WPS5682
Policy Research Working Paper 5682
Is Infrastructure Capital Productive?
A Dynamic Heterogeneous Approach
César Calderón
Enrique Moral-Benito
Luis Servén
The World Bank
Development Research Group
Macroeconomics and Growth Team
June 2011
Policy Research Working Paper 5682
Abstract
This paper offers an empirical evaluation of the output the pooled mean group estimator, which allows for
contribution of infrastructure. Drawing from a large unrestricted short-run parameter heterogeneity across
data set on infrastructure stocks covering 88 countries countries while imposing the (testable) restriction of
and spanning the years 1960–2000, and using a panel long-run parameter homogeneity. The long-run elasticity
time-series approach, the paper estimates a long-run of output with respect to the synthetic infrastructure
aggregate production function relating GDP to human index ranges between 0.07 and 0.10. The estimates are
capital, physical capital, and a synthetic measure of highly significant, both statistically and economically,
infrastructure given by the first principal component and robust to alternative dynamic specifications and
of infrastructure endowments in transport, power, and infrastructure measures. There is little evidence of long-
telecommunications. Tests of the cointegration rank run parameter heterogeneity across countries, whether
allowing it to vary across countries reveal a common heterogeneity is unconditional, or conditional on their
rank with a single cointegrating vector, which is level of development, population size, or infrastructure
taken to represent the long-run production function. endowments.
Estimation of its parameters is performed using
This paper is a product of the Macroeconomics and Growth Team, Development Research Group. It is part of a larger
effort by the World Bank to provide open access to its research and make a contribution to development policy discussions
around the world. Policy Research Working Papers are also posted on the Web at http://econ.worldbank.org. The author
may be contacted at ccaldero@worldbank.org.
The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development
issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the
names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those
of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and
its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent.
Produced by the Research Support Team
Is infrastructure capital productive?
A dynamic heterogeneous approach*
César Calderóna, Enrique Moral-Benitob, Luis Servéna
a
The World Bank, 1818 H Street NW, Washington DC 20433, USA
b
Bank of Spain, Alcalá 48, 28014, Madrid, Spain
JEL Classification: H54, E23, O40
Keywords: Infrastructure, panel cointegration, parameter heterogeneity.
* We are grateful to Nicola Limodio and Stephane Straub for useful comments and suggestions. We also
thank participants at the Toulouse conference on ‗Infrastructure Economics and Development‘, the
Australian National University conference on ‗The Economics of Infrastructure‘, the IMF conference on
‗Investment Scaling-up in Low-Income Countries‘, the 2010 Symposium of Economic Analysis, and
seminars at Brookings and the Bank of Spain. However, any remaining errors are ours only. Rei Odawara
and Junko Sekine provided excellent research assistance. This work was partly supported by the
Knowledge for Change Program as well as the Government of Japan through the Consultancy Trust Fund
Program (CTF) of the World Bank. The views expressed in this paper are only ours and do not
necessarily reflect those of the World Bank, its Executive Directors, or the countries they represent.
1. Introduction
The macroeconomic literature has long been interested in the contribution of
infrastructure capital to aggregate productivity and output. Numerous theoretical papers have
approached it using an aggregate production function including public capital as an additional
input, first in the context of Ramsey-type exogenous growth models (e.g., Arrow and Kurz 1970)
and later in endogenous growth models (Barro 1990, Futagami, Morita and Shibata 1993). This
analytical literature has grown enormously in the last fifteen years, exploring a multitude of
variants of the basic models, such as alternative financing schemes, simultaneous consideration
of public capital and productive current spending flows, utility-yielding public capital, or public
infrastructure congestion.1
Quantitative assessments of the contribution of infrastructure are critical for many policy
questions – such as the output effects of fiscal policy shocks instrumented through public
investment changes (e.g., Leeper, Walker and Yang 2010; Ilzetzki, Mendoza and Végh 2010), or
the extent to which public infrastructure investment can be self-financing (Perotti 2004). The
empirical literature offering such quantitative assessments took off with the seminal work of
Aschauer (1989) on the effects of public infrastructure capital on U.S. total factor productivity.
The literature has boomed over the last two decades, with dozens of papers using a large variety
of data and empirical methodologies, and with widely contrasting empirical results. 2 For
example, Bom and Ligthart (2008) report that in a large set of empirical studies using industrial-
country data in a production function setting, estimates of the output elasticity of public capital
range from -0.175 to +0.917.
However, much of the empirical literature on the contribution of infrastructure to
aggregate output is subject to major caveats. Studies based on time-series have often ignored the
non-stationarity of aggregate output and infrastructure capital, which typically display stochastic
trends. This has sometimes led to implausibly high estimates of the productivity of infrastructure,
owing to spurious correlation between both variables (Gramlich 1994).3 In addition, empirical
1
See for example Turnovsky (1997), Glomm and Ravikumar (1997), Baier and Glomm (2001), and Ghosh and Roy
(2004).
2
See for example Sánchez-Robles (1998); Canning (1999); Demetriades and Mamuneas (2000); Röller and
Waverman (2001); Esfahani and Ramirez (2003); Calderón and Servén (2004). A recent overview of relevant
empirical literature is provided by Romp and de Haan (2007).
3
One example is Aschauer‘s original estimate of the output elasticity of public capital, which was so high that the
implied marginal product of infrastructure capital was close to 100% per year.
2
studies also have to deal with potential simultaneity between infrastructure and income levels.
For example, richer or faster-growing countries are likely to devote increased resources to
infrastructure development. Failing to control for these and similar forms of reverse causality
implies that estimates of the output elasticity of infrastructure may be confounded with the
income elasticity of the demand for infrastructure services, and hence may suffer from upward
biases.4 Finally, studies using cross-section or panel macroeconomic data typically fail to
account for the potential heterogeneity in the output elasticity of infrastructure across countries
or states, which could arise from technological features such as network effects, scale economies
and other factors that may affect the output elasticity of public capital.5
This paper estimates the contribution of infrastructure to aggregate output using a
production function framework including as inputs infrastructure assets, human capital, and non-
infrastructure physical capital. We use a large cross-panel dataset comprising 88 countries and
over 3,500 country-year observations, drawn from countries with very different levels of income
and infrastructure endowments.
One distinguishing feature of our approach is that, in contrast with much of the earlier
literature, we use physical measures of infrastructure rather than monetary ones – such as a
public investment flow or its accumulation into a public capital stock. We do this for two
reasons. First, as an abundant literature has argued, public expenditure can offer a very
misleading proxy for the trends in the public capital stock, as the link between spending and
capital is mediated by the extent of inefficiency and corruption surrounding project selection and
government procurement practices, which can vary greatly across countries and over time (e.g.,
Pritchett 2000; Keefer and Knack 2007). Second, our interest here is infrastructure capital, rather
than broader public capital, and in many countries the two can be very different owing to the
involvement of the public sector in non-infrastructure industrial and commercial activities (a
common occurrence in virtually all countries over a good part of our sample period), and due
4
A way out of this problem is to use a full structural model in the empirical estimation. In this vein, some empirical
studies have used stripped-down versions of Barro‘s (1990) framework (e.g., Canning and Pedroni 2008). An
alternative is to use some kind of instrumental variable approach, ideally featuring outside instruments for
infrastructure. For example, Calderón and Servén (2004) employ demographic variables as instruments -- alone or in
combination with internal instruments -- in a GMM panel framework. Roller and Waverman (2001) follow a similar
approach.
5
In this vein, Gregoriou and Ghosh (2009) estimate the growth effects of public expenditure in a panel setting, and
find that they exhibit considerable heterogeneity across countries.
3
also to the increasing participation of the private sector in infrastructure industries worldwide,
especially since the 1990s.
The paper‘s approach allows us to tackle some of the main methodological problems of
earlier literature and extend it in several dimensions. First, we take account of the
multidimensionality of infrastructure6 and, in contrast with the abundant literature that measures
infrastructure in terms of an investment flow or its cumulative stock, or in terms of a single
physical asset (such as telephone density), we consider three different types of core infrastructure
assets – in power, transport and telecommunications – summarized into a synthetic infrastructure
index, constructed through a principal-component procedure. Second, we use a panel
cointegration approach to deal with the non-stationarity of the variables of interest and avoid the
‗spurious regression‘ problem of much of the earlier time-series literature. Third, to address
concerns with identification and reverse causality, we establish that only one cointegrating
relation exists among the variables, and that this applies to all the countries in the panel. We
interpret this relationship as the aggregate production function, and verify that our infrastructure
index and the other productive inputs are exogenous with respect to its parameters – the
parameters of interest in our context, in the terminology of Engle, Hendry, and Richard (1983).
We estimate these parameters using the Pooled Mean Group estimator of Pesaran, Shin and
Smith (1999), which allows for unrestricted cross-sectional heterogeneity of the short-run
dynamics while imposing homogeneity of the long-run parameters. Fourth, we deal explicitly
with potential cross-country heterogeneity of the (long-run) parameters of the production
function through individual and joint Hausman tests of parameter homogeneity, as well as
through additional experiments that let the output elasticity of infrastructure vary with selected
country characteristics.
Our estimates of the output elasticity of infrastructure lie in the range of 0.07 to 0.10.7
Moreover, our estimates are very precise, and robust to the use of alternative econometric
specifications and alternative synthetic measures of infrastructure. Likewise, the estimated
elasticities of the other inputs – human and non-infrastructure physical capital – are in line with
6
Canning (1999) also considers the multidimensionality of infrastructure using three different physical measures;
however, reverse causality issues are not addressed and the single cointegration rank hypothesis is imposed and not
tested.
7
This is very close to the value that emerges from the meta-study by Bom and Ligthart (2008) of the output
elasticity of public capital. After adjusting for publication bias, they place the output elasticity of public capital at
0.086.
4
those found in the empirical macroeconomic literature (Bernanke and Gurkaynak, 2001; Gollin,
2002). They are also highly significant and robust to the various experiments we perform.
We also find little evidence of heterogeneity across countries in the output elasticities of
the inputs of the aggregate production function. Specifically, the output elasticity of
infrastructure does not seem to vary with countries‘ level of per capita income, their
infrastructure endowment, or the size of their population.
The rest of the paper is organized as follows: Section 2 describes the dataset. Section 3
lays out the methodological approach. Section 4 describes the empirical results. Finally, section 5
concludes.
2. Data
Our goal is to estimate the contribution of infrastructure capital to output in a large panel
data set using an infrastructure-augmented aggregate production function framework, in which
aggregate output is produced using non-infrastructure physical capital, human capital, and
infrastructure. The data set is a balanced panel comprising annual information on output,
physical capital, human capital, and infrastructure capital for 88 industrial and developing
countries over the period 1960-2000, thus, totaling 3,520 observations. The Appendix lists the
sample countries used in the analysis.8
Real output is measured by real GDP in 2000 PPP US dollars from the Penn World
Tables 6.2 (Heston, Summers, and Aten, 2006). The data on physical capital was constructed
using the perpetual inventory method. To implement it, the initial level of the capital stock was
estimated using data on the capital stock and real output from PWT 5.6 for those countries for
which such data is available. We extrapolate the data for countries without capital stock
information in PWT 5.6 by running a cross-sectional regression of the initial capital-output ratio
on (log) real GDP per worker.9
As a robustness check, we also constructed an alternative ‗back-cast‘ projection of capital
per worker. Specifically, to construct an initial capital stock for the year 1960, we assume a zero
capital stock in the distant past. Using the average in-sample growth rate of real investment
8
Country coverage is dictated by the availability of information. In particular, time coverage is limited by the
human capital indicator, which is not available after 2000.
9
The regression used for extrapolation is: K/Y = -1.1257+0.2727*ln(Y/L), where K is the capital stock, Y is real
GDP, and L is the labor force. The depreciation rate employed in the perpetual inventory calculations is 6%.
5
(1960-2000), we project real investment back to 1930. Next, ignoring the capital stock that may
have existed in that year, we accumulate the projected real investment forward into a capital
stock series. The resulting level of the latter in 1960 is then taken as the initial capital stock, and
the in-sample capital stock series is constructed accumulating observed investment.10
Our preferred measure is the capital stock series obtained from the PWT data. Assuming,
as we do for the back-casting, that the pre-sample growth rate of real investment was equal to the
average of the 1960-2000 period could be misleading, in view of the severe global shocks of the
1930s and 1940s (e.g. the Great Depression and World War II), which likely had a non-
negligible reflection on the rates of growth capital stocks around the world. Nevertheless, we
also report estimates using the capital stock series constructed through back-casting,
In turn, the stock of human capital is proxied by the average years of secondary schooling
of the population, taken from Barro and Lee (2001). Finally, the labor input is proxied by the
total labor force as reported by the World Bank‘s World Development Indicators.
Measuring physical infrastructure poses a challenge. Typically, the empirical literature on
the output effects of infrastructure has focused on a single infrastructure sector. Some papers do
this by design,11 while others take a broad view of infrastructure but still employ for their
empirical analysis an indicator from a single infrastructure sector. 12 In reality, ‗physical
infrastructure‘ is a multi-dimensional concept that refers to the combined availability of several
individual ingredients – e.g., telecommunications, transport and energy. In general, none of these
individual ingredients is likely to provide by itself an adequate measure of the overall availability
of infrastructure. For instance, a country may have a very good telecommunications network and
a very poor road system or a highly unreliable power supply. In such situation, the availability of
telecommunications services alone would provide a misleading indicator of the status of overall
physical infrastructure.
However, attempting to capture the multi-dimensionality of infrastructure by introducing
a variety of infrastructure indicators as inputs in the production function also poses empirical
10
The rationale behind this calculation is that the assumed level of the capital stock in 1930 has only a very minor
effect on the capital stock that results for 1960, and hence it is immaterial whether we set the level of capital stock at
zero or some other arbitrary level in 1930.
11
For example, Röller and Waverman (2001) evaluate the growth impact of telecommunications infrastructure, and
Fernald (1999) analyzes the productivity effects of changes in road infrastructure.
12
In the empirical growth literature, for example, the number of telephone lines per capita is usually taken as the
preferred indicator of overall infrastructure availability; see for example Easterly (2001) and Loayza, Fajnzylber and
Calderón (2005).
6
difficulties. It could lead to an over-parameterized specification, and hence to imprecise and
unreliable estimates of the contribution of the individual infrastructure indicators. In our
framework this is a concern not only for the usual reasons of multicollinearity – indeed, several
13
of the infrastructure indicators we shall use are fairly highly correlated -- but also because, as
described below, we shall use a nonlinear procedure to estimate the parameters of the production
function. In these conditions, a parsimonious specification with relatively few regressors is much
more likely to result in stable estimates robust to alternative choices of initial values.
For these reasons, we follow a different strategy. We use a principal component
procedure to build a synthetic index summarizing different dimensions of infrastructure. 14 We
focus on three key infrastructure sectors: telecommunications, power and road transport. This
choice is consistent with previous literature on the output impact of infrastructure, which has
typically focused on one of these individual sectors, most often telecommunications. The
synthetic infrastructure index is the first principal component of three variables measuring the
availability of infrastructure services in these three sectors. Specifically, the variables underlying
the index are:
(a) Telecommunications: Number of main telephone lines, taken from the International
Telecommunications Union‘s World Telecommunications Development Report CD-
ROM. As a robustness check, we also experiment with an alternative measure , namely
the total number of lines (main lines and mobile phones), from the same source.
(b) Electric Power: Power generation capacity (in Megawatts), collected from the United
Nations‘ Energy Statistics, the United Nations‘ Statistical Yearbook, and the U.S. Energy
Information Agency‘s International Energy Annual.15
(c) Roads: Total length of the road network (in kilometers), obtained from the International
Road Federation‘s World Road Statistics, and complemented with information from
13
For instance, in our panel data set the full-sample correlation between the total number of phone lines (main and
mobile) and overall power generation capacity is 0.92, while the correlation between total road length and overall
power generation capacity is 0.65, and that between road length and main telephone lines is 0.61. In turn, the
correlation between paved (as opposed to total) road length and power generation capacity is 0.83, while that
between paved road length and main telephone lines is 0.84.
14
A similar approach is employed by Alesina and Perotti (1996) in their analysis of investment determinants, and by
Sánchez-Robles (1998) to assess the growth effects of infrastructure.
15
The International Energy Annual (IEA) is the Energy Information Administration‘s main report of international
energy statistics, with annual information on petroleum, natural gas, coal and electricity beginning in the year 1980.
See webpage: http://www.eia.doe.gov/iea/
7
national statistical agencies and corresponding national ministries.16 To conduct
robustness checks, we use two alternative measures of transport infrastructure: the length
of the paved road network, collected from the same sources, and the combined total
length of the road and railway network. The railway information is obtained from the
World Bank‘s Railways Database and complemented with data from national sources.17
As we shall impose constant returns to scale in the estimations (see below), the three
variables underlying the index (phone lines, power generation capacity and the length of the road
network) are measured in per-worker terms, and expressed in logs.18 Their first principal
component accounts for 82 percent of their overall variance and, as expected, it is highly
correlated with each of the three individual variables.19 More specifically, the correlation
between the first principal component and main telephone lines per worker is 0.96, its correlation
with power generation capacity is 0.97, and its correlation with the total length of the road
network is 0.74. In addition, all three (log-standardized) variables enter the first principal
component with approximately similar weights:
Z Z Z
zit 0.364 ln 1 0.354 ln 2 0.282 ln 3
L it L it L it
where z is the synthetic infrastructure index, (Z1/L) is the number of main telephone lines (per
1,000 workers), (Z2/L) is the power generation capacity (in GW per 1,000 workers), and (Z3/L)
represents the total length of the road network (in km per 1,000 workers).
Table 1 shows descriptive statistics for output, physical and human capital, and the
various infrastructure indicators, for the cross-section corresponding to the year 2000. Output
and the capital stock are expressed in PPP US dollars at international 2000 prices, while
infrastructure variables are expressed in per worker terms.
16
One caveat regarding these data, as noted by Canning (1999), is that they may exhibit significant variations in
quality. In particular, they do not reflect the width of the roads nor their condition.
17
The railways database can be found at http://go.worldbank.org/13EP3YJVV0
18
Before applying principal component analysis, the underlying variables are standardized in order to abstract from
units of measurement.
19
As shown below, the individual infrastructure measures display stochastic trends, and hence we obtain the first
principal component by computing the weights from the (stationary) first-differenced series.
8
3. Econometric Methodology
The core of our empirical analysis consists in estimating the following production
function:
(1)
where y denotes real output, k and h represent physical capital and human capital, respectively,
and z denotes the infrastructure capital. All variables (except human capital) are expressed in log
per worker terms (e.g. kit = ln(Kit/Lit) where Lit represents the workforce) and, in keeping with the
majority of earlier literature, constant returns to scale have been imposed. The subscripts i and t
index countries and years, respectively; i and t capture country-specific and time-specific
productivity factors, and it is a random disturbance that will be assumed uncorrelated across
countries and over time. 20
3.1 Panel unit root testing
Empirical assessments of the output contribution of infrastructure using time-series data
have often failed to deal adequately with the non-stationarity of the variables. Here we address
the issue using panel unit root and cointegration tests developed in the recent panel time-series
literature. Unlike the traditional panel literature, which deals with samples in which the cross-
sectional dimension N is large but the time dimension T is small, the panel time-series literature
is concerned with situations in which both N and T are of the same order of magnitude; see
Breitung and Pesaran (2008) for an overview. As a considerable literature has shown, the panel
time-series (or multivariate) approach to integration and cointegration testing yields higher test
power than separate, conventional tests for each unit in the panel; see, for example, Levin, Lin
and Chu (2002).
The first step is to test for the stationarity of the variables under consideration, namely,
output, the stocks of physical and human capital, and the composite index of infrastructure
capital, all (except for human capital) measured in logs per worker. As a preliminary step, we
remove the cross-sectional means from the data, to render the disturbances cross-sectionally
20
As noted by Canning (1999), infrastructure appears twice in (1): first as z, and then as part of overall physical
capital k. Hence the total elasticity of output with respect to infrastructure capital can be approximated as
, where is the share of infrastructure in the overall physical capital stock. Evaluation of requires
data on the price of infrastructure, which are not widely available. Nevertheless, calculations based on the data of
Canning and Bennathan (2000) suggest that it is a small number. For the countries in our sample with available data,
its median is 0.08, and its standard deviation is 0.05.
9
independent. To test for the presence of a unit root in each panel series, we employ the unit root
test of Im, Pesaran and Shin (2003) (IPS), which allows for heterogeneous short-run dynamics
for different cross-sectional units. Specifically, the testing procedure averages the individual unit
root test statistics.21 The basic regression framework is the following:
pi
yit i yi ,t 1 ik yi ,t k i it (3)
k 1
with the null hypothesis of non-stationarity H0: i=1, for all i, and the alternative H1: i<1, for
some i. The test is based on a t -statistic, defined as the average of the individual ADF-t statistics,
N
1
t
N
t ( ) , where t(i) is the individual t-statistic for testing the null hypothesis in equation
i 1
i
(3). The critical values are tabulated by Im, Pesaran and Shin (2003).22
3.2 Panel cointegration testing
If the null of a unit root fails to be rejected, we next proceed to test for cointegration
among the variables of interest. Several tests have been proposed in the literature for this purpose
—e.g. McCoskey and Kao (1998), Kao (1999), and Pedroni (2004). However, all these tests
simply evaluate the presence of cointegration and do not account for the potential existence of
more than one cointegrating relationship. To assess the cointegration rank, we follow the
approach of Larsson and Lyhagen (2000). Assume that the p-dimensional vector
Yit ( yit , kit , hit , zit ) ' for country i (where p=4 in our case and i = 1,…,N) has an error correction
model (ECM) representation (if the Granger representation theorem holds). We first test the
hypothesis that each of the N countries in the panel has at most r cointegrating relationships
among the p variables. In other words, we test the null H 0 : i ri r for all i=1,…,N, against
the alternative H a : i p for all i=1,…,N, where i is the number of cointegrating
21
If the data are statistically independent across countries, under the null we can regard the average t-value as the
average of independent random draws from a distribution with known expected value and variance (that is, those for
a non-stationary series). This provides a much more powerful test of the unit root hypothesis than the usual single
time series test. In particular, this panel unit root test can have high power even when a small fraction of the
individual series is stationary. In this context, Karlsson and Lothgren (2000) find that the power of the IPS test
increases monotonically with: (i) the number N of cross-sectional units in the panel; (ii) the time dimension T of
each individual cross-sectional unit, and (iii) the proportion of stationary series in the panel.
22
It has been shown that the empirical size of the IPS test is fairly close to its nominal size when N is small, and that
is has the most stable size among the various panel unit root tests available (Choi, 2001). However, when linear time
trends are included in the model, the power of the test declines considerably (Breitung, 2000; Choi, 2001).
10
relationships present in the data for country i. To conduct this test, Larsson and Lyhagen (2000)
define the LR-bar statistic as the average of the N individual trace statistics of Johansen (1995),
LR H (r ) H ( p)
N LR NT ( H (r ) / H ( p)) E (W )
Var (W )
where LR NT ( H (r ) | H ( p)) is the average of the individual trace statistics and E(W) and Var(W)
are the mean and the variance of the variable W, whose asymptotic distribution is the same as
that of the individual trace statistic. The cointegrating rank suggested by the testing procedure
based on the standardized LR-bar statistic equals the maximum of the N individual ranks.
Further, under fairly general conditions, Larsson et al. (2001) show that the standardized LR-bar
statistic for the panel cointegration rank test is asymptotically distributed as a standard normal.
Since the time dimension of our sample is too short for the asymptotic properties of the
individual trace statistics to hold, in our empirical application we use Reimers‘ (1992) small-
sample correction —i.e. we multiply the individual trace statistics by T Lp / T , where L is
the lag length used to construct the underlying VAR, and p is the total number of variables.23
Next, we follow Larsson and Lyhagen (2000) and test for the smallest cointegration rank
in the panel using the panel version of the principal component test developed by Harris (1997).
Specifically, we test the null hypothesis H 0 : i ri r against the alternative H a : i ri r .
Thus, this hypothesis is the opposite of that used for the LR-bar test in the sense that the
alternative is that there are more than r cointegrating vectors. For this purpose, Larsson and
Lyhagen (2000) developed the standardized PC-bar statistic:
N cr E (W )
PC r
Var (W )
T
where cr is the mean of the individual test statistics cr T 2 St'*1St , E(W) and Var(W) are
ˆ ˆ ˆ ˆ
nn
t 1
the mean and the variance respectively of the variable W, whose asymptotic distribution is the
23
As done for the panel unit root tests, we remove the cross-sectional means from the data prior to implementing the
panel cointegration tests.
11
j ˆ
same as that of cr , and we have defined St j 1 n j and * j T 1 k ab ( j ) , where a
T 1
ˆ ˆ t
ˆ ˆ
nn
m
and b are any time series, k(.) is a lag window, m is the bandwidth parameter and
ab ( j ) T 1 t 1 at j bt . In large samples, the PC-bar test follows a standard normal distribution.
ˆ T
If at least one of the individual ranks is less than the hypothesized value, the test asymptotically
rejects the null. Hence, the PC-bar statistic gives the minimum cointegration rank amongst all
the cross-sectional units.
In short, we first use the LR-bar test to estimate the maximum number of cointegration
relations, and then we use the PC-bar test to assess if for any country the number of
cointegrating relations is less than the maximum given by the LR-bar test. If in the second step
the null hypothesis cannot be rejected, the conclusion is that the number of cointegrating
relations is the same for all cross-sectional units.
3.3 Heterogeneous panel data techniques
As we report below, the panel cointegration tests indicate a common unit cointegration
rank among GDP, physical capital, human capital and the composite index of infrastructure. We
interpret the single cointegration vector (whose parameters may vary across countries) as a long-
run production function. To estimate its coefficients, we adopt a single-equation approach. If
there were more than one cointegrating relation, single-equation estimation would only
determine a suitable combination of the various cointegrating relations. However, in the presence
of a single cointegrating vector, Johansen (1992) shows that if the equations of the marginal
model have no cointegration, the single-equation estimator is equivalent to the estimator
resulting from system estimation of all the equations.24
To estimate the coefficients in equation (1), we use the pooled mean group (PMG)
estimator developed by Pesaran, Smith, and Shin (1999).25 In practical terms, we embed the
production function equation (1) into an ARDL(p,q) model:
p 1 q 1
yi i yi ,1 Fi ,1 i ,h yi , h i,h Fi , h i i (4)
h 1 h 1
24
The single-equation analysis could be inefficient under certain circumstances (see Johansen 1992).
25
This estimator has been previously implemented in different contexts, for example Cameron and Muellbauer
(2001) analyze the relationship between earnings, unemployment and housing in a panel of UK regions, while Égert
et al. (2006) consider exchange rates, productivity and net foreign assets in a panel of countries.
12
where i 1,..., N denotes the cross section units, and we impose homogeneity of the long-run
coefficients i i . Here yi yi1 ,..., yiT ' is the T x 1 vector that contains the T observations
of GDP for unit i in the panel, Fi = (ki, hi, zi) is the T x 3 matrix of inputs (physical capital, human
capital and infrastructure), and i are the coefficients that measure the speed of adjustment
towards the long-run equilibrium. Also, is a T x 1 vector of ones and i represents a country-
specific fixed effect. The disturbances i i1 ,..., iT ' are assumed to be independently
distributed across i and t, with zero means and country-specific variances i2 0 . As before, all
the variables are cross-sectionally de-meaned prior to estimation in order to remove common
factors, as required by the assumption of cross-sectional independence.
As equation (4) makes explicit, the PMG estimator restricts the long-run coefficients to
be equal over the cross-section, but allows for the short-run coefficients, speed of adjustment and
error variances to differ across cross-sectional units.26 We therefore obtain pooled long-run
coefficients and heterogeneous short-run dynamics. Thus, the PMG estimator provides an
intermediate case between full parameter homogeneity, as imposed by the dynamic fixed effects
estimator, and unrestricted heterogeneity, as allowed by the mean group (MG) estimator of
Pesaran and Smith (1995), based on separate time-series estimation for each cross-sectional unit.
Estimation of the long-run coefficients in (4) is based on the concentrated log-likelihood
function under normality. The pooled maximum-likelihood estimator of the long-run parameters
is computed using an iterative non-linear procedure. Once the long run parameters have been
computed, both the short-run and the error-correction coefficients can be consistently estimated
running individual OLS regressions of yi on yi ,1 Fi ,1 .
To test the validity of the long-run parameter homogeneity restrictions, we use Hausman
tests of the difference between MG and PMG estimates of the long-run coefficients. These are
preferable to likelihood ratio tests owing to the ‗large N‘ setting, which would cause the number
of parameter restrictions to be tested by the likelihood ratio test to rise with sample size.
As described, the empirical strategy adopted in the paper is based on the single-equation
estimation of the only cointegrating vector present in the data, which we interpreted as the
26
In the context of country-level production functions, it seems reasonable to allow for heterogeneity of the short-
run-dynamics due to, for instance, differences in adjustment costs across countries.
13
aggregate production function. Our estimates of the output elasticity of physical capital, human
capital and infrastructure, and the associated inference, are obtained from an equation describing
the time path of GDP per worker, with the time path of the three inputs determined by some
unspecified marginal model. For this approach to be valid, the inputs have to be weakly
exogenous -- in the sense of Engle, Hendry, and Richard (1983) -- for the parameters of the
cointegrating relation. In this context, weak exogeneity means that changes in the inputs (e.g.
infrastructure) do not react to deviations from the long-run equilibrium, although each input may
still react to lagged changes of both GDP per worker and the other inputs of the production
function. If changes in the inputs did react to deviations from the estimated long-run equation,
the implication is that the single equation used in the analysis could be capturing the demand for
physical capital, human capital or infrastructure rather than the production function – or a
combination of both.
The requirement that the inputs be weakly exogenous can be verified through a standard
variable-addition test. Specifically, as shown by Johansen (1992) and Boswijk (1995), weak
exogeneity for the long-run parameters can be checked by testing the significance of the
cointegrating vector in a reduced-form regression of each input on its own past and those of
output and the other inputs of the production function.
Formally, weak exogeneity of the inputs amounts to the requirement that the
coefficients not be significantly different from zero in the following system of equations
(Johansen 1992):
ˆ
kit ki fit 1 ki fit 2 ki yit 1 ki yit 2 kiit ( ) vit
1 2 k
h f f 1 y 2 y ( ) v h ˆ (5)
it hi it 1 hi it 2 hi it 1 hi it 2 hi it it
ˆ
zit zi f it 1 zi fit 2 zi yit 1 zi yit 2 ziit ( ) vitz
1 2
ˆ
where ít ( ) yi ,t 1 fi ,t 1 is the estimated long-run equilibrium error term from equation (4)
above, and fit 1 (kit 1 , hit 1 , zit 1 ) . We estimate the system of equations country by country
using the SURE estimator proposed by Zellner (1962). Once we have all the country-specific
SURE estimates we compute the Mean Group (MG) estimator (Pesaran and Smith 1995) and we
carry out a Wald test under the null that the three coefficients on the added error terms are jointly
zero. If soothe null is not rejected, we can conclude that the three inputs are weakly exogenous
with respect to the parameters of the cointegrating relation.
14
4. Empirical Results
Our empirical implementation starts by checking the order of integration of the different
variables and testing for the existence of cointegration among them. Then we turn to the
estimation of the parameters of the cointegrating relation(s).
4.1 Integration and cointegration
Table 2 reports the panel integration and cointegration tests. Panel A in the table shows
the results of applying the panel unit root test of Im, Pesaran and Shin (2003) to each of the
model‘s variables. In every case, the test statistic lies well below the 5% critical level, thus
failing to reject the null of a unit root. Individual tests for each country (not shown) yield a
similar verdict – they fail to reject the null in the overwhelming majority of cases. After taking
first differences, however, the panel test (not reported) rejects the null of nostationarity for each
of the variables. From this we conclude that all the variables are I(1).
We next test for cointegration. A battery of residual-based panel tests (not reported to
save space), whose alternative hypotheses variously include homogeneous and heterogeneous
cointegration (Kao, 1999; Pedroni, 1995, 1999), strongly support the view that the model‘s
variables are cointegrated. However, as already noted, these tests are uninformative about the
number of cointegrating relations, and with more than two I(1) variables under consideration, the
possibility of multiple cointegration vectors cannot be ruled out. Further, in a panel context the
possibility that different cross-sectional units may have different orders of cointegration cannot
be dismissed either.
To assess the cointegration rank, we turn to the LR-bar test of Larsson, Lyhagen and
Lothgren (2001) and the panel version of the PC-bar test of Harris (1997) proposed by Larsson
and Lyhagen (2000). As already mentioned, we proceed in two stages. We first use the LR-bar
test to establish the maximum cointegrating rank – i.e., the maximum number of cointegrating
relations present in any of the panel‘s cross-sectional units (countries). We then use the panel
version of the PC-bar test to establish the minimum cointegrating rank.
As Panel B of Table 2 reports, the LR-bar test overwhelmingly rejects the null that the
maximum rank is zero (the test statistic of 9.03 is far above the 5% critical value of 1.96), but
cannot reject a maximum rank of one. In turn, panel C shows that the PC-bar test cannot reject a
15
minimum cointegrating rank of one – the computed test statistic of 1.21 is well below the critical
5% value of 1.96.
Since the maximum cointegration rank from the LR-bar test and the minimum
cointegration rank from the PC-bar test coincide, the null hypothesis of a common cointegrating
rank for all countries in the panel cannot be rejected. Hence, taken together the test results imply
that, for each of the sample countries, there exists one single cointegrating vector among the four
variables in our study, which we shall interpret as the infrastructure-augmented production
function.
4.2 Estimation results
The next step is to estimate the parameters of the single cointegrating vector, which in
principle might differ across countries. As discussed, we opt for the PMG estimator of Pesaran,
Shin and Smith (1999), which estimates the coefficients of the long-run relation along with those
characterizing the short-term dynamics. We use Hausman specification tests to assess the
validity of the homogeneity restrictions imposed by PMG on the long-run parameters.
Table 3 reports a variety of PMG estimates of the long-run parameters, using alternative
dynamic specifications – i.e., different orders of the ARDL formulation of the equation of
interest– and including time dummies to account for common factors (columns 1-5) or excluding
them (column 6). The first thing to note is that, with the exception of the last column in the table,
the parameter estimates in the different columns are very similar to each other. They are also
very precisely estimated, which is unsurprising given the large number of observations (over
3,500) and the relatively parsimonious model employed.
In the first column, the order of the ARDL specification is determined (separately for
each country) using the Schwarz criterion, subject to a maximum of two lags for both the
dependent and independent variables. The estimated coefficient of the capital stock is 0.34, very
close to the values commonly encountered in the empirical macroeconomic literature. The
coefficient of the human capital variable is 0.10, likewise in the range of previous estimates in
the literature, while that of the synthetic infrastructure index equals 0.08.27 All three estimates
27
The estimated coefficient of human capital ranges from 0.08-0.085 in Bloom et al. (2004), to 0.11-0.13 in Temple
(1998), and 0.06-0.11 in Miller et al. (2002). On the other hand, our estimated coefficient of infrastructure capital is
similar to those reported by Le and Suruga 2005 (0.076 ), Eisner 1991 (0.077), Duffy-Deno et al. 1991 (0.081), and
Mas et al. 1996 (0.086).
16
are significantly different from zero at the 1 percent level. Further, the Hausman tests of
parameter homogeneity, reported also in the table, show little evidence of cross-country
heterogeneity of any of the individual parameters (all the p-values exceed 0.20). The same
applies to the Hausman test of the joint null of homogeneity of all parameters, reported at the
bottom of the table, whose p-value equals 0.44. The second column of Table 3 uses the Akaike
information criterion rather than the Schwarz criterion to determine lag length, still subject to a
2-lag maximum. As is customary, this choice leads to somewhat more generous lag
specifications, with a majority of countries selecting longer lag lengths than under the Schwarz
criterion. However, it causes little change in the size or significance of the parameter estimates in
the table, and it does not affect the Hausman tests of parameter homogeneity.
In turn, column 3 of the table imposes equal lag length (two lags) for all variables and
countries, instead of allowing it to be determined by information criteria. Relative to columns 1
and 2, this results in a further loss of degrees of freedom, to an extent that depends on the
country-specific number of lags that were being selected by the information criteria, and a slight
deterioration of the precision of the estimates. However, it is of little consequence for the values
of the estimates, their overall significance, or the verdict of the Hausman tests.
We next assess the effect of alternative choices of maximum lag length, using again the
Schwarz criterion. Column 4 restricts the maximum lag length to 1. Relative to column 1, this
adds 88 observations to the estimation sample, but is otherwise of little consequence for the
coefficient estimates, their precision, and the Hausman tests. Column 5 summarizes the opposite
exercise, raising maximum lag length to 4. This leads to the loss of 176 observations relative to
column 1, but again there is no material change in any of the results.
Lastly, column 6 in Table 3 examines the role of common factors by re-estimating the
specification in the first column omitting the time dummies. This does cause major changes in
the parameter estimates: the coefficient of the capital stock rises above 0.40, and that of the
infrastructure synthetic index becomes negative and insignificant. This confirms the importance
of taking into account common factors (i.e., GDP and productivity shocks correlated across
countries) in the estimation.
In Table 4 we explore the robustness of the results to the use of alternative measures of
infrastructure and the capital stock. In all cases we employ the Schwarz criterion with a
maximum lag length of 2 to select the dynamic specification. For ease of comparison, column 1
17
just reproduces the results from the first column of Table 3. In column 2, we replace the indicator
of telephone density underlying the synthetic infrastructure index, using total phone lines (fixed
plus mobile) instead of main lines, which is the variable conventionally employed in the growth
literature. We recalculate the synthetic index as the first principal component of total phone lines,
roads, and power generation capacity, all expressed in log per worker terms. This causes fairly
modest changes in the estimates: the human capital parameter falls from 0.10 to 0.07, and overall
precision declines somewhat, but there is little change in the infrastructure coefficient estimate
and the results of the homogeneity tests.
Column 3 replaces road density with the density of land transport lines, including both
roads and railways. As before, this leads to a new synthetic infrastructure index, but the
estimation results obtained with it are virtually identical to those in the first column. In column 4,
we use a narrower measure of roads, namely paved roads. The only noticeable change concerns
the estimated coefficient of the human capital variable, which declines by half, while its standard
error doubles. However, there is virtually no change in the other estimates. In turn, the Hausman
tests now show some borderline evidence against the cross-country homogeneity of the
coefficient of the human capital stock. Column 5 presents the results obtained replacing the
principal-component index with an average index of infrastructure in which all the three
infrastructure variables (roads, phone lines and electricity generating capacity) receive the same
weight. Compared with our baseline specification in Column 1, the use of the average index
causes practically no changes in the estimates.
Lastly, column 6 assesses the robustness of the results to the use of an alternative capital
stock series, constructed through the back-casting method described earlier. Once again, the
estimation results – including remarkably the coefficient on the capital stock itself -- are virtually
indistinguishable from those in the first column of the table, although now there is some
indication of cross-country heterogeneity of the capital stock coefficient.
Overall, these experiments suggest that the parameter estimates of the infrastructure-
augmented production function are fairly robust to alternative specifications concerning the
short-run dynamics as well as the precise choice of explanatory variables. Moreover, the
experiments also reveal little evidence of cross-country heterogeneity in the output elasticity of
infrastructure.
18
However, the tests reported so far are concerned with unconditional heterogeneity, and it
might be possible to gain power by testing for more specific forms of parameter heterogeneity.
For example, it could be argued that, owing to network effects, the elasticity of output with
respect to infrastructure should be higher in countries with larger infrastructure endowments than
the rest.28 Alternatively, the elasticity could vary with the level of development – as captured for
example by GDP per worker – reflecting the fact that poorer countries are less able to use
infrastructure effectively. As another hypothesis, the output elasticity of infrastructure could
depend negatively on the size of the overall population, owing to congestion effects.
To verify this, we re-estimate the model in column 1 of Table 3 without imposing
homogeneity across countries of the long-run parameter of the infrastructure synthetic index, and
then look for patterns of heterogeneity in the individual-country estimates of that parameter
along the three dimensions just mentioned – GDP, infrastructure endowment (both in per worker
terms), and population size .
Figure 1 plots the resulting country-specific estimates of the infrastructure long-run
coefficient against each of the three variables just mentioned. While there are some obvious
outliers, the conclusion from all three graphs is clear: there is no relationship between the
country-specific coefficient estimates and the three variables considered. This points to the
absence of cross-country heterogeneity of the output elasticity of infrastructure along any of
these dimensions.
Table 5 presents the results of more formal tests of parameter heterogeneity along these
dimensions, using the country-specific estimates of the output elasticity of infrastructure
obtained above. The first two columns of the table test if the output contribution of infrastructure
varies across countries with their respective level of income per worker. We divide the country-
specific estimates into two groups, one consisting of countries with high income and the other of
countries with low income. In column 1, the groups are drawn using the World Bank‘s list of
‗high income‘ countries; the low-income group is made up by all other countries in the sample.
In column 2, the grouping is based instead on the sample median income per worker in the year
2000. In each case, the table reports the simple average of the parameter estimates of each of the
two groups, along with the p-value of the test of difference in group means. In both columns, the
28
This is similar in spirit to Gregoriou and Ghosh (2009), who let the growth contribution of public expenditure
vary with countries‘ average level of expenditure.
19
mean estimate is slightly larger in the low-income group, but the difference is small and
statistically insignificant.
Column 3 of Table 5 reports a similar experiment distinguishing between countries with
high and low infrastructure endowments, again defined by the sample median. The mean
estimates of the infrastructure elasticity in the two groups are numerically and statistically very
similar. Thus, there is little evidence that the output elasticity of infrastructure varies
systematically with the degree of infrastructure development. Lastly, column 4 defines the two
country groups according to country size, as given by population, with the sample median as the
relevant dividing line. The output contribution of infrastructure might be expected to be larger in
countries with smaller population, owing to congestion effects. The pattern of the mean estimates
of the two groups seems to accord with this view: the mean estimate is much higher for small
countries than for large ones (where it is actually negative and close to zero). However, the
difference between the two falls well short of statistical significance.
In summary, our results indicate that the elasticity of GDP per worker with respect to the
synthetic infrastructure index is around 0.08. This finding is robust to alternative econometric
specifications and alternative definitions of the synthetic infrastructure index, as well as
alternative measures of the capital stock. In addition, we find little evidence of heterogeneity of
such elasticity across countries. Further experiments also suggest that the output contribution of
infrastructure does not vary with countries‘ population, their level of income, or their
infrastructure endowment. In light of our empirical specification, this suggests that cross-country
variation in the marginal productivity of infrastructure is solely driven by variation in the ratio of
infrastructure to output. In other words, the marginal product of infrastructure is higher wherever
the (relative) infrastructure stock is lower.
Finally, we turn to the test of weak exogeneity of the production inputs described in
section 3. The Wald test statistic computed from estimation of the system of equations (5)
equals 5.97. Under the null of weak exogeneity of the three inputs, it follows a chi-square
distribution with 3 degrees of freedom, and hence the test yields a p-value of 0.12, failing to
29
reject the null . Therefore we conclude that physical capital, human capital and infrastructure
are weakly exogenous for the parameters of the cointegrating vector. This supports our
29
This corresponds to a baseline specification including two lags of all the variables. However, similar results were
obtained with different lag specifications.
20
interpretation that we are in fact estimating the production function instead of, for instance, an
infrastructure demand equation, or a combination of both relations.
Our estimates of the output contribution of infrastructure are significant not only
statistically, but also economically. To illustrate this, consider an increase in the level of
infrastructure provision from the cross-country median in the year 2000 (an index of -4.65,
roughly similar to the value observed in Tunisia in 2000) to the 75th sample percentile in the
same year (an index of -3.69). This would translate in a 7.7 percent (=0.08*(-3.69+4.65))
increase in output per worker.30 Similar calculations show that: (a) an increase in infrastructure
provision from the median level observed among lower-middle income countries (-4.67, roughly
equivalent to Bolivia in the year 2000) to that of the median upper-middle income country (-
4.02, Uruguay) would yield an increase in output per worker of 5.2 percent, and (b) raising the
level of infrastructure provision from the value observed in the median upper-middle income
country to that of the median high-income country (-2.93, corresponding to Ireland) would raise
output per worker by 8.7 percent.
5. Conclusions
This paper adds to the empirical literature on the contribution of infrastructure to
aggregate output. Using an infrastructure-augmented production function approach, the paper
estimates the output elasticity of infrastructure on a large cross-country panel dataset comprising
over 3,500 annual observations. The paper addresses several limitations of earlier literature. It
uses a multi-dimensional concept of infrastructure, combining power, transport and
telecommunications infrastructure into a synthetic index constructed through a principal
component procedure. The econometric approach deals explicitly with the non-stationarity of
infrastructure and other productive inputs, reverse causality from output to infrastructure, and
potential cross-country heterogeneity in the contribution of infrastructure (or any other input) to
aggregate output.
The empirical strategy involves the estimation of a production function relating output
per worker to non-infrastructure physical capital, human capital, and infrastructure inputs. Our
estimates, based on heterogeneous panel time-series techniques, place the output elasticity of
infrastructure in a range between 0.07 and 0.10, depending on the precise specification
30
Note that 0.08 is the estimated coefficient of the infrastructure index in regression [1] of Table 3.
21
employed. The estimates are highly significant and robust to a variety of experiments involving
alternative econometric specifications and different synthetic measures of infrastructure. Some
illustrative calculations show that the output contribution of infrastructure implied by these
results is also economically significant. Moreover, our estimates of the output contribution of
human capital and non-infrastructure physical capital are likewise significant and broadly in line
with those reported by earlier literature.
Lastly, tests of parameter homogeneity reveal little evidence that the output elasticity of
infrastructure varies across countries. This is so regardless of whether heterogeneity is
unconditional, or conditional on the level of development, the level of infrastructure
endowments, or the size of the overall population. The implication is that, across countries,
observed differences in the ratio of aggregate infrastructure to output offer a useful guide to the
differences in the marginal productivity of infrastructure.
22
References
Alesina, A., and R. Perotti (1996) ―Income Distribution, Political Instability, and Investment.‖ European
Economic Review 40, 1202-1229
Arrow, K.J. and M. Kurz (1970) Public investment, the rate of return and optimal fiscal policy. Baltimore,
MD: The Johns Hopkins University Press
Aschauer, D., 1989. Is Public Expenditure Productive? Journal of Monetary Economics 23, 177-200
Baier, S.L., and G. Glomm (2001) ―Long-run growth and welfare effects of public policies with
distortionary taxation.‖ Journal of Economic Dynamics and Control 25, 2007-2042.
Barro, R.J. (1990) ―Government spending in a simple model of exogenous growth.‖ Journal of Political
Economy 98, 103-125.
Barro, R.J., and J.W. Lee (2001) ―International Data on Educational Attainment: Updates and
Implications.‖ Oxford Economic Papers 53(3), 541-63
Bernanke, B.S., and R.S. Gürkaynak (2002) ―Is Growth Exogenous? Taking Mankiw, Romer, and Weil
Seriously.‖ In: Bernanke, B.S. and K.S. Rogoff, eds., NBER Macroeconomics Annual 2001.
Cambridge, MA: National Bureau of Economic Research, pp. 11-72
Bloom, D.E., D. Canning, and J. Sevilla (2004) ―The Effect of Health on Economic Growth: A
Production Function Approach.‖ World Development 32(1), 1-13
Bom, P.R.D., and J.E. Ligthart (2008) ―How productive is public capital? A meta-analysis.‖ CESIfo
Working Paper 2206, January
Boswijk, H. (1995) ―Efficient Inference on Cointegration Parameters in Structural Error Correction
Models.‖ Journal of Econometrics 69, 133-158
Breitung, J. (2000) ―The Local Power of Some Unit Root Tests for Panel Data‖, in B. Baltagi (ed.)
Nonstationary Panels, Panel Cointegration, and Dynamic Panels, Advances in Econometrics,
Vol. 15, JAI: Amsterdam, pp. 161-178.
Breitung, J., and M.H. Pesaran (2008) "Unit Roots and Cointegration in Panels", in L. Matyas and P.
Sevestre (eds.), The Econometrics of Panel Data: Fundamentals and Recent Developments in
Theory and Practice, Third Edition, Springer Publishers, Ch. 9, pp. 279-322.
Calderón, C., and L. Servén (2003) ―The Output Cost of Latin America‘s Infrastructure Gap.‖ In:
Easterly, W., and L. Servén, eds., The Limits of Stabilization: Infrastructure, Public Deficits, and
Growth in Latin America. Stanford University Press and the World Bank, 2003, pp. 95-117
Calderón, C. and L. Servén (2004): ―Trends in infrastructure in Latin America‖, World Bank Policy
Research Working Paper 3401
Cameron, G., and J. Muellbauer (2001) ―Earnings, Unemployment, and Housing in Britain‖, Journal of
Applied Econometrics, 16, 203-220
Canning, D., 1999. "The Contribution of Infrastructure to Aggregate Output." The World Bank Policy
Research Working Paper 2246
Canning, D., and P. Pedroni (2008) ―Infrastructure, long-run economic growth and causality tests for
cointegrated panels.‖ The Manchester School 76(5), 504-527
Canning, D., and E. Bennathan (2000) ―The social rate of return on infrastructure investments.‖ The
World Bank Policy Research Working Paper Series 2390, July
Choi, I. (2001) ―Unit Root Tests for Panel Data‖, Journal of International Money and Finance, 20, 249-
272
Demetriades, P. and T. Mamuneas (2000) ―Intertemporal Output and Employment Effects of Public
Infrastructure Capital: Evidence from 12 OECD Economies.‖ The Economic Journal 110, 687–
712.
Duffy-Deno, K. T., and R. W. Eberts (1991) ―Public Infrastructure and Regional Economic Development:
A Simultaneous Equations Approach.‖ Journal of Urban Economics 30, 329-343
23
Easterly, W. (2001) ―The Lost Decades: Explaining Developing Countries‘ Stagnation in spite of policy
reform 1980-1998.‖ Journal of Economic Growth 6(2), 135-157.
Égert, B., K. Lommatzsch, and A. Lahréche-Révil (2006) ―Real Exchange Rate in Small Open OECD and
Transition Economies: Comparing Apples with Oranges?‖, Journal of Banking & Finance, 30,
3393-3406
Eisner, R. (1991) ―Infrastructure and Regional Economic Performance: Comment.‖ New England
Economic Review, September/October, 47-58
Engle, R.F., and C.W.J. Granger (1987) ―Co-integration and Error Correction: Representation,
Estimation, and Testing‖, Econometrica, 55, 251–276
Engle, R.F., D.F. Hendry, and J.F. Richard (1983) ―Exogeneity‖, Econometrica, 51, 277-304
Esfahani, H. and M. Ramirez (2003) ―Institutions, Infrastructure and Economic Growth.‖ Journal of
Development Economics 70(2), 443-477
Fernald, J.G. (1999) ―Roads to Prosperity? Assessing the Link between Public Capital and Productivity.‖
The American Economic Review 89, 619-38
Futagami, K., Y. Morita, and A. Shibata (1993) ―Dynamic analysis of an endogenous growth model with
public capital.‖ Scandinavian Journal of Economics 95, 607-625
Ghosh, S. and U. Roy. 2004. ―Fiscal policy, long-run growth, and welfare in a stock-flow model of public
goods.‖ Canadian Journal of Economics 37(3), 742-756
Glomm, G., and B. Ravikumar (1997) ―Productive government expenditures and long-run growth.‖
Journal of Economic Dynamics and Control 21(1), 183-204
Gollin, D. (2002) ―Getting Income Shares Right.‖ Journal of Political Economy 110(2), 458-474
Gramlich, E.M. (1994) "Infrastructure Investment: A Review Essay." Journal of Economic Literature
32(3), 1176-96,
Gregoriou, A. and S. Ghosh (2009) ―On the heterogeneous impact of public capital and current spending
on growth across nations.‖ Economics Letters 105(1), 32-35
Harris, D. (1997) ―Principal Components Analysis of Cointegrated Time Series‖, Econometric Theory,
13, 529-557
Hausman, J. (1978) ―Specification Tests in Econometrics‖, Econometrica, 46, 1251-1271
Heston, A., R. Summers, and B. Aten (2006) ―Penn World Table Version 6.3.‖ Philadelphia, PA:
University of Pennsylvania, Center for International Comparisons of Production, Income and
Prices, September
Ilzetzki, E., E. Mendoza and C. Végh (2010): ―How big (small) are fiscal multipliers?‖, NBER Working
Paper 16479.
Im, K.S., M.H. Pesaran, and Y. Shin (2003) ―Testing for Unit Roots in Heterogenous Panels‖, Journal of
Econometrics, 115, 53–74
Johansen, S. (1988) ―Statistical Analysis of Cointegration Vectors,‖ Journal of Economic Dynamics and
Control, 12, 231-254
Johansen, S. (1992) ―Cointegration in Partial Systems and the Efficiency of single-equation Analysis‖,
Journal of Econometrics, 52, 389-402
Johansen, S. (1995) ―Likelihood-based Inference in Cointegrated Vector Autoregressive Models‖,
Oxford: Oxford University Press
Kao, C. (1999) ―Spurious Regression and Residual-based Tests for Cointegration in Panel Data‖, Journal
of Econometrics, 90, 1-44
Karlsson, S., and M. Löthgren (2000) ―On the Power and Interpretation of Panel Unit Root Tests‖,
Economic Letters, 66, 249-255
Keefer, P. and S. Knack (2007): ―Boondoggles, Rent-Seeking, and Political Checks and Balances: Public
Investment under Unaccountable Governments‖, Review of Economics and Statistics 89, 566-
572.
Larsson, R., and J. Lyhagen (2000) ―Testing for common cointegrating rank in dynamic panels‖, Working
Paper Series in Economics and Finance, No. 378, Stockholm School of Economics
24
Larsson, R., J. Lyhagen, and M. Lothgren (2001) ―Likelihood-based Cointegration Tests in Heterogenous
Panels‖, Econometrics Journal, 4, 109–142
Le, M. V., and T. Suruga (2005) ―Foreign Direct Investment, Public Expenditure and Economic Growth:
The Empirical Evidence for the Period 1970-2001.‖ Applied Economics Letters 12, 45-49
Leeper, E.M., T.B. Walker and S. Yang (2010): ―Government Investment and Fiscal Stimulus in the
Short and Long Runs.‖ Journal of Monetary Economics (forthcoming)
Levin, A., C.F. Lin, and C.S. Chu (2002) ―Unit Root Tests in Panel Data: Asymptotic and Finite-Sample
Properties‖, Journal of Econometrics, 108, 1-24
Loayza, N.V., P. Fajnzylber, and C. Calderón (2005) ―Economic Growth in Latin America and the
Caribbean: Stylized Facts, Explanations and Forecasts." Washington, DC: The World Bank, Latin
America and the Caribbean Studies, 156 pp.
Mas, M., J. Maudos, F. Pérez, and E. Uriel (1996) ―Infrastructure and Productivity in the Spanish
Regions.‖ Regional Studies 30, 641-50
McCoskey, S., and C. Kao (1998) ―A Residual-Based Test of the Null of Cointegration in Panel Data‖,
Econometric Reviews, 17, 57–84
Miller, S.M., and M.P. Upadhyay (2002) ―Total factor productivity and the convergence hypothesis.‖
Journal of Macroeconomics 24, 267-286
Pedroni, P.L. (1999) ―Critical values for cointegration tests in heterogeneous panels with multiple
regressors.‖ Oxford Bulletin of Economics and Statistics 61(4), 653-690.
Pedroni, P.L. (2004) ―Panel Cointegration: Asymptotic and Finite Sample Properties of Pooled Time
Series Tests with an Application to the Purchasing Power Parity Hypothesis,‖ Econometric
Theory, 20, 597-625
Perotti, R. (2004) ―Public investment: another (different) view.‖ IGIER Working Paper 277, December
Pesaran, H., Y. Shin, and R. Smith (1999) ―Pooled Mean Group Estimation of Dynamic Heterogeneous
Panels‖, Journal of the American Statistical Association, 94, 621-634
Pesaran, H., and R. Smith (1995) ―Estimating long-run Relationships from Dynamic Heterogeneous
Panels‖, Journal of Econometrics, 68, 79-113
Pritchett, L. (2000) ―The Tyranny of Concepts: CUDIE (Cumulated, Depreciated, Investment Effort) Is
Not Capital.‖ Journal of Economic Growth 5 (4), 361–84
Reimers, H.E. (1992) ―Comparison of Tests for Multivariate Cointegration‖, Statistical Papers, 33, 335-
359
Röller, L-H. and L. Waverman (2001) ―Telecommunications Infrastructure and Economic Development:
A Simultaneous Approach.‖ American Economic Review 91, 909–23
Romp, W. and J. de Haan (2007), ―Public Capital and Economic Growth: A Critical Survey,‖
Perspektiven der Wirtschaftspolitik 8(s1), 6-52
Sanchez-Robles, B. (1998) ―Infrastructure Investment and Growth: Some Empirical Evidence.‖
Contemporary Economic Policy 16, 98-108
Temple, J. (1998) ―Robustness tests of the augmented Solow model.‖ Journal of Applied Economics
13(4), 361-375
Turnovsky, S.J. (1997) ―Fiscal policy in a growing economy with public capital.‖ Macroeconomic
Dynamics 1, 615-639
Zellner, A. (1962) ―An efficient method of estimating seemingly unrelated regressions and tests for
aggregation bias‖ Journal of the American Statistical Association 57: 348-368.
25
Table 1
Descriptive Statistics
Output and Inputs for the year 2000
Mean Std. Dev. Min. Max. Unit
GDP 21536 20048 1603 75288 2000 US Dollars
Physical Capital 48539 58035 600 248032 2000 US Dollars
Physical Capital (BC) 48644 58153 597 247570 2000 US Dollars
Secondary Education 1.5882 1.1113 0.0712 4.4438 Years
Electricity 0.0017 0.0022 0.0000 0.0118 Gigawatts
Main Phone Lines 0.4561 0.4713 0.0028 1.4051 Number of lines
Cell Phones 0.4479 0.5453 0.0004 1.6927 Number of lines
Roads 0.0141 0.0163 0.0011 0.0827 Kilometers
Paved Roads 0.0079 0.0116 0.0001 0.0540 Kilometers
Rails 0.0006 0.0008 0.0000 0.0049 Kilometers
All variables are expressed in per worker terms. The basic descriptive statistics were computed over a sample of 88
countries in the year 2000. BC refers to the back-casting method of construction of the capital stock series, where
the initial capital stock is computed by projecting the level of real investment into the past and assuming a negligible
level of capital stock in 1930.
26
Table 2
Panel Unit Root and Cointegration Tests
PANEL A: Panel Unit Root Test
Variable Test Statistic
GDP -6.20
Physical Capital -7.08
Secondary Education -1.77
Infrastructure -3.35
5% critical value for the null hypothesis of unit root is 1.96 in all cases.
The sample covers 88 countries and the years 1960-2000
Test employed: Im, Pesaran and Shin (2003)
PANEL B: Panel LR-bar Test
Maximum rank Test Statistic
0 9.03
1 0.85
The null hypothesis of maximum cointegration rank is sequentially tested against the alternative of
maximum rank equal to p (i.e. the number of variables considered). The 5% critical value is 1.96.
The sample covers 88 countries and the years 1960-2000
Test employed: Larsson, Lyhagen and Lothgren (2001)
PANEL C: Panel PC-bar Test
Minimum rank Test Statistic
1 1.21
Given the maximum cointegration rank tested in Panel B, the null hypothesis of minimum
cointegration rank is sequentially tested against the alternative of smaller minimum cointegration
rank. The 5% critical value is 1.96.
The sample covers 88 countries and the years 1960-2000
Test employed: Larsson and Lyhagen (2000)
In all tests variables are expressed in log per worker terms and common factors in the series are
removed.
27
Table 3
Estimation of the Production Function
Alternative Dynamic Specifications
Column (1) (2) (3) (4) (5) (6)
Max # of lags 2 2 2 1 4 2
Information criterion SBC AIC Imposed SBC SBC SBC
Common factors Yes Yes Yes Yes Yes No
Physical Capital 0.34 0.33 0.36 0.35 0.34 0.41
t-ratio 35.2 30.5 22.7 31.4 32.4 33.4
hausman p-value 0.54 0.95 0.43 0.78 0.44 0.52
Secondary Education 0.10 0.12 0.10 0.12 0.11 0.12
t-ratio 15.6 14.8 8.09 18.7 17.1 16.0
hausman p-value 0.24 0.19 0.21 0.19 0.20 0.64
Infrastructure 0.08 0.07 0.10 0.08 0.08 -0.02
t-ratio 7.45 6.73 6.58 8.33 8.77 -1.49
hausman p-value 0.21 0.18 0.16 0.40 0.88 0.40
joint hausman p-value 0.44 0.38 0.24 0.25 0.45 0.85
2 0.36 0.40 0.48 0.28 0.42 0.35
Average R
Observations 3432 3432 3432 3520 3256 3432
Dependent variable is log GDP. All variables are expresed in log per worker terms. Infrastructure is an aggregate index of
electricity generating capacity, main phone lines and roads. Country specific short run dynamics are either imposed or
determined by information criteria (Schwarz (SBC) or Akaike (AIC)). For each regressor, the p-value from the test of the null of
cross-country homogeneity is reported under the t-statistic of its respective coefficient estimate; the p-value from the joint test
is reported at the bottom of the table.
28
Table 4
Estimation of the Production Function
Alternative measures of infrastructure and the capital stock
Column (1) (2) (3) (4) (5) (6)
Average
Total Phone Roads plus BC Physical
Variable Changed Base Paved Roads Infrastructure
Lines Rails Capital
Index
Physical Capital 0.34 0.35 0.34 0.34 0.34 0.33
t-ratio 35.2 32.8 35.2 26.6 35.5 18.0
hausman p-value 0.54 0.80 0.48 0.58 0.92 0.05
Secondary Education 0.10 0.07 0.10 0.05 0.11 0.10
t-ratio 15.6 6.84 15.8 3.98 16.2 10.3
hausman p-value 0.24 0.55 0.24 0.11 0.26 0.20
Infrastructure 0.08 0.07 0.08 0.07 0.08 0.09
t-ratio 7.45 5.45 7.51 5.20 7.80 5.53
hausman p-value 0.21 0.37 0.23 0.41 0.36 0.14
joint hausman p-value 0.44 0.69 0.43 0.33 0.63 0.20
Average R2 0.36 0.37 0.36 0.35 0.37 0.35
Dependent variable is log GDP. All variables are expresed in log per worker terms. Infrastructure is an aggregate index of
electricity generating capacity, main (or main plus cells) phone lines and roads (or roads plus rails or paved roads). BC refers to
the Back Cast construction method of the physical capital stock. Sample size is 3432 in all columns. Country specific short run
dynamics are determined by the Schwarz information criterion with a maximum # of lags of 2. For each regressor, the p-value
from the test of the null of cross-country homogeneity is reported under the t-statistic of its respective coefficient estimate; the
p-value from the joint test is reported at the bottom of the table.
29
Table 5
Additional Homogeneity Tests
Column (1) (2) (3) (4)
Per Capita Per Capita Infrastructure Total
Income (A) Income (B) Endowment Population
High 0.054 0.044 0.059 -0.016
Low 0.059 0.062 0.055 0.131
p-value 0.985 0.940 0.988 0.576
This table reports the results of tests of difference in means with unequal variances
carried out by sub-groups in which heterogeneity of the effects of infrastructure might
be a concern. For this purpose, country specific PMG infrastructure coefficients are
estimated and group specific means are computed. The null hypothesis of equality of
group specific means is tested and p-values are reported. Countries are grouped into
'high' and 'low' categories, where high refers to countries with high levels of per capita
income (above the sample median per capita income (A) or according to the World
Bank's definition of high income (B)), infrastructure (above the sample median) or
population (above the sample median).
30
Figure 1
Output Elasticity of Infrastructure across countries
1.1 Output elasticity of infrastructure vs. the level of output
SLV
5
PAK TUN TTO
Long-run coefficient
NIC SGP
RWA TGO ROM JPN
CMR COL
PER
KEN JORBRA
NGA
BEN LSO INDCHN IDN THA EGY DZA URY KOR NZL
GRC
ESP
MDG
BFA SEN
NPL SYR
CIV ZWE
GIN GTM
MAR TUR
CHL
ZAF MYS PRT SWE USA
DOM MEX ARGMUS ISLCHEBLX
BOL PHL CPVPRY PAN
CAN
ISRFRA
DNK
AUS
0
GHA FIN NLD
GBR
ITAIRL
GMB
ETH MLI
MWI UGA LKA
MOZ ECU NOR
HND IRN
VENCRI
JAM GAB AUT
TZA
-5
NER
7 8 9 10 11
Logarithm of GDP per worker
1.2 Output elasticity of infrastructure vs. aggregate infrastructure
SLV
5
PAK TUN TTO
Long-run coefficient
NIC SGP
RWA TGO ROM JPN
CMR COL
PER
KEN JORBRA
NGA THA EGY KOR ESP NZL
LSO
BEN
MDG CIV
CHN
IDN IND DZA MEX URY PRT GRCFRA CAN
GTM CPVDOMARG
SYRMYS ZAF
CHL ISR CHE USA
DNKAUSISL
BFA NPL GIN SEN ZWE BOL MUS
PHL
MAR TUR SWE
GBR BLX
0
PANPRY NLD FIN
GHA ITA IRL
ETH MLI MWI
UGA GMB LKA
MOZ ECU NOR
HND IRN
VEN CRI
GAB JAM AUT
TZA
-5
NER
-8 -6 -4 -2
Infrastructure index per worker
1.3 Output elasticity of infrastructure vs. population
SLV
5
TTO TUN PAK
Long-run coefficient
NIC
SGP RWA
TGO ROM JPN
CMR PERCOL
JOR KEN BRA
NZL KOR
ESPTHA NGA
EGY
LSOURYDNK PRTMDG DZA FRA MEX IDN
BEN GRC MYS CHN
IND
ISL CPV MUS ISRSWECHLNPLARG TUR
CHE GTM
DOM CIV CAN
SEN SYR
ZWE
BFA ZAF PHL USA
PRYBOL AUS
PAN FINGIN NLD MAR GBR
BLX
0
GHA ITA
GMB IRL MLI LKA
UGA
MWI MOZ ETH
NOR
HND ECU IRN
CRI VEN
GAB JAM AUT
TZA
-5
NER
12 14 16 18 20 22
Logarithm of population
31
Appendix
Table A1: List of Countries
Panel A: Rich countries
Australia Iceland Portugal
Austria Ireland Singapore
Belgium-Luxemburg Israel Spain
Canada Italy Sweden
Denmark Japan Switzerland
Finland Netherlands United Kingdom
France New Zealand United States
Greece Norway
Panel B: Developing Countries
Argentina Egypt, Arab Rep. Ghana
Brazil El Salvador Guinea
Chile Guatemala India
Costa Rica Honduras Indonesia
Gabon Iran, Islamic Rep. Kenya
Korea, Rep. Jamaica Lesotho
Malaysia Jordan Madagascar
Mauritius Morocco Malawi
Mexico Paraguay Mali
Panama Peru Mozambique
South Africa Philippines Nepal
Trinidad and Tobago Romania Nicaragua
Turkey Sri Lanka Niger
Uruguay Syrian Arab Republic Nigeria
Venezuela Thailand Pakistan
Algeria Tunisia Rwanda
Bolivia Benin Senegal
Cape Verde Burkina Faso Tanzania
China Cameroon Togo
Colombia Cote d'Ivoire Uganda
Dominican Republic Ethiopia Zimbabwe
Ecuador Gambia
Rich countries are those defined as high income countries by The World Bank
32