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Review of Regional Research
Published in: Review of Regional Research 2/2012

01-09-2012 | Original Paper

Bivariate K functions as instruments to analyze inter-industrial concentration processes

Authors: Prof. Dr. Hans-Friedrich Eckey, Prof. Dr. Reinhold Kosfeld, Dipl.-Ök. Alexander Werner

Published in: Review of Regional Research | Issue 2/2012

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Abstract

While several procedures are available to measure spatial concentration of economic activities, methods of uncovering phenomena of co-agglomeration and repulsion of various industries are rare. Traditional bivariate procedures are usually too short-sighted. Arbia et al. (Empir. Econ. 34(1):81–103, 2008) have shown that the concept of bivariate K functions can be used as an instrument for spatial point processes in the economy. In this article we use the instrument of bivariate K functions in order to uncover reciprocal dependencies in location determination of companies mainly in manufacturing industry in Germany. The results of the bivariate K functions serve as a basis for cluster analyses, by means of which various clusters of allied sectors can be formed for various spatial scales.
previous article Identifying spatial nonstationarity in German regional firm start-up data
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Appendix
Available only for authorised users
Footnotes
1
A process of this sort is also described as homogeneous or stationary, for which the standard term is “complete spatial randomness” (CSR). In the case of an inhomogeneous process λ is no longer the same for all spatial points, but diverges between them. An example is the different location quality between the spatial points because of natural (e.g. topography) and non-natural (e.g. infrastructure) location factors.
 
2
Through the marginal correction, however, the symmetry is lost; \(\hat{K}_{12} \ne\hat{K}_{21}\) is true, so that the efficient estimator \(\hat{K}_{12}^{*} = \frac{\hat{\lambda}_{2} \cdot \hat{K}_{12}( r ) + \hat{\lambda}_{1} \cdot \hat{K}_{21}( r )}{\hat{\lambda}_{1} + \hat{\lambda}_{2}}\) is recommended.
 
3
The data is available at „Regionaldatenbank Deutschland“, Statistische Ämter des Bundes und der Länder.
 
4
This sort of geographical information is envisaged for display in the companies register, so that in future it is recommended to use data from that source (cf. Sturm and Tümmler 2006, especially p. 1030 f.).
 
5
Calculations of the K functions are based on the R-package Splancs (Rowlingson and Diggle 2008) and own enhancements.
 
6
Table 2 in the Appendix gives a comprehensive overview of the K values in the interval 0≤r≤2.
 
7
The K values for r=0.1 and r=0.5 can be found in Table 3 in the Appendix.
 
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Metadata
Title
Bivariate K functions as instruments to analyze inter-industrial concentration processes
Authors
Prof. Dr. Hans-Friedrich Eckey
Prof. Dr. Reinhold Kosfeld
Dipl.-Ök. Alexander Werner
Publication date
01-09-2012
Publisher
Springer-Verlag
Published in
Review of Regional Research / Issue 2/2012
Print ISSN: 0173-7600
Electronic ISSN: 1613-9836
DOI
https://doi.org/10.1007/s10037-012-0067-0

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