An Account of Geographic Concentration Patterns in Europe

Abstract

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Measuring concentration: Lorenz curves and their decompositions

“…If concerned, for example, with the concentration of manufacturing industries, t could represent the distribution of total manufacturing employment among regions (as in Amiti 1999 andBrülhart 2001). If concerned with a broader perspective, t could represent instead the distribution of overall employment, services included (as in Brülhart and Traeger 2005). Let us denote by x ≡ (x 1 , x 2 , .…”

“…While additive decompositions of the generalized entropy family of indexes have been proposed in the literature of industrial concentration (Brülhart and Traeger 2005), as far as we know, no decompositions of the employment Lorenz curves have yet been suggested. Following the decomposition of the standard Lorenz curve proposed by Bishop et al (2003) in an inequality context, in what follows, we offer two forms of decomposition of these curves: one by groups of locations, and the other by subsectors.…”

“…To check the robustness of this finding, we use bootstrapping for the above α indexes, since there are arguments in favor of using this method in the case of entropy measures (Brülhart and Traeger 2005;Cutrini 2009). The bootstrap inference, based on 1,000 replications, confirms the previous conclusion for α = 0.1, 0.5, 1, and 2 at the 95% level of significance (see Table 4 in Appendix).…”

“…However, some of the most widely used concentration measures are derived from the literature on income inequality. Thus, the Gini index has been adapted to analyze spatial location patterns of manufacturing industries (Krugman 1991;Amiti 1999;Brülhart 2001;Suedekum 2006 among many others), and some of the indexes included in the generalized entropy family have been adapted as well (Brülhart and Traeger 2005;Mori et al 2005;Brakman et al 2005;Pérez-Ximénez and Sanz-Gracia 2007;Cutrini 2009). …”

“…These properties are borrowed not only from the literature on income distribution, but also from that of occupational segregation (Hutchens 1991(Hutchens , 2004Alonso-Villar and Del Río 2007). Second, additive decompositions of this curve by subsectors and by groups of locations are proposed, since even though additive decompositions of the generalized entropy family of indexes have been used to measure industrial concentration (Brülhart and Traeger 2005), as far as we know, no decompositions of the employment Lorenz curves have yet been suggested. One of the decompositions parallels that proposed by Bishop et al (2003) in a context of income distribution.…”