The spatial distribution of income inequality. in the European Union

Transcription

1 The spatial distribution of income inequality in the European Union Roberto Ezcurra Department of Economics Universidad Pública de Navarra July 2005 Abstract This paper examines the distribution of income inequality among the regions of the European Union from 1993 to The results obtained show that the levels of inequality vary considerably between regions. Nevertheless, we have detected a high level of positive spatial dependence in the distribution under consideration. However, 57 per cent of the regions considered registered no statistically significant variations in the degree of income dispersion over time, though there was a reduction in 40 per cent of them. The empirical evidence presented indicates the existence of a process of regional convergence in terms of inequality during the period considered, due mainly to the evolution of regions whose initial levels of inequality were relatively high. Moreover, our analysis highlights the important roles played by the national component, activity and unemployment rates, GDP per capita, and the weight of the agricultural sector in total employment, in accounting for differences in the degree of income dispersion across the European regions. Key words: Inequality, income, regions, European Union. JEL code: O15, R11, R12. The author thanks Pedro Pascual, Juan Prieto-Rodríguez and Manuel Rapún for their helpful comments. Financial support from MCYT (Project BEC ) and the Fundación BBVA is gratefully acknowledged. Address for correspondence: Roberto Ezcurra, Department of Economics, Universidad Pública de Navarra, Campus de Arrosadia s/n Pamplona (Spain). roberto.ezcurra@unavarra.es.

2 1 Introduction For a number of reasons, the current distribution of income in the European Union is worthy of analysis. In recent years, the effect of increasing immigration and technological advances in social integration processes across Europe has begun to attract growing interest. There is also deep concern about the danger of certain sections of society being excluded from the structural change processes characterising today s societies. At the same time, during the past decade, traditional redistribution policies appear to have given way to alternative measures to promote equal opportunities. Furthermore, the emphasis placed by the Treaty of the European Union on achieving real convergence and economic and social cohesion between the various Member States can not be disassociated from observed changes in the evolution of the income distribution (European Commission, 2004). From a theoretical point of view, it should not be overlooked that the neoclassical growth model not only predicts a reduction in territorial per capita income and productivity disparities over time, it also forecasts long term convergence in the distribution of personal income (Benabou, 1996). Thus, once augmented with idiosyncratic shocks, the neoclassical growth model implies convergence in the whole distribution: countries or regions with the same fundamentals should tend towards the same invariant distribution of income and wealth. Hence, not only average levels, but also dispersion must converge. Despite its unquestionable significance, however, this issue has been largely ignored by the numerous works that have appeared in recent years exploring the validity of the neoclassical convergence hypothesis in the European setting (see Armstrong (2002), or Terrasi (2002) for a review of this literature). Coinciding with the launch of the European Community Household Panel (ECHP), 1

3 the last few years have seen the publication of several studies examining the degree of income dispersion in the Member States (Eurostat, 1997; Beblo and Knaus, 2001; Álvarez-García et al., 2004). So far, however, no study has tackled this issue from the regional perspective. To cover this gap, this paper undertakes an initial analysis of the distribution of inequality among the regions of the European Union, paying special attention to the role played in this context by the spatial dimension. It also assesses the contribution of several different factors in explaining income dispersion levels in the various regions considered. The ultimate aim is to achieve deeper understanding of the nature of observed regional disparities in the European Union, in order to draw some kind of inference that may be of use to regional policy-makers. One of the main innovations of this paper has to do with the methodological instruments used to accomplish our objectives. Thus, we have completed the usual approach in studies of this type, based mainly on the calculation of a variety of inequality measures, with the information provided by various spatial econometric techniques and a series of instruments made popular by Quah (1993, 1996a, 1997) for the examination of distribution dynamics in the context of the economic growth literature. The analysis presented in this paper is based on data drawn from the ECHP. The ECHP, which was constructed under Eurostat coordination, is the only homogeneous survey of its kind covering the whole of the European Union and able to supply regionally disaggregated data. This source has supplied us with data for the period 1993 to 2000 on income distribution in 71 European regions, most of them NUTS-1, in the fifteen countries that formed the Union prior to its enlargement in Interested readers will find more detailed information concerning the ECHP in the Appendix. The content of the paper is structured as follows. The section following this intro- 2

4 duction examines the level and evolution of income inequality in the European regions. The results of this are further enhanced in section 3 with an analysis of the dynamics of the distribution under study. In section 4 we examine the role played by a range of variables in explaining regional differences in the level of income dispersion within the European Union. Finally, in section 5, we present the main conclusions of the paper. 2 The spatial distribution of regional inequality In this section, we start by examining the degree and evolution of inequality in the income distribution within each of the European regions. Before attempting this analysis, however, we need to clarify various methodological issues. Thus, given the nature of our study, we have opted to take the household as our unit of reference. Nevertheless, since this will involve the comparison of households with different characteristics, we will require some kind of equivalence scale to enable us to adjust the income of each household according to its potential needs (Deaton and Muellbauer, 1980; Nelson, 1988; Atkinson et al., 1995). Following the usual practice in the recent literature, it was decided for the purposes of this paper to employ the equivalence scale proposed by Coulter et al. (1992a,b). This means that we take households to differ only in the number of members, enabling us to reduce the equivalence scale to a single parameter. The advantage of this is that it makes it easier to interpret scale economies within households, thus enabling us to consider several different situations in our analysis. Formally, we can define the equivalent income of each household, y [θ] h, as follows: y [θ] h = y h N θ h (1) 3

5 where y h and N h respectively stand for total net income and number of members in each household. Likewise, θ [0, 1] is a parameter that captures the role played by scale economies in the analysis. Note that θ = 0 implies infinite economies of scale, since y [0] h = y h. If, on the other hand, θ = 1, this assumes no economies of scale, in which case all calculations are made in per capita terms, since y [1] h = y h N h. In order to test the sensitivity of the results to the equivalence scale selected, we have considered different values of the θ parameter in all subsequent calculations. Specifically, θ = 0, 0.5, 1. Keeping these issues in mind, we have calculated the Gini indices for each of the 71 regions considered, using the information provided by the ECHP 1. To test the statistical significance of observed changes in regional inequality over time, we have used bootstrap inference (Mills and Zandvakili, 1997). With this approach, the sampling distribution of the Gini index is estimated by multiple random resampling with replacement from the data set. [INSERT TABLE 1] The results are summarised in Table 1. Though certain exceptions can be observed, there is clearly a strong similarity between the various regional rankings generated for different values of the θ parameter. In order to confirm this impression, we have calculated the degree of statistical association between the different regional rankings shown in Table 1, all of which have significant Spearman correlation coefficients above 0.90 (Table A2). 1 To check the robustness of subsequent analysis to the inequality measure used to capture the degree of income dispersion within each region, we have also calculated for each region the two entropy indices proposed by Theil (1967). The results, which are very similar to those yielded by the Gini index, are omitted here for the sake of brevity, but are available from the authors upon request. 4

6 The analysis carried out also reveals that, on average, 57 per cent of the regions analysed did not register statistically significant variations in their Gini indices over time. This is not surprising, given the shortness of the sample period. Nevertheless, income inequality across households decreased in 40 per cent of the regions considered. It is interesting to note that this is, in fact, the case of a fair proportion of the less developed regions of the Union (the whole of Portugal, Voreia Ellada, Kentriki Ellada, Sicilia, Abruzzo-Molise, Brandenburg, Sachsen, etc.). Since these were the priority areas of the European regional policy over the period analysed, the empirical evidence presented in Table 1 suggests the possible presence of some potential, though as yet unknown, impact of the Structural Funds on personal income distribution. This would help us to qualify the findings of various papers that question the capacity of European regional policy to prepare the ground for long-term sustainable development (Boldrin and Canova, 2001; Rodríguez-Pose and Fratesi, 2004). Finally, the above considerations notwithstanding, the analysis reveals that the degree of dispersion in the distribution of income increased in only 3 per cent of the regions included in the study. In any event, it is worth noting that the percentages mentioned in this paragraph vary only slightly for different values of the θ parameter. To complete these results, Figures 1, 2 and 3 illustrate the spatial distribution of inequality in the European setting for the different equivalence scales contemplated in our analysis, taking the average Gini index values during the period for which ECHP data are available as the reference. As can be observed, the degree of inequality varies considerably between regions. Thus, for example, with θ = 0.5, the regional Gini indices range on average between for Thüringen and for the Açores, which is almost 100 per cent variation. Nevertheless, close observation of the various Figures 5

7 reveals the existence of an apparent spatial non-stationarity in the distribution of interest. Indeed, the presence in this context of some level of spatial heterogeneity is quite evident. In particular, the most egalitarian income distributions in the European Union are to be found in central and northern European regions, while the regions with the highest inequality levels are mainly those of Ireland, the United Kingdom and part of the southern periphery. This initial examination, therefore, suggests that the variable under analysis is not randomly distributed in space. There appears, on the contrary, to be a positive spatial relationship between adjacent areas, in so far as neighbouring regions tend to register similar degrees of income dispersion. [INSERT FIGURE 1] [INSERT FIGURE 2] [INSERT FIGURE 3] Some caution is recommended when interpreting the data shown in Figures 1, 2 and 3, since the conclusions that might be drawn from them are highly sensitive to the number of intervals used to represent the variable of interest. Bearing this in mind, and in order to formally verify the existence of spatial autocorrelation in the regional distribution of inequality in the European Union, we now proceed by calculating Moran s I and Geary s c global tests (Cliff and Ord, 1973, 1981; Haining, 1990) 2. 2 The expressions used to calculate the various spatial dependence statistics employed in this section are included in the Appendix, along with some remarks relating to their interpretation. 6

8 Nevertheless, before performing these tests it is necessary to define a spatial weight matrix W to capture the strength of the interdependence between each pair of regions i and j. A first option is to use the concept of first order contiguity, according to which w ij = 1 if regions i and j are physically adjacent and 0 otherwise (López-Bazo et al., 1999; Rey and Montouri, 1999). However, the use of this type of matrix may raise problems in the European context, given that the presence of islands means that W will include rows and columns containing only zeros. This implies that the observations in question are not considered in the analysis, which in turn has an effect on the interpretation of the results obtained. For this reason, the spatial weight matrix used in this paper takes into account interactions beyond adjacent regions. In particular, following Le Gallo and Ertur (2003), we consider a row-standardised matrix W based on the ten nearest neighbours, calculated using the geographical distance between the corresponding regional centroids (Pace and Barry, 1997; Pinkse and Slade, 1998) 3. Table 2 summarises the results of the two global spatial autocorrelation tests mentioned earlier. It can be seen that the standardised Moran s I (Geary s c) statistics are positive (negative) and statistically significant 4. This is clear evidence of the existence of a pattern of positive spatial association, which is consistent with the initial impression drawn from Figures 1, 2 and 3. We can therefore conclude that, in the European setting, spatially adjacent regions tend on the whole to exhibit a similar degree of income dispersion. To further confirm this finding, we also constructed the Moran scatterplots for the distribution under consideration. These are graphs on which the standardised 3 To check the robustness of our findings, we use various different spatial weight matrices. In particular, we construct two additional matrices W based on the five and fifteen nearest neighbours, which in all cases yield results similar to those discussed below. 4 The results of the various Wald s tests ensure the normality of the distributions under analysis. We therefore based the significance of the Moran s I and Geary s c statistics on the normality assumption. For more detail on this issue, see Cliff and Ord (1973, 1981) or Upton and Fingleton (1985). 7

9 values of the variable to be analysed are plotted on the horizontal axis and the spatial lag of the same variable on the vertical axis. Thus, the four quadrants correspond to different types of spatial association. As can be seen from Figures A1, A2 and A3, in all cases, there is a high concentration of regions in quadrants I and III. This confirms that the European Union is characterised by the presence of spatial clusters of regions with similar inequality levels, while there are relatively few cases in which a region registers a degree of income dispersion markedly different from the average of its neighbours. [INSERT TABLE 2] It is important to keep in mind, however, that both Moran s I and Geary s c are calculated on a global basis for the whole of the sample. Hence, we do not know whether, irrespective of the overall dependence pattern, there exist clusters of regions in which the concentration of high or low inequality levels is significantly greater than would be predicted in a homogeneous spatial distribution. It is also impossible with these tests to check for the presence of groupings of regions with dissimilar values of the variable under analysis, that is, regions with inequality levels significantly different from their neighbours. To overcome these shortcomings, we calculated the local Moran s I, I i (Anselin, 1995). As in the global tests considered earlier, the usual practice in the case of I i is to assume a normal asymptotic distribution when calculating the corresponding significance levels. Anselin (1995), however, has shown that the first and second order moments used in the standardisation of the I i statistic are obtained under the null hypothesis of no global spatial autocorrelation. This contrasts with the information yielded by Table 2, however. Therefore, following the proposal of Anselin (1995), we have calculated the 8

10 corresponding pseudo-significance levels by means of an empirical distribution derived from 10,000 random permutations. Figures 4, 5 and 6 show the significant regional groupings detected, and indicate whether or not they concentrate similar inequality values. Figures A4, A5 and A6, meanwhile, report the significance level for each region. It can be seen that the conclusions to be drawn from this analysis are consistent with the results obtained earlier. Thus, the various regional clusters derived from the calculation of I i are mostly made up of regions with similar inequality levels. In particular, it is possible to observe how the concentrations of low income dispersion levels are situated in Finland, Sweden, Denmark, the Netherlands, Germany and the North of Italy, while the groupings of regions characterised by high inequality levels are located in Ireland, the United Kingdom, Portugal, Spain and Greece. [INSERT FIGURE 4] [INSERT FIGURE 5] [INSERT FIGURE 6] In any event, the empirical evidence presented reveals that the results differ to some extent depending on the equivalence scale adopted in each case. Specifically, for θ = 1, the I i statistics for the continental area of Portugal and most of Spain, are not statistically significant. 9

11 Furthermore, all other considerations notwithstanding, it is worth noting that comparison of Figures 4, 5 and 6 with the regional distribution of per capita GDP within the European Union suggests the possible existence of an inverse relationship between this variable and income inequality levels in the European setting. This would be consistent with the predictions of the Kuznets curve (Kuznets, 1955) once a critical level of development is reached (see Barro (2000) for a review of this literature). A degree of caution must be taken when interpreting this result, however, since there are a number of exceptions to be borne in mind. The most striking of these concerns the regions of former East Germany, which, despite their relatively low level of development, are characterised by having some of the most egalitarian income distributions in the whole of the European Union. This finding will be discussed in greater detail later in the paper, however. 3 The dynamics of regional inequality To complete the results obtained so far, in this section, we will carry out a detailed exploration of the dynamics of the distribution of inequality in the European regions. For an analysis of this type, however, it is necessary to use a sample of regions for which we have dispersion income data for each year of the study period. We therefore decided to reduce the time frame to the period , which in turn obliged us to omit Luxembourg, Austria, Finland and Sweden from the analysis, thus reducing the number of regions analysed to 65. It should be noted, however, that this modification of the geographical horizon considered in the previous section does not constitute a major limitation to the analysis, since, in 1993, the four countries in question represented only 6 per cent of the population covered by the original sample. 10

12 Table 3 shows the average and standard deviation of the distribution of inequality among the regions of the European Union during the period , for the various equivalence scales contemplated. The results obtained in all cases reveal a reduction in the distribution average during the six years considered, which in turn is consistent with the information shown in Table 1. The analysis also shows that there was a process of regional convergence in terms of inequality within the European Union over the period considered. In fact, the standard deviation of the distribution under study decreased by between 8 and 13 per cent, depending on the value adopted by the θ parameter 5. [INSERT TABLE 3] It is widely known that the various measures calculated in Table 3 fail to capture with accuracy a series of potentially interesting characteristics relating to the distribution of inequality among the regions of the European Union, since they do not consider, for example, the possible existence of homogeneous clusters of regions with income dispersion levels distinct from the rest. This approach also fails to take into account the fact that the various regions may modify their relative positions in terms of inequality over time, thus ignoring intradistribution mobility 6. In light of these circumstances, we will now address these particular issues using a variety of instruments proposed by Quah (1993; 1996a,b; 1997) within the framework of the economic growth literature. Figures 7, 8 and 9 show the density functions for the regional distribution of inequality for 1993 and The Gini index values (multiplied by 100) are plotted on 5 It is worth noting that we considered again using bootstrap inference in this context to construct the corresponding confidence intervals. However, the analysis performed earlier reveals the presence of spatial autocorrelation in the regional distribution of income inequality in the European setting. The existence of such dependence violates the random sampling assumption at the heart of the bootstrap methodology. For more detail on this point, see Rey (2001) or Brülhart and Traeger (2005). 6 In fact, these criticisms can be extended to the approach adopted by Benabou (1996) and Ravallion (2003) to test for the possibility of convergence in inequality in an international framework. 11

13 the horizontal axes, while the vertical axes indicate the associated density. The estimations are based on calculations using Gaussian kernel functions and the smoothing parameter has been selected in all cases following Silverman (1986, p. 47). [INSERT FIGURE 7] [INSERT FIGURE 8] [INSERT FIGURE 9] The results reveal certain differences in the shape of the densities during the study period, showing that the initial situation did not remain stable over time. Indeed, in all cases considered, there was a shift of the density towards the left during the period examined, while the distance between the two ends narrowed. These results support the conclusions drawn from the information summarised in Table 3. Likewise, whereas the various functions estimated for 1993 are unimodal, with most of the density concentrated around the one mode, the situation changes in subsequent years for θ = 0 and θ = 0.5. To gain further insight into this issue, therefore, and given that the non-parametric approach does not reveal the exact magnitude of changes in the degree of polarisation over time, we next explore the issue using the methodology developed by Esteban and Ray (1994). Thus we are able to study the evolution of the polarisation of regional inequality in the European Union between 1993 and 1998 for the two-group case (bipolarisation). 12

14 Esteban and Ray (1994) use the following axiomatically derived index to measure the degree of polarisation of a distribution f partitioned into a number of exogenously defined groups: P ER (f, α) = m m j=1 k=1 p 1+α j p k µ j µ k (2) where, in the context of this paper, µ j and p j are, respectively, the average inequality index and the population share of group j. Likewise, α [1, 1.6] is a parameter that captures the sensitivity of P ER to polarisation. As can be seen from expression (2), the degree of polarisation in the distribution under consideration depends on the distance between the various groups in terms of average inequality, and on the differences in their relative sizes. In order to establish the dividing line between the various groups, following Esteban et al. (1999), we have used the algorithm proposed by Davies and Shorrocks (1989). In this way, it is possible to obtain the optimal partition of the original distribution that minimises the level of within-group dispersion. Additionally, in our analysis we have considered different values of the sensitivity to polarisation parameter, namely, α = 1, 1.6. [INSERT TABLE 4] Table 4 shows that the results vary according to the equivalence scale applied in each case, which confirms the findings in Figures 7, 8 and 9. Thus, over the sample period, for θ = 0 and θ = 0.5, there was a slight increase in the degree of polarisation of the distribution. Indeed, the values of P ER increased by 4 and 2 per cent respectively. For θ = 1, however, there was a reduction in bipolarisation between 1993 and In fact, 13

15 the value of P ER decreased by 5 per cent in this case. In any event, it is interesting to note that these results hold whatever the value adopted by the parameter α. Nevertheless, the analysis carried out so far is based exclusively on the information obtained from a series of cross-sectional observations of the distribution under consideration and, thus, does not take into account the fact that the various economies may, over time, modify their relative positions in terms of inequality. For this reason, and in order to complete the results obtained so far, we now examine the intradistribution dynamics for the period Most of the papers that have addressed this issue in the context of the literature devoted to the study of regional disparities in per capita GDP or productivity have done so on the basis of the information provided by discrete transition matrices, obtained by dividing the distribution into a series of exhaustive and mutually exclusive classes (see Quah (1996b) or López-Bazo et al. (1999) for examples applied to the European case). This approach presents a problem, however, since the results it yields are sensitive to the way in which the observed distribution is divided up. In fact, since there is no procedure for determining the optimum number of classes in each case, the researcher s decision is inevitably arbitrary (Cheshire and Magrini, 2000; Johnson, 2000). However, when describing the law of motion governing the evolution of the distribution of interest as a Markovian stochastic process, it is important to remember that arbitrary discretisation has the undesired effect of removing the Markov property (Bartholomew, 1981; Bulli, 2001). In order to overcome this problem, Quah (1996a, 1997) suggests substituting the transition matrix with a stochastic kernel to capture the probabilities of transition between a hypothetically infinite number of classes, reducing their size infinitesimally. The 14

16 stochastic kernel can be obtained by estimating the density function of the distribution for a given period, t + k, conditioned on the values corresponding to a previous period, t. Specifically, the joint density function at moments t and t + k is estimated and then divided by the implicit marginal distribution, in order to obtain the corresponding conditional probabilities. Figures 10, 11 and 12 show the stochastic kernels estimated for the regional distribution of inequality in the European context for a six-year period (t = 1993 and t + k = 1998), varying the equivalence scale used as a reference. Gaussian kernel functions are again used, while the smoothing parameter is selected following Silverman (1986, p. 86). Each of these three-dimensional graphs can be intuitively interpreted as a transition matrix with an infinite number of classes, that informs about the probabilities associated with each pair of values in the first and last years of the sample period. In other words, the stochastic kernel indicates, in a way analogous to that of a discrete transition matrix, the probability distribution of 1998 inequality for regions with a given inequality level in Thus, if the probability mass is concentrated along the main diagonal, the intradistribution dynamics are characterised by a high level of persistence in the relative positions of the regions over time. If, on the other hand, the density is located on the diagonal opposite the main diagonal, this would indicate that regions situated at each end of the distribution switch their relative positions over time. Finally, the probability mass could, in theory, accumulate parallel to the t axis. This would indicate that regional inequality had converged towards a given level of income dispersion over the sample period. To aid interpretation of the graphs, we have also included in Figures 10, 11 and 12 the corresponding contour plots, on which the lines connect points at the same height on the three-dimensional kernel. 15

17 [INSERT FIGURE 10] [INSERT FIGURE 11] [INSERT FIGURE 12] As can be seen from Figures 10, 11 and 12, most of the the probability mass is concentrated along the main diagonal. This can be taken as evidence of low mobility in the regional distribution of inequality over the period The European regions, therefore, appear on the whole to maintain their relative positions over the six years considered, whatever equivalence scale is adopted. Nevertheless, the analysis also reveals the existence of a slight skew at the upper end of the distribution. This highlights the important role played in explaining the convergence process observed during the study period by the dynamics of those regions with relatively high inequality levels in The explanatory factors of regional inequality This section aims to examine the role of a series of variables in accounting for the dynamics of the distribution of regional inequality in the European setting. For this, we will use various instruments, proposed by Quah (1996a, 1997) and presented earlier in this article, which will enable us to assess to what extent the distribution of interest changes when we introduce into the analysis factors other than the degree of income dispersion registered in the regions considered. 16

18 Thus, ever since the pioneer work by Molle et al. (1980), authors dealing with spatial disparities in per capita GDP or aggregate productivity within the European setting have repeatedly emphasised the importance of country-specific factors in regional growth processes (Quah, 1996b; Rodríguez-Pose, 1999; Ezcurra et al., 2005). Taking this into account, it is interesting to consider the potential role of the national component in accounting for the income inequality observed in the European regions. Leaving aside any effects deriving from political-administrative factors, we have also considered, in this context, the potential impact of a set of regional labour market variables on the level of dispersion in the distribution of personal income (Bound and Johnson, 1992; Blau and Kahn, 1996; Acemoglu, 2002). In particular, we have analysed the role played by regional activity rates and unemployment levels. The influence of these two variables has been highlighted in the literature that explores the relationship between income inequality and the labour market (Nolan, 1986; Topel, 1994; Partridge et al., 1996; Penha, 2004). We have also investigated the relevance of the development level of the sample regions in this context. It is worth noting that this issue has been widely addressed in the literature over the last decades, coinciding with the publication of the seminal paper by Kuznets (Kuznets, 1955), in which the relationship between income inequality and the level of per capita income is described by an inverted-u (Ahluwalia, 1976a,b; Papanek and Kyn, 1986; Anand and Kanbur, 1993; Li et al., 1998; Barro, 2000). It is worth remembering, in connection with this, that one of the basic elements in the argument used to explain the inverted U-shaped pattern of the conventional Kuznets curve is the fall in agricultural employment that takes place with the progression of the development processes (Robinson, 1976). For this reason, we have also analysed to what extent 17

19 European regions with high shares of agricultural employment present differentiated inequality levels. Finally, we have studied the influence of regional size on the observed differences in income dispersion levels across the European regions, in order to gain a first impression of the extent to which our findings are influenced by the level of territorial disaggregation used in this paper. One of the first options when aiming to assess the relevance of the above mentioned factors in this context is to regress the Gini index values calculated for each region on the different variables considered. It is important to realise, however, that an analysis of this type yields information about the effects of the different explanatory variables on the level of inequality of a single representative economy, with no reference at all to their influence on the distribution as a whole (Quah, 1996a). For this reason, following the strategy proposed by Quah (1996b, 1997), we decided to construct six conditioned distributions. Thus, to assess the role played by the national component, we have normalised the Gini index for each region according to average inequality in the country to which it belongs, calculated without including the region in question. Additionally, we have used the information provided by the Cambridge Econometrics database to classify the various regions by deciles, taking as a reference their activity and unemployment rates, per capita GDP, the agricultural share in total employment, and population over the whole of the sample period. This enables us to generate five new conditioned distributions, in this case normalising the Gini index of each region according to the average inequality of those regions in the same decile. The various conditioned distributions defined above can be intuitively interpreted as that part of the original distribution that remains unexplained by the set of variables 18

20 considered. For a better understanding of this idea, let us imagine a situation in which the country effect, for example, had no influence whatsoever on the evolution of the distribution under analysis, so that regions where the inequality level were lower (higher) than the European average, would continue in the same position relative to the national average. In this hypothetical setting, the original distribution would coincide with the conditioned distribution. If, on the other hand, the national component were to play a relevant role, it would be reasonable to expect less (more) egalitarian regions to register a Gini index value close to the average of the group to which they belong, defined this time in political-administrative terms. To overcome the limitations associated with the use of discrete transition matrices in this context, we have opted in this paper to use a non-parametric approach based on the estimation of stochastic kernels and contour plots. This type of methodology has been used, for example, by Fingleton and López-Bazo (2003) and Ezcurra et al. (2005) to investigate the causes of territorial imbalances in development across the European Union. Before going on to discuss our findings, however, it might be worth clarifying a few points relating to the interpretation of stochastic kernels and contour plots in this context. Within this framework, these instruments provide information concerning the probabilities of transition between the initial distribution and the conditioned distribution, and not between two moments of time as in the previous case. Thus, if the factors considered do not contribute to explain the distribution dynamics, the probability mass should appear concentrated around the main diagonal. If, on the other hand, the selected variables play a decisive role in the evolution of the distribution analysed, the density will tend to accumulate parallel to the axis corresponding to the initial distribution, and around the average. 19

21 Figures 13, 14, 15, 16, 17 and 18 present the results obtained when this methodology is used to examine the role played by the above-mentioned factors in explaining the level of income inequality registered within the European regions over the period considered 7. As can be checked, the various graphs show that, with the sole exception of regional size, the selected variables contribute to explaining the dynamics of the distribution under analysis. [ INSERT FIGURE 13] [ INSERT FIGURE 14] [INSERT FIGURE 15] [INSERT FIGURE 16] [INSERT FIGURE 17] [INSERT FIGURE 18] Thus, on the one hand, the empirical evidence presented reveals the importance of the national component in this context. This enables us qualify to some extent the 7 Figures 13, 14, 15, 16, 17 and 18 are based on θ = 0.5. It should be noted, however, that the results vary little for different equivalence scales. The estimations for θ = 0 and θ = 1 are omitted for the sake of brevity, but are available from the authors upon request. 20

22 conclusions drawn from the analysis of the spatial distribution of income inequality carried out in section 2 of this article. This result suggests, in particular, that some of the spatial dependence detected earlier might be due to the so-called country effect. The impact of the country-effect may in turn be related to factors such as the presence of rigid national education and innovation systems in the European setting. In any event, the importance of activity and (to a lesser degree) employment rates means that we cannot ignore the role played in this context by region-specific elements, relating to cultural, demographic or institutional features. At the same time, the results show that the regions at the upper end of the distribution tend to share similar per capita GDP values. The regional development degree, meanwhile, proves to be less crucial in explaining the dynamics of the distribution in areas with low or intermediate levels of income dispersion. This is, in any event, consistent with the empirical evidence presented earlier. Finally, it can be seen how the agricultural share in total employment is particularly relevant in regions with high levels of inequality, a large proportion of these being located in the southern periphery of the European Union. All other considerations notwithstanding, the results obtained in this section have important implications for economic policy-makers with regard to the choice of instruments to reduce the level of income inequality within the European regions. 5 Conclusions In this paper we have examined the regional distribution of income inequality in the European Union for the period , by means of the information provided by various methodological instruments. Specifically, we have completed the usual ap- 21

23 proach in studies of this type, based mainly on the calculation of a variety of inequality measures, with the information provided by various spatial econometric techniques and a series of instruments made popular by Quah (1993, 1996a, 1997) for the examination of distribution dynamics in the context of the economic growth literature. The analysis carried out shows that inequality levels vary considerably across regions. Nevertheless, we have detected the presence of positive spatial dependence in regional inequality levels. This means that, in the European setting, the variable considered in our analysis is not randomly distributed in space, and therefore neighbouring regions tend to register similar degrees of income dispersion. More specifically, the most egalitarian income distributions are found in the Scandinavian countries, the Netherlands, Germany, Austria and the North of Italy. On the contrary, the regions with the highest degrees of income dispersion are located mainly in Ireland, the United Kingdom, Portugal, Spain and Greece. In any event, it is worth mentioning that, in 57 per cent of the regions included in the analysis, no statistically significant changes in inequality were detected for the sample period, while in approximately 40 per cent of them, the level of income dispersion was seen to decrease. The empirical evidence presented in this respect indicates the presence of a process of regional convergence in terms of inequality within the European Union between 1993 and This was mainly due to the reduction in the degree of income dispersion that took place in regions that began the period with relatively high inequality levels. At the same time, variations in the polarisation of the distribution depend decisively on the equivalence scale applied in each case. In any event, due to the shortness of the sample period, caution is recommended when interpreting these results, which could be sensitive to the economic cycle. 22

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