Detecting Convergence and Divergence Sub-Clubs: An Illustrative Analysis for Greek Regions

The Empirical Economics Letters, 11(8): (August 2012) ISSN 1681 8997 Detecting Convergence and Divergence Sub-Clubs: An Illustrative Analysis for Greek Regions Artelaris Panagiotis * Department of Geography, Harokopio University, Kallithea, Athens, Greece Kallioras Dimitris Department of Planning and Regional Development, University of Thessaly Greece Email: dkallior@uth.gr Karaganis Anastasios Department of Economic and Regional Development, Panteion University of Social and Political Sciences, Greece Email: akaragan@panteion.gr Petrakos George Department of Planning and Regional Development,University of Thessaly Greece Email: petrakos@uth.gr Abstract: The paper aims to extend the method of convergence clubs, as it is suggested in Chatterji (1992), by allowing for the identification of convergence/divergence sub-clubs. Identifying convergence/divergence subclubs allows for further deciphering the spatial pattern of development of the economy under consideration. The proposed extension is applied to data for Greek NUTS III regions. Keywords: Convergence Clubs; Convergence/Divergence Sub-Clubs; Greek Regions JEL Classification Number: R11, R12, R15 * Corresponding author. Email: partelar@hua.gr

The Empirical Economics Letters, 11(8): (August 2012) 822 1. Introduction The (regional) convergence/divergence issue has been the subject of an intense debate in the past two decades, stimulating numerous studies. From the theory perspective, proponents of neoclassical paradigm argue that disparities are bound to diminish with growth (see Barro and Sala-i-Martin, 1995, for a review), while other schools of thought such as the endogenous (new) growth theories (see Aghion and Howitt, 1998, for a review) and the new economic geography (see Fujita et al., 1999, for a review) tend to agree that growth is a spatially cumulative process, which is likely to increase inequalities. In the middle of this imaginable spectrum, some scholars have proposed new theoretical models that allow for multiple regimes and club convergence among economies (for a review see Azariadis, 1996). Club convergence implies convergence to a common level only for economies sharing similar characteristics (Galor, 1996). In other words, convergence may come about for different groups of economies, indicating, thus, the possibility for the emergence of convergence clubs. From the empirical perspective, the majority of studies have examined convergence/divergence processes utilising econometric models of linear specification, thus, ruling out the possibility that economies can form convergence clubs (for reviews see Magrini, 2004; Petrakos and Artelaris, 2009). However, a few pieces of empirical research have asserted the presence of nonlinearities in the growth process employing a wide variety of methods (e.g. Durlauf and Johnson 1995; Liu and Stengos 1999; Hansen 2000). An alternative econometric approach, in order to investigate for the existence of convergence clubs, has been suggested by Chatterji (1992). This technique, that requires the identification of a lead economy, relates the economic gap (i.e. the difference between the per capita GDP of the leading economy and the per capita GDP of each the economies under consideration) at one date with the corresponding economic gap at an earlier date, including further powers of those earlier levels. On empirical grounds, and at the regional level, this approach has been employed in several studies (e.g. Armstrong, 1995, for European regions; Chatterji and Dewhurst, 1996, for the regions of UK; Kangasharju, 1999, for the regions of Finland; Artelaris et al., 2010, for the regions of the new EU member-states). The paper extends the method of (regional) convergence clubs, as it is suggested in Chatterji (1992), by allowing for the identification of (regional) convergence/divergence sub-clubs. Identifying convergence/divergence sub-clubs allows for further deciphering the spatial pattern of development of the economy under consideration. Paradoxically, this issue has not received any attention in the literature. The proposed extension is applied to data for 51 Greek regions in the period 1995-2005.

The Empirical Economics Letters, 11(8): (August 2012) 823 The remainder of the paper is organized as follows: section 2 extends the convergence clubs method, suggested in Chatterji (1992), section 3 offers an illustrative empirical analysis for the Greek regions, and section 4 presents the conclusions. 2. An Extension of Convergence Clubs Method for the Identification of Sub-Clubs The investigation for the existence of convergence clubs, as proposed by Chatterji (1992), is based on the econometric estimation of the equation: K F, l _ r k= 1 k ( GB, l _ r k G = γ ) (1) where B denotes the initial (base) year of estimation, F denotes the final year of estimation, r denotes the regions under consideration, l denotes the richest of the regions under consideration (lead region), G is the difference (gap) of the logarithms of the variable under consideration (i.e. per capita GDP) between the lead and each of the regions under consideration, γ (1, 2,, K ) is the coefficient of G, and k (1, 2,, K ) are the powers of G. Thus, it is possible for a non-linear relation between the income gap (among the richest and the other of the regions under consideration) in an initial year and the respective gap in a final year to be found. The paper, moving a step further, extends the aforementioned convergence clubs method, by identifying regional convergence/divergence sub-clubs. It does so by calculating the second derivative of the estimated convergence clubs equation, and by finding the corresponding turning points. 3. Identifying Convergence/Divergence Sub-clubs: An Illustrative Empirical Analysis for the Greek Regions The empirical analysis for the Greek regions covers the period 1995-2005, utilizing per capita GDP data, derived from the Hellenic Statistical Authority (HSA), for the Greek NUTS III regions. Prior to the presentation of the results, two important remarks have to be made. The first remark is that the regression is estimated using the Weighted Least Squares (WLS) method, following Artelaris et al. (2010). The conventional Ordinary Least Squares (OLS) method tends to overlook the relative importance (usually in terms of size) of each region in the national setting, treating all regional observations as equal. The WLS method, contrariwise, is able to overcome this major drawback allowing regions to have an influence, which is analogous to their relative size, on the regression results (Petrakos and Artelaris, 2009). The second remark is the unification of the capital region of Attiki with

The Empirical Economics Letters, 11(8): (August 2012) 824 its satellite regions of Voiotia and Korinthia (hereinafter, this is the region of AVK), for the needs of the present paper. This is so, since Attiki has exported a significant part of its industrial activity to Voiotia and Korinthia in order to deal with negative externalities (i.e. major congestion and environmental degradation problems) and to exploit the incentives provided by the Greek State for the decentralization of industrial activity (for further details, see Petrakos and Artelaris, 2008). This might distort the picture obtained, having no data for the regional counterpart of GNP. Table 1 presents the results of the econometric investigation for the emergence of regional convergence clubs, in per capita GDP terms. The dependent variable of the regional convergence clubs equation is the GDP per capita gap (between the richest and each of the regions under consideration) in the year 2005 ( G 2005, l _ r ) and the independent variable is the respective gap in the year 1995 ( G 1995, l _ r ). The lead region is considered to be the region of AVK since this was the richest region in the year 2005, the final year of the Table 1: Convergence Clubs among the NUTS III Regions of Greece, 1995-2005 Variables Estimated coefficients p-value G ) 6.278 0.000 ( 1995, l _ r 2 ( 1995, l _ r ) G 17.928 0.000 3 ( 1995, l _ r ) G 17.758 0.006 Diagnostics R 2 -adjusted 0.737 F-statistic 119.510 0.000 Weighting variable: POP1995 N = 49 observations (NUTS III regions) Source: HSA data / Authors Elaboration. analysis. The variable of relative regional population in the year 1995 (POP1995) is the weighting variable. Since considerable multicollinearity between the various powers of the independent variable makes difficult the choice of the best parsimonious estimation (Chatterji, 1992; Chatterji and Dewhurst, 1996), the final specification of the equations was made under the rule of dropping out the statistically insignificant terms. When two or more equations had statistically significant coefficients, the specification with the lowest value of the Akaike Information Criterion (AIC) criterion was chosen. Under these rules, the third power regional convergence clubs equation was chosen. The estimated equation takes the form:

The Empirical Economics Letters, 11(8): (August 2012) 825 3 2 y = 17.758x 17.928x + 6. 278x (2) where x stands for G 1995, l _ r, and y stands for G, l _ r 2005. The overall explanatory 2 power of the model is very satisfactory. The R adj. figure is relatively high for crosssection data and the independent variable has a statistically significant impact (at the level of 1%) in all powers. Figure 1 depicts the estimated equation. Having the equation y = x as a benchmark (see the dotted straight line), it is evident that all Greek regions diverge from the lead region during the period 1995-2005. This is because, for all Greek regions, the per capita GDP gap in the final year is higher comparing to the respective gap in the initial year (the line of the estimated equation is above the line of the benchmark equation). Figure 1: Convergence Clubs among the NUTS III Regions of Greece, 1995-2005 Source: HSA data / Authors Elaboration. The first derivate of the estimated equation is always positive, indicating that as the initial gap increases, the final gap, also, increases (i.e. the line of the estimated equation is genuinely ascending). The convexity of the estimated equation, however, indicates that, despite the overall trend of regional divergence (i.e. the line of the estimated equation is above the line of the benchmark equation), there are differences, among regions, in the corresponding pace. Calculating the second derivate of the estimated equation, and finding the turning points, it is proved that when the initial gap is lower than 0.337 the line of the estimated equation is concave down (the second derivative is negative) and when the initial gap is higher than 0.337 the line is concave up (the second derivate is positive). This

The Empirical Economics Letters, 11(8): (August 2012) 826 means that divergence follows a diminishing pace only when the initial gap is lower than 0.337. In contrast, divergence follows an incremental pace when the initial gap is higher than 0.337. Figure 2 presents the spatial pattern of divergence in Greece. The expansion of the convergence clubs method allows for the identification of regional divergence (in the current case) sub-clubs. Indeed, in an overall framework of divergence (from the lead region, i.e. the region of AVK), a dualism seems to exist in Greece. This is so, since half of the Greek regions diverge with diminishing pace from the lead region, whereas the other half diverges with increasing pace. Figure 2: Regional Divergence Sub-clubs in Greece, 1995-2005 Source: HSA data / Authors Elaboration.

The Empirical Economics Letters, 11(8): (August 2012) 827 4. Conclusions The paper extends the convergence clubs method, as it is suggested in Chatterji (1992), allowing for the identification of (regional) convergence/divergence sub-clubs. Applied to data for NUTS III Greek regions, this extension allows for the identification of regional divergence sub-clubs. It is revealed that, during the period 1995-2005, in an overall framework of divergence (from the lead region), a dualism seems to exist in Greece. References Aghion P. and Howitt P., 1998, Endogenous Growth Theory, Cambridge MA: MIT Press. Armstrong H., 1995, An Appraisal of the Evidence from Cross-Sectional Analysis of the Regional Growth Process within the European Union, In Armstrong H. and Vickerman R. (Eds.), Convergence and Divergence among European Union, London: Pion, 40-65. Artelaris P., Kallioras D. and Petrakos G.,2010, Regional Inequalities and Convergence Clubs in the European Union New Member-States, Eastern Journal of European Studies, 1(1): 113-133. Azariadis C., 1996, The Economics of Poverty Traps Part One: Complete Markets, Journal of Economic Growth, 1: 449-486. Barro R. and Sala-i-Martin X., 1995, Economic Growth, New York: McGraw-Hill. Chatterji M., 1992, Convergence Clubs and Endogenous Growth, Oxford Review of Economic Policy, 8: 57-69. Chatterji M. and Dewhurst J. H. L., 1996, Convergence Clubs and Relative Economic Performance in Great Britain: 1977-1991, Regional Studies, 30: 31-40. Durlauf S. and Johnson P., 1995, Multiple Regimes and Cross-Country Growth Behaviour, Journal of Applied Econometrics, 10(4): 365-384. Fujita M., Krugman P. and Venables A., 1999, The Spatial Economy, Cambridge MA: MIT Press. Galor O., 1996, Convergence? Inferences from Theoretical Models, Economic Journal, 106: 1056-1069. Hansen B., 2000, Sample Splitting and Threshold Estimation, Econometrica, 68(3): 575-603.

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