The role of spatial effects in the empirical analysis of regional concentration

Spatial Localization in Manufacturing: A Cross-Country Analysis

“…Weights represent contiguity relationships: w il > 0 if and only if (i, l) are contiguous regions and zero otherwise (with w ii = 0, all i). As discussed in Arbia (2001), this index does not solve all the space-related problems described above. For example, the Moran index is invariant to different spatial permutations involving the same number of contiguous regions.…”

“…Rosenthal and Strange, 2001;Devereux et al, 2004, for a discussion of this point). Second, as argued at more length in Arbia (2001), the very computation of cumulative shares of economic activity concentrated in spatial subunits implies disregarding the spatial nature of the data. Indeed, indices based on cumulative shares (like the E&G index) are generally invariant to any spatial permutation of the subunits under investigation.…”

“…the degree of spatial correlation in firms' location decisions (cf. Arbia, 2001; Lafourcade and Mion, 2007;Duranton and Overman, 2005). Two indices that account for the spatial features of industrial data are those proposed by Moran (1950) and by Duranton and Overman (2005).…”

“…Finally, clusters of firms located at the borders of neighboring regions and/or spanning over the area covered by a single region are treated in the same way as clusters in two very distant regions. More precisely, as pointed out in Arbia (2001) and Lafourcade and Mion (2007), indices requiring the division of the space into smaller units are only able to capture "spatial concentration" of industrial activity into some areas. They are not able to measure instead "true agglomeration", that is the degree of spatial correlation between firms' location choices.…”

“…Furthermore, to account for spatial features of the data we employ the D&O index rather than the Moran index (Moran, 1950). This choice has been made because, as discussed at more length in Arbia (2001), the Moran index cannot entirely capture the observed variability in spatial permutations. For example, the Moran index measures the extent to which an industry is spread across L neighboring regions.…”