EIB Papers Volume 13. n°1/2008 - European Investment Bank

Some recent empirical studies that use the VAR methodology to examine the relationship between
public capital and economic growth are summarized in Table 1 (see Kamps 2004 for a survey of older
studies).
As pointed out by Kamps (2004), only few studies analyse a group of OECD countries. Also, most
studies rely on annual data, as capital stock data are often not available at higher frequency.
The majority of studies use a model with four variables, namely public capital, private capital,
employment and output. In some studies investment has been substituted for capital or additional
variables have been included in the model. Apart from theoretical reasons (for instance, the
production function approach versus a growth model), the order of integration of the series can be a
reason to use either the (log of) the capital stock or the (log of) investment.
The results of unit root tests point in different directions. Whereas many studies suggest that all
variables usually included – i.e., the log of output, employment, private capital, and public capital –
are non-stationary I(1) series (i.e., series integrated of order one), some studies (for instance, Pereira
2000) report that the log of private and public investment are non-stationary I(1) series. In view of
the low power of the Dickey-Fuller test for relatively short time series, it is quite remarkable that
almost all papers do not use other tests for stationarity.
In various papers, notably in the work by Pereira, it is found that output, employment, and private
and public capital stocks (or investment) are not cointegrated. Pereira and his co-authors therefore
employ the growth rates of the variables included in the VAR. For the case of Portugal, Pereira and
Andraz (2005, p. 181-182) argue that “the absence of cointegration is not problematic conceptually
either. In fact, in the case of economies in a transition stage of their development, such as the
Portuguese economy, not finding cointegration is hardly surprising. This means that the data does
not show evidence of convergence to the so-called great ratios among the aggregate variables in
the economy.” However, the question is whether there is really no cointegration, or whether the
finding is just a reflection of the testing procedure followed. As follows from Table 1, the conclusion
of Pereira and his co-authors is always based on the Engle-Granger test for cointegration. Ligthart
(2002) employs both the Engle-Granger test and the Johansen tests and finds that the tests yield
different outcomes. Under the Engle-Granger test, the null hypothesis of no cointegration cannot be
rejected, while the Johansen tests strongly reject the hypothesis of no cointegration in favour of at
least one cointegrating relationship. In addition, Pina and St. Aubyn (2005) also report evidence of a
cointegrating relationship for the case of Portugal using the Johansen tests.
3. New evidence on the impact of public capital on output using VARs
The most extensive study on the impact of public capital on output in which VARs are used is the
study of Kamps (2004). This author has made a comparable data set for 22 OECD countries for the
public and private capital stock, using the perpetual inventory method (Kamps, 2006). 4 The data set
covers the period 1960-2001. Figure 1 presents the government-capital-stock-to-GDP ratio and the
private-capital-stock-to-GDP ratio for the beginning and the end of this period. It becomes clear
that there is quite some variation across the countries in the sample, both with respect to the level
of the government capital stock ratio and the change of this ratio. In 2001, Japan has the highest,
while Ireland has the lowest government capital ratio. In 13 countries the government capital ratio
declined, while in nine it increased between 1960 and 2001. The private capital stock ratio also
differs considerably among the OECD countries, both with respect to the level and its change over time.
4 Available at: http://www.uni-kiel.de/ifw/forschung/netcap/netcap.htm.
Some other studies
have found no long-run
relationship between
output, employment,
and private and public
capital.
EIB PAPERS Volume13 N°1 2008 61