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A spatial econometric model for evaluating conditional β-convergence across EU regions

1
A spatial econometric model for evaluating conditional
β
-convergence across EU regions.
Cristina Brasili
1
, Francesca Bruno
1
, Annachiara Saguatti
2 1
Department of Statistics “P.Fortunati”,
2
Faculty of Political Science, University of Bologna Email: cristina.brasili@unibo.it; francesca.bruno@unibo.it The aim of this paper is to assess European Union Cohesion Policy by estimating a conditional
β
-convergence model for a sample of 196 EU regions over the period 1980-2006, using a spatial econometric perspective and a distance-based weight matrix. Under the assumption of substantial coincidence of geographical and economic periphery in EU-15, the final model combines the identification of two regimes and spatial dependence. In particular, we consider Objective 1 and non Objective 1 regions, relatively to 1994-1999 period. A spatial auto-regressive model (Anselin, 1988) with two spatial regimes, including cross-regressive terms to further investigate the role of geographical spillover effects on regional convergence, was estimated. Moreover, the conditioning variables, the regional employment rate and the agricultural share on total employment, allow for further heterogeneity within each regime. The results of this work support the importance of an explicit consideration of spatial effects in convergence analysis (as highlighted in Piras and Arbia, 2007 and Ramajo et al, 2008). The main finding is that the convergence process among EU regions is affected by a polarization into two different clusters converging separately to different steady states, thus implying relative income differences to be persistent. Furthermore, Objective 1 regions are more affected by geographical spillover effects and converge faster to their steady state than non Objective 1 regions. These findings suggest a positive role of EU Regional Policy on convergence among Objective 1 regions and, at the same time, call for a better consideration of spatial spillover effects in planning Regional Policy. Keywords:
β
-convergence; Geographic Spillovers; Spatial Heterogeneity; EU Regional Policy. JEL Codes: C21; C51; O52; R11; R15. This paper was the result of a joint collaboration
.
Professor Cristina Brasili authored Sections 2 and 5.1; Professor Francesca Bruno authored Sections 3 and 5.2; Doctor Annachiara Saguatti authored Sections 4.1 and 4.2. The introduction and the conclusions were jointly contributed by the authors.
2
1
Introduction
The process of European integration ventured along the path of enlargement as far as to the adhesion of 12 new member States (2004-2007) and to the Monetary and Economic Union. This process is rooted in the objective of economic and social cohesion, explicitly formulated since the Single European Act (1986), but already mentioned in the Treaty of Rome of 1957 as a need to reduce regional disparities. The evolution of European Cohesion policies acknowledges that both the deepening of European integration and the territorial enlargement of the Union are not sustainable without a proper redistribution of resources between the member States and their regions as well, thus recognizing the regional dimension of development as the major framework of Structural policies. These great ambitions of deeper integration give birth to great questions. The political and financial sustainability of EU Regional policies, the possible trade-off between social cohesion and competitiveness (Fitoussi, 2006) are often debated, especially in light of the increasing funds devoted to the poorest regions, which have been granted 70% of the Structural Funds in the period 1989-1993 and 81% of them in 2007-2013 (European Commission, 1996; Regulation EC 1083/06). Therefore, criticisms towards Regional policies, perceived just as solidarity measures which damage European competitiveness, are not missing (Fadda, 2006). This paper aims to assess the effects of Cohesion policies on economic convergence among European regions by estimating a conditional
β
-convergence model with spatial effects, thus taking the contribution of New Economic Geography to a substantially neoclassical-born methodology into the due consideration. The debates about the parametric analysis of economic convergence are not ignored and we are aware of the irreducible multidimensional nature of economic growth, which cannot reasonably be synthesised in one single parameter. However, we believe that the rather recent techniques of spatial econometrics that are used in this analysis can lead to interesting findings. The structure of this paper is as follows. Section 2 presents the definition of
β
-convergence and discusses the advantages and disadvantages of this measure of economic convergence. The spatial econometrics techniques that were used for the present analysis are presented in Section 3 and their added value is highlighted. Section 4 describes the data and the results of the exploratory spatial analysis. Model specification and results are presented in Section 5. Finally, the main conclusions and some possible strategies of economic policies are discussed in Section 6.
3
2
Economic Convergence
Convergence is defined as a socio-economic process that is revealed by the progressive reduction of disparities in social and economic indicators of well-being relative to a group of economies (Leonardi, 1995). The existence of a convergence process can therefore reveal the real chances of reaching the aim of better cohesion among different territories and this is the main reason why the measures of economic convergence are so popular, particularly in the field of European Regional policies studies (Button and Pentecost, 1999; Leonardi, 1995; López-Bazo et al., 2004; Rodriguez–Pose and Fratesi, 2004; Ertur et al., 2006; Dall’Erba and Le Gallo, 2007; Piras and Arbia, 2007; Ramajo et al., 2008). Since Baumol’s (1986) pioneering work, convergence studies have been developed through several different techniques of analysis, each of them being able to highlight different dimensions of this phenomenon. The “classical” (Sala-i-Martin, 1996) method of analysis of absolute and conditional convergence –notably the estimation of
β
-convergence in a cross-section of economies- is a parametric technique which srcinates directly from Solow’s neoclassical model of economic growth and whose elaboration is mainly due to the contribution of Robert Barro (1991) and Sala-i-Martin (1991, 1992, 1995). The concept of
β
-convergence suggests the tendency of per capita income of the poorest economies to grow faster than the richest ones’, given a negative correlation between the growth rate of per capita income and its initial level, thus generating a process of convergence (Sala-i-Martin, 1996). If we define
τ γ
/ ])n(l)n([l
0
t iit it
y y
−=
as the average growth rate of per capita GDP in region
i
over the period
0
t
and
t
in a cross-section of
N
economies and for a
τ
number of years, then the classical model that is proposed to test the existence of a convergence process is:
it it it
yba
ε γ
+⋅+=
)ln(
0
(1) where
i=
1, ..., N,
i
y
is the level of per capita GDP in economy
i
, ),0(~
2
σ ε
N
is the error term,
a
and
b
are parameters which are assumed to be stable across the economies. A negative estimation of the parameter
b
in model (1) indicates
absolute
convergence, following the neoclassical theory. Barro and Sala-i-Martin (1992) show how model (1) can be derived through a log-linear approximation from the equation that expresses the dynamic of transition in a
4 neoclassical model of growth with technological progress. The speed of convergence (
β
) can be estimated through the linear regression (1)
1
, following the relation
τ
βτ
/ )1(
−
−=
eb
:
τ τ β
/ )ˆ1ln(ˆ
b
−−=
(2) By calculating the
half life
(
T
) of convergence (Barro and Sala-i-Martin, 1995), it is possible to calculate the number of years that it would take for half of the initial gap between economies to be eliminated. Following 2 / 1
=
−
T
e
β
,
β β
/ 69,0 / )2ln(
==
T
(3) The
absolute
convergence hypothesis is not supported by any empirical proof, though, particularly when studying the economies of different States or regional economies of different States. Barro and Sala-i-Martin (1991) themselves admit the need to take some other factors –called
conditioning variables
- into account, as they prevent the convergence to a unique steady-state to take place. The subsequent model is a model of
conditional
convergence, in which structural differences modify the steady-states of the economies; empirically, the steady-states of the economies (
*
~
i
y
) need to be kept constant in order to estimate
β
. The most common way to do this is to add one or more conditioning variables to model (1):
it it it it
X yba
ε ψ γ
++⋅+=
00
)ln( (4) where
0
t
X
is the vector of conditioning variables and
ψ
is its parameter. Once added the conditioning variables are included, a negative estimate of
b
indicates that a process of
conditional
convergence is taking place. The economic theory can guide the search of the best conditioning variables to include: the Solow model suggests the saving rate, the level of technology and the growth rate of the technological progress, the population growth rate and the rate of depreciation of capital. Other theories may rather suggest the
1
The estimation of
β
following the linear regression (1) leaves the standard error unknown.
)ˆ1( / ˆˆ
β τ σ σ
β
−=
b
can be calculated as an approximation for the unknown standard error. Alternatively it is possible to estimate
β
as the coefficient of a non linear model through the
non linear least squares
(NLS) method, thus obtaining the estimation of the
standard error
(Sala-i-Martin, 1996).
5 inclusion of the expenditure in R&D, the level of human capital, the economic structure, the labour market structure, the political stability, etc…
2
. One of the main criticisms that have been raised against the
β
-convergence approach is that the estimates of
β
persistently tend to equal a value around 0.02 (Quah, 1995). This empirical regularity cannot be considered the product of an economic mechanism: in fact, if this value expressed a general regularity of convergence processes, it would predict a catching up of poorest economies towards the richest ones within 70 years. However, the literature demonstrates that this recurrence is explained by purely statistical reasons (Quah, 1995; Canova and Marcet, 1995). Not surprisingly, the assumptions which the concept of
β
-convergence is based on have been criticised too. Quah (1993) highlights the lack of empirical evidence of a stable long-term trend in the growth of economies. The growth process is rather continuously influenced by shocks that make any assumption of stable growth paths unreal. According to Quah, it is impossible to describe the dynamics of changes that take place in time through a parametric analysis, because what is actually observed is just the situation at the beginning and at the end of the period, under the assumption that a regular trend ruled the changes in between. Finally, the cross-country parametric approach has been criticised because it hardly reveals the presence of multiple regimes in a convergence process, because this concept contrasts with the idea that a unique linear specification exists, which is common to all the observed economies. Possible alternative approaches either identify multiple locally stable steady-states (Durlauf and Johnson, 1995) or analyse effects of polarisation or stratification (Quah, 1997) in search of
convergence clubs
(Canova, 2004).
3
Spatial effects
Intuitions derived from the New Economic Geography show the importance of the spatial location of economies in explaining their growth path, inasmuch as it srcinates a
2
On the choice of possible conditioning variables, see Barro e Sala-i-Martin (1995).

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