Geographic Concentration and Territorial Disparity in OECD Countries

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.

Concentration ratios0

Country 1 Country 2 Region Production Area Concentration Production Area Concentration (as % of total) (as % of total) ratio (as % of total) (as % of total) ratio 1 40 20 2.0 30 20 1.5 2 20 20 1.5 30 20 1.5 3 20 40 1.0 30 20 1.5 4 20 20 1.0 10 40 1.0

3 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.

Regional distribution of production0

3.5% Country 1 Country 2 3.0% n o i t c u

d 2.5% o r p

o 2.0% i t a n

e 1.5% r a h s

n 1.0% o i g e R 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.

Geographic concentration of GDP - 199920

.70 5 6 . 8

.60 5 . 3 2 5 5 . 1 . 0 0 5 . 5 5 9 . . 8 4 7

.50 7 . 7 4 7 . 4 4 4 . 4 . . . 1 4 . 8 8 8

.40 7 3 3 3 . 3 6 . . . 5 3 . 3 . 3 3 2 . 1 3 . 3 . 9 2

.30 . 3 2 .

.00 L X T L K E A T S P A A R L N N E R C D N K U N D I E U T E V S O R U S R Z R A L P R K O N E I W O U F I A J F B S U P A E M P C C N U K D D S N H G Source: OECD Territorial Database

Geographic concentration of unemployment - 199920

5 .60 .

6 6 .50 . 4

. 5 4 4

3 7 .40 .

. 7 .30 6

2 5 2 .

. 4 4 2

.20 1 .

.00 L L L T T A K A X S P E K E A D N U R N C N D N R I E Z L R T S R E O S U V K A R N E U P R U O O I I F W J B P E A F C N P S U A U C D D K M H G N S

Source: OECD Territorial Database

2 . Data for Greece, Mexico, Norway and the US refer, respectively, to 1998, 1995, 1998 and 1994.

Geographic concentration of population - 199920

.70 9 5

.60 . 2 1 1 5 5 . 0 5 . . 5 9 . 8 4

.50 . 4 . 3 3 3 4 4 . 2 . 4 . 1 4 . 4 . .40 6 3 4 . 3 3 . 3 . 1 3 0 . 9 3 . 2 .30 . 6 2 5 . 4 2 2 3 . . 2 2 . 1 2 . 2 . .20 2 1 .

.00 L L L T T A X K S P A K E E R A D N D N N R C U N I E L Z R T S S E V R U O K U A R N E P U R O O I I W F J B E F N C S P A P U A U C D D K M H N G S 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.

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.

Percentage of geographic concentration of GDP due to inequality in GDP per capita - 199920

50% 8 4 % 3 4 %

40% 8 3 % 3 3 % 1 3 30% % % 6 % 5 2 4 2 2 % % 9 % 9 % 1 8 1

20% 8 1 % 1 6 % 1 % 5 % 4 1 3 1 % % 1 1 1 % 1 1 0 % 1

10% 9 % 7 % 3 % % % 2 2 2 0% L L L T T K K E A X A P S N A E U D D N R R N C N I E Z L R T V E S O U R S E N K U A R P U R O O I I F W B J S C N F E P A P U A D D U C H M K N G S Source: OECD Territorial Database

3 . The decomposition methodology is detailed in Annex 1.

Percentage of geographic concentration in unemployment due to inequality in unemployment rates - 199920

70% % 3 6

60% % 9

40% % 7 3 % % 3 3 3 3 % % % % 9 9 9 % 8 2 2 2 30% 8 2 % % 2 % 6 6 5 % 2 % 2 % 2 4 4 3 2 2 2 % % 0 9 % % 2 1 8 20% 8 1 1 % % % % 4 4 3 3 1 1 1 1

10% % 7

0% L L L T T P K A X S E A K E A N R D U N D C N R N I E Z L T S R E S V U O R K U E R N A P U R O O I I F W B J C E S F N A P P U A U D D C H M K G N S 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.

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 available 5, 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.

Territorial disparity in GDP per capita (1994-2000)0

.250 0 0 2 .200 . 8 7 1 . 9 5 3 1 5 . 5 1 0 . 4 6 4 1 .

.150 3 1 9 . 6 1 4 2 . 2 2 1 . 6 1 1 . . 1 6 1 . 1 0 7 0 1 . 9 1 9 . 0 5 8 .

.100 2 8 0 8 . 0 . 0 0 . 7 7 5 6 0 6 . 0 7 . 4 0 . 5 5 6 0 . 0 . 4 1 0 4 4 .

.050 0 3 . 0 .

.000 T L T L L E X A N P S R A K R A E N N N C U D K D I R U E T R O L Z E S U V S U R P R E A K O O N I I F W J P A B P N F C U H S E A D C U K D N M G S

Territorial disparity in average productivity (1994-2000)0

.180 7 5 6 6 1 . 1 . .160

.140 0 2 1 .120 .

.100 8 5 8 3 8 0 8 . 0 . 0 .

.080 7 4 4 6 6 6 9 0 . 0 0 5 . . 2 0 0 . 5

.060 5 4 4 0 2 2 0 . 0 . 4 4 4 4 4 0 0 4 0 0 . . . . 0 3 .

.040 0 . 0 2 0 .020 .

.000 L N T K L A S R E U D R A E P D L A N I L E S U Z U E K N O S U R O R T O W I I F B A N P U E H F A C D U D K N S

Territorial disparity in unemployment rates (1994-2000)0

.450 3 9 3

.400 .

.300 3 6 1 2 . 2 1 4 6 5 3 3 3 2 5 2 2 . .250 2 2 2 1 2 . 2 . 1 1 2 . . 5 . 2 1 0 9 0 . 9 0 9 2 8 2 . 1 . 8 1 1 . .

.200 . 9 1 4 3 1 . 5 4 5 5 0 5 1 4 1 1 . 4 1 . . . 1 9 1 7 . 4

.150 . 1 1 1 1 1 1 . . . 7

.100 7 0 .

.050 L T L E T X R R A N K P S

.000 E C A U N L K D N A D N I R E U E Z L O S U V U S T R R E O A R N O K P W I I F J P B A C N P F E U H S A D K N U C D M G S Source: OECD Territorial Database

Territorial disparity in activity rates (1994-2000)0

.160 2 4 1 . .140

.120 5

.100 9 0 . 1 8 0 . .080 2 0 6 8 6 0 . 5 0 3 3 . 0 .

.060 5 5 0 0 . . 3 0 4 0 8 4 0 4 . 3 0 4 0 4 . . 0 3 3 .040 . 0 0 . 6 . 5 5 2 2 2 1 0 0 0 . 2 . . 7 6 6 0 5 4 1 . 3 1 1 2 1 1 0 1 0 0

.020 . 1 . 0 . 0 . 0 . 0 . .

.000 L T T L E X R R A S N P K L E C A U D N K N A D N I R U E O E L Z S S V U R U R T R E K O A O N P W I I F J P A B P F N C U H E S A D U K C N D G M S Source: OECD Territorial Database

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.

Percentage of territorial disparity in GDP per capita due to disparity in productivity, employment and activity rates (1994-2000)0 1

100% 2 2

4 Activity rate 0 1 9 3 3 1 1 5 5 5 1 1

7 Commuting 0 1 1 1 9 1 1 8 0

1 Employment rate 7 1 9 2 2 2 3 3 5

6 Productivity 6 3 8 3 0 1

80% 1 4 0 7 1 2 0 9 9 1 7 3 0 6 3 4 8 6 2 6 6 4 1

60% 7 1 7 3 1 8 9 1 0 3 2 1 1 3 6 8 2 9 40% 8 7 5 7 4 0 7 7 5 6 6 1 0 5 6 1 5 2 5 7 5 9 7 4 4 2

20% 4 4 2 3 3 8 5 2 3 2 2

0% N L A S K L T E U R D E P D N A R A I S Z E L U R T E U K N U S O R O F I I W B U C A A E N H D F U D K N S

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.

REFERENCES

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.

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 2 H   yi i1

where yi 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 2 EG   (yi  ai ) 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):

N GC   yi  ai 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:

MAX CG   ai  1  amin 1  1  2amin  21  amin  imin

where 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

yi  ai  yi  pi   pi  ai 

where pi is the population share of region i.

Therefore, the AGC index for production can be rewritten as

N N yi  pi pi  ai AGC   yi  ai   yi  ai i1 yi  ai i1 yi  ai

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:

ui  ai  ui  li   li  ai 

where ui and li are, respectively, the unemployment share and the labour force share of region i.

The AGC index for unemployment is then equal to

N N ui  li li  ai AGC   ui  ai   ui  ai i1 ui  ai i1 ui  ai

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 i A i GDP / P  F  Q   i  i i   i i  A  Am  G  i1  i1  j 1 j1  N 1 N 1/ 2  Fi i1 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 A GDP m   i i i1 A Pi

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.

Concentration area with grouped and ungrouped data0

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 Fi  Qi  i 1 TG  A1   Fi i 1 A1 A2 AN  GDP1 / P1  GDP2 / P2  GDPN / PN   A  i  A  A1  i  .... A  A1  A2  ......  AN 1  i   Am  Am  GDP  1   i1 i 1 i 1   A  1/ 2 A  i A  1 GDP / P  A  A  A  i  i i  i   j 2  Am  1  i 1  j 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.

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

TG ATG  , TG MAX where

MAX A A 1 TG  1 N N . A1

Decomposition of the Gini coefficient

By definition, the logarithm of GDP per capita is equal to:

GDP GDP E L C L ln  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):

COV lnX ,lnGDP / P s  *100 X VarlnGDP / P and

s GDP  s E  s L  s L  100 E LC LC P

8 . Less than 5 per cent with only 10 units and rapidly decreasing with the size of the sample.

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)

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

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 Guide, European Communities 2002. http://europa.eu.int/comm/eurostat/Public/datashop 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

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.