Measuring spatial dispersion: an experimental test on the M-index

In this paper, we assess the viability of a geographic approximation aimed to reduce the computational intensity necessary to measure spatial agglomeration with Marcon & Puech's (2017) M index. Indeed, despite representing a potentially very accurate way of measuring spatial distribution, M has not been sufficiently exploited so far because its computation needs crossing every point (i.e. firms, plants) with each other within the area under analysis - such a figure rapidly grows to unmanageable levels when the area is larger than a neighborhood or when every industry is taken into account. Consequently, practical applications of M have been exclusively experimental and circumscribed to very limited areas or to a handful of sectors. In our opinion, this is much regrettable since M provides many advantages compared to conventional measures of spatial distribution and also to other distance measures. In order to verify whether a slight geographic approximation is tolerable – which would be consistent with Marcon & Puech's (2017, p. 30) assumption that "cumulative functions are insensitive to errors at smaller scales than the distance they consider" - we compute both actual M (with no approximation whatsoever) and approximate M for every industry in Sardinia. Our aim is to compare the results obtained when plants are located exactly where they are with those obtained when plants' positions are approximated to the centroid of the municipality where they are located. We rely on a comprehensive dataset that allows us to identify the location, the specific industry and the number of employees for every single plant, and not only for firms as a whole. Our dataset's scope is not restricted to manufacturing, as it is often the case, but covers every area of activity, ranging from construction to transports and from retailers to other service industries. Moreover, we did not considered distance between approximated positions as the crow flies, but we relied on actual street distance and travel time between them - in the frequent case of orographically dishomogenous territories, it might be the case that such a measurement more accurately reflects the actual distance between establishment, than theoretical flying distance between actual locations. If our approximation in the location of plants is positively outweighed by the great accuracy of M in operationalizing detailed geographic and economic information, then such an index could really be exploited for assessing agglomeration and dispersion patterns across space and along time, especially when much information is available, as it is ever more often the case.