Distance-based measures of spatial concentration: introducing a relative density function

Abstract

For more than a decade, distance-based methods have been widely employed and constantly improved in spatial economics. These methods are a very useful tool for accurately evaluating the spatial distribution of economic activity. We introduce a new distance-based statistical measure for evaluating the spatial concentration of industries. The m function is the first relative density function to be proposed in economics. This tool supplements the typology of distance-based methods recently drawn up by Marcon and Puech (2017). By considering several simulated and real examples, we show the advantages and the limits of the m function for detecting spatial structures in economics.

Agglomeration of creative industries: An intra‐metropolitan analysis for Barcelona

“…To measure agglomeration and co‐agglomeration, we use the M and m functions, which are distance‐based methods introduced by Marcon and Puech (, ) and Lang et al (). These functions can be understood as the natural counterparts of the well‐known location quotient in a continuous space approach.…”

“…Both the M and the m functions are comparable across industries, control for the overall agglomeration patterns of industries and for industrial concentration, remain unbiased across geographical scales, and allow for statistical significance testing (Marcon and Puech ; Lang et al ). They also control for inhomogeneous space and enable a straightforward interpretation and comparison of the results.…”

“…An alternative distance‐based measure that also satisfies these properties is the Kd function used by Duranton and Overman (). However, the M, m and Kd functions cannot be considered substitutes for one another (Lang et al ). While Kd and m are both probability density functions of point‐pair distances because they are calculated on the basis of the average number of neighbours at given distance, the M function is cumulative, calculated on the basis of the number of neighbours up to each distance.…”

“…We also examine whether different CIs co‐agglomerate. To deal with methodological limitations arising from the use of geographically aggregated data and area‐based methods, we use geo‐referenced data for the MAB in order to calculate the relative distance‐based M and m cumulative and density functions of agglomeration and co‐agglomeration (Marcon and Puech ; Lang et al ).…”

“…Moreover, like the NNC, the methodology we have used in our paper (M and m functions) also satisfies the main requirements of a good concentration measure. In addition, it controls for inhomogeneous space, provides the statistical significance of the agglomeration at each distance, and makes it easier to interpret the results (Marcon and Puech , ; Lang et al ).…”