Villar O. y del Río C. La concentración de la actividad económica: un marco analítico, Regional Studies. El objetivo de este trabajo es ofrecer un marco analítico dentro del cual examinar tanto la concentración relativa de un sector como la del conjunto de sectores. Tomando propiedades de la literatura de distribución de la renta y de segregación y adaptándolas a un contexto de localización, este artículo caracteriza las medidas de concentración derivadas de la familia de índices de entropía generalizada y muestra las propiedades del índice L. Además, ofrece también otras medidas derivadas de la literatura de segregación. Todas estas herramientas son usadas para analizar los patrones espaciales de la industrias manufactureras españolas entre 1977 y 2008, prestando especial atención a sus intensidades tecnológicas.

Concentración geográfica Medidas de desigualdad

Keywords:

• Geographic concentration
• Inequality measures

JEL classifications:

• D63
• R12

Acknowledgements

Financial support from the Xunta de Galicia (Grant Number INCITE08PXIB300005PR) and from the FEDER is gratefully acknowledged.

Notes

Some of these properties have been used by Alonso-Villar (2011) to characterize employment Lorenz curves.

For an econometric approach to the roles played by natural advantages and technological spillovers, see Botazzi et al. (2008).

For the properties of entropy measures outside economics, see Shannon (1948) and Kapur and Kessavan (1992).

For other proposals, see Bickenbach and Bode (2008) and Alonso-Villar and Del Río (2010b).

The GE family also includes:

The values of these indexes are unbounded.

For technical definitions, see Appendix A.

Properties (2) and (4) imply aversion to inequality in distribution:

This is related to a property proposed in the literature of income distribution according to which the greater inequality increase, the lower the income of the poorer individual involved in a regressive transfer from the poorer to the richer (Atkinson, 1970). In the present context, this means that disequalizing movements of workers between locations leads to higher concentration increases in the sector when these movements occur between locations in which the relative presence of this sector, as compared with overall employment there, is low.

G ^s and D ^s take values in the interval [0,1).

For additional properties, see Mora and Ruiz-Castillo (2010).

If grouping (say) three-digit industries into two-digit industries, overall concentration at a three-digit level can be expressed as aggregate concentration at a two-digit level (the between-group component) plus the concentration inside each two-digit industry considered separately (the distribution of each three-digit industry is compared with that of the two-digit industry to which it belongs rather than with distribution t).

As opposed to the IS index, which is based on comparisons between and in each location, in the global concentration index proposed by Mulligan and Schmidt (2005),

is contrasted with .

In fact, the Spearman correlation coefficient between these indexes ranges from 0.94 to 0.98.

The values of these indexes for 2008 are shown in Fig. 1, which includes not only these figures, but also those for the whole period.

This result is not a consequence of the small weight of the high-technology industry in the economy since the GE family is unaffected by the size of the sector (see property 3).

The change from 1992 to 1993 is due to the use of a different classification of manufacturing industries: From 1977 to 1992, the EPA gathered information at a two-digit level according to classification CNAE-1974, while from 1993 to 2008 the classification used was CNAE-93.

This finding corroborates that obtained by Paluzie et al. (2004), who used alternative indexes and data sets for the period 1955–1995.

For arguments in favour of using this method in the case of entropy measures, see Brülhart and Traeger (2005) and Cutrini (2010).

Since classification of the manufacturing industry at a two-digit level between 1977 and 1992 is different from that used between 1993 and 2008, another technological grouping was used (see Tables B1 and B2 in Appendix B). In any case, a broad criterion similar to that used in 2008 was used for the whole period.

The case where α = 0 is discarded, because when the sector has no employment in location l (that is, when ) and α = 0, the index value would be infinite and, therefore, it makes no sense. The case where α = 1 does not have the same problem since: