Using entropy measures to disentangle regional from national localization patterns

Abstract

Localization of economic activities is a manifestation of two closely-related economic phenomena: the specialization of geographical units and the spatial concentration of industries. Nonetheless, the direction of changes in concentration and specialization, across national boundaries, may differ from those occurring within countries. Combining a regional approach with an international perspective, the paper introduces an entropy index of overall localization that allows specialization to be conceptualized as the mirror image of concentration, and also focuses attention on the possible divergence in agglomeration patterns at the different spatial scales

A typology of distance-based measures of spatial concentration

“…In the latter, the territory being analyzed is divided in several exclusive zones (e.g. a country is divided in turn into regions) and the spatial concentration of activities is evaluated at a given level of observation with the Gini (1912), the Ellison and Glaeser (1997) or the entropy indices of overall localization (Cutrini, 2009), for example. However, the issues arising from discrete spaces are now well known and linked to the Modifiable Areal Unit Problem -MAUP (Arbia, 1989;Openshaw and Taylor, 1979): the position of the zoning boundaries and level of observation have an impact (Briant et al, 2010).…”

Concentration of Economic Activity: An Analytical Framework

“…The M-index satisfies continuity and is invariant to: An advantage of this index is that it can be decomposed additively by groups (CUTRINI, 2009). Thus, if the manufacturing sectors are classified into several mutually exclusive groups, it is possible to determine whether aggregate manufacturing concentration is due mainly to the between-group (B) component (i.e., to differences in the spatial distribution of employment between these groups) or to the within-group (W) …”

“…In other words, in measuring concentration in the manufacturing industry, the benchmark considered is outside that industry. Others have proposed instead the use of the average concentration of the sectors involved, making use of an external benchmark unnecessary (AIGINGER and DAVIS, 2004;MULLIGAN and SCHMIDT, 2005;CUTRINI, 2009CUTRINI, , 2010. However, as far as we know, there has been no debate on overall concentration measurement in terms of basic properties.…”

“…In this regard, the Gini index has traditionally been used for analyzing spatial location patterns of manufacturing industries (KRUGMAN, 1991;AMITI, 1999;BRÜLHART, 2001;SUEDEKUM, 2006, inter alia). More recently, the generalized entropy family of indexes (GE, henceforth) has been used as well because of its advantages in terms of decomposability (BRÜLHART and TRAEGER, 2005;BRAKMAN et al, 2005;PÉREZ-XIMÉNEZ and SANZ-GRACIA, 2007;CUTRINI, 2009). The properties of the inequality measures on which these concentration indexes are based are well known because the literature on income distribution has dealt with inequality from an axiomatic perspective; however, the corresponding geographical concentration measures are being applied without explicitly stating the consequences of using them.…”

“…This set-up allows us to characterize the GE family of concentration indexes of a sector (BRÜLHART and TRAEGER, 2005) and show the properties of the aggregate concentration index, the Lindex (CUTRINI, 2009(CUTRINI, , 2010, resulting from the weighted sum of the one of them (the Theil index). For that purpose, some properties borrowed from the literature on income inequality and segregation are adapted to our context (ALONSO-VILLAR and DEL RÍO, 2010a;FRANKEL and VOLIJ, 2010).…”