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PUBLIC GOVERNANCE AND TERRITORIAL DEVELOPMENT DIRECTORATE
TERRITORIAL DEVELOPMENT POLICY COMMITTEE
For Official Use
Working Party on Territorial Indicators
GEOGRAPHIC CONCENTRATION AND TERRITORIAL DISPARITY IN OECD COUNTRIES
OECD Headquarters, 13 January 2003
This document, prepared by the Secretariat, presents an analysis of geographic concentration and territorial
disparity in 25 OECD countries. The document is a revision of [DT/TDPC/TI(2002)9] and is submitted to the
Delegates of the Working Party on Territorial Indicators FOR DISCUSSION AND APPROVAL for publication
in the "OECD Territorial Outlook".
English - Or. English
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Incomplete document on OLIS
GOV/TDPC/TI(2002)2
GEOGRAPHIC CONCENTRATION AND TERRITORIAL DISPARITY
IN OECD COUNTRIES
1. Introduction
The aim of this study is to present an international comparison of two major territorial
development issues in OECD countries: geographic concentration and territorial disparity.
Geographic concentration indicates the extent to which a small number of regions account for a
large proportion of a certain economic phenomenon, e.g.: unemployment. Territorial disparity, instead,
refers to the degree to which the intensity of this phenomenon differs between regions, e.g.: unemployment
rates.
The assessment of the economic relevance of these two issues is crucial to provide a sound
rational for place-base policy and define its objectives. For instance, consider a country composed of two
regions. In Region 1, labour force equals 1 000 and unemployment 50, so that the unemployment rate is
5 per cent. In Region 2, labour force equals 100, unemployment 6 and the unemployment rate is 6 per
cent. A policy aimed to reduce total unemployment in the country should focus on Region 1, i.e. the
region where unemployment is mostly concentrated. However, any policy aimed to reduce territorial
disparity in unemployment would focus on Region 2, i.e. the region where unemployment rate is the
highest.
Similar considerations apply to geographic concentration of production and disparity in income.
Low international comparability of regional data represents a major obstacle to the comparative
analysis of geographic concentration and disparity. While in the study of income inequality individuals are
the obvious unit of analysis, there is no such straightforward parallel in regional economics. The size of
regions varies significantly both within and between countries so that the degree of geographic
concentration and territorial disparity depends on the very definition of a region. Typically, as the size of a
region increases, territorial differences tend to be averaged out and disparities to decrease.
A second order of problems is due to limited availability of regional data. Frequently, territorial
indicators cannot be computed in the same year for all countries. As a consequence, international
comparisons may be affected by differences in the economic cycle. This problem is mitigated by the fact
that geographic concentration and territorial disparities are mainly the result of structural factors, so that
the related indicators typically do no show large variations over a short time span. Nonetheless, a careful
check of the results is appropriate when data are based on different years.
Although perfect comparability in not achievable in practice, a major objective of this study is to
derive statistical indicators of geographic concentration and territorial disparity that are suited for
international comparisons.
The study is organised as follows. Section 2 compares geographic concentration of GDP,
unemployment and population between OECD countries. Section 3 presents new evidence on territorial
2
GOV/TDPC/TI(2002)2
disparities in GDP per capita, productivity, unemployment rates and activity rates. An economic
interpretation of the observed disparities is provided in Section 4. Finally, Section 5 summarises the main
conclusions of the study.
2. Geographic concentration
The last decade has registered a renewed interest in the issue of geographic concentration of
economic activities. New growth and trade theories have pointed out the key role of endogenous
externalities in production and innovation stemming from firms clustering and labour markets pooling. As
these effects tend to be localised in space, geographic concentration has returned high in the research
agenda of many economists.
Although an increasing body of empirical literature has investigated this issue, there seems to be
little agreement on which statistics is most appropriate to measure geographic concentration. Furthermore,
from the OECD perspective the issue is complicated by the problem that available indexes are not well
suited for international comparisons.
Geographic concentration indicates the extent to which a small area of the national territory
accounts for a large proportion of a certain economic phenomenon. Conventionally, this concept has been
measured in two different ways.
The first measure is the concentration ratio, i.e. the ratio between the economic weight of a
region and its geographic weight. Taking production as an example, the concentration ratio is calculated
by ranking regions by their level of production and dividing the share in national production of the first
“n” regions with their share in national territory, i.e. their area as a percentage of the total area of the
country. The larger this ratio, the higher geographic concentration.
This method, however, is unsuitable for international comparison because the measure of
geographic concentration crucially depends on “n”, the number of regions arbitrarily chosen for the
comparison.
As an example, consider the geographic distribution of production in two countries as reported in
table 1. If the concentration ratio is measured on the first region, production appears more concentrated in
country 1 than in Country 2. However, if the concentration ration is based on two regions, then
production in Country 1 turns out to be as concentrated as in Country 2. Finally, the ranking is reversed
when the concentration ratio is computed on three regions.
Table 1. Concentration ratios
Region
1
2
3
4
Production
(as % of total)
40
20
20
20
Country 1
Area
(as % of total)
20
20
40
20
Concentration
ratio
2.0
1.5
1.0
1.0
Production
(as % of total)
30
30
30
10
3
Country 2
Area
(as % of total)
20
20
20
40
Concentration
ratio
1.5
1.5
1.5
1.0
GOV/TDPC/TI(2002)2
The second method of measuring geographic concentration is the so-called “locational Gini
coefficient” (Krugman, 1991). This is simply a modification of the Gini inequality index where individuals
are replaced by regions and weights are given by the regional shares in total population or employment.
The drawback of this measure, however, is that it confuses inequality and concentration whereas
these are two distinct concepts1. The locational Gini, therefore, is best suited as a measure of territorial
disparity not geographic concentration.
This point has been stressed by several authors (Arbia, 1989; Wolfson, 1997) and can be
illustrated by comparing the geographic distribution of production in two countries as depicted in Figure 1.
In both countries, the Gini coefficient equals 0.33 so that inequality is the same. However, it can be easily
proven (see Annex 1) that concentration is higher in Country 2 than in Country 1.
To overcome the limitations of both concentration ratios and the locational Gini coefficient, this
study develops a new measure of concentration, the Adjusted Geographic Concentration index (AGC).
The methodology underlying the construction of this index is detailed in Annex 1 but, in its essential term,
the AGC index is constructed by transforming a commonly used measure of concentration (the Herfindahl
index) as to take into account within-and between-country differences in the size of regions.
Figure 1.
Regional distribution of production
3.5%
Country 1
Country 2
Regional share in national production
3.0%
2.5%
2.0%
1.5%
1.0%
0.5%
0.0%
1
2
3
4
5
6
7
8
9
10
Regions
Figures 2, 3 and 4 present a ranking of 25 OECD countries based on the geographic concentration
index of GDP, unemployment and population, as measured by the AGC index.
1.
The confusion probably arises from the fact that the Gini coefficient is based on the Lorenz or so-called
“concentration” curve.
4
GOV/TDPC/TI(2002)2
Geographic concentration of GDP - 19992
Figure 2.
.47
.47
.47
MEX
AUT
NOR
.31
NLD
.23
.30
.29
.32
DEU
.37
POL
.33
.38
GRC
.36
.38
HUN
.35
.38
.40
IRL
.41
.48
ESP
.47
.49
.50
FIN
.50
CAN
.50
AUS
.52
.51
SWE
KOR
.53
.60
UKD
.58
.65
.70
.20
.10
SVK
CZE
BEL
ITA
DNK
FRA
JPN
PRT
USA
.00
Source: OECD Territorial Database
Figure 3.
Geographic concentration of unemployment - 19992
.24
.24
NLD
HUN
.18
.25
.26
DEU
IRL
.27
DNK
.30
.29
.32
.37
.38
.40
.40
.41
.43
.44
.46
JPN
GRC
.46
SWE
.45
.47
CAN
ESP
.48
AUS
.52
.50
.49
.54
.60
MEX
.59
.70
.67
.80
.08
.20
.10
Source: OECD Territorial Database
2.
Data for Greece, Mexico, Norway and the US refer, respectively, to 1998, 1995, 1998 and 1994.
5
SVK
POL
BEL
CZE
FIN
NOR
FRA
AUT
ITA
PRT
USA
UKD
KOR
.00
GOV/TDPC/TI(2002)2
Geographic concentration of population - 19992
Figure 4.
.43
.43
.43
.42
.41
ESP
FIN
JPN
NOR
.50
UKD
MEX
.51
PRT
.48
.51
SWE
.50
.49
.52
KOR
.60
.59
.70
.22
.21
HUN
CZE
.24
.23
DEU
BEL
.25
POL
.29
DNK
.26
.30
.30
IRL
.31
.34
.33
FRA
GRC
.36
.40
.12
.20
.10
SVK
NLD
ITA
AUT
CAN
AUS
USA
.00
Source: OECD Territorial Database
Production in OECD countries seems fairly concentrated with the index equal to 0.43 for the
average of Member countries. However, there appear to be significant international differences in the
degree of geographic concentration, with the index going from 0.65 in the US (the highest rank) to 0.23 in
the Slovak Republic (the lowest rank). Among the countries with high geographic concentration we find
Portugal, the UK, Sweden and Korea while Belgium, Germany, the Netherlands and the Czech Republic
are located at the bottom of the ranking.
Similar results emerge for the geographic concentration of unemployment (Figure 3). On
average, geographic concentration of unemployment is significant (the AGC index being equal to 0.39) but
there are large differences between countries, with the AGC index going from 0.67 in Korea (the highest
rank) to 0.08 in the Slovak Republic (the lowest rank).
Interestingly enough, in many countries geographic concentration of unemployment does not
mirror geographic concentration of production. In twelve countries out of twenty-five, production appears
much more concentrated than unemployment (especially in Poland, the Slovak Republic, Hungary, Finland
and Ireland) whereas in Korea, Italy and Greece unemployment turns out to be more localised than
production. In the remaining ten countries geographic concentration is about the same for both production
and unemployment.
Although concentration and inequality are two distinct concepts, territorial disparity does have an
impact on geographic concentration. To appreciate this point, assume that GDP per capita was the same in
all regions. In this case, geographic concentration of production would simply reflect geographic
concentration of population. On the contrary, if population density (i.e. population/area) were the same in
each region, then geographic concentration would be entirely due to regional differences in GDP per
capita.
6
GOV/TDPC/TI(2002)2
In order to assess the effect of territorial disparities on geographic concentration of production,
the AGC index can be decomposed into two components: geographic concentration of population and
territorial disparity in GDP per capita3. The percentage of geographic concentration of production due to
territorial disparity in GDP per capita is reported in Figure 5.
The impact of territorial disparity appears considerable: on average, about 18 per cent of
geographic concentration of production in OECD countries is due to territorial disparity in GDP per capita.
International differences are even larger. Only in a very few cases (Korea, Sweden, Canada and Australia)
geographic concentration of production mainly reflects concentration of population. In a large group of
countries, above 25 per cent of geographic concentration of production appears to be the result of territorial
disparity in GDP per capita. This figure is above 30 per cent in the Czech Republic, Belgium and Poland
and reaches 43 per cent in Hungary and 48 per cent in the Slovak Republic.
A similar exercise can be repeated for unemployment by decomposing the AGC index into
geographic concentration of the labour force and territorial disparity in unemployment rates. Figure 6
shows that the impact of disparity in unemployment rates is substantial in all OECD countries. In half of
the countries, above 25 per cent of geographic concentration of unemployment is due territorial disparities
in unemployment rates. This figure is above 30 per cent in Korea, Spain and the Czech Republic and
reaches 49 per cent in Belgium and 63 per cent in Italy.
Figure 5.
Percentage of geographic concentration of GDP due to inequality in GDP per
capita - 19992
10%
9%
ESP
11%
GRC
USA
11%
13%
NOR
JPN
14%
MEX
18%
ITA
15%
18%
NLD
16%
19%
DNK
24%
DEU
19%
25%
AUT
20%
PRT
26%
30%
IRL
33%
40%
31%
38%
43%
50%
48%
60%
2%
2%
2%
CAN
SWE
KOR
3%
7%
10%
Source: OECD Territorial Database
3.
The decomposition methodology is detailed in Annex 1.
7
AUS
UKD
FIN
FRA
CZE
BEL
POL
HUN
SVK
0%
GOV/TDPC/TI(2002)2
Figure 6.
Percentage of geographic concentration in unemployment due to inequality in
unemployment rates - 19992
63%
70%
14%
14%
13%
13%
GRC
JPN
NOR
18%
MEX
NLD
18%
CAN
19%
IRL
23%
FRA
20%
24%
DEU
20%
DNK
24%
PRT
25%
28%
UKD
26%
28%
SVK
SWE
29%
AUT
26%
29%
HUN
POL
29%
30%
FIN
33%
KOR
40%
33%
37%
50%
ESP
49%
60%
7%
10%
AUS
USA
CZE
BEL
ITA
0%
Source: OECD Territorial Database
3. Territorial disparity
Territorial disparity indicates the degree to which the intensity of a certain economic
phenomenon differs between regions within a same country. The concept of disparity, therefore, refers to
regional differences in GDP per capita, productivity, unemployment and activity rates.
As discussed above, inequality indexes -- such as the Gini coefficient -- provide an appropriate
measure of territorial disparities. In practice, however, there are an important number of problems arising
from the application of the Gini coefficient to the issue of territorial disparity.
First, the Gini coefficient is constructed for the analysis of income inequality between individuals
whereas we are interested in disparities between regions. A majority of regional studies overlook this
problem and measure territorial disparities in GDP per capita as income inequality between group of
individuals living in different regions. However, the index so obtained says very little about territorial
disparities because it does not control for the spatial distribution of population.
Second, the Gini coefficient is sensitive to the level of spatial aggregation. Grouped data
underestimate systematically the degree of territorial disparity so that the Gini coefficient is not suitable for
international comparisons when the level of aggregation of regional data differs significantly between
countries.
In order to overcome these two problems, this study develops a new index of territorial disparity,
the adjusted territorial Gini coefficient. A full discussion of the methodology underlying the construction
of this index is reported in Annex 1.
8
GOV/TDPC/TI(2002)2
Before presenting the results of the analysis, a few comments on the time period are in order. Due
to limited data availability, the reference period tends to differ between countries4. In order to ensure time
consistency between variables (GDP, employment at the workplace, employment at the place of residence,
labour force and population), a single reference year (the most recent one) has been selected for each
country. As the whole set of variables is not available in the same year for all countries, the period of
observation spans from year 1995 (1994 for the US only) to year 2000.
Although territorial disparities are the result of structural factors and typically do not show large
variations over a short time span, it is important to check the implications of comparing countries on the
basis of different years. For all countries where data were available5, territorial disparities in GDP per
capita were calculated in the first and last year of the period considered, 1995 and 2000, respectively. The
ranking based on year 1995 was then correlated on the ranking based on year 2000. The correlation
coefficient turned out to be very high (0.97), suggesting that the relative position of each country has
remained stable over the period considered. This implies that, for the countries and the period considered,
the bias due to the fact of comparing territorial disparities on the basis of different years is likely to be
small.
Figures from 8 to 11 report the values of the adjusted territorial Gini for GDP per capita, average
labour productivity6, unemployment rates and activity rates in a sample of OECD countries.
International differences in territorial disparities are very large, the Gini coefficient for GDP per
capita ranging from 0.20 to 0.03. Mexico, the US, Hungary, Italy and Germany appear to be the countries
with the highest disparities while Sweden, the Czech Republic, Norway, Australia and Denmark lie at the
bottom of the ranking.
As for average labour productivity, the Gini coefficient ranges from 0.17 in Poland to 0.02 in
Denmark. Disparity appears particularly large also in the US and Germany while tends to be smaller in the
Check Republic and the North European countries.
International differences are even more remarkable when one looks at territorial disparities in
unemployment rates. For the OECD average, the Gini coefficient is equal to 0.19 (higher than for both
GDP per capita and productivity) and ranges from 0.39 in Italy to 0.08 in Australia. Spain, Portugal,
Belgium, and Germany are the other countries with large disparities; Denmark, Japan and Ireland lie at the
bottom of the ranking.
Finally, territorial disparities in activity rates seem less pronounced than in the other variables.
The Gini coefficient in fact goes from 0.14 in Ireland to 0.01 in Denmark, the Czech Republic and Sweden.
4.
Reference years are the following. For the Check Republic, Poland and the Slovak Republic: 2000. For
Australia, Finland, France, Germany, Italy, the Netherlands, Spain and Sweden: 1999. For Denmark,
Norway, Hungary, Korea and Norway: 1998. For Austria and Ireland: 1997. For Canada and Greece: 1996.
For Belgium, Japan, Mexico and the UK: 1995. For the US: 1994.
5.
Data were not available in both years for Korea, Japan, Mexico and the US.
6
Average labour productivity is defined as the ration between GDP and employment at the workplace.
Measuring employment at the workplace, rather than at the place of residence, permits to control for the
effects of commuting.
9
.140
.120
.100
.080
.060
.040
.020
.000
10
.020
.064
BEL
Source: OECD Territorial Database
.042
.042
.040
NOR
CZE
NLD
DNK
.034
.044
FIN
SWE
.044
.050
FRA
AUS
.052
.124
JPN
Source: OECD Territorial Database
Territorial disparity in average productivity (1994-2000)
SWE
CZE
NOR
AUS
.034
.041
.046
.054
.057
.067
.065
FRA
DNK
.070
.082
.085
FIN
KOR
NLD
.089
.097
BEL
IRL
.101
.106
POL
UKD
.116
ESP
.136
.126
GRC
.145
.153
.140
SVK
.000
.129
.050
AUT
CAN
.100
HUN
.059
.064
ESP
ITA
.067
UKD
.083
PRT
DEU
ITA
.159
.178
.200
Figure 7.
AUT
.085
KOR
Figure 8.
.088
.120
HUN
USA
MEX
.150
IRL
DEU
.165
.160
USA
.180
.167
.200
POL
GOV/TDPC/TI(2002)2
Territorial disparity in GDP per capita (1994-2000)
.250
IRL
.000
.043
11
Source: OECD Territorial Database
.025
BEL
JPN
DNK
AUS
.015
.014
.013
.012
SWE
CZE
DNK
IRL
SVK
FIN
CAN
FRA
POL
NLD
UKD
SWE
GRC
NOR
AUT
CZE
HUN
MEX
USA
NOR
.080
.016
.120
AUS
.140
.016
.160
NLD
Figure 10. Territorial disparity in activity rates (1994-2000)
.017
Source: OECD Territorial Database
SVK
.021
.025
AUT
JPN
.026
FIN
.034
MEX
.038
FRA
.034
.040
KOR
CAN
.040
PRT
.053
KOR
.000
ESP
HUN
.053
DEU
BEL
.100
.077
.263
.241
.232
.231
.226
.225
.223
.215
.201
.201
.195
.191
.189
.180
.159
.154
.153
.151
.144
.140
.119
.117
.114
.393
Figure 9.
USA
.058
.020
UKD
.040
.060
.060
ITA
PRT
.150
.062
ITA
.200
ESP
.250
DEU
.081
.142
.300
POL
.100
.095
.400
GRC
GOV/TDPC/TI(2002)2
Territorial disparity in unemployment rates (1994-2000)
.450
.350
.050
GOV/TDPC/TI(2002)2
4. An economic interpretation of territorial disparity.
Section 3 has presented new statistical evidence on several aspects of territorial disparity. The
aim of this section is to interpret these different aspects in a unified analytical framework.
Territorial disparity in GDP per capita can be explained as the result of four underlying
disparities in:
1.
average labour productivity;
2.
employment rates;
3.
commuting rates;
4.
activity rates.
Each of these components can be regarded as an indicator of the determinants of territorial
disparity in GDP per capita.
Average labour productivity is a proxy for the productivity of the regional production system;
employment rate is an indicator of the effective functioning of the local labour market; commuting rate
measures workers mobility across regions; activity rate summarises the characteristics of the regional
labour force.
Figures 12 reports the contribution of each of these components to territorial disparities in GDP
per capita in 18 OECD countries7. The methodology for decomposing the Gini coefficient is detailed in
Annex 1.
On average, disparities in labour productivity seem to be the main determinant and explain about
54 per cent of the disparity in GDP per capita. Territorial differences in commuting and activity rates
account for 19 and 17 per cent, respectively, while the remaining 10 per cent of the disparity in per capita
GDP is due to differences in employment rates.
These findings suggest two results. The first is that a decrease in regional differences in
productivity should be a primary objective of any policy aimed at reducing disparities in GDP per capita.
The second result is that the analysis of territorial disparity should take into account the effects of workers
commuting as this explains a significant proportion of disparity in GDP per capita.
Although productivity appears to be the main cause of territorial disparities, Figure 12 shows that
the relative importance of the three underlying factors varies considerably between countries.
The contribution of productivity is more pronounced in the US, the Check Republic, Germany,
Korea and Australia while it is much smaller in Ireland, Italy, the Netherlands, Hungary and Denmark.
In these last three countries, territorial disparities in GDP per capita are mainly explained by
workers commuting whereas this component is almost negligible in the Check Republic, Germany and
Italy.
As for the contribution of disparities in activity rates, this is more significant in the UK, Italy,
Ireland, Finland and Hungary but rather small in Germany, Denmark and the Netherlands.
Finally, the effect of disparity in employment rate is very pronounced in Italy and Spain while it
is extremely small in the US and Austria.
7
In the US, regions are defined as commuting zones so that the contribution of commuting is none.
12
GOV/TDPC/TI(2002)2
4
10
27
Productivity
37
7
35
32
36
32
6
65
SWE
Employment rate
68
64
2
38
29
7
10
5
4
25
23
HUN
DNK
28
32
ITA
NLD
34
IRL
42
47
UKD
FRA
AUS
KOR
0%
USA
20%
ESP
49
52
AUT
FIN
55
BEL
61
70
79
DEU
75
82
40%
CZE
86
31
10
1
17
60%
31
7
16
4
3
0
67
NOR
19
9
20
14
18
6
0 10
80%
Activity rate
Commuting
19
15
17
11
13
15
18
15
0 9
9
10 13
100%
2
21
Figure 11. Percentage of territorial disparity in GDP per capita due to disparity in
productivity, employment and activity rates (1994-2000)
Source: OECD Territorial Database
5. Conclusions
This document has presented an international comparison of geographic concentration and
territorial disparities in selected OECD countries. The analysis has tried to deal with the issue of low
comparability of regional data due to different sizes of regions and different periods of observation.
However, it has to be stressed that perfect comparability of regional data is in not achievable in practice
and caution should be used when interpreting the results.
The main findings of the analysis can be summarised as follows.
a) Production in OECD countries seems to be significantly concentrated, the geographic concentration
index being equal to 0.43 for the average of Member countries. However, there appear to be
significant international differences in the degree of geographic concentration, the index going
from 0.67 in the US (the highest rank) to 0.23 in the Slovak Republic (the lowest rank).
b) Similar results emerge for the geographic concentration of unemployment. On average, geographic
concentration of unemployment is substantial (the geographic concentration index being equal to 0.39)
but there are significant differences between countries, the index going from 0.67 in Korea (the highest
rank) to 0.08 in the Slovak Republic (the lowest rank).
13
GOV/TDPC/TI(2002)2
c) The impact of territorial disparity on geographic concentration appears considerable. In a large
majority of countries, above 25 per cent of geographic concentration of production and unemployment
appears to be the result of territorial disparity in GDP per capita and unemployment rates.
d) International differences in territorial disparities are substantial. Mexico, the US, Hungary, Italy and
Germany appear to be the countries with the highest disparities in GDP per capita while Sweden, the
Czech Republic, Norway, Australia and Denmark lie at the bottom of the ranking. Disparities in
productivity appear to be very large in Poland, the US and Germany whereas they are quite small in
the Check Republic and the North European countries.
e) International differences are even more pronounced when one looks at territorial disparities in
unemployment rates. The Gini coefficient ranges from 0.39 in Italy to 0.08 in Australia. Spain,
Portugal, Belgium and Germany are the other countries with largest disparities; Denmark, Japan and
Ireland lie at the bottom of the ranking.
f) As for territorial disparities in activity rates, they seem less pronounced than in the other variables.
The Gini coefficient goes in fact from 0.14 in Ireland to 0.01 in Denmark, the Czech Republic and
Sweden.
g) Disparities in labour productivity seem to be the main determinant of the disparity in GDP per capita.
On average, disparities in labour productivity seem to be the main determinant and explain about
54 per cent of the disparity in GDP per capita. Territorial differences in commuting and activity rates
account for 19 and 17 per cent, respectively, while the remaining 10 per cent of the disparity in per
capita GDP is due to differences in employment rates.
h) The impact of productivity, employment and activity rates on territorial disparity varies considerably
between countries. The contribution of productivity is more pronounced in the US, the Check
Republic, Germany, Korea and Australia while it is much smaller in Ireland, Italy, the Netherlands,
Hungary and Denmark. The effect of disparities in employment rates is very pronounced in Italy and
Spain. As for the contribution of disparities in activity rates, this is more significant in the UK, Italy,
Ireland, Finland and Hungary. Finally, commuting account for a large proportion of disparity in GDP
per capita in Denmark, the Netherlands and Hungary.
14
GOV/TDPC/TI(2002)2
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ARBIA, G. (1989),
Spatial data configuration in statistical analysis of regional economic and related problems, Kluwer
Academic Publisher.
DELTAS, G. (2001),
"The Small Sample Bias of the Gini Coefficient: Results and Implications for Empirical Research",
University of Illinois, mimeo.
ELLISON, G. and GLAESER, E. (1997),
"Geographic Concentration in US Manufacturing Industry: a Dartboard Approach", Journal of
Political Economy, Vol. 105, No. 5, pp. 889-927.
FIELDS, G.S. (2001),
Cornell University, School of Industrial Relations, Ithaca, NY, mimeo.
KRUGMAN, P. (1991),
Geography and Trade, The MIT Press, Cambridge, MA.
OECD (2001), OECD Territorial Outlook, OECD Publications Service, Paris.
SHORROCKS, A.F. (1983),
"Inequality Decomposition by Factor Components", Econometrica, Vol. 50, pp. 193-212.
SPIEZIA, V. (2002),
" Geographic Concentration of Production and Unemployment in OECD countries", Cities and
Regions, December Issue.
WOLFSON, M. (1997),
"Divergent Inequalities -- Theory and Empirical Results", Analytical Studies Branch Research
Paper Series, Statistics Canada.
15
GOV/TDPC/TI(2002)2
ANNEX 1: STATISTICAL METHODOLOGY
The Adjusted Geographic Concentration index (AGC)
A common measure of concentration is the Herfindahl index (H), which is defined as:
N
H   y i2
i 1
where
y i is the production share of region i and N stands for the number of regions. The index lies between 1/N (all
regions have the same production share, i.e. there is no concentration) and 1 (all production is concentrated in one
region, i.e. maximum concentration). In the example depicted in Figure 1, where all regions have the same area, the
Herfindahl index equals 0.127 in Country 1 and 0.135 in Country 2, so that production is more concentrated in
Country 2 than in Country 1.
In general, however, regions have different areas so that a correct measure of geographic concentration has
to compare the production share of each region with its share in the national territory. An index that takes into
account regional differences is the one proposed by Ellison and Glaeser (1997):
N
EG   ( y i  a i ) 2
i 1
where
ai is the area of region i as a percentage of the country area. If the production share of each region equals its
relative area, then there is no concentration and EG equals 0. Therefore, the bigger the value of EG, the higher
geographic concentration.
A major drawback of the EG index is that it is not suitable for international comparisons because it is very
sensitive to the level of aggregation of regional data. This feature is due to the fact that the differences between the
production share and relative area of each region are squared.
To examine the effect of this procedure, suppose that there are two regions with equal production share and
relative area (say 0.4 and 0.3, respectively).
The EG term for these two regions would then be
(0.4 - 0.3)² + (0.4 - 0.3)² = 0.02. Suppose now that data were not available for each of these two regions but only for
the bigger region resulting from the aggregation of the small ones. The corresponding EG term would be
(0.8 -0.6)² = 0.04, which is smaller than 0.02. In this example, therefore, aggregation would make the EG index
overestimate geographic concentration.
Consider now a second example where production shares and relative area are equal to 0.4 and 0.3 in
Region 1 and 0.4 and 0.6 in Region 2. The EG term would be (0.4 - 0.3)² + (0.4 - 0.6)² = 0.05, if these two regions
are taken separately, and (0.8 - 0.9)² = 0.01, if the two regions are aggregated into a single region. In this second
example, the EG index would then underestimate concentration.
To correct for this bias due to aggregation, the EG index can be reformulated into the following index of
Geographic Concentration (GC) (Spiezia, 2002):
16
GOV/TDPC/TI(2002)2
N
GC   y i  a i
i 1
where │ │ indicates the absolute value. Going back to our two examples, it is clear that in both cases the aggregation
bias would be smaller for the GC index than for the EG index.
In the first example the EG index would overestimate concentration whereas the GC index would provide
the correct measure of concentration. In fact, GC = │0.4 - 0.3│ + │0.4 - 0.3│ = │0.8 - 0.6│ = 0.2. In the second
example both indexes would underestimate concentration but the error due to aggregation would be smaller for the
GC index. In fact, the GC term would be │0.4 - 0.3│ + │0.4 - 0.6│ = 0.3, if the two regions are taken separately, and
│0.8 - 0.9│ = 0.1, if the regions are aggregated into a single region. The aggregation bias of the GC index would
then be [(0.3 - 0.1)/0.1] = 2, which is half of the aggregation bias of the EG index [(0.05 - 0.01)/0.01] = 4.
International comparability of the GC index can be increased further by noticing that the index reaches its
maximum when all production is concentrated in the region with the smallest area. The maximum value of the GC
index is the equal to:
CG MAX 
a
i  min
where
i
 1  a min  1  1  2a min  21  a min 
amin is the relative area of the smallest region.
The GC index, therefore, is not internationally comparable if the size of regions differ systematically
between countries. This would be the case, for instance, if one compared a country in which regions are classified at
the territorial level 2 with a country where regional data are available at the territorial level 3.
A natural correction for this second aggregation bias is provided by the adjusted geographic concentration
index (AGC), defined as
AGC  GC / GC MAX .
As the AGC index lies between 0 (no concentration) and 1 (maximum concentration) in all countries, it is
suitable for international comparisons of geographic concentration.
Decomposition of the AGC index
The AGC index can be decomposed in two components: geographic concentration of population and
territorial disparity. In the case of production
y i  ai   y i  pi    pi  ai 
where
p i is the population share of region i.
Therefore, the AGC index for production can be rewritten as
N
AGC  
i 1
N
y i  pi
p  ai
y i  ai   i
y i  ai
y i  ai
i 1 y i  a i
17
GOV/TDPC/TI(2002)2
The first term on the right-hand measures the effect of territorial disparity in GDP per capita and the
second term the effect of geographic concentration of population.
In the case of unemployment:
u i  ai  u i  l i   l i  ai 
where
u i and l i are, respectively, the unemployment share and the labour force share of region i.
The AGC index for unemployment is then equal to
N
AGC  
i 1
N
ui  li
l  ai
u i  ai   i
u i  ai
u i  ai
i 1 u i  a i
The first term on the right-hand measures the effect of territorial disparity unemployment rates and the
second term the effect of geographic concentration of the labour force.
The Adjusted Territorial Gini Coefficient
Inequality indexes -- such as the Gini coefficient -- provide a natural starting point for the analysis of
territorial disparity. However, an important number of specific issues have to be taken into account in the application
of the Gini coefficient to the study territorial disparity.
The first issue is that the Gini coefficient is constructed for the analysis of income inequality between
individuals whereas we are interested in disparities between regions. In general, these two measures, the one based
on population and the other based on regions, are very different. To appreciate this point, consider a country where
all population is concentrated in a single region and each individual has the same income. In such a country, income
inequality between individuals is none (all individuals have the same income) and the Gini coefficient based on
population would be equal to zero. However, territorial disparities are very large because income is zero in all
regions except the one where all population is concentrated. The Gini coefficient based on regions would then be
equal to 1.
The implication of this simple example is that territorial disparities should be measures in the geographic
space rather than in the individual space. Accordingly, in this study the Gini coefficient is constructed by weighting
regions by their areas rather than by their population.
For instance, in a country having area A, income GDP and population P and composed of N regions with
area Ai income GDPi and population Pi, the Gini coefficient of territorial disparity in income per capita is defined as:
N 1
N 1
G

i
i
Ai
 F  Q     A  
i 1
i
i
N 1
F
i 1

i 1
j 1
j 1
GDPi / Pi  
N  1 / 2
Am


i
where Fi and Qi represent, respectively, the cumulative frequency and cumulative income shares up to region i and m
stands for the area-weighted average of GDP per capita, defines as:
N
m
i 1
Ai GDPi
A Pi
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GOV/TDPC/TI(2002)2
A second group of problems with territorial disparity indexes are similar to those encountered in the
analysis of income inequality with grouped data. First, the level of aggregation is crucial. To appreciate this point,
Figure 7 depicts the concentration curve associated to the same geographical distribution when data are grouped
(broken line) or ungrouped (continuous line). As the Gini coefficient measures the area delimited by the
concentration curve, it is clear that grouped data underestimate systematically the degree of territorial disparity. This
observation implies that the Gini coefficient is not suitable for international comparisons when the level of
aggregation of regional data differs significantly between countries.
Figure 12. Concentration area with grouped and ungrouped data
1.00
0.90
0.80
0.70
0.60
0.50
0.40
0.30
0.20
0.10
0.00
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
1.00
Two strategies seem appropriate to minimise the downward bias due to grouped data. The first is
obviously to use data at the lowest level of aggregation available. Accordingly, regions refer to territorial level three
for all countries but Australia, Canada, Mexico and Norway for which data are available only at level two.
The second strategy is to construct the concentration curve as if the variable analysed was continuous and
to assume a uniform distribution within each region. Going back to the example of disparity in GDP per capita, the
Territorial Gini coefficient (TG) is then computed as:
A 1
TG 
 F  Q 
i 1
i
A 1
 Fi
i

i 1
 A1
GDP1 / P1   A2  A  A  i  GDP2 / P2   ....  AN  A  A  A  ......  A  i  GDPN / PN 


  A  i 

1
1
2
N 1
Am
Am
GDP 
i 1
i 1
i 1
1 

 A  1 / 2
A
i

 A  1  GDPi / Pi 
Ai  A   Aj  i

2 
Am
i 1
j 1

1
 A  1 / 2
A final problem is that, when data are grouped, the maximum value of the Gini coefficient is below one,
the difference being higher the larger the group with the highest income. This is so because, by definition, the Gini
coefficient equals one when all income is concentrated in a single unit, a condition that cannot be true when the
income of each unit is unknown because data are grouped.
19
GOV/TDPC/TI(2002)2
In order to correct for this bias, the territorial Gini coefficient has then been divided by its true maximum
value. The adjusted territorial Gini resulting from this correction has two properties (Deltas, 2001): the bias is very
small8 and its direction cannot be signed (i.e., disparities are not systematically underestimated).
Therefore, the Adjusted Territorial Gini coefficient (ATG) is computed as
ATG 
TG
,
TG MAX
where
TG MAX  1 
AN  AN  1
.
 A  1
Decomposition of the Gini coefficient
By definition, the logarithm of GDP per capita is equal to:
ln
GDP
GDP
E
LC
L
 ln
 ln
 ln
 ln
P
E
LC
L
P
where P, E, L and C stand, respectively, for population, employment at the workplace, labour force and net inward
commuting. Therefore, GDP per capita (in logarithms) equals the sum of average labour productivity (GDP/E),
employment rate (E/(L+C)), commuting rate ((L+C)/L) and activity rate (L/P).
Let define s X as the percentage of disparity in GDP per capita (as measured by the Gini coefficient) due to
disparity in the variable X. According to Shorrocks (1982) and Fields (2001):
sX 
COV ln  X ,ln GDP / P 
* 100
Var ln GDP / P 
and
s GDP  s
E
8.
E
L C
s
L
L C
 s L  100
P
Less than 5 per cent with only 10 units and rapidly decreasing with the size of the sample.
20
GOV/TDPC/TI(2002)2
ANNEX 2: SOURCES AND DEFINITIONS BY COUNTRY
Australia
Territorial level: 2 (8 States/Territories).
Source: Australian Bureau of Statistics (ABS)
Population, Labour Force, Employment at place of residence: Census of Population and Housing;
Australian Demographic Statistics.
Employment at place of work: Employed persons by region.
Gross Domestic Product: Australian National Accounts, State Accounts, Gross State Product only. Chain
volumes measures are derived indirectly by calculating a deflator from the expenditure components of the
State series concerned.
Austria
Territorial level: 3 (35 Gruppen von Politischen Bezirken).
Sources:
Population, Labour Force, Unemployment, Employment at place of residence, Gross Domestic product:
Eurostat-Regio (see variables definition below).
Employment at place of work: Census of population, Employment at place of work by activity;
Hauptverband der Sozialversicherungsträger/Employees social security contributions (Statistik Österreich).
Belgium
Territorial level: 3 (11 Provinces).
Source: Eurostat-Regio
See variables definition below
Canada
Territorial level: 2 (12 Provinces).
Source: Statistics Canada
Population: CANSIM, Census of Population 1981, 1986, 1991, 1996, 2001, (Persons unless otherwise
noted); Estimates of population for Census Divisions (component method).
Labour force, Unemployment: Census of Population 1981, 1986, 1991, 1996, 2001; Number of persons
classified by labour force activity, employed, unemployed.
Employment at place of residence: Census of Population, Labour force activity, persons employed.
Gross Domestic Product: Provincial Gross Domestic Product by Industry at factor cost, 1992 constant
canadian dollars; The provincial data are the sum for all industries, the estimates for each province do not
sum to the Canadian totals.
Czech republic
Territorial level: 3 (14 Kraje).
Sources:
Population, Labour force, Unemployment, Employment at place of residence, Gross Domestic Product:
Eurostat-Regio (see variables definition below).
Employment at place of work: Česky statisticky úřad (CSO); Regional Accounts, Research Institute for
Labour and Social Affairs.
Denmark
Territorial level: 3 (15 Amter).
Source: All variables from Eurostat-Regio (see variables definition below).
Finland
Territorial level: 3 (20 Maakunnat).
Source: All variables from Eurostat-Regio (see variables definition below).
France (without DOM-TOM)
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GOV/TDPC/TI(2002)2
Territorial level: 3 (96 Départements).
Source: All variables from Eurostat-Regio (see variables definition below).
Germany
Territorial level: 3 (49 Regierungsbezirke; modified).
Sources:
Population, Labour Force, Unemployment, Employment at place of residence,Employment at workplace:
Eurostat-Regio (see variables definition below).
Gross Domestic product: Statistisches Bundesamt Deutschland; Spatial Monitoring System of the BfLR
.The regional gross value added is based on data of the 16 German Länder. These data have been
regionalised at NUTS 3 level and adjusted to EU standards.
Greece
Territorial level: 4 Groups of Development regions; 13 Development regions.
Source: All variables from Eurostat-Regio (see variables definition below).
Hungary
Territorial level: 3 (20 Megyek +Budapest).
Sources:
Population, Labour Force, Unemployment, Employment at place of residence: Eurostat-Regio (see
variables definition below).
Employment at place of work: Központi Statisztikai Hivatal (HCSO); Regional data/Survey on
employment and earnings, Persons employed by industry.
Ireland
Territorial level: 2 (8 Regional Authority Regions).
Source: All variables from Eurostat-Regio (see variables definition below).
Italy
Territorial level: 3 (103 Province).
Sources:
Population, Labour Force, Unemployment, Employment at place of residence: Eurostat-Regio (see
variables definition below).
Employment at place of work: Istituto Nazionale di Statistica (ISTAT); Occupati per settore di attività.
Japan
Territorial level: 3 (47 Prefectures).
Source: Japanese Statistics Bureau.
Population: Census of population.
Labour force, Unemployment, Employment at place of residence: Census of population.
Gross Domestic Product: Gross Prefectural Domestic Product, by expenditure, at factor cost.
Korea
Territorial level: 3 (16 Special city, Metropolitan area and Province).
Source: All variables from Korean National Statistical Office (KNSO).
Gross domestic product: in current prices.
Mexico
Territorial level: 2 (32 Estados).
Source: Instituto Nacional de Estadística, Geografía e Informática (INEGI)
Population, Labour force, Unemployment, Employment at place of residence: Censo General de Población
y Vivienda; Conteo de Población y Vivienda; Encuesta Nacional de la Dinámica Demográfica.
Gross domestic product: Sistema de Cuentas Nacionales de México, Producto Interno Bruto por Entidad
Federativa.
Netherlands
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GOV/TDPC/TI(2002)2
Territorial level: 3 (12 Provinces).
Source: All variables from Eurostat-Regio (see variables definition below).
Norway
Territorial level: 2 (7 Landsdeler)
Source: All variables from Statistisk sentralbyrå.
Labour force, Unemployment, Employment at place of residence, Employment at the workplace: Labour
Force Sample Survey; Estimated number of employed persons by place of work and place of living,
unemployed persons and total labour force by county.
Gross domestic product: Norvegian Regional Accounts; Gross value added (GVA) in million NOK, per
county and economic sector (ISIC1, ISIC2-5, ISIC6-9). "Extra county" excepted (petroleum sector,
embassies etc., activity at Svalbard)
Poland
Territorial level: 3 (45 Subregions).
Source: All variables from Eurostat-Regio (see variables definition below).
Portugal
Territorial level: 3 (30 Grupos de Concelhos).
Source: All variables from Eurostat-Regio (see variables definition below).
Slovak republic
Territorial level: 3 (8 Kraj).
Source: All variables from Eurostat-Regio (see variables definition below).
Spain (without Canarias and Ceuta y Melilla)
Territorial level: 3 (48 Provincias).
Source: All variables from Eurostat-Regio (see variables definition below).
Sweden
Territorial level: 3 (21 Län).
Source: All variables from Eurostat-Regio (see variables definition below).
United-Kingdom
Territorial level: 3 (133 Upper tier authorities or groups of lower tier authorities or groups of unitary
authorities or LECs or groups of districts).
Source: All variables from Eurostat-Regio (see variables definition below).
United-States
Territorial level: 3 (765 Commuting zones).
Sources:
Population, Labour Force, Unemployment, Employment at place of residence: Bureau of Labor Statistics;
Census of population and housing.
Employment at place of work: USDA/Bureau of Economic Analysis; Total jobs includes part-time, part
year; wage and salary and self-employment.
Gross domestic product: USDA/Bureau of Economic Analysis; State GDP allocated to counties on the
basis of earnings and aggregated to commuting zones.
Eurostat-Regio definitions
Source: European Regional Statistics Reference
http://europa.eu.int/comm/eurostat/Public/datashop
Guide,
European
Communities
2002.
Population
The population statistics refer to resident population. In accordance with this concept, persons normally
resident in a country but temporarily absent on business or holidays, etc., are included; whilst foreigners
23
GOV/TDPC/TI(2002)2
temporarily resident in the country for similar reasons are excluded. Nationality is not taken into
consideration and foreigners whose usual place of residence is in that country are included along the citizens
of that country. Armed forces personnel and members of the diplomatic corps of that country and their
family who happen to be abroad are considered as normally resident. Whereas foreign armed forces
personnel and members of foreign diplomatic corps and their families are excluded. Merchant seamen who
have their domicile in that country and who are working on ships trading abroad are included.
Data are annual average population (except for Germany, Ireland, United-Kingdom and Netherlands).
Labour force
The results of labour force survey (LFS) refer exclusively to private households. The Community labour
force survey is conducted on a sample basis. The LFS divides population of working age (15 years and
above) into three exclusive and exhaustive groups: persons in employment, unemployed persons and inactive
persons. The definitions are in conformity with the ILO recommendations.
Labour force (or active or working population) was defined as comprising persons in employment and the
unemployed. All those persons who are not classified as employed or unemployed are defined as inactive.
Unemployment
Unemployed persons are those who during the reference period of interview, were aged 15 years and over,
without work, available for work within the next two weeks and has used an active method of seeking work
at some time during the previous four weeks.
Employment
Employment at place of residence: Community labour force survey on private households, Employed
persons full and part time.
Employment at place of work: Employment by NACE-Clio-R3 from 1980 to 1990; by NACE-Rev.1-A3
from 1995.
Gross Domestic Product
Gross Domestic product and Gross value Added by Activity: Eurostat-European System of Integrated
economic Accounts (ESA79 and ESA95), GDP at market prices and in current PPP’s and GVA at basic
prices.
Gross domestic product at market prices is the final result of the production activity of resident producer
units. (ESA 1995, 8.89) It corresponds to the economy's output of goods and services less intermediate
consumption, plus VAT on products and net taxes (i.e. taxes less subsidies) linked to imports.
24