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

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

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

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

  5. In the same way, dispersion and repulsion are synonyms.

  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. 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. 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. 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.

References

  • Alfaro L, Chen MX (2014) The global agglomeration of multinational firms. J Int Econ 94(2):263–276

    Article  Google Scholar 

  • Arbia G (1989) Spatial data configuration in statistical analysis of regional economic and related problems. Kluwer, Dordrecht

    Book  Google Scholar 

  • Arbia G (2001) The role of spatial effects in the empirical analysis of regional concentration. J Geogr Syst 3(3):271–281

    Article  Google Scholar 

  • Arbia G (2016) Spatial econometrics: a broad view. Found Trends® Econom 8(3–4):145–265

    Article  Google Scholar 

  • Arbia G, Espa G (1996) Statistica economica territoriale. Cedam, Padua

    Google Scholar 

  • Arbia G, Espa G, Quah D (2008) A class of spatial econometric methods in the empirical analysis of clusters of firms in the space. Empir Econ 34(1):81–103

    Article  Google Scholar 

  • Arbia G, Espa G, Giuliani D, Mazzitelli A (2012) Clusters of firms in an inhomogeneous space: the high-tech industries in Milan. Econ Model 29(1):3–11

    Article  Google Scholar 

  • Baddeley AJ, Turner R (2005) Spatstat: an R package for analyzing spatial point patterns. J Stat Softw 12(6):1–42

    Article  Google Scholar 

  • Baddeley AJ, Møller J, Waagepetersen RP (2000) Non- and semi-parametric estimation of interaction in inhomogeneous point patterns. Stat Neerl 54(3):329–350

    Article  Google Scholar 

  • Bade FJ, Bode E, Cutrini E (2015) Spatial fragmentation of industries by functions. Ann Reg Sci 54(1):215–250

    Article  Google Scholar 

  • Barlet M, Briant A, Crusson L (2013) Location patterns of service industries in France: a distance-based approach. Region Sci Urban Econ 43(2):338–351

    Article  Google Scholar 

  • Behrens K, Bougna T (2015) An anatomy of the geographical concentration of Canadian manufacturing industries. Region Sci Urban Econ 51:47–69

    Article  Google Scholar 

  • Behrens K, Guillain R (2017) The determinants of coagglomeration: evidence from functional employment patterns. Discussion Paper 11884, CEPR—Centre for Economic Policy Research

  • Billings SB, Johnson EB (2012) A non-parametric test for industrial specialization. J Urban Econ 71(3):312–331

    Article  Google Scholar 

  • Bocci C, Rocco E (2016) Modelling the location decisions of manufacturing firms with a spatial point process approach. J Appl Stat 43(7):1226–1239

    Article  Google Scholar 

  • Bonneu F (2007) Exploring and modeling fire department emergencies with a spatio-temporal marked point process. Case Stud Bus Ind Gov Stat 1(2):139–152

    Google Scholar 

  • Bonneu F, Thomas-Agnan C (2015) Measuring and testing spatial mass concentration with micro-geographic data. Spat Econ Anal 10(3):289–316

    Article  Google Scholar 

  • Briant A, Combes PP, Lafourcade M (2010) Dots to boxes: do the size and shape of spatial units jeopardize economic geography estimations? J Urban Econ 67(3):287–302

    Article  Google Scholar 

  • Brülhart M, Traeger R (2005) An account of geographic concentration patterns in Europe. Reg Sci Urban Econ 35(6):597–624

    Article  Google Scholar 

  • Buzard K, Carlino GA, Hunt RM, Carr JK, Smith TE (2017) The agglomeration of American R&D labs. J Urban Econ 101:14–26

    Article  Google Scholar 

  • Chain CP, Santos AC, Castro LG, Prado JW (2019) Bibliometric analysis of the quantitative methods applied to the measurement of the industrial clusters. J Econ Surv 33(1):60–84

    Article  Google Scholar 

  • Combes PP, Overman HG (2004) The spatial distribution of economic activities in the European Union. In: Henderson JV, Thisse JF (eds) Handbook of urban and regional economics, Chap 64, vol 4. Elsevier, Amsterdam, pp 2845–2909

    Google Scholar 

  • Combes PP, Mayer T, Thisse JF (2008) Economic geography, the integration of regions and nations. Princeton University Press, Princeton

    Book  Google Scholar 

  • Diggle PJ (1983) Statistical analysis of spatial point patterns. Academic Press, London

    Google Scholar 

  • Diggle PJ, Chetwynd AG (1991) Second-order analysis of spatial clustering for inhomogeneous populations. Biometrics 47(3):1155–1163

    Article  Google Scholar 

  • Dubé J, Brunelle C (2014) Dots to dots: a general methodology to build local indicators using spatial micro-data. Ann Reg Sci 53(1):245–272

    Article  Google Scholar 

  • Duranton G (2008) Spatial economics. In: Durlauf SN, Blume LE (eds) The new Palgrave dictionary of economics. Palgrave Macmillan, New York

    Google Scholar 

  • Duranton G, Overman HG (2005) Testing for localisation using micro-geographic data. Rev Econ Stud 72(4):1077–1106

    Article  Google Scholar 

  • Duranton G, Overman HG (2008) Exploring the detailed location patterns of UK manufacturing industries using microgeographic data. J Reg Sci 48(1):213–243

    Article  Google Scholar 

  • Ellison G, Glaeser EL (1997) Geographic concentration in U.S. manufacturing industries: a dartboard approach. J Polit Econ 105(5):889–927

    Article  Google Scholar 

  • Ellison G, Glaeser EL, Kerr WR (2010) What causes industry agglomeration? Evidence from coagglomeration patterns. Am Econ Rev 100(3):1195–1213

    Article  Google Scholar 

  • Florence PS (1972) The logic of British and American industry: a realistic analysis of economic structure and government, 3rd edn. Routledge & Kegan Paul, London

    Google Scholar 

  • Gini C (1912) Variabilità e mutabilità, vol 3. Università di Cagliari

  • Giuliani D, Arbia G, Espa G (2014) Weighting Ripley’s K-function to account for the firm dimension in the analysis of spatial concentration. Int Reg Sci Rev 37(3):251–272

    Article  Google Scholar 

  • Gómez-Antonio M, Sweeney S (2018) Firm location, interaction, and local characteristics: a case study for Madrid’s electronics sector. Pap Reg Sci 97(3):663–685

    Article  Google Scholar 

  • Guimarães P, Figueiredo O, Woodward D (2009) Dartboard tests for the location quotient. Reg Sci Urban Econ 39(3):360–364

    Article  Google Scholar 

  • Henderson JV, Thisse JF (2004) Handbook of urban and regional economics. Elsevier, Amsterdam

    Google Scholar 

  • Howard E, Newman C, Tarp F (2016) Measuring industry coagglomeration and identifying the driving forces. J Econ Geogr 16(5):1055–1078

    Article  Google Scholar 

  • Illian J, Penttinen A, Stoyan H, Stoyan D (2008) Statistical analysis and modelling of spatial point patterns. Statistics in practice. Wiley-Interscience, Chichester

    Google Scholar 

  • Jensen P, Michel J (2011) Measuring spatial dispersion: exact results on the variance of random spatial distributions. Ann Reg Sci 47(1):81–110

    Article  Google Scholar 

  • Kerr WR, Kominers SD (2015) Agglomerative forces and cluster shapes. Rev Econ Stat 97(4):877–899

    Article  Google Scholar 

  • Koh HJ, Riedel N (2014) Assessing the localization pattern of German manufacturing and service industries: a distance-based approach. Reg Stud 48(5):823–843

    Article  Google Scholar 

  • Krugman P (1991) Geography and trade. MIT Press, London

    Google Scholar 

  • Law R, Illian J, Burslem D, Gratzer G, Gunatilleke CVS, Gunatilleke I (2009) Ecological information from spatial patterns of plants: insights from point process theory. J Ecol 97(4):616–628

    Article  Google Scholar 

  • Marcon E, Puech F (2003) Evaluating the geographic concentration of industries using distance-based methods. J Econ Geogr 3(4):409–428

    Article  Google Scholar 

  • Marcon E, Puech F (2010) Measures of the geographic concentration of industries: improving distance-based methods. J Econ Geogr 10(5):745–762

    Article  Google Scholar 

  • Marcon E, Puech F (2012) A typology of distance-based measures of spatial concentration. HAL SHS 00679993 (version 1)

  • Marcon E, Puech F (2015) Mesures de la concentration spatiale en espace continu: théorie et applications. Écon Stat 474:105–131

    Google Scholar 

  • Marcon E, Puech F (2017) A typology of distance-based measures of spatial concentration. Reg Sci Urban Econ 62:56–67

    Article  Google Scholar 

  • Marcon E, Traissac S, Puech F, Lang G (2015) Tools to characterize point patterns: dbmss for R. J Stat Softw 67(3):1–15

    Google Scholar 

  • Møller J, Waagepetersen RP (2004) Statistical inference and simulation for spatial point processes, Monographs on statistics and applies probabilities, vol 100. Chapman and Hall, London

    Google Scholar 

  • Mori T, Smith TE (2013) A probabilistic modeling approach to the detection of industrial agglomerations. J Econ Geogr 14(3):547–588

    Article  Google Scholar 

  • Nakajima K, Saito YU, Uesugi I (2012) Measuring economic localization: evidence from Japanese firm-level data. J Jpn Int Econ 26(2):201–220

    Article  Google Scholar 

  • Ó hUallacháin B, Leslie TF (2007) Producer services in the urban core and suburbs of Phoenix, Arizona. Urban Stud 44(8):1581–1601

    Article  Google Scholar 

  • Openshaw S, Taylor PJ (1979) A million or so correlation coefficients: three experiments on the modifiable areal unit problem. In: Wrigley N (ed) Statistical applications in the spatial sciences. Pion, London, pp 127–144

    Google Scholar 

  • Pavia J (2015) Testing goodness-of-fit with the kernel density estimator: Gofkernel. J Stat Softw 66(1):1–27

    Google Scholar 

  • Penttinen A (2006) Statistics for marked point patterns. The yearbook of the Finnish statistical society. The Finnish Statistical Society, Helsinki, pp 70–91

    Google Scholar 

  • Penttinen A, Stoyan D, Henttonen HM (1992) Marked point processes in forest statistics. For Sci 38(4):806–824

    Google Scholar 

  • R Core Team (2018) R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria

  • Ripley BD (1976) The second-order analysis of stationary point processes. J Appl Probab 13(2):255–266

    Article  Google Scholar 

  • Ripley BD (1977) Modelling spatial patterns. J R Stat Soc B 39(2):172–212

    Google Scholar 

  • Rosenthal SS, Strange WC (2001) The determinants of agglomeration. J Urban Econ 50(2):191–229

    Article  Google Scholar 

  • Silverman BW (1986) Density estimation for statistics and data analysis. Chapman and Hall, London

    Book  Google Scholar 

  • Sweeney S, Gómez-Antonio M (2015) Localization and industry clustering econometrics: an assessment of Gibbs models for spatial point processes. J Reg Sci 56(2):257–287

    Article  Google Scholar 

  • Sweeney SH, Feser EJ (1998) Plant size and clustering of manufacturing activity. Geogr Anal 30(1):45–64

    Article  Google Scholar 

  • Waller L (2010) Point process models and methods in spatial epidemiology. In: Gelfand A, Diggle P, Guttorp P, Fuentes M (eds) Handbook in spatial statistics, CRC handbooks of modern statistical methods series, Chap 22. Chapman & Hall, London, pp 403–423

    Google Scholar 

  • Zhou T, Clapp JM (2015) The location of new anchor stores within metropolitan areas. Reg Sci Urban Econ 50:87–107

    Article  Google Scholar 

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Authors and Affiliations

  1. UMR MIA-Paris, AgroParisTech, INRA, Université Paris-Saclay, Paris, France

    Gabriel Lang

  2. AgroParisTech, UMR EcoFoG, Cirad, CNRS, INRA, Université des Antilles, Université de Guyane, Kourou, France

    Eric Marcon

  3. RITM, Univ. Paris-Sud, Université Paris-Saclay and CREST, Sceaux, France

    Florence Puech

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  1. Gabriel Lang
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  2. Eric Marcon
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  3. Florence Puech
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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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