Download SPATIAL APPROACH TO TERRITORIAL CONVERGENCE

SPATIAL APPROACH TO TERRITORIAL CONVERGENCE ACROSS
THE EU-15 REGIONS AND THE CAP
Maria Sassi
The European Commission is promoting a reflection on territorial convergence. At the core of its political
agenda there is the understanding of the features of the centre-periphery equilibrium and uneven development,
the common challenges across regions and the territorial impact of the CAP. These issues represent the topic of
the paper, referred to 166 EU-15 regions at NUTS II level and to the time period from 1995-2005. As the CAP is
still a strictly sectoral policy, it primarily affects agricultural growth and through this way economic
convergence. Thus, the empirical analysis, first, characterises the agricultural and economic conditional
catching-up process and, subsequently, compare the local sectoral parameters of convergence. The role of spatial
nonstationarity is detected comparing OLS and GWR estimates. Empirical findings suggest GWR as more
appropriate model specification and preferable for explanatory spatial data analysis in accordance with a
territorial perspective to convergence. Furthermore, there is a high heterogeneity in the behaviour of the different
agricultural and economic regions referable to convergent clubs across neighbouring regions. The analysis also
underlines a general negative correlation between agricultural and economic speed of catching up although the
great diversity between sub-groups of regions calls for a better understanding of the determinants of these
relationships and of the sectoral productivity growth. In this context, the role of the technological capital
accumulation process is underlined, particularly in the light of a CAP that has not been able to support catching
up.
Keywords: economic convergence, agricultural convergence, OLS, GWR
1. Introduction
Cohesion has been reconfirmed as one of the key objectives of the European Union (EU) also
for the current programming period and real convergence is a priority area for reducing
regional disparities and supporting the Regional Policy.
With the Treaty of Lisbon the Cohesion Policy has broaden its scope to include, with a greater
emphasis, the territorial dimension of economic and social cohesion and, on October 2008,
with the Green Paper on Territorial Cohesion the European Commission, is moderately a
lively period of reflection on this perspective with a view of deepening the understanding of
the concept and its impact for policies and cooperation (Commission of the European
Communities, 2008a).
The EU is supporting a local approach to economic and social cohesion as a way for
improving competitiveness of its territories. According to the above mentioned Green Paper,
this target requires to translate into policy actions the three key challenges of concentration,
overcoming differences in density, of connecting territories, getting over distance, and of
cooperation, overcoming administrative borders (Commission of the European Communities,
2008b). These objectives put at the core of the policy agenda at least three key points relevant
for real convergence consisting in understanding the features of the centre-periphery
equilibrium and uneven development in the EU regions; the common challenges across
territorial units; and the policy coordination at local level with a specific focus on the
Common Agricultural Policy (CAP) whose impact should be better understood.
In the light of these considerations, the paper provides empirical findings on the relevance of
these issues considering the role spatial dependence and heterogeneity on real agricultural and
economic convergence across a sample of 166 EU-15 regions at NUTS II level, from 19952005 comparing results from Ordinary Least Squares (OLS) and Geographically Weighted
Regression (GWR) estimates.
As the CAP is still a strictly sectoral policy it is assumed that it primarily affects agricultural
growth and through this way economic convergence. For this reason, the empirical analysis
first investigates the global and local absolute and conditional convergence in the agricultural
1
sector and in the overall economy separately in order to characterise the two specific
processes. Than, it focuses on the possible relationship between the speed of agricultural and
economic convergence at the regional level, comparing the estimated local parameters of
conditional convergence. This section is aimed at assessing whether the intensity of the
convergence process is similar and convergent in the two sectors and if there is consistency or
dissonance between the local agricultural and economic systems.
Concerning the empirical approach, traditional analysis of convergence refers to OLS
estimates of global parameters. However, it can be expected that not only the explanatory
variables differ across space but that also the regression coefficients are location specific.
More precisely, variation in the total responses from a particular variable would be caused by
variation in the independent variable, variation in its marginal response, and covariance
between the two (Ali et al., 2007). To include the aspect, the role of spatial nonstationarity
has been detected comparing results from OLS and GWR.
In this respect, the interest is in understanding, first, the capacity of the OLS approach to
represent properly the agricultural and economic convergence and the improvement of GWR
over OLS; second, the importance of a territorial approach to convergence through the
discussion of the local parameters estimated particularly of the control regressors of policy
nature. Despite the focus on the role of the CAP, the paper does not follow a normative
approach, but a positive approach. It only analyses the contribution of the agricultural policy
to the catching-up process in the EU-15 without any consideration on the possible reform of
the policy.
Mapping results from GWR it is investigated whether spatial heterogeneity is linked to the
concept of convergence clubs, characterised by multiple, locally stable, steady state equilibria
(Durlauf, Johnson, 1995) and their spatial autocorrelation. This information is of specific
importance for the evaluation of the possibility of networks across regions in policy design
and implementation in order to reinforce actions through synergic effects, as suggested by the
European Commission.
The paper is structured as follows: section 2 presents the background of the study, section 3
illustrates the methodology, section 4 assesses critically the appropriateness of the OLS model
to represent the process under analysis and the improvement of GWR model, section 5
discusses the absolute and conditional local parameters of convergence and section 6 the role
of control regressors and of the intercept term, section 7 compares agricultural and economic
parameters of convergence and section 8 concludes.
2. Background
As mentioned in the Introduction the today debate on territorial convergence should consider
at least three key issues consisting in the understanding of the features of the centre-periphery
equilibrium and uneven development that characterises the economic activities in the EU; the
common challenges across territorial units for a better design of local policies; and a possible
effective policy co-operation at local level starting from the assessment of the territorial
impact of policies and particularly on the CAP (European Commission – DG Regional Policy,
2008).
The first topic has been strongly debated by the theoretical literature. The starting point in the
analysis of regional differentials in per capita income and labour productivity is the
neoclassical model of long-run growth of Solow (1956) and Swan (1956) on the basis of
which Barro and Sala-i-Martin (1992) have elaborated the concept of absolute -convergence
and Mankiwet et al. (1992) that of conditional -convergence. The traditional assumption at
the basis of this approach is that, due to diminishing marginal returns of input factors in a
production function with constant return to scale, regions converge to a dynamic steady state,
where the evolution is only driven by the rate of technological progress (Eckey et al., 2007).
2
As knowledge is entirely disembodied and, technically, understood as a pure public good,
distance does not play a role in the convergence process. In other words, regional differentials
of income and their growth rates cannot be explained on the basis of regional divergences in
the stock of knowledge: knowledge spillover diffuses instantaneously across any territorial
unit that, imitating the more successful technology, catches up immediately the other regions
(Döring, Schnellenbach, 2006).
This assumption, that is also at the basis of the neoclassical new growth theory and of the
early endogenous growth theory, has been strongly criticised by the theoretical and empirical
literature. The economic geography theory usually assumes that knowledge is a regional
public good with limited spatial range and plays the same role as classical spatial interaction
related to population, capital and material (Abreu et al., 2005). From this assumption there is
the possibility of different paths of regional growth and of coexistence of divergent and
convergent groups of territorial units. This theoretical perspective explains the agglomeration
process and the geographic spillover in the interaction between geography and growth.
Consequently to these theoretical approaches, the search for spatial autocorrelation has
emerged as an approach to the explanatory analysis of regional interdependence.
Empirical literature can be articulated into three main strands. There are studies that:
- Establish links between agglomeration, the evolution of regional income and the level of
overall growth (Fujita, Thisse, 2002; Martin, Ottaviano, 2001; Baldwin, Forslid, 2000)
- Investigate the impact of spatial spillovers effects on innovation, growth and regional
disparities (Anselin et al., 1997; Bottazzi, Pieri, 2003; Funke, Niebuhr, 2005; Fingleton,
2003);
- Detect the role of spatial heterogeneity on regional convergence on the basis of the concept
of convergence clubs (Quah, 1996; Baumont et al., 2003).
The need to consider agglomeration and spillovers in convergence process has also been
supported by results of the empirical literature that has suggested to take into consideration
the spatial dependence of regions (Temple 1999) in the light of the problem of bias regression
coefficients or invalidation of significant tests when detecting the neoclassical hypothesis of
convergence by an OLS model (Anseline, 1988; Cliff, Ord, 1973).
To address the issue, new techniques of analysis have been introduced. The approaches
followed by the empirical literature on spatial effect in convergence process can be divided
into univariate and multivariate spatial data statistics. The former, that includes Getis-Ord
Statistics, Moran Scatterplot, Anselin Local Indicators of Spatial Association, is aimed at
describing and visualising spatial distributions, identifying outliers, detecting spatial
association and cluster, and suggesting spatial heterogeneity (Fingleton 2003; Fotheringam et
al., 2006). These approaches do not allow estimating the impact of the spatial component on
the speed of convergence. In this respect, the multivariate spatial data statistics are more
appropriated. Among them, spatial global regressions (Spatial Lag, Cross-Regressive and
Error models) have been widely applied (Le Gallo et al., 2003). These models introduce in the
estimation equation an endogenous or exogenous spatial lag variable or assume that the
spatial dependence works through omitted variables. They produce parameter estimates that
represent an average type of behaviour (Fotheringam et al., 2006). However, according to the
principles of the regional science not only explanatory variables might differ across space but
also their marginal responses (Ali et al., 2007). The GWR technique, developed by Brusdon,
Charlton and Fotheringam (Fotheringham et al., 2002) and adopted in the paper, addresses the
issue estimating locally different parameters. This possibility makes the model of specific
interest for detecting territorial approach to convergence. Despite its strong points, this
econometric technique is not widely adopted in the empirical literature mainly due to its
relatively recent development.
3
The GWR approach is also promising referring to the need for understanding the lines of a
possible cooperation across regions. In fact, the technique develops hypothesis on
convergence clubs from the data (Fotheringham et al., 2006) as opposed to the traditional
types of analysis in which data is used to test a priori hypothesis of groups of regions whose
initial conditions are near enough to converge towards the same long-term equilibrium1. The
possibility of mapping the local parameters estimated provides a visual inspection of a likely
spatial autocorrelation, that is, the coincidence of attribute similarity and locational similarity
(Anselin, 1988). Information on spatial concentration of economic activities in the EU not
only allows to overcome the traditional empirical assumption of spatial independence
between regions of the OLS estimates but also to understand if rich and poor regions tend to
be geographically clustered.
Finally, the need for policy coordination on the ground of territorial cohesion calls for the
assessment of the territorial impact of secotral policies and among them, according to the
Green Paper, a specific attention should be deserved to both the Pillars of the CAP. The issue
has also been debated and confirmed as a priority area of understanding during the French
Presidency conference on Territorial Cohesion and the Future Cohesion Policy hold on 30-31
October 2008 (Délégation Interministérielle à l’Aménagement et la Compétitivité des
Territoirs, 2008). In this respect, the GWR approach allows to consider how much of a policy
response might be related on the amount of resources allocated in a certain region, on the
capacity of the region to make use of them and on spillover. The information is relevant
concerning the CAP because the hot issue is how to centre it more on a territorial dimension
than a sector.
3. Methodology
3.1. OLS model
The empirical analysis starts testing the neoclassical hypothesis of absolute -convergence by
an OLS approach for the agricultural sector and the overall economy. The econometric
specification makes reference to a version of the model developed by Barro and Sala-i-Martin
(1991, 1992) and Sala-i-Martin (1996) and is given by the following equation:

y
1
T
i,

y0

ln

b
b
ln

i

 0 1 i,
Ny
i
,
0



2
No,
I
(1)
where y is the explanatory variable, i (i=1, 2, …, M) the 166 NUTS II regions, N the 11 years
in the time period [0, T] where 0 is 1995 and T 2005,  the stocastic error, b0 the intercept
and b1 the coefficient of convergence that is expected to be negative for the absolute
convergence hypothesis to hold in the sample (Barro, 1991a, 1991b; Baumol, 1986; Barro,
Sala-I-Martin, 1992; Quah, 1993).
The explanatory variables, from EUROSTAT, are:
- Gross Agricultural Value Added per Agricultural Working Unit (AVA/AWU), in detecting
agricultural convergence;
- Gross Domestic Product in PPP per worker (GDP/WOR), in testing economic catching-up.
AVA/AWU is indicated by the literature as a proxy of the agricultural income even if a
measure of the labour productivity. The assumption can be supported in the EU contest where
a large share of farms are family farms and thus own the majority of primary productive
factors. Furthermore, the agricultural working units2 have been preferred to the number of
workers. It introduces a homogeneous measure of the labour force in a sector characterised by
1
For a survey of the models that generate clubs of convergence see, for example, Gallor (1996).
The number of hours comprising an AWU should correspond to the number of hours actually worked in a fulltime job within agriculture.
2
4
a significant share of workers that participate to the annual agricultural activity with a limited
number of hours as par-time or seasonal workers.
Concerning the estimation referred to the economy, the literature commonly makes reference
to three measures of growth:
- Growth output, as indicator of the growth of productive capacity that depends on the extent
to which regions are affecting capital and labour force from other territorial units;
- Growth of output per worker, as indicator of productivity growth and thus of the change in
the competitiveness of a region;
- Growth of output per capita, as indicator of change in economic welfare (Amstrong, Taylor,
2000).
The GDP per worker has been preferred to per capita GDP because more accurate from a
theoretical standpoint and more robust from an empirical perspective. GDP per capita is equal
to GDP per worker only assuming the unrealistic hypothesis, at least in the EU context, of
full employment.
The second step in empirical analysis consists on detecting conditional -convergence making
reference to the following equation:


y
1
i
,
T




ln

b

b
ln
y

b
(
x
)

(2)
0
1
i
,
0
j
i
,
j
i


j
N
y
i
,
0

where xi,j is the control regressor j in region i.
A negative coefficient of the core explanatory variable supports conditional convergence
hypothesis to be hold in the sample, i.e. when differences in control regressors across regions
and time are controlled for, low values of income per capita would be associated with higher
growth rates in subsequent years.
The conditional -convergence for agriculture is detected including in equation (2) the weigh
of the EU support to the sector on the agricultural value added, whit the reference years
strongly dependent on data availability. The role of the CAP is estimated in terms of:
- Total Transfers to the agricultural sector per unit of agricultural value added (TAS/AVA);
transfers relate to both price support and direct and other payments provided by the II EUCohesion report and are referred to 1996;
- Structural Fund expenditure provided by ESPON (2005) and related to Agriculture, Rural
Development and Fishery (Objective 5b and 6, EAGGF, IAGF) per unit of agricultural value
added (SFA/AVA) from1994-1999.
The denominator for this latter variable is a relevant issue: results might vary significantly
according to its choice3. For this reason, the analysis also testes Structural Fund expenditure
related to Agriculture, Rural Development and Fishery per ha of utilised agricultural area, per
AWU and over GDP. The best results are achieved with AVA as a denominator.
The conditioning variables selected for the economy are those that the theory traditionally
suggests as important for growth (see, for example, Barro, 1991b; Levine, Renelt, 1992), that
is:
- Human capital stock, approximated by the number of students in the lower and upper
secondary education on population aged 15-19;
- Investment, captured by gross fixed capital formation as a percentage of GDP that measure
the level of investment in the regions;
- Research and development, approximated by the number of patent applications on
population and on workers;
- Average annual growth rate of employment.

3
The empirical literature, for example, suggests that there are substantial differences in labour and land intensity
due to different agricultural production systems (see, for example, European Commission – DG Regional Policy,
2003).
5
The variables refer to the EUROSTAT dataset whose availability, in some cases, represents a
constraint for the definition of the variables to be included in the empirical analysis.
3.2. GWR approach
Spatial nonstationarity and heterogeneity across the regions of the sample is detected by the
GWR approach that replaces global OLS regression coefficients by local parameters i so that
the global absolute and conditional -convergence models are rewritten respectively as:



y
1
i
,
T



ln

b
(
u
,
v
)

b
(
u
,
v
)
ln
y

i
i
i
1
i
i
i
i
,
0
i

0
N
y
i
,
0


(3)



y
1
i
,
T





ln

b
(
u
,
v
)

b
(
u
,
v
)
ln
y

b
(
u
,
v
)
ln(
x
)

0
i
i
1
i
i
i
,
0
i
,
j
i
,
j
,
ji
i
,
j
i


j
N
y
i
,
0


(4)
where (ui , vi ) denotes the geographic coordinates of the ith region of the sample.
As illustrated in Figure 1, in GWR each data point is a regression point that is weighted by it
distance from the regression point itself. Through this method, a spatial kernel adapts to the
data.
Figure 1 – GWR and spatial kernel
X regression point; Wij weight of data point j at regression point i; ● data point
Weighted regressions in local estimates allows to overcome the problem of more unknown
parameters than degrees of freedom rose in calibrating equations (3) and (4). The weight
assigned to observations is an inverse function of the distance from region i, that is:

1
ˆ


b
(
u
,
v
)

X
'
W
(
u
,
v
)
X
X
'
W
(
u
,
v
)
y
i
i
i
i
i
i
(5)
with

(
u
,v
)
(
u
,v
)

(
u
,v
)


k
1
1
0 11 1 11


(
u
,v
)
(
u
,v
)

(
u
,v
)


0
2
2
1
2
2
k
2
2
ˆ
b
(
u
v

i,
i)
 

 





(
u
,v
)
(
u
,v
)

(
u
,v
)
0
n
n
1
n
n
k
n
n


6
(5.a)
a n set of local parameters each of which is estimated by
ˆ
1X
b
X
'W
X
'W
Y
n 
n
n
(5.b)
where n represents a row of the matrix in (5.a). Wn is a diagonal n by n matrix in the form of
0
w
 11
w

22
W
n 



0 0

 0

0 
  


w
nq

(5.c)
with wij the weight of the data at point j on the calibration of the model around points i.
The spatially weighting scheme selected is an adaptive bi-square function (Brunsdon et al
1998, Bivand, Brunstad, 2005) defined as:
  

22
1

d
/h

ij
w


ij

0

ifd

h
ij
(6)
otherwise
where h represents the different bandwidths. The scheme is adaptive in the sense that the
bandwidth expresses the number of regions to retain within the weighting Kernel window
irrespective of the geographic distance (Fotheringam et al., 2002). The choice of the spatial
weighting function is based on the comparison among the statistics tests referred to the
alternative fixed Gaussian or near-Gaussian schemes.
The optimal number of the regions to retain in the Kernel window is selected minimising the
Akaike Information Criterion (AIC) (Hurvich et al., 1998; Fotheringham et al., 2006) a
method also adopted for assessing whether GWR provides a better fit than the global
approach. Finally, the individual parameters spatial stationarity is investigated by the Monte
Carlo test (Fotheringham et al., 2006).
3.3. Agricultural and economic convergence: a comparison
Once estimated the local agricultural and economic speeds of convergence, they are compared
on the regional level in order to investigate a possible relationship.
Regions are classified as strongly convergent when the local parameter of convergence is
greater than the global, as convergent if lower but negative and as divergent in the case of a
positive local parameter of convergence. Results are mapped and the intensity of association
summarised by the Spearman's rank correlation coefficient given by:
s 1
6
di2

i
(7)
2
N
(N

1
)
where di is the difference between the ranks of corresponding variables, and N is the number
of values in each data set (same for both sets). The correlation coefficient can only reach -1 in
the case of maximum negative correlation and +1 when there is maximum positive
correlation between the two sets of variables.
4. Do OLS estimates represent properly agricultural and economic convergence?
This section is aimed at testing the capacity of the OLS models to provide a good
representation of the agricultural and economic convergence process.
7
Table I and II show results from absolute and conditional -convergence for agriculture,
while Table III and IV for the economy, presenting, in this latter case, only the model of
conditional convergence with the significant control regressor according to the statistics tests,
that is the change in employment (CWOR).
Table I - Agriculture: Absolute -convergence – OLS method (1995-2005)
Coefficient Standard Error
t-Value
Pr> | t |
B0
0.0939
0.0106
8.87
< 0.0001
AVA/AWU
-0.0241
0.0034
-6.91
< 0.0001
Adjusted r-squared
0.2208 Residual sum of squares
0.11656
Sigma
0.02666 F-value
47.76
AIC
-728.1406 Pr>F
<0.0001
Coefficient of determination
0.22105
Table II - Agriculture: Conditional -convergence – OLS method (1995-2005)
Coefficient Standard Error
t-Value
Pr> | t |
B0
0.0926
0.0102
9.0822
<0.0001
AVA/AWA
-0.0239
0.0017
-6.6591
<0.0001
TTA/AVA
-0.00495
0.0016
-3.1067
0.0029
SFA/AVA
0.00233
0.0011
2.1590
0.0238
Adjusted r-squared
0.26025 Residual sum of squares
0.1080
Sigma
0.02582 F-value
21,2
AIC
-736.5581 Pr>F
<0.0001
Coefficient of determination
0.2781
Table III - Economy: Absolute -convergence – OLS method (1995-2005)
Coefficient Standard Error
t-Value
Pr> | t |
B0
0.0945
0.0078
12.1938
0.0000
GDP/WOR
-0.0225
0.0021
-10.4970
0.0000
Adjusted r-squared
0.3945 Residual sum of squares
0.0106
Sigma
0.0080 F-value
110.2
AIC
-1126.0938 Pr>F
0.0000
Coefficient of determination
0.4018
Table IV - Economy: Conditional -convergence – OLS method (1995-2005)
Coefficient Standard Error
t-Value
Pr> | t |
B0
0.0024
0.0146
0.1648
0.8693
GDP/WOR
-0.0222
0.0019
-11.8232
0.0000
CWOR
-0.0488
0.0068
-7.1476
0.0000
Adjusted r-squared
0.5374 Residual sum of squares
0.5458
Sigma
0.0070 F-value
97.53
AIC
-1169.6958 Pr>F
0.0000
Coefficient of determination
0.5458
All the regressions estimated support the neoclassical hypothesis of convergence. Without
entering in more detail into the results achieved, it should be noticed that introducing the
control regressors in both agricultural sector and in the overall economy, the speed of
catching-up does not change significantly, confirming the legendary 2 per cent convergence
rate. This achievement seems to hold the view expressed by a part of the empirical literature
8
that finds this rate of convergence as almost ubiquitous (Abreu et al., 2005), or quoting Sala-iMartin (1996) as a “natural constant”.
In this respect, more recent investigations (see, for example, Abreu et al., 2005) found that
correcting for the endogeneity of the explanatory variables has a substantial effect on the
estimates (Islam, 2003). It is also observed that potential heterogeneity in estimates of the rate
of convergence within the literature on catching-up may be related to differences in the way
technology is treated. This consideration suggests relaxing the core neoclassical assumption
of exogenous technological change.
These considerations also find support in the analysis developed. In fact, turning to the
regressions estimated, the low adjusted r-squared indicates that a significant percentage of the
variance in the agricultural and economic labour productivity is unexplained. Theoretical and
empirical literature suggest that some of this unexplained variance might result from
assuming the relationships in the models to be constant over space or from the omission of
some relevant explicative variables related to geography (see, for example, Fotheringam et al.,
2006).
This possibility is detected mapping residuals from the models of conditional convergence
(Figure 2 and 3).
Figure 2 - Agriculture: OLS model residual surface
Figure 3 - Economy: OLS model residual surface
9
A visual inspection of the two maps reveals quite a distinct geographic pattern of residuals. In
this situation the relationships estimated cannot be taken as a good representation of the
process under investigation (Arbia, 2006). For this reason, the role of spatial dependence and
heterogeneity is investigated in the empirical study.
4.1. The role of space in convergence process: improvement of GWR over OLS
Table V and VI compare global and local models of agricultural and economic convergence
respectively.
Table V - Agriculture: Comparison among global and local models
Equation (1) Equation (3) Equation (2) Equation (4)
OLS
GWR
OLS
GWR
AIC
-728.1406
-805.6361
-736.5581
-825.1968
Effective number of parameters
2.0000
42.5198
4.0000
40.9235
p-value Monte Carlo Test:
b0i
0.0000***
0.0000***
AVA/AWA - b1i
0.0000***
0.0000***
TTA/AVA - b2i
0.0000***
SFA/AVA - b3i
0.0000***
*** = significant at .1 % level; ** = significant at 1% level; * = significant at 5% level
Table VI - Economy: Comparison among global and local models
Equation (1) Equation (3) Equation (2) Equation (4)
OLS
GWR
OLS
GWR
AIC
-1126.0938 -1271.0323 -1169.6958
-1289.8923
Effective number of parameters
2
14.4298
3
23.62
p-value Monte Carlo Test:
b0i
0.0000***
0.0000***
GDP/WOR - b1i
0.0000***
0.0000***
10
CWOR - b2i
0.0000***
*** = significant at .1 % level; ** = significant at 1% level; * = significant at 5% level
In both cases, the lowest AIC refers to the conditional -convergence estimated with the
GWR approach. Furthermore, concerning the agricultural sector, also the complexity of the
model reduces.
According to the Monte Carlo Test, all the explanatory variables are significantly spatially
nonstationary. The observed spatial variation of all the explanatory variables is sufficient to
reject the hypothesis that their parameter is globally fixed.
The better performance of the GWR model than the OLS model is also underlined by an
approximate F-test (Table VII and VIII).
Table VII – Agriculture: Goodness-of-fit test for improvement in model fit of GWR over OLS
Source
SS
DF
MS
F
OLS Residuals
0.1
4.00
GWR
0.1
36.92
0.0020
Improvement
GWR Residuals
0.0
125.08
0.0003
7.3400***
SS: sum of squares; DF: effective degree of freedom; MS: mean square; F: F-statistic: p-value: the probability of
F-distribution with degrees of freedom 4 and 36.92; *** = significant at .1 % level
Table VIII – Economy: Goodness-of-fit test for improvement in model fit of GWR over OLS
Source
OLS Residuals
GWR
Improvement
GWR Residuals
SS
0.0
0.0
DF
3
32.70
MS
0.0003
0.0
130.30
0.0001
F
5.1162***
SS: sum of squares; DF: effective degree of freedom; MS: mean square; F: F-statistic: p-value: the probability of
F-distribution with degrees of freedom 3 and 32.70; *** = significant at .1 % level
The parameters estimates are better modelled as a spatially variable parameters from region to
region within the EU-15. In other words, the simple linear relationship between the dependent
and the independent variables is not constant across the study area.
Table IX and X summarise the local parameters estimated according to equation (4) for
agriculture and the overall economy respectively.
Table IX - Agriculture: Parameter summaries equation (4) - GWR method
Minimum Lwr Quartile
Median
Upr Quartile
Maximum
b0i
-0.0193
0.0345
0.0552
0.0772
0.2753
AVA/AWA -0.0876
-0.0199
-0.0128
0.0067
0.0272
b1i
TTA/AVA - b2i
-0.0595
-0.0070
-0.0024
0.0028
0.0270
SFA/AVA - b3i
-0.0214
-0.0035
-0.0001
0.0041
0.0197
Optimal bandwidth
35 regions
Residual sum of squares
0.0341
Sigma
0.0165
Coefficient of Determination
0.7720
Adjusted r-square
0.6968
11
Table X - Economy: Parameter summaries equation (4) - GWR method
Minimum Lwr Quartile
Median
Upr Quartile
Maximum
b0i
-0.1154
-0.0145
0.0319
0.0742
0.3685
GDP/WOR - b1i
-0.0457
-0.0349
-0.0221
-0.0109
0.0063
CWOR - b2i
-0.1064
-0.0483
-0.0297
-0.0054
0.0982
Optimal bandwidth
34 regions
Residual sum of squares
23.6278
Sigma
0.0045
Coefficient of Determination
0.8370
Adjusted r-square
0.8098
Comparing OLS (Table II and IV) and GWR regression diagnostics, it is confirmed that the
GWR regression outperforms the OLS method. GWR estimates not only show a better
goodness of fit, as suggested by the improvement of the adjusted r-squared, but also a smaller:
- Residual sum of squares, underlining that GWR model is closer to the observed date;
- Sigma, pointing out the lowest standard deviation for the residuals provided by the GWR
approach.
Furthermore, as standardised residuals are between –3 and +3 no observation is unusual.
Figure 4 and 5 map the locals r-squared of the two models that inform on how stable is the
model in the neighbourhood regions. In other words, it measures how well the model
calibrated at regression point i can replicate the data in its vicinity or neighbourhood. As our
models are potentially non-stationary, estimated local r-square is predicted to be low.
Figure 4 – Agriculture: Local r-squared
Figure 5 – Economy: Local r-squared
12
Contrary to this expectation, a high percentage of the variability in the dependent variable,
particularly for the agricultural sector, is explained by the independent variables at each
regression point. The process modelled is relatively stable in a wide group of regions.
5. The local parameters of conditional convergence
Table IX and X show that the hypothesis of convergence verified with the global estimates
does not find confirmation in all the NUTS II agricultural and economic regions and when it
is supported the rate of convergence varies across the territorial units. Figure 6 and 8 provide
more accurate information on the spatial variability of the agricultural and economic local
parameters of convergence mapping their values. Figure 7 and 9 represent the respective local
absolute t values classified to different significant levels specified in the caption. This latter
test has a purely explanatory role due to the multiple hypothesis testing problem4, so it should
be interpreted as highlighting parts of the map where interesting relationships appear to be
occurring (Fotheringam et al., 2006).
Figure 6 - Agriculture: Estimated local parameters of agricultural convergence from the
model (4)
4
In GWR lots of t tests are run. If alpha=0.05 is set as significance level, we will reject the null 5 times out of a
100. In other words, in lots of tests we would expect to reject the null hypothesis even when it is correct.
13
Figure 7 - Agriculture: local t value from the model (4)
t-student
Pr
1.28
0.10
1.64
0.05
2.58
0.005
3.29
0.0005
Figure 8 - Economy: Estimated local parameters of economic convergence from the model (4)
14
Figure 9 - Economy: local t value from the model (4)
t-student
Pr
1.28
0.10
1.64
0.05
2.58
0.005
3.29
0.0005
The speed of catching-up for the agricultural and the economic sector is included between two
extremes. On the end there is a club of strongly convergent regions and on the other that of
divergent regions. In between, there are some well-defined sub-groups of convergence
territorial units with different speeds of catching-up. Furthermore, there is a high degree of
coincidence between attribute similarity and location similarity.
15
It is interesting to notice that in a large number of regions the t-test suggests a strong
relationship between the dependent and independent variable. The weakest relationships are,
mainly, in the Central-Northern part of the EU-15.
In general terms, during the time period analysed it seems that there has not been a clear
change towards a more convergent Europe considering both the economy and the agricultural
sector.
5.1. Comparison between absolute and conditional b-convergence
GWR findings contradict the OLS estimates when they suggest a similar speed of absolute
and conditional catching-up in both the agricultural sector and the economy. As illustrated in
Figure 10, the local parameters estimated with the conditional -convergence model changes
also significantly with respect to those estimated with the absolute -convergence model.
Figure 10 – Box plot of the local parameters of convergence
BASA = Agriculture: local parameters of convergence referred to the absolute agricultural -convergence
BOCA = Agriculture: local parameters of convergence referred to the conditional agricultural-convergence
BESA = Economy: local parameters of convergence referred to the absolute economic -convergence
BCOE = Economy: local parameters of convergence referred to the conditional economic -convergence
The aspect is better illustrated in Figure 11 and 12 where regions have been classified
according to the level of the local absolute -convergence and to its change with respect to the
local parameter of conditional -convergence in the 14 classes listed in Table XI.
Table XI – Classification of local absolute and conditional parameters of convergence
Number
Absolute -convergence
Conditional -convergence
with respect to the absolute
1
Strong convergence
Reduction but convergent
2
Strong convergence
Reduction and divergent
3
Strong convergence
Stable
16
4
5
6
7
8
9
10
11
12
13
14
Strong convergence
Average convergence rate
Average convergence rate
Average convergence rate
Weak convergence
Weak convergence
Weak convergence
Weak convergence
Divergence
Divergence
Divergence
Reinforcement
Reduction but convergent
Stable
Reinforcement
Reduction but convergent
Reduction and divergent
Stable
Renforcement
Reduction and convergence
Reinforcement
Reduction in divergence
Strong convergence = more than the average convergent rate plus 10%; average convergent rate = between
+10% and –10% the average convergence rate; weak convergence = less than the average convergence rate
menus 10%
When differences in control regressors across regions and time are controlled for, the local
parameters of conditional convergence improve in the majority of the agricultural regions in
the sense that there is a reinforcement of the speed of convergence or a reduction in that of
divergence.
Figure 11 - Comparison between the estimated local parameters of agricultural convergence
from model (3) and (4)
On the contrary, for the economic convergence changes are negligible for a wide number of
strong convergent regions in the Eastern side of the EU-15, while for the other territorial units
the change is mixed but with a general tendency towards an improvement of the speed of
catching-up.
Figure 12 - Comparison between the estimated local parameters of economic convergence
from model (3) and (4)
17
These findings call for the understanding of the agricultural and economic control regressors
in agricultural and economic growth process.
6. The role of the control regressors
Contrary to what suggested by the global parameters estimate, the impact of both TAS/AVA
and SFA/AVA on catching-up process is mixed in terms of direction of the impact. The
marginal response of TAS/AVA shows a wider local variability ranging from -5.95 to 2.70
per cent while for SAF/AVA it is from -2.14 to 1.97 per cent (Table IX). These values suggest
that in certain regions the impact of the EU support to agriculture on the sectoral growth has
been significantly different from the global value, an aspect difficult to be predicted with the
global estimates.
The cartographic representation of the local parameters estimated and of their t value provides
interesting additional information.
First, it underlines that the significant and stronger impact of TAS/AVA only refers to a little
number of regions, mainly concentrated in the Eastern side of the EU-15, where it has
negative singe suggesting that direct transfers have run counter the convergence process
(Figure 13 and 14).
Figure 13 – Local estimates of TAS/AVA
18
Figure 14 - Local t value for TAS/AVA
t-student
Pr
1.28
0.10
1.64
0.05
2.58
0.005
3.29
0.0005
Concerning SFA/AVA, the positive and strong relationship refers to a major number of
territorial units but its intensity is very low (Figure 15 and 16).
Figure 15 - Local estimates of SFA/AVA
19
Figure 16 - Local t value for SFA/AVA
t-student
Pr
1.28
0.10
1.64
0.05
2.58
0.005
3.29
0.0005
A different situation characterises the control regressor for the economy. The marginal
response to changes in employment is more intense and, in the majority of the regions,
negative (Figure 17). Moreover, it is a robust relationship in all the territorial units but the
regions in the Central area of EU-15 (Figure 18).
20
Figure 17 - Local estimates of CWOR
Figure 18 – Local t value for CWOR
t-student
Pr
1.28
0.10
1.64
0.05
2.58
0.005
3.29
0.0005
6.1. The intercept term
In the equations estimated, b0 is the total factor productivity, that is a parameter accounting
for effects in total output not caused by the explanatory variables of the model. One of its
21
most important components is technological growth, a key concept of the traditional
neoclassical approach to convergence. Results from the GWR models contradict this view,
according to which the initial level of technology and its rate of growth are constant and
identical for all the countries, contributing to the underway discussion concerning the more
appropriate models of relaxing this assumption (see, for example, Abreu et al., 2005).
As illustrated in Table IX and X, the value of the intercept for the agricultural sector and the
overall economy varies across regions and Figure 19 and 21 provides a more accurate
representation of its geographic distribution with Figure 20 and 22 showing the local t value.
Figure19 - Agriculture: Map of the intercept term from model (4)
Figure 20 – Agriculture: Local t- value for intercept from the model (4)
22
t-student
Pr
1.28
0.10
1.64
0.05
2.58
0.005
3.29
0.0005
Figure 21 - Economy: Map of the intercept term from model (4)
Figure 22 - Economy: Local t- value for the intercept term from the model (4)
23
t-student
Pr
1.28
0.10
1.64
0.05
2.58
0.005
3.29
0.0005
In both the sectors the role of this component as a driver of growth is relevant and the
relationship with the dependent variable is strong in a large number of regions.
Regarding the agricultural sector, it is interesting to notice that, in general, the intercept has a
strong and significant impact in the regions where relationship between sectoral growth and
direct transfers is weak and where the agricultural productivity is higher than the average.
7. Agricultural and economic convergence: a comparison
According to the OLS estimates conditional agricultural and economic convergence show a
similar speed. The GWR models do not support this result.
The central tendency of the local parameters estimated suggests a higher speed of
convergence for the economy (Table IX and X) while the middle 50% of the distribution is
closer to the median value in the case of the agricultural sector that, on the other hand, shows
a large number of outliers (Figure 10).
At the regional level, a general identification between the overall economic and agricultural
speed of convergence emerges. The Spearman’s rank correlation coefficient equal to -0.5258
underlines a negative correlation between the two rates of catching-up.
However, considering the single local systems, findings point out the implementation of
different regional paths of agricultural and economic catching-up, as illustrated in Figure 23
that compares agricultural and economic local parameters of convergence classified with
respect to their global value.
Figure 23 – Agricultural and economic local parameters of convergence
24
The three prevailing typologies of regions are those characterised by:
- Strong economic convergence and agricultural convergence;
- Agricultural and economic convergence;
- Strong agricultural convergence and economic convergence.
Figure 23 also shows a distinct spatial coherence between different agricultural and economic
parameters of convergence although a great diversity between sub-groups exists.
This result, already shown by the single sectors, confirms the operational of specific
characteristics that seems to be connected to the national or sub-national level.
In addition to this, the classification has carried out significant differences among sub-groups
underlining that the relationship between agricultural and economic productivity can be
affected differently not only by EU wide measures, but also by territorial specific
interventions.
8. Conclusions
The paper has detected the agricultural and economic absolute and conditional convergence
process across 166 EU-15 regions at NUTS II level over 1995-2005 comparing OLS and
GWR estimates.
The OLS models have displayed a clear evidence of -convergence at a speed of 2%
independently on the sector and controlling regressors. However, various tests aimed at
investigating the presence of spatial effects lead to a GWR model as more appropriate model
specification. Neglecting these effects, results are unreliable. More precisely, OLS estimates
reveal quite distinct geographic pattern of residuals, affected by a spatial variation of the
relationships in the model that contribute to the legendary 2 per cent speed of catching-up.
GWR models seem to be preferable to OLS techniques when real convergence is detected and
is a useful tool for explanatory spatial data analysis in accordance with a territorial
perspective to convergence.
These results do not support the neoclassical approach that underlines the existence of a
homogeneous convergence process, generally of the conditional type. In fact, it seems that
that a rather complex process exists in which the most significant characteristic is the high
heterogeneity in the behaviour of the different agricultural and economic regions. Findings
are in line with the recent theoretical literature referred to the new economic geography and
endogenous growth framework.
25
According to this perspective, convergence clubs have been observed. In this respect, it has
emerged that spatial autocorrelation in both the agricultural and economic convergence
process affect neighbouring regions mainly within national borders underlining the possible
importance of short-distance spillovers and growth dependency and the need for further
assessment of the role of national factors, such as national institutions, policies and
legislation. On this point, the empirical literature does not concur that spatial spillover factors
are more important than national factors in affecting agglomerations (Quah, 1996;
Bräuninger, Niebuhr, 2005).
The analysis has pointed out a prevailing negative correlation between agricultural and
economic speed of convergence at the regional level. This suggests the need for further
investigation of the reasons of this relationship. In fact, it can be attributed to various factors
among which the different weight of the agricultural and the economic sectors in the regions
and to its interaction with their average productivity levels or the different rhythm of
resources transfer from the agriculture to other sectors at the regional level (Cuadrado-Roura
et al., 1999).
The economic convergence process across the EU-15 regions has not achieved significant
results and returns, to the future, an EU that need to identify growth strategies and
instruments of economic policy more suitable and effective. This is of specific importance in
the light of the reconfirmed priority given the cohesion policy by the EU.
In this context, the analysis suggests a better understanding not only of the relationship
between agricultural and economic convergence at the regional level, but also of the
determinants of the regional agricultural productivity growth and, particularly, of the
technological capital accumulation process in a situation in which the CAP measures seem to
have not supported the sectoral catching-up.
REFERENCES
- Abreu, M, de Groot, HLF & Florax, RJEM (2005), A meta-analysis of b-convergence: the
legendary 2%, Journal of Economic Surveys, 19, 3, pp. 389-420.
- Ali, K, Partridge, MD & Olfert, MR (2007), Can Geographically Weighted Regressions
Improve Regional Analysis and Policy Making?. International Regional Science 30, 3, pp.
300-329.
- Amstrong, A & Taylor, J (2000), Regional Economics and Policy, Blackwell Publishers,
Oxford.
- Anselin, L (1988), Spatial Econometrics Methods and Models, Kluwer, Dordrecht.
- Anselin, L, Varga, A & Acs, Z (1997), Local Geographical Spillovers between University
Reseach and High Tecnology Innovations, Journal of Urban Economics, 42, 3, pp. 422-448.
- Arbia, G (2006), Spatial Econometrics, Springer, Berlin.
- Baldwin, RE & Forslid, R (2000), The Core-periphery Model and Endogenous Growth:
Stabilizing and Destabilizin Integration. Economica, 80, pp. 307-324.
- Barro, RJ (1991a), A Cross-Country Study of Growth, Saving, and Government, National
Saving and Economic Performance, University of Chicago Press, Chicago.
- Barro, RJ (1991b), Economic Growth in a Cross-Section of Countries, Quarterly Journal of
Economics, 106, pp. 407-443.
- Barro RJ, Sala-i-Martin, X (1991), Convergence across States and Regions, Brooking
Papers on Economic Activities, vol. 1, pp. 107-182
- Barro RJ, Sala-i-Martin, X (1992), Convergence, Journal of Political Economy, 100, pp.
223-251.
26
- Baumont, C, Ertur, C & Le Gallo, J (2003), ‘Spatial Convergence Clubs and European
Regional Growth Process, 1980-1995’, In B Fingleton (ed), European Regional Growth,
Springer, Berlin.
- Baumol, WJ (1986), Productivity Growth, Convergence and Welfare: What the Long Run
data Show, American Economic Review, 76, pp. 1076-1085.
- Bivand, R, Brunstad, R (2005), ‘Further explorations of interactions between agricultural
policy and regional growth in Western Europe: approaches to nonstationarity in spatial
econometrics’, Proceeding of the 45th Congress of the European Regional Science
Association, Amsterdam 23-27 August.
- Bottazzi L & Pieri G (2003), Innovation and Spillovers in Regions: Evidence from European
Patent Data, European Economic Review, 47, pp. 687-710.
- Bräuninger, M & Niebuhr, A (2005), Agglomeration, Spatial Interaction and Convergence
in the EU, Schmollers Jahrbuch - Journal of Applied Social Science Studies/Zeitschrift für
Wirtschafts- und Sozialwissenschaften, Bd. 128, Nr. 3, S. 329-349..
- Brusdan, CF, Fotheringham, AS & Charlton, ME (1998), Spatial nonstationarity and
autoregressive models, Environment and Planning, A 30, pp. 957-973.
- Cliff, AD & Ord, JK (1973), Spatial Autocorrelation, Pion Press, London.
- Commission of the European Communities (2008a), Communication from the Commission
to the Council, the European Parliament, the Committee of the Regions and the European
Economic and Social Committee – Green Paper on Territorial Cohesion – Turning territorial
diversity into strength. SEC (2008) 2550, COM(2008) 616 final, Brussels.
- Commission of the European Communities (2008b), Commission Staff Working Document
accompanying the Green Paper of Territorial Cohesion Turning Territorial Diversity into
Strenght, Sec(2008), Brussels.
- Cuadrado-Roura J, Garcia-Greciano B & Raymond JL (1999), Regional Convergence in
Productivity and Productive Structure : The Spanish case, International Regional Science
Review, 22, pp. 35-53.
- Délégation Interministérielle à l’Aménagement et la Compétitivité des Territoirs (2008),
‘Reform of the Common Agricultural Policy and the European Cohesion Policy’,
Proceedings, Conference on Territorial Cohesion and the Future of the Cohesion Policy.
Paris, 30-31 October.
- Döring, T & Schnellenbach, J (2006), What Do We Know About Geographical Knowledge
Spillovers and Regional Growth? – A Survey of the Literature, Research Notes, Regional
Studies, 40, 3, pp. 375-395.
- Durlauf, SN & Johnson, PA (1995), Multiple Regimes and Cross-Country Growth
Behaviour, Journal of Applied Econometrics, 10, pp. 365-384.
- Eckey, HF, Dreger, R & Türck M (2007), Regional Convergence in Germany: a
Geographically Weighted Regression Approach, Spatial Economic Analysis, 2, 1, pp. 45 – 64.
- European Commission – DG Regional Policy (2003), ‘Analysis of the impact of Community
Policies
on
Regional
Cohesion’,
viewed
10
October
(2008),
<http://ec.europa.eu/regional_policy/sources/docgener/studies/pdf/3cr/impact_full.pdf>.
- European Commission – DG Regional Policy (2008), European Commission adopts Green
Paper on Territorial Cohesion, IP/08/1460.
- Fingleton, B (Ed.) (2003), European Regional Growth, Springer, Berlin.
- Fotheringham, AS, Brunsdon, C & Charlton, M (2002), Geographically weighted
regression: The analysis of spatially varying relationships, Wiley, West Sussex.
- Fotheringham, AS, Brunsdon, C & Charlton, ME (2006), Geographically Weighted
Regression, Wiley, West Sussex .
- Fujita, M & Thisse, JF (2002), Economics of Agglomeration. Cities, Industrial Location,
and Regional Growth, Cambridge University Press, Cambridge.
27
- Funke, M & Niebuhr, A (2005), Regional Geographic R&D Spillovers and Economic
Growth: Evidence from West Germany, Regional Studies, 39, 1, pp. 143-153.
- Gallor, O (1996), Convergence? Inferences from Theoretical Models, Economic Journal,
106, pp. 1056-1069.
- Hurvic, CM, Simonoff, JS & Tsai, CL (1998), Somoothing parameter selection in
nonparametric regression using and improved Akaike information criterion, Journal of the
Royal Society Series, B 60, pp. 271-293.
- Islam, N (2003), What have we learnt from the convergence debate? Journal of Economic
Surveys, 17, pp. 309–362.
- Le Gallo, J, Ertur, C & Baumont, C (2003), ‘A Spatial Econometric Analysis of
Convergence Across European Regions, 1980-1995’, In B Fingleton (Ed), European Regional
Growth, Springer, Berlin.
- Levine, R & Renelt, D (1992), A sensitivity analysis of cross-country growth regressions,
American Economic Review, 82, pp. 942-963.
- Mankiw, NG, Romer, D & Weil, DN (1992), A Contribution to the Empirics of Economic
Growth, Quarterly Journal of Economics, 107, 2, pp. 407-437.
- Martin, P & Ottaviano, GIP (2001), Growth and Agglomeration, International Economic
Review, 42, pp. 947-968.
- Quah, D (1993), Empirical cross- section dynamics in economic growth, European
Economic Review, 37, pp. 426-434.
- Quah, D (1996), Regional Convergence Cluster across Europe, European Economic Review,
40, pp. 951-958.
- Sala-i-Martin, X (1996), The classical approach to convergence analysis, Economic Journal,
106, pp. 1019-1036.
- Solow, RM (1956), A contribution to the theory of economic growth, Quarterly Journal of
Economics, 70, pp. 65-94.
- Swan, TW (1956), Economic Growth and capital accumulation, Economic Record, 32, pp.
334-351.
- Temple, J (1999) The New Growth Evidence, Journal of Economic Literature 37, pp. 112156.
28