European regional convergence revisited: The role of space and the intangible assets

Transcription

1 European regional convergence revisited: The role of space and the intangible assets Jesús Peiró-Palomino Universitat Jaume I Abstract The number of contributions that have evaluated the convergence patterns across European regions using a wide variety of approaches is now substantial. However, if we focus on the most recent period ( ), the number of contributions shrinks dramatically, and those considering the role of the intangible assets in the enlarged European Union are entirely yet to come. This article focuses on the convergence patterns of income per capita in 6 European regions during the period. Following the distribution dynamics approach, several conditioning schemes are considered, including geography and a set of intangible assets. Opposite to studies focused on earlier periods, the results suggest an intense process of convergence, especially in the most recent years. In addition, while the conditioning factors introduced in the analysis played a remarkable role at the beginning of the analyzed period (995), facilitating convergence, their influence gradually decreases over time, indicating that regional convergence has obeyed to other forces in the latest years. Keywords: conditioning schemes, European regional convergence, income distribution dynamics, intangible assets JEL classification: C4; D30; O47; R Communications to: Jesús Peiró Palomino, Departament d Economia, Universitat Jaume I, Campus del Riu Sec, 07 Castelló de la Plana, Spain. Tel.: , fax: , Ô ÖÓ Ù º.

2 . Introduction Regional socioeconomic cohesion is one of the issues to which the European Union (EU) has historically devoted major attention. This subject was especially reinforced in The Treaty of the European Union (99), which claimed for a balanced development, as well as economic and social cohesion. The necessity for policies aiming at promoting both regional development and a reduction of the economic disparities across regions has remarkably increased after the latest enlargements of 004 and 007. Accordingly, the agenda of the so-called Cohesion Policy is articulated around thee main objectives namely, regional convergence, regional competitiveness and European territorial cooperation. However, the economic resources devoted to these policies are not equally distributed. In particular, the objective of regional convergence, aimed at reducing regional disparities by helping those regions whose income per capita is below the 75% of the EU average is especially important, given that it receives the 8.5% of the budget. At the same time, the issue of convergence has witnessed an intense debate in the economic literature. Different theories, concepts and measures of convergence, as well as a wide variety of statistical techniques have been proposed (see, for a excellent review, Islam, 003; Magrini, 004). Focusing on the European regional context, a remarkable number of studies have relied on the distribution dynamics approach, popularized by Danny Quah (see Quah, 993a,b, 996a,b,c, 997). This approach allows for evaluating how the entire crosssection distribution of income per capita evolves over time, both changes in its external shape and the intra-distribution dynamics. A list of the main contributions includes but is not restricted to Quah (996b), López-Bazo et al. (999), Cuadrado-Roura et al. (00), Le Gallo and Ertur (003), Le Gallo (004) and Fischer and Stumpner (008). From these studies we might draw a common result, namely the bimodality of the crosssection of the income distribution, which means that there are two differentiated groups of regions, or convergence clubs. There is, on the one hand, a group of relatively poor regions and, on the other hand, another group conformed by regions around the mean income. These two groups are particularly persistent over time. This result would be compatible with the pioneering findings by Quah (996b), who firstly suggested the existence of these two groups, the so-called twin peaks, which show the tendency of the economies to diverge rather than to converge. Most of these studies, however, are focused on periods ending at the beginning of the last decade, before the EU witnessed its biggest enlargement with twelve new accessions

3 in years 004 and 007. In addition, the new members are all former members of the Soviet bloc, and are now economies in transition with levels of income per capita far below the EU average. Therefore, the analysis of the most recent years might be of interest from the convergence point of view. This paper aims to contribute to the literature by focusing on the distribution dynamics of income per capita for a sample of 6 European regions (NUTS ) during the period , which has been possible thanks to the update of the Eurostat database. Additionally, despite the study of the convergence patterns in this period is per se, innovative, a major novelty is the attention devoted to the conditioning factors that might have affected the convergence process. I firstly analyze the role of the spatial spillovers, which has been proved to be a relevant factor for convergence in the European context (see Le Gallo, 004; Ertur et al., 006; Fischer and Stumpner, 008). However, evidence for the most recent years is still yet to come. In a further stage, I consider a set of intangible assets as conditioning factors including technological, human and social capital. The endogenous growth theory claims that innovation and learning processes accompanied by high levels of human capital are essential for development. The model proposed by Azariadis and Drazen (990) suggests that low levels of human capital might be responsible for a poverty trap. Other contributions, such as Acemoglu (996) and Redding (996), indicate that the complementarities between R&D and education are the likely determinants. In addition, these activities are reinforced by social interaction and face-to-face contact, which facilitate assimilation and knowledge transmission. This is actually the function of the other piece of the puzzle, namely social capital. Some recent contributions such as Akçomak and Ter Weel (009) and Barrutia and Echebarria (00) suggest that social capital is linked to innovation and others such as Dearmon and Grier (0) and Bjørsnskov (009) conclude that social capital is also positive for human capital formation. The remarkable importance of these intangible assets in order to promote regional efficiency is one of the reasons to be considered as strategic factors for the Europe 00 Strategy, which sets the bases for economic development on knowledge, innovation, efficiency and competitiveness. Recently, Dettori et al. (0) found positive links between intangible assets and efficiency, which translate into productivity improvements. Consequently, the different endowments of intangible assets might explain the differences in regional performance, as well as it might have affected the regional income convergence process. Unfortunately, the same updating process has made data for the Italian, Austrian and Hungarian regions only available from 000. Accordingly, these three countries are excluded from the analysis.

4 Despite these conditioning schemes are not completely innovative contributions such as Ezcurra et al. (005) and Mora (008) considered similar proposals the existing evidence confine the analysis to the late nineties and the samples do not include the new European members. Therefore, the contribution of this study to the literature is twofold. First, it expands previous studies by considering the period and a wider sample including the regions from countries that recently joined the EU. Second, apart from the spatial conditioning, it closely focuses on the role of three types of intangible assets, for which it provides an in-depth separate analysis. In this regard, it is especially innovative the inclusion of social capital as a conditioning factor. The beneficial effects of social capital are not exclusively confined to promote innovation and human capital, but it also positively influences economic development at both regional and country level (see, for instance Putnam, 993; Knack and Keefer, 997; Beugelsdijk and Van Schaik, 005). Yet, as indicated, its role for the European convergence process remains entirely unexplored. In this study I will proceed in two steps. I will first focus on the dynamics of the cross-section of income distribution without conditioning. This will allow to evaluate whether there is evidence of convergence, or whether the twin-peaks in the distribution of income persists for the most recent period. In a second step, I will deeply examine the implications of the different conditioning factors by computing nonparametric conditional stochastic densities. In doing so, I will follow Quah s (997) suggestions, as well as the visualization tools introduced by Hyndman et al. (996) which, despite providing particularly clear insights for the conditioning effects, have been used in many few occasions (see Fischer and Stumpner, 008; Poletti Laurini and Valls Pereira, 009). The reminder of the paper is structured as follows. Section provides both a general review of the convergence approaches and technical notes on distribution dynamics, which is actually the approach followed. Section 3 is devoted to present the sample and the data and Section 4 displays the results for the non-conditioned scenario as well as for the different conditioning schemes. Finally, Section 5 provides some concluding remarks. 3

5 . The empirical framework.. Competing methods for studying convergence The study of convergence has been addressed from different perspectives. One of these is the regression analysis, represented by Barro and Sala-i Martin (99) and Mankiw et al. (99). This approach is mainly focused on evaluating the existence of the so-called β- convergence and its findings are consistent with the neoclassical growth model (Durlauf, 996). There is evidence of β-convergence when a negative coefficient for β in the following equation is found: ln( y i,t ) = a+ β ln(y i,t )+µ i,t () where ln( y i,t ) is the growth of income between periods t and t, a is a constant term capturing technology, β ln(y i,t ) is the lagged income and µ i,t is the error term. β-convergence can be either conditional or unconditional, depending on whether or not the above equation includes control variables capturing particular conditions of the analyzed geographical areas. Conditional β-convergence means that economies are catching up their own steady state, conditioned by the particular conditions of each area. However, unconditional β-convergence is a much broader concept that implies that the poorer economies catch up with the richer ones. The regression approach, both for conditional and unconditional convergence has been examined by using cross-section approaches (Barro and Sala-i Martin, 99; Mankiw et al., 99), as well as time series (Lee et al., 997; Evans and Karras, 996), and panel data (Islam, 995; Evans, 998). Unfortunately, any of these approaches is free from criticism. Cross-section approaches might have been affected by omitted variable bias, since the constant a in Equation () might be reflecting other features apart from technology, such as climate or institutions (Durlauf and Johnson, 995). Time series analysis are limited to reduced form equations, with no attempt to link the estimation results with parameters of the growth model, and therefore limiting policy implications (Islam, 003). Finally, panel data specifications, despite addressing some of the drawbacks of both cross-section and time series approaches, are also exposed to some problems, namely, the likely existence of Equation () describes the basic framework of β-convergence without control variables. Common controls are the population growth and both physical and human capital investment (see Barro and Sala-i Martin (99) and Mankiw et al. (99)). 4

6 endogeneity bias (Caselli et al., 996), as well as both the small sample bias and the issue of short frequency (see Islam, 003). In general terms, as suggested by Evans (997) and Durlauf and Quah (999), the problems faced by the regression approach are all linked to the accomplishment of the restrictive parametric assumptions of the regression models to produce consistent estimators. In order to overcome the limitations of the regression approach, other techniques are focused on the cross-section distribution of income. Within this approach scholars have based their analysis on the study of either σ-convergence (see Lichtenberg, 994; Lee et al., 997), or the distribution dynamics developed by Dany Quah (see Quah, 993b, 996c, 997), whose findings are consistent with the endogenous growth theories (Durlauf, 996). While both perspectives are focused on the income distribution, they are not closely related. 3 Whereas the former is referred to a reduction in the dispersion of levels of income across economies i.e it only focuses on one feature of the distribution, namely the variance the latter evaluates how the entire shape of the distribution evolves over time, as well as it permits to identify the position of each economy within the distribution, i.e whether intradistribution mobility exits. On the contrary, one drawback is that the absence of a model prevent from studying the determinants of convergence. This limitation, however, has been overcome with the introduction of the so-called conditioning schemes (Quah, 997), which permits the distribution of income to be conditioned by a set of factors potentially affecting convergence. Therefore, the distribution dynamics approach might become a more attractive technique in order to study the convergence patterns, which has made the number of applications to increase remarkably, including those contributions mentioned in the Introduction... Technical notes on distribution dynamics Distribution dynamics methods focus on the study of the cross-section distribution of the variable of interest, in general income per capita. This approach is framed within the set of nonparametric techniques, which are particularly powerful to study the data structure. Nonparametric methods have the advantage of not requiring any preliminary assumptions on the distribution and are especially convenient for explanatory aims. They rely completely on the data and let them to speak by themselves, thus providing a better understand- 3 In fact, σ-convergence is actually more related to β-convergence. Islam (003) provides a detailed explanation on their relationship. 5

7 ing on how they behave. Following this approach, we find evidence of convergence when the probability mass in the distribution of income accumulates around a certain value. If the data are standardized, then we have convergence to the mean when the probability mass concentrates around the unity. Yet this nonparametric approach, which mainly rely on visual tools, has been criticised (see Scott, 99), since if the technique allows for any particular feature of the data to be unveiled, then the final graphical result might become difficult to be interpreted in case the number of observations is high. Nevertheless, this problem can be solved by smoothing the data. While there are different alternatives aimed at this purpose, the most popular for its good properties is kernel smoothing. The approach consists of estimating the following density function for income per capita at different periods t: ˆf t (y) = n ( ) nh K h y Y i i= where n is the number of regions, Y i is the income per capita (standardized), K is a kernel function and h is the bandwidth parameter. Finally,. is a measure of distance, in this case Euclidean distance. The kernel selected is the Gaussian kernel, although differences between competing alternatives are slight, 4 being much more important the selection of the bandwidth (h), which determines the amplitude of the bumps (Silverman, 986). () When h is too small it produces an excessive number of bumps (undersmoothing), which strongly difficulties the understanding of the data structure. On the contrary, in case h is too large, some of the features of the data might remain hidden (oversmoothing). Therefore, the selection of the appropriate bandwidth parameter becomes an essential point in kernel smoothing. The bandwidth was selected by using the method proposed by Sheather and Jones (99), based on the solve-the-equation plug-in approach, whose good performance has been tested in several studies (see Jones et al., 996). While the above analysis is a good strategy to study the cross-section of income in a given period (t), it does not permit to study the internal dynamics of the distribution, which actually shows if the economies remain stable in their relative positions or, on the contrary, they transit to a different stage of development, i.e another convergence club. This 4 Other alternatives are the triangular, the rectangular or the Epanechkinov kernel. In particular, the Gaussian kernel obeys to the expression K(x) = π exp ( ) ( x). 6

8 issue can be approached by means of stochastic kernels, which allow to examine the law of motion describing how the income distribution at time t, denoted by F t, converts into F t+s at period t+s. The distribution F t+s evolves according to the following n-th order Markov process: s : F t+s = M s F t (3) where M maps F s transition from period t to period t+s. The construction of M can be both discrete or continuous. In the discrete case, M is a transition probability matrix measuring the probability of one economy to move between a finite number of states, measured as intervals of income. Each element (i, j) in M is the probability that an economy in the state i moves to state j in the next period. However, Bulli (00), among others, pointed out that the long-run behavior of F s distribution is conditioned by the number of states, defined a priori by the researcher. Income level is a continuous variable, and therefore a continuous approach that considers an infinite number of states is a more appropriate strategy (Fischer and Stumpner, 008). In the continuous approach, M becomes a representation of a stochastic kernel describing the evolution of the cross-section distribution of income over time. Let us to denote Y i and M i the income of the region i in periods t and t+s (s > 0), respectively. Then, the associate cross-section distributions for all the regions in the sample can be denoted by f t (y) and f t+s (m) and its time evolution is expressed as: f t+s (m) = 0 v s (m y) f t (y)dy (4) where v s (m y) is the conditional density which shows the probability of a region to transit between two specific states, given its relative income at period t. This conditional density can be estimated following Rosenblatt s (969) proposal (see Hyndman et al., 996), which consists of computing the conditional density by dividing the bivariate density function by the implied marginal: ˆv s (m y) = ˆf t,t+s (y, m) ˆf t (y) (5) where 7

9 ˆf t,t+s (y, m) = n ( ) ( ) nh y h m K y Y i y K m M i z h i= y h m is the join density of (M, Y) and (6) ˆf t (y) = n ( ) nh y K y Y i y h i= y is the marginal density of Y, being h y and h m the bandwidth parameters. The conditional densities are computed using Hyndman et al. s (996) visualization tools, which provide different alternatives in order to display the densities. I select, on the one hand, a tree-dimensional plot that shows the stacked conditional densities for a grid of values of the conditioning variable, which is particularly useful to interpret the results of conditioning. On the other hand, I consider high density region plots (HDR), where high density areas are displayed and easily identified by shadowed areas of different intensity. In particular, the colored areas contain, from the darkest to the lightest the 50%, 90% and 99% of the probability mass, respectively. Both the stacked densities and the HDR plots actually map the transition from the original distribution of income to the conditioned one, constructed according to the level of the conditioning factor in each region. If the probability mass in the graphs concentrates along the main diagonal it means that the conditioning factor does not have any influence, since the relative position of the economies remains unaltered. However, if we observe that the probability mass accumulates toward the conditioned series, then the conditioning factor explains the intra-distributional dynamics in the income distribution. (7) 3. Sample and data The sample consists of 6 European regions at NUTS level, which is the level of disaggregation for which the Cohesion Policy objectives are addressed. Regional income per capita for the entire period is provided by Eurostat. 5 I consider income in Purchasing Parity Standards (PPS), in order to control for the different value of the currencies, especially before the introduction of the Euro. Regional data for the intangible assets are provided by different sources. In this case I do not consider data for the entire period, yet our strategy consists of taking data for a year as close as possible to the beginning of 5 See ØØÔ»» ÔÔº ÙÖÓ Ø Øº º ÙÖÓÔ º Ùº 8

10 the period. 6 This strategy will allow to evaluate how the initial regional level of intangible assets has conditioned the convergence profiles for the entire period. The first intangible asset considered is technological capital (TC). It is measured as the number of patent applications adhering to the Patent Cooperation Treaty (PTC). This ensures the economic value of the patents, since registering a patent in this international organism is expensive. The data come from the OECD REGPAT database, 7 and the indicator is constructed by taking the stock of patents over the total population in 998 (first year available). The data is regionalized according to the residence of the inventor. In case of more than one inventor, each region receives a proportional quota. The indicator of human capital (HC) is constructed by considering the percentage of population with ages comprised between 4 and 65 with tertiary education (ISCED 5 and 6) in 000, which is the first year for which data on human capital is provided. The data come from Eurostat. Finally, social capital (SC) is perhaps the most difficult asset to be measured, since this concept encompasses a mixture of different components (Bjørnskov, 006). In this paper, social capital is proxied by an indicator of interpersonal trust, which is by far the most used in the social capital literature (see, for instance, Zak and Knack, 00; Dearmon and Grier, 009; Bjørnskov, 0; Bjørnskov and Méon, 03). The indicator is constructed using data from the European Values Study (EVS) 8, which provides regional data on social values and beliefs. Interpersonal trust is measured by the question Generally speaking, would you say that most people can be trusted, or that you cannot be too careful in dealing with people?. Two possible answers are provided, namely: (i) most people can be trusted ; and (ii) can t be too careful. The trust index is constructed by considering the percentage of respondents who answered most people can be trusted in the wave of Table provides some descriptive statistics for the three conditioning variables. Despite the differences are noticeable for the three assets, technological capital is that showing the major disparities. 6 Unfortunately, the data for the intangible assets are not available for 995. For this reason our strategy consisted of taking the first year available. 7 See ØØÔ»»ÛÛÛºÓ ºÓÖ» Ø» ÒÒÓ»Ó Ô Ø ÒØ Ø º ØÑ 8 See ØØÔ»»ÛÛÛº ÙÖÓÔ ÒÚ ÐÙ Ø٠ݺ Ù. 9 In contrast with all the other variables in the analysis, aggregated at NUTS level, the indicator of social capital is constructed at NUTS level because this is the smallest level of disaggregation for some countries. Accordingly, all the regions belonging to the same NUTS area are supposed to hold identical level of social capital. 9

11 4. Results In this section the techniques described above are applied. The 4 year period ( ) is subdivided in two subperiods of seven years, taking as a reference the years 995, 00 and 009. For each of these three years I compute in a first stage the kernel density of income without conditioning to any other variable (univariate analysis). This simple analysis, whose results will be provided in Section 4., is a powerful tool to analyze how the distribution of income across Europe s regions has evolved along the period considered. In a further stage, I consider multiple conditioning schemes, explained in detail in Section 4.. This more comprehensive analysis will allow to evaluate with precision the role played by the different conditioning factors in the convergence process. 4.. Unconditioned analysis The result for the dynamics of the cross-section of relative income are provided in both Figures a) and b). Figure a) displays box plots. They show a remarkable reduction of the disparities, especially during the subperiod The size of the box, containing 50% of the probability mass has reduced substantially, and the two adjacent values i.e the horizontal lines at the bottom and the top of the box plots are closer in 009. In addition, the position of the median inside the box has changed along the period. In 995 the distribution was quite asymmetric, opposite to 009, year in which the median is in the middle of the box. These two changes summarize a process of convergence between the period 995 and 009, accelerated in the subperiod However, the outlying observations corresponding to overperformers have increased from three in 995 to nine in 009. In general terms, however, the box plots highlight a reduction of the income disparities across the European regions. Perhaps more informative is the information provided by Figure b), which shows kernel densities for the cross-section of income corresponding to the years 995, 00 and 009. The density for 995 reveals a marked bimodality. On the one hand the largest group of regions is located around. times the average income. On the other hand there is a great amount of probability mass below the times the average income. This bimodality in 995 is a well-known result, in line with previous contributions using the distribution dynamics approach (see, for instance Le Gallo, 004; Fischer and Stumpner, 008; Ezcurra, 00). The density for 00 shows that the bimodality persists, although it reduced sub- 0

12 stantially. However, as introduced in the preceding paragraph, the major process of convergence takes place in the period The density for 009 shows that the second mode, corresponding to the regions below the, has almost disappeared. In addition, the largest mode has moved to the left and the biggest density of probability is now around the mean. Therefore, the general conclusion of this first analysis is that the disparities across European regions have shrunk dramatically between 995 and 009. Whereas previous contributions such as Quah (996b), Le Gallo (004) and Fischer and Stumpner (008) concluded that the income distribution presented a marked bimodality, when the most recent period (00 009) is included the distribution evolves towards unimodality. The above analysis helps to the understanding of the evolution of the cross-section of income over time. However, the different economies might have modified their relative position in the distribution of income, and therefore the next step in the analysis will be the evaluation of the intra-distributional mobility. In order to do so, we compute stochastic kernels which, as previously introduced, shows the probabilities of transition for an infinite number of states. Thus, the stochastic kernel is computed by estimating the distribution of income at period t + s, conditioned on the income distribution at period t. The conditional probabilities are obtained by estimating the joint density at periods t and t+s and then dividing by the marginal distribution. In our particular case, t corresponds to year 995 and t+s to year 009. Figures a) and b) show the stacked densities and the HDR plot, respectively. Both plots are complementary tools in order to study the intra-distribution mobility. As previously introduced in Section., a great amount of probability mass around the main diagonal is synonym of persistence, which would be linked to the idea that the economies have remained in the same position over the studied period. Looking at Figures a) and b) the reader might notice this is not actually the case. Only a small group of rich economies and some economies around 0.7 times the average income have remained stable. However, those economies above the average in 995 have worsened their relative position in 009 and those below the average have improved (it might be especially well observed from Figure b)). This pattern of intra-distribution mobility, in which the poorer economies slightly improve and the richer ones worsen substantially supports the change in the shape of the kernel densities analyzed before. Our results differ from the the ones reached in previous contributions for the European regions following the distribution dynamics approach. These different results, however,

13 are explained by the period analyzed. The availability of data for the latest years have enabled us to extend contributions such as Ezcurra et al. (005) or Fischer and Stumpner (008), who found strong evidence of persistence for periods ending in 998 and 003, respectively. Our analysis has extended the time span until 009 and our findings suggest convergence, especially in the subperiod Factors conditioning the convergence process So far, the analysis has been focused on the study of both the evolution of the distribution of income and its intra-distribution mobility. This section goes further and evaluate the contribution of different variables to the convergence process. In particular, I focus on two different aspects. On the one hand, I introduce in the analysis the influence of the space i.e the physical neighbors whose importance has been stressed by Le Gallo and Ertur (003) and Le Gallo (004), or more recently by Fischer and Stumpner (008). On the other hand, other contributions such as Dettori et al. (0) have highlighted the importance of the intangible assets to promote productivity in the European context. Therefore, I have considered the contribution to convergence of the set of intangible assets described in Section 3. I have followed an analogous strategy to that followed in Section 4., when examining the intra-distribution mobility. Nevertheless, in this section the conditional distribution and the transition probabilities are not computed considering the relative position of each economy at period t. Instead, for each of the conditioning schemes, each economy s income will be relativized according to its level of the conditioning variable. Therefore, this strategy aims to compare each economy s income to its physical neighbors (for the case of the spatial conditioning scheme) and to its neighbors in terms of intangible assets, which would be those regions with similar values of the intangible asset considered in each case. In doing so, I have transformed the original series of data, where income in each economy is relativized to the sample average. In the transformed series the income in each region is relativized to the average of the neighbors excluding the region itself. Figure 3 displays the kernel densities for all the conditioned series of income. The results will be individually commented in the following subsections. 0 Figures a) and b) were also computed for the subperiods and The results for the first subperiod are aligned to the findings by Fischer and Stumpner (008). These results are not included in order to save space but can be provided upon request.

14 4... Spatial conditioning I first consider the effect of the physical neighbors in the convergence process. As commented on in the preceding paragraph, the original series of data have been transformed into a spatially conditioned series. In order to make the transformation, a spatial-weights matrix W is constructed. In doing so, I first calculated the distance between the region s capital cities. Then, following Le Gallo (004), a threshold corresponding to the first quartile of the distance is established. Accordingly, the spatial effects are supposed to take place only below this threshold and those regions far away that distance are replaced by zero in the matrix. After that, the rows in the matrix are normalized such that each row sums one, and therefore the influence of each neighbor is relative to the distance to which it is located. Finally, the income in each region is relativized according to the average income of its neighbors, excluding the region itself, and taking into account the varying influence of each neighbor given by the spatial-weights matrix. The kernel density for the spatially conditioned income is displayed by the doted red line in Figure 3 for the years 995, 00 and 009. The result is revealing, especially for 995. Compared to the original distribution, displayed by the black solid line, the mode below the times the average income has disappeared. Another mode around.4 times the average has emerged but, in general terms, the distribution is tighter than the original one, indicating that there is evidence of converge if each region is compared to its physical neighbors. In years 00 and 009 the distribution becomes even sharper, reinforcing the hypothesis of spatial convergence, although the small second mode around.4 times the average persists. A more precise picture of the neighboring effects is provided by Figure 4 a) and c). From these pictures it can be easily noticed a counter-clockwise shift reversal movement of the probability mass toward the conditioned series of income. When income data is relativized to the neighbors income, the poorest regions improve and the richest worsen. This result evidences that the spatial effects are important in the European context. As suggested by Fischer and Stumpner (008), such a result would imply that the probability of the poorer regions to move up is limited by the existence of spatial effects. I also study the dynamics of the spatially filtered data, analogously to the intra-distribution dynamics Another possibility would be to consider the centroid of each region. However, for some regions the centroid may correspond to an inhabited area. I therefore preferred considering the capital cities in order to capture centers of intense economic activity from where the spatial spillovers would be spread across space. For those regions with no official capital city I selected the most economically influential city. 3

15 analysis carried out in the preceding section. Figures 4 b) and d) provide the results. In line with the case of non-conditioned data, there is evidence of strong persistence for the richest regions. However, for the regions in the middle of the distribution the hypothesis of convergence holds. Therefore, when studying the dynamics of the neighbor-relative income we cannot find evidence supporting the hypothesis that the spatial effects are so strong to avoid economies to transit across income states Intangible assets conditioning I consider now the likely influence of the intangible assets. As in the previous analysis, the original series of data, relative to the global average, has been transformed into series relative to the neighbors average. However, in this section the neighbors are not the physical neighbors, yet they will be those regions with similar values of intangible assets. In order to establish which regions are similar in terms of this type of assets, I consider the quartiles of the intangible assets distributions in a year as close as possible to the beginning of the period (995). Therefore, those regions in the same quartile will be considered neighbors. Each region s income is therefore relativized according to the average of its neighbors, excluding the region itself. We start by focusing on the influence of technological capital. The doted green line in Figure 3 shows the kernel density for the income relative to the average of the technological capital neighbors for 995, 00 and 009. When the data is conditioned, i.e the original series of income are relativized according to the level technological capital of each region, we find evidence of convergence in the three years. The marked mode that the original distribution shows around times the average in 995 completely disappears in the technological capital relative data. In addition, the main mode is slightly below the average and another small mode around.5 times the average emerges, although it is admittedly small compared to the main one. This secondary mode smoothes in 00 and appears again in 009, but the main feature that can be drawn from the distribution is that it becomes progressively sharper, which is a signal of convergence. Figure 5 a) shows the transit from the original distribution of income to the technological capital conditioned. The stacked kernel densities are far away from the main diagonal and the probability mass tends to concentrate, as shown by the kernels in Figure 3. The high density region (HDR) plot displayed in Figure 5 c) clearly reflects this process. The regions below the average improve substantially and those regions far above the average moderate 4

16 their performance when their income is relativized to the technological capital neighbors. Figure 5 b) and d) show the intra-distributional dynamics for the conditioned data. There is evidence of persistence for some relatively rich regions, as well as some regions in the range of income between and 0.7 times the average, approximately. However, the general trend is a downward movement of those regions above the average, especially the regions between and times the average. Therefore, the main conclusions that can be drawn after conditioning for technological capital are, on the one hand, that technological capital is a factor heavily affecting regional disparities, especially in 995. On the other hand, the convergence process between 995 and 009 is similar when comparing both the unconditioned and the conditioned series, what means that technological capital has not seriously limited the process towards cohesion. We focus now on the influence of human capital. The dashed-dotted dark blue line in Figure 3 shows the kernel density for the income relative to the average of the human capital neighbors for 995, 00 and 009. Compared to the original series, one might observe that the second mode around times the average in 995 disappears in the conditioned series. However, the latter distribution presents more dispersion, especially if it is compared with both the spatial and the technological conditioned distributions. Nevertheless, for years 00 and 009 the distribution becomes tighter, indicating convergence. In 009 a small mode appears around.8 times average income, in line with the non-conditioned distribution. The effects of human capital conditioning are more visible in Figures 6 a) and c). Human capital has the major effects in the poorest regions (below 0.6 the average), which improve when their income is compared to the regions with similar levels of human capital. Nevertheless, for those regions between and times the average income, as well as for the richest regions, human capital seems not to be so relevant for convergence. The probability mass along the main diagonal, perfectly visible by the dark shaded area in Figure 6 c) would be corroborating the existence of persistence in the relative position, especially compared with the previous conditioning schemes, both spatial and technological capital. Figures 6 b) and d) provide information on the intra-distributional mobility of the human capital conditioned distribution. The figures suggest strong evidence of convergence except for a relatively small group of rich regions. Analogously to the previous analysis, the hypothesis of persistence does not hold for the conditioned data. Finally, we consider the influence of social capital. The dashed light blue line in Figures 5

17 3 displays the kernel distribution for the income relative to the neighbors in social capital for the years 995, 00 and 009. The density in 995 presents remarkable differences compared to the unconditioned distribution. As in the previous conditioned series, the mode below the times the average income has completely disappeared. Nevertheless, it emerges the mode around.5 times the average income that also appeared in both the original and the human capital conditioned series. In 00 this second mode is exacerbated but it is substantially smoothed in 009. In the latter year, the distribution of the social capital conditioned series is very similar to the ones for the original data and the human capital conditioned. In order to better analyze the role of social capital in the convergence process, Figure 7 a) and c) show the stacked densities and the HDR plots, respectively. In comparison to technological and human capital conditioning, the role of social capital seems to be more limited, especially for the regions between and times the average as well as the richest regions. However, for the group of poorest economies (those below times the average income), the conditioning process makes them to improve substantially. The intradistribution dynamics of the conditioned series of data, provided by Figures 7 b) and d), shows a similar pattern than the ones showed by the unconditioned analysis series as well as all the conditioning schemes. There is a catching up process especially leaded by a worsen of the relatively rich economies. 5. Concluding remarks The issue of regional convergence in the European regions has generated an intense academic debate in relatively recent times. This paper has assessed the dynamics of income per capita for a sample of 6 European regions. It has attempted to contribute to the literature in two different aspects. First, it has expanded the time span of previous contributions by considering the period Second, it has considered a set of conditioning factors of the convergence process including the spatial effects as well as a set of intangible assets. The study has been carried out the using conditional density estimation and the visualization tools introduced by Hyndman et al. (996), which have permitted to analyze with quite precision the effects of conditioning. The non-conditioned analysis has shown a remarkable process of convergence, especially reinforced in the period , although the convergence process already elucidated in the period Such a result is new for the European case and opposite to 6

18 previous contributions, which found strong evidence of polarization, i.e club convergence. Therefore, it seems that the most recent period has reshaped the map of the income distribution across Europe s regions, and the regions in 009 are much more similar than in 995 in terms of income. The results for the conditioning schemes reveal that the conditioning variables considered had a remarkable effect in 995. Both the spatial effects, i.e the neighboring spillovers, and the technological capital are the conditioning factors with major influence, although human capital and social capital also show a considerable effect. Once the series are conditioned, the two modes that characterize the original distribution of income tend to dilute. This process from bimodality to unimodality is highlighted by the stochastic kernels, which show the transit process from the original series to the conditioned ones. However, the influence of these conditioning factors seems to be less determinant in the most recent years. While the conditioned distributions of income are always sharper than the original ones, the differences tend to become smaller, especially in 009. Such a result might suggest that, according to the endogenous growth theory and previous findings for the European context, at the beginning of the period the spatial spillovers and the different endowments of intangible assets explained the existence of two convergence clubs. The conditioning factors considered still have some explanatory power in 009, but it is far more limited. Therefore, other forces seem to have lead convergence in the recent years. Summarizing, this study has provided evidence to further understanding of the convergence process in the European context. The results found contribute to the convergence debate, since the well-established characterization of the twin peaks in the income distribution does not hold for the most recent period. In addition, while in 995 the twin peaks could be explained by the spatial spillovers and the intangible assets relative endowments, in 009 the hypothesis of convergence holds without conditioning by any of these factors, which might suggest that other factors such as the process of European enlargement itself might be the responsible for the reduction of the disparities. Therefore, this fact leaves the door opened for further research initiatives to be developed in the immediate future, especially when even more recent regional data will be available. This will be essential for assessing if the convergence tendency remains unaltered during the economic crisis years. 7

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