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Public capital and private sector productivity: a review of the empirical evidence.
Abstract:
This paper contains a survey of recent empirical research on the relationship between public capital and private sector production. The implications of these empirical studies for policy debates over the appropriate level of public capital are also examined.

Article Type:
Report
Subject:
Infrastructure (Economics) (Research)
Public sector (Labor relations)
Labor productivity (Research)
Authors:
Otto, Glenn
Voss, Graham
Pub Date:
06/01/1995
Publication:
Name: Economic and Labour Relations Review Publisher: Centre for Applied Economic Research and Industrial Relations Research Centre Audience: Academic Format: Magazine/Journal Subject: Business Copyright: COPYRIGHT 1995 Centre for Applied Economic Research and Industrial Relations Research Centre ISSN: 1035-3046
Issue:
Date: June, 1995 Source Volume: 6 Source Issue: 1
Topic:
Event Code: 310 Science & research; 280 Personnel administration Canadian Subject Form: Labour productivity
Product:
Product Code: 9918220 Productivity Improvement
Geographic:
Geographic Scope: Australia Geographic Code: 8AUST Australia
Accession Number:
237940745
Full Text:
1. Introduction

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 results.

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 marginal cost

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 substitutes.

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.

2.2 Causality

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 policy.

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 states.

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 effects allowed).

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 percent.

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 techniques.

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 function estimates.

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 capital.

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 Jones (1991).

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 consumption risk.

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 public capital.

5. Conclusion

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 aggregate data.

Appendix

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 States economy.

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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Notes

(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 only 0.874.

(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 eleven countries.

(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 time.

(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 set.

(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 investment.

(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 industries.

(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.
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