A typology of distance-based measures of spatial concentration

Abstract

To cite this version:Eric Marcon, Florence Puech. A typology of distance-based measures of spatial concentration. 2012. halshs-00679993v6Hal 00679993v6 A Typology of Distance-Based Measures of Spatial ConcentrationEric Marcon 1 , Florence Puech 2 * Abstract Over the last decade, distance-based methods have been introduced and then improved in the field of spatial economics to gauge the geographic concentration of activities. There is a growing literature on this theme including new tools, discussions on their specific properties and various applications. However, there is currently no typology of distance-based methods. This paper fills that gap. The proposed classification helps understand all the properties of distance-based methods and proves that they are variations on the same framework.JEL Classification: C10, C60, R12

W Function: A New Distance‐Based Measure of Spatial Distribution of Economic Activities

“…Duranton and Overman's Kd function (Duranton and Overman ) and the original cumulative version of Marcon and Puech's M function (Marcon and Puech ) have been the most used distance‐based methods in economics during the last decade. The Kd function is a density function that evaluates absolute concentration (Marcon and Puech ), whereas the M function is a relative function that compares the local proportion of plants of interest in the neighborhood of the reference plants to the proportion of neighbours of interest in the area as a whole (Marcon and Puech ). Recently, a density version of the M function, called as m , has been proposed.…”

“…Three types of distance‐based methods have been developed (Marcon and Puech ): topographic, relative and absolute. For topographic methods, the physical space is chosen as the benchmark, for relative methods another variable (another distribution of points, e.g.…”

“…all plants at the aggregate industrial level) is chosen, and for absolute methods, there is no reference, thus they are not benchmarking methods. These distance‐based methods are further defined as cumulative or density functions (Marcon and Puech ). Historically, topographical measures have been used most often (Law et al , Illian et al ), however from an economic point of view, a relative measure of geographic concentration of economic activities is preferred in modern analyses (Combes and Overman ; Duranton and Overman ; Combes, Mayer, and Thisse ).…”

“…In this article we introduce a new relative density distance‐based method, the W function, which follows the typology recently defined by Marcon and Puech (), and satisfies Duranton and Overman's five criteria of an ideal index. Its main aim is to detect phenomena of attraction (also called clustering or localization), repulsion (dispersion) and independence (randomness) between those entities in a set territory.…”

“…The objective of this article is to compare our proposed method with existing absolute and relative measurements of spatial distribution of economic activities. As Marcon and Puech () pointed out, these types of methods of measurement are complementary, and provide different perspectives on the spatial pattern under study. Currently, the m function is used alone as the relative density measure, but we propose that the W function ought to be used alongside it to provide further accuracy.…”