JOURNAL OF ECONOMIC DEVELOPMENT 1

Volume 40, Number 4, December 2015

EFFECTS OF PUBLIC CAPITAL ON ECONOMIC GROWTH AND

PRODUCTIVITY IN SPAIN DURING THE PERIOD 1980-2007

JUSTO DE JORGE MORENO a , CESAR CAMISON ZORZONAb, JUAN MURO ROMERO a

c*
AND LEOPOLDO LABORDA CASTILLO

a
University of Alcala, Spain
b
University of Valencia, Spain
c
World Bank, USA

In line with the existing literature, the main aim of this study is to analyse the effects of
public capital on growth in the Spanish regions for the period 1980-2007. The methodology
used adopts a parametric approach following the recommendations intended to eliminate the
effects of demand and estimate only the medium-term impacts, ultimately eliminating any
possible inverse causality relationship. The estimates made put the elasticity of the
productivity of labour with respect to the delays in investment in infrastructures at 0.183,
while elasticity with respect to private investment stands at 0.294. This means it can be
concluded that investment in public capital contributes to increasing productivity by
approximately 62 per cent in the Spanish regions as a whole. Meanwhile, the analysis of the
convergence of the estimated efficiency levels shows that the least efficient regions have
benefited from the technology existing in the regions closest to the efficiency frontier.
Finally, some reflections are compiled on the role investment in public capital can play
in the context of a crisis like the current one, together with other pillars incorporated into the
debate, such as fiscal consolidation and structural reforms.

Keywords: Public Capital, Efficiency, Convergence, Spanish Regions, Economic Growth

JEL classification: O38, O44, O47

1. INTRODUCTION

The great proliferation of empirical studies in the literature for analysing the effects
of public capital on economic growth and productivity at national and international

*
We would like to thank the anonymous referee for valuable comments. All remaining errors are our
own.
2 J. DE JORGE MORENO, C.CAMISON, J. MURO AND L.LABORDA

level,1 are a clear sign of the interest that has been aroused by this issue, particularly in
a context of economic crisis like the current one, where classical issues, such as the role
of the public sector in the economy, occupy a central role position.
Taking the case of the European Union in general and Spain in particular as an
example, we can see that, alongside advances in integration, Community institutions
have driven development policies in which public investment constitutes a significant
tool. In accordance with authors like Delgado and Álvarez (2004), the arguments put
forward to justify this type of action include: (1) the need to balance economic
conditions between the different countries (2) the capacity of public capital to generate
positive externalities on production, and, ultimately, to promote economic convergence.
In general, the majority of the existing empirical literature takes the pioneering
studies by Ratner (1983), Eberts (1986) and Aschauer (1989, 1989), which coincide in
indicating that the infrastructure provisions are an important factor in explaining
economic growth in the United States, as a reference. Specifically, taking a
Cobb-Douglas production function as a basis, these authors observe that an increment of
1% in infrastructures is related to increases of between 0.24-0.39 per cent in private
sector output.
Although many subsequent studies, such as those by Munell (1990, 1993),
García-Milà and McGuire (1992), Otto and Voss (1994), Mas and others or Cantos and
others (2005), to mention some examples, obtained similar or lower intensity results for
the influence mentioned above, the fact is that the existing empirical evidence is a long
way from being conclusive, as shown by other studies where either a negative effect has
been obtained (Voss, 2002; Moreno and others, 2007) or no significant effect has been
found -such as the studies by Holtz-Eakin (1994), Baltagi and Pinnoi (1995),
García-Milá and Mcguire (1992), García-Milà, McGuire and Porter (1996) or
Gómez-Antonio and Fingleton (2008).
The studies carried out for the Spanish economy appear to show more optimistic
results. In particular, both the analyses of the impact of infrastructures using production
functions with annual data for the whole of the Spanish economy (Bajo and Sosvilla,
1993; Argimón and others, 1994; Mas and others, 1994; and Serra and García-Fontes,
1994) and those using panel data for the regions (Mas et al., 1993; Serra and García-
Fontes, 1994; Dabán and Murgui, 1997) obtain positive results, although with less
impact than in the pioneering study by Aschauer which we have already mentioned.
Nevertheless, some authors, such as Gramlich (1994), Draper and Herce (1994), De la
Fuente (1996) and Sanau (1997), have found results contradicting the hypothesis we
have mentioned, detecting an inverse relationship between public capital and
infrastructures.

1
We would direct the interested reader to consult the studies including those by Gramlich (1994), Draper
and Herce (1994), De la Fuente (1996), Gil (2001), De la Fuente (2002) and Álvarez et al. (2003), which
make a detailed summary of this important issue.
EFFECTS OF PUBLIC CAPITAL ON ECONOMIC GROWTH AND PRODUCTIVITY 3

Associated with this considerable proliferation of studies analysing the effects of

public capital on economic growth and productivity, an interesting methodological
debate has emerged not unrelated to the disparity of empirical results obtained which has
already been pointed out. Because of its importance we will deal with it, although only
briefly, later on in this study.
Considering all this, and in line with the empirical literature mentioned, The main
contribution of our paper is to show that a suitable decomposition of capital (public and
private) can be applied to a fairly large sample of heterogeneous regions for an extensive
period of time (1980-2007) in order to eliminate the effects of demand and estimate only
the medium-term impacts in the productivity growth. We are not aware at this time of
any other SFA study for the Spaniard economy that has produced quantitative results
showing that in terms of convergence the less efficient regions have benefited from the
technology existing in the regions closest to the efficiency frontier. The period analyzed
in this study, as Alañon and Gómez (2010) have taken it on themselves to point out, is
particularly appropriate in the Spanish context for testing Aschauer’s (1989) hypothesis,
as, during this period, there were positive growth rates in public investment regardless of
the economic cycle. In particular, due to Spain’s incorporation into the European Union
in 1986, there has been a notable growth in the provision of infrastructures as a
consequence of transfers from European structural funds.
In order to meet the objective indicated, this study is structured in the following way:
Section 2 deals with a series of aspects relating to the methodology used in this study.
Section 3 describes the data used and presents the results obtained. Finally, section 4
summarises the main conclusions and implications of this study and some limitations
and extensions.

2. ANALYSIS METHODOLOGY

As has been mentioned in the introduction, the aim of this study is to analyse the
impact of public capital on economic growth. To do this, an approach is adopted based
on analysing parametric frontiers in which the distance separating the productive units
from the efficient production frontier is quantified.
In the systematisation carried out by Muro (1984) concerning parametric frontier
models, these can be classified depending on whether or not their adaptation completes
the microeconomic concept of production function in two different categories: (1)
determinist or strict frontiers2 and (2) stochastic frontiers.3

2
These frontiers are characterised by being causal models constructed on the hypothesis that the
production process related to the units analysed is a determinist one. They are determinist models in the sense
that all the units in the sample observed share a common family of production, cost and benefit frontiers and,
consequently, all the variations observed in a unit’s result are attributed to inefficiency with respect to the
4 J. DE JORGE MORENO, C.CAMISON, J. MURO AND L.LABORDA

Although a detailed analysis of the different ways of parametrically modelling a

production frontier would lead us far beyond the aims of this study, because of their
importance we would direct the interested reader to the studies by Forsund, Lovell and
Schmidt (1980), Kopp (1981) or Kumbhakar and Lovell (2000).
As our empirical analysis uses these two approaches, it is important to note that both
determinist and stochastic frontiers show clear advantages and considerable
disadvantages. Based on the first approach, any deviation from the efficient frontier is
attributed to inefficiency, while, based on the stochastic approach, an attempt is made to
distinguish the part of the deviation of the frontier due to inefficiency itself from that
obeying the effects of random disturbances.
The advantage of determinist models is that all production units considered are
below or above the production frontier, making it possible to assimilate measurements of
inefficiency into Farrell’s proposals (1957). Their main disadvantage is that random
disturbances can affect the inefficiency measurement obtained.
For their part, stochastic models show the advantage that, if the functional form is
correctly specified, there are greater guarantees that what we identify as inefficiency
actually is that, and is not due to deviations produced by random causes; in other words,
it allows (in)efficiency to be isolated from the effect of random disturbances. By contrast,
the disadvantage of the latter approach is that estimating efficiency requires not only the
imposition of a functional form, it also requires the specification of strong assumptions
on the distribution of the two components of the error.

2.1. Determinist Model with Panel Data

Although the choice of the production function is generally not free of limitations,
including, most importantly, excessive rigidity in substitution relationships (see, for
example, Berndt and Hanson, 1991; or Morrison and Schwartz, 1992), aspects such as
its simplicity, ease of interpretation and popularity in terms of comparison help to
explain the frequent use of the Cobb-Douglas production function as a structural form in
the analysis that concerns us.4

common family of frontiers. Strict frontiers faithfully represent the theoretical content of a microeconomic
production function. The impossibility of observations exceeding the maximum represented by the
production frontier is reflected in these models in the way the error term is distributed.
3
Stochastic frontiers do not sustain the strictly deterministic nature of the production process. The
existence of a set of factors beyond the control of the analysis unit justifies the rejection of an out-and-out
determinist position. Some of the factors not considered to constitute inefficiency would be those beyond the
control of the analysis unit (region, company, etc.): so-called statistical noise; measurement errors assumed to
have occurred in the dependent variable, and specification errors in the relationship formulated.
4
The Cobb-Douglas function has been used, among others, for the analysis of the Spanish regions by Mas,
Maudós, Pérez and Uriel (1994), García-Fontes and Serra (1994), Mas, Maudós, Pérez and Uriel (1996),
EFFECTS OF PUBLIC CAPITAL ON ECONOMIC GROWTH AND PRODUCTIVITY 5

In dealing with the impact of public capital, most of the studies mentioned use an
aggregated approach based on estimating a Cobb-Douglas frontier function where
private capital (KP) and labour (L) are added to public capital (KG), plus a parameter to
reflect technological progress:

Yit  Yit ( Ait KPit Lit KG it ) , (1)

where Yit is the product obtained by an economy i in the period t; Ait represents its
technological level -that is the level of efficiency with which the economy operates- and
the production factors; KPit , Lit and KG it are, respectively, private capital, labour
and public capital. Using Reg and a Dummy variable to include the effect of the regions
(ACs), we can express the above Equation (1) as a dynamic model with panel data, as
proposed by Arellano and Bond (1991):

17
ln Yit  θi  θit  θ KG ln KGit  θ KP ln KPit  θ L ln Lit   Re g it  eit . (2)
i 1

Having reached this point, it is important to mention a considerable methodological

limitation of the production function, indicated by Nombela (2005), when an attempt is
made to analyse the effect of infrastructures as a production factor related to the implicit
assumption that infrastructures have contemporary effects on production. As the stock of
public capital is incorporated at each instant of time t and related to the production for
that period, it is possible to consider that the infrastructures are operative and, therefore,
generate added value in the period under consideration.
Whenever time savings, greater safety or cost reductions are among the effects of
infrastructures to be considered in the long term in the modelling described above, we
will consider the hypothesis of delays occurring from the time the infrastructure comes
into service to the point where it is considered a productive factor in the production
process. We will also assume that public capital investment involves a certain time
between its completion and commissioning, while, from a statistical point of view, the
stock of capital increases from the moment the investment is made.
Bearing in mind the above considerations, it is necessary to determine whether or not
investments in infrastructures have delayed effects on the productivity of labour.
Following Nombela (2005), the function to be estimated will be as follows:

Daban and Murgui (1997), Moreno, Artis, López-Bazo and Suriñach (1997), Delgado and Alvarez (2000),
Freire and Alonso (2002), Pedraja, Ramajo and Salinas (1999), Álvarez, Orea and Fernández (2003), Cantos,
Gumbau-Albert and Maudós (2005), Nombela (2005), Rodríguez-Valez, Álvarez, Arias and Fernández
(2009).
6 J. DE JORGE MORENO, C.CAMISON, J. MURO AND L.LABORDA

ln Yit  θ0  θ1 ln( Inv _ KPpt Q )  θ2 ln( Inv _ KGpt Q )  uit , (3)

where Yit is the gross added value of the ACs, Lit the level of employment;
Inv _ KPpt Q the average private investment during the five-year period preceding the
year t; Inv _ KG pt Q the average public investment, also in the five-year period
preceding t; and u it random noise.
The parameters to be estimated are θ 0 , θ1 and θ 2 , which are the elasticity of
productivity per employee with respect to public infrastructure investment delays and
θ 2 the fundamental parameter we wish to obtain.
In summary, with the hypothesis to be tested being that this elasticity is positive and
statistically significant, the estimated value will enable us to determine the impact of the
effects of public capital on productivity.

2.2. Stochastic Model with Panel Data

We will now deal with the stochastic frontier approach to analysing the impact of
infrastructures on economic growth. In accordance with the pioneering work of Aigner,
Lovell and Schmidt (1977) and Meeusen and Van den Broeck (1977), we start with the
expression:

Yit  f ( xit , β )  μit , (4)

where Yit represents the aggregated value for the AC (i  1,..., n) , X it the input
vector, in the case that concerns us private capital (KP), labour (L), and public capital
(KG), with β the parameter vector to be estimated and μit  vi  ui the deviations of
the frontier, where the variable vi is distributed i.i.d. N (0, σ v2 ) and captures the
exogenous or random effects beyond the control of the unit analysed, while the error
term ui includes technical inefficiency and is distributed i.i.d. N (ηi , σ u2 ) with the
condition that it is distributed independently of vi and is not negative, which allows all
observations of the sample to be on or below the efficient frontier. The frontier function
parameters are estimated by maximum likelihood, as suggested by Coelli, Prasada and
Battese (1998). To estimate the efficiency of each unit i observed, we apply
EFi  E (Yi* ui , xi ) / E (Yi* ui  0, xi ) , taking values between 0 and 1. As included in
Battesse and Coelli (1992), the value of the above expression can only be estimated
based on predicting ui , which is, in turn, determined by previous conditioned
expectation based on the value of vi  u i . Finally, the inefficiency of each unit
EFFECTS OF PUBLIC CAPITAL ON ECONOMIC GROWTH AND PRODUCTIVITY 7

evaluated is calculated using EFi  exp( ui ) .

Along these lines, adopting a Cobb-Douglas-type functional form analogous to the
one included in (2), in this case we have the expression:

17
ln Yit  θi  θit  θ KG ln KGit  θ KP ln KPit  θ L ln Lit   Re g it  (vit  uit ) . (5)
i 1

3. RESULTS

The following subsections include the principal empirical results obtained.

Specifically, in 3.1 a descriptive analysis is made of the data used in subsection 3.2 to
estimate the determinist frontier with panel data and in subsection 3.3 for the estimate
with stochastic frontier methods and panel data, as explained in the previous section.

3.1. Descriptive Data Analysis

As a step prior to the econometric analysis suggested in this study to achieve the aim
proposed here relating to the impact public capital has on economic growth in the
productive private sector, the BD-Mores database has been used.5 This database is
broken down for the seventeen Spanish autonomous communities (ACs), which makes it
possible to obtain different input and output values for each region for the whole
productive private sector.
The variables from the BD-Mores to be used will be the employment series, gross
added value, private productive capital and public productive capital. Figure 1 shows the
development of public and private capital for the analysis period 1980-2007.
Table 1 shows characteristic features of regional disparities in the variables analysed
for the autonomous communities (ACs). The ACs with the highest values in average
terms are Madrid, Catalonia and Andalusia, while those with the lowest values are
Cantabria, La Rioja and Navarre.
Table 2 shows the public/private capital and public capital/product ratios considering
their development over time. As can be seen, there is a growing trend towards public
rather than private capital, starting in 1999.

5 The Spanish economic BD-MORES regional database shows characteristics that mean it is of interest
for Spanish regional research. The basic methodology for drawing it up can be found in De Bustos et al.
(2008). The current version adopts 2000 as a base year and follows the latest Spanish National Accounting
methodology (SEC95, Last updated: December 2011).
8 J. DE JORGE MORENO, C.CAMISON, J. MURO AND L.LABORDA

Source: Self-created, based on the BD-Mores.

Figure 1. Development of Public and Private Capital during the Period 1980-2007

Table 1. Average values by Autonomous Communities

Autonomous Community Y Public_K Private_K Employed people
Andalusia 33000000 12400000 11800000 2226
Aragon 7063669 2519305 2511405 503
Asturias 5154190 1756747 1741348 382
Balearic Islands 8267375 2346659 2359163 322
Canary Islands 12100000 3996629 3981928 589
Cantabria 3031816 969008 940974 196
Catalonia 47600000 15700000 14000000 2631
Castile-La Mancha 6637899 2614372 2621583 609
Castile and León 12400000 4365486 4437334 952
Extremadura 3391563 1492627 1557488 335
Galicia 12100000 4202501 4107489 1057
Madrid 49100000 18300000 15300000 2241
Murcia 5473622 1959817 1854318 404
Navarre 3435507 1275416 1193420 244
Basque Country 14600000 4933498 4634610 860
La Rioja 1537128 495063 516301 116
Valencian C. 24400000 25100000 8032991 1559
Total 14700000 6145526 4804000 896
Source: Self-created based on the BD-Mores.
EFFECTS OF PUBLIC CAPITAL ON ECONOMIC GROWTH AND PRODUCTIVITY 9

Table 2. Development of Public/Private Capital and Public Capital/Product Ratios 1980-2003

KG/KP KG/Y
Mean Standard Dev. Mean Standard Dev.
1980 0.8598 1.6226 0.0777 0.0721
1981 0.8695 1.6414 0.0906 0.0823
1982 0.8351 1.5660 0.0992 0.0877
1983 0.8311 1.5088 0.1155 0.0985
1984 0.8392 1.4487 0.1254 0.1043
1985 0.8545 1.3981 0.1360 0.1022
1986 0.8330 1.3361 0.1485 0.1135
1987 0.8296 1.3437 0.1619 0.1255
1988 0.8258 1.3265 0.1744 0.1267
1989 0.8230 1.2264 0.1916 0.1358
1990 0.8352 1.2021 0.2170 0.1531
1991 0.8331 1.1792 0.2423 0.1672
1992 0.8608 1.1277 0.2726 0.1823
1993 0.8411 1.1147 0.2824 0.1866
1994 0.8266 1.1280 0.2818 0.1909
1995 0.8319 1.1638 0.2993 0.2037
1996 0.8307 1.1863 0.3170 0.2176
1997 0.8286 1.2301 0.3217 0.2302
1998 0.8251 1.2456 0.3316 0.2375
1999 0.8183 1.2276 0.3402 0.2404
2000 2.1226 0.7093 0.6036 0.1678
2001 2.1546 0.7053 0.6278 0.1691
2002 2.1470 0.6951 0.6511 0.1738
2003 2.0973 0.6455 0.6698 0.1801
2004 2.0736 0.6254 0.6826 0.1816
2005 2.0565 0.6428 0.6950 0.1877
2006 2.0466 0.6256 0.7131 0.1960
2007 2.0155 0.6026 0.7325 0.1988
Source: Self-created based on the BD-Mores.

3.2. Estimating the Determinist Model with Panel Data

The results obtained after estimating Equation (2) are shown in Table 3, where it can
be seen that the elasticity of the inputs is positive and statistically significant.
Specifically, the elasticity referring to public capital is 0.025. This value is found to be
coherent with those obtained in previous studies measuring the impact of public capital
on the Spanish economy, as included in Table A.1 presented in the appendix to this
study, where it can be seen that it lies within the range of elasticities determined for the
10 J. DE JORGE MORENO, C.CAMISON, J. MURO AND L.LABORDA

Spanish economy by other authors.

Table 3. Estimate of the Cobb-Douglas Function at National Level

Parameter Coefficient t-ratio
Constant θi 12.99** 43.8
LnKP θ KP 0.031* 3.98
LnKG θ KG 0.025** 2.14
Ln(L) θL 0.407** 17.25
t θt 0.014 8.86
AC dummies
Aragon β1 -0.826** -19.34
Asturias β2 -0.998** -19.55
Balearic Islands β3 0.464** -8.83
Canary Islands β4 -0.375** -10.41
Cantabria β5 -1.231** -17.88
Catalonia β6 0.311** -26.09
Valencian C. β7 -0.967** -25.07
Castile-La Mancha β8 -0.562** -21.57
Castile and León β9 -1.363** -25.12
Extremadura β10 -0.618** -24.14
Galicia β11 0.395** 32.36
Madrid β12 -0.982** -19.98
Murcia β13 -1.212** -19.42
Navarre β14 -0.354** -12.78
Basque Country β15 -1.663** -19.82
La Rioja β16 -1.145** -8.17
Fixed effects
Nº Obser. 426
Nº groups 17
Wald chi2 (21) 27968 0.000
Hausman test 37.78 0.000
Levin-Lin-Chu test 2.852 0.000
Notes: **,* significant at 99% and 95% respectively. Variable omitted: AC of Andalusia. The null hypothesis
of constant performance on the chi2 scale is rejected = 367.3 (0.000).
Source: Self-created based on the BD-Mores.
EFFECTS OF PUBLIC CAPITAL ON ECONOMIC GROWTH AND PRODUCTIVITY 11

The data used for estimating the Equation (3) at autonomous community level has
also been taken from the BD-Mores database and corresponds to the investments made
in both public and private infrastructure during the period 1980-2007.
The Table 4 includes the results obtained with the available data panel showing
significant effects of the investments made with both public and private capital. In
particular, the elasticity of productivity with respect to public capital investment delays
is around 0.18.

Table 4. Estimate of the Delayed Investment Function for the ACs

Parameter Coefficient t-ratio
Constant θ0 9.840** 53.58
Ln(Inv_Kpt-Q) θ1 0.294** 15.99
Ln(Inv_KGt-Q) θ2 0.183** 14.93
AC dummies
Aragon β1 -0.573** -17.54
Asturias β2 -0.736** -21.00
Balearic Islands β3 -0.878** -36.32
Canary Islands β4 0.497** 11.56
Cantabria β5 -2.320** -111.66
Catalonia β6 1.200** 46.05
Valencian C. β7 -0.673** -21.25
Castile-La Mancha β8 -0.179** -5.94
Castile and León β9 -1.069** -29.08
Extremadura β10 -0.529** -20.51
Galicia β11 1.070** 35.32
Madrid β12 -1.842** -91.63
Murcia β13 -2.016** -93.49
Navarre β14 0.248** 6.66
Basque Country β15 -2.529** -98.47
La Rioja β16 0.227** 9.77
Fixed effects
Nº Obser. 408
Nº groups 17
F 4572.5 (0.000)
Hausman test 30.23 (0.000)
Notes: **,* significant at 99% and 95% respectively. Variable omitted: AC of Andalusia.
Source: Self-created based on the BD-Mores.
12 J. DE JORGE MORENO, C.CAMISON, J. MURO AND L.LABORDA

3.3. Estimating the Stochastic Model with Panel Data and the Sigma and Beta
Convergence of Efficiency

The results of estimating the model are presented in Table 5. Firstly, it is shown that
public capital is an important factor in private sector production, with elasticity of 0.113.
This result is in line with the most recent empirical evidence obtained on the direct
contribution of this stock (as can be seen in Table A.1, which we have already
mentioned, in the appendix to this study, this value is within the range of values
estimated using other methodologies for the Spanish economy).
Along these lines, the results obtained in this study back the effectiveness of public
investment as a tool of economic policy orientated towards growth and productivity.

Table 5. Estimate of the Cobb-Douglas Function with Stochastic Frontiers at National Level
Parameter Coefficient t-ratio
Constant θ i 10.86** 77.72
LnKP θ KP 0.075** 15.35
LnKG θ KG 0.113** 24.29
Ln(L) θL 0.442** 20.42
t θt 0.001** 3.64
AC dummies
Aragon β1 -0.565** -18.26
Asturias β2 -0.696** -18.97
Balearic Islands β3 -0.126** -2.94
Canary Islands β4 -0.191** -6.71
Cantabria β5 -0.815** -16.88
Catalonia β6 0.287** -26.03
Valencian C. β7 -0.724** -26.15
Castile-La Mancha β8 -0.404** -20.51
Castile and León β9 -1.042** -26.64
Extremadura β10 -0.457** -25.39
Galicia β11 0.354** 31.48
Madrid β12 -0.681** -19.29
Murcia β13 -0.847** -18.91
Navarre β14 -0.2** -9.31
Basque Country β15 -1.13** -18.82
La Rioja β16 -0.182** -11.31
EFFECTS OF PUBLIC CAPITAL ON ECONOMIC GROWTH AND PRODUCTIVITY 13

μ -7.234 -26.94
γ -5.984 -23.37
Log_L 858.96
Nº Obser. 426
Notes: **,* significant at 99% and 95% respectively. Variable omitted: AC of Andalusia.
Source: Self-created based on the BD-Mores.

Based on the estimated stochastic frontier model, we obtain the productive efficiency
values for the ACs during the period 1980-2007, included in Table 6 below:

Table 6. Initial, Final and Average Efficiency Values

1980 2007 1980-2007 Average growth
Andalusia 0.979 0.988 0.966 0.009
Aragon 0.974 0.974 0.963 0.000
Asturias 0.942 0.988 0.961 0.048
Balearic Islands 0.975 0.851 0.945 -0.127
Canary Islands 0.926 0.981 0.963 0.060
Cantabria 0.971 0.980 0.967 0.009
Catalonia 0.933 0.987 0.964 0.058
Castile-La Mancha 0.973 0.981 0.961 0.008
Castile and León 0.977 0.987 0.962 0.010
Extremadura 0.947 0.991 0.962 0.047
Galicia 0.964 0.989 0.963 0.026
Madrid 0.912 0.990 0.957 0.086
Murcia 0.969 0.990 0.960 0.022
Navarre 0.926 0.985 0.965 0.064
Basque Country 0.961 0.975 0.963 0.014
La Rioja 0.972 0.975 0.956 0.003
Valencian C. 0.961 0.981 0.967 0.020
Total 0.956 0.976 0.961 0.021
Source: Self-created based on the BD-Mores.

Comparing the levels of productive efficiency by regions at the start and at the end
of the period, a degree of mobility is observed. For example, in 1980 Andalusia, Castile
and Leon, the Balearic Islands and Aragon occupied the top positions. However, in 2007
it is Madrid, Murcia and Galicia that occupy the first places. In general terms, the ACs
show slight growth, with the exception of the Balearic Islands.
To check whether during these years when exchanges of goods and services have
been taken place there has also been a process of spreading the existing technology
14 J. DE JORGE MORENO, C.CAMISON, J. MURO AND L.LABORDA

between the regions, we propose a convergence analysis with the aim of checking
whether the greater integration (exchange) between the ACs has encouraged the
assimilation of technology existing in the ACs nearest to the frontier (“catch-up effect”).
An initial approach to the proposed convergence analysis consists of analysing the
convergence sigma based on the standard deviation of the log of the efficiency level,
making it possible to extract information on the existing dispersion over time. Figure 2
shows two clear trends. Between 1980 and 1999 there is a convergence process, while in
the period 1999-2007 there is divergence, increasing inequalities.

Source: Self-created based on the BD-Mores.

Figure 2. Sigma Convergence of Efficiency during the Period 1980-2007

Finally, we also analyse beta β -convergence using the following regression model
(6), where θi1997 , θi2006 represent the initial and final efficiency levels for each region.

1  θi2006 
ln  α  β ln θi1997  εi . (6)
T  θi1997 

In order to make our analysis more robust, we make use of the approach suggested
by Lozano-Vivas and Pastor (2006). Along these lines, the test is carried out with the
conventional variance-covariance matrix and the corrected matrix obtained using the
bootstrap process proposed by Simar and Wilson (2003).
The results included in Table 7 show the existence of convergence if we take into
account the negative sign and statistical significance (at 90%) of coefficient β .
EFFECTS OF PUBLIC CAPITAL ON ECONOMIC GROWTH AND PRODUCTIVITY 15

Table 7. Regression of Convergence Beta

Coefficient t-ratio SD 95% Conf. Interval Adjusted R2
-0.827 1.92 0.430 -1.670 0.015 0.023
Note: Corrected variance-covariance inference using the bootstrap method (with 2000 replications).
Source: Self-created based on the BD-Mores.

As, in order for the convergence hypothesis to be fulfilled there has to be a negative
relationship between the efficiency growth rate in the period and its initial level, which
means β must be negative and significant at conventional levels, the existence of a
certain technological “catching up” process is confirmed, under which the regions
starting from lower efficiency indices have benefited from the spread of existing
technology and the resource management improvements of the regions nearest the
frontier.
Having analysed the development of efficiency (in the case that concerns us,
orientated towards output), it is of interest also to know the dynamic of its distribution in
terms of change in the form of distribution and internal distribution dynamic. The
justification of the above statement can be found in the argument put forward by Quah
(1993, 1996 and 1997), under which convergence coalitions or clubs can be formed
endogenously through all the regions, that the different convergence dynamics will
depend on the initial distribution of the characteristics of these regions.
In order to understand the technical efficiency dynamic throughout the distribution,
the use of stochastic kernel estimators is proposed, in a similar way to the approach
adopted by Birchenal and Murcia (1997) for analysing convergence.6
Figure 3 shows the efficiency distribution dynamic by estimating kernel density
functions following the proposal by Lucy and others (2002). With the specifications
indicated, convergence (divergence) and persistence (mobility) in the average level of
technical efficiency for the estimates made for the 17 Spanish autonomous communities
(CAs) during the sub-periods 1993-1980, 2007-1993 and throughout the period 2007-
1980 are denoted in Figure 3, as been mentioned.
To make it easier to interpret Figure 3, one strategy is to illustrate the extreme cases
in which the whole distribution shows mobility, persistence and convergence
respectively. In this situation, persistence would be translated into the whole distribution
maintaining its characteristics between the periods t and t+s, with the efficient ACs
continuing to be efficient and the more inefficient ones also continuing to be so; in the
case of mobility, we would have a total reversal of the initial conditions of the ACs, so
that those considered as inefficient in period t would become efficient in the period t+s,

6
To analyse this dynamic without distorting it, it is proposed to divide the efficiency space into an infinite
number of regions or continuum. In this case, the corresponding transition probability matrix will towards a
continuum of rows and columns, becoming a stochastic kernel.
16 J. DE JORGE MORENO, C.CAMISON, J. MURO AND L.LABORDA

while those considered efficient would become inefficient.7 Finally, if with the passage
of time the distribution is concentrated around a plane parallel to the t axis when
efficiency was initially distributed normally throughout the cross-section (that is, the
group is presented around the value t+s=1), it is said that the distribution converges
towards equality in the efficiency levels of the ACs.

Source: Self-created based on the BD-Mores.

Figure 3. Distribution Dynamic of Output-Orientated Efficiency

7
According to Birchenal and Murcia (1997) an easy way to appreciate the previous phenomena is by
observing whether the contour lines of the distribution are concentrated on the 45 degree line drawn on the
t–t+s plane (in this case, the distribution persists during the periods). Now, if the distribution contour lines are
concentrated on a line perpendicular to 45 degrees, we would have complete mobility within the distribution.
EFFECTS OF PUBLIC CAPITAL ON ECONOMIC GROWTH AND PRODUCTIVITY 17

As we can see, both considering the sub-period 2007-1993 and the total for the
period 2007-1980, with the passage of time, the distribution (apart from a few
exceptions) is concentrated around a plane parallel to the t axis, while initially income
was distributed normally throughout the cross-section. As this group appears around the
value t+s=1, we say that the distribution converges towards equality at the efficiency
levels achieved.

4. CONCLUSIONS AND FINAL REFLECTIONS

As economies develop, their citizens demand higher levels of public capital in

infrastructures. Because of this, governments use a considerable part of their budgets for
investment in public capital in order to improve levels of welfare and productivity in
their economies. Alongside the importance given to investments by economic agents in
public capital, there has been a considerable development of empirical studies trying to
find out the impact this has on productive activity, achieving results that do not always
coincide on the direction of causality or the magnitude of the impact.
Joining forces with the effort made in the literature that has gone before, in this study
we have analysed the effects of public capital on growth in the Spanish regions for the
period 1980-2007. To do this, we have opted to use a double parametric methodological
approach with which Cobb-Douglas-type production functions have been estimated.
Their inputs have included private and public infrastructures as independent productive
factors, making it possible to obtain values for the elasticity of output (VAB) with
respect to the stock of infrastructure capital. This analysis has been carried out at
aggregate level for the Spanish economy controlled by Autonomous Communities
(ACs).
The results achieved are found to be in line with other, previous studies carried out
in the Spanish economy also analysing the impact of public infrastructures. Specifically,
the estimates made for the Autonomous Communities as a whole show positive,
significant elasticities of public capital of around 0.025 and 0.113.
Given the doubts aroused in the empirical literature by the estimation of elasticities
using Cobb-Douglass production technology, specifically because of the assumption that
there is a contemporary relationship between the stock of public capital and the
operativity of the infrastructure, 8 it was resolved in this study to estimate the
relationship between the productivity of labour and investments in public and private
infrastructures.
To get round the problem of oscillations in investment in infrastructures, a
productivity relationship in the year t is assumed with the average investment made in

8
Due to the fact that the latter assumes that it provides its service in the same period as when it begins,
without considering that a certain number of years elapse from its construction to the beginning.
18 J. DE JORGE MORENO, C.CAMISON, J. MURO AND L.LABORDA

the previous five-year period. As Nombela mentions (2005), this option makes it
possible to eliminate the effects of demand and estimate only the medium-term impacts,
ultimately eliminating any possible inverse causality relationship.
The results obtained with this estimate have been clearly significant and confirm the
positive elasticities obtained through the proposed Cobb-Douglas production functions.
The estimates made with the panel of data from the ACs obtain an elasticity of the
productivity of labour with respect to the delays in investment in infrastructures at 0.183,
while elasticity with respect to private investment stands at 0.294. These results make it
possible to determine that investment in public capital contributes to increasing
productivity by approximately 62 per cent.
Finally, the analysis of convergence in efficiency shows that the least efficient
regions have benefited from the existing technology from the regions closest to the
efficiency frontier, which are the most efficient regions.
Having explained the main empirical results obtained and considering the influence
that investment in public capital can have on economic growth and productivity at both
national and international level, as already indicated, it seems relevant to conclude this
study with some reflections on economic policy that could be applied in a context of
economic crisis, like the one currently affecting several European economies, such as
Spain.
In fact, in a situation like the current one, we believe that, although fiscal
consolidation and certain structural reforms are inevitably desirable, it is no less
important to pay attention to the development of active public policies orientated
towards achieving sustainable growth.
We think the crisis includes not only fiscal and macroeconomic imbalance
components, as the majority tend to argue, but also that, ultimately, it is due to
considerable divergences in competitiveness, so structural reforms could be the right
policy for correcting these misalignments.
Along these lines, we believe it is reasonable to use public investment in essential
areas for improving competitiveness, such as energy, transport, innovation and
communication infrastructures, etc. also serving as a stimulus for mobilising private
investment and, ultimately, the economic growth and productivity of economies.
In relation to the above argument, we are aware of the reticence of the private sector
to invest in this type of project in economic circumstances like the current ones, despite
the fact that there is demand, also bearing in mind that the banking sector continues to be
affected by the crisis. However, the combination of banking and public investment
appear to be clearly needed to put this type of policy into practice.
Finally, we think proposals like that from the European Commission to create
instruments such as bonds for infrastructure investment projects could facilitate the
mobilisation of the private sector.
EFFECTS OF PUBLIC CAPITAL ON ECONOMIC GROWTH AND PRODUCTIVITY 19

APPENDIX

Table A1. Work on the Productivity of Public Capital in Spain

Independents Functional
Authors Years Sector variables Form CRS Kprivate Kpublic
Más et al. (1993) 80-89 I K, L, GP CD - 0.43 0.06
Más et al. (1994) 80-90 A K, L, GP CD Si 0.43 0.19
García Fontes and Serra (1994) 80-88 A K, L, GP CD - 0.49 0.06
Argimón et al. (1994) 64-89 A K, L, GP CD Si 0.17 0.02
Argimón et al. (1996) 64-90 A K, L, GP CD Si 0.09 0.71
Bajo and Sosvilla (1993) 64-88 A K, L, GP CD Si 0.42 0.21
Más et al. (1996) 80-90 A K, L, G CD Si 0.42 0.07
Flores de Frutos et al. (1998) 64-92 A K, L, GP CD Si 0.03 0.69
Más et al. (1996) 64-91 A K, L, G CD Si 0.42 0.07
Argimón et al. (1997) 64-92 A K, L, G CD - 0.69 0.19
Dabán and Murgui (1997) 80-91 A L, K*CU, GP/S,H CD - 0.06* 0.05*
Moreno et al. (1997) 64-91 A K, L, GP, GS CD Si 0.51 0.05
Pedraja et al. (1999) 80-92 I K, L, G CD Si 0.16 0.24
Delgado and Álvarez (2000) 86-96 A K, L, I CD - 0.29 0.20
Freire and Alonso (2002) 64-93 A K, L, G, H, S CD Si 0.30 0.12
Cantos et al. (2002) 65-96 A K, L, IT CD - 0.34 0.04
Álvarez et al. (2003) 80-95 A K, L, GP CD - 0.07* 0.00*
Cantos et al. (2005) 80-95 A K, L, G CD 0.34 0.04
Rodríguez-Vélez et al. (2009) 80-98 A K, L, G CD Si 0.34 0.29
Jaen and Piedra (2010) 71-02 A K, L, G CD 0.46 0.26
Notes: A: Aggregate; I, Industry, L, Labour, K, Private C, G, Public, C, Gi, Capital in infrastructure GS, Social
infraestructure, CU, Rate of capacity utilization, I, Index of infraestructure, H, Human Capital, S, Surface, C;
Intermediate consumption, CD, Cobb-Douglas, CRS, Constans returns to scale.*No significance.
Source: Jaen y Piedra (2010), Rodríguez-Vélez (2009) and self elaboration elaboración propia.

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Mailing Address: Justo de Jorge Moreno, Univeristy of Alcala, Business and Economic
Department, Plaza de la Victooria s/n, 28802 Alcala de Henares, Spain.
E-mail:justo.dejorge@uah.es.

Received December 19, 2014, Revised October 29, 2015, Accepted November 26, 2015.