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Testing convergence of European regions: A semiparametric approach
Economic Modelling 28 (2011) 1202–1210
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Economic Modelling j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / e c m o d
Testing convergence of European regions: A semiparametric approach Théophile T. Azomahou a, Jalal El ouardighi b, Phu Nguyen-Van c,⁎, Thi Kim Cuong Pham b a b c
UNU-MERIT and Maastricht University, Keizer Karelplein 19, 6211 TC Maastricht, The Netherlands BETA, Université de Strasbourg, 61 avenue de la Forêt Noire, F-67085 Strasbourg Cedex, France BETA-CNRS, Université de Strasbourg, 61 avenue de la Forêt Noire, F-67085 Strasbourg Cedex, France
a r t i c l e
i n f o
Article history: Accepted 21 December 2010 JEL classification: C14 O40 O52
a b s t r a c t We provide a reappraisal of income convergence across European regions over the last two decades by using a semiparametric partially linear model to approximate the relationship between the average growth rate of GDP per capita and the initial GDP per capita. Estimation results point out both country heterogeneity and nonlinearity in the convergence process. The findings suggest that low income regions, in particular those from new adhesion countries, diverge while medium income regions converge and that there is no evidence of convergence for high income regions. © 2011 Elsevier B.V. All rights reserved.
Keywords: Convergence Heterogeneity Non-linearity Kernel estimator European regions
1. Introduction The convergence hypothesis according to which poorer economies catch up wealthier ones has been studied in both exogenous and endogenous growth models setting. In the exogenous model setting, which assumes that persistent growth is primarily driven by exogenous technological process, capital accumulation is the source of (conditional) convergence. Endogenous growth models on the other hand emphasize a broad measure of physical and human capital as the main engines of growth, and the convergence or lack thereof, results from the differences in technology levels across economies and increasing returns to capital (Romer, 1986). Starting with Baumol (1986), these hypotheses have been extensively tested empirically. Most of the theoretical and empirical works are summarized in, e.g., Barro and Sala-í-Martin (1995), Temple (1999), De la Fuente (1997, 2002) and Islam (2003). This study aims to provide a reappraisal of the convergence process at the regional level in the European Union. We emphasize the notions of heterogeneity and non-linearity, that is, the convergence/ divergence differs according to initial regional conditions.1 We estimate the relationship between the average growth rate of GDP per capita and the initial GDP per capita using a semiparametric
⁎ Corresponding author. Tel.: +33 3 68 85 20 39; fax: +33 3 68 85 20 71. E-mail address: [email protected] (P. Nguyen-Van). 1 This encompasses the usual concept of conditional convergence. 0264-9993/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.econmod.2010.12.010
partially linear model. Country dummies are included in the model to capture the influence of national characteristics on regional growth and to describe differences in the steady-state at the country level. As noted by Armstrong (1995), when country dummies are included, the convergence coefficient measures the within-country convergence. We also provide a measure to control for regressor endogeneity in order to establish robust estimations. We use two datasets to investigate the convergence among European regions. The first dataset includes only 157 regions from 9 European Union countries, and for which the data (series on population and GDP) is available over a long period, 1990–2005. Other socioeconomic factors (investment, research and development, communication, human capital, trade, transaction costs, etc.) that could also be considered are not easily collected at regional level. The second dataset contains a large sample of regions from 20 EU countries, new adhesion countries included. Hence, 255 regions are observed, but only in a shorter period, from 1998 to 2007. Including such regions would be interesting in terms of EU integration and policy making. The main results that emerge from this study are the following. First, the shape of the nonparametric relationship shows non-linearity in growth, and suggests that low-income regions (in particular those from new adhesion countries) diverge and that only medium-income regions converge while there is no evidence of convergence for high income regions. Secondly, we also find that regional convergence depends on national contexts. Finally, compared to the parametric approximation, test results suggest that the semiparametric model gives a sufficiently accurate description of the data.
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The findings of the paper may lead to some policy implications for regional development. Indeed, the European economic integration is traditionally thought of as being beneficial for its regions in terms of higher allocation efficiency and increased competition in particular for low-income regions. However, there is a risk that economic integration in Europe will be followed by an increase in inequalities among regions. Important efforts were put forth to increase the attractiveness of these regions, in particular by developing public infrastructure. As a result, the question of European integration goes hand in hand with regional convergence policies.2 In this respect, European structural funds aim to attenuate development disparities among European regions and to correct imbalances which may result from the development of the single market and the single currency.3 However, the efficiency of these regional policies seems to be compromised.4 Our results underline the risk of persistence in inequality mentioned above. The remainder of the paper is organized as follows. Section 2 presents key concepts and literature background with regard to both the regional convergence and the role of non-linearity and heterogeneity. The econometric specifications are presented in Section 3. Section 4 describes the data. Estimation results are discussed in Section 5. Section 6 concludes the study.
2. Background Our study is related to many earlier contributions on income convergence. Two measures of convergence conceptually different are σ-convergence and β-convergence (see, e.g., Barro and Sala-í-Martin, 1995). The first concept describes how the distribution of cross-section incomes evolves over time, whereas the second emphasizes the income mobility. β-convergence may be unconditional, which implies that all the economies have the same level of steady state, or conditional on auxiliary variables, allows each economy to converge to its own steady state5. In this section, we do not have the intention to review the broad theoretical as well as empirical literature on convergence (see, e.g., De la Fuente, 1997; Islam, 2003). We mainly point out some salient empirical facts concerning both regional convergence and the roles of nonlinearity and heterogeneity, which constitute the main focus of the paper. Research over the last two decades has considerably improved our understanding of convergence and has raised several conflicting issues as well; see e.g., Bernard and Durlauf (1996) and Caselli et al. (1996). At regional level, Dewhurst and Mutis-Gaitan (1995) use a dataset of 63 European regions between 1981 and 1991 and find that the national growth rate has a significant influence on the speed of regional convergence. Sala-í-Martin (1996) analyses the regional convergence hypothesis by using regional data for the United States (48 states for the 1880–1990 period), Japan (47 prefectures, 1955– 1990), Europe (90 regions, 1950–1990), and Canada (10 provinces, 1961–1991). Relying on a parametric specification, the author finds that regions tend to converge at a speed of approximately 2% per year.6 Garofalo and Yamarik (2002) use a new US dataset covering the 1977–1996 period and confirm the result established by Barro and Sala-í-Martin (1991).
2 See, e.g., Kutan and Yigit (2007) who recognize the beneficial effect of integration from a long-term perspective. 3 Note that these funds, which amount to a third of the total expenditure, constitute the second largest part of the budget of the European Union after the Common Agricultural Policy. 4 This is consistent with the findings of Boldrin and Canova (2001, 2003). 5 Levine and Renelt (1992) list no less than fifteen auxiliary variables used in the literature on growth. The authors conclude that the convergence relationship keeps its robustness with respect to investment and initial income, while other variables lose their significance (e.g., population growth, monetary and fiscal variables, etc.). 6 The result is also in favour of the σ-convergence hypothesis because the interregional distribution of income in all countries has shrunk over time.
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Some recent studies have analyzed the spatial effects (spatial autocorrelation and spatial heterogeneity) on convergence. For example, Baumont et al. (2006) use a sample of 138 European regions over the 1980–1995 period to estimate the spatial spillover effect. Their findings show that the average growth rate of GDP per capita of a given region is positively affected by the average growth rate of its neighboring regions. Battisti and Di Vaio (2008) propose a model where the convergence parameters capture both structural heterogeneity and the spatial effects, i.e. the choice of regional growth models is determined in an endogenous manner which avoids an arbitrary selection of the North–South regions or centre-periphery. Their results point out that the spatial effects prevail. In particular the data shows a slow speed of convergence or an absence of convergence. Arbia et al. (2010) investigate the spatial effects due to both institutions and geography for European regions. They underline the dominant role of institutions with respect to geographical factors. Moreover, the authors show a positive effect of geo-institutional proximity on spatial dependence of regional output per worker on the one hand, and on the convergence speed on the other hand. Our paper does not deal with the spatial effects. However, it would be interesting to extent our modelling to address this issue in a future work. It has been shown that the catching-up of poor regions in Europe is slow, and sometimes even non-existent, since the variation of income amounts to approximately 2% per year. This figure is recognized as a ‘stylized fact’ (see e.g., Barro and Sala-í-Martin (1991), Barro and Sala-íMartin (1995), Sala-í-Martin (1996), Armstrong (1995) and Neven and Gouyette (1995)). However, at this rate, 35 years would be necessary to cut by half the initial inequalities of income per capita. Moreover, Martin (1997)) points out that, since the beginning of 1980s, the speed of convergence among European regions decreased and fell to 1.3% between 1978 and 1992. This deceleration could be related to an absence of convergence between poor and rich regions in the same country, whereas convergence between countries continues (see European Commission, 1996). According to Neven and Gouyette (1995), a process of divergence is in progress across European regions. It appears that in less prosperous countries, only the richest regions have benefited from a process of convergence with rich countries. Quah (1996b) finds that among the poorest countries in Europe, Spain and Portugal, which have a faster aggregated growth than Greece, experienced a stronger increase in regional inequalities. More generally, this type of evolution supports the idea that an arbitration between global growth and regional equity could exist. Mora et al. (2005) detect a pattern of convergence clubs for the European regions over the period 1985–2000. Ramajo et al. (2008) find that regions in the European Union cohesion-fund countries (Ireland, Greece, Portugal and Spain) converge separately from the rest of regions of the EU. In particular, Canova (2004) tests for convergence clubs using a predicted density approach. This methodology enables determination of the number of groups, locate the break points as well as estimate the parameters of each group. The results show little evidence of income convergence of European regions. Poorer regions converge to their steady state faster than rich ones, and tend to cluster around a weak pole of attraction (below the average).7 The common feature to the above studies is the assumption usually made in the convergence test hypothesis, that is, all economies have a common linear specification. The assumption of a common linear specification, inherent in the Solow growth model with a single steady state, is not held in models with multiple steady states as stressed in the theoretical study of Azariadis and Drazen (1990). Furthermore, several authors show that results based on cross-section data are biased because they ignore unobserved national/regional specific effects. A direct way to overcome the drawback related to cross-section data bias is to include auxiliary variables and country/regional specific 7 Moreover, significant dispersion of the steady state around each pole of attraction suggests that clustering is more prevalent than convergence (see Canova, 2004).
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effects. For the case of regional data, the choice of auxiliary variables is limited because of data unavailability. Generally, the distinction of conditional convergence from unconditional convergence consists in testing the specificity common to regions of the same country by incorporating country dummies or variables which reflect the differences in national or local structure. An alternative way is to use panel data models (see, e.g., Islam, 1995). One weakness associated to this methodology is that the convergence speed resulting from its use appears higher. The other as noted by Nerlove (1999), is that the estimation results based on panel data are very sensitive to the estimation method (level or difference regressions, fixed or random effects, etc.). Two other lines of research have emerged in the literature. The first one analyses the distribution dynamics of economies. Quah (1996a,c,d, 1997) finds evidence of polarization and stratification in the growth process. Bianchi (1997)) states that the determinants of the steady state vary across economies. Using parametric panel data models (102 countries between 1960 and 1989), Lee et al. (1997) show that estimates of ?β-convergence traditionally defined in the literature are subject to substantial biases in a stochastic Solow growth model. They also show that steady-state growth rates differ significantly across countries. The second line of research involves the investigation of heterogeneity and non-linearity in the growth process (see, e.g., Durlauf and Johnson, 1995; Liu and Stengos, 1999; Durlauf, 2000, 2001; and Durlauf et al., 2001).8 These studies generally find the existence of non-linearity and heterogeneity at the country level. In particular, Durlauf and Johnson (1995) use a sample of 96 countries between 1960 and 1985 and regression tree techniques. They reject the linear model in favour of a multiple regime alternative in which different economies obey different linear models when grouped according to initial conditions. Moreover, Liu and Stengos (1999) question the single linear regime. They employ a semiparametric additive partially linear model on a data of 86 countries between 1960 and 1990 and find the existence of heterogeneity or non-linearity in the relationship between initial output and schooling level, and growth rate. These results confirm the presence of multiple growth regimes which is also corroborated by Huang (2005). By using the framework of distribution dynamics and a threshold regression model, Fiaschi and Lavezzi (2007) show that income growth is nonlinear. In a nutshell, the majority of the studies relate to the national level. Hereafter, we provide a reappraisal of income convergence by focusing on heterogeneity and non-linearity at the regional level. 3. Econometric specification We propose a semiparametric partially linear model to investigate the convergence process on European regions over the 1990–2005 period. The model is given by gi = m x0;i + Zi′ γ + εi ;
i = 1; ⋯; n:
ð1Þ
We assume for the moment that ε is an independent random error with E(εi|x0,i, Zi) = 0 and V(εi|x0,i, Zi)=σ 2(x0,i, Zi); gi is the average growth rate of region i over the period of study; x0,i is the logarithm of GDP per capita in 1990; m (.) is an unspecified function of x0,i that may be non-linear; Zi is a K × 1 vector of other variables that enter linearly in Eq. (1). We specify Z as a set of country dummies, which account for country heterogeneity or differences in the steady state. This heterogeneity may represent economic determinants and other factors (legislation, various subsidies for regional development purposes, etc.) that are common to a group of regions of the same country.
8
See also Phillips and Sul (2007) for a survey.
We implement the procedure proposed by Robinson (1988) sketched as follows to estimate Eq. (1). Taking the expectation of Eq. (1) with respect to x0, i yields E gi jx0;i = m x0;i + E Zi jx0;i ′ γ + E εi jx0;i :
ð2Þ
Then, taking the difference between Eqs. (1) and (2), we obtain h i gi −E gi jxi;0 = Zi −E Zi jxi;0 ′ γ + εi −E εi jx0;i :
ð3Þ
ˆ Then, We can estimate γ by Ordinary Least Squares, denoted as γ. an estimator of m(x0, i) is given by E
h i ˆ x0;i : gi −Zi′γˆ jx0;i = m
ð4Þ
ˆ x0;i are estimated In relations (3) and (4), E(Zi|x0, i), E(gi|x0, i), and m nonparametrically by the kernel method. We use both the local constant kernel (known also as the Nadaraya–Watson estimator) and local linear kernel estimators. Moreover, this method requires the choice of a kernel function and a smoothing parameter. For our calculations, we use the Gaussian function and several choices of smoothing parameter (the rule of thumb and the cross-validation method, see Silverman, 1986; Pagan and Ullah, 1999). As the results given by these two estimators are very similar, we only discuss the results based on the Nadaraya–Watson method. It should be also noted that the semiparametric specification (1) mixes continuous (x0, i) and discrete (Zi) regressors. Thanks to Bierens (1987), we know that when the regressors in Eq. (1) are a mix of continuous and discrete, if we apply the kernel method as if all regressors were continuous, we still get consistent estimates. The only thing we should be careful about is the convergence rate and the asymptotic distribution of the estimator of E (Zi|x0, i). We also use an alternative specification which accounts for the endogeneity of x0. Statistically, it corresponds to assumptions E(εi|Zi)=0 and E(εi|x0, i)≠0. This model can be estimated by the approach of Newey et al. (1999). Let us assume that there exists a set of instruments Wi such that E(εi|Wi)=0 and x0;i = W i′η + νi
ð5Þ
where E(νi|Wi) = 0. Following Newey et al. (1999), we also assume that E(εi|Wi, νi) = ρνi, which implies that εi = ρνi + ζi. Hence, the model becomes gi = m x0;i + Zi′ γ + ρνi + ζi ;
ð6Þ
where ζi is the new standard error term. Estimation of this model is similar to that of the model without endogeneity as previously described but now with an additional linear component. As νi is not observed, it will be replaced by the residuals computed from the ordinary least squares regression of (5). 4. Data description The dataset is built from the Eurostat-Regio database. For reasons of homogeneity, we use regions at level NUTS-2 for all countries.9 The resulting data provides us with two sets of regions. The first one contains 157 regions covering 9 EU countries (see Table 1). The data is available over the 1990–2005 period which can be considered long enough to be appropriate to study the long-term convergence. The second dataset contains a larger number of regions from 20 EU 9 The nomenclature in European regions, Nomenclature of Territorial Units for Statistics (NUTS), is a hierarchical classification established by EUROSTAT. This classification starts from country level information (NUTS-0) to community level (NUTS-5).
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Table 1 Descriptive statistics, 157 EU regions, 1990–2005. Dispersion of GDPc
GDP per capita (in PPS) Country
Number of regions
1990a
2005a
Growth rate (%)b
1990
2005
Growth rate (%)d
Belgium Germany Spain France Greece Italy The Netherlands Portugal United Kingdom All countries Min. 1st quartile Median 3rd quartile Max.
11 30 17 22 13 20 12 5 27 157
14,781 17,115 11,347 14,419 8,240 14,596 14,416 8,776 13,521 13,803 5,901 11,563 13,691 15,722 27,856
25,922 28,429 22,532 23,492 17,851 23,636 26,796 17,528 24,640 24,313 13,007 20,688 23,587 26,962 49,985
3.77 3.34 4.61 3.26 5.15 3.23 4.11 4.62 3.97 3.84 5.27 3.88 3.36 3.60 3.90
0.233 0.189 0.201 0.150 0.168 0.269 0.134 0.194 0.105 0.273
0.219 0.220 0.168 0.141 0.165 0.259 0.165 0.183 0.137 0.226
− 0.42 1.02 − 1.23 − 0.44 − 0.12 − 0.25 1.39 − 0.42 1.81 − 1.25
a b c d
For each country, figures are averages computed on values of GDP per capita (in Purchasing Power Standard, PPS) of its regions. Annual growth rate of GDP per capita over the 1990–2005 period. The figures reported are the standard deviation of log(GDP per capita). Annual growth rate of the standard deviation of log(GDP per capita) over the 1990–2005 period.
Table 2 Descriptive statistics, 255 EU regions, 1998–2007. Dispersion of GDPc
GDP per capita (in PPS) a
Country
Number of regions
1998
Belgium Bulgaria Czech Republic Germany Ireland Greece Spain France Italy Hungary The Netherlands Austria Poland Portugal Romania Slovenia Slovak Republic Finland Sweden United Kingdom All countries Min. 1st quartile Median 3rd quartile Max.
11 6 8 40 2 13 19 22 21 7 12 9 16 7 8 2 4 5 8 35 255
20,100 4,467 12,050 19,720 18,600 13,900 15,832 17,741 19,857 8,557 20,817 21,478 7,569 12,643 4713 13,550 10,350 19,200 20,050 18,857 16,448 3,600 12,900 16,700 19,850 51,100
a b c d
2007
a
27,600 8,483 20,150 27,673 33,050 19,446 25,732 24,236 25,081 13,743 31,742 29,633 12,406 19,386 10,888 22,400 20,300 28,640 29,325 27,069 23,947 6,400 18,700 24,200 28,450 83,200
Growth rate (%) 3.54 6.71 5.47 3.88 6.30 3.66 5.45 3.46 2.64 5.01 4.70 3.63 5.41 4.78 8.76 5.54 7.10 4.53 4.24 3.93 4.40 6.39 4.13 4.12 4.00 5.42
b
1998
2007
Growth rate (%)d
0.311 0.186 0.273 0.277 0.317 0.172 0.209 0.141 0.275 0.282 0.163 0.229 0.180 0.218 0.222 0.237 0.476 0.246 0.154 0.241 0.464
0.312 0.330 0.336 0.222 0.365 0.202 0.183 0.142 0.260 0.351 0.157 0.205 0.216 0.208 0.378 0.268 0.558 0.202 0.144 0.259 0.400
0.04 6.35 2.30 − 2.44 1.58 1.74 − 1.49 0.13 − 0.06 2.43 − 0.39 − 1.24 2.04 − 0.51 5.91 1.38 1.76 − 2.15 − 0.69 0.81 − 1.67
For each country, figures are averages computed on values of GDP per capita (in Purchasing Power Standard, PPS) of its regions. Annual growth rate of GDP per capita over the 1998–2007 period. The figures reported are the standard deviation of log(GDP per capita). Annual growth rate of the standard deviation of log(GDP per capita) over the 1998–2007 period.
countries, new adhesion countries included (see Table 2). This sample is composed of 255 regions at NUTS-2, which covers a shorter period, from 1998 to 2007. Table 1 presents the descriptive statistics on regional GDP per capita in PPS (Purchasing Power Standards) for each country.10 We 10 Expressing GDP in purchasing power standards makes it possible to eliminate the price levels differences between economies. However, a precaution must be mentioned. It might be more relevant to take into account the inflation rate when GDP is compared across different years. Unfortunately, neither regional GDP deflator nor regional conversion factors (i.e., purchasing power parities) are available (see for a more discussion Eurostat regional yearbook publications). Notwithstanding, the use of GDP in PPS will not affect noticeably our results owing to the fact that the estimated specifications take account of national heterogeneity.
observe that disparities between regions around the European average are strong. Indeed, the highest level of GDP per capita is approximately 4.7 times the lowest level in 1990 (see the bottom of Table 1). The gap slightly narrowed in 2005. If we look at the situation in the middle 50% of the data, the IQR (interquartile range, i.e., third quartile minus first quartile) exhibits a greater spread of the levels of GDP per capita from the centre of the distribution. In a nutshell, the highest levels of GDP per capita are observed in Germany, and the lowest ones in Greece and Portugal. The evolution of GDP per capita between 1990 and 2005 shows an average growth rate of 3.84%. Growth is particularly important in Greek, Portuguese and Spanish regions. In contrast, Italian and French regions are characterized by the lowest growth, 3.23% and 3.26% on
density
0.00008
density
0.00004 0.00000
10000
20000
30000
40000
0e+00 1e−05 2e−05 3e−05 4e−05 5e−05 6e−05 7e−05
T.T. Azomahou et al. / Economic Modelling 28 (2011) 1202–1210 0.00012
1206
50000
20000
GDP per capita
40000
60000
80000
GDP per capita
Fig. 1. Kernel estimation of the distribution of GDP per capita. Left: dataset with 157 EU regions, GDP per capita in 1990 (solid) and 2005 (dashed). Right: dataset with 255 EU regions (new adhesion countries included), GDP per capita in 1998 (solid) and 2007 (dashed).
Table 3 Parametric and semiparametric estimations, 157 EU regions, 1990–2005. (1)
(2)
(3)
Variable
Coef.
t-stat.
Coef.
t-stat.
Coef.
t-stat.
Intercept log(initial GDP)(a) Belgium Germany Greece Spain France Italy The Netherlands Portugal ρ
0.070⁎ ⁎ −0.0034 −0.0017 −0.0051⁎ ⁎ 0.0093⁎ ⁎ 0.0053⁎ ⁎ −0.0065⁎ ⁎ −0.0068⁎ ⁎
3.662 −1.709 −1.059 −4.069 5.117 3.676 −4.992 −5.131 0.915 1.930 –
– – −0.0021 −0.0058⁎ ⁎ 0.0061⁎ 0.0045⁎ −0.0066⁎ ⁎ −0.0076⁎ ⁎
– – −1.362 −4.729 3.13 3.169 −5.263 −5.806 0.871 0.795 –
– – −0.0015 −0.0046⁎ ⁎ 0.0038⁎ 0.0035⁎ ⁎ −0.0057⁎ ⁎ −0.0071⁎ ⁎
– – −0.951 −3.701 2.334 2.615 −4.563 −5.378 1.154 −0.062 5.101
0.0014 0.0029 –
0.0013 0.0019 –
0.0017 0.0001 0.0054♮
Notes. Specification: (1) parametric model, (2) semiparametric model, and (3) semiparametric model with endogeneity of x0. The dependent variable is the average growth rate of GDP per capita. (a) ln(initial GDP) is the logarithmic value of GDP per capita in 1990. Estimations are performed on a sample of 157 European regions for the period 1990–2005. ⁎Significance at the 5% level. ⁎⁎Significance at the 1% level. ♮The coefficient is significant at the standard 1% level and as regards the t-stat value compared to the wild bootstrap (1000 replications) 95% t-stat critical values (− 2.433 ; 3.178).
average respectively. To illustrate the concept of convergence, we also report in Table 1 the standard deviations of the logarithm of GDP per capita in 1990 and 2005. On the one hand, we note that the dispersion of GDP per capita tends to be reduced over time, with a decrease of 1.25% on average. The reduction of inequalities is particularly strong between the Spanish regions (−1.23%). On the other hand, we observe an increase in the dispersionof the GDP per capita between the regions in the United Kingdom (1.81%), in the Netherlands (1.39%) and in Germany (1.02%). These findings suggest the presence of some country heterogeneity. Table 2 presents the situation of the 255 regions sample. As we can see, the disparities across regions around the European average are more pronounced. The GDP mean level of Austrian regions is 4.8 times higher than that of Bulgarian regions, and 4.6 times than that of Romanian regions. The situation remains almost the same in 2007, that is, the level of Irish regions is 3.9 times the level of Bulgarian regions. As shown at the bottom of Table 2, the spread of the GDP per capita levels from the centre of distribution is more marked by including regions of the EU new members. The inspection of the regional per capita GDP growth rates over the 1998–2007 period also shows the sharp contrasts. The strong growth of the GDP levels of the Romanian, Slovak and Bulgarian regions was accompanied by an aggravation of income inequalities among regions of the same country (see the last column of Table 2). However, one can note a convergence process between all regions of the widened European Union, i.e., a decrease of income inequality by 1.67% on average.
The same patterns can be revealed in Fig. 1 which displays two almost uni-modal distributions of regional GDP per capita in 1990 and 2005, and 1998 and 2007, respectively. These distributions contain a non negligible upper tail corresponding to high income regions. They also describe a global increase of income over time. However, income per capita in final dates has a lower mode and a higher dispersion than that of income per capita in initial dates. 5. Estimation results Table 3 reports estimation results of the models with and without controlling for endogeneity of initial regional GDP per capita (x0) for the first dataset, i.e. 157 regions from 9 EU countries. Table 4 presents the corresponding results for the second dataset, i.e. 255 regions from 20 EU countries (new adhesion countries included).11 For the model with endogeneity of regional GDP per capita at the initial date (x0), we use the national GDP per capita at the same date (computed from regional GDP per capita observed in 1990 and 1998 for the first and second dataset, respectively) as an instrument for x0.12 The Spearman correlation coefficient indicates a value equal to 0.633 for the first dataset and 0.054 for the second dataset. Moreover,
11
Estimation codes are written in R and available from the authors upon request. It would be interesting in a further study to address this issue by using information on other variables if their availability allows it. 12
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Table 4 Parametric and semiparametric estimations, 255 EU regions, 1998–2007. (1) Variable
(2)
Coef. 0.0640⁎ ⁎
Intercept log(initial GDP)(a) Belgium Bulgaria Czech Republic Germany Ireland Greece Spain France Italy Hungary The Netherlands Austria Poland Portugal Romania Slovenia Slovak Republic Finland Sweden ρ
−0.0029 −0.0034 −0.0209⁎ ⁎ 0.0125⁎ ⁎ 0.0003 0.0021⁎ ⁎ −0.0032 0.0132⁎ ⁎ −0.0043 −0.0115⁎ ⁎ 0.0074 0.0072⁎ −0.0023 0.0107⁎ ⁎ 0.0065 0.0395⁎ ⁎ 0.0136⁎ 0.0265⁎ ⁎ 0.0055 0.0030 –
(3)
t-stat.
Coef.
t-stat.
Coef.
t-stat.
2.816 −1.263 −1.155 4.204 3.617 −0.172 3.478 −1.152 5.434 −1.896 −4.942 1.883 2.556 −0.717 3.260 1.802 8.610 2.206 5.650 1.363 0.917 –
– – −0.0037 −0.0048⁎ ⁎ 0.0117⁎ −0.0001⁎ 0.0201⁎ ⁎
– – −1.364 6.983 3.135 −0.058 3.560 −1.904 5.327 −1.697 −5.209 1.326 3.172 −0.480 2.176 1.445 10.070 2.202 4.941 1.446 1.565 –
– – −0.0032 0.0048⁎ ⁎ 0.0119⁎ ⁎
– – −1.196 6.996 3.191 −0.159 3.543 −1.706 5.243 −1.873 −5.378 1.348 3.238 −0.313 2.106 1.474 10.031 2.278 4.971 1.548 1.662 2.071
−0.0052 0.0121⁎ ⁎ −0.0036 −0.0112⁎ ⁎ 0.0057 0.0084⁎ ⁎ −0.0014 0.0089⁎ 0.0051 0.0652⁎ ⁎ 0.0126⁎ 0.0024⁎ ⁎ 0.0054 0.0048 –
−0.0003 0.0200⁎ ⁎ −0.0046 0.0120⁎ ⁎ −0.0040 −0.0121⁎ ⁎ 0.0057 0.0085⁎ ⁎ −0.0009 0.0086⁎ 0.0052 0.0647⁎ ⁎ 0.0129⁎ 0.0242⁎ ⁎ 0.0058 0.0051 0.0063♮
Notes. Specification: (1) parametric model, (2) semiparametric model, and (3) semiparametric model with endogeneity of x0. The dependent variable is the average growth rate of GDP per capita. (a) ln(initial GDP) is the logarithmic value of GDP per capita in 1998. Estimations are performed on a sample of 255 European regions for the period 1998–2007. ⁎Significance at the 5% level. ⁎ ⁎Significance at the 1% level. ♮The coefficient is significant at the standard 5% level, but not significant as regards the t-stat value compared to the wild bootstrap (1000 replications) 95% t-stat critical values (− 2.608 ; 3.141).
Fig. 2 presents the correlation between regional GDP per capita and national GDP per capita at the initial dates for both datasets. These features motivate the use of national GDP per capita as an instrument for regional GDP per capita, especially for the first dataset. For comparison purposes, we also include estimation results for the standard parametric model often used in the convergence literature, where all parameters enter linearly: gi = δx0;i + Zi′ γ + εi :
ð7Þ
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ˆ h ðx0 Þ with the corresponding Fig. 3 presents the estimated function m 95% pointwise confidence interval for datasets with 157 and 255 European regions, respectively. We also plot the parametric counterpart, δˆ x0 . The difference between the parametric and the semiparametric models is salient. We observe that an important part of the
parametric curve lies outside the nonparametric confidence interval in both cases. To compare the parametric and the semiparametric models without the endogeneity of x0 (the two specifications are nested), we use the test statistic proposed by Li and Wang (1998). The null hypothesis corresponds to the parametric specification, and the alternative is the semiparametric one. The test is one-sided and its statistic asymptotically follows a standard normal distribution. Li and Wang (1998) find that the normal approximation does not perform well for small or moderate samples and suggest the use of a bootstrap. As the sample sizes of our two datasets are 157 and 255 respectively, we use the bootstrap version for the first dataset and the asymptotic version for the second one. For the 157 regions dataset, the computed value of the test statistic is 1.065, much higher than the bootstrap critical values at the 5% level (0.339). For the dataset with 255 EU regions, the statistic is 1.944 which is higher than the asymptotic critical value at the 5% level (1.654). These test
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Fig. 2. Correlation between regional and national GDP per capita. The solid line represents the OLS regression, the dashed lines are the corresponding 95% confidence bands. Left: dataset with 157 EU regions. Right: dataset with 255 EU regions (new adhesion countries included).
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ˆ h ðx0 Þ, Fig. 3. Nonparametric estimation of m(x0) without accounting for endogeneity of x0, where x0 is log of initial regional GDP per capita. The solid curve represents the estimate m ˆ 0 . Left: dataset with 157 EU regions. Right: dataset with the dashed curves correspond to the 95% pointwise confidence bands. The solid line corresponds to the parametric estimate δx 255 EU regions (new adhesion countries included).
8.5 8.75 9.0 9.25 9.5 9.75 10.0 10.25 10.5
initial GDP per capita (in log)
ˆ h ðx0 Þ, the Fig. 4. Nonparametric estimation of m(x0) accounting for endogeneity of x0, where x0 is log of initial regional GDP per capita. The solid curve represents the estimate m dashed curves correspond to the bootstrap (1000 replications) 95% pointwise confidence bands. The solid line corresponds to the parametric estimate δˆ x0 . Left: dataset with 157 EU regions. Right: dataset with 255 EU regions (new adhesion countries included).
results lead to the reject of the null of the associated parametric specification for both samples. We can conclude that the semiparametric model without the endogeneity of x0 provides a better approximation of the data than the parametric one. Now, in order to determine the most suitable fit for the data among the two nested semiparametric models (models with and without controlling for endogeneity of x0), we use the simple t test for the null hypothesis ρ = 0. As the regressions with endogeneity of x0 contain a generated regressor, i.e. νi, the t test should be bootstrapped.13 As shown in Tables 3 and 4, ρ is significant compared to the bootstrap 95% t-stat critical values for the 157 regions dataset but is not significant for the 255 regions dataset. This result favours the choice of the model with endogeneity of x0 for the first dataset and the model without endogeneity of x0 for the second one. Fig. 3 shows the nonparametric estimation without accounting for endogeneity for models with 157 and 255 European regions, respectively. Fig. 4 shows the result with endogeneity of initial regional GDP per capita (x0). When accounting for endogeneity of x0, we calculate the bootstrap (with 1000 replications) 95% pointwise confidence interval for the nonparametric estimator.14 13
We are thankful to an anonymous referee for suggesting this idea. We thank an anonymous referee for suggesting this idea. See also Lyssiotou et al. (1999) for details. 14
Estimation results point out both country heterogeneity and nonlinearity in the convergence process. Using data without new adhesion countries (i.e. 157 regions), we found a little evidence of convergence for high income regions while only lower income regions converge (with income approximately between 7,000 and 13,400 PPS). The convergence process for these regions is non-linear as shown in Figs. 3 and 4 (left graphs), the shape of the nonparametric curve is decreasing and convex, i.e. the lower is income, the higher is the convergence rate. Further estimation with 255 regions that include new adhesion countries confirms the same pattern than the previous dataset, i.e. for regions with income approximately higher than 7,000 PPS. However, it adds an interesting feature following that low income regions, i.e. income lower than 7,000 PPS, diverge. Therefore, taking the findings obtained from both datasets, we can observe that low income regions (in particular those from new adhesion countries) diverge while medium income regions converge and that there is no evidence of convergence for high income regions. The lack of estimated convergence for the poorer regions is indeed consistent with the increase of within-country income dispersion for adhesion countries, which is depicted in Table 2. There are also country effects as several country dummies (United Kingdom considered as the reference) are statistically significant. This suggests that national economic performance has significant impact on regional growth and in turn regional convergence process.
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6. Concluding remarks The aim of this study was to take advantage of new datasets to reexamine the growth process between European regions, relying on a semiparametric framework. Our major findings can be summarized as follows: i) There is non-linearity and heterogeneity in the convergence/ divergence process. ii) Compared to parametric approximations, test results indicate that semiparametric models perform better. Relying on our findings, some comments regarding the efficiency of regional policy are in order. Previous studies suggest that, from 1950 to 1990, a convergence process took place in Europe. On average, regions that had a lower initial income per capita had a higher growth rate than others. However, our estimates based on a different period (the last two decades) suggest a divergence for low income regions, a convergence for medium income regions, and no evidence of convergence for high income regions. The semiparametric specification adopted in our study takes into account country heterogeneities while estimating regional convergence. Country dummies represent country-specific steady states whereas the unspecified function of regional income per capita is supposed to capture the transitional dynamics which is allowed to be non-linear in contrast to existing parametric forms that usually assume a linear pattern for all regions. The result that only medium income regions converge implies a certain skepticism because these regions may be held in a “intermediate income trap”. Moreover, we think that the non-convergence of higher income regions means that they may have already achieved their own steady states. Low income regions show a diverging pattern, meaning that regions with low initial income have relatively low growth rates. It seems to us that existing policies that aim to foster convergence of these regions (including those from new countries that have joined the European Union) have not produced their expected effect yet. Regional policies should take this diverging pattern and the “intermediate income trap” into account in order to improve economic integration within European regions, in particular for the new adhesion countries when their incomes attain a medium level. It would be promising in further studies to integrate recent findings in geography economics – which insist on the phenomenon of local spillovers in the spirit of Krugman (1991) and Krugman and Venables (1995) on the one hand, and on the spatial heterogeneity and spatial spillovers underlined by Baumont et al. (2006), Battisti and Di Vaio (2008), Ramajo et al. (2008), Pfaffermayr (2009) and Arbia et al. (2010), among others, on the other hand. Acknowledgements This paper has immensely benefited from the comments of two anonymous referees and an editor of this journal. We thank Daniel Opolot for his stimulating remarks. Financial supports from ANR grant no. ANR-05-JCJC-0134-01 (CEDEPTE) and the Université de Strasbourg are gratefully acknowledged. All errors remain our own. References Arbia, G., Battisti, M., DiVaio, G., 2010. Institutions and geography: empirical test of spatial growth model for European regions. Economic Modeling 27, 12–21. Armstrong, H.W., 1995. Convergence among the regions of the European Union. Papers in Regional Science 74, 143–152. Azariadis, C., Drazen, A., 1990. Threshold externalities in economic development. Quarterly Journal of Economics 105, 501–526. Barro, R.J., Sala-í-Martin, X., 1991. Convergence across states and regions. Brookings Papers on Economic Activity 1, 107–182. Barro, R.J., Sala-í-Martin, X., 1995. Economic Growth. McGraw-Hill, New York. Battisti, M., Di Vaio, G., 2008. A spatially filtered mixture of β-convergence regressions for EU regions, 1980–2002. Empirical Economics 34, 105–121.
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Contents lists available at ScienceDirect
Economic Modelling j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / e c m o d
Testing convergence of European regions: A semiparametric approach Théophile T. Azomahou a, Jalal El ouardighi b, Phu Nguyen-Van c,⁎, Thi Kim Cuong Pham b a b c
UNU-MERIT and Maastricht University, Keizer Karelplein 19, 6211 TC Maastricht, The Netherlands BETA, Université de Strasbourg, 61 avenue de la Forêt Noire, F-67085 Strasbourg Cedex, France BETA-CNRS, Université de Strasbourg, 61 avenue de la Forêt Noire, F-67085 Strasbourg Cedex, France
a r t i c l e
i n f o
Article history: Accepted 21 December 2010 JEL classification: C14 O40 O52
a b s t r a c t We provide a reappraisal of income convergence across European regions over the last two decades by using a semiparametric partially linear model to approximate the relationship between the average growth rate of GDP per capita and the initial GDP per capita. Estimation results point out both country heterogeneity and nonlinearity in the convergence process. The findings suggest that low income regions, in particular those from new adhesion countries, diverge while medium income regions converge and that there is no evidence of convergence for high income regions. © 2011 Elsevier B.V. All rights reserved.
Keywords: Convergence Heterogeneity Non-linearity Kernel estimator European regions
1. Introduction The convergence hypothesis according to which poorer economies catch up wealthier ones has been studied in both exogenous and endogenous growth models setting. In the exogenous model setting, which assumes that persistent growth is primarily driven by exogenous technological process, capital accumulation is the source of (conditional) convergence. Endogenous growth models on the other hand emphasize a broad measure of physical and human capital as the main engines of growth, and the convergence or lack thereof, results from the differences in technology levels across economies and increasing returns to capital (Romer, 1986). Starting with Baumol (1986), these hypotheses have been extensively tested empirically. Most of the theoretical and empirical works are summarized in, e.g., Barro and Sala-í-Martin (1995), Temple (1999), De la Fuente (1997, 2002) and Islam (2003). This study aims to provide a reappraisal of the convergence process at the regional level in the European Union. We emphasize the notions of heterogeneity and non-linearity, that is, the convergence/ divergence differs according to initial regional conditions.1 We estimate the relationship between the average growth rate of GDP per capita and the initial GDP per capita using a semiparametric
⁎ Corresponding author. Tel.: +33 3 68 85 20 39; fax: +33 3 68 85 20 71. E-mail address: [email protected] (P. Nguyen-Van). 1 This encompasses the usual concept of conditional convergence. 0264-9993/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.econmod.2010.12.010
partially linear model. Country dummies are included in the model to capture the influence of national characteristics on regional growth and to describe differences in the steady-state at the country level. As noted by Armstrong (1995), when country dummies are included, the convergence coefficient measures the within-country convergence. We also provide a measure to control for regressor endogeneity in order to establish robust estimations. We use two datasets to investigate the convergence among European regions. The first dataset includes only 157 regions from 9 European Union countries, and for which the data (series on population and GDP) is available over a long period, 1990–2005. Other socioeconomic factors (investment, research and development, communication, human capital, trade, transaction costs, etc.) that could also be considered are not easily collected at regional level. The second dataset contains a large sample of regions from 20 EU countries, new adhesion countries included. Hence, 255 regions are observed, but only in a shorter period, from 1998 to 2007. Including such regions would be interesting in terms of EU integration and policy making. The main results that emerge from this study are the following. First, the shape of the nonparametric relationship shows non-linearity in growth, and suggests that low-income regions (in particular those from new adhesion countries) diverge and that only medium-income regions converge while there is no evidence of convergence for high income regions. Secondly, we also find that regional convergence depends on national contexts. Finally, compared to the parametric approximation, test results suggest that the semiparametric model gives a sufficiently accurate description of the data.
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The findings of the paper may lead to some policy implications for regional development. Indeed, the European economic integration is traditionally thought of as being beneficial for its regions in terms of higher allocation efficiency and increased competition in particular for low-income regions. However, there is a risk that economic integration in Europe will be followed by an increase in inequalities among regions. Important efforts were put forth to increase the attractiveness of these regions, in particular by developing public infrastructure. As a result, the question of European integration goes hand in hand with regional convergence policies.2 In this respect, European structural funds aim to attenuate development disparities among European regions and to correct imbalances which may result from the development of the single market and the single currency.3 However, the efficiency of these regional policies seems to be compromised.4 Our results underline the risk of persistence in inequality mentioned above. The remainder of the paper is organized as follows. Section 2 presents key concepts and literature background with regard to both the regional convergence and the role of non-linearity and heterogeneity. The econometric specifications are presented in Section 3. Section 4 describes the data. Estimation results are discussed in Section 5. Section 6 concludes the study.
2. Background Our study is related to many earlier contributions on income convergence. Two measures of convergence conceptually different are σ-convergence and β-convergence (see, e.g., Barro and Sala-í-Martin, 1995). The first concept describes how the distribution of cross-section incomes evolves over time, whereas the second emphasizes the income mobility. β-convergence may be unconditional, which implies that all the economies have the same level of steady state, or conditional on auxiliary variables, allows each economy to converge to its own steady state5. In this section, we do not have the intention to review the broad theoretical as well as empirical literature on convergence (see, e.g., De la Fuente, 1997; Islam, 2003). We mainly point out some salient empirical facts concerning both regional convergence and the roles of nonlinearity and heterogeneity, which constitute the main focus of the paper. Research over the last two decades has considerably improved our understanding of convergence and has raised several conflicting issues as well; see e.g., Bernard and Durlauf (1996) and Caselli et al. (1996). At regional level, Dewhurst and Mutis-Gaitan (1995) use a dataset of 63 European regions between 1981 and 1991 and find that the national growth rate has a significant influence on the speed of regional convergence. Sala-í-Martin (1996) analyses the regional convergence hypothesis by using regional data for the United States (48 states for the 1880–1990 period), Japan (47 prefectures, 1955– 1990), Europe (90 regions, 1950–1990), and Canada (10 provinces, 1961–1991). Relying on a parametric specification, the author finds that regions tend to converge at a speed of approximately 2% per year.6 Garofalo and Yamarik (2002) use a new US dataset covering the 1977–1996 period and confirm the result established by Barro and Sala-í-Martin (1991).
2 See, e.g., Kutan and Yigit (2007) who recognize the beneficial effect of integration from a long-term perspective. 3 Note that these funds, which amount to a third of the total expenditure, constitute the second largest part of the budget of the European Union after the Common Agricultural Policy. 4 This is consistent with the findings of Boldrin and Canova (2001, 2003). 5 Levine and Renelt (1992) list no less than fifteen auxiliary variables used in the literature on growth. The authors conclude that the convergence relationship keeps its robustness with respect to investment and initial income, while other variables lose their significance (e.g., population growth, monetary and fiscal variables, etc.). 6 The result is also in favour of the σ-convergence hypothesis because the interregional distribution of income in all countries has shrunk over time.
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Some recent studies have analyzed the spatial effects (spatial autocorrelation and spatial heterogeneity) on convergence. For example, Baumont et al. (2006) use a sample of 138 European regions over the 1980–1995 period to estimate the spatial spillover effect. Their findings show that the average growth rate of GDP per capita of a given region is positively affected by the average growth rate of its neighboring regions. Battisti and Di Vaio (2008) propose a model where the convergence parameters capture both structural heterogeneity and the spatial effects, i.e. the choice of regional growth models is determined in an endogenous manner which avoids an arbitrary selection of the North–South regions or centre-periphery. Their results point out that the spatial effects prevail. In particular the data shows a slow speed of convergence or an absence of convergence. Arbia et al. (2010) investigate the spatial effects due to both institutions and geography for European regions. They underline the dominant role of institutions with respect to geographical factors. Moreover, the authors show a positive effect of geo-institutional proximity on spatial dependence of regional output per worker on the one hand, and on the convergence speed on the other hand. Our paper does not deal with the spatial effects. However, it would be interesting to extent our modelling to address this issue in a future work. It has been shown that the catching-up of poor regions in Europe is slow, and sometimes even non-existent, since the variation of income amounts to approximately 2% per year. This figure is recognized as a ‘stylized fact’ (see e.g., Barro and Sala-í-Martin (1991), Barro and Sala-íMartin (1995), Sala-í-Martin (1996), Armstrong (1995) and Neven and Gouyette (1995)). However, at this rate, 35 years would be necessary to cut by half the initial inequalities of income per capita. Moreover, Martin (1997)) points out that, since the beginning of 1980s, the speed of convergence among European regions decreased and fell to 1.3% between 1978 and 1992. This deceleration could be related to an absence of convergence between poor and rich regions in the same country, whereas convergence between countries continues (see European Commission, 1996). According to Neven and Gouyette (1995), a process of divergence is in progress across European regions. It appears that in less prosperous countries, only the richest regions have benefited from a process of convergence with rich countries. Quah (1996b) finds that among the poorest countries in Europe, Spain and Portugal, which have a faster aggregated growth than Greece, experienced a stronger increase in regional inequalities. More generally, this type of evolution supports the idea that an arbitration between global growth and regional equity could exist. Mora et al. (2005) detect a pattern of convergence clubs for the European regions over the period 1985–2000. Ramajo et al. (2008) find that regions in the European Union cohesion-fund countries (Ireland, Greece, Portugal and Spain) converge separately from the rest of regions of the EU. In particular, Canova (2004) tests for convergence clubs using a predicted density approach. This methodology enables determination of the number of groups, locate the break points as well as estimate the parameters of each group. The results show little evidence of income convergence of European regions. Poorer regions converge to their steady state faster than rich ones, and tend to cluster around a weak pole of attraction (below the average).7 The common feature to the above studies is the assumption usually made in the convergence test hypothesis, that is, all economies have a common linear specification. The assumption of a common linear specification, inherent in the Solow growth model with a single steady state, is not held in models with multiple steady states as stressed in the theoretical study of Azariadis and Drazen (1990). Furthermore, several authors show that results based on cross-section data are biased because they ignore unobserved national/regional specific effects. A direct way to overcome the drawback related to cross-section data bias is to include auxiliary variables and country/regional specific 7 Moreover, significant dispersion of the steady state around each pole of attraction suggests that clustering is more prevalent than convergence (see Canova, 2004).
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effects. For the case of regional data, the choice of auxiliary variables is limited because of data unavailability. Generally, the distinction of conditional convergence from unconditional convergence consists in testing the specificity common to regions of the same country by incorporating country dummies or variables which reflect the differences in national or local structure. An alternative way is to use panel data models (see, e.g., Islam, 1995). One weakness associated to this methodology is that the convergence speed resulting from its use appears higher. The other as noted by Nerlove (1999), is that the estimation results based on panel data are very sensitive to the estimation method (level or difference regressions, fixed or random effects, etc.). Two other lines of research have emerged in the literature. The first one analyses the distribution dynamics of economies. Quah (1996a,c,d, 1997) finds evidence of polarization and stratification in the growth process. Bianchi (1997)) states that the determinants of the steady state vary across economies. Using parametric panel data models (102 countries between 1960 and 1989), Lee et al. (1997) show that estimates of ?β-convergence traditionally defined in the literature are subject to substantial biases in a stochastic Solow growth model. They also show that steady-state growth rates differ significantly across countries. The second line of research involves the investigation of heterogeneity and non-linearity in the growth process (see, e.g., Durlauf and Johnson, 1995; Liu and Stengos, 1999; Durlauf, 2000, 2001; and Durlauf et al., 2001).8 These studies generally find the existence of non-linearity and heterogeneity at the country level. In particular, Durlauf and Johnson (1995) use a sample of 96 countries between 1960 and 1985 and regression tree techniques. They reject the linear model in favour of a multiple regime alternative in which different economies obey different linear models when grouped according to initial conditions. Moreover, Liu and Stengos (1999) question the single linear regime. They employ a semiparametric additive partially linear model on a data of 86 countries between 1960 and 1990 and find the existence of heterogeneity or non-linearity in the relationship between initial output and schooling level, and growth rate. These results confirm the presence of multiple growth regimes which is also corroborated by Huang (2005). By using the framework of distribution dynamics and a threshold regression model, Fiaschi and Lavezzi (2007) show that income growth is nonlinear. In a nutshell, the majority of the studies relate to the national level. Hereafter, we provide a reappraisal of income convergence by focusing on heterogeneity and non-linearity at the regional level. 3. Econometric specification We propose a semiparametric partially linear model to investigate the convergence process on European regions over the 1990–2005 period. The model is given by gi = m x0;i + Zi′ γ + εi ;
i = 1; ⋯; n:
ð1Þ
We assume for the moment that ε is an independent random error with E(εi|x0,i, Zi) = 0 and V(εi|x0,i, Zi)=σ 2(x0,i, Zi); gi is the average growth rate of region i over the period of study; x0,i is the logarithm of GDP per capita in 1990; m (.) is an unspecified function of x0,i that may be non-linear; Zi is a K × 1 vector of other variables that enter linearly in Eq. (1). We specify Z as a set of country dummies, which account for country heterogeneity or differences in the steady state. This heterogeneity may represent economic determinants and other factors (legislation, various subsidies for regional development purposes, etc.) that are common to a group of regions of the same country.
8
See also Phillips and Sul (2007) for a survey.
We implement the procedure proposed by Robinson (1988) sketched as follows to estimate Eq. (1). Taking the expectation of Eq. (1) with respect to x0, i yields E gi jx0;i = m x0;i + E Zi jx0;i ′ γ + E εi jx0;i :
ð2Þ
Then, taking the difference between Eqs. (1) and (2), we obtain h i gi −E gi jxi;0 = Zi −E Zi jxi;0 ′ γ + εi −E εi jx0;i :
ð3Þ
ˆ Then, We can estimate γ by Ordinary Least Squares, denoted as γ. an estimator of m(x0, i) is given by E
h i ˆ x0;i : gi −Zi′γˆ jx0;i = m
ð4Þ
ˆ x0;i are estimated In relations (3) and (4), E(Zi|x0, i), E(gi|x0, i), and m nonparametrically by the kernel method. We use both the local constant kernel (known also as the Nadaraya–Watson estimator) and local linear kernel estimators. Moreover, this method requires the choice of a kernel function and a smoothing parameter. For our calculations, we use the Gaussian function and several choices of smoothing parameter (the rule of thumb and the cross-validation method, see Silverman, 1986; Pagan and Ullah, 1999). As the results given by these two estimators are very similar, we only discuss the results based on the Nadaraya–Watson method. It should be also noted that the semiparametric specification (1) mixes continuous (x0, i) and discrete (Zi) regressors. Thanks to Bierens (1987), we know that when the regressors in Eq. (1) are a mix of continuous and discrete, if we apply the kernel method as if all regressors were continuous, we still get consistent estimates. The only thing we should be careful about is the convergence rate and the asymptotic distribution of the estimator of E (Zi|x0, i). We also use an alternative specification which accounts for the endogeneity of x0. Statistically, it corresponds to assumptions E(εi|Zi)=0 and E(εi|x0, i)≠0. This model can be estimated by the approach of Newey et al. (1999). Let us assume that there exists a set of instruments Wi such that E(εi|Wi)=0 and x0;i = W i′η + νi
ð5Þ
where E(νi|Wi) = 0. Following Newey et al. (1999), we also assume that E(εi|Wi, νi) = ρνi, which implies that εi = ρνi + ζi. Hence, the model becomes gi = m x0;i + Zi′ γ + ρνi + ζi ;
ð6Þ
where ζi is the new standard error term. Estimation of this model is similar to that of the model without endogeneity as previously described but now with an additional linear component. As νi is not observed, it will be replaced by the residuals computed from the ordinary least squares regression of (5). 4. Data description The dataset is built from the Eurostat-Regio database. For reasons of homogeneity, we use regions at level NUTS-2 for all countries.9 The resulting data provides us with two sets of regions. The first one contains 157 regions covering 9 EU countries (see Table 1). The data is available over the 1990–2005 period which can be considered long enough to be appropriate to study the long-term convergence. The second dataset contains a larger number of regions from 20 EU 9 The nomenclature in European regions, Nomenclature of Territorial Units for Statistics (NUTS), is a hierarchical classification established by EUROSTAT. This classification starts from country level information (NUTS-0) to community level (NUTS-5).
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Table 1 Descriptive statistics, 157 EU regions, 1990–2005. Dispersion of GDPc
GDP per capita (in PPS) Country
Number of regions
1990a
2005a
Growth rate (%)b
1990
2005
Growth rate (%)d
Belgium Germany Spain France Greece Italy The Netherlands Portugal United Kingdom All countries Min. 1st quartile Median 3rd quartile Max.
11 30 17 22 13 20 12 5 27 157
14,781 17,115 11,347 14,419 8,240 14,596 14,416 8,776 13,521 13,803 5,901 11,563 13,691 15,722 27,856
25,922 28,429 22,532 23,492 17,851 23,636 26,796 17,528 24,640 24,313 13,007 20,688 23,587 26,962 49,985
3.77 3.34 4.61 3.26 5.15 3.23 4.11 4.62 3.97 3.84 5.27 3.88 3.36 3.60 3.90
0.233 0.189 0.201 0.150 0.168 0.269 0.134 0.194 0.105 0.273
0.219 0.220 0.168 0.141 0.165 0.259 0.165 0.183 0.137 0.226
− 0.42 1.02 − 1.23 − 0.44 − 0.12 − 0.25 1.39 − 0.42 1.81 − 1.25
a b c d
For each country, figures are averages computed on values of GDP per capita (in Purchasing Power Standard, PPS) of its regions. Annual growth rate of GDP per capita over the 1990–2005 period. The figures reported are the standard deviation of log(GDP per capita). Annual growth rate of the standard deviation of log(GDP per capita) over the 1990–2005 period.
Table 2 Descriptive statistics, 255 EU regions, 1998–2007. Dispersion of GDPc
GDP per capita (in PPS) a
Country
Number of regions
1998
Belgium Bulgaria Czech Republic Germany Ireland Greece Spain France Italy Hungary The Netherlands Austria Poland Portugal Romania Slovenia Slovak Republic Finland Sweden United Kingdom All countries Min. 1st quartile Median 3rd quartile Max.
11 6 8 40 2 13 19 22 21 7 12 9 16 7 8 2 4 5 8 35 255
20,100 4,467 12,050 19,720 18,600 13,900 15,832 17,741 19,857 8,557 20,817 21,478 7,569 12,643 4713 13,550 10,350 19,200 20,050 18,857 16,448 3,600 12,900 16,700 19,850 51,100
a b c d
2007
a
27,600 8,483 20,150 27,673 33,050 19,446 25,732 24,236 25,081 13,743 31,742 29,633 12,406 19,386 10,888 22,400 20,300 28,640 29,325 27,069 23,947 6,400 18,700 24,200 28,450 83,200
Growth rate (%) 3.54 6.71 5.47 3.88 6.30 3.66 5.45 3.46 2.64 5.01 4.70 3.63 5.41 4.78 8.76 5.54 7.10 4.53 4.24 3.93 4.40 6.39 4.13 4.12 4.00 5.42
b
1998
2007
Growth rate (%)d
0.311 0.186 0.273 0.277 0.317 0.172 0.209 0.141 0.275 0.282 0.163 0.229 0.180 0.218 0.222 0.237 0.476 0.246 0.154 0.241 0.464
0.312 0.330 0.336 0.222 0.365 0.202 0.183 0.142 0.260 0.351 0.157 0.205 0.216 0.208 0.378 0.268 0.558 0.202 0.144 0.259 0.400
0.04 6.35 2.30 − 2.44 1.58 1.74 − 1.49 0.13 − 0.06 2.43 − 0.39 − 1.24 2.04 − 0.51 5.91 1.38 1.76 − 2.15 − 0.69 0.81 − 1.67
For each country, figures are averages computed on values of GDP per capita (in Purchasing Power Standard, PPS) of its regions. Annual growth rate of GDP per capita over the 1998–2007 period. The figures reported are the standard deviation of log(GDP per capita). Annual growth rate of the standard deviation of log(GDP per capita) over the 1998–2007 period.
countries, new adhesion countries included (see Table 2). This sample is composed of 255 regions at NUTS-2, which covers a shorter period, from 1998 to 2007. Table 1 presents the descriptive statistics on regional GDP per capita in PPS (Purchasing Power Standards) for each country.10 We 10 Expressing GDP in purchasing power standards makes it possible to eliminate the price levels differences between economies. However, a precaution must be mentioned. It might be more relevant to take into account the inflation rate when GDP is compared across different years. Unfortunately, neither regional GDP deflator nor regional conversion factors (i.e., purchasing power parities) are available (see for a more discussion Eurostat regional yearbook publications). Notwithstanding, the use of GDP in PPS will not affect noticeably our results owing to the fact that the estimated specifications take account of national heterogeneity.
observe that disparities between regions around the European average are strong. Indeed, the highest level of GDP per capita is approximately 4.7 times the lowest level in 1990 (see the bottom of Table 1). The gap slightly narrowed in 2005. If we look at the situation in the middle 50% of the data, the IQR (interquartile range, i.e., third quartile minus first quartile) exhibits a greater spread of the levels of GDP per capita from the centre of the distribution. In a nutshell, the highest levels of GDP per capita are observed in Germany, and the lowest ones in Greece and Portugal. The evolution of GDP per capita between 1990 and 2005 shows an average growth rate of 3.84%. Growth is particularly important in Greek, Portuguese and Spanish regions. In contrast, Italian and French regions are characterized by the lowest growth, 3.23% and 3.26% on
density
0.00008
density
0.00004 0.00000
10000
20000
30000
40000
0e+00 1e−05 2e−05 3e−05 4e−05 5e−05 6e−05 7e−05
T.T. Azomahou et al. / Economic Modelling 28 (2011) 1202–1210 0.00012
1206
50000
20000
GDP per capita
40000
60000
80000
GDP per capita
Fig. 1. Kernel estimation of the distribution of GDP per capita. Left: dataset with 157 EU regions, GDP per capita in 1990 (solid) and 2005 (dashed). Right: dataset with 255 EU regions (new adhesion countries included), GDP per capita in 1998 (solid) and 2007 (dashed).
Table 3 Parametric and semiparametric estimations, 157 EU regions, 1990–2005. (1)
(2)
(3)
Variable
Coef.
t-stat.
Coef.
t-stat.
Coef.
t-stat.
Intercept log(initial GDP)(a) Belgium Germany Greece Spain France Italy The Netherlands Portugal ρ
0.070⁎ ⁎ −0.0034 −0.0017 −0.0051⁎ ⁎ 0.0093⁎ ⁎ 0.0053⁎ ⁎ −0.0065⁎ ⁎ −0.0068⁎ ⁎
3.662 −1.709 −1.059 −4.069 5.117 3.676 −4.992 −5.131 0.915 1.930 –
– – −0.0021 −0.0058⁎ ⁎ 0.0061⁎ 0.0045⁎ −0.0066⁎ ⁎ −0.0076⁎ ⁎
– – −1.362 −4.729 3.13 3.169 −5.263 −5.806 0.871 0.795 –
– – −0.0015 −0.0046⁎ ⁎ 0.0038⁎ 0.0035⁎ ⁎ −0.0057⁎ ⁎ −0.0071⁎ ⁎
– – −0.951 −3.701 2.334 2.615 −4.563 −5.378 1.154 −0.062 5.101
0.0014 0.0029 –
0.0013 0.0019 –
0.0017 0.0001 0.0054♮
Notes. Specification: (1) parametric model, (2) semiparametric model, and (3) semiparametric model with endogeneity of x0. The dependent variable is the average growth rate of GDP per capita. (a) ln(initial GDP) is the logarithmic value of GDP per capita in 1990. Estimations are performed on a sample of 157 European regions for the period 1990–2005. ⁎Significance at the 5% level. ⁎⁎Significance at the 1% level. ♮The coefficient is significant at the standard 1% level and as regards the t-stat value compared to the wild bootstrap (1000 replications) 95% t-stat critical values (− 2.433 ; 3.178).
average respectively. To illustrate the concept of convergence, we also report in Table 1 the standard deviations of the logarithm of GDP per capita in 1990 and 2005. On the one hand, we note that the dispersion of GDP per capita tends to be reduced over time, with a decrease of 1.25% on average. The reduction of inequalities is particularly strong between the Spanish regions (−1.23%). On the other hand, we observe an increase in the dispersionof the GDP per capita between the regions in the United Kingdom (1.81%), in the Netherlands (1.39%) and in Germany (1.02%). These findings suggest the presence of some country heterogeneity. Table 2 presents the situation of the 255 regions sample. As we can see, the disparities across regions around the European average are more pronounced. The GDP mean level of Austrian regions is 4.8 times higher than that of Bulgarian regions, and 4.6 times than that of Romanian regions. The situation remains almost the same in 2007, that is, the level of Irish regions is 3.9 times the level of Bulgarian regions. As shown at the bottom of Table 2, the spread of the GDP per capita levels from the centre of distribution is more marked by including regions of the EU new members. The inspection of the regional per capita GDP growth rates over the 1998–2007 period also shows the sharp contrasts. The strong growth of the GDP levels of the Romanian, Slovak and Bulgarian regions was accompanied by an aggravation of income inequalities among regions of the same country (see the last column of Table 2). However, one can note a convergence process between all regions of the widened European Union, i.e., a decrease of income inequality by 1.67% on average.
The same patterns can be revealed in Fig. 1 which displays two almost uni-modal distributions of regional GDP per capita in 1990 and 2005, and 1998 and 2007, respectively. These distributions contain a non negligible upper tail corresponding to high income regions. They also describe a global increase of income over time. However, income per capita in final dates has a lower mode and a higher dispersion than that of income per capita in initial dates. 5. Estimation results Table 3 reports estimation results of the models with and without controlling for endogeneity of initial regional GDP per capita (x0) for the first dataset, i.e. 157 regions from 9 EU countries. Table 4 presents the corresponding results for the second dataset, i.e. 255 regions from 20 EU countries (new adhesion countries included).11 For the model with endogeneity of regional GDP per capita at the initial date (x0), we use the national GDP per capita at the same date (computed from regional GDP per capita observed in 1990 and 1998 for the first and second dataset, respectively) as an instrument for x0.12 The Spearman correlation coefficient indicates a value equal to 0.633 for the first dataset and 0.054 for the second dataset. Moreover,
11
Estimation codes are written in R and available from the authors upon request. It would be interesting in a further study to address this issue by using information on other variables if their availability allows it. 12
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Table 4 Parametric and semiparametric estimations, 255 EU regions, 1998–2007. (1) Variable
(2)
Coef. 0.0640⁎ ⁎
Intercept log(initial GDP)(a) Belgium Bulgaria Czech Republic Germany Ireland Greece Spain France Italy Hungary The Netherlands Austria Poland Portugal Romania Slovenia Slovak Republic Finland Sweden ρ
−0.0029 −0.0034 −0.0209⁎ ⁎ 0.0125⁎ ⁎ 0.0003 0.0021⁎ ⁎ −0.0032 0.0132⁎ ⁎ −0.0043 −0.0115⁎ ⁎ 0.0074 0.0072⁎ −0.0023 0.0107⁎ ⁎ 0.0065 0.0395⁎ ⁎ 0.0136⁎ 0.0265⁎ ⁎ 0.0055 0.0030 –
(3)
t-stat.
Coef.
t-stat.
Coef.
t-stat.
2.816 −1.263 −1.155 4.204 3.617 −0.172 3.478 −1.152 5.434 −1.896 −4.942 1.883 2.556 −0.717 3.260 1.802 8.610 2.206 5.650 1.363 0.917 –
– – −0.0037 −0.0048⁎ ⁎ 0.0117⁎ −0.0001⁎ 0.0201⁎ ⁎
– – −1.364 6.983 3.135 −0.058 3.560 −1.904 5.327 −1.697 −5.209 1.326 3.172 −0.480 2.176 1.445 10.070 2.202 4.941 1.446 1.565 –
– – −0.0032 0.0048⁎ ⁎ 0.0119⁎ ⁎
– – −1.196 6.996 3.191 −0.159 3.543 −1.706 5.243 −1.873 −5.378 1.348 3.238 −0.313 2.106 1.474 10.031 2.278 4.971 1.548 1.662 2.071
−0.0052 0.0121⁎ ⁎ −0.0036 −0.0112⁎ ⁎ 0.0057 0.0084⁎ ⁎ −0.0014 0.0089⁎ 0.0051 0.0652⁎ ⁎ 0.0126⁎ 0.0024⁎ ⁎ 0.0054 0.0048 –
−0.0003 0.0200⁎ ⁎ −0.0046 0.0120⁎ ⁎ −0.0040 −0.0121⁎ ⁎ 0.0057 0.0085⁎ ⁎ −0.0009 0.0086⁎ 0.0052 0.0647⁎ ⁎ 0.0129⁎ 0.0242⁎ ⁎ 0.0058 0.0051 0.0063♮
Notes. Specification: (1) parametric model, (2) semiparametric model, and (3) semiparametric model with endogeneity of x0. The dependent variable is the average growth rate of GDP per capita. (a) ln(initial GDP) is the logarithmic value of GDP per capita in 1998. Estimations are performed on a sample of 255 European regions for the period 1998–2007. ⁎Significance at the 5% level. ⁎ ⁎Significance at the 1% level. ♮The coefficient is significant at the standard 5% level, but not significant as regards the t-stat value compared to the wild bootstrap (1000 replications) 95% t-stat critical values (− 2.608 ; 3.141).
Fig. 2 presents the correlation between regional GDP per capita and national GDP per capita at the initial dates for both datasets. These features motivate the use of national GDP per capita as an instrument for regional GDP per capita, especially for the first dataset. For comparison purposes, we also include estimation results for the standard parametric model often used in the convergence literature, where all parameters enter linearly: gi = δx0;i + Zi′ γ + εi :
ð7Þ
10.0 9.5 8.5
9.0
regional GDP per capita
9.75 9.5 9.25 9.0 8.75
regional GDP per capita
10.0
10.5
10.25
ˆ h ðx0 Þ with the corresponding Fig. 3 presents the estimated function m 95% pointwise confidence interval for datasets with 157 and 255 European regions, respectively. We also plot the parametric counterpart, δˆ x0 . The difference between the parametric and the semiparametric models is salient. We observe that an important part of the
parametric curve lies outside the nonparametric confidence interval in both cases. To compare the parametric and the semiparametric models without the endogeneity of x0 (the two specifications are nested), we use the test statistic proposed by Li and Wang (1998). The null hypothesis corresponds to the parametric specification, and the alternative is the semiparametric one. The test is one-sided and its statistic asymptotically follows a standard normal distribution. Li and Wang (1998) find that the normal approximation does not perform well for small or moderate samples and suggest the use of a bootstrap. As the sample sizes of our two datasets are 157 and 255 respectively, we use the bootstrap version for the first dataset and the asymptotic version for the second one. For the 157 regions dataset, the computed value of the test statistic is 1.065, much higher than the bootstrap critical values at the 5% level (0.339). For the dataset with 255 EU regions, the statistic is 1.944 which is higher than the asymptotic critical value at the 5% level (1.654). These test
9.2
9.4
9.6
national GDP per capita
9.8
15.0
15.2
15.4
15.6
15.8
16.0
national GDP per capita
Fig. 2. Correlation between regional and national GDP per capita. The solid line represents the OLS regression, the dashed lines are the corresponding 95% confidence bands. Left: dataset with 157 EU regions. Right: dataset with 255 EU regions (new adhesion countries included).
T.T. Azomahou et al. / Economic Modelling 28 (2011) 1202–1210
0.01
average growth rate 8.75
9.0
9.25
9.5
9.75
10.0
−0.04 −0.03 −0.02 −0.01 0.00
0.010 0.005 0.000
average growth rate
0.02
1208
10.25
8.5 8.75 9.0 9.25 9.5 9.75 10.0 10.25 10.5
initial GDP per capita (in log)
initial GDP per capita (in log)
0.02
9.0
9.25
9.5
9.75
10.0
10.25
initial GDP per capita (in log)
0.01
average growth rate 8.75
−0.04 −0.03 −0.02 −0.01 0.00
0.010 0.005 0.000 −0.005
average growth rate
0.015
0.03
0.020
ˆ h ðx0 Þ, Fig. 3. Nonparametric estimation of m(x0) without accounting for endogeneity of x0, where x0 is log of initial regional GDP per capita. The solid curve represents the estimate m ˆ 0 . Left: dataset with 157 EU regions. Right: dataset with the dashed curves correspond to the 95% pointwise confidence bands. The solid line corresponds to the parametric estimate δx 255 EU regions (new adhesion countries included).
8.5 8.75 9.0 9.25 9.5 9.75 10.0 10.25 10.5
initial GDP per capita (in log)
ˆ h ðx0 Þ, the Fig. 4. Nonparametric estimation of m(x0) accounting for endogeneity of x0, where x0 is log of initial regional GDP per capita. The solid curve represents the estimate m dashed curves correspond to the bootstrap (1000 replications) 95% pointwise confidence bands. The solid line corresponds to the parametric estimate δˆ x0 . Left: dataset with 157 EU regions. Right: dataset with 255 EU regions (new adhesion countries included).
results lead to the reject of the null of the associated parametric specification for both samples. We can conclude that the semiparametric model without the endogeneity of x0 provides a better approximation of the data than the parametric one. Now, in order to determine the most suitable fit for the data among the two nested semiparametric models (models with and without controlling for endogeneity of x0), we use the simple t test for the null hypothesis ρ = 0. As the regressions with endogeneity of x0 contain a generated regressor, i.e. νi, the t test should be bootstrapped.13 As shown in Tables 3 and 4, ρ is significant compared to the bootstrap 95% t-stat critical values for the 157 regions dataset but is not significant for the 255 regions dataset. This result favours the choice of the model with endogeneity of x0 for the first dataset and the model without endogeneity of x0 for the second one. Fig. 3 shows the nonparametric estimation without accounting for endogeneity for models with 157 and 255 European regions, respectively. Fig. 4 shows the result with endogeneity of initial regional GDP per capita (x0). When accounting for endogeneity of x0, we calculate the bootstrap (with 1000 replications) 95% pointwise confidence interval for the nonparametric estimator.14 13
We are thankful to an anonymous referee for suggesting this idea. We thank an anonymous referee for suggesting this idea. See also Lyssiotou et al. (1999) for details. 14
Estimation results point out both country heterogeneity and nonlinearity in the convergence process. Using data without new adhesion countries (i.e. 157 regions), we found a little evidence of convergence for high income regions while only lower income regions converge (with income approximately between 7,000 and 13,400 PPS). The convergence process for these regions is non-linear as shown in Figs. 3 and 4 (left graphs), the shape of the nonparametric curve is decreasing and convex, i.e. the lower is income, the higher is the convergence rate. Further estimation with 255 regions that include new adhesion countries confirms the same pattern than the previous dataset, i.e. for regions with income approximately higher than 7,000 PPS. However, it adds an interesting feature following that low income regions, i.e. income lower than 7,000 PPS, diverge. Therefore, taking the findings obtained from both datasets, we can observe that low income regions (in particular those from new adhesion countries) diverge while medium income regions converge and that there is no evidence of convergence for high income regions. The lack of estimated convergence for the poorer regions is indeed consistent with the increase of within-country income dispersion for adhesion countries, which is depicted in Table 2. There are also country effects as several country dummies (United Kingdom considered as the reference) are statistically significant. This suggests that national economic performance has significant impact on regional growth and in turn regional convergence process.
T.T. Azomahou et al. / Economic Modelling 28 (2011) 1202–1210
6. Concluding remarks The aim of this study was to take advantage of new datasets to reexamine the growth process between European regions, relying on a semiparametric framework. Our major findings can be summarized as follows: i) There is non-linearity and heterogeneity in the convergence/ divergence process. ii) Compared to parametric approximations, test results indicate that semiparametric models perform better. Relying on our findings, some comments regarding the efficiency of regional policy are in order. Previous studies suggest that, from 1950 to 1990, a convergence process took place in Europe. On average, regions that had a lower initial income per capita had a higher growth rate than others. However, our estimates based on a different period (the last two decades) suggest a divergence for low income regions, a convergence for medium income regions, and no evidence of convergence for high income regions. The semiparametric specification adopted in our study takes into account country heterogeneities while estimating regional convergence. Country dummies represent country-specific steady states whereas the unspecified function of regional income per capita is supposed to capture the transitional dynamics which is allowed to be non-linear in contrast to existing parametric forms that usually assume a linear pattern for all regions. The result that only medium income regions converge implies a certain skepticism because these regions may be held in a “intermediate income trap”. Moreover, we think that the non-convergence of higher income regions means that they may have already achieved their own steady states. Low income regions show a diverging pattern, meaning that regions with low initial income have relatively low growth rates. It seems to us that existing policies that aim to foster convergence of these regions (including those from new countries that have joined the European Union) have not produced their expected effect yet. Regional policies should take this diverging pattern and the “intermediate income trap” into account in order to improve economic integration within European regions, in particular for the new adhesion countries when their incomes attain a medium level. It would be promising in further studies to integrate recent findings in geography economics – which insist on the phenomenon of local spillovers in the spirit of Krugman (1991) and Krugman and Venables (1995) on the one hand, and on the spatial heterogeneity and spatial spillovers underlined by Baumont et al. (2006), Battisti and Di Vaio (2008), Ramajo et al. (2008), Pfaffermayr (2009) and Arbia et al. (2010), among others, on the other hand. Acknowledgements This paper has immensely benefited from the comments of two anonymous referees and an editor of this journal. We thank Daniel Opolot for his stimulating remarks. Financial supports from ANR grant no. ANR-05-JCJC-0134-01 (CEDEPTE) and the Université de Strasbourg are gratefully acknowledged. All errors remain our own. References Arbia, G., Battisti, M., DiVaio, G., 2010. Institutions and geography: empirical test of spatial growth model for European regions. Economic Modeling 27, 12–21. Armstrong, H.W., 1995. Convergence among the regions of the European Union. Papers in Regional Science 74, 143–152. Azariadis, C., Drazen, A., 1990. Threshold externalities in economic development. Quarterly Journal of Economics 105, 501–526. Barro, R.J., Sala-í-Martin, X., 1991. Convergence across states and regions. Brookings Papers on Economic Activity 1, 107–182. Barro, R.J., Sala-í-Martin, X., 1995. Economic Growth. McGraw-Hill, New York. Battisti, M., Di Vaio, G., 2008. A spatially filtered mixture of β-convergence regressions for EU regions, 1980–2002. Empirical Economics 34, 105–121.
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