OECD Culture and Local Development.pdf - PACA

ANNEX 2
This indicator may also be written as follows:
[N(S,Z)/N(S) ] . [T/T(Z)]
or, after transformation:
[N(S,Z)/T(Z)] . [N(S)/T]
where N(S,Z)/T(Z) is the share of sector S in employment in territory Z and N(S)/T
is the share of that same sector in the national economy. The concentration indicator
measures, for a given sector, the degree of a territory’s specialisation compared to
the nationwide degree of specialisation. It allows territories to be compared among
themselves, and it can be used as a first approximation to the existence of districts.
The higher this ratio is above 1 the stronger is the presumption of a cluster.
We may also use other indices for identifying the concentration for each branch
of activity and for each territory.
Taking k as the index for the sector and i as the index for the geographical unit,
the Herfindhal index is defined by:
m
m
i 2
H
k
= ∑(
sk
) = ∑
i=
1
i=
1
n
i
n
(
n
i
k
k
)
2
where
k
is employment in sector k in unit i and k is total employment in sector
k. The Herfindhal index falls between 1/m and 1. As is tends toward 1, concentration
is maximised, and as it tends towards 1/m, geographic dispersion is maximised.
Because this index does not account for the structure of employment by sector
or by geographic unit, and seems to measure specialisation rather than concentration,
we use another index, the GINI, to control employment in sector k by employment
in all sectors in the zone. There are two possible measures of the GINI index. The
first, or Gini G i, is given by:
n
G
k
s x
= 0,5
− ∑ ∑ ∑
m i i m i
k
i j
− x sk
i= 1 2 i= 2 j=
2
1
x
i
i
n
=
N
with which represents the share of total employment in region i.
The index falls between 0 and 0.5. If it is 0.5, concentration is maximised, and if it is
0, dispersion is maximised.
184 CULTURE AND LOCAL DEVELOPMENT - ISBN 92-64-00990-6 - © OECD 2005