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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 (J Econ Geogr 3(4):409–428, 2003). By considering several simulated and real examples, we show the advantages and the limits of the m function for detecting spatial structures in economics.

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Notes

  1. 1.

    See Duranton and Overman (2005), Marcon and Puech (2003, 2010), Arbia et al. (2012), Mori and Smith (2013), Jensen and Michel (2011), Bonneu and Thomas-Agnan (2015), Howard et al. (2016), among others.

  2. 2.

    Duranton and Overman (2008) provide many concrete examples of the problems such functions can solve.

  3. 3.

    Other developments may be cited as the one explained by Dubé and Brunelle (2014).

  4. 4.

    The following terms: spatial concentration, concentration, agglomeration and aggregation, are used as synonyms in this article.

  5. 5.

    In the same way, dispersion and repulsion are synonyms.

  6. 6.

    To give an example, if the aim is to evaluate the spatial distribution of the textile industry, the analysis of the distribution of textile plants around textile plants is relevant. In that case of intra-industrial analysis, the intratype function should be used. If the focus is now on the co-agglomeration of the textile and clothing sectors, the intertype functions will deal with the distribution of textile plants around clothing plants or the distribution of clothing plants around textile plants.

  7. 7.

    The vocabulary “cases” and “controls” is well established in the literature of point processes (Diggle 1983; Arbia et al. 2012), but some authors such as Billings and Johnson (2012) prefer to employing, respectively, “samples” and “counterfactuals.”

  8. 8.

    The Poisson process is commonly used for simulating CSR patterns. As Diggle (1983) wrote, the Poisson process “is the cornerstone on which the theory of spatial point processes is built. It represents the simplest possible stochastic mechanism for the generation of spatial point patterns, and in applications is used as an idealized standard of complete spatial randomness (…)” (p. 50).

  9. 9.

    In a few words, densities are underestimated around the limits of the interval. This is due to the fact that outside the interval, densities are not equal to zero as they should be. This border effect problem is known (Silverman 1986) and can be easily corrected in practice by using for example the GoFKernel package (Pavia 2015) for the R software. The idea is to use the reflection at the borders to correct the underestimated densities inside the interval but around the limits of the interval.

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Correspondence to Florence Puech.

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Lang, G., Marcon, E. & Puech, F. Distance-based measures of spatial concentration: introducing a relative density function. Ann Reg Sci 64, 243–265 (2020). https://doi.org/10.1007/s00168-019-00946-7

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Keywords

  • Spatial concentration
  • Aggregation
  • Point patterns
  • Agglomeration
  • Economic geography

JEL Classification

  • C10
  • C60
  • R12