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Dots to dots: a general methodology to build local indicators using spatial micro-data

Abstract

Empirical studies in regional science have so far largely relied on discrete conceptualizations of space and aggregated metrics, which do not take into consideration spatial heterogeneity and variability at the micro-level. This paper explores the use of these indicators when dealing with observations at the subregional level, based on micro-data sets that impose the conceptualization of spatial interactions in a continuous and multidirectional space. We propose a general methodology to build local indicators for spatial micro-data sets. Based on distance matrix and matrix calculations, some classical indices of specialization and diversity are extended to their local counterparts to explore the full spatial heterogeneity and variability of space. The methodology is applied to 9,839 establishments covering all economic sectors in the Lower St-Lawrence region (Quebec, Canada). We find that the distribution of the local indicator varies significantly with distance, which suggests that the effects of specialization or diversity are not constant over space. Treating space as continuous may become of prime importance, given that more individual data sets are now available, combined with the fact that the performance of microcomputers is still improving.

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Notes

  1. 1.

    This approach is also explained in detail by Deaton (1985) and Verbeek and Nijman (1992) for constructing individual units for pseudo-panel approaches.

  2. 2.

    Of course, the variance of the index, based on its distribution, can also be related to the choice of the number of economic sectors, \(S\).

  3. 3.

    Or, equivalently, to \(\mathrm{log}\left( 1/p\right) \), where \(p=1/S\).

  4. 4.

    Assuming that the optimal radius of influence is previously known.

  5. 5.

    Of course, the difference may be inversely related to the size of the boxes or hexagons.

  6. 6.

    Of course, the definition of the distance can be changed to implement any other distance criteria (Manhattan, network, etc.) using the general distance definition given by:

    $$\begin{aligned} d_{ij}=\root p \of {\left| X_{i}-X_{j} \right| ^{p}\left| Y_{i}-Y_{j} \right| ^{p}} \qquad \forall \,i,j=1,2,\ldots , N \end{aligned}$$

    When \(p=2\), we obtain the usual Euclidian distance, while \(p=1\) gives the Manhattan distance. Moreover, other distances such as network distances can also be considered.

  7. 7.

    The connectivity matrix can be generalized to consider the inverse distance reflecting the first law of geography of Tober (1970). Such transformation imputes a larger value to observations that are spatially closer.

  8. 8.

    The matrix notation accelerates the calculation time.

  9. 9.

    Thus, we then have: \( \mathop {N\times S}\limits ^{\mathbf{X}_{{{\varvec{s}}}}}= [\mathop {\left( N\times 1\right) }\limits ^{\mathbf{x}_{\mathbf{1}}}\,\, \mathop {\left( N\times 1\right) }\limits ^{\mathbf{x}_{\mathbf{2}}}\,\,\cdots \,\, \mathop {\left( N\times 1\right) }\limits ^{\mathbf{X}_{{{\varvec{s}}}}}]\).

  10. 10.

    Using the definition of the global matrix, \({\mathbf {X}}_{{\mathbf {s}}}\), the total of number of jobs or firms can be obtained with a simple matrix calculation: \(\mathop {\left( N\times 1\right) }\limits ^{\mathbf{x}}= \mathop {\left( N\times S\right) }\limits ^{\mathbf{X}_{{{\varvec{s}}}}} \times \mathop {(S\times 1)}\limits ^{{\varvec{\upiota }}_{{{\varvec{s}}}}}\), where \({{\varvec{\upiota }}}_{{\mathbf {S}}}\) is a vector of one of dimension \(\left( S\times 1 \right) \).

  11. 11.

    Using the Mata platform on Stata software.

  12. 12.

    For simplicity’s sake and parsimony of the presentation, the results are only presented for some cut-off distance value. The full set of results is available from the authors upon request.

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Acknowledgments

This research is funded by the Social Sciences and Humanities Research Council of Canada (SSHRC). The authors would like to thank David Folch (U. Colorado) for helpful comments on a previous version.

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Correspondence to Jean Dubé.

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Dubé, J., Brunelle, C. Dots to dots: a general methodology to build local indicators using spatial micro-data. Ann Reg Sci 53, 245–272 (2014) doi:10.1007/s00168-014-0627-z

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JEL Classification

  • D22
  • R12
  • R3