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DIPARTIMENTO DI SCIENZE ECONOMICHE AZIENDALI E STATISTICHE
Via Conservatorio 7 20122 Milano
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VIII Milan European Economic Workshop, June 11th - 12th 2009 Università degli Studi di Milano
EIBURS project, European Investment Bank
Pubblicazione depositata ai sensi della L. 106/15.4.2004 e del DPR 252/3.5.2006
REGIONAL INFRASTRUCTURE AND CONVERGENCE: GROWTH IMPLICATIONS IN A SPATIAL FRAMEWORK
CHIARA DEL BO MASSIMO FLORIO GIANCARLO MANZI
Working Paper n. 2009-34
NOVEMBRE 2009
JEAN MONNET CHAIR
Economics of European Integration
Regional infrastructure and convergence: growth implications in a spatial framework
Chiara Del Boa*, Massimo Florioa, Giancarlo Manzia
This Version: Novembre 24th 20091
a Università degli Studi, Milano * Corresponding author: chiara.delbo@unimi.it
Abstract In this paper we contribute to the debate on convergence, by presenting an overview of the catch up process of the EU regions between 1995 and 2006, focusing on both absolute and conditional β convergence. Our focus is on the role of infrastructure stock in shaping the growth and convergence process between EU regions and to what extent the spatial dimension of the data affects results. We also explicitly examine the link between infrastructure evolution and regional economic growth with a spatial panel data approach. Our results confirm an ongoing convergence process at the EU regional level, and assess the important role of transport and telecommunication infrastructure, with traditional and spatial estimation techniques. We also confirm, in a panel setting, the strong positive correlation between transport and TLC indicators and GDP growth at the regional level. JEL: H54, O11, E62, R11 Keywords: infrastructure capital, regional growth, convergence, spatial econometrics.
1. Introduction and Motivation
The question of whether countries and regions are converging in terms of income levels over
time has been an intensively debated topic, and several empirical and theoretical contributions have
tried to shed light on the issue (for a comprehensive review, see Barro and Sala-i-Martin, 2004).
With respect to the situation of the EU, the convergence hypothesis is extremely relevant since one
of the main aims of Cohesion Policy is to promote increasing equality amongst Member States’
regions through the instrument of Structural Funds. Infrastructure provision is also an important
factor driving growth (Romp and De Haan, 2007), calling for a detailed analysis of its effect on
economic activity and the catching-up process among regions.
Several authors have analysed the problem by considering countries as the unit of analysis
(Barro and Sala-i-Martin, 1992; Levine and Renelt, 1992), US states and regions in single or few
EU countries (Evans and Korras, 1996; De La Fuente, 2002; Carrington, 2006; Eckey et al. 2007;
Morana, 2004) and regions in the EU-27 as a whole (Magrini, 2004; Ertur and Koch, 2006; Fischer
and Stirbock, 2005; Debarsy and Ertur, 2006). From a technical standpoint, the main measure of
convergence refers to the speed of adjustment, given the initial conditions. With respect to β-
1 Acknowledgments: This paper has been prepared under the EIBURS research grant to the University of Milan (“Public Investment under Budgetary Constraints in New Member States”). The authors wish to thank A. Caragliu, and participants at the VIII Milan European Economic Workshop, June 2009, , for helpful suggestions and discussions on an earlier version, and J.P. LeSage an J.P. Elhorst for providing Matlab routines. The usual disclaimer applies.
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convergence, both unconditional and conditional regressions have been performed, leading to a
wide array of conclusions. Recently, the interest in the regional spatial disaggregation, has led to a
strand of research that explicitly accounts for spatial dependence and autocorrelation issues. The
stress on the spatial dimension characterizes other studies that assess conditional convergence
among regions and the impact of infrastructure on growth (for example Mas et al., 1995; Kelejian
and Robinson, 1997, Lopez-Bano et al., 2004; Le Gallo and Dall’Erba, 2006; Arbia et al. 2008) and
results support the conclusion of convergence towards a middle-rich level for richer regions and
convergence towards a lower level for poorer regions (Quah, 1996). The specific role of
infrastructure to regional development has also been object of an interesting strand of literature,
(Biehl et, 1986; Rothengatter and Schaffer, 2004), while its effects on the convergence process are
receiving increasing attention (Canaleta et al., 2002; Ding et al., 2008;). When testing the impact of
infrastructure on growth for the European regions, some recent studies find that the economic effect
of the investments in infrastructure are stronger in the more developed regions where there is an
environment that can exploit them (e.g. Cappelen et al., 2003).
Our main contribution with this paper is to present an overview of the convergence process
of European regions between 1995 and 2006, distinguishing between unconditional and conditional
β convergence, with an explicit focus on the New Member States (NMS) and physical infrastructure
stocks, and to consider the spatial dimension of the data. Our main research questions are to verify
whether EU regions are converging to a common steady state and the role of three potential factors
that may shift this process: the recent wave of enlargement, transport and telecommunications
(TLC) infrastructure levels and, finally, the presence of spatial interactions. We also explicitly
examine the link between infrastructure evolution and regional economic growth with a panel data
approach. Our results point to the direction of an EU-level convergence process, with a complex
behaviour of regions belonging to NMS, a non trivial role for infrastructure and relevant spatial
issues. We also confirm the strong positive correlation between transport and TLC indicators and
GDP growth at the regional level.
The paper is structured as follows. Section 2 describes the data and general trends and
provides visual evidence of the link between infrastructure and economic growth while Section 3
presents results for unconditional convergence. Section 4 reports results of conditional convergence
analysis and examines the role of infrastructure, accounting for spatial issues in the data as well.
Section 5 exploits the time dimension and highlights the correlation between transport and
telecommunication infrastructure and economic activity with panel model estimation, also in a
spatial framework. Finally, Section 6 summarizes and concludes.
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2. Data and descriptive statistics
The variables used in the empirical analysis are yearly data for the 1995-2006 period at the
national and NUTS2 regional level and are taken from EUROSTAT and the Cambridge
Econometrics database. Aggregated data for the overall EU-27 and for the 15 pre- (EU15) and 12
post- (EU12) EU last enlargements (2004 and 2007) are also considered for descriptive and
comparison analysis. Our main variable of interest is the growth of GDP per inhabitant. Data are
processed and averages of yearly rates are considered for the models described below.
To verify the role of infrastructure we considered traditional transport within regions, measured by
the overall length of internal motorways and, for the investments in TLC, we used the number of
mobile phone subscriptions. The EUROSTAT database does not provide the regional values of
subscribers. We overcame this issue by first obtaining the national number of subscribers per capita
(by dividing the national number of subscribers to the national population), and then by multiplying
this figure to the regional population.
Some control variables are also used. The stock of physical capital is derived from the gross fixed
capital formation series at NUTS2 level from Cambridge Econometrics, by applying the perpetual
inventory method, with base year 1990 and a linear yearly depreciation rate of 2.5. Labour force is
measured by regional employment levels in terms of population with 15 years and over from the
Cambridge Econometrics dataset. The last control variable is human capital which is measured as
the percentage of labour force working in the science and technology (S&T) sector.
Our choice of infrastructure indicators was driven by the fact that the levels and growth in
the length of motorways and mobile phone subscriptions captures the evolution of two important
aspects of the regional infrastructure stock that may be linked to economic performance and growth.
Roads represent the traditional communication infrastructure, which has been considered, in the
literature, extremely relevant to economic activity (Aschauer, 1990; Romp and De Haan, 2007;
Haque and Kim, 2003; Rioja, 2005; Button, 1998), while mobile phone subscriptions are a proxy
for the increasing role of TLC and information technologies in general in shaping growth patterns
(Ding et al., 2008; Datta and Agarwal, 2004; Calderon and Chong, 2004; Camagni and Capello,
2005).
A note of caution should be put forward with respect to the spatial unit of analysis, namely
the EU NUTS2 (nomenclature des unités territoriales statistiques) classification. As pointed out by
several authors (see for example Basile, 2008 and citations herein for a discussion of this issue), this
classification is mainly formal and not functional, giving rise to MAUP (Modifiable Areal Unit
Problem), originally put forth by Unwin (1996), which implies that estimation results may be
affected by the choice of the level of spatial disaggregation. While Functional Areas would be the
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ideal spatial disaggregation, the NUTS2 system has several advantages, since it is comparable
across EU countries and allows the use of official EUROSTAT data on relevant control variables,
such as the infrastructure characteristics we are examining in this paper. It also important to note
that decisions on infrastructure expenditures are often taken at the NUTS2 administrative level,
which represents the government decision level of, for example, Structural Funds allocation and
spending.
When considering the impact of regional infrastructure endowment on GDP growth, a
preliminary analysis can be performed by examining descriptive statistics. Table 1 displays the
regional averages of growth of GDP per capita, length of motorways and mobile phone
subscriptions between 1995 and 2006 for the whole sample and splitting it according to timing of
accession in the EU. We are therefore focusing on the road and TLC components of the overall
infrastructure capital stock at the regional level.
Table 1 shows the average yearly growth of per capita GDP, the motorways length average
growth and the mobile phones growth of the EU countries and of EU15 and EU12 countries
separately. It can be noted that the GDP growth of EU12 countries has more than doubled that of
EU15 countries during the 1995-2006 period. However, the variability of the GDP in each group is
low, being very similar the standard deviation of per capita GDP in both groups (0.0173 for EU12
and 0.0178 for the EU15).
As for the motorways growth, only Italy, Lithuania Sweden and UK have decreased the
length of their motorways network (-0.001 for Italy, -0.02 for Lithuania, -0.045 for Sweden and -
0.01 for the UK), whereas the Czech Republic and Hungary have experienced substantial growth.
The motorways growth of EU12 countries is significantly higher than that of EU15 countries during
the period (0.114 and 0.0135, respectively).2 Standard deviations are quite different though, and are
equal to 0.233 and 0.017, respectively.
A more widespread growth rate of mobile phones subscriptions can be noted for the EU12
countries. The eastern countries in particular have had average growth levels which are twice the
size of the average values for western countries. In particular Romania (5.7%), Czech Republic
(5.6%), Poland (5.1%), Slovakia (4.9%), and Lithuania (4.8%) have mobile phone subscriptions’
growth rates close to 5% or above.
Figure 1 illustrates the spatial distribution of GDP in Euro per inhabitant and of the logarithm of
mobile phone subscribers in three years of the period considered in the EU-27, according to five
classes of GDP and five classes of the logarithm of mobile phone subscribers. This figure gives a
visual idea of the evolution of GDP and the mobile phone subscribers in the last years: the Eastern 2 Slight differences with respect to figures provided by national statistical offices might be due to different definitions of the level of government to which motorways refer to.
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regions GDP growth towards western levels is evident, and a general tendency towards common
levels of mobile phone subscribers is even more evident. Figure 2 shows the spatial distribution of
the motorways length per labour force unit: in this case a few changes can be observed, except for
the Eastern countries which registered a more intense growth.
Country averages
GDP growth
Motorways growth
Mobile Phones growth
Austria 0.026 0.003 0.302 Belgium 0.028 0.002 0.307 Bulgaria 0.073 0.020 0.519 Cyprus 0.046 0.035 0.248
Czech Republic 0.081 0.343 0.568 Germany 0.015 0.011 0.256 Denmark 0.034 0.025 0.163 Estonia 0.131 0.036 0.33 Spain 0.054 0.039 0.323
Finland 0.039 0.036 0.141 France 0.027 0.059 0.306 Greece 0.047 0.02 0.306
Hungary 0.076 0.358 0.301 Ireland 0.088 0.087 0.281
Italy 0.041 -0.001 0.249 Lithuania 0.135 -0.02 0.485
Luxembourg 0.051 0.014 0.272 Latvia 0.128 0 0.415 Malta 0.045 0 0.288
Netherlands 0.037 0.018 0.295 Poland 0.074 0.033 0.516
Portugal 0.049 0.02 0.297 Romania 0.083 0.018 0.577 Sweden 0.035 -0.045 0.128 Slovenia 0.055 0.056 0.351 Slovakia 0.089 0.033 0.49
United Kingdom 0.059 - 0.01 0.21 EU 0.047 0.035 0.306
EU15 0.038 0.014 0.263 EU12 0.079 0.114 0.471
Note: EU15: Austria, Belgium, Germany, Denmark, Spain, Finland, France, Greece, Ireland, Italy, Luxembourg, Netherlands, Portugal, Sweden, UK. EU12: Bulgaria, Cyprus, Czech Rep., Estonia, Hungary, Lithuania, Latvia, Malta, Poland, Romania, Slovenia, Slovakia.
Table 1: GDP and Infrastructure Growth (EUROSTAT data; authors’ elaboration)
1995 2000 2006
1995 2000 2006
Figure 1. GDP in Euro per inhabitants (in thousands of Euro) and log of mobile phone subscribers according to different levels.
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1995 2000 2006
Figure 2. Motorways in km over Labour Force.
3. Unconditional Regional Convergence in the EU
The aim of this section is to present our empirical investigation of the unconditional
convergence process of growth rates in the European region. Our first research question is: do we
find evidence of convergence at the NUTS2 level, and can we say something about different sub-
samples of EU regions? In sub Section 3.1, we consider the regional growth rate of GDP per capita
between 1995 and 2006, and regress it against the initial level of per capita GDP, therefore testing
the so called hypothesis of “unconditional β convergence”. We also consider the possibility of
distinct convergence processes between groups of regions, by looking at old and new Member
States, at regions that received Structural Funds and also account for the possibility of an
infrastructural gap.
3.1 Unconditional β-convergence
The theoretical foundation for absolute β convergence is the standard neoclassical growth
model, and empirical applications, formalized in the context of cross-section analyses by Barro and
Sala-i-Martin (2004), regress the annual average growth rate of GDP per capita against the natural
logarithm of initial level of per capita GDP. Therefore, the general testable convergence equation is
of the form:3
εβα ++Α= totT yg 0, (1.)
where is annual average growth rate of GDP per capita between 1995 and 2006, is
logarithm of the initial level of per capita GDP in 1995,
0,tTg toy
Α is the constant (or unity vector) and the
error term is . ),0( 2εσε iid≈
There is evidence of a process of convergence if β is negative and statistically significant.
This theoretical framework allows the computation of the average speed of convergence of the
economies considered and the corresponding half life in terms of years necessary to reach the
steady state, following Mankiw et al. (1992) and Barro and Sala-i-Martin (2004).
We will perform an absolute convergence test first on the whole sample of the 264 EU
regions considered,4 with GDP in per capita terms from 1995-2006, then we will explore the
possibility of the existence of convergence clubs (Quah, 1996; Debarsy and Ertur, 2006; Fischer
and Stirbock, 2006) allowing for the possibility of the existence of multiple steady states, and
shaping different process of convergence by clustering regions with similar characteristics. We
follow Durlauf and Johnson (1995) by selecting clubs exogenously, first dividing the sample
3 Subscript i for the regional dimension omitted for clarity of exposition. 4 A list of the NUTS2 used in the empirical analysis is presented in the Appendix.
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between regions in old and new Member States, then separating the recipient of Structural Funds
(Objective 1 regions) from the others and finally looking at regions with low initial stocks of
physical transport and telecommunication infrastructure.
Table 1 provides evidence in favour of convergence amongst European region for the 12
year time span considered by robust OLS estimation. The estimated parameter on the initial level of
income is negative and statistically significant in all specifications. The implied value of
convergence speed ranges from 3.6% (EU 15 regions, Column 2) to 2.4% (Non-Objective 1
regions, Column 5), with an average value for the whole sample of 2% (Column 1).5 In terms of
half life, the average value is of 31 years. These figures are comparable with values found in some
previous studies: Barro and Sala-i-Martin (2004) found a 2% convergence speed, as Fisher and
Stribock (2006), Yudong and Weeks (2000) and Bond et al. (2001).
Dep. Var. GDP Growth Rate 1. All 2. EU15 3. EU12 4. Obj. 1
5. Non Obj. 1
6. Low Infra. 7. Others
Initial GDP -0.02402*** -0.0297*** -0.0082 -0.0284*** -0.0215*** -0.0223*** -0.0382*** 0.000 0.000 0.213 0.000 0.000 0.000 0.000 Constant 0.2747*** 0.3291*** 0.1502** 0.3131*** 0.2505*** 0.26*** 0.4084*** 0.000 0.000 0.005 0.000 0.000 0.000 0.000 R2 0.599 0.338 0.0451 0.6475 0.4693 0.5717 0.6968 N° Obs. 264 209 55 93 171 213 51
Note: p-values associated with robust standard errors in italics. ***, **, * indicate significance at the 1%, 5% and 10% level. EU15: Austria, Belgium, Germany, Denmark, Spain, Finland, France, Greece, Ireland, Italy, Luxembourg, Netherlands, Portugal, Sweden, UK. EU12: Bulgaria, Cyprus, Czech Rep., Estonia, Hungary, Lithuania, Latvia, Malta, Poland, Romania, Slovenia, Slovakia. Obj. 1 regions: where GDP is below 75% of the Community average.
Table 2: Absolute Convergence (1995-2006) Moving on to the analysis of exogenous convergence clubs, grouping regions in our sample
according to whether they belong to NMS (Columns 2 and 3, Table 2), whether they were
classified, according to the EU Structural Funds classification, as Objective 1 regions (Columns 4
and 5, Table 2), and finally by performing a cluster analysis based on the 1995 infrastructure stock
(both transport and TLC) level (Columns 6 and 7, Table 2), we can highlight some interesting
results.
With respect to the NMS, they appear to be converging, but at a slower pace with respect to the
EU15 sub-sample, and the result is not statistically significant at any conventional level. Given that
regions in NMS tend to have, on average, lower initial GDP levels, but are experiencing a rather
heterogeneous growth path, it might be that the convergence process in the whole sample is driven
5 Considering a standard Cobb- Douglas production function, the implied rate of annual convergence is derived by:
Te Tβ
γ −−=
1 , while the half life is derived from )1ln(/)2ln( βτ +−= .
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by a subset of regions. To further explore this idea, we have divided the EU12 regions according to
initial values of GDP (Table 2) and indeed find that the more endowed regions (Column 1, Table 3)
are converging with a 2% convergence speed, while no statistically significant process seems to be
occurring in the lower GDP sub-sample.
Dep. Var. GDP Growth Rate
1. EU12 high GDP
2. EU12 low GDP
Initial GDP -0.0223* -0.0067
0.09 0.516 Constant 0 .2717** 0.1395*
0.021 0.090 R2 0.1988 0.0117
N° Obs. 16 39 Note: p-values associated with robust standard errors in italics. ***, **, * indicate significance at the 1%, 5% and 10% level. EU12: Bulgaria, Cyprus, Czech Rep., Estonia, Hungary, Lithuania, Latvia, Malta, Poland, Romania, Slovenia, Slovakia.
Table 3: Convergence for NMS
Considering Columns 4 and 5 of Table 1, Objective 1 regions, which are those that are
below 75% of the Community average in terms of GDP, are converging at a slightly faster rate than
the average, though the two groups seem rather homogeneous.6 When instead we consider the
existence of the infrastructure gap, the regions with very low initial transport and TLC stock appear
to be converging at a lower speed than the others (Columns 6 and 7 of Table 1).
This preliminary analysis of absolute β convergence therefore points in the direction of the
existence of a process of convergence among European regions, especially in those belonging to
structurally less endowed, but highly dynamic countries.
In the following Section we want to extend this intuition by considering conditional
convergence and highlighting the role of infrastructure endowment in explaining growth of regions
and the convergence process.
4. Conditional convergence and the role of infrastructure capital on regional growth
In this Section we will examine the role of infrastructure on growth in more detail, with an
explicit focus on the process of conditional convergence, and taking into account spatial interactions
that might characterize our data. As stressed by Le Gallo and Ertur (2003) and Magrini (2004), the
presence of spatial autocorrelation, both in levels and in growth rates of GDP, in European regions
6 A recent criticism to the definition of Objective 1 regions in the UK is put forth by Gripaios and Bishop (2006), which conclude that the qualifying regions may not have been optimally selected, possibly providing an explanation to the small difference we find between the two groups in Table 3.
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calls for the application of spatial econometric models to overcome the misspecification bias due to
the underlying spatial process and the possible presence of omitted spatial variables.
Therefore, our contribution in this Section is twofold. First, we will assess the contribution
of regional infrastructure endowment on the growth process of the EU regions with classical
regression models and verify whether the absolute convergence hypothesis still holds when
considering additional controls (Table 4). Second, we will explicitly consider issues of spatial
autocorrelation by estimating appropriate spatial models, and verify the conditional convergence
behaviour of EU regions in a spatial framework (Table 5).
Dependent variable: GDP Growth Rate OLS
Initial GDP -0.0293***
0.000 Δ(Capital) 0.3826
1.35 Δ (Labour) 0.066***
0.000 Human Capital 0.0631***
0.002 Motorways 0.0936***
0.000 Mobile Phones 0.3113***
0.000 Constant 0.2933***
0.000 R2 0.716 N° Obs. 264
Note: p-values associated with robust standard errors in italics. ***, **, * indicate significance at the 1%, 5% and 10% level.
Table 4: Conditional Convergence
We now turn our attention to the impact of road and TLC infrastructure levels in 1995 on
GDP growth between 1995 and 2006. Our measures consider the physical stock of transport and
TLC infrastructure. For transport infrastructure we consider the length of motorways and the
number of mobile phone subscriptions, variables which were described in detail in Section 1. We
add to the regression the regional capital stock and labour force, the percentage of labour force
working in S&T, as a proxy for human capital, along with the initial level of GDP to test the
convergence hypothesis. We include the capital and labour variables in growth form and consider
initial levels of infrastructure endowment and human capital to control for initial conditions other
than the GDP level and to overcome possible issues of reverse causation.
Table 4 shows estimates of a log-linearized regression of the general form:
ελγβα ++Δ++Α= XXyg totT 0, (2.)
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where the dependent variable is annual average growth rate of GDP per capita between 1995 and
2006, is the initial level of per capita GDP in 1995, toy Α is the constant (or identity vector), XΔ
is the matrix of growth rates of control variables and X is the matrix of initial levels of control
variables, and the error term is . Specifically, in Column 1, ),0( 2εσε iid≈ XΔ includes the variation
of the fixed capital stock and labour over 1995-2006, the stock of human capital and the level
motorways and mobile phone subscriptions in 1995.
By performing robust OLS methods (Column 1, Table 4) we still find evidence of a
convergence process and show that human capital endowment has a significant and positive
elasticity. The estimated convergence parameter is on average equal to -0.029 with the inclusion of
additional variables and controlling for the effect of infrastructure, in line with results for absolute
convergence in Section 2 (Table 2, Column 1), therefore we do not find evidence of faster
convergence when infrastructure is included in the specification. An improvement of model fitting
(R2 of 0.716 in Column 1 of Table 4) can also be noted. The estimated coefficient of infrastructure
measures, highlighting the correlation with GDP growth, is of around 30% for mobile phones and
9% for kilometers of motorways. We will also see, in Table 5, by accounting for spatial patterns in
the data, that these effects are still statistically significant and with a comparable value of the
estimated coefficient. This may imply the existence of synergic effects among spatial units in terms
of transport infrastructure efficiency. The coefficient associated to the initial value of mobile phone
subscriptions is quite high,7 possibly reflecting the advantage of early adoption of a new
technology.8
These results may however be misleading if we don’t account for the possibility that
infrastructure capital and other variables in the model may be spatially linked among regions, and
that our OLS estimates could be missing important features of the data. We therefore investigate
whether spatial autocorrelation is present (Anselin, 2001). Spatial autocorrelation may arise if the
empirical data are generated by an underlying spatial process or if there are spatially correlated
missing variables.
While a thorough discussion of the several spatial econometric models is beyond the scope
of this paper, we shall briefly summarize the main features of the most commonly used models,
namely the spatial lag (SAR), spatial error (SEM) and the unconstrained Spatial Durbin (SDM). For
a formal treatment of specification, estimation and diagnostics, LeSage and Pace (2009) provide an
excellent introduction to recent advances in spatial econometrics.
7 In order to rule out the possibility the intial level of mobile phones may be capturing convergence effects, we added an interaction between the initial level of GDP and mobile phones. The coefficient associated to initial level of mobile phones is larger still significant, therefore ruling out the convergence critique. 8 In our initial period of 1995, mobile phones were still not very widespread and were a significant new technology.
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A linear regression model of the form: εβ += Xy can be spatially augmented,9 in a SAR
specification, by introducing the spatially weighted dependent variable as an additional regressor:
εβρ ++= XWyy , where W is a weight matrix that accounts for distances amongst each couple of
regions and ρ is the autoregressive spatial parameter measuring the degree to which the dependent
variable is autocorrelated over space.
Spatial issues can also be incorporated in the error structure, by considering spatial
dependence in the error disturbance, and this leads to the spatial error model (SEM): εβ += Xy
with μελε += W where . In this case, the spatial autoregressive coefficient λ
reflects the intensity of spatial interdependence in the error term.
),0( 2μσμ iid≈
Finally, the SDM specification allows for a more general treatment of spatial interactions, and its
structural form is: μγρβ +++= WXWyXy . The SAR is a restricted SDM with the linear
restriction: 0=γ , while the SEM is a restricted SDM with the non-linear restriction: 0=+ λβγ .
These restrictions can be tested by appropriate common factor test (Burridge, 1981).
The first indication of the presence of spatial issues is the global Moran’s I test of residuals
(Anselin, 1988), which however does not allow to distinguish between the origin of spatial
autocorrelation. Moran’s I statistic on residuals from the regression in Table 4, is positive and
significant (test statistic of 4.584 with a p-value of 0.000). Using the Lagrange Multiplier tests to
choose between the spatial lag and spatial error model (Anselin and Florax, 1995) we conclude that
OLS is not an appropriate estimation method. The Robust Lagrange Multiplier tests, however, are
both not significant, not allowing a clear answer to the choice of the specification. However, the
SEM model has both a slightly higher R2 (0.7419 versus 0.7119) and log-likelihood (876.824 versus
874.723) with respect to the SAR model, and is therfore the preferred specification.
We thus estimate a spatial error model for the same specifications we described and results
are shown in Columns 1 and 2 of Table 5.10 The first observation relates to the positive and
significant value, across all specifications, of the spatial parameter, with value of approximately
0.36. It is also interesting to note that the general conclusions of Table 4 still hold, both in terms of
the presence of significant economic convergence amongst EU regions and on the role of the
control variables. The estimated coefficients of infrastructure measures are slightly lower than in
Column 1 (Table 4), but point in the same direction, and the transport indicator (motorways over
labour) becomes fully significant. We can conclude that the contribution of motorways and mobile
phone subscriptions to GDP growth, in a spatial convergence framework, is of approximately 6% 9 We will present the structural forms of the three spatial models considered. 10 We used a geographical distance based spatial weight matrix and a rook second order contiguity matrix, to verify robustness to alternative specifications, and results were stable to both specifications. We report results for the geographical distance-based matrix W.
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and 15%, respectively. It is interesting to comment these results in light of the evolution of regional
infrastructure development between 1995 and 2006, as reported in Table 1, Columns 2 and 3. Over
the time period under examination, the TLC measure experienced a relevant increase, especially in
the NMS, with an average growth of 31%, while the average growth rate of motorways was
approximately 3%. However, the NMS have also experienced an increase in the length of
motorways, related to the relative gap in terms of infrastructure stock with respect to regions in
EU15 countries. These results are overall supportive of our initial prior of the positive correlation
between transport and TLC growth with economic activity.
Dependent variable: GDP Growth Rate 1. SEM 2. SDM
Initial GDP -0.0282*** -0.0281*** 0.000 0.000 Δ(Capital) 0.2238 0.0271 0.343 0.911 Δ (Labour) 0.0628*** 0.061*** 0.000 0.000 Human Capital 0.0737*** 0.0829*** 0.000 0.000 Motorways 0.0676*** 0.0558*** 0.006 0.002 Mobile Phones 0.0677** 0.0926 0.036 1.26 Constant 0.2865*** 0.2149*** 0.000 0.000 Spatial coefficient 0.36*** 0.3789*** 0.020 R2 0.7419 0.74 N° Obs. 264 264
Note: p-values in italics. ***, **, * indicate significance at the 1%, 5% and 10% level. Table 5: Growth of infrastructure: spatial models (1995-2006)
We now test a more general spatial model, the Spatial Durbin Model (SDM), which
accounts for both spatially lagged variables and autocorrelation in the error term. Log likelihood
tests indeed indicate that this is the preferred model, against the SEM specification (the likelihood
ratio test rejects the common factor restriction with a test statistic of 25.7, p-value 0.000), indicating
that spatial disturbances may be substantive phenomena, not simply linked to diffusion in space of
random shocks. Results are presented in Column 2 of Table 5.11 All the estimated coefficients are in
line with findings, but tend to be slightly higher, providing evidence of the better performance of
the more general SDM specification. However, the qualitative conclusions are unaltered, with the
exception of the capital stock estimated coefficient, which is insignificant. Furthermore, the initial
11 We have omitted estimated coefficients for the spatially lagged variables due to space limitations. Few are statistically significant. Detailed results available upon request.
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GDP estimated coefficient is negative and highly significant (as in the case of the SEM model),
whereas the estimated coefficients of other relevant variables are still positive with similar levels of
significance.
5. Infrastructure and Growth: Panel analysis
In this Section we want to fully exploit the time dimension of our data and focus explicitly
on the relation between infrastructure and regional growth for the European Union between 1995
and 2006. To this end, we estimate a fixed Effect model (chosen against the Random Effects model
with a Hausman test) both in a standard and spatial setting. Fixed Effects (FE) panel data models
explicitly model the regional and time specific effects, therefore correcting the possible bias in cross
section analyses due to omission of variables and/or regional and time heterogeneity (Columns 1
and 2, Table 6).12
Spatial panel models were introduced by Anselin (1988) and further developed by Elhorst
(2003 and 2009). Given the results in Section 4, we will focus our attention to the Fixed Effect
spatial error model, by including both regional and time fixed effects (Columns 3 and 4, Table 6).
Table 6 presents the main results which confirm the positive role of disaggregated
infrastructure on GDP growth in EU regions for the period considered. By estimating an
infrastructure augmented production function over time, we want to single out the correlation of
disaggregated infrastructure stock and regional growth. To this aim, we estimate an equation of the
form:
tititititititi mobmothlky ,,5,4,3,2,1, lnlnlnlnlnln εβββββα +++++= (3.)
with regional and time fixed effects, in a standard and spatial setting, where , where y is per capita
GDP, k is the fixed capital stock, l is labour force, h, is the indicator of human capital, measured by
the percentage of labour force in S&T, mot is the length of motorways and mob is mobile phone
subscribers.
In Column 1, we add regional fixed effects to our baseline specification and verify that a one
percent variation in the physical capital stock ratio is associated with an estimated coefficient of
0.27, while the coefficient associated with labour is of 0.39; in this specification human capital
seems to play a smaller role (0.07) while infrastructure account together for 0.11. Adding time fixed
effects (Column 2, Table 6) adds to our understanding of the relation between variables of interest.
The relative importance of physical capital and labour is slightly lower in this specification with
respect to Column 1, while human capital is associated with a small negative coefficient, indicating
12 We used a rook second order contiguity matrix, and verified robustness to alternative specifications.
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a complex relationship between the variation over time of the distribution of high skilled workers
and time fixed effects. The estimated coefficient for the motorways vector is remarkably stable,
probably due to the small increase in investment for this infrastructure stock over the time period
considered (see Table 1), while the coefficient on mobile phones is slightly lower, possibly
reflecting the dynamics of ICTs over the period analyzed. We conclude that the effect of
infrastructure on growth is non negligible and statistically significant.
Given the spatial properties and relationships that characterize our variables, as shown in
Section 4, we perform the same analysis including spatial fixed effects (Colums 3 and 4, Table 6).
The spatial autocorrelation parameter with only regional FE (Column 3) is positive and significant,
indicating that there is a positive contagion effects between regions. The estimated parameters of
physical and human capital and labour are higher than those in the a-spatial setting (Column 1,
Table 6), and it is interesting to note that also infrastructure variables are associated with slightly
higher estimated coefficients (0.017 for motorways and 0.175 for mobile phones) when spatial
issues are fully accounted for. This might be due to the fact that spatial synergies and interactions
might affect the return to transport infrastructure and that once they are fully specified in the
empirical mo Spatial coefficient del, the actual estimated effect is higher.
Finally, in Column 4, we add time FE in a spatial setting. Previous results are confirmed, and the
estimated parameters are comparable with those in Column 2. Once again, however, the coefficients
are higher. The interesting result is that the spatial autocorrelation parameter is slightly less
significant and negative. This issue could reflect some underlying economic mechanisms or
complex interactions between time and space and calls for a more detailed analysis of the role of
time evolution in a spatial setting, and will be object of future research.
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4. Two way Spatial FE Dependent variable:
GDP 1. FE 2. Two way
FE 3. Spatial FE
(SEM) (SEM)
Capital Stock 0.2795*** 0.1959*** 0.4696*** 0.4409*** 0.000 0.000 0.000 0.000
Labour
0.3962*** 0.3018*** 0.5492*** 0.5271*** 0.000 0.000 0.000 0.000
Human Capital
0.0753*** -0.088*** 0.6206*** 0.6547*** 0.000 0.000 0.000 0.000
Motorways
0.0127*** 0.0104*** 0.0172*** 0.0162*** 0.001 0.001 0.000 0.000
Mobile Phones
0.0972*** 0.0796*** 0.175*** 0.1744*** 0.000 0.000 0.000 0.000 Constant 2.0136*** 5.1229*** lambda 0.3479*** -0.3759** 0.000 0.000 0.000 0.001 Region Fixed Effects Yes Yes Yes Yes Time Fixed Effects No Yes No Yes
R2:
overall 0.2164 0.1873 0.7661 0.7642 within 0.7424 0.7876
between 0.1929 0.154 N° Obs. 3168 3168 3168 3168
Note: p-values in italics. ***, **, * indicate significance at the 1%, 5% and 10% level. Table 6: Panel Analysis- FE and Spatial FE Models
5. Concluding remarks Considering data from 1995 to 2006, we have found evidence of a convergence process occurring
across European regions, with an estimated speed of β convergence of approximately 2%. This
result holds also when we move on to consider conditional convergence, and take explicitly into
account the role of infrastructure capital. We find evidence of a positive effect of the endowment of
TLC and transportation infrastructure on economic growth, with estimated coefficients robust to
several econometric specifications and methods. The time period considered allows us to capture a
significant technological change with the widespread adoption and diffusion of modern Information
and Communication Technologies, which are shown to be significantly correlated with economic
growth. During the same period, transport infrastructure have increased at a much slower pace, but
we still find evidence of positive and significant effects on economic activity.
We explicitly consider spatial correlation issues and correct the bias with appropriate econometric
techniques, by estimating spatial models both in a cross section and panel setting. Our results
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suggest a non negligible role played by infrastructure provision and growth in shaping the economic
growth and convergence behaviour of EU regions.
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Appendix: List of regions in the sample Austria Bulgaria DE3 DEB1 ES12 FI19 FR72 HU21 ITF5 NL31 Portugal SE07 UKI1 UKM2 AT34 BG23 DE92 DED2 ES7 FI18 FR23 HU1 ITC1 NL23 PT16 SE04 UKL2 UKG3 AT22 BG21 DEA2 DE24 ES42 France FR71 HU31 ITF6 NL11 PT3 SE06 UKJ4 UKD1 AT31 BG11 DEE2 DE23 ES22 FR22 Greece Ireland ITC2 NL41 PT18 SE08 UKD4 UKG1 AT11 BG22 DEB3 DE8 ES23 FR3 GR25 IE01 ITE3 NL22 PT17 Slovenia UKD3 UKK3 AT12 BG13 DE12 DE73 ES43 FR63 GR24 IE02 ITF3 Poland PT15 SI UKH1 AT21 BG12 DE72 DEB2 ES41 FR53 GR43 Italy Lithuania PL43 PT11 Slovakia UKH3 AT33 Cyprus DE94 DEA3 ES11 FR21 GR22 ITD2 LT PL22 PT2 SK03 UKJ3 AT13 CY DEA5 DE25 ES64 FR61 GR23 ITE1 Luxembourg PL51 Romania SK01 UKF3
AT32 Czech
Republic DE71 DE91 ES62 FR26 GR13 ITF1 LU PL41 RO04 SK04 UKK2 Belgium CZ05 DEE1 DE13 ES52 FR62 GR11 ITF2 Latvia PL31 RO06 SK02 UKJ2
BE33 CZ04 DED1 DEA4 ES51 FR43 GR41 ITC3 LV PL34 RO02 United
Kingdom UKD2 BE21 CZ08 DE41 DEA1 ES53 FR1 GR21 ITD1 Malta PL52 RO05 UKC2 UKG2 BE31 CZ02 DE26 DE93 ES3 FR25 GR42 ITD4 MT PL33 RO03 UKC1 UKE1 BE32 CZ06 DE21 DE11 ES63 FR24 GR12 ITG2 Netherlands PL62 RO07 UKJ1 UKL1 BE23 CZ03 DE6 DEF ES21 FR81 GR14 ITD5 NL34 PL11 RO01 UKM4 UKN BE24 CZ01 DEE3 Denmark ES24 FR42 GR3 ITC4 NL42 PL12 RO08 UKE4 UKF1 BE35 CZ07 DE5 DK ES13 FR83 Hungary ITF4 NL32 PL21 Sweden UKK4 UKI2 BE22 Germany DEC Estonia Finland FR41 HU22 ITD3 NL21 PL63 SE0A UKK1 UKD5 BE25 DEG DE42 EE FI2 FR82 HU32 ITE2 NL12 PL42 SE01 UKM3 UKE3 BE34 DE22 DE27 Spain FI1A FR51 HU33 ITE4 NL33 PL32 SE02 UKM1 UKE2 BE1 DED3 DE14 ES61 FI13 FR52 HU23 ITG1 NL13 PL61 SE09 UKH2 UKF2
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