A Divergence Statistic for Industrial Localization

Abstract

In this paper, we propose a statistical index of industrial localization based on Kullback-Leibler divergence. This index is particularly well suited to cases where industrial data is only available at the regional level. Unlike existing regional-level indices, our index can be employed to test the significance of industrial localization relative to a hypothesized reference distribution of probable locations across regions. In addition, one can test relative degrees of localization among industries. Finally, as with all Kullback-Leibler divergence indices, our index can be decomposed into components representing localization at various levels of spatial aggregation.

Measuring economic localization: Evidence from Japanese firm-level data

“…The pioneering study for this second generation of indices is that by Ellison and Glaeser (1997), which compares the degree of spatial concentration of employment in a given sector with the degree of concentration that would arise if all plants in this sector were located randomly across locations (like darts thrown randomly at a map). Other studies that have developed alternative measures, but follow a similar approach, include Maurel and Sedillót (1999), Devereux, Griffith, and Simpson (2004), and Mori, Nishikimi, and Smith (2005). 1 However, these indices are still susceptible to several problems due to aggregation at a given level of geographical units.…”

The regional concentration of industries and the performance of firms: a multilevel approach

“…The reasons for their origins can be linked to very distinct factors. While some industries may be concentrated in a region due to the availability of specific resources, proximity to consumer markets, or even as a historical accident, other industries do not have any natural tendency towards a concentrated location (Mori, Nikishimi, & Smith, 2005).…”

Identification of Employment Concentration Areas

“…In the second category of measures, analogously called spatial measures, the region is not divided in predefined areas or the spatial relationship between the predefined areas is explicitly analyzed. Well-known and commonly used a-spatial measures are the locational Gini coefficient (Krugman, 1991), the EG-index (Ellison and Glaeser, 1997), the MS-index (Maurel and Sedillot, 1999), and the D-index (Mori et al, 2005). The most commonly used spatial measures were developed by Moran (1950) and Duranton and Overman (2005).…”

“…Alternative measures to analyze relative spatial concentration are, among others, γ EG (Ellison and Glaeser, 1997), γ M S (Maurel and Sedillot, 1999), and the D-index (Mori et al, 2005). The γ EG and the γ M S have the same properties: the indices are scaled, such that these control for industrial concentration.…”

“…The D-index (Mori et al, 2005) is designed to be statistically testable, since none of the above described measures are. However, this index can only be used for an analysis of spatial concentration of firms, because it is based on the independence of the single units, which means that the D-index is not suitable for the measurement of employment concentration (Fratesi, 2008).…”