Evidence on convergence in the EU 27 regions
To explore ß-convergence at a regional level for the total GVA, Figure A.1 shows the relationship between the log level of total GVA per worker in 1991 and its growth rate between 1991 and 2007 for 259 EU 27 regions. There is a clear pattern of catching-up. The rate of convergence for the NUTS II regions is estimated at 1.55% per year. This suggests that it takes about 39 years to cover half the initial gap between a poor and a rich regions. The degree of absolute ß-convergence between EU 27 regions seems to be in line with the magnitude that Sala -i-Martin (1996) reports for different samples. The regions with the smaller values of initial log labour productivity and faster growth are situated in the NMS.
Figure A.1 Convergence among EU 27 regions 1991 - 2007 – total GVA per worker
In the same way we explore the ß-convergence for the agriculture GVA; Figure A2 shows the relationship between the log level of GVA Agriculture per worker in 1991 and its growth rate between 1991 and 2007 for 259 EU 27 regions. In this case the rate of convergence is slightly greater, 1,64% and the half-life is about 36 years, less than total GVA. How to previously, the regions with the smaller values of initial log labour productivity and faster growth are potentially situated in the NMS.
An important problem with the concept of unconditional ß-convergence is that it assumes that all regions converge to the same steady state. This implies that the economies in all the different regions can be identically represented. This assumption may be too forced for the different European regions. Indeed, it seems likely that steady states differ among EU 27 regions because of variation in institutional settings, sectoral patterns of production (due to different comparative advantages), educational levels, technology, preferences and so on.
Figure A.1 Convergence among EU 27 regions 1991 - 2007 – agriculture GVA per worker
The more recent literature in convergence has always more often considered the presence of the spatial interdependences (spatial spillovers) that influence the processes of regional convergence by the spatial econometric models (see the references in Dall’Erba et al. (2007) (Sandy Dall’Erba, Rachel Guillain, Julie Le Gallo, Impact of Structural Funds on Regional Growth: How to Reconsider a 7 Year-Old Black-Box?, GRD 06-07 May 2007).
Abreu et al. (Maria Abreu, Henri L.F. De Groot and Raymond J.G.M. Florax, Space and Growth:a Survey of Empirical Evidence and Methods, Region et Developpement, n. 21, 2005, pp. 13-44) underline that the two approaches, traditional and spatial approach to regional convergence, are complementary; the spatial econometric approaches would benefit from considering more carefully the underlying reasons for spatial dependence, while the non-spatial econometric approaches would benefit from testing for spatial dependence, since ignoring it could result in biased coefficients.
Always following Abreu et al (2005) it is necessary to made a distinction between models of absolute and relative location: the former refers to the impact of being located at a particular point in space, while the latter refers to the effect of being located closer or further away from other specific regions. This distinction is also related to a usually classification in spatial econometrics: spatial heterogeneity and spatial dependence: Spatial heterogeneity is joined with the absolute location, while spatial dependence with the relative location.
(da fare: evidenza della componente spaziale, spiegazione delle successive figure)
Magrini (2004) (Magrini, S. (2004): 'Regional (Di)Convergence', in: V. Henderson and l-F. Thisse (eds), Handbook oJ Urban and Regional Economics, Elsevier Science Publishers, Arnsterdam.) presents an overview of the empirical literature on convergence, including studies from both the broader and the spatial econometric literatures. The author argues that regions and countries are not interchangeable concepts, and regional convergence studies should be based on different empirical methods from the ones developed to study cross-country convergence. He concludes by noting that convergence is often confined to groups of geographically contiguous regions.
The spatial econometrics literature has tended to focus on the structural form of the spatial lag and spatial error models, in which the spatial lag terms appear directly on the right hand side of the model. Also the spatial effects captured by the spatial error model are global in the sense that a shock at any location will be transmitted to all other locations by the spatial multiplier process (Anselin, 2002) (Anselin, L. (2002): 'Under the Hood. Issues in the Specification and Interpretation of Spatial Regression Models', Agricultural Economics, 27, pp. 247-267).
Entrambi i modelli, spatial lag e spatial error, utilizzati nello studio della b-convergenza regionale forniscono risposte che aiutano a meglio comprendere tali processi a livello locale solamente se con the exploratory spatial data analysis, that can help with the identification of the spatial regimes, si definiscono ex-ante i club di convergenza (see for example Baumont et al. (2003) (Baumont, C., C. Ertur and J. Le Gallo (2003): 'Spatial Convergence Clubs and the European Regional Growth Process, 1980-1995', in: B. Fingleton (ed.), European Regional Growth, pp. 131-158, Springer, Berlin.); Pecci, Sassi, 2005 (Clueb, Bologna)). In caso contrario the spatial econometric models sulla b-convergenza regionale possono, attraverso la componente spaziale, migliorare l’attendibilità della stima ma non rivelano la presenza di cluster di regioni con differenti regimi.
Per cercare di superare questa limitazione di individuare in precedenza with the exploratory spatial data analysis i cluster di regioni si è optato per utilizzare a different approach to capture spatial effects from that predominant in the literature: the spatial error and spatial lag models.
The aim of our work is to estimate a convergence model with locally different parameters for the EU 27 regions, taking into consideration the problems specified above e per gestire the spatial non-stationarity del coefficiente beta. To the purpose we have used a geographically weighted regression (GWR) che in precedenza è stata utilizzata nei processi di convergenza regionale tra gli altri da (Bivand, R., and R.J. Brunstad. 2003. “Regional Growth in Western Europe: An Empirical Exploration of Interactions with Agriculture and Agricultural Policy.” In B. Fingleton, ed. European Regional Growth. Berlin: Springer- Verlag, pp. 351–373), and Eckey, Hans-Friedrich, Kosfeld, Reinhold and Türck, Matthia (2007) 'Regional Convergence in Germany: a Geographically Weighted Regression Approach', Spatial Economic Analysis, 2:1, 45 – 64
GWR approach
Geographically weighted regression (GWR) is a useful technique to explore spatial nonstationarity (Fotheringham et al, 2002) by calibrating a varying coefficient regression model with the form
(1) , i = 1, 2,….., n,
where yi are the observed dependent variables, (xi1, xi1,…, xip) the explanatory variables at the location (ui,vi) in the studied area and ei are the error terms that are assumed to be independent and normally distributed with zero mean and common variance s2.
Each set of the estimated coefficients at n locations can produce a map of variation which may give useful information on nonstationarity of the regression relationship.
The parameters in the GWR model are locally estimated by the weighted least squares approach. The weights at each location (ui,vi) are taken as a function of the distance from (ui,vi) to other locations where the observations are collected.
The calibration of a MGWR model, as proposed in Fotheringham et al. (2002) is summarized below in matrix notation
,
, i = 1, 2,….., n,
and
where is the ith row of X and
(4) W(ui,vi) = diag[w1(ui,vi), w2(ui,vi), …, wn(ui,vi)]
is an n ´ n diagonal weight matrix at location (ui,vi) (ui,vi are the geographic coordinates of each region), and the weights are taken as a function of the distance from (ui,vi) to other analysed regions. The element of the weight matrix are calculated with a bi-square function (Fotheringam et al., 2002)
(5) wij = [1-(dij/b)2]2 if dij < b
= 0 otherwise
where b is referred to as the bandwidth. If i and j coincide, the weighting of data at that point is equal to unity and the weighting of other data decrease according to a Gaussian curve as the distance between i and j increases. An exhaustive discussion of the matrix S is in Leung et al. (2000).
In the GWR are estimated separate parameters for every region, which is an advantage over the spatial error and the spatial lag model (Anselin, 1988). A spatial dependence in the error term can be caused by a missing spatial varying relationship (Brunsdon et al., 1999, p. 497).
The bandwidth indicates the extent to which the distances are weighted. With a greater bandwidth the smoothing increases. Then regions i and j get a relative larger (smaller) weighting wij, if they are far from (close to) each other. The bandwidth is computed by minimizing the Akaike information criterion (Fotheringham et al., 2002).
To test whether the GWR model is appropriate Brunsdon et al. (1999) have proposed a global test of non-stationarity; this test compares a regression of y on X with sum of squared residuals to a geographically weighted regression. If the null hypothesis of stationarity is rejected, the GWR model is appropriate. The GWR-OLS comparisons may be expressed in the form of an ANOVA table, with residual mean squares for both GWR and OLS. The hypothesis could be tested with a pseudo-F statistic.
GWR – EU 27 Total
Coefficient / Minimum / Lower quartile / Median / Upper quartile / Maximum / Global OLSa0i or a0 / -0.212 / 0.012 / 0.591 / 0.095 / 0.194 / 0.069
b1i or b1 / -0.089 / -0.023 / -0.013 / 0.002 / 0.064 / -0.015
R2i or R2 / 0.036 / 0.676 / 0.892 / 0.954 / 0.996 / 0.522
AIC = - 1719.360; Adaptative bandwidth = 12/259; Global test of non-stationarity: F = 5.828**
Notes: R2: coefficient of determination; R2i: local coefficient of determination; F = empirical F-value; *** p-value < 0.001.
Local R-squared Total GVA
Let us make some general considerations on the validity of the GWR model. The pseudo-F test is highly significant. The local R-squared prove the model fit for every region. In more than 75 % of the regions we have a local coefficient of determination, which is higher than 0.892. The estimation in the greatest part of the regions of New Member States has a good explanatory power.
GWR – EU 27 Agr
Coefficient / Minimum / Lower quartile / Median / Upper quartile / Maximum / Global OLSa0i or a0 / -0.070 / 0.071 / 0.098 / 0.148 / 0.258 / 0.075
b1i or b1 / -0.071 / -0.040 / -0.025 / -0.013 / 0.046 / -0.016
R2i or R2 / 0.131 / 0.480 / 0.680 / 0.843 / 0.984 / 0.314
AIC = - 1355.054; Adaptative bandwidth = 19/259; Global test of non-stationarity: F = 5.994***
Notes: R2: coefficient of determination; R2i: local coefficient of determination; F = empirical F-value; *** p-value < 0.001.
(da fare: spiegazione dei modelli spaziali, concordanze con la bibliografia)
Local R-squared Agricolture GVA
The convergence of 71 regions shows a negative value. The diverging regions are distributed in different areas all over the EU (excluded: Italy, Latvia, Estonia, Lithuania, Finland and Malta).
The highest convergence rates are found above all in Germany and in many regions of the New Member States. Many areas of the New Member States have the highest growth rates, they seem to have a great distance to their steady state values.
These findings suggest that there is no unique convergence rate all over Europe. We detect even considerably different values of the beta-coefficient of regions from one Member State.