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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.

15

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

17

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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