Localisation Patterns of Knowledge-Creating Services in Paris Metropolitan Region

Abstract

Based upon an hermeneutic approach, which explicitly takes into account the role space plays within the knowledge economy, the article is aimed at providing the geography of knowledge-based activities in the Paris metropolitan area and at depicting the shape of their external economies and agglomeration forces. The added value supplied by this paper consists in: a) the spatial extent covered (the Paris Metropolitan Region), in order to consider the role that the pivot city and the surrounding towns/cities jointly play within the urban regional structure; and b) the improved explicative capability of a hermeneutic approach descending from its cross-fertilisation with the “knowledge source-based approach”, which distinguishes between analytic, synthetic and symbolic services according to their prevailing source of knowledge. The proposed methodology makes it possible to depict the spatial relationships both within KCS and between KCS and manufacturing activities in a more appropriate manner.

Appendix

• (1) The Location Quotient (LQ) is defined as follows:

  $$ LQ=\raisebox{1ex}{$\frac{e_{i,j}}{e_j}$}\!\left/ \!\raisebox{-1ex}{$\frac{E_i}{E}$}\right. $$

  (1)

  where e _i,j is the number of employees in the industry i of the sub-area j (ZE or municipality in our case), e _j is the total number of employees of sub-area j, E _i is the total number of employees in the industry i in the total area (PMR or ZE in our case), and E is the total number of employees in the total area.

• (2) Relative Entropy (RE) index is calculated according to the following formula:

  $$ RE=\frac{\left({\displaystyle {\sum}_{i=1}^nPDE{N}_i\times \log \frac{1}{PDE{N}_i}}\right)}{ \log (N)} $$

  (2)

  where:

  $$ PDE{N}_i=\frac{DE{N}_i}{{\displaystyle {\sum}_{i=1}^nDE{N}_i}} $$

  DEN _i represents the density of a given variable in the sub-area i, and n is the number of considered sub-areas.

  The main advantage of using the RE index is that the number of sub-areas involved in the analysis does not affect the results. The index ranges between 0 and 1: the closer it is to 1, the less population or jobs are concentrated, and vice versa. The disadvantage, on the contrary, is that RE cannot be used when zero-densities appear.

• (3) Delta Index is calculated as follows:

  $$ \delta =\frac{1}{2}{\displaystyle {\sum}_{i=1}^n\left|\frac{x_i}{X}-\frac{a_i}{A}\right|} $$

  (3)

  Where $\frac{x_i}{X}$ is the share of a given variable in sub-area i with respect to total area and $\frac{a_i}{A}$ is the share of the extension of the sub-area i on the extension of the total area.

  The index allows us taking into account the spatial extension of a sub-area i when aiming at assessing concentration with respect to a given phenomenon. It ranges between 0 and 1: higher values of Delta Index indicate a greater concentration of a given variable in a relatively small number of sub-areas, while, when closer to 0, a more uniform distribution affects the area.

• (4) Modified Wheaton (MW) measures the speed at which the cumulative proportion of employment increases along the radius joining the CBD with the farthest sub-areas, and is calculated as follows:

  $$ MW=\frac{\left({\displaystyle {\sum}_{i=1}^n{E}_{i-1}DCB{D}_i}-{\displaystyle {\sum}_{i=1}^n{E}_iDCB{D}_{i-1}}\right)}{DCBD*} $$

  (4)

  Where E _i is the cumulative proportion of the population or employment in the sub-area i; DCBD _i is the distance between the sub-area i and the CBD; DCBD* is the distance between the CBD and the farthest sub-area i. MW ranges between 0 and 1, with 1 representing a perfect centralisation.

• (5) Spatial autocorrelation index of Anselin (1995), also known as LISA (Local Indicator of Spatial Association) is calculated as follows:

  $$ LISA=\frac{\left({X}_i-\overline{X}\right){\displaystyle {\sum}_j^n{W}_{ij}\left({X}_j-\overline{X}\right)}}{{\displaystyle {\sum}_i^n\raisebox{1ex}{${\left({X}_i-\overline{X}\right)}^2$}\!\left/ \!\raisebox{-1ex}{$N$}\right.}} $$

  (5)

  where N is the total number of sub-areas, X _i and X _j population or employment in the sub-area i and j and W _ij the weights matrix related to the Euclidian distance between i and j. LISA enables us to identify sub-areas where variables values are strongly positively (or negatively) associated with one another, depicting a cluster.