Regional Convergence, Growth and Interpersonal Inequalities across EU 1

Transcription

1 Regional Convergence, Growth and Interpersonal Inequalities across EU 1 Report Working Paper of Philippe Monfort Directorate General Regional Policy European Commission January This working paper has been written in the context of the report "An Agenda for a reformed Cohesion Policy". It represents only the opinion of the expert and does not necessarily reflect the views of the European Commission.

2 TABLE OF CONTENTS 1. INTRODUCTION EMPIRICAL EVIDENCE ON REGIONAL CONVERGENCE Summary measures of disparities Distribution dynamics Growth, convergence and regional disparities Disparities, economic development and growth Beta-convergence ANALYSING THE MACRO-EFFECTS OF COHESION POLICY THE RELATIONSHIP BETWEEN REGIONAL DISPARITIES AND INTERPERSONAL INEQUALITY CONCLUSIONS REFERENCES

3 1. INTRODUCTION The Treaty establishing the European Community sets economic and social cohesion as one of the main priorities of the Union. This priority is operationalised by the EU cohesion policy whose objectives are defined by Articles 2 and 4, and Title XVII of the Treaty. According to Article 2, cohesion policy should contribute to «promote economic and social progress as well as a high level of employment, and to achieve balanced and sustainable development». Article 158 adds «in particular, the Community aims to reduce the disparities between the levels of development of the different regions and the backwardness of the least favoured regions or islands, including rural areas». Since its inception and the first programming period, the Treaty general mission has very often been interpreted as the promotion of convergence among regions, measured in terms of GDP per head. This type of convergence has also become a major aspect in assessing the effectiveness of European cohesion policy. The perspective of per-capita income convergence is actually quite limited, for two reasons. First, income captures (especially from the point of view of measuring inequality) only one of the several dimensions of well-being. Second, and apart from that, regional convergence does not adequately capture the Treaty cohesion goal. This goal can in fact be interpreted as a combination of two general goals: an efficiency goal of offering to all regions the opportunity to more fully use their potential; an equity goal of promoting a reduction in the disparities of living standard of people living in different regions. The under-utilisation of capacity of a lagging region can successfully be reduced while a per-capita income gap with successful highly-performing regions increase; on the other hand, convergence of a lagging region can take place, but, due to rising interpersonal inequality within it, overall inequality might be on the rise. These considerations do not suggest to disregards the analysis of convergence. Since we have very little tools to satisfactorily measure the productive potential of regions, the measure of GDP gap among regions and of how well is one region doing compared to other regions can offer some relevant information. It can also allow to explore the very complex relationship between growth, regional disparities and personal inequalities and to examine how it changes with time, place and/or context. The objective of this paper is to take stock of the contributions that highlight the various dimensions of this relationship and present some additional findings. The paper is structured as follows. Section 2 provides an assessment of convergence among EU regions and Member States. Section 3 then examines the relationship between economic growth and convergence. Section 4 extends the analysis to the relationship between growth and interpersonal inequality. Very tentative conclusions are presented in section 5. 3

4 2. EMPIRICAL EVIDENCE ON REGIONAL CONVERGENCE This section examines regional convergence among EU regions using different approaches and methodologies. The analysis is based on various measures capturing the evolution of regional disparities in order to verify the existence, a process through which disparities tend to decrease in time (or sigma-convergence 2 ). The section also reviews methods allowing for an in-depth inspection of the distribution of regional performance Summary measures of disparities One of the most frequently used summary measures of sigma-convergence is the coefficient of variation of regional GDP per head 3. The following figure shows the evolution of the coefficient of variation computed on the EU-15 and EU-27 NUTS 2 regions for the period and respectively 5. Figure 1: Coefficient variation: GDP per head, NUTS 2 regions, EU-12, EU-15 and EU-27 EU EU-27 EU EU-15 EU EU Source: Cambridge Econometrics and EUROSTAT database. DG REGIO own calculation. The results confirm the findings of previous analysis (see for instance Neven and Gouyette, 1995, Magrini 2004 or Ertur et al. 2006) that convergence among EU-15 regions has been strong up to the mid 90's but the process has since then lost momentum. From 1980 to 1996, the evolution of disparities among EU-15 regions indeed features a clear downward trend, the coefficient of variation decreasing from 0.33 to On the contrary, from 1996 onwards, it remains relatively stable at around Note that in the absence of counterfactual, these results are The literature identifies two main concepts of convergence, beta and sigma convergence. Betaconvergence mainly focuses on detecting possible catching-up processes. Disparity measures can of course be computed on other dimensions than GDP per head. In particular, the analysis of regional disparities can be completed with dimensions such as the employment rate, unemployment rate or education attainment which also convey information concerning social cohesion. Series covering the period 1980 to 2005 in fact combine two databases, the Cambridge Econometrics database from 1980 to 1994 and EUROSTAT database from 1995 to Strictly speaking, the data have some differences. However, these are marginal and it has been checked that they do not produce significant breaks in the series. Series have been smoothed by means of a moving average to eliminate possible influence of the business cycle on the extent of regional disparities. 4

5 uninformative concerning the effectiveness of cohesion policy: it is not based on such type of observation that Boldrin and Canova (2001) conclude to the relative failure of cohesion policy. On the other hand, disparities decrease rapidly among EU-27 regions, the coefficient of variation falling from 0.43 in 1995 to 0.35 in This has led many observers to conclude that if convergence is still at work within the EU-27, it is due to the fact that the poorest regions in the new Member States catch-up on the Union's richest ones, while among EU-15 regions convergence is no longer taking place. Both conclusions require refinements. First of all, in several Member States which have recently joined the Union regional disparities have generally increased, as underlined by the evolution of the coefficient of variation computed for the EU-12 (Figure 1). The following figure completes the analysis by displaying the evolution of the coefficient of variation calculated on regional GDP per head for each new Member States. Figure 2: Coefficient variation: GDP per head, NUTS 2 regions, EU-12 countries Coefficient variation: GDP/head, NUTS-2 regions, EU-12 countries BG CZ HU PL RO SI For all countries considered, disparities have increased, sometimes dramatically like in Romania where the coefficient of variation rose from 0.15 in 1995 to almost 0.40 in These results might indicate a phenomenon that is frequent in the early stages of economic catching up at country level: a few core regions drive the catching up since strong agglomeration effects are at work, while peripheral regions are more sluggish. On the other hand, these results might be strongly biased by a commuting effect. 5

6 The commuting effect tends to overestimate GDP in capital or big cities where many people produce and do not live and underestimate it for commuter belt or dormitory regions. Overall, it therefore rises measurable regional disparities. Correction for the commuting effect can lead to significant reduction in the extent of measured regional disparities. A recent study finds that the mean log deviation index is reduced by 15% across the EU-25 as a whole in 2005 and by around 30% in the EU-15 when adjusting for the commuting effect. The effect is even greater is some countries like Belgium, the UK, Slovakia and the Czech Republic 6. This effect has increased in the new Member countries in recent years and contributes to the observed increased within-country regional disparities. Differences in the evolution of regional disparities at the EU and country levels should of course be thoroughly taken into consideration when examining convergence of EU regions. This is particularly the case when analysing regions performance according to their level of development. The next figure is a scatter plot of regional growth rates (annual average) between 1995 and 2005 and regional GDP per head in 1995, both variables measures relative to the EU average. Figure 3: GDP per head, growth and levels, NUTS 2 regions, EU-27, ,0% 5,0% 4,0% GDP per head growth , EU-27=0 y = -0,0001x + 0,014 R 2 = 0,2009 3,0% 2,0% 1,0% 0,0% ,0% GDP per head EU-27=100-2,0% -3,0% -4,0% The graph clearly shows a catching-up process, poor regions (as measured by their GDP poor head level in 1995) tending to grow faster than rich ones. The regions located in North-West quadrant of the graph are those which at the same time were poorer but have grown faster than the average. They are usually referred as the catching-up regions in the literature (see for instance Ezcurra, 2007) and represent 6 Applica, Ismeri Europa and WiiW (2008), Ex Post Evaluation of Cohesion Policy Programmes financed by the European Regional Development Fund in Objective 1 and 2 Regions, on behalf of the European Commission. 6

7 32% of the regions considered here. This leads to the conclusion that convergence 7 is taking place as such process indeed contributes to reduce regional disparities among EU regions. However, results are quite different once regional economic performance is measured relative to Member States average instead of EU average, as shown by the following figure. Figure 4: GDP per head, growth and levels, NUTS 2 regions, EU-27, % 4.0% 3.0% GDP per head growth , MS=0 y = 4E-05x - 0,0042 R 2 = 0, % 1.0% 0.0% % GDP per head MS= % -3.0% There is no longer a significant relationship between the two variables and hence no signs of a general catching-up process. Interestingly, the proportion of catching-up regions is almost the same (31%). The min difference is that the proportion of regions located in the South-West quadrant, i.e. those that were relatively poor in 1995 and that has a negative relative growth rate (sometimes referred as losing regions) is much more important, 38% against 18% in case measures are taken against the EU-27 average. Convergence is therefore much less likely within country as in a number of cases (typically the ones observed in the new Member States), poorest regions seem to be left out of a rapid development process. A part from these cautionary notes, the evidence in so far reviewed has led to the conclusion that in the last ten years disparities have diminished among countries and increased within countries. The Theil index, a frequently used dispersion indicator, allows to explore this issue by decomposing dispersion into within subgroups and among subgroups components. Applied to the context of EU regions, the Theil index can split disparities into between-countries (Bc) and within-countries (Wc) disparities. 7 This is in fact a so-called beta-convergence process, see section 3.2 below. 7

8 Figure 5: Theil index: GDP per head, NUTS 2 regions, EU-27 decomposed into Member States component (Bc) and regional component (Wc) Total Betweeen Within The index clearly confirms an overall reduction of disparities among EU regions. It also confirms that this reduction is due to the fact that disparities among Members States are strongly decreasing. On the contrary, disparities among regions within Member States are slightly increasing. The ratio Wc/Bc corresponds to the share of global disparities explained by regional disparities within countries while its complement measures the share explained by disparities among Member States. In 1995, 70% of regional disparities among EU regions reflected disparities among Member States, the remaining 30% being due to regional disparities within Member States. By 2006, disparities among Member States only account for 53% of regional disparities which for 47% are explained by regional disparities within Member States. The same type of conclusion emerges when considering separately the EU-15 over the period 1980 to Regional disparities have decreased but this is mainly due to decrease in disparities between Members States, their share in global disparities falling from 55% in 1980 to 14% in The jump observed for Wc in 1991 corresponds to the German reunification and the inclusion of East- German Länders in the data. 8

9 Figure 6: Theil index: GDP per head, NUTS 2 regions, EU-15 decomposed into Member States component (Bc) and regional component (Wc) For the EU-12, regional disparities have increased between 1995 and This again mainly reflects a strong increase in disparities within the Member States but, compared to the EU-15, the reduction in disparities between Member States is much more modest, the index falling from 1995 to 2000 but increasing afterwards. Figure 7: Theil index: GDP per head, NUTS 2 regions, EU-12 decomposed into Member States component (Bc) and regional component (Wc) Wc Bc T Wc Bc T Notice finally that other summary measures, like for instance the Gini index, the Atkinson index or the MLD, qualitatively yield the same type of results. Disparity measures can of course be computed on other dimensions than GDP per head. In particular, the analysis of regional disparities on the dimension of GDP per head is often completed with one on dimensions such as the unemployment and the employment rates which also convey information concerning social cohesion. The following figures display the coefficient of variation calculated on these dimensions. 9

10 Figure 8: Coefficient variation: Unemployment rate, NUTS 2 regions, EU-15 and EU EU-15 EU Figure 9: Coefficient variation: Employment rate, NUTS 2 regions, EU-15 and EU EU-15 EU Regional disparities are declining, both for the EU-15 and the EU-27, which points to the fact that the convergence process is at work on these dimensions, even in the EU-15 where it seemed less vivid on the dimension of GDP per head. These variables are likely to be linked to one another and one would like to check if low levels of development are systematically associated with low performance on the labour market. The following figures illustrate the correlation between GDP per head, unemployment rate and employment rate for a panel data covering EU-27 NUTS 2 regions between 2000 and

11 Figure 10: Correlation between GDP per head and unemployment rate (UR), NUTS 2 regions, EU-27, UR y = x R 2 = GDP per head Figure 11: Correlation between GDP per head and employment rate, NUTS 2 regions, EU-27, Employment rate y = x R 2 = GDP per head GDP per head is negatively correlated with the unemployment rate (coefficient of correlation is -0.49) and positively correlated with the employment rate (coefficient of correlation is 0.54). Lagging regions therefore often feature relatively lower rates of the labour force utilisation. The scope for tapping on unused resources may therefore be quite large in such regions. 11

12 Finally, GDP per head, defined as the ratio of GDP to population, can be decomposed as follows: GDP/Population = (GDP/Employment) * (Employment/Working age population) * (Working age population/population) The first element of the right hand side of the equality is labour productivity (L Pr), the second is the employment rate (ER) and the third is the share of the population in working age (WA). Convergence of GDP per head could therefore stem from convergence in each of these dimensions 9. The next table reports the coefficient of variation for the variables at stake from 2000 to Table 1: Coefficient of variation, GDP/head, L Pr, ER and WA, EU-27, EU-15 and EU-12, GDP/head EU-27 L Pr ER WA GDP/head EU-15 L Pr ER WA GDP/head EU-12 L Pr ER WA For the EU-15, increasing disparities in terms of labour productivity and the share of the population in working age have been somewhat compensated by a reduction in disparities in the employment rate. For the EU-12, the evolution of GDP per head disparities reflects a coincidence of movements in disparities on the dimensions of labour productivity and the employment rate Distribution dynamics Summary measures of disparities have the interest of greatly synthesising the information but they are not capable of capturing changes in the positions of individual regions in the ranking of regions when this change does not affect the distribution. Furthermore these summary measures are left unaffected by changes of the distribution that compensate each other. The examination of changes in the ranking of individual regions and of the different parts of the distribution can add considerable insights to the analysis of regional disparities by providing more details about the mechanisms at work in the convergence process. We therefore conduct a visual inspection of the distribution and its dynamics by relying on nonparametric estimation of the density functions and Salter graphs. We then turn to 9 10 The covariance of the components could also partly explain the convergence of the GDP per head. Note that the coefficient of variation of GDP per head cannot be reconstructed from the coefficients of variation of its components. In particular, it does not correspond to the product the coefficients of variation of its components. 12

13 Markov chain analysis which allows for a statistical characterisation of the distribution dynamics (see for instance Quah, 1996, Fingleton, 1997 or Pellegrini, 2002). The non-parametric estimation of the density functions is based on Gaussian kernels. The next figures show the estimation of the GDP per head distributions for the EU-27 and EU-15 NUTS 2 regions for the years 1995 and Figure 12: GDP/head (EU-27=100): Distribution EU-27 NUTS 2 regions, , Gaussian kernel estimation Frequency GDP/head Figure 13: GDP/head (EU-15=100): Distribution EU-15 NUTS 2 regions, , Gaussian kernel estimation Frequency GDP/head 13

14 The estimated distributions reveal a convergence process at work both for the EU- 15 and the EU-27. Frequencies around the mean increase while they tend to decrease for values below 80% and above 120% of the EU average. For the EU-27, the distribution also evolves from bimodal to unimodal. This is particularly interesting as most analysis had indeed detected a bimodal distribution from the 1980's up to the end of the 1990's, leading to the conclusion that a polarisation process was taking place in Europe, with a "club" of poor regions converging towards a low steady state (around 40% of the EU average in Figure 12) and another club of richer regions converging towards a high steady state (around 110% of the EU average in figure 13). The shape of the distribution in 2005 is much less suggestive of polarisation, making the scenario of various convergence clubs among EU regions less likely. Note that the visual examination of the distribution does not allow identifying the regions that actually move in the distribution. In particular, there is no way to know if this evolution towards a unimodal distribution is due to the catching-up of poor regions all over the EU or to the catching-up of some Member States. Salter's graph is another method which allows for a visual examination of the distribution dynamics. It consists in ranking regions along the horizontal axis according to their GDP per head and report the corresponding level of GDP per head on the vertical axis for a base year. Then holding the base year rank positions of regions constant on the horizontal axis, new series show the regions' GDP per head for subsequent years. As a result, any significant changes in the regional distribution of GDP per head become visible. In addition, regions can be identified and their performance compared. Such graphs can be used to detect patterns of persistence or gradual change in the regional distribution on GDP per head. In particular, the more the series is horizontal, the more it reflects a distribution where disparities are limited. The following figure reports the Salter graph for the EU-27 NUTS 2 regions, comparing the distributions of their GDP per head in 1995 and Figure 14: GDP/head (EU-27=100): Salter graph, NUTS 2 regions, GDP/head Közép-Magyarország Southern and Eastern Mazowieckie Border, Midland and Western Praha Bucureşti - Ilfov Bratislavský kraj Inner London Berkshire, Buckinghamshire and Oxfordshire Eesti Latvija Attiki Poly. (2005) Poor regions Sicilia Dytiki Ellada Guyane Malta Molise Lüneburg Münster Berlin Prov. Hainaut Région de Bruxelles-Capitale / Brussels Hoofdstedelijk Gewest Rich regions EU regions 14

15 The graph indicates a general tendency towards increased horizontality of the series, which is the sign of convergence among EU regions. This is emphasised by comparing the 1995 series with the dashed line which is a polynomial approximation of the series for The graph also shows that this evolution is clearly due to a process where poor regions catch up on the richest ones. The frequency of upward movements in the distribution is indeed higher in the low end of the distribution compared to that of downward movements in the high end of the distribution. Such movements are of course not uniform among poor and rich regions. Some poor regions see their relative GDP per head decline during the period of observation (this is for instance the case for Dytiki in Greece or Hainaut in Belgium) while for some rich regions, relative GDP per head increases (e.g. Inner London). Figure 15: GDP/head (EU-15=100): Salter graph, NUTS 2 regions, GDP/head Border, Midland and Western Região Autónoma da Madeira Bratislavský kraj Southern and Eastern Inner London Berkshire, Buckinghamshire and Oxfordshire Andalucia Cantabria Attiki Aragón País Vasco Poly. (2005) Guyane Poor regions Sicilia Molise Abruzzo Köln Koblenz Berlin Umbria Valle d'aosta Schleswig-Holstein Rich regions EU regions The same type of conclusion can be drawn at the EU-15 level. The series clearly has a tendency to become more horizontal, with frequent upward movements at the low end of the distribution ad downward movements at the high end of the distribution. This information is conveniently complemented by mapping changes in GDP per head between two particular dates, as displayed in the following figure for the period 1995 to

16 Figure 16: GDP/head (EU-27=100): Change in GDP per head, EU-27 NUTS 2 regions, The issue of how persistent is the distribution, whether and how quickly regions with lower-than-average income move up and the convergence to a long term stationary distribution can be analysed by the Markov chain analysis. If the Markov process which is supposed to underlie the dynamics of the distribution is ergodic 11, there exist a stationary distribution corresponding to a steady state towards which the distribution will converge in time and which can be interpreted as a projection of the distribution in the future given the transition process described today by the data. 11 A Markov chain is ergodic if it is possible for the variable under examination to move from every state of the distribution to any other state in a finite number of steps. Ergodicity and the existence of a stationary distribution is ensured when the modulus of the second eigenvalue of the transition matrix is strictly smaller than 1. 16

17 1995 The pace of convergence towards the steady state can be assessed by computing the half-life of the process, i.e. the amount of time it will take to cover half the distance separating the current distribution from the stationary distribution. The speed of the transition process may also be examined by assessing how long it takes to transit from one state to another. In Markovian terminology, this is called the mean first passage time. Finally, it is possible to characterise the stability of the process, i.e. the probability of having no movements within the distribution (stability index) or the extent to which it is driven by convergence forces, i.e. the probability that movement from the original distribution to the final one is in the direction of an increasing convergence toward the mode of the stationary distribution (convergence index). Obviously this analysis just allows to project and appreciate the long term effects of past trends. They are mute on whether the past trends are actually likely to persist, as this statistical analysis assumes. Applying these concepts to our example yields the following results: Table 2: GDP/head (EU-27=100): Transition probability matrix, EU-27 NUTS 2 regions, Transition probability matrix 2005 GDP/head Percentage of regions % 75.8% 24.2% 0.0% 0.0% 0.0% % 0.0% 80.6% 19.4% 0.0% 0.0% % 0.0% 7.7% 76.9% 15.4% 0.0% % 0.0% 0.0% 14.4% 80.2% 5.4% 150-7% 0.0% 0.0% 0.0% 44.4% 55.6% Summary statistics Stationary distribution 0% 15% 39% 41% 5% Half-life S 0.74 C C periods Mean first passage time * * * * * Quah (1993) or Legallo (2004) rely on a different method for computing the transition probability matrix where cell ij is the number of occurrence of passages from class i to class j during the whole period of observation. This has the advantage of exploiting the panel dimension of the data and of giving a more precise estimation of the true transition probabilities. Adopting this approach did not led to substantial differences in the results presented here and we therefore chose to measure transition between the two end dates of the period of observation as it makes it easier to interpret the transition probability matrix. 17

18 Table 2 presents results when the classes of GDP per head are predefined with thresholds at 50%, 75%, 100% and 150% of average values. The transition probability matrix measures movements within the distribution. Each element ij represents the percentage of regions in GDP per head class i moving to class j between 1995 and For instance, the transition probability matrix above indicates that 24.2% of the regions which were in the class [0, 50] in 1995 moved to the class ]50, 75] in On the other hand, all the remaining 75.8% remained in the same category. The transition probability matrix indicates a relative persistence of the distribution. The values on the diagonal are quite high, suggesting a high probability to remain in the same class of GDP per head. Following Pellegrini (2002), we compute a stability index based on the trace of transition probability matrix, i.e. the sum of the elements of the main diagonal. Its value is 0.74 which confirms a relatively high persistence of the distribution. However, persistence is less pronounced at the end classes of the distribution. In particular, as we saw, 24.2% of the poorest regions in 1995 moved up to the next category in 2005, while 19.4% of the regions in the class ]50, 75] in 1995 moved to the class ]75, 100] in 2005, and none to the lower class. In general, for regions with GDP per head lower than 100% of the EU average, movements towards upper categories are much more frequent than movements down, the reverse being true for regions with GDP per head above this threshold. This suggests a convergence process where poorer regions catch-up on the other ones, the distribution evolving towards one with lower frequencies at the tails, as clearly indicated by the stationary distribution. The distribution is therefore likely to feature fewer disparities in the long-run with a concentration of observations in the central categories. The underlying convergence process can be summarised by a convergence index proposed by Pellegrini (2002), measuring the probability to stay or move to a cell that increases convergence. The convergence index is 0.40 for convergence towards the class ]100, 150] and 0.36 for convergence towards the class ]75, 100] which confirms a transition dynamics containing strong convergence forces. Convergence towards the stationary distribution is rather slow with a half-life of 3.9 periods of 10 years, i.e. 39 years. The thickness of the system is also well captured by the mean first passage time matrix (MP) whose element ij measures the time necessary on average to move from class i to class j. The elements outside the main diagonal of MP indicate that the transitions to other categories are relatively slow, the lower passage time being 4.13 periods from the class ]0, 50] to the class ]50, 75]. However, the pace of transition is systematically higher for low GDP per head classes while in general movements up are faster than movements down. The same analysis conducted on the EU-15 regions lead to similar conclusions as summarised in the following table. 18

19 1995 Table 3: GDP/head (EU-15=100): Transition probability matrix, EU-15 NUTS 2 regions, Transition probability matrix 2005 GDP/head Percentage of regions % 54.5% 45.5% 0.0% 0.0% 0.0% % 8.3% 52.8% 38.9% 0.0% 0.0% % 0.0% 6.7% 76.4% 16.9% 0.0% % 0.0% 0.0% 24.6% 73.8% 1.5% 150-3% 0.0% 0.0% 0.0% 14.3% 85.7% Summary statistics Stationary distribution 2% 9% 51% 35% 4% Half-life 4.5 periods S 0.69 C C Mean first passage time In particular, the analysis indicates that, although at a much slower pace than for the EU-27, a convergence process has definitely taken place among EU-15 regions for the period considered. The stability index is only 0.69 which is mainly explained by the low values observed on the diagonal for the lower GDP per head classes and important movements to upper categories. Indeed, 45.5% (respectively 38.9%) of the regions in the class ]0, 50] (respectively ]50, 75]) moved to the next class between 1995 and The stationary distribution shows that if most of the convergence has already taken place for the classes of GDP per head above 75% of the EU average, the process remains vivid for the lower classes and is expected to continue in the future. The convergence index is 0.43 for the class ]100, 150] and 0.40 for the class ]75, 100]. This tendency is however not captured by the aggregate inequality measures reviewed in the preceding section. The explanation is that the number of regions in the lower categories is relatively small and even if within the EU-15, poor regions are rapidly catching-up, their weigh is too small for this movement to be reflected in summary measures. This calls for a prudent attitude when drawing conclusions based on this type of instruments. By summarising the dispersion of the distribution into one measure, they provide convenient and helpful indicators. However, they fail to capture movements that may be relatively small in statistical terms but are nevertheless of importance from a policy point of view. 19

20 Transition probability matrices allow to identify which regions are moving and in which categories. For instance, the EU-27 regions moving from the [0, 50] class to the ]50, 75] class between 1995 and 2005 are the following: Estonia, Lithuania, Közép-Dunántúl (Hungary), Wielkopolskie (Poland), Dolnośląskie (Poland), Pomorskie (Poland), Bucureşti Ilfov (Romania) and Západné Slovensko (Slovakia). Figures 17 and 18 respectively map movements within EU-27 and EU-15 regions between 1995 and Regions are identified according to three fundamental transition regimes: upwardly mobile (green), stationary (orange) and downwardly mobile (red). The category of GDP per head in 1995 is also represented, darker tones indicating lower categories of GDP per head in Figure 17: GDP/head (EU-27=100): Mapping of transition, EU-27 NUTS 2 regions,

21 Figure 18: GDP/head (EU-15=100): Mapping of transition, EU-15 NUTS 2 regions, The maps reveal the predominance of regions in the stationary regime. It also shows that regions in the upwardly (respectively downwardly) mobile regime are mainly poor (respectively rich) regions. Finally, the map reflects a strong country component in regional evolutions, with a tendency for regions belonging to a same country to move in relatively similar directions. Results of Markov chain analysis are strongly dependent on the discrete approximation of the range of values into non-overlapping classes. The choice of the classes indeed uniquely determines the transition matrix and hence the whole set of results. In order to overcome such problem, it is sometimes preferred to define the classes using quantiles so that each class includes the same number of observations. The definition of the classes is then less arbitrary. As a matter of example, the following tables report the results obtained following this approach for the EU

22 Table 4: GDP/head (EU-15=100): Transition probability matrix, EU-15 NUTS 2 regions, Transition probability matrix 2005 GDP/head Percentage of regions % 66.7% 31.0% 2.4% 0.0% 0.0% % 12.2% 63.4% 19.5% 2.4% 2.4% % 0.0% 23.8% 35.7% 35.7% 4.8% % 0.0% 2.4% 31.7% 43.9% 22.0% % 0.0% 0.0% 2.4% 26.2% 71.4% Summary statistics Stationary distribution 8% 22% 20% 25% 25% Half-life 3.8 periods S 0.56 C Mean first passage time The stationarity (i.e. high values of the diagonal) is less concentrated than with this definition of categories than with the preceding one. This simply reflects the fact that the former are narrower in the centre of the distribution and hence are record more movements than between categories at the tail of the distribution which much wider. However, the stationary distribution still indicates convergence of the poorest towards higher levels of GDP per head. Results are therefore not qualitatively different from those obtained with the categories previously chosen. Given the particular evolution, we also conducted a Markov chain analysis of the regional distribution of GD P per head among the new Member States. 22

23 1995 Table 5: GDP/head (EU-12=100): Transition probability matrix, EU-12 NUTS 2 regions, Transition probability matrix 2005 GDP/head Percentage of regions % 91.7% 8.3% 0.0% 0.0% 0.0% % 21.7% 60.9% 13.0% 4.3% 0.0% % 0.0% 16.7% 83.3% 0.0% 0.0% % 0.0% 0.0% 40.0% 40.0% 20.0% 150-3% 0.0% 0.0% 20.0% 30.0% 50.0% Summary statistics Stationary distribution 55% 21% 22% 2% 1% Half-life 5.3 periods S 0.65 C Mean first passage time The dynamics of the distribution within the group of New Member States is radically different. Persistence is particularly high at the low end of the distribution. In addition, for poor regions the frequency of downward moves within the distribution is higher than that of upward moves. This reveals a tendency for the distribution to evolve toward concentration in low GDP per head categories as indicated by the stationary distribution according to which 55% of EU-12 regions could end up with a GDP per head below 75% of the EU-12 average. 13 This is clearly revealing of a divergence process which could take place among EU-12 regions. This result is obviously strongly influenced by the commuting effect discussed above and holds under the rather strong and un-discussed assumption that the trend can be projected in the next decades Growth, convergence and regional disparities What is the relationship between growth, regional disparities and convergence? Have countries characterised by high growth rates recorded growing or decreasing disparities among their regions? To what extent is the (regional or global) growth process supportive or detrimental to regional convergence? And to what extent is convergence supportive or detrimental to (regional or global) growth? These are very complex questions for which we cannot expect to provide an answer. But we can aim at clarifying these issues by reviewing and discussing results in the literature. 13 For this group of regions, the categories of GDP per head had to be adapted so as to have sufficient observations in each category. 23

24 Disparities, economic development and growth In a seminal paper on income distribution, Kuznets (1955) examines the historical relationship between the level of development (measured by GDP per head) and inequalities in the distribution of personal income (measured by the Gini coefficient) for a sample of countries. The main result of his analysis is that the relationship between the two variables yields an inverted- U curve. At the first stage of development, inequalities would tend to grow with GDP per head while at later stage of development, they would tend to decrease when the level of GDP per head increases. The issue tackled by Kuznets is a central one: whether development leads to rising or diminishing inequality among individuals. We ll see in section 5 that the availability of better data and of the experience of five more decades show that the pattern assumed by Kuznet is not at work. But here a different issue must be addressed. The relationship envisaged by Kuznets has opened up a very different field of works where the inverted-u curve has been claimed to hold for disparities across regions (not across individuals) and for the stages of development of different regions in the same moment in time (not of the same region in different moments in time). In particular, Williamson (1965) compares the level of development of the US States (measured again by GDP per head) with that of regional disparities internal to each State. The results are similar in nature to those obtained by Kuznets. For regions at lower stage of development, regional disparities seem to be the higher, the higher is the GDP per head while at a higher stage, the link between the two variables seems inverted, regional disparities being the lower, the lower is the level of GDP per head. Some authors (see for instance Barrios and Strobl, 2005 or Ezcurra and Pascual, 2007) have examined this relationship using more sophisticated statistical techniques and confirm the existence of an inverted-u curve linking GDP per head and regional disparities for the EU. An inverted-u curve seems indeed lo link in 2005 the level of country GDP per head and the extent of internal regional disparities, as measured by the standard deviation of regional GDP per head (in logarithm). Based on similar observations, it has sometimes been argued that: (i) development will inevitably create regional disparities; and (ii) that regional disparities will "naturally" vanish as economies develop. However, it should be stressed that this graph corresponds to a cross-section analysis and must be interpreted as such. In particular, it says nothing concerning the relationship between growth and regional disparities, nor does it allow to infer that regional disparities will be naturally reduced by growth along the path towards development. 24

25 Figure 19: Inverted-U curve: GDP/head (EU-27=100), EU-27 NUTS-2 regions, 2005 Slovenská Republika 0.6 St Dev of Log GDP/head Romania Magyarország?eská Republika Belgique-België 0.3 Ireland Balgarija Polska Portugal Slovenija Italia France Ellada 0.2 España United Kingdom Suomi / Finland Österreich Danmark Nederland Sverige Log GDP/head This caution is confirmed once we introduce time and dynamics in the above chart. The following figure also plots country GDP per head and the extent of internal regional disparities, but also adds a temporal dimension by showing the trajectory of each country on these two dimensions between 1995 and For every country, each point corresponds to a year and shows the level of GDP per head level and the extent of regional disparities. Different patterns seem to co-exist. Let us first focus on the new Member States. In some countries, an increase in GDP per head is accompanied through time by an increase in the extent of regional disparities (Hongrie, Poland, ) (green arrows). However, there are countries (the Czech Republic and Romania) for which disparities increase, but no substantial increase in GDP per head takes place (orange arrows) In the first group, growth in the other regions, although not as high, is still substantial. For instance, in Slovakia, the growth rate over the ten years period in the capital city regions of Bratislavský kraj is 45% but the average growth rate in the other regions of the country is 22%. In the second group, growth in the peripherical regions is much lower, which eventually leads to poor growth performance at the national level. For instance, in Romania, the capital city regions of Bucureşti-Ilfov has grown by 77% but on average the other regions have only grown by 5%, GDP per head in Sud-Vest Oltenia even decreasing by 5%. 25

26 Figure 20: Inverted-U curve: GDP/head (EU-27=100), EU-27 NUTS-2 regions, St Dev of Log GDP/head Slovenská Republika Romania Magyarország Česká Republika Belgique-België Ireland 0.3 Italia Balgarija Slovenija United Kingdom Österreich Polska Portugal 0.2 Ellada España Nederland Sverige 0.1 Log GDP/head As for the EU-15, the pattern predicted by the inverted-u curve, whereby an increase in relative GDP per head is accompanied by a decrease in regional disparities, holds only in Ireland (only partly) and Spain (with very small changes). For a number of other countries, disparities have reduced but at the same time relative GDP per head has decreased. In fact, cyclical effects seems to be dominating by which periods of high (low) growth are generally associated to periods of increasing (decreasing) regional disparities Beta-convergence These observations underline the complex relationship between economic growth and regional disparities. For some countries, episodes of high growth seem to be associated with growing regional disparities. For others, regional disparities are increasing even in the absence of growth. The relationship between regional disparities and growth in economic theory An attempt of discovering regularities in the relation between disparities and growth has been made by the literature on beta-convergence. Beta-convergence refers to a process in which poor regions grow faster than rich ones and therefore catch-up on them. The concept of beta-convergence is directly related to neo-classical growth theory (Solow, 1956) whose one of the key assumptions is that factors of production, in particular capital, are subject to diminishing returns. Accordingly, the growth process should lead economies to a long run steady-state characterised by a rate of growth which depends only on the (exogenous) rates of technological progress and the growth of labour force. Diminishing returns also implie that the growth rate 26

27 of poor economies should be higher and their income and /or GDP per head levels should therefore catch up with those of rich economies. When all economies are assumed to converge towards the same steady-state (in terms of GDP per head), beta-convergence is said to be absolute. However, one can envisage that the steady-state depends on features specific to each economy, in which case convergence will still take place but not necessarily to the same long-run levels. This will be the case when GDP per head is supposed to depend on a series of determinants, such as for instance factor endowment or institutions, which can vary from one economy to an other even in the long-run. Beta-convergence is then said to be conditional. In any case, in the context of a beta-convergence process, growth contributes to convergence as poor regions grow faster than rich ones. However, some schools of thought inspired by the work of Myrdal (1957) argue that growth is in fact a spatially cumulative process, which is likely to increase disparities. Different strands of research, like theories of development (Rosenstein and Rodan 1943, Fleming 1955, Hirschman 1958), urban economics (Segal 1976, Henderson 1988), new economic geography (Krugman 1991, 1993, Fujita, Krugman and Venables 1999, Thisse 2000), and endogenous growth (Romer 1986), have in common the idea that there are local economies of scale and increasing rates of return. In such context, economic growth will tend to concentrate in a few places in a self-sustained, spatially selective and cumulative process 15. Under these assumptions, economic growth fosters regional divergence rather than convergence. But several of these theories also argue that, beyond a certain level, due to congestion or social effects, agglomeration can reduce efficiency, i.e. increasing return come to an end. Ultimately the theory does not offer strong general predictions, but rather offers tools to explore every specific case. At the same time, the extent of regional disparities could also impact on the global efficiency of an economy and therefore be a determinant of economic growth. A rich literature focuses on social/income inequalities and their impact on growth but it does not lead to univocal conclusions, some contributions suggesting a positive impact of inequalities on growth, others a negative one (see Aghion et al., 1999 for a extended survey). In addition, the extent to which these results can be used to highlight the role of regional disparities on global growth is limited. In particular, the link between social/income inequalities and regional disparities is not unidirectional and important social/income inequalities can co-exist with low regional disparities (see section 4 below). Testing the relationship between regional disparities and growth If economic theory does not offer firm general conclusions on the relationship between regional disparities and economic growth, clear-cut results are not offered by empirical analysis either. 15 See also Perroux (1955) concept of growth poles. 27

28 The seminal papers by Barro and Sala-i-Martin (1992) and Mankiw et al. (1992) have launched a huge empirical literature attempting to detect and measure the extent of beta-convergence in various contexts. In particular, number of beta-convergence analysis have been conducted on the EU regions. Some are based on absolute convergence frameworks. For instance, Cuadrado-Roura (2001) tests the hypothesis that regions with an initial level of GDP per head below the EU average have an above-average growth rate. Data cover EU-12 old Member States over the period 1977 to The main finding is that there is a convergence process but it is rather weak and very slow. The estimated convergence rate is less than 2 %, with a half-life of about 35 years. This type of result is also obtained by other analyses like for instance López-Baso (2003) on data covering the EU-12 old Member States over the period 1975 to A number of contributions have also examined the possibility that the convergence rate is not necessarily constant in time. For instance, Cuadrado- Roura (2001) or Martin (2001) find that the convergence speed decreases in time. However, other analyses find that the convergence rate decreases until the mid 1980 s and increases afterwards (see for instance Yin et al., 2003 or Geppert et al. 2005). Others frameworks allow for conditional convergence, notably by taking into account the different economic conditions of countries or groups of countries. Results differ from one analysis to the other. For instance, Fagerberg and Verspagen (1996), Cappelen et al. (2003) or Geppert et al. (2005) point to low or even to absence of a convergence process. On the contrary, Neven and Gouyette (1995) consider two different regimes for Northern and Southern European regions and find a significant convergence rate. Identically, Basile et al. (2005) find evidence of a significant convergence process. Martin (2001) distinguishes various groups of regions among which Objective 1 regions and different sub-periods. Convergence is detected for all groups and periods, with a convergence rate that decreases in time for all groups except for Objective 1 regions among which convergence rate increases. More recent contributions also introduce a spatial dimension in the formulation of the problem (see for instance Baumont et al., 2003 or Dall erba and Le Gallo, 2006). There are indeed reasons to believe that the omission of a space from the analysis of regional beta-convergence is likely to produce biased results. In particular, working with regional data imposes to address the specific issue of spatial dependence. The proximity and numerous linkages between (more or less) neighbouring regions imply that regional economic variables are likely to be interdependent which conflicts with the assumptions under which convergence equations can be validly estimated. Solution consists in introducing so-called spatial lags or crossregressive models (accounting for the fact that the growth rate of one region also depends on either the growth rate or the level of income of surrounding regions) or considering spatial error models (accounting for possible systematic measurement errors due to the spatial correlation of the variables 28