Since the influential work by Aschauer (1989a, 1989b) there has
been renewed interest by economists in the effect that public capital,
in particular public 'infrastructure' capital, has on private
sector production and productivity. Infrastructure capital is commonly
defined to include an economy's stock of highways and streets,
water and sewer systems, urban transport systems, education, fire,
police and judicial facilities, hospitals, electricity generation and
distribution facilities, ports, airports etc. While not all of the
components of infrastructure capital need be publicly owned or operated
(witness the recent moves towards privatization in many developed
countries) historically the public sector has in fact been involved in
the provision of various types of infrastructure capital..}
Economists' interest in the contribution that public capital
can make to private sector production was in part reawakened due to two
empirical papers by David Aschauer. Aschauer (1989a) presents evidence
that links the slowdown in the growth rate of productivity that occurred
in the United States (and elsewhere) during the 1970s and 1980s to the
slower growth of the stock of public capital that occurred around the
same period. In a companion paper Aschauer (1989b) claimed to find
evidence for the United States that, on balance, increases in public
investment lead to additional rather than less private investment
expenditure, i.e. public and private investment tend to be complements
rather than substitutes.
Not surprisingly both of these findings have become the subject of
considerable controversy and debate. Some economists and policy-makers
have interpreted Aschauer's work as providing a strong case for
increasing government expenditure on public infrastructure projects, see
Munnell (1990a). It is however important to stress that the increased
public investment is viewed to be beneficial primarily because of its
positive supply-side effects on private sector productivity. (1) However
Aschauer's work has not been without its critics, see for example
Aaron (1990), Jorgenson (1991), Tatom (1993) and Gramlich (1994). These
critics have questioned a number of aspects of Aschauer's work,
including the econometric analysis and the interpretation of the
In addition to engendering a debate over public policy,
Aschauer's results have spawned a large (and growing) number of
empirical studies on the question of public capital and private
production. Many of these studies have sought to extend Aschauer's
work in a variety of directions, e.g. to countries other than the United
States, by use of cross-section as well as time series data and via the
use of different models and econometric techniques. In light of the
increasing number of quantitative studies concerned with the public
capital/private production question, we have set out in this paper to
review some of the more recent work on the subject.
Our primary aim is to survey the recent empirical studies, with a
view to considering the extent to which such work can contribute to
policy debates about the appropriate level of public capital. We begin
in Section 2 by reviewing some of the post-Aschauer empirical studies.
Many of these studies can be viewed as seeking to confirm or refute
Aschauer's original finding of an important role for public capital
as an input into private production. In addition some of the recent
studies have attempted to address specific criticisms that have been
leveled at Aschauer's work.
In Section 3 we look at the implications that can be drawn from
these various studies. In particular we examine the extent to which this
empirical research can contribute to the policy debates about the
appropriate (or optimal) level of public capital or investment. For a
variety of reasons we believe the answer to be 'not very
much'. To this end Section 4 contains a discussion of some recent
work which we consider useful for addressing the optimality question in
a quantitative sense. Section 5 concludes.
2. Recent Empirical Studies
There are a large number of studies that seek to quantitatively
measure the contribution of public capital to private production. In
this section we survey some of the more recent papers on this issue. (2)
In order to simplify matters we classify the studies into two basic
types; those studies based on pure time series observations and those
which have a cross-section dimension, eg. panel data studies. Another
reason for employing this distinction is that there is some suggestion
that different conclusions about the importance of public capital in
private production are obtained from use of cross-section as opposed to
time series data. We consider this issue below.
2.1 Time Series Studies
In his (1989a) study Aschauer used annual data (1949-85) for the
United States to estimate a production function for private sector
output which includes, among other things, government capital as a
separate input. Using a Cobb-Douglas specification for private sector
production he finds evidence that government capital has a significant
effect (on both statistical and economic criteria) on private sector
productivity. (3) Essentially his estimates suggest that the elasticity
of private output with respect to public capital is about 0.40. (4) This
is an unexpectedly large coefficient, particularly in light of
Ratner's (1983) earlier estimate of 0.06. Not surprisingly
Aschauer's estimates imply very high returns to additional
investment in public capital.
Using a similar methodology to Aschauer, but a slightly longer
sample period (1949-87), Munnell (1990a) obtains estimates for the
elasticity of private output with respect to public capital in the range
0.31 to 0.39, i.e. very similar to Aschauer. Three differences in
Munnell's approach to that used by Aschauer are worth noting. She
uses private sector labour productivity as the dependent variable in her
model, in contrast to Aschauer who uses private sector capital
productivity. Munnell also needs to correct for significant first-order
serial correlation in her models, whereas Aschauer did not find this
necessary. Finally in contrast to Aschauer, Munnell does not include a
linear deterministic time trend in her model.
Attempts to replicate Aschauer's study, using data for
countries other than the United States have met with mixed results. Otto
and Voss (1994a) estimate Aschauer's model for Australia using
annual data over the period 1967/68 to 1989/90. Their findings tend to
confirm Aschauer's findings for the United States, with their best
estimate of the elasticity of private output with respect to public
capital being in the order of 0.45.
Berndt and Hansson (1991) used annual data for Sweden (1960-88) but
were unable to get economically sensible results with Aschauer's
specification, for example in one set of estimates they obtain a
negative elasticity on private capital (-1.666), a labour elasticity of
(1.072) and public capital elasticity of (1.601). (5)
Ford and Poret (1991) estimate a version of Aschauer's model
for eleven OECD countries, including the United States, Australia and
Sweden. In contrast to Aschauer they estimate a model in log
first-differences and not in log levels. (6) Their point estimates of
the effect of the growth of public capital on the growth of private
factor productivity vary markedly across countries, although it is worth
noting that a positive coefficient is found for most countries (Norway
being a notable exception). The positive estimates range from 0.13 to
1.39. However many of the estimated coefficients (while large) are not
statistically significant. On the basis of their results Ford and Poret
conclude that Aschauer's findings for the United States do not
appear to be particularly robust to the use of data for other countries.
As noted above, Aschauer's results and the conclusions he
draws from them have been subject to a variety of criticisms. We now
identify a number of these criticisms and examine the various ways it
which they have been addressed.
One criticism of Aschauer's approach is that the Cobb-Douglas
technology used to model private sector production is too restrictive.
(7) Modern production economics uses much more general or flexible
functional forms for technology and relies on results from duality
theory to derive estimable equations, see Varian (1992). While there
have been few attempts to directly estimate more general forms for
private sector technology, although see Munnell (1990b), a number of
studies have made use of results from duality theory in seeking to model
the role of public capital in private production.
In addition to the restrictiveness of the Cobb-Douglas
specification, Berndt and Hansson (1991) also point out that direct
estimation of production functions by least squares potentially suffers
from simultaneous equation bias, i.e. private inputs (especially labour
and measures of capacity utilization) are likely to be jointly
determined with the dependent variable, private output. (8) Under such
conditions the ordinary least squares estimator is inconsistent.
Therefore after failing to obtain economically sensible results for
Sweden using Aschauer's model, Berndt and Hansson examine the
importance of public capital in private production by using a cost
function approach. Berndt and Hansson also argue that the cost function
approach has the advantage of reflecting optimizing behavior by firms
and in addition permits an assessment of the benefits of public capital,
essentially by providing an estimate of the effect of public capital on
the costs of production in the private sector.
Using annual data for Sweden, Berndt and Hansson specify a
short-run private sector variable cost function, which is dual to a
production function and depends on; private output, the input prices for
variable inputs, public capital, private capital and technology. Their
basic aim is to try and measure the shadow value of public capital; i.e.
what is the effect, ceteris paribus, on the firm's costs of an
exogenous increase in the stock of public capital? This reflects the
marginal benefit to the private sector of an increase in public capital
and is simply measured as the partial derivative of the cost function
with respect to public capital.
Rather than directly reporting the estimated shadow value of
capital, Berndt and Hansson compute the optimal level of public capital
implied by their estimates. This is the level of public capital that
equates the social marginal benefits of public capital to the social
price. (9) By examining the ratio of optimal to actual public capital
for the private business sector Berndt and Hansson find evidence that
for 1988 the actual level of public capital in Sweden was too large by
about 9 per cent, i.e. the stock of public capital was too large given
its measured marginal benefit in reducing private business costs and its
Takahashi and Maki (1992) follow Berndt and Hansson's approach
by employing a cost function approach to investigate the nature of
returns to scale in the Japanese private business and manufacturing
sectors when public capital is an input to production. They motivate the
use of a cost function approach by claiming that it reduces the impact
of simultaneous equations bias which can arise with direct estimation of
the production function. Unlike Berndt and Hansson, Takahashi and Maki
actually begin with a Cobb-Douglas model for technology and explicitly
derive the cost function implied by cost minimization. The cost function
is then estimated directly using annual data for the period 1955 to
1982. Their estimates suggest that in Japan a 1 per cent increase in
public capital lowers the private total cost in manufacturing by about
-0.12 and in private business by about -0.08. Finally as an interesting
twist they estimate their model using data for the Swedish manufacturing
sector for the period 1970-89 and obtain plausible results. For example
a 1 per cent increase in public capital lowers costs in the
manufacturing sector by about -0.12. They claim this result is in line
with those of Berndt and Hansson.
Lynde and Richmond (1992) use annual data (1958-89) for the United
States to examine the effects of public capital on private sector
production. The inputs to private production are labour, private capital
and public capital, the latter being external to the firm and is assumed
to be supplied free of charge by the government. Lynde and Richmond
begin with a private sector cost function which they specify to have a
translog form. From this cost function they derive four equations which
determine the shares in total cost of private labour, private capital,
public capital and total output. Due to adding up conditions they can
only estimate two of the four share equations and they choose the
equations for private labour and public capital. Their results suggest
that public capital is an important input to private production and that
while the marginal product of public capital is diminishing, it is
estimated to be positive over the entire sample period. Lynde and
Richmond interpret this finding as evidence that public capital has not
been provided in such quantities as to drive its marginal product to
zero (which is conceivably possible).
An interesting aspect of Lynde and Richmond's study is that
they can compute the elasticities of demand for private inputs (i.e.
labour and capital) with respect to public capital. They estimate the
average elasticity of demand of private labour with respect to public
capital to be -0.45 and for private capital with respect to public
capital to be 0.71. This suggests that private and public capital are
complements in production, while private labour and public capital are
Each of these cost function based studies suggests that public
capital has ceteris paribus the ability to reduce private costs of
production. As a consequence it seems reasonable to interpret these
studies as tending to confirm Aschauer's finding that public
capital is an important input into private production.
While the advantages of greater flexibility is evident in the above
studies it comes with some costs. One of these costs is in terms of
degrees of freedom, eg. Berndt and Hansson have 28 observations and
estimate 11 parameters. However another important issue relates to the
question of the potential non-stationarity in the time series data used
in these studies. (10) Many authors do not treat this issue explicitly
and thereby implicitly assume that any non-stationarity in their data is
due to deterministic trends. However recent work has highlighted the
need to consider the possibility that the variables used in these
studies may well contain a stochastic trend (i.e. a unit root). If this
is the case, then an interesting question arises as to whether there
exists a valid long-run relationship among private sector production
variables and public capital. In fact it is worth noting that one early
criticism of Aschauer's study was that the relationship he found
simply reflected a 'spurious correlation' or spurious
regression, see Aaron (1990).
In response to the spurious regression claim there have been a
number of studies which use cointegration analysis to test for and
estimate the long-run relationships among private production variables
and public capital. A detailed discussion of these studies must be
rather technical and therefore is given in the appendix.
On balance the studies reviewed in the appendix tend to indicate
that the correlation between public capital and private
output/productivity in time series data is non-spurious. However it is
important to realize that the finding that public capital and private
sector variables appear to be cointegrated simply implies that the
series move together over the long-run. The direction of causality
cannot be inferred from the existence of a cointegrating relationship
alone. We discuss the issue of causality in the following sub-section.
Virtually all of the time series studies on public capital involve
regressions of private output or productivity on contemporaneously dated
variables. Apart from the problem of simultaneous equations bias, there
is the more difficult question of causality; i.e. does the direction of
causality run from public capital to private production or from private
production to public capital?
One, apparently valid, interpretation of the significant
correlation between public capital and private output/productivity, is
that the level of public investment and consequently public capital is
largely demand determined. Thus when the private economy is growing
strongly, demand for public capital also grows and additional
infrastructure projects can be afforded by governments due to growth in
tax receipts. The reverse is true when the economy or productivity grows
more slowly. This demand side hypothesis is sometimes called
Wagner's Law and involves the notion that public expenditures are a
superior good. A more formal analysis is provided by Clarida (1993) who
suggests that endogeneity of public capital and bi-directional causality
between public capital and private productivity would seem to be assured
in any optimal growth model which features an optimal public investment
A number of authors have examined the causality issue by the use of
Granger-causality tests. In his cross-country study Clarida tested
whether productivity was exogenous with respect to public capital. He
found strong evidence against this hypothesis in the data for the four
countries he considered. However he also found evidence that public
capital is not exogenous with respect to productivity. Ho and Sorensen
(1993) also look at the nature of causality between public capital and
productivity in their study of U.S. manufacturing. At the aggregate
level they find strong evidence of reverse causality, i.e. there is
evidence of an income effect from productivity that caused investments
in public capital. There is also evidence of causality in the reverse
direction. They interpret these findings as picking up causality from
aggregate productivity to public capital.
Otto and Voss (1994b) examine the question of causality within the
context of a VAR model for private output, private labour, private
capital and public capital. They use quarterly data for the Australian
economy, 1959:3 to 1992:2. What their results suggest is that there
seems to be virtually no feedback from shocks to private output to
public capital. This is true even when public capital is ordered last in
the VAR model. This provides some evidence against the hypothesis that
the estimated relationship between private output and public capital is
primarily due to the response of public capital to changes in private
output. According to their results the private variable most affected by
public capital is private capital.
The empirical evidence about causality between public capital and
private output is mixed and somewhat sketchy. However on the basis of
existing evidence one would have to conclude that there may well be
feedback from changes in private productivity/output to the level of
public investment and public capital.
2.3 Panel Data Studies
A number of studies use cross-section or panel (i.e. pooled
cross-section and time-series) data to examine the relationship between
public capital and output or productivity in the private sector. Many of
these studies have used data on the states or regions of the United
States. Results have been mixed.
Munnell (1990b) constructed relevant data for each of the 48
continental United States for the years 1969 to 1986. Using this panel
data to estimate Aschauer's model she found that public capital had
a positive and statistically significant relationship with private
output. The estimated elasticity for public capital was 0.15, about half
the size of that found by Aschauer (1989) and Munnell (1990) using only
aggregate time series data. An implication of her estimates is that they
do not imply the very high rates of return to public capital that are
suggested by the time series findings. In fact the implied marginal
productivities for private and public capital are approximately the
same. Reasonably similar results can be obtained if the states are
divided up into four geographical regions, i.e. the estimated
elasticities range from 0.07 to 0.36. (11)
Recently Holtz-Eakin (1992) has re-examined the state data but
unlike Munnell he controls for the effects of unobserved, state-specific
effects (eg. land area, location, weather, endowments of raw materials
etc.) on the model. The consequence of doing so leaves no role for
public capital in explaining differences in the economic performance of
Using ordinary least squares and ignoring state effects,
Holtz-Eakin obtains a estimate of the elasticity of private output with
respect to public capital of 0.203, which is significant and similar to
that obtained by Munnell. Using a number of techniques to account for
state specific effects leads Holtz-Eakin to conclude that the positive
elasticity for public capital seems to be an artifact of the
restrictions placed on the error structure. He argues that the most
plausible estimate of the elasticity is zero. Similar results also
appear to hold for regional data. In addition the similarity of
estimated coefficients for state and regional data suggests that
aggregation of the data does not capture additional spillover effects.
Holtz-Eakin's findings tend to support the work of Hulten and
Schwab (1987) who use growth-accounting techniques to apportion regional
economic growth and find the pattern of the resulting Solow residuals is
at odds with regional patterns of public sector investment.
Another interesting use of panel data is due to Canning and Fay
(1993). They use cross-country data to estimate the social rates of
returns of transport infrastructure networks for 96 countries. They use
physical measures of these networks, i.e. kilometers of paved roads and
kilometers of railways. Their data is for the period 1960-85 and is
taken at 5-year intervals. They estimate two models; the first is a
Cobb-Douglas production function for aggregate output, where the inputs
are physical capital, labour force, human capital per worker, and paved
roads and railways per worker. (12) In this model transportation
infrastructure has a positive and significant elasticity of about 0.10.
However as with Holtz-Eakin (1992) when fixed effects are allowed (i.e.
to reflect possible cross-country differences in productivity) the
coefficient on transportation becomes small and insignificant. When the
model is estimated by 2SLS to allow for potential endogeneity of
regressors, the estimated transport elasticity is 0.07 with a standard
error of 0.03 and 0.102 with a standard error of 0.078 (with fixed
Canning and Fay also estimate reduced form models for the growth
rate of output. The derived model can include both level variables
(measured in the initial year of each five-year period) and the growth
rates of variables. For example if infrastructure enters as a direct
input to production it enters in growth rates, while if
infrastructure's main role is in promoting growth in total factor
productivity it should enter in levels. Since the estimated coefficients
of the growth rate form are small and insignificant, it is that second
channel that appears to be important. Canning and Fay interpret their
regression results as implying that infrastructure has little immediate
effect on output, but tends to affect the rate of growth, apparently by
allowing for increased productivity growth.
As a final exercise Canning and Fay use their estimates of the
elasticity of output with respect to infrastructure to compute the
marginal product of an additional kilometer of transportation
infrastructure. Dividing these numbers by the cost of construction of a
kilometer of road gives the social rate of return to road construction
in each country. Estimated rates of return are highest in NIC's
like South Korea and Chile, (eg. over 200 percent) and lowest in the
established members of the developed world, (eg. for United States and
Canada etc.) For Australia the estimated rate of return is only 0.06
The papers reviewed in this section suggest that confirmation of
Aschauer's results using cross-section or panel data is not
necessarily straight-forward. Even when a positive relationship can be
found between public capital and private production, the magnitude of
the coefficient estimate tends to be smaller then what is obtained from
the time series data.
3. What have we learned?
A wide variety of data sets and econometric models have been used
to try and ascertain the nature of the relationship between public
capital and private sector production. If we are prepared to accept that
causality runs predominantly from public capital to private production,
then there does seem to be a substantial body of empirical evidence
which suggests that public capital makes a positive and significant
contribution to private production. On the whole this conclusion appears
to be robust to a relatively wide variety of countries and modeling
However there does remain considerable uncertainty as to the
precise magnitude of the effect that a marginal change in public capital
has on private production. We interpret the existing empirical evidence
as suggesting that the very high estimates of the elasticity of private
output with respect to public capital (i.e. in the order of 0.35 to 0.45
found by Aschauer (1989a), Munnell (1990a) and Otto and Voss (1994))
have not proved robust to more sophisticated analysis of the time series
data. These alterative techniques typically yield elasticity estimates
about half the size of Aschauer's results, say between 0.10 and
0.20. The smaller elasticity implies smaller, although generally still
significant, returns to additional investment in public capital. (13)
We now consider what implications quantitative studies of the type
discussed in Section 2 might have for government policy. As noted
earlier the results from these studies have sometimes been used to
justify a policy of increased government expenditure on public
infrastructure projects. The relatively large estimates of private
output with respect to public capital and the resulting high marginal
returns to public capital often form the basis of an argument for
increased public investment spending.
One interpretation of the relatively high rates of return to public
capital that are implied by some of the aggregate studies is that it
reflects under-investment in public capital. In particular the rates of
return from aggregate studies have tended to be at least an order of
magnitude larger than benefit estimates obtained for individual public
projects from cost-benefit studies. This raises the question as to why
such high returns are not typically evident in cost-benefit studies of
individual infrastructure projects. (14)
One answer is that the results from aggregate studies are biased
upwards. However Aschauer (1993) argues that the problem may actually
lie with the cost-benefit studies, which he claims may have difficulty
in measuring the indirect benefits of public infrastructure projects.
The standard explanation for the difference has been that the aggregate
studies are directly capturing spillover or external effects from public
capital that are not measured by traditional cost-benefit analysis. (14)
Munnell (1992) uses this spillover argument to explain why
estimates of the elasticity Of public capital tend to increase with the
level of aggregation of the data, eg. the smallest numbers arise for
studies that use city or local data while the largest estimates are
obtained from national data. One limitation of this argument is that it
is not spelled-out exactly what are these spillovers that are not
accounted for by cost-benefit studies. Nevertheless an implication of
this argument would seem to be that public infrastructure projects which
may not be strictly justified on the basis of conventional cost-benefit
analysis should be considered.
In a recent paper Hulten (1993) compares the likely performance of
the aggregate production/cost function approach and cost-benefit
analysis in measuring the benefits of public capital under different
circumstances. According to Hulten aggregation problems are endemic to
the aggregate approach, i.e. across firms, industries and commodities.
Unfortunately it would seem virtually impossible to work out in general
what the impact of such aggregation problems might be on production/cost
Hulten also argues that spillover externalities of the type used by
Romer (1986) to provide an engine for endogenous growth are unlikely to
apply to to public capital. In Romer's model the total stock of
private capital (which includes knowledge capital) enters into the
production functions of individual firms. Thus there is a social return
to private capital as well as a private return. When firms ignore these
spillover benefits sub-optimal equilibrium are obtained. The question
arises as to whether the same type of analysis can be applied to public
capital. It is not obvious that this is so. To the extent that public
capital is a public good, it already enters into all individual firms
production functions as an aggregate stock. Aggregation does not tend to
increase its importance. In addition there is no reason to think that
cost-benefit analysis will miss the public good aspect of infrastructure
Hulten suggests that a more pertinent case might be if the economy
is characterized by increasing returns to scale. If increasing returns
results in multiple equilibria and the economy is stuck at a low level
equilibrium, then infrastructure investment might be sufficient to move
the economy to a higher equilibrium. For example Murphy, Shleiffer and
Vishny (1989) construct a model in which increasing returns interact
with expectations to produce low-income and high-income equilibria. When
the market is too small, no firm that acts in isolation from other
producers has an incentive to invest because the market cannot absorb
the additional output at the required rate of return. However if all
firms act together, increasing returns to scale come into play and the
size of the market is expanded sufficiently to justify the investment,
i.e. the 'big-push' triggers self-fulfilling expectations and
subsequent economic growth.
While it is possible to imagine circumstances where public
infrastructure induces economic growth in the private sector, it is also
clear that existing empirical studies do not shed much light on the
likelihood of such outcomes. In our view what the existing empirical
studies do (or at least what they should do) is to make policy-makers
aware of the (historical) contribution made by public capital to private
production and to suggest that sudden large reductions to public
investment may have important consequences for economic growth in the
future. Under-investment in public capital is presumably as wasteful as
over-investment. Thus reducing public investment purely as a means of
cutting back the size of the government sector is unlikely to be an
optimal policy in any longer-term framework, see Alesina, Gruen and
This is not to imply that the level of public investment should
never fall, or that the cuts to public investment in Australia during
the late 1980s were unwarranted. It may be that the existing stock of
public capital is excessive, although this tends not to show up in
(most) empirical evidence. One interpretation of the recent decline in
the public investment to GDP ratio and the fall in the public capital to
private output ratio observed in the second half of the 1980s is that we
are simply using the existing stock of infrastructure more efficiently.
This more efficient use might arise through the use of appropriate
pricing policies for public services (where pricing is feasible), or
from the fact that there is less political interference in decision
making over infrastructure projects. So less essentially useless
'white elephants' are being built. However as we have already
noted it is difficult to evaluate the validity of such arguments from
the results of aggregate studies.
4. Testing for the Efficiency of Public Capital
A feature of the vast majority of empirical studies on the effect
of public capital on private production is that they are basically
concerned with establishing whether or not a relationship actually
exists. There have been very few attempts to test whether actually
existing levels of public capital are at or close to their efficient
levels, although Berndt and Hansson (1991) is one exception.
As Finn (1993) points out it is difficult to say much about about
the optimal level of public capital or investment from existing studies.
While increased government capital can have output raising effects, this
must be balanced against the fact that taxes raised to finance
government investment can have distorting effects on the private
economy, (eg. taxes on labour will have dis-incentive effects on work
effort) and consequently lower private production. Thus it is not clear
that optimality necessitates the equality of marginal returns to private
and public capital as is sometimes suggested. Additional complications
arise if uncertainty is allowed in the analysis. In this case real
returns to investing in different assets are generally not equated,
reflecting the differential roles that various assets play in hedging
A recent paper which attempts to explicitly address the efficiency
issue is Otto and Voss (1994c). In this study the authors use a simple
dynamic optimizing model to characterize the efficient allocation of
resources in an economy with private and public capital, under
uncertainty. By solving a planner's problem they obtain two
intertemporal conditions which are necessary for the efficient provision
of private and public capital. These conditions are then estimated and
tested using quarterly data for the Australian economy over the period
1959:3 to 1992:2. (15)
The results obtained by Otto and Voss are somewhat variable and
depend in part on the choice of instruments used in the estimation.
However, perhaps surprisingly, for some sets of instruments they are not
able to reject the hypothesis that public capital has been efficiently
provided in Australia over the sample period under consideration. More
importantly even when the the sample is split at 1979:4, there appears
to be no evidence of inefficient provision during the second half of the
sample relative to the earlier period. While these results are
preliminary, they do suggest that the recent decline in public
investment in Australia is not inconsistent with efficient levels of
In this paper we have reviewed a number of recent studies which are
concerned with quantifying the relationship between public capital and
private production. While most of the studies which use aggregate data
find evidence of a large, positive correlation between public capital
and private output/productivity, the implications for public policy of
this finding are less obvious. Questions concerning the direction of
causality and the optimality of existing levels of public capital stocks
have not been fully examined. In addition models which specify the
precise linkages between public capital and private production at the
micro level are required to help interpret the results obtained from the
This appendix contains a survey of some recent evidence on the
relationship between public capital and private production which makes
use of cointegration analysis.
Otto and Voss (1994b) constructed a quarterly data set for
Australia (1959:3 to 1992:2) and used cointegration techniques to
re-examine Aschauer's model. They used both Phillips and
Hansen's (1990) and Hansen's (1992) 'fully modified'
single equation estimator and the system estimator due to Johansen
(1992). Results from both techniques are qualitatively similar, in that
the private sector variables appear to be cointegrated with various
measures of the stock of public capital and also in that the estimates
of the elasticity of private output with respect to public capital are
about 0.16 to 0.20. These figures are about half the size of those
obtained in Otto and Voss (1994a) and Aschauer (1989), although they are
still of economically significant magnitudes. (16) A number of authors
have tested for the presence of long-run relationships between Solow
residuals (or total factor productivity) and public capital. Clarida
(1993) uses annual data for four OECD economies, United States
(1949-89), France (1964-89), Germany (1964-89) and the United Kingdom
(1964-88) to test whether the Solow residuals for these countries are
cointegrated with their non-military public capital stocks. Using the
Johansen procedure he finds evidence of a single cointegrating
relationship between these two variables for all four countries. The
point estimates of the long-run elasticity of productivity with respect
to public capital range from 0.37 to 0.48 and each is significantly
different to zero at the one percent level.
Ho and Sorensen (1993b) use cointegration analysis to test for the
existence of a long-run relationship between public capital and
productivity growth in United States manufacturing industries. They use
annual data (1948-85) for manufacturing at the 2-digit SIC level. This
gives them 21 industries in total. Solow residuals are constructed for
each of these industries. They consider tri-variate groups of the Solow
residuals (based on industry size) and after including public capital,
test for the number of cointegrating vectors. (17) In general when
public capital is included all groupings suggest at least one
cointegrating vector, although the elasticities implied by this
procedure are often unreasonably large. Ho and Sorensen respond by
considering bivariate models, which include productivity for each
industry and public capital. They find evidence of cointegration for all
industries, with the estimated elasticities varying from 0.07 for
printing to 0.71 for machinery. For aggregate manufacturing the
estimated elasticity is 0.26, again considerably smaller than the number
initially found by both Aschauer and Clarida for the aggregate United
A recent paper which allows for stochastic non-stationarity of
variables within an optimization framework is by Lynde and Richmond
(1993). These authors employ a profit function approach to the problem.
By using a translog profit function they are able to derive a linear
share model suitable for cointegration techniques. They use annual data
(1958-89) for the United States non-financial corporate sector. Public
capital is a primary factor of production and is assumed to be supplied
in fixed quantity and at zero marginal cost. Lynde and Richmond estimate
the average elasticity of output with respect to public capital to be
0.20 for their sample period. In addition they show that on the basis of
their estimates about 41 percent of the decline in United States labour
productivity growth can be attributed to the decline in the public
capital to labour ratio.
A somewhat different approach to the productivity of public capital
is taken by Finn (1993). Finn uses annual data for the United States for
the period 1950-89 to examine whether a particular component of public
capital, viz highway capital, seems to play a measurable role in private
production. She argues a priori that only three components of United
States public capital, government-owned, privately operated capital,
government enterprise capital and highway capital will have a direct
effect on private production, (19) and that the first two of these are
likely to be close substitutes with private capital. Accordingly Finn
adds the first two components to private capital and only considers the
direct effects of highway capital.
A second novelty of the paper is that Finn employs a dynamic
equilibrium model for the private sector. The model is not completely
general as the decision process for public capital is not modeled, i.e.
agents make their optimizing decisions based on the exogenously given
level of public capital. Finn's model can be seen as dynamic
generalization of the cost or profit function approach.
Finn derives the intertemporal and intratemporal efficiency
conditions that characterize the competitive equilibrium of the model
and estimates these along with the production function and a balanced
growth equation. Estimation of the parameters of the model is done via
generalized method of moments (GMM). Finn obtains a point estimate for
highway capital's productivity coefficient of 0.16, with a standard
error 0.08. The other coefficient estimates are sensible and the
model's over identifying restrictions are not rejected.
Finn draws three implications from her study. First she emphasizes
the relative imprecision of the productivity coefficient estimate.
Second, she uses the estimates in a growth accounting exercise and finds
that for the period 1970-89 the slowdown in highway capital growth
reduced output growth by about 0.1 per cent. Finally her results imply
that the real return to investment in highway capital averages about 87
percent per annum compared to about 25 percent for private capital.
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(1.) This contrasts with the more traditional Keynesian aggregate
demand effects which are sometimes viewed to arise from increased
government expenditure, whether current or capital in nature.
(2.) For a more complete survey of the evidence, especially for the
United States, see Munnell (1993).
(3.) Aschauer uses both private output per unit of private capital
and private multifactor productivity as alterative dependent variables
in his regressions.
(4.) This implies that ceteris paribus, a 1 percent increase in the
public capital stock leads to a 0.4 percent increase in private output.
(5.) When they exclude the time trend from their model
(Munnell's specification) their estimated coefficients become more
reasonable, however the Durbin-Watson statistic for this regression is
(6.) The first-differences specification is justified on the basis
of (unreported) pretests for cointegration. Ford and Poret claim to be
unable to reject the null hypothesis of no-cointegration for all their
(7.) For example the Cobb-Douglas specification restricts all
inputs to be complements in production.
(8.) Aschauer (1989a) tests for exogeneity of public capital in his
regressions but not for any of the other variables in the model.
(9.) In practice Berndt and Hansson only measure the benefits that
accrue to the private business sector.
(10.) In non-technical terms a time series variable is said to be
non-stationary if either the population mean or variance varies with
(11.) In a comment on Munnell's paper Eisner (1991) shows that
her results are primarily due to the cross-section variation in her data
(12.) Also included in the estimated regression model are, the
contribution of oil to GDP, the per cent of the work force in industry,
government consumption as a per cent of GDP, a homogeneity index and a
dummy variable for each five year period.
(13.) For example see Lynde and Richmond (1993), Finn (1993) and
Otto and Voss (1994b).
(14.) This fact has been used to criticize Aschauer's results,
in that they seem to imply unbelievably high returns to public
(15.) Estimation of the Euler conditions is done via a generalized
method of moments procedure.
(16.) These point estimates have reasonably large standard errors,
although the estimates are usually significantly different to zero.
Another interesting aspect of this study is that the implied rate of
return to public capital averages about 16 percent per annum and is less
than the estimated return to private capital.
(17.) In another paper Ho and Sorensen (1993b) find little evidence
of cointegration among various groupings of Solow residuals for these 21
(18.) Two industries have negative elasticities.
(19.) Highway capital includes, highways, streets, bridges,
tunnels, overpasses, viaducts and associated lighting and erosion
controls. Government-owned privately operated capital includes, R and D
facilities, atomic energy facilities, nuclear weapon factories, arsenals
and shipyards. Government enterprise capital includes, various credit
and insurance corporations, the Post Office, gas and electric utilities,
water and sewerage utilities, public transit agencies and airport and
maritime terminal operators.
Glenn Otto and Graham Voss *
* School of Economics, The University of New South Wales. This is a
revised version of a paper presented at the Conference of Economists
held at the Gold Coast in 1994. Financial support from the Australian
Research Council is gratefully acknowledged.