Infrastructure and Productivity: A Literature Review

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Table of Contents

• 1 Executive Summary
• 2 Description of Study Objectives and Methodology
• 3 Models Used to Investigate the Relationship between Infrastructure and Productivity
  • 3.1 Production function approach
    • 3.1.1 Theoretical Background
    • 3.1.2 Empirical Results
    • 3.1.3 Summary
  • 3.2 Cost Function Approach
    • 3.2.1 Theoretical Background
    • 3.2.2 Empirical Results
    • 3.2.3 Summary
  • 3.3 Growth Models
    • 3.3.1 Theoretical Background
    • 3.3.2 Empirical Results
    • 3.3.3 Summary
  • 3.4 General Equilibrium Models
    • 3.4.1 Theoretical Background
    • 3.4.2 Empirical Results
    • 3.4.3 Summary
  • 3.5 Data-Oriented Models
    • 3.5.1 Theoretical Background
    • 3.5.2 Empirical Results
    • 3.5.3 Summary
• 4 Data Gaps and Problems
  • 4.1 Estimation Related Problems
    • 4.1.1 Definition of infrastructure
    • 4.1.2 Missing Variables
    • 4.1.3 Long-term Relations Misspecification
    • 4.1.4 Causality Direction
  • 4.2 Data Related Problems and Gaps
    • 4.2.1 Stationarity
    • 4.2.2 Spurious Correlation
    • 4.2.3 Multicollinearity
    • 4.2.4 Limited Data Availability
• 5 Key Findings
  • 5.1 Key General Findings
  • 5.2 Area of Agreement
  • 5.3 Area of Significant Debate
• 6 Suggestions for Further Study in the Canadian Context
  • 6.1 Summary of Findings on Canada
  • 6.2 Research Gaps Between Canada and Other Countries
  • 6.3 Issues for Further Investigation
  • 6.4 A Review of Available Canadian Data to Conduct Research
  • 6.5 Potential Uses of the Available Data Sets
  • 6.6 Next Steps
• Endnotes

1 Executive Summary

Purpose of the literature review

The main objective of this paper is to review theories and empirical findings of how public infrastructure investments can impact productivity and economic growth. The link between investing in infrastructure and productivity is often, yet not necessarily always, positive. It is far from being unidirectional and easily measurable. In addition, despite numerous statements by public officials that recognize the importance of infrastructure for prosperity and competitiveness, few empirical studies have focus on these issues in Canada. Those that have are limited in scope and methodology. Given that the public and private sector currently invest over $40 billion per year in Canadian public infrastructure,⁽¹⁾ and given that there is little empirical evidence to show whether these investments are well targeted to promoting productivity, more research should be conducted on this topic.

The main purposes of this literature review are to: 1) conduct a comprehensive review of studies that examine and attempt to measure relationships between infrastructure investments and productivity; 2) identify areas of agreement and disagreement between authors; and 3) identify the best course of action for future research. This paper reviews existing theoretical foundations and applied econometric approaches used by economists to quantify the benefits of investments in infrastructure for productivity and identify the conditions necessary to realize those benefits.

Background

There is a recognition that modern public infrastructure has an important role to play in improving quality of life and in making economies more competitive by enabling activities that provide public benefits. It is widely accepted that the rapid productivity growth of the postwar period ended in the mid-1970s and was followed by dismal productivity growth accompanied by stagnation in real incomes. In their attempt to explain productivity slowdown in the 1970s, some authors identified a strong link between declining productivity growth and significantly reduced public infrastructure investments during the same period. Early studies on infrastructure and productivity in the 1980s suggested that reduced public infrastructure investments were one of the main contributing factors to the productivity slowdown in the 1970s. These studies have spurred further research in this area.

Methodology

Economists have taken five types of econometric approaches to investigate and quantify the relationship between infrastructure and productivity: production function; cost function; growth models; general-equilibrium models; and data-oriented models.

• The production function approach models the amount of output that can be produced for each factor of production (or inputs), given technological constraints.
• The cost function approach is more advantageous compared to the production function approach, as it takes into account factor prices such as the price of labour, machinery, and finance.
• Growth models are constructed to estimate the impact of all factors of production on output using total factor productivity. These models are used to understand the relationship between total factor productivity and inputs into production, like public capital.
• General-equilibrium models (GEMs) are considered to be more comprehensive than the models above, as they provide an understanding of the whole economy, using a bottom-up approach. GEMs model behaviour of individual agents in a price-changing market environment where the prices and production of all goods are interrelated. A set of assumptions is imposed to ensure that the economy reaches an equilibrium state. As will be discussed, theoretical models can be restrictive and often do not take these elements into account.
• Data-oriented models are particularly useful for identifying the direction of causality between infrastructure and productivity as they analyze relations between several data series and do not rely heavily on economic theory.

Findings

Early studies based on the production function approach report findings of very high impacts of public capital investments on productivity and economic growth. However, these early studies are plagued with several econometric problems. Authors of the later studies applied more sophisticated approaches and report lower, but typically still positive impacts of infrastructure investment on productivity. Some authors report that their results are inconclusive. Most authors limit their analysis to the effects arising from investments into core infrastructure, as opposed to complementary infrastructural spending, and find them to positively affect output and productivity.

Several authors note that, beyond a certain optimal threshold, public capital investments may result in a negative net benefit to society as economic and social benefits are exceeded by related costs. Some authors also provide evidence that infrastructure investment creates income divergence across regions due in part to the fact that employment income is higher in regions with significant infrastructure investments. These areas typically have higher labour concentration and employment growth due to increasing number of individual establishments.

Some authors note that infrastructure investments positively affect the relative attractiveness of geographical areas and land values, and suggest that infrastructure investments can potentially redirect economic growth from infrastructure-poor areas to those areas that have invested more heavily. It is also possible that some benefits resulting from new infrastructure investments create positive spillover effects in neighbouring areas and hence total positive regional infrastructure effects may, in reality, be higher than what is reported. For these reasons, decision-makers need to consider the impact of infrastructure investment decisions at a regional level and not just nationally.

Several additional findings are also noted in the studies:

• Some studies indicate that public capital is complementary and that it promotes private capital formation.
• Most of the authors agree that core infrastructure, such as roads and railways, tend to exert the most influence on productivity.
• Some authors identify a negative relationship between investments in public infrastructure and employment levels. Consistent with economic theory, these are found to be substitutes for each other. In other words, investments in public infrastructure do not result in higher levels of employment, but instead reduce employment levels.

There is a significant amount of discussion regarding the data and econometric problems that arise in studies of the relationship between infrastructure investments and productivity. For example, one problem with models which use single equations is understanding the direction of causality, as it is just as possible for output growth to cause changes in demand for public capital stock as it is for more infrastructure investments to cause an increase in private sector productivity. The databased models allow researchers to overcome this problem and several authors suggest that infrastructure investments positively affect private sector output and productivity. At the same time, studies based on this approach conclude that public capital is not as productive as it has been shown in studies based on production or cost functions.

It is important to note that the corrections for statistical problems help to quantify the relationship between infrastructure and productivity, holding other factors constant. In other words, the corrections help to isolate the direct effect of infrastructure investment on productivity. When statistical problems are not dealt with, the parameter estimates are likely to be biased as they may capture other effects as well. For example, David Aschauer's⁽²⁾ estimates of public capital elasticities are argued to be implausibly large due to the fact that he does not adequately account for the econometric issues inherent in time series analysis. To be more specific, the model Aschauer uses does not capture time invariant factors that influence regional output, such as geography and natural resource endowments. If those time invariant effects are correlated with stocks of public infrastructure, then failing to include such effects will bias econometric estimates.

Suggestions for further research

In order to better inform decision-makers in Canada, more work should be done in the following areas: identification of key research and policy question based research, development and testing of a new methodology, assessment of existing data series and collection of new data required.

In terms of key research questions, more work should be done to analyze how public infrastructure investments in Canada and the provinces impact national economic growth and competitiveness. More work should also be conducted to understand the costs and benefits of regional public capital investments and their industry-specific impacts across regions. In addition, many of the papers that were reviewed define public infrastructure as a flow of investment dollars; thus, they completely ignore the impact public capital investment has on the demand for infrastructure. Investment in public capital such as highways can actually increase the demand for highway use, which leads to congestion, and, in turn, lowers productivity by having impact on labour. Negative feedback mechanisms need to be considered more closely.

More work can be done to advance methodological issues of infrastructure impact on productivity. It is necessary to analyze the relationships between various inputs of production, such as labour, energy, materials, services and private and public capital stock. Models that are used to study the relationship between infrastructure and economic output typically use restricted functional forms that may not best reflect the relations between public and private capital. More emphasis should be placed on developing models with functional forms that are flexible enough to take into account the complexity of relations between various inputs of production. This would provide a more realistic explanation of how investments in infrastructure impact productivity and economic growth.

Finally, depending on the quality of existing Canadian data, there are several studies that could be conducted using readily available data sets, such as recently updated Statistics Canada public capital stock series. It is also important to identify what questions are critical but cannot be addressed with data sets exiting today. Options for obtaining the data of interest (i.e. surveys, linkage of data sets, use of publicly available information such as annual reports) and anticipated benefits and costs associated should be considered.

The next steps required to extend existing research using econometric models would be to:

• Clearly define the hypotheses being tested;
• Review various estimation methodologies and modelling techniques and associated pros and cons;
• Identify the data requirements for chosen estimation method;
• Conduct detailed quality assessment of all readily available data series and consider options for correcting common econometric problems;
• Develop options for obtaining the missing data of interest (i.e. surveys, linkage of data sets, use of publicly available information such as annual reports) and assess feasibility of obtaining required data;
• Identify the anticipated benefits and costs associated with those options;
• Prepare data series;
• Construct econometric model and test the hypothesis; and
• Analyse findings and suggest policy related actions.

It is suggested that as a preliminary step, additional analysis of the new Statistics Canada data set on investment and capital stocks is needed to better understand analysis options and data limitations and to develop a basis for a new data development strategy. For example, the existing data could be used to identify any strong relationships between key variables by using simplified econometric approaches, while recognizing the limitations of the data. Synthetic data could then be created to provide a better understanding of what additional data is required in order to test the various hypotheses discussed in this report.

2 Description of Study Objectives and Methodology

There is a recognition that modern public infrastructure has an important role to play in improving quality of life and in making economies more competitive by enabling activities that provide public benefits. Yet there is little understanding of the effects that public infrastructure⁽³⁾ investments have on productivity.⁽⁴⁾ This presents a serious challenge for decision-makers. Without knowledge of the magnitude of the effects, and the conditioning factors, decision-makers cannot make informed decisions about how much to invest and under what circumstances.

The purpose of this paper is to examine the literature in this area and describe what is known about the link between productivity and infrastructure, how it can be measured, what the debates are, and what the best course of action for further developing our understanding is.

The type of research that will be reviewed in this paper is that of econometricians who seek to quantify the impact of investments on productivity, and illustrate the necessary conditions for positive impacts. It is important to first have an understanding of the theoretical foundations of their applied work. The distinction between the work of economic theorists and that of econometricians is clarified in Box 1.

Following the plan of this paper, section 3 starts with a general discussion of the models studied in this literature review. Each sub-section in section 3 begins with a discussion of the theory and follows with an attempt to answer some specific research questions. The general questions to be addressed are:

• What is known in detail about the relationship between infrastructure and productivity?
• What are the gaps in the knowledge concerning infrastructure and productivity?
• What are the areas of further study that have been identified?
• Who are the significant research personalities and perspectives in this area?
• Why is there a lack of consensus on the topic? What aspects have generated significant debate on the topic?

In Section 4, the data gaps and methodological problems as well as areas of agreements and debates encountered in the literature reviewed are presented. In Section 5, key findings and recommendations for further research are presented. More specifically, the following research questions are addressed:

• What is the most productive way forward for research relevant to Canada based on the literature reviewed?
• What is the current status of research in this area?
• What sources of information or data were identified that might be useful?

3 Models Used to Investigate the Relationship between Infrastructure and Productivity

In the 1980s and early 1990s, decision-makers and economists became keenly interested in the role that infrastructure plays in stimulating economic growth and productivity. Since that time many economists have used neoclassical⁽⁵⁾ production theory to assess the relationship between infrastructure and productivity. Many economists have made contributions to the theory by including additional factors of production such as infrastructure. Infrastructure is seen as an important input to production because without power sources and roads, for example, manufacturers would be significantly less, or perhaps not at all, productive.

Economists have taken at least five different approaches to investigate the relationship between infrastructure and productivity:

• production function approach;
• cost function approach;
• growth models;
• general-equilibrium models; and
• data-oriented models.

The production function approach models the amount of output that can be produced for each factor of production, given technological constraints. The cost function approach is different from the production function approach in that it takes into account factor prices such as the price of labour, machinery and finance. Growth models are constructed to estimate the impact of all factors of production on output using total factor productivity. These models are used to understand the relationship between total productivity and production inputs, like public capital. General-equilibrium models (GEMs) are considered to be more comprehensive than the models above, as they provide an understanding of the whole economy, using a bottom-up approach. GEMs model behaviour of individual agents in a price changing market environment. Theoretical models are restrictive and do not take certain elements into account. Consequently, to identify the direction of causality between infrastructure and productivity, several researchers resort to data-oriented models. Data-oriented models analyze relations between several data series and do not rely heavily on economic theory.

In all cases, these models shed light on the impact of infrastructure on productivity. They also illustrate the other contributing factors to productivity performance, and, in some cases, identify other factors that are related to infrastructure and may be required to achieve the benefits of infrastructure. By quantifying the impact of infrastructure on productivity, the models can help to support informed decision making on how much to invest in infrastructure and under what circumstances.

3.1 Production function approach

3.1.1 Theoretical Background

Production functions are used to explain the relationship between economic output and its factors of production (i.e. private and public capital and labour). A general form of the production function is presented in Equation 1.⁽⁶⁾

Equation 1: Y = f(AK, L, G)

The variables used in the production function are defined as follows:

• Y is the level of economic output
• f is a function that represents technological feasibility⁽⁷⁾
• A is the “effectiveness of capital”
• K is the stock in private capital
• L is the stock of labour
• G is the stock in public capital⁽⁸⁾

In order to quantify the impact various factors of production have on economic output, a specific function is required. The most common function used in empirical work to accomplish this is the Cobb-Douglas production function, which is shown in Equation 2.

Equation 2: Y = AKδLαG γ

The parameters in the function, which represent the quantitative relationship between the input variable and output, are defined below:

• δ is the elasticity of output⁽⁹⁾ with respect to private capital
• α is the elasticity of output with respect to labour
• γ is the elasticity of output with respect to public capital

One critical point to note is that econometric analysis typically does not demonstrate the causal impact. Rather, it illustrates the relationship between a particular variable and output, assuming that all the other variables remain fixed. Hence, the relationship between an input variable and output may be due to another factor that is causing change in both of those variables.

The most common method to estimating⁽¹⁰⁾ the parameters in the production function is an econometric approach called ordinary least squares (OLS).⁽¹¹⁾ One of the basic requirements when using the OLS method is that the function being estimated must be linear. Therefore, to estimate the parameters of the production function, the equation must be transformed into a linear form that allows the application of this econometric technique. Transforming the equation into log-linear form will accomplish this task. This is achieved by taking the natural logarithm⁽¹²⁾ of both the left and right hand sides of the equation. The outcome of this transformation is highlighted in Equation 3.

 Equation 3: lnY = lnA + δlnK + αln L + γlnG

Estimates of γ quantify the relationship between public capital stock and economic output.

3.1.2 Empirical Results

David Aschauer

In 1989, David Aschauer⁽¹³⁾ published a critical study to examine the relationship between infrastructure and productivity. In this paper, Aschauer examines the relationship between U.S. national aggregate productivity and the stock and flow of government spending. More specifically, using U.S. data covering the period from 1949-1985 and a Cobb-Douglas production function approach, he estimates the impact of government spending variables on private output and total factor productivity.⁽¹⁴⁾ Aschauer uses various econometric techniques to attempt to eliminate the possibility that output or productivity increases demand for government spending and that, as a result, estimates of the impact of government spending on productivity are spurious or falsely correlated. That is, Aschauer attempts to ensure that it is not just mere coincidence that productivity and government spending are correlated but rather a true statistical relationship. He concludes that:

• the stock of non-military public capital is more important than either the flow of non-military spending or military spending;
• the impact of public capital is highest during the period of 1949-1967 and the lowest from 1953-1985;
• the most productive capital stock over the 1949-1985 period is core infrastructure which includes such things as streets, highways, airports, mass transit, sewers and water systems;
• productivity decreases from 1971 to 1985 are a result of a reduction in public capital spending.

Aschauer's estimated impact of a 1% increase in non-military public capital on output per unit of capital ranges from 0.39% (in 1949-81) to 0.56% (in 1949-67). His estimated impact of a 1% increase in non-military public capital on total factor productivity ranges from 0.36% (in 1949-67) to 0.49% (in 1968-85).

For decision-makers in the United States, the implications from this study are significant. First and foremost, the results from this study suggest that more emphasis should be placed on public investment decisions, specifically on core infrastructure. Second, these results imply that reductions in public capital spending have had a negative impact on economic productivity.

Several authors⁽¹⁵⁾ have argued that Aschauer's results are plagued with weaknesses. Some economists⁽¹⁶⁾ argue that the oil shock of the 1970s was a contributing factor to the decline in both labour productivity and public infrastructure spending, and that as a result, there is no correlation between infrastructure and productivity. Other economists⁽¹⁷⁾ have been critical of Aschauer stating that it is productivity growth that has led to an increase in the demand for public infrastructure and not the other way around. Aschauer did not effectively address this problem - known as endogeneity.⁽¹⁸⁾ Finally, according to H.J. Aaron⁽¹⁹⁾, Aschauer's estimates are so high that they imply that investments in non-military public capital would be paid for in one year from productivity gains. For example, if we assume that public capital investments share in total GDP is measured at 10 percent, an estimated output elasticity of 0.5 for public capital implies that if one dollar is invested in public capital assets, total GDP would increase by five dollars. Assuming a 20 percent tax rate, an original one dollar investment in infrastructure would be completely recovered in just one year.

Critics of Aschauer's study have also suggested that using regional level data reduces the chances of obtaining spurious⁽²⁰⁾ results.⁽²¹⁾ One of the serious challenges, as alluded to above, is that in all likelihood many of the input and output variables are dependent on each other. Simple regression is adequate when all of the input variables are independent of each other and from the output variable being modelled. There are, however, likely to be significant feedback loops between productivity and infrastructure. If this is indeed the case, it is important to estimate the independent variables separately but in a related way.

Aklilu A. Zegeye

In “U.S. Public Infrastructure and Its Contribution to Private Sector Productivity”, Aklilu A. Zegeye uses a multiple equations production model⁽²²⁾ to study the impacts between infrastructure⁽²³⁾ and productivity of the manufacturing sector for 1,500 U.S. counties and all 50 states.⁽²⁴⁾ In his study, Zegeye uses cross sectional census data from 1982, 1987 and 1992. Since the three equations he uses employ some of the same variables, Zegeye estimates the equations jointly, using three different methods.

To overcome weaknesses that have been ignored in other studies that use a production function, the author explicitly tests the assumptions inherent in the Cobb-Douglas production function (i.e. constant returns to scale).⁽²⁵⁾ Zegeye also uses regional dummy variables to control for differences in productivity that are purely a result of regional characteristics and not infrastructure. This type of model is commonly known as a fixed-effects model.⁽²⁶⁾  Using this model the author finds that the estimated impact of public infrastructure on per capita output is 0.133. This is much lower than what has been found in previous studies, most likely because Zegeye models interdependencies. The result does not suggest that infrastructure is less important. Rather, it illustrates that the benefit depends on similar increases in other input variables.

In addition, the author finds that state level data shows a stronger relationship between public capital and productivity than the county level data. Therefore, he concludes that states are in a better position to take on infrastructure projects. He also notes that the estimated impact of infrastructure on productivity tends to increase as the level of aggregation increases, which would partly explain Aschauer's elevated estimates.

Peter Wylie

As a continuation to Aschauer's work, Peter Wylie⁽²⁷⁾ examines the role of infrastructure in Canadian economic growth over the period 1946-1991. Wiley uses a production function, which he calls a “goods value added production function.”⁽²⁸⁾ He estimates a translog production function⁽²⁹⁾ for the Canadian goods sector using an OLS regression. The results of this paper imply that a 1% increase in infrastructure capital stock per hour worked would increase output per person hour worked in goods production with a productivity elasticity of 0.52. This result is much higher than Aschauer, though Wiley does not discuss explicitly how his analysis controls for the common estimation problems encountered in these studies, such as multicollinearity and spurious correlation. Wiley attributes this result to the fact that Canada has had higher population growth, lower population density and a harder physical climate relative to the United States, and, as a result, Canada is more dependent on infrastructure.

Achim Kemmerling and Andreas Stephan

Although the main purpose of Kemmerling and Stephan's paper, “The Contribution of Local Public Infrastructure to Private Productivity and its Political Economy” is to study political decisions about public infrastructure projects, it does share insight about the relationship between regional road infrastructure and regional output.⁽³⁰⁾ The authors use a translog production function composed of a system of equations to estimate the impact regional road infrastructure has on regional output for 87 German cities. In this study, investment into infrastructure is specific to construction and equipment. The authors use maximum-likelihood estimation⁽³¹⁾ to estimate the system of equations. As noted above, the advantage of using multiple equations is that it reduces the risk of reverse causation or endogeneity, which occurs often when single equations are estimated. Kemmerling and Stephan do test for reverse causation in each of the equations, but find it to be weak.

The authors find that: (1) anticipation of federal funding of infrastructure projects is not taken into account when regions are planning regional infrastructure projects; (2) there is positive correlation between the infrastructure demands of cities (e.g., the number of automobiles) and the level of local infrastructure investment; (3) regions with higher debt invest less in infrastructure; and (4) cities where labour productivity of manufacturing is lower spend less on infrastructure investment.

In summary, the authors find that the estimated coefficient, with respect to infrastructure, is positive and statistically significant, with a value of about 0.17 (output per labour hour). In other words, inputs into regional infrastructure do promote regional output.

Andreas Stephan

In his study entitled “Regional Infrastructure Policy and Its Impact on Productivity: A Comparison of Germany and France,”⁽³²⁾ Stephan uses a Cobb-Douglas production function to study the effects of public infrastructure on productivity. The author examines investment into regional capital stocks for road infrastructure from French and German states between 1970 and 1995. By combining the data across two regions and increasing the studied sample, the author increases the reliability of the data. The author uses a log-linear Cobb-Douglas production function equation⁽³³⁾ but divides regional inputs by the stock of labour in order to reduce the problem of heteroscedasticity,⁽³⁴⁾ which often poses problems in estimating panel data.

The Cobb-Douglas production function restricts the elasticity effects of independent variables. For this reason, the author uses a translog production function, which has a more flexible form, and which he estimates using the maximum-likelihood method. Using this method, Stephan finds that investment into road infrastructure does promote regional output. The estimated impact of infrastructure on regional output is 0.1282 (output per labour hour). In addition, the author finds that infrastructure investments will increase productivity in infrastructure and labour more significantly than their demand.

Frederico Bonaglia, Eliana La Ferra and Massimiliano Marcellino

In, “Public Capital and Economic Performance: Evidence from Italy,” Bongalia et al.⁽³⁵⁾ present the impact of infrastructure on regional and national growth in Italy. The authors use three different methodologies; however, only the production function approach is discussed in this part of the review. The authors use annual regional data from the period 1970-1994 and focus on the impact of investment in roads, airports, railways, ports, water, energy, communication schools, public buildings, sanitation and public land. Unlike Aschauer, Bonaglia et al. formally test for endogeneity using the Hausman test⁽³⁶⁾ and are able to reject the hypothesis that endogeneity exists. The authors find that public capital does play a significant role in output (the estimated coefficient is 0.140 value add per worker for all of Italy) for all regions except in the North-West. In addition, the authors find that investment in public transportation appears to be the most productive in all regions, with the exception of the center of Italy. In Central Italy investment in water⁽³⁷⁾ is found to be the most productive investment.

Maria Jesus Delgado and Inamculada Alvarez

Delgado and Alvarez's “The Effect of Public Infrastructure on Private Activity: Evidence from the Spanish Regions” ⁽³⁸⁾ argues that more attention should be given to the indirect role that public capital plays by promoting private capital formation. Public capital in this study includes roads, railways, airports, ports, energy networks and telecommunications. The authors use a translog production function and provide estimates of the technical relations among the inputs for 17 Spanish regions using annual data from 1980 to 1995. The authors also use the Hausman test to test for model specification and find that it is necessary to use a fixed-effects model. The authors use OLS to estimate the factors of production using a translog production function with fixed-effects⁽³⁹⁾ to see if productive infrastructure capital and private capital are complementary and if productive capital and labour are substitutes.⁽⁴⁰⁾

The authors find that both labour and private capital are endogenous. Therefore, first differences⁽⁴¹⁾ are used to minimize this problem. On the one hand, the results from their study indicate that public capital⁽⁴²⁾ promotes private investment; that is, public and private capital are complementary. On the other hand, public capital and private labour are substitutes, meaning that demand for public capital will decrease the demand for private labour. This represents a challenge for decision-makers - the first effect, increasing private capital is positive, while the second effect is negative. These findings suggest that further study is required to assess all of the externalities and net impacts of these opposing effects.

Jaume Puig-Junoy

Puig-Junoy's study⁽⁴³⁾, “Technical Inefficiencies and Public Capital in U.S. States: A Stochastic Frontier Approach” uses a translog production function to measure and explain changes in technical efficiency.⁽⁴⁴⁾ Puig-Junoy uses panel data that covers 48 U.S. states for the period 1970 through 1983. Public capital investments were broken into three categories: highways, water and sewers, and other. Given that the aim of the paper is to focus on the efficiency of the estimates, the author suggests that the presence of multicollinearity is not an issue. In this study, the author finds that the level of public capital investments in relation to private capital and the proportion of public investments in highways have had the most important effects in determining the levels of technical inefficiency.

The results of this study suggest that the ratio of public capital to private capital is positively correlated with technical inefficiency, meaning more investment into private capital will result in higher productivity. Puig-Junoy also finds that the proportion of public capital devoted to highways is negatively correlated with technical inefficiency, or, in other words, more investment into highways will likely result in higher productivity. The author concludes that an increase in the public/private capital ratio may negatively influence overall technical efficiency by investing in non-productive public capital; however, this effect could be positive if the capital is properly invested, such as in highways.⁽⁴⁵⁾ Puig-Junoy claims that the reason for this is that private sector investments into private capital contribute more to innovation and, therefore, to technical efficiency/productivity. Once again, this illustrates a challenge for decision-makers - they must choose not only the right amount to invest but also the right area in which to invest.

Eric Wang

“Public Infrastructure and Economic Growth: A New Approach Applied to East Asian Economies” by Wang employs a two sector production function to study the impact of public capital on private production. ⁽⁴⁶⁾ Wang's paper attempts to propose a production function framework for analyzing the interrelation between public infrastructure expansion and private production growth and for identifying their externality effects. An important issue regarding infrastructure is how efficiently the government manages the existing stocks.

The author argues that public capital⁽⁴⁷⁾ contributes indirectly to output or productivity. In other words, it is the benefits produced by the public capital that are used as inputs by other production sectors and not the stock of public capital itself. The traditional one sector production function, like the one presented in Equation 1, is used to estimate the direct impact of public capital on output or productivity. For this reason, a two sector model must be used to asses the indirect impact of public capital on output and productivity.

One of the two sectors, which Wang focuses on, includes agents that rely heavily on public capital stock. The other sector is a combination of all agents that produce private goods. The central hypotheses being tested are: 1) an increase in public capital stock creates a benefit spilling over to agents producing private sector goods, and 2) as the private sector benefits from the increase in public capital, the private sector will also demand more public capital stock as the demand for production increases.

Wang estimates and tests the two-sector model for seven East Asian countries for the period from 1979-1998, using OLS regression. The author finds that the responsiveness of private production to a 1% change in expected public capital output is positive for five⁽⁴⁸⁾ out of the seven countries and significant for all countries combined. For the five countries in which the responsiveness of private capital is positive, the average relation is 0.2%. This implies that a 1% increase in expected public capital will increase private production by 0.2%. Similarly, the author finds that a 1% increase in private production increases the demand for public capital by 0.8% - 1.08%.⁽⁴⁹⁾ As a result, these tests indicate that a spillover effect exists in both directions and that keeping a balance between infrastructure growth and private sector growth is important for economic development.

Lauren Bin Dong

Bin Dong⁽⁵⁰⁾ examines the effects of public capital on the performance of Canadian business sector. She analyses the relationship between business sector output and the stock of public capital for the time period of 1987 to 2002. She uses the production function to estimate how changes in business sector output are influenced by the stock of public capital. The analytical framework of her research is the Cobb-Douglas function where she adds the public capital as an input. Her approach includes the estimation of the rate of return on public infrastructure, and the comparison between this rate and the return on the private capital from 1987 to 2002. She uses the estimation of a variant of her production model to evaluate the economic externalities associated with public infrastructure across provincial borders.

The first mean empirical finding of Bin Dong's research is a positive impact of the public infrastructure on business sector. She obtains statically significant estimated coefficients for private capital, for labour input and for public capital. Each 1% change in public capital leads to 0.20% change in GDP in the Canadian business sector over the period 1987 to 2002 on average.

The second mean finding is the estimated rate of return on Canadian public capital that is about 7.70% on average between 1987 and 2002. This rate is lower than that for private capital because of the difference in risk faced by the public and the private sectors. But it is comparable with the Canadian government long-term bond rate over the time period concerned.

The third mean finding is the approach she uses to evaluate the economic externalities of public infrastructure across provinces. She observes that the rate of return on public infrastructure using data at the national level is higher than that she has with data at provincial level. She concludes that this difference suggest the existence of public infrastructure externalities across the provinces.

3.1.3 Summary

Research reviewed in this section uses production functions to study the relationship between infrastructure and output or productivity. There are several key findings from these studies:

• Most of the authors find a statistically significant relationship between infrastructure investment and productivity or output. However, estimates vary significantly from study to study, with higher results as data aggregation increases. The range of estimates varies from 0.20 to 0.51 for studies that focus on country level data, while ranges vary from 0.12 to 0.17 for studies that have used regional or pooled data.⁽⁵¹⁾ The majority of the studies indicate that public capital is complementary and that it promotes private capital formation. Finally, most of the authors agree that core infrastructure, such as roads and railways, tend to exert the most influence on productivity.
• Although there is significant debate about the direction of causality, most authors examined in this section tend to support the hypothesis that public capital drives productivity, and not the other way around. The Hausman test is the most commonly used instrument to test for endogeneity.
• Some authors note a negative relationship between investments in public infrastructure and employment levels. They find, consistent with economic theory, that these are substitutes for each other.
• While not much has been studied about the sector specific impacts, there is some evidence that infrastructure investment tends to be directed to underdeveloped areas with lower productivity of labour because decision-makers believe this is where returns from infrastructure investment will be the highest.⁽⁵²⁾

These findings stimulate several key considerations for decision-makers:

• First, investments in infrastructure are said to increase productivity, although the size of the impact and the conditioning factors are debated. Hence, the specific amount, type and timing of investments cannot be determined from these studies.
• Second, decision-makers need to consider the opportunity costs of investments in infrastructure. On the one hand, research shows that investments in public infrastructure stimulate investment in private infrastructure. Nevertheless, some research shows that investment directed towards private capital may increase productivity more so than investment into public capital. Hence, while investments in public capital seem to have a positive effect on private capital formation and productivity, decision-makers need to consider whether direct investment in public infrastructure has a stronger net impact on productivity than policies designed to simulate private investments in infrastructure.
• Finally, studies show that investments in infrastructure tend to be negatively associated with labour. Hence, decision-makers need to consider the equity impacts associated with investments in infrastructure, even when they lead to productivity gains.

It is also important to note that the econometric challenges - raised here and discussed in greater detail in section 4 - present serious concerns about the findings listed under section 3.1. This does not imply that these studies are invalid. Rather, it requires judgement and caution when using this information to make specific policy decisions.

3.2 Cost Function Approach

3.2.1 Theoretical Background

One of the limitations of the production function approach is that it does not take into consideration the role of factor prices such as the price of labour, machinery, and financial capital. Factor prices have an impact on the utilization of factors of production like labour, machinery and financial capital. For example, when fuel prices increase, the demand for machinery may decrease. For that reason and others,⁽⁵³⁾ economists have used an alternative approach. This alternative is the cost function that measures the impact of public capital on productivity in terms of cost savings. The basic aim of the cost function is to examine if the cost of output decreases with higher stocks in public infrastructure. The most common specification used by economists when using this approach is the dual cost function. Equation 4 shows the general cost function.

Equation 4: C = C(w, r, Y, Z)

The following is a definition of the variables used in the cost function:

• C is total cost of private output
• w is the wage rate
• r is the price of private capital
• Y is output
• Z is public infrastructure services

According to microeconomic theory, the cost variable is expected to decrease with an increase in infrastructure services. Yet some economists would caution that increased infrastructure services are only justified if their cost is smaller than the resulting productivity gains.

3.2.2 Empirical Results

Jose Miguel Albala-Bertrand and Emmanouel C. Mamatzakis

In their paper, “The Impact of Public Infrastructure on the Productivity of the Chilean Economy”, Bertrand and Mamatzakis⁽⁵⁴⁾ study the effectiveness of public infrastructure on the cost structure of the Chilean economy. The authors use a translog cost function to estimate the cost savings shares of product inputs from investments in infrastructure for 1960 to 1998. The authors find that over the period infrastructure investments resulted in a 33% savings to the economy. In addition, the study finds that public capital is complementary to private capital in the last 25 years of the period studied. This implies that increases in public capital investment increase the demand for private capital.

Frederico Bonaglia, Eliana La Ferra and Massimiliano Marcellino

In “Public Capital and Economic Performance: Evidence from Italy”, Bonaglia et al.⁽⁵⁵⁾ present the impact of infrastructure on regional and national growth in Italy. The authors use three different methodologies; however, only the cost function approach is discussed here. As indicated in section 3.1.2, the authors use annual regional data from the period 1970-1994 and focus on the impact of investment into roads, airports, railways, ports, water, energy, communication schools, public buildings, sanitation and public land. Bonaglia et al. use a variable cost function⁽⁵⁶⁾ to estimate the impact infrastructure has on manufacturing costs.

The elasticity of total costs to public capital for the Centre of Italy is 0.3 (dollar per unit of public capital); that is, for every dollar spent on public capital, total costs are expected to decrease by 30 cents. In addition, the authors find that the benefits, in terms of cost savings, from public investment have not been high enough to outweigh the opportunity cost. These results are due, in part, to the fact that the cost to finance public investment infrastructure and the depreciation costs are higher than the cost savings generated.

Robert Ezcurra, Carlos Gil, Pedro Pasqual and Manuel Rapún

Using a cost functions approach, Ezcurra et al.⁽⁵⁷⁾ use the duality approach and panel data to estimate the impact of infrastructure on Spanish regional production costs in the agricultural, industrial and services sectors for the period 1964-1991.⁽⁵⁸⁾ Public capital is included as an unpaid factor of production and two separate variables, depreciation and rent of capital, are used to establish whether the different categories of public capital have varying effects on costs. Since this was a regional study the authors did not feel endogeneity was a significant problem.⁽⁵⁹⁾

Results from this study show that public infrastructure reduces private costs and increases productivity. The estimated cost impact of infrastructure investments is -0.154 for industrial sector costs and -0.145 (dollar costs per unit of public capital) for services sector costs, implying that the greatest savings in private costs are found to be in the industrial sector, followed by the service sector. In addition, cost savings through public investment have a positive effect on production because the lower cost per unit of public capital increases the demand for capital and, therefore, production.

Rosina Moreno, Enrique López-Bazo and Manuel Artís

Moreno, López-Bazo and Artís⁽⁶⁰⁾ examine a wide range of infrastructure effects both in the short and long run. In their paper “Public Infrastructure and the Performance of Manufactures: Short and Long Run Effects,” the authors use a translog cost function and examine annual data for 12 manufacturing sectors in 15 Spanish regions from 1980 to 1991. The authors find that a 1% increase in public infrastructure results in a 0.027% increase in production costs in the short run. The potential explanation for this is that input prices may increase in the short run. This implies that, in the short run, manufacturing firms do not benefit from an increase in public infrastructure. In the long term, a 1% increase in public infrastructure leads to a 0.025% decrease in production costs. This means that, over the long run, firms are willing to pay a premium for public infrastructure.

Jeffery P. Cohen and Catherine J. Morrison-Paul

Cohen and Morrison-Paul⁽⁶¹⁾ apply a cost function model to 1982-1996 state-level U.S. manufacturing data to analyse the private cost-saving effects of inter- and intra- state public infrastructure investment. The objective of the study, “Public Infrastructure, Investment, Interstate, Spatial Spillovers and Manufacturing Costs,” is to determine the private cost-saving effects of intrastate public infrastructure investment. To account for spatial spillovers, the authors also implement two spatial adaptations, including a spatial spillover index in the theoretical model, and allow for spatial autocorrelation in the stochastic structure. The authors test for the potential of endogeneity using a Hausman specification test and find that it is not present. Cohen and Morrison-Paul use a full information maximum likelihood estimator technique⁽⁶²⁾ and find that there are productive effects of intrastate public-infrastructure investments that seem to be increasing over time.

The shadow price of public infrastructure (i.e. variable cost savings per investment of infrastructure) is approximately -0.31 (dollar per unit of public capital) and the largest intra-state infrastructure effects appear in the western part of the United States. The smallest effects appear in the east and south. These results support the findings of Hulten and Schwab (1991) of a higher public infrastructure impact in the “snowbelt” than in the “sunbelt”. This could suggest that for a state such as California, which is both large and relatively densely populated, inter-state infrastructure investment is not nearly as important as intra-state infrastructure investment. Some of the greatest impacts appear in the less populated Mountain and West North Central states.

Authors conclude that the full network of highway infrastructure in these areas seem to confer important productive contributions to manufacturing firms in such states. Another conclusion of Cohen and Morrison is that “output growth motivated by the cost-depressing effect of infrastructure investment may stimulate capital investment and labour employment, even though overall short run public infrastructure-private input substitutability is evident at existing output levels.”⁽⁶³⁾

Biswal Bagala, Sahni Balbir and Paul Satya

Bagala et. al.⁽⁶⁴⁾ analyse the effects of public infrastructure on the performance of Canadian manufacturing industries. They measure these effects in terms of both cost-saving and output-augmenting. The authors use the cost-function approach to investigate the productive effects of public capital in the performance of Canadian manufacturing industries. They estimate a translog cost-function incorporating public capital infrastructure for each industry separately with annual time-series data for 1961-1995. They also investigate how public capital influences the input demand and cost structure in each industry and calculate the rate of return to public capital. Bagala et al. finds variations of the productivity effects of public capital across manufacturing industries. They show a substitution of the public infrastructure services for both labour and private capital in most of industries. For most industries, they find that the cost elasticity vary in the range between -0.10 and -0.40.

In addition, the study highlights positive and statistically significant marginal benefits of public capital for most industries. However, it tends to show that rates of return to public capital are quite modest, 11% for cost saving and 31% for output, in comparison with the same rates estimated for Canada and United States by other researches⁽⁶⁵⁾. The empirical analysis of Bagala et. al is based on the assumption that public infrastructure provides no benefits to consumers and other producers in the economy. But the authors recognise the limit of this assumption. They argue that most components of public infrastructure such as highways, roads, sewage and water pipes generate some benefits to consumers. The estimation of these benefits to all consumers would require the use of a general equilibrium model, which is out of the scope of their study.

James A. Brox and Christina A. Fader

Brox and Fader⁽⁶⁶⁾ use a translog cost function to study the interactions of the public and private sectors. The authors examine Canadian manufacturing firm data from 1961 to 1997 and use the stock of public capital stock to study the cost characteristics of the Canadian manufacturing industry by using a Constant Elasticity and Substitution Translog Function (CES-TL).⁽⁶⁷⁾ The cost and share equations of labour, capital and energy are jointly estimated by the method of Full Information Maximum Likelihood. Full Information Maximum Likelihood is suitable for estimating systems of equations involving constrained coefficients⁽⁶⁸⁾ of different structural equations⁽⁶⁹⁾ and certain restrictions on the error structure.⁽⁷⁰⁾ One of the significant findings from this report is that output is responsive to factor price changes; that is, when factor prices like the price of labour increases, output decreases.⁽⁷¹⁾

The authors find public capital to be a substitute for private capital within the Canadian manufacturing sector. Indeed, when they include public infrastructure in private sector cost functions, their estimate of cost elasticity is -0.476 for Canadian manufacturing. This means that an increase of 10% in public capital leads to decrease of 4.76% in cost of manufacturing output production. They find significant factor bias effects, which bring them to conclude that there is evidence that the average factor productivity is impacted when infrastructure levels change. Therefore, they find that Canadian public capital has been private capital-saving, and labour, energy and materials using. This is why they infer that public capital is a substitute for private capital in the Canadian manufacturing sector.

The authors explain that in Canada the two capital types (i.e. public and private capital) were complementary at the beginning of the period, however, towards the middle and end of the period, capital investment slowed substantially, which would explain why public and private capital are now substitutes. This means that an increase in public capital would decrease the demand for private capital. In addition, the study demonstrates that the services of public capital enhance the productivity of private capital.

Catherine J. Morrison Paul and Amy Ellen Shwartz

Morrison and Shwartz use a cost function of infrastructure investment to study the relationship between infrastructure investment and manufacturing productivity.⁽⁷²⁾ The authors take into consideration the stock of privately owned and publicly owned infrastructure, as well as the quantity and prices of output, labour and energy for 48 U.S. states from 1970-1987. The authors find that infrastructure investment provides a significant return to manufacturing firms and augments productivity growth. They note that returns on infrastructure/shadow prices are significant (estimate of -0.4761 dollar per unit of public capital). These savings, however, decline from 1970 to 1987 for manufacturing firms. The authors also suggest that the net return to investment in public infrastructure accruing to manufacturing is close to zero. In their opinion, the net benefits of infrastructure investment may or may not be positive, depending upon the social costs of infrastructure investment and the relative growth rates of output and infrastructure.

Tarek M. Harchaoui and Faouzi Tarkhani

Harchaoui and Tarkhani⁽⁷³⁾ use the cost function approach to quantify the contribution of public capital⁽⁷⁴⁾ to productivity growth in the Canadian business sector. Their approach also incorporates demand and supply forces, including the contribution of public capital, which may affect productivity performance. The authors estimate the model using disaggregated data composed of 37 industries in the Canadian business sector for the period 1961-2000. The results indicate that the main contributors to productivity growth, both at the industry and aggregate levels, were technical change and exogenous demand representing the effect of aggregate income and population growth.

Three mean empirical findings are derived from the research of Harchaoui and Tarkhani. The first is the measure of public capital effects on business sector production costs, level of output and demand for labour, capital, and intermediate goods. The second is the marginal benefits to industry sectors and aggregate business sector when public capital increases. The last is the contribution of public capital to productivity growth.

The authors show that an increase in public capital reduces the total cost of output production in almost all industries. They use cost elasticity value to measure this impact. They find that cost reductions are relatively large for some industries. When there is an increase of 1% in public capital, it reduces cost production of output for 15% in transportation, for 12% in wholesale, for 9% in other utility, and for 12% in retail. These reductions are in range of 0.2% to 6% in the manufacturing sector, and in range of 0.1% to 5% in the primary sector. The average cost elasticity of public capital for the Canadian business sector is about -6.20% during the period of 1961-2000.

Harchaoui and Tarkhani define the marginal benefit of public capital as a measure of producers' “willingness to pay” for additional unit of public capital. So in some industries such as construction, transportation, wholesale, retail, communication and other utility, producers are willing to pay from 19 cents to 42 cents for an increase of the marginal benefits of $1 in public capital. For all industries, $1 marginal benefits increase in public capital results, on average, in 17 cents of yearly cost savings⁽⁷⁵⁾ for producers.

The authors conclude that public capital accounted for about 18% of the overall business sector multifactor productivity growth over the 1961-2000 period, but the magnitudes of the contribution of public capital to productivity growth vary significantly across industries, with the largest impact occurring in transportation, trade and utilities. Nevertheless, the authors note that the magnitude of infrastructure capital contributions to productivity growth is relatively modest in comparison to the contribution of exogenous demand and technological change. They also conclude that most of the contribution of public capital to productivity growth occurred in the pre-1973 period and, since 1981, public capital has made a small contribution to multifactor productivity. Harchaoui and Tarkhani find that public capital plays a positive but small role in supporting productivity growth in contrast to the results reported by Wylie (1996)⁽⁷⁶⁾ for Canada and other proponents⁽⁷⁷⁾ of large contributions of infrastructure capital.

3.2.3 Summary

The studies reviewed in this section all look at the role infrastructure plays in reducing costs. Although the authors employ various cost functions, the translog cost function is the most common specification. The translog function can be estimated with traditional OLS regression and the function is well specified. For that reason, it is a common function to be used.

Most authors that have used the cost function approach find that the shadow prices of public capital with respect to cost is around -.30, however, estimates to range from -0.15 to -0.4761. Others, as Bagala et al., estimate the cost-saving for business sector around of 11% in term of rate of return to public capital. Overall, the consensus is that public capital is cost reducing and that estimates using this methodology imply a much smaller effect than those estimated with the production function. Unlike the production function models, cost models tend to suggest that public and private capitals are substitutes and are not complementary. The main reason for this difference is that the cost model incorporates factor prices and is typically estimated with several equations, thus allowing researchers to estimate the cross elasticity between all model inputs.⁽⁷⁸⁾

Most of the studies reviewed in this section test for endogeneity (i.e. is it costs that drive infrastructure spending, or infrastructure spending that drives costs) and find that infrastructure does impact costs and not the other way around. The Hausman test is the most commonly used instrument to test for endogeneity.

The studies reviewed in this section, although not as extensively consensual as those that use the production function, do have similarities. First and foremost, they show evidence that the relationship between public and private capital as well as costs do change over time, and therefore, caution should be taken when estimating these relationships. Unlike the production function approach, estimates do not vary as greatly from country to country and from national to sector level data.

For decision-makers the results presented in this section reinforce the positive and beneficial impacts of public capital investment demonstrated by authors who have used the production function approach. Using the prices of factor of production as an input into the cost saving generated from public infrastructure investment, authors have been able to demonstrate these benefits. However, these benefits tend to be smaller and take longer to accrue than what would be concluded using the production function approach. For this reason, decision-makers should consider the pay back from investments in infrastructure over the long term and should expect only modest returns.

Once again, it is important to consider some of the issues raised in the previous section. For example, estimation of the true impacts, and the circumstances under which varying impacts occur are challenged by a host of data and econometric problems. Additionally, these studies were not designed to investigate or address the issue of equity or distribution of public benefits.

3.3 Growth Models

Unlike the production and cost function approaches, most growth models look at the impact that infrastructure has on all inputs of production at the same time. This is because growth models are interested in the impact on total productivity and not just individual factors of production like labour and/or capital.

3.3.1 Theoretical Background

The majority of growth models use total factor productivity (TFP). Factors of production like labour and capital tend to have strong inter-relationships which make it difficult to estimate the individual impacts of either. As a result, it is often easier to estimate the impact of all factors of production on output. This is exactly for what TFP is used. Growth models are used to understand the relationship between TFP and factors of production, like public capital.

3.3.2 Empirical Results

The three TFP models that are most commonly used are the Solow, Kendrick and Divisia-Törnquist models. The Kendrick index is based on a linear production function while the Solow model uses a non-linear production function.⁽⁷⁹⁾ One of the criticisms of the Solow model is that only under constant returns to scale and in competitive equilibrium⁽⁸⁰⁾ will TFP be equal to the variation in the aggregate output not due to variation in aggregate input.⁽⁸¹⁾ The Divisia index approach is used to calculate the impact of public capital on total factor productivity. Divisia-Törnquist model is defined as a weighted average of rates of growth in which the components are weighted in proportion to their total value share. An estimate of TFP Index is not comparable to other estimates of TFP because other estimates are single variables and not indexes.

Eva Aguagyo, Pilar Expósito, Xose Anton Rodríguez and Emilia Vázquez

In “Human Capital and Other Factors of the Total Factor Productivity in Spanish Regions,” Aguayo, Expósito, Rodríguez and Vázquez use the Divisia index to explain the relationship between TFP and the factors that may determine TFP.⁽⁸²⁾ The authors define infrastructure as highways, ports, hydraulics constructions, railways, and use data from 1976-1995 to calculate the components of the factors of TFP. The authors consider endogeneity a serious issue; however, they argue that conventional methods of dealing with endogeneity would jeopardize the reliability of the estimates because of the small sample size. Hence, the authors graph the regression residuals and find that there is no evidence of more than one possible estimate - unit root problem.⁽⁸³⁾ In addition, they test for the possibility that estimates might be getting larger through time (change in estimates variability or heteroscedasticity) and that variables used in the estimation are correlated⁽⁸⁴⁾ from one period to the next and thus suffer from a problem of autocorrelation. The authors also use a statistical test called the Hausman test to determine if the fixed-effects or a random-effects model is more appropriate⁽⁸⁵⁾.

The study finds that for all of Spain partial labour productivity was higher than the total productivity of all factors. The authors find this to be the result of the differentiating effect of the capital input. Over the period capital grew much faster than the gross value added and as a result the partial capital productivity was negative offsetting the increases in partial labour productivity. The reason for this is because total factor productivity is being defined by the sum of partial labour productivity and partial capital productivity. In addition, the authors find that public capital, and human capital exhibit a positive effect on the growth of productivity. The authors also find that the estimated impact of public infrastructure on TFP is 0.04 (percentage growth in TFP per unit of public capital). For example, if investments in public infrastructure are to grow by 1 percent, total factor productivity index would increase by 0.04 percent.

Frederico Bonaglia, Eliana La Ferra and Massimiliano Marcellino

In “Public Capital and Economic Performance: Evidence from Italy”, Bonaglia et al. present the impact of infrastructure on regional and national growth in Italy using a Solow growth model.⁽⁸⁶⁾ The authors use three different methodologies, however only the growth modelling approach is discussed here. As indicated before, the authors use annual regional data from the period 1970-1994 and focus on the impact of investment in roads, airports, railways, ports, water, energy, communication schools, public buildings, sanitation and public land. The authors use several instruments to account for endogeneity and find that it is of no concern in this case. Overall, the authors find that the growth of public capital has a positive and a rather large impact on total factor productivity growth. The share of TFP growth that can be attributed to public capital is approximately 0.47 (percentage growth in TFP per unit of public capital) for all of Italy.

David Canning and Peter Pedroni

Canning and Pedroni's “The Effect of Infrastructure and Long Run Economic Growth” examines the long-run impact of infrastructure on per capita income in a panel of countries over the period 1950-1992.⁽⁸⁷⁾ The authors use a total factor productivity model as well as an applied Granger causality test⁽⁸⁸⁾ and co-integration tests to yield robust results that are free of the problem of heterogeneity. The authors determine the causality direction and magnitude of the effect of public infrastructure on income. The results provide evidence that, in the majority of cases, infrastructure investments induce long-term economic growth effects; however, there is a great deal of variation in the results across individual countries.

The results demonstrate that telephones, electricity generating capacity and paved roads are provided at close to the growth maximizing level on average but are under-supplied in some countries and over-supplied in others. According to the model, there is a growth maximizing level of infrastructure above which the diversion of resources from other productive uses outweighs the gain from having more infrastructure. Below this level, increases in infrastructure provision increase long-term income, while above this level an increase in infrastructure reduces long run income. It follows that the effect of infrastructure provision on long run income levels gives an indication of where a country's infrastructure stock stands relative to its optimum level from a growth maximizing perspective.⁽⁸⁹⁾

Philippe Martin

Martin demonstrates the contribution of different types of public policies on growth, economic geography and spatial income distribution.⁽⁹⁰⁾ Martin constructs a two-region endogenous growth model to study where industrial location and public infrastructures play key roles in public policy. His model implies that an improvement⁽⁹¹⁾ in public infrastructure that reduces transaction costs inside the poorest region decreases both the spatial concentration of industries and the growth rate. In contrast, the model also implies that an improvement in public infrastructure that reduces transactions between regions has the opposite effect. The author admits that his model is incomplete and that certain assumptions made in the analysis may be unfair to regional policies. Nevertheless, Martin asserts that his results indicate that regional policies can have negative consequences, not only at the local level but also at the national level. Martin further theorises that public policies, which reduce the cost of innovation,⁽⁹²⁾ can attain the objectives of higher growth and more even spatial distribution of both income and economic activities.

3.3.3 Summary

The authors reviewed in this section all use growth models to demonstrate the impact of infrastructure on productivity. Each author uses different theoretical constructs to study the relationship:

• Aguagyo et al. use a Divisia index model to study the impact of infrastructure on Total Factor Productivity.
• Bongalia et al. use a Solow growth model approach to analyze the impact of infrastructure on regional and national growth in Italy.
• Canning and Pedroni use a total factor productivity model to study the long-run impact of infrastructure on per capita income in a panel of countries.
• Martin constructs a two-region endogenous growth model to demonstrate how contributions to public policy from improved infrastructure can, for example, lead to a more even distribution in income.

Despite using different modelling methods, the authors reach a similar conclusion - public capital does have a positive impact on economic performance. Other key findings are as follows:

• The authors reviewed in this section note that reverse causality is not a problem.
• There is evidence that public capital formation exhibits negative returns beyond a certain threshold at which point investment into infrastructure is not beneficial.
• There is some evidence that infrastructure investment creates income divergence across regions. Further, public policies that use infrastructure to bring about a more equal distribution of economic activities across regions can result in lower growth for both regions. These results could be of interest to public policy especially in developed countries where public infrastructure development is mature and there exists income divergence.

3.4 General Equilibrium Models

3.4.1 Theoretical Background

The approaches described above are based on the estimates of the technical constraints facing firms in the form of production or cost functions. While useful for their "bottom-line" estimates of productivity effects, several authors⁽⁹³⁾ have argued that theoretical models shed little light on how and why infrastructure influence firms, markets, labour, prices, and equilibrium levels of production in each sector of the economy. More comprehensive economic models of the productivity impacts of infrastructure, which include a broader range of factors, exist. These are generally referred to as general equilibrium models⁽⁹⁴⁾. They are equipped to provide an understanding of the whole economy, using a bottom-up approach. That is, general equilibrium models use individual markets and agents and conclude with a comprehensive model that simulates their behaviour in a price-changing environment.

General equilibrium models are typically capable of modelling a multitude of different goods markets, assuming flexible prices and market agents' ability to choose. In any market system, the prices and production of all goods are interrelated and changes in the price of one good may affect another price. Calculating the equilibrium price of just one good, in theory, requires an analysis that accounts for all of the different goods that are available. One of the major qualities of the general equilibrium models is in their ability to trace the consequences of large changes in a particular sector throughout the entire economy. They share this property with input-output analysis⁽⁹⁵⁾ but allow a more flexible treatment of the consumer side of the economy and are less rigid in the requirements placed on the productive side. This flexibility in the conceptual framework of general equilibrium models allows for the possibility of variations in income, and is especially useful when modelling major policy changes that frequently have significant impacts on the distribution of income.

3.4.2 Empirical Results

Andrew F. Haughwout

Haughwout⁽⁹⁶⁾ proposes a spatial⁽⁹⁷⁾ general equilibrium model of an economy with non-traded, localized⁽⁹⁸⁾ public goods such as infrastructure. He also offers a method for identifying the role of public capital in firm production and deriving household preferences to be used in the model. According to the author, public capital may influence social welfare in two ways: (1) by raising income via increased private productivity and (2) by increasing benefits enjoyed by households via heightened economic services. Haughwout suggests that results from productivity and household studies must be combined with cost information as this will help to determine the optimal level of public investment.

Based on the empirical evidence from a sample of large U.S. cities, Haughwout suggests that while public capital provides significant productivity and consumption benefits, an ambitious program of locally funded infrastructure provision would likely generate negative net benefits for these cities given that substantial increases in city public infrastructure provision are unlikely to provide social benefits sufficient to offset their costs. The author suggests that, on the other hand, some of the benefits of city infrastructure investments will likely spill over into neighbouring suburban jurisdictions. From the point of view of the central city, it is quite likely that generous capital aid from other levels of government might make substantial capital investments worth their local cost.

The author concludes that his model and empirical evidence emphasize the importance of infrastructure investments in affecting the relative attractiveness of places, potentially redirecting economic growth from infrastructure-poor areas to those, which have invested more heavily. The author also suggests that the estimates of infrastructure effects presented in the study may be higher in reality as some benefits resulting from new infrastructure investments are redirected and consumed in other neighbouring suburban areas.

In another paper, Haughwout⁽⁹⁹⁾ examines indirect relationship between state infrastructure policies and aggregate productivity for the United States. The author develops and uses a general equilibrium model of regional growth that incorporates the local impacts of infrastructure investments and other fiscal differentials. Using his theoretical model, he concludes that infrastructure investments either funded or provided by higher levels of government (Federal and State) have significant effects on local land values and employment as additional infrastructure created locally makes the area more attractive. At the same time, highways contribute to a decentralization of employment⁽¹⁰⁰⁾ that might undermine economies of agglomeration⁽¹⁰¹⁾ and productivity growth as firm's concentration would decrease given availability and attractiveness of new and modern infrastructure in new areas.

Douglas Holtz-Eakin and Mary E. Lovely

Holtz-Eakin and Lovely⁽¹⁰²⁾ construct a general equilibrium model that includes several features of the empirical literature on infrastructure productivity: potentially different effects on the manufacturing and non-manufacturing sectors, potential cost reductions in manufacturing, and returns to scale in manufacturing. The authors also note that their model accounts for factor price changes induced by the provision of infrastructure, assuming that benefits provided by new infrastructure can lead to lower prices.

The analysis of the model suggests that the results are based upon the degree to which infrastructure investments can lead to a reduction in the fixed costs of production or can provide a subsidy to variable costs, which means that firms' production costs are lower when suitable infrastructure is available. The authors note that there is little evidence of direct output being positively affected by infrastructure investments and, as a result, there are no productivity effects outside the manufacturing sector and no influence on output per establishment. However, the authors conclude that infrastructure investments can lead to an increased number of individual establishments. This would lead to an increase in manufacturing output. It would also lead to increases in manufacturing productivity to the extent that the increase in the number of establishments can create external returns, given increased concentration of the firms, and hence benefit from economies of scale.

Felix K. Rioja

Rioja⁽¹⁰³⁾ designs and tests a two-sector neoclassical dynamic general equilibrium⁽¹⁰⁴⁾ model, which includes public infrastructure by assuming the existence of an external input in the production process, which is provided by the government⁽¹⁰⁵⁾. The author estimates the model by using data from seven countries.⁽¹⁰⁶⁾ His results indicate that devoting additional resources to infrastructure investment can payoff in terms of sizable increases in output and private investment. Rioja's significant contribution is to estimate aggregated welfare effects of infrastructure investment. According to him, more infrastructure investments do not always improve welfare, and very high levels of infrastructure investments can, in fact, adversely affect welfare. The author provides specific quantitative recommendations for infrastructure policy that result in the largest welfare gains - he suggests how much more to invest in public capital per year. For the seven Latin American countries analyzed in the study, maximum welfare gains can be obtained by increasing infrastructure investment by about 4% of GDP (presently being about 6% of GDP).

Jeremy B. Rudd

Rudd⁽¹⁰⁷⁾ tests a modified version of the canonical Roback public goods pricing model⁽¹⁰⁸⁾ based on the assumption that land rents and wages differ across regions according to the presence or absence of region specific characteristics. Before proceeding with a description of his model, the author lists several limitations related to the production function approach in estimating infrastructure's impact on productivity - namely, requirements of inputs and input prices, specification problems, inclusion of state-specific fixed effects and choice of functional form.

According to Rudd, the basic advantage of the general equilibrium method is that, although it does require data on regional public capital stocks, it does not require estimates of private capital or labour inputs. This is a clear advantage because often there are no regional data series of sufficient quality collected on private and public capital by industry. The author claims that, by using less objectionable existing measures of public capital, he can obtain an "independent" estimate of the productive effect of private capital, one which does not directly rely on a production or cost function estimate and limitations related to the functional forms of both approaches.

Rudd notes that in addition to the problems resulting from omitted variables, another caveat regarding the results of the study is related to data limitations. Estimates are based on a single cross section of Census data and cover only 40 urban regions, as there are only few cities whose public investment data are long enough to permit the estimation of a capital stock series. The author notes that results would be much more convincing if they estimated over a panel of standard metropolitan statistical areas, primarily because such a procedure would permit the inclusion of controls for fixed effects In turn, this would better allow to determine whether the public capital terms are merely proxying for other characteristics, such as how wealthy urban regions are.

In his model, Rudd estimates the implied productive contribution of public capital⁽¹⁰⁹⁾ measured as a percentage cost reduction that can be obtained from a one percent increase in public capital per person. For highway infrastructure, investments are reported to consistently raise productivity, while results for water and sewer infrastructure are not as significant. Water infrastructure is estimated to have only some productive value, while sewer capital has none. At the same time, the author notes that using a methodology that is very different from the standard production or cost function-based approach, he was able to find a small but statistically significant output elasticities for public capital.

Rudd reports that his estimate of the output elasticity of total public capital was about 0.08. For all infrastructure capital, the author reports an estimated elasticity of 0.12, while the elasticity for highway capital was reported at 0.07. The output elasticity of total public capital is significant only at the 10% significance level, while the other elasticities are significant at the 1% significance level. It should be noted that these results are not robust to different specifications. In another specification, Rudd finds that the output elasticities of total public capital, infrastructure capital and highway capital are 0.10, 0.08 and 0.08, respectively.

Rudd emphasizes in his conclusion that he did not review the question of whether the measured positive effect of public capital on private output lends support to the view that government should increase its spending on infrastructure because this would require knowledge of the social cost of raising additional public funds, including any excess burden that might obtain from imposing higher tax rates.

3.4.3 Summary

The papers reviewed in this section are all based on the general equilibrium model that provide a more comprehensive framework as it offers an understanding of the whole economy, using a bottom-up approach. The general equilibrium model simulates behaviour of individual agents in a price changing market environment using supply and demand equilibrium. Compared to restrictive theoretical frameworks discussed above, the general equilibrium model is capable of analysing dependencies and relations between various components of complex economic systems.⁽¹¹⁰⁾

Some of the main findings of the papers reviewed in this section:

• The general consensus among all authors is that public capital investments positively impact regional economic performance, either due to increased productivity or as a result of increased number of individual establishments. Haughwout emphasizes the importance of infrastructure investments in affecting the relative attractiveness of places suggesting that infrastructure investments can potentially redirect economic growth from infrastructure-poor areas to those which have invested more heavily.
• It is also suggested that because some benefits resulting from new infrastructure investments can be redirected and consumed in other neighbouring areas, the positive regional infrastructure effects presented in the studies may be higher in reality.
• Some authors note that infrastructure investments may lead to an increased number of individual establishments that lead to regional employment growth and potentially increasing productivity levels, to the extent that the increase in the number of establishments can create external returns given increased concentration of the firms.
• Additional infrastructure created locally also increases land values in the region by making the area more attractive for new businesses.
• Optimal level of infrastructure investments is required to improve welfare, as very high levels of infrastructure investments can, in fact, adversely affect welfare simply due to high associated costs.

3.5 Data-Oriented Models

3.5.1 Theoretical Background

Because of theoretical limitations and significant empirical controversies over the impact of infrastructure on private sector productivity, several researchers choose to use as little economic theory as possible. Most often, these researchers apply Granger-causality tests⁽¹¹¹⁾ in a multi-equation setting to find relationships between variables. These causality tests are typically carried out within the framework of Vector Auto Regression (VAR) models.⁽¹¹²⁾ In a VAR model, a limited number of variables is distinguished and explained by their own lags and the lags of the other variables, meaning that all variables are treated as jointly determined. This implies that no a priori causality directions are imposed unlike in single-equation econometric frameworks that exclude the dynamic feedbacks among the variables in the model. In theory, the causality might run from output to infrastructure, which is the opposite of what is usually assumed. An additional advantage of VAR models is that they allow for and analyze the fact that infrastructure might indirectly influence output by raising the return to machinery and equipment of private capital.

3.5.2 Empirical Results

Stefan Mittnik and Thorsten Neumann

Mittnik and Neumann examine three questions related to the role of public investments in the economy: (1) Does higher public investments lead to increase in economy output?, (2) What is the direction of causality between output and public investments? , and (3) What are the effects of budget shift from public consumption to public investment?⁽¹¹³⁾ The authors note that the VAR approach is particularly suitable to answer these questions as it imposes little a priori structure in terms of casual directions, allowing analysis of direct and indirect relations between model variables as well as short- and long-term effects.

Based on the empirical data set from six countries,⁽¹¹⁴⁾ the authors conclude that although VAR results are different from country to country, public investments exert a positive effect on output, and shifts from public consumption to public capital investments have short- and long-term positive effects on economic growth. Specifically, impulse response functions of GDP to a 1% shock in public investment indicate positive short- and long-run elasticity, which, with one exception, do not exceed 0.1%. The exception is Canada, where the authors' estimates show an increase of 0.15% after 20 quarters. The authors do not find any evidence to support the hypothesis of reverse causation from output to public investment.

S-H. Lau and C. Sin

Lau and Sin use the VAR procedure to assess the impact of public capital on economic performance. According to the results obtained by Lau and Sin,⁽¹¹⁵⁾ the impact of public capital on economic performance is much smaller than reported by studies based on the single-equation regressions (Aschauer and his followers). Lau and Sin estimate that the elasticity of output with respect to public capital over 1925-1989 in the U.S. was only 0.11. Because of the nature of the model used, Lau and Sin were only able to consider the issue of causality between GDP and one type of public sector investment in infrastructure and concluded that public sector infrastructure investments impact economic growth.

Alfredo M. Pereira and Oriol Roca-Sagalés

Pereira and Roca-Sagalés⁽¹¹⁶⁾ assess regional impacts of infrastructure on private sector performance measured by analysing regional output and employment series. The authors estimate VAR models for Spain and its seventeen regions. Their results suggest that infrastructure investments positively affect private output and crowd-in private sector inputs. In other words, the authors find that public investment in infrastructure does not compete with or discourage private expenditure on infrastructure. According to the authors, the estimation results also suggest that the aggregate effects of public capital cannot be captured in their entirety by the direct effects for each region from public capital installed in the region itself. According to Pereira and Roca-Sagalés, infrastructure contributes to disparity between regions as central regions are typically the main beneficiaries of new investments in infrastructure and, hence, infrastructure can be considered as the source of increasing disparity between central and peripheral Spanish regions.

Jan-Egbert Sturm, Jan Jacobs and Peter Groote

Using three data sets related to Dutch economic development, Sturm, Jacobs and Groote⁽¹¹⁷⁾ test the impact of infrastructure investments on productivity in a VAR framework based on GDP, public infrastructure capital and private machinery and equipment capital. Compared with other studies, the authors divide infrastructure investments into basic infrastructure and complementary infrastructure.⁽¹¹⁸⁾ Results of the causality tests provide evidence only for a unidirectional relationship between infrastructure and GDP; that is, investments in infrastructure cause changes in GDP. The authors also conclude that splitting up the infrastructure series into basic and complementary infrastructural capital spending shows that only basic infrastructure causes GDP changes. This may be explained by the difference between how basic infrastructure impacts economy compared with complementary infrastructure. Supplementary infrastructure, as specified by the authors, would have little or no direct impact on economic performance but would rather create social benefits. There was no evidence found that infrastructure might indirectly influence GDP through private machinery and equipment investments.

Sturm, Jacobs and Groote also conclude that based on the data set used, infrastructure investments have significant positive effects on GDP in the Netherlands in the second half of the nineteenth century. At the same time, the authors note that⁽¹¹⁹⁾ infrastructural investment might not have the long-run effects on production as is often assumed and that positive long-run effects of basic infrastructure are missing nowadays, leading to the final conclusion that public capital investments hardly affects output anymore.⁽¹²⁰⁾

Metin Karadag, A. Ozlem Onder and Ertugrul Deliktas

Karadag, Onder and Deliktas⁽¹²¹⁾ investigate the impact of public capital formation on private manufacturing sector performance at national and regional levels in Turkey. The authors also choose to employ a vector auto regression model to avoid methodological problems associated with the production function approach. The model is based on output, labour, private and public capital. The results indicate that public capital has a positive effect on private sector output in most regions and at the national level. The long-term accumulated elasticity of output with respect to public capital was negative in only two regions - the Meditteranean (-0.171) and the Black Sea (-0.250). At the national level, the long-term accumulated elasticity of output with respect to public capital was 1.45. The results also reveal that public capital crowds-in private sector inputs in some regions, as additional infrastructure investments made them more attractive. The authors suggest some spillover effects as public investment in one region have some positive effect on the production process of other regions.

Xiaobo Zhang and Shenggen Fan

Zhang and Fan⁽¹²²⁾ also use a data based approach in their study and conduct a causality test to investigate the relationship between technology and infrastructure. The methodology the authors apply is a dynamic system Generalised Method of Moments⁽¹²³⁾ estimator to the set of auto regression equations.⁽¹²⁴⁾ The authors conclude that infrastructure development and productivity often affect each other in the long-term but not in the short term. This finding is noted to have significant implications for evaluating new infrastructure investments because of the established relation between infrastructure investments and productivity.

In order to examine the magnitude of the productivity impact of infrastructure, Zhang and Fan explore different model specifications and conclude that a model in levels⁽¹²⁵⁾ yields positive and larger effects, while a model in differences⁽¹²⁶⁾ gives insignificant results. More specifically, the coefficient that captures the productivity effect of roads is found to be 0.019 but statistically insignificant when the regression is in difference form, and when a level equation is used this coefficient is estimated to be 0.078 and statistically significant. However, the estimate declines from 0.078 to 0.069 when autocorrelation is considered, and further declines to 0.043 when the level equation is corrected for an endogeneity problem. These findings are said to be consistent with findings in previous literature.⁽¹²⁷⁾ Nevertheless, the authors conclude that infrastructure development has a significant and positive impact on productivity growth.

Cesar A. Calderon and Luis Serven

Calderon and Serven⁽¹²⁸⁾ conduct an empirical evaluation of the impact of infrastructure development on economic growth and income distribution. The study is based on a large panel data set from over 100 countries and for 1960-2000. The authors extend previous studies along various dimensions; that is, instead of focusing on one particular infrastructure sector, they simultaneously consider transport, power and telecommunications. Also, both quantity and quality⁽¹²⁹⁾ of infrastructure were taken into account in contrast with other studies, where typically only quantity of infrastructure is considered. The authors use several GMM estimators and report results using both disaggregated and synthetic measures⁽¹³⁰⁾ of infrastructure quantity and quality.

As a preliminary result, the authors note that the correlation between growth and the principal component of infrastructure stocks equals 0.18. The correlation between growth and individual stocks of infrastructure is also found to be positive - 0.15 for main lines, 0.13 for power generating capacity and 0.12 for road length. The authors perform a variety of specification tests and the results suggest that the causal impact of infrastructure quantity and quality on growth and inequality is positive. They conclude that economic growth is positively affected by changes in infrastructure assets quantity and quality. Analysis performed suggests that these impacts are economically significant (e.g. more infrastructure investments are required to fuel continuous economic growth) and highlight the growth acceleration that would result from increased availability and quality of infrastructure.

Another conclusion the authors note is that income inequality generally declines with higher infrastructure quantity and quality. They also suggest that infrastructure development can be highly effective to combat poverty and boost economic growth in less developed countries because it will provide basic needs in the areas with little or no infrastructure.

3.5.3 Summary

Papers reviewed in this section are all designed on data based models with no a priori causality directions imposed between economic growth and infrastructure investments, unlike in single-equation econometric framework that typically excludes the dynamic feedbacks among the variables in the model.

Despite the fact that all papers reviewed in this section use different data sets and theoretical constructs, all authors in general agreed that public capital investments positively impact private sector output. Some authors conclude that infrastructure development productivity often affect each other in the long-term but not in the short-term. Other results of the papers reviewed in this section are as follows:

• The authors do not find any evidence to support the hypothesis of reverse causation from output growth to investments in infrastructure. Furthermore, only basic infrastructural spending (as opposed to complementary infrastructural spending) is found to cause changes in output.
• Some authors find that infrastructure is a source of increasing disparity between regions. Others conclude that public investment in one region may have positive spillover effects on the production processes of other regions. Decision-makers need to consider the impact of investment decisions at a regional level and not just nationally.

4 Data Gaps and Problems

Policy implications on the link between infrastructure and productivity are made under the assumption that estimation techniques are appropriate. However, as discussed in the literature, there are a host of data gaps and problems associated with ascertaining the causal relationship between infrastructure and productivity. In addition, some of the more simplistic approaches to modelling the relationship between infrastructure and productivity are useful for telling only the direction of the net effect of infrastructure on growth and not its magnitude. These data gaps and problems related to estimation techniques are summarised below. In order to establish robust correlation between infrastructure and productivity, these gaps will have to be filled and the problems resolved. Yet there are often costs associated with addressing econometric issues. For instance, the sample size may be reduced considerably, which imposes restrictions on how the results may be interpreted. Further, resolving certain econometric issues may be difficult if not impossible due to data limitations.

4.1 Estimation Related Problems

4.1.1 Definition of infrastructure

There is no standard definition of infrastructure. Various authors model a variety of different indicators of infrastructure. In the absence of a standard definition of infrastructure, it is challenging to generate estimates that are comparable. With respect to public policy, having no common definition of infrastructure makes it difficult for decision-makers to develop uniform policies with respect to infrastructure.

4.1.2 Missing Variables

Explanatory factors that may explain changes in the productivity levels but are not related to infrastructure investments are simply omitted from some models. Ignoring these factors overstates the impact of infrastructure on productivity which can misinform decision-makers about the expected results from infrastructure investments. Some of the variables suggested by E.M. Gramlich , J.A. Tatom, Catherine J. Morrison-Paul and Amy Ellen Shwartz include the amount of public infrastructure expenditures and the price or quantity of energy.⁽¹³¹⁾ If these variables are added to other models, the estimates of infrastructure effect on productivity are much lower in comparison to models that omit these variables. Growth theory also stresses the importance of production factors such as knowledge, human capital or research and development investments. According to Piotr Rosik, estimates of infrastructure impacts on productivity very often lack references to these factors.⁽¹³²⁾

4.1.3 Long-term Relations Misspecification

To avoid stationarity problems, some researchers use various forms of differencing methods. The basic problem with these studies is that they estimate only short-term impacts, but cannot capture long-term impacts. In other words, first differencing methods override any long-term relationships. According to Xiaobo Zhang and Shenggen Fan, there are often long-term lags between infrastructure investments and productivity growth.⁽¹³³⁾ It has been proposed that researchers should first test for causality in their data to check the length of lagged relationships before specifying a final model and estimating procedure on the relations between investments or stock of infrastructure and productivity growth.

4.1.4 Causality Direction

Since variables in a single regression model are likely to be endogenous, the true direction of causality is yet another puzzle mentioned in various studies. Causality may run in both directions. While infrastructure may give rise to higher productivity and output, past and future economic growths also tend to increase the demand for infrastructure services and, hence, induce increased supply of infrastructure. Although it is difficult to determine the direction in which the causality runs, a number of studies apply the Granger causality test to the data. Using a series of lead-lag tests, some authors conclude⁽¹³⁴⁾ that the increase in private sector productivity levels leads to the growth of public infrastructure. Other authors⁽¹³⁵⁾ do not agree with the direction of causality that result from these studies. They claim that slowdowns in productivity in the 1970s appear larger in the industries highly dependent on automobile transportation, despite massive road-building during the 1950s and 1960s. It is important to note that estimates of strong relations between productivity and public capital obtained by Fernald are very similar to those of Aschauer. One of the most common approaches suggested and used by different authors in more recent studies to overcome the problem of the direction of causality is the vector auto regression procedure. This approach treats every variable in the system of equations as a function of the lagged values of all other variables in the system.

4.2 Data Related Problems and Gaps

4.2.1 Stationarity

Data series used as inputs in some models⁽¹³⁶⁾ are often not stationary - in other words, several data series are moving in the same direction over time; hence, they are positively correlated with each other. Such correlations often cannot be equated with causality. Correlations estimates in such models may therefore be spurious. A common way to solve this problem is to use year-to-year changes in the measures of public capital instead of the levels. This approach usually generates much lower estimates of marginal rate of return of infrastructure investments or results from these models often lead to the conclusion that the effect of public infrastructure on economic growth is insignificantly different from zero.

4.2.2. Spurious Correlation

Correlations between data series that are both numerically large and judged statistically significant may actually contain no real information. Such correlations are called spurious (or nonsense) correlations. Spurious correlation exists when the dependent variable (productivity in this case) and independent variable (infrastructure in this case) evolve together because both are influenced by another variable that is not included in a particular model. Researchers who do not test for this problem run the risk of generating results that exist simply because output and infrastructure investment have moved in the same direction over time and not because there is a meaningful and useful relationship between the two variables. For decision-makers, spurious correlations can mean misdirected investment and potentially negative impacts on the economy.

4.2.3 Multicollinearity

The problem of multicollinearity arises when two (or more) variables in the model are related in the sense that they measure the same thing. Few studies address multicollinearity as a problem. Especially in the case of production and cost functions, labour and public capital tend to have a strong relationship, making it challenging to estimate the individual impacts of either input on output or productivity. This creates measurement error or biased estimates which make the estimation results misleading and can result in the misallocation of infrastructure investments.

4.2.4 Limited Data Availability

Limited availability and quality of infrastructure and public capital stock related data is commonly acknowledged. Such limitation significantly diminish the number of options for sophisticated econometric analysis.  For example, limited number of data observations (e.g. small sample size) imposes restrictions on the types of models that can be used, the hypotheses that can be tested and the methods that may be employed for correcting common econometric problems listed above. Regression analysis using available aggregated data (e.g. at provincial/territorial levels) on infrastructure investment may also lead to erroneous or misleading results not necessarily because public investment in infrastructure has no effect on private productivity, but rather because of weaknesses in the data used to quantify this relationship. To be more specific, there can be a considerable variability in public infrastructure investments across the provinces for reasons that may be unrelated to expected return on investments. This would likely yield large standard errors and, consequently, parameter estimates that are statistically insignificant.

5 Key Findings

5.1 Key General Findings

In the late 1980s, economists began to take an interest in explaining the productivity slowdown experienced in the 1970s. Many researchers found that investments in public infrastructure have significant positive impacts on private sector productivity and economic growth. The original studies were primarily based on classic economic model approaches, namely production and cost functions and generally reported a positive impact of infrastructure investments on economic growth and productivity. This suggested that decision-makers should invest in infrastructure.

Following these works, other researchers suggested that depending on how econometric and data corrections are implemented, there might be no significant relation between public capital investment and private sector productivity using the production or cost function approach. Other critiques of the classical models indicated that public infrastructure expenditures are only one of many explanatory variables of lower productivity level and that the models often lack reference to other production factors such as knowledge, investments in human capital or research and development.

Several additional findings were also noted throughout the studies:

• Some studies indicated that public capital is complementary and that it promotes private capital formation.
• Most of the authors agree that core infrastructure, such as roads and railways, tend to exert the most influence on productivity.
• Some authors have noted a negative relationship between investments in public infrastructure and employment levels. They have found, consistent with economic theory, that these are substitutes for each other.

There was a significant amount of discussion on some of the data and econometric problems. For example, one problem with single equation models is the direction of causality, as it is just as possible for output growth to cause changes in demand for public capital stock as it is for more infrastructure investments to cause an increase of private sector productivity. The data-based models allowed researchers to overcome the problem of the direction of causality and most authors who used this type of analysis suggested that infrastructure investments positively affect private sector output and productivity. At the same time, studies based on this approach came to a conclusion that public capital is not as productive as it has been shown in studies based on production or cost functions.

It is important to note that the corrections for statistical problems only quantify the relation between infrastructure and productivity, holding other factors constant. However, even though the parameter estimates with these corrections may be lower, this doesn't suggest that infrastructure is less important, it just illustrates that the benefit depends on similar increases in other input variables - in all likelihood, the impact of all variables would be less if similar changes were not seen in other variables.

After reviewing all the approaches and reported problems, it is quite challenging to be confident in the specific quantitative estimates in the models presented above. This is partly due to disadvantages presented in many of the studies, like difficulties in defining the quantity of the relevant public capital stock, constructing relevant data series, model misspecifications, spurious regression, missing variables, the direction of the causality, and data problems related to the fact that the results of aggregate time series do not show the real regional consequences of public infrastructure investment. The differences in modelling techniques make it impossible to directly compare results. However, the more important is the fact that most authors reviewed in this paper tend to agree that infrastructure investments positively impact economic growth and productivity.

5.2 Area of Agreement

Across all methodologies, infrastructure is believed to have a positive impact on the economy. Most authors reviewed tend to agree that it is investment into public infrastructure that is driving productivity and not the other way around. Most of the studies also indicate that public capital and private capital tend to be complementary. Researchers also tend to agree with Aschauer that investments into core infrastructure provide the most important productivity returns. Investments in roads tend to provide the highest returns, depending on the size of the stock. Economists also are inclined to agree that the impact of infrastructure on output is likely to be higher at the national level than at the regional level. In addition, consensus exists around the notion that local infrastructure projects benefit local economies where projects are taking place, but spillover effects may negatively impact other neighbouring regions. This last observation is significant because financing public infrastructure projects should consider the cost and benefit to other regions or industries that are impacted even if they are not the recipients of the investments.

5.3 Area of Significant Debate

Although researchers agree with respect to the role of infrastructure in economic output, there are also significant debates. The first and foremost heavily debated area is the magnitude of infrastructure impacts on productivity or economic output. Those who use the production function approach tend to have estimates larger than those who use the cost function and other approaches. In addition, there are debates about the short- and long-term impacts of infrastructure investments. Most authors tend to think that infrastructure investments have a short-term positive direct impact on output and a long-term positive indirect impact through private capital. Other authors have shown that only certain categories of infrastructure are beneficial to productivity and that investments in core infrastructure result in higher impact on productivity, compared to investments in other types of infrastructure. Still other studies show that the impact of infrastructure investments depends on the sector and location, competition practices and business governing policies in the region of interest.

6 Suggestions for Further Study in the Canadian Context

Similar to the majority of international studies that focus on the direct impact of public capital investment on output, growth, costs and productivity, studies based on the Canadian context generally support the main conclusion that investments in public infrastructure have a positive impact on economic growth and productivity. At the same time, Canadian studies do not cover many other issues that were raised in the international work. This section reflects on the Canadian findings discussed in the literature review and provides suggestions for further study in the Canadian context. Further investigating key issues will not only bring Canadian research on infrastructure and productivity on par with international studies, but will also provide a broader evidence base to inform decision-makers.

6.1 Summary of Findings on Canada

Only a few researchers⁽¹³⁷⁾ have attempted to empirically analyze relationships between infrastructure and productivity within the Canadian context. Wylie estimates a Cobb-Douglas production function model of goods sector productivity using Canadian data for the period 1946-1991 and finds that public infrastructure has had a significant and positive impact on national economic growth and productivity. The results of his paper imply that a 1% increase in infrastructure capital stock per hour worked would increase output per person hour worked in goods production with a productivity elasticity of 0.52.

Brox and Fader examine the relationship between Canadian public infrastructure and private output using a Constant Elasticity and Substitution-Translog cost model and annual data (1961-1997) on manufacturing industries. They find that while public capital and private capital are substitutes in the Canadian manufacturing sector, the services of public capital enhance the productivity of private capital. Their estimate of cost elasticity of Canadian manufacturing is -0.476 when they consider public infrastructure in the private sector cost functions.

Bin Dong measures the effects of public capital on the performance of Canadian business sector. She analyses the relationship between business sector output and the stock of public capital for the time period of 1987 to 2002. She estimates this relation with the Cobb-Douglas function where she adds the public capital as an input. She finds that each 1% change in public capital leads to 0.20% change in GDP in the Canadian business sector over the period 1987 to 2002 on average. She estimates the rate of return on Canadian public capital that is about 7.70% on average between 1987 and 2002.

Harchauoui and Tarkhani use a cost function approach to study the relationship between public capital and productivity growth using disaggregated data on 37 industries in the Canadian business sector for the period 1961-2000. The authors show that for all industries, a $1 marginal benefits increase in public capital results on average in 17 cents of cost savings⁽¹³⁸⁾ for producers per year and that public capital accounted for about 18% of the overall business sector multifactor productivity growth from 1961 to 2000.

Bagala et. al. examine the effects of public infrastructure on the performance of Canadian manufacturing industries in terms of both cost-saving and output-augmenting. They use a translog cost-function incorporating public capital infrastructure for each industry separately with annual time-series data for 1961-1995. For most industries, they find that the cost elasticity vary in the range between -0.10 and -0.40.

Finally, Mittnik and Neumann analyse the dynamic effects of public investment on output using VAR and data from six industrialised countries, including Canada. Their results indicate that public investment tends to have a positive influence on national output. The authors estimate that a 1% increase in public investment will increase economic growth by 0.15%.

6.2 Research Gaps Between Canada and Other Countries

The few studies that have focused on the Canadian context do not match the breadth and scope of a broad body of international work that has been published with regards to infrastructure and productivity dating back to the late 1980s. The main reason for this is the limited availability of infrastructure-related data in Canada. For example, some of the international studies look at the spillover effect resulting from regional infrastructure investment, arguing that gains from infrastructure investment in one area may come at the expense of another area due to re-distribution of economic benefits. International studies show that either infrastructure is a source of increasing disparity between regions or that public investment in one region has positive spillovers on the production processes of other regions.

6.3 Issues for Further Investigation

As suggested in the previous section, research on the impact of infrastructure investment decisions at a regional level in Canada should be done. There are also a number of other issues that need to be further investigated, both in Canada and abroad. These are noted below.

More work should be considered to understand the costs and benefits of region- and industry-specific public capital investments across regions. More research on industry-specific impacts across regions, and not only on the region in which the capital project takes place, is also necessary. Future work should also test the sensitivity of earlier findings to alternative specifications (e.g. different types of government expenditure, different industries, etc.).

Some economists have also argued that investment into public capital reduces firm costs and, therefore, would increase the competitiveness of certain industries. In the Canadian context, more research in this area should be conducted to study the relationship between public capital investment and competition. In addition, many of the papers that were reviewed define public infrastructure as a flow of investment dollars and completely ignore the impact public capital investments have on the demand for infrastructure. Investment in public capital such as highways can actually increase the demand for highway use, leading to congestion, thus lowering productivity. Analysis of the relationships between infrastructure investments and demand for public capital in Canada is needed to identify how current investments in particular types of infrastructure can lead to a change in demand for infrastructure capital.

More work needs to be conducted on the relations between various inputs of production, such as labour, energy, materials, services, private and public capital stock. Models that have been used to study the relationship between infrastructure and economic output have typically used restricted functional forms that may not best reflect the relations between public and private capital. In the Canadian context, this analysis would be useful to develop comprehensive policies and programs aimed at infrastructure and taking other factors of production into account.

Finally, more emphasis should be placed on developing models with functional forms that are flexible so it would be possible to take into account the complexity of relations between various inputs of production to give a more realistic explanation of how investments in infrastructure impact productivity and economic growth. For example, principal component analysis, which identifies patterns across variables could be used (by creating indices to reflect those patterns). More specifically, one could perform principal components analysis on a host of input variables, such as public infrastructure, private infrastructure, investment in research, university graduates, etc. The principal component analysis would identify what patterns of combinations were most common. Productivity could then be regressed on the principal component. In the Canadian context, this sort of analysis would be particularly important given the shortage of infrastructure stock and investments related data in Canada.

The methods that could be used to carry out further studies in the Canadian context are highly dependent on the type and quality of available data and on the specific hypotheses being tested. Additional research is required to analyze various sources of data on Canadian infrastructure and how they can be used to analyze the effect of infrastructure investments on economic growth and productivity. For example, data on infrastructure quality was identified in some studies as being very useful in measuring the impact of infrastructure on the economy and on society.

6.4 A Review of Available Canadian Data to Conduct Research

Historically, Statistics Canada data on public capital was not available by type of asset. Sample sizes were increased so as to provide new data on investment and capital stock by asset group, by asset function and by province for federal, provincial, territorial, local, municipal and regional assets (1961 to 2005).⁽¹⁴⁰⁾ This data represents a significant expansion of the detail and usefulness of the data.

A number of data quality related issues must be taken into consideration when using this dataset for analysis.

• Small sample sizes at the lowest level of aggregation. According to Statistics Canada, only a “small subset, often less than 100 respondents, contribute to an estimate for a particular industry in a particular province” and “the sample gets even thinner when the dimension of asset type is added.” Consequently, estimates at the most detailed level are not as robust as those at more aggregate levels.
• Reporting errors. Statistics Canada notes that reporting error or inconsistency (e.g. measurement error) may be another issue in this dataset. For instance, different governments may use different accounting conventions, and because complete conversion to a single accounting base is not possible, the dataset accepts the convention used by individual governments. This is a source of measurement error. Measurement errors in explanatory variables can also impose additional biases on parameter estimates. More specifically, if there is a measurement error in the infrastructure investment data, output elasticity estimates will be misrepresentative.
• Restricted number of years and/or regions. While there are a number of new data dimensions available in data set (e.g. by asset, by asset function, by province, by type of investment), the total number of observations - 10 provinces over 17 years - remains relatively small for sophisticated econometric analysis. As a result, including the additional dimensions in the analysis would reduce the explanatory power of the model.⁽¹⁴¹⁾

Statistics Canada's Investment and Capital Stock Division suggests that the best way to deal with the issue of data quality is to use aggregate data. This means that the Statistics Canada data set may be used to produce reliable aggregate-level descriptive statistics using simplified approaches but may be insufficient for sophisticated econometric analysis, such as those presented in the literature reviewed here. To be more specific, there will be considerable variability in public infrastructure investments across the provinces for reasons that may be unrelated to expected return on investments. This would likely yield large standard errors and, consequently, parameter estimates that are statistically insignificant.

6.5 Potential Uses of the Available Data Sets

Despite the problems and limitations associated with the existing Canadian data series noted above, the new data set produced by Statistics Canada can potentially offer new opportunities for research and address some gaps that were not covered in previous Canadian studies. These gaps include cross provincial comparison in levels of infrastructure investments, new options for analysis of effects attributable to certain infrastructure assets and assets groups, linkage between economic performance and age of infrastructure, review and analysis of public capital stock and investments by function of infrastructure.

It is suggested that the data be used to calculate a variety of summary statistics illustrating key trends. For instance, the data could be used to estimate annual growth rates in capital stocks and flows by asset group, which can then be compared to productivity growth rates for that particular asset group. In addition, correlation coefficients may be calculated using a number of different approaches; however, it should be emphasized that correlation does not imply causality (it merely illustrates a relationship that should then be investigated through more sophisticated econometric techniques). These statistics would provide information on the basic features of the data and could form the basis of more sophisticated quantitative analysis.

Another way in which the available data could be analyzed is through principle component analysis (PCA).⁽¹⁴²⁾ PCA is a mathematical technique that transforms a number of variables that may be correlated into a smaller number of uncorrelated variables known as principal components. These principle components represent indices that demonstrate movement in similar variables by assigning similar weights to like variables. The purpose of PCA is to reduce the dimensionality of the data set and to identify meaningful new underlying variables. In other words, PCA could be used to construct indices of infrastructure investment patterns from the larger array of infrastructure variables. This would enable use of a smaller number of infrastructure variables in regression analysis. So long as the groupings of investment are meaningful (which can be assessed by examining the principle component weights), this should enable more robust estimation.

The data could also be used to identify any strong relationships between key variables. That is, a simple linear model (e.g. the production or cost function approach), which recognises the limitations of the available data, can be developed and estimated in order to identify those relationships that are statistically significant. For example, this approach would allow identifying those infrastructure assets that impact economic growth and productivity more that others. This may provide a better understanding of what additional data is required in order to test the various hypotheses discussed in the literature review.

In addition, to support new data collection efforts, synthetic data could be created and analysed. The problem of insufficient data to reliably test hypotheses is common. One option to deal with this issue is to create a synthetic data file. Synthetic data files contain both real data and computer-generated plausible data (or artificial data). The artificial data are designed to resemble reasonable and likely records. Statistical analysis using synthetic data would not be as accurate as analysis on actual observations. Hence, the purpose of creating synthetic data is not to conduct formal analysis but rather to provide information on the type of data that would be required to accurately investigate the hypotheses of interest. In other words, synthetic data files are used to plan research.

6.6 Next Steps

The next steps required to extend existing research using econometric models would be to:

• Clearly define the hypotheses being tested;
• Review various estimation methodologies and modelling techniques and associated pros and cons in light of the hypotheses chosen;
• Identify the data requirements for chosen estimation method;
• Conduct detailed quality assessment of all readily available data series and consider options for correcting common econometric problems;
• Develop options for obtaining the missing data of interest (e.g. surveys, linkage of data sets, use of publicly available information such as annual reports) and assess feasibility of obtaining required data;
• Identify the anticipated benefits and costs associated with those options;
• Prepare data series;
• Construct an econometric model and test hypotheses; and
• Analyse findings and suggest policy related actions.

It is suggested that as a preliminary step, additional analysis of the new Statistics Canada data set on investment and capital stocks is needed to better understand analysis options and data limitations and to develop a basis for a new data development strategy. For example, the existing data could be used to identify any strong relationships between key variables by using simplified econometric approaches, while recognizing the limitations of the data. Synthetic data could then be created to provide a better understanding of what additional data is required in order to test the various hypotheses discussed in this report.

Endnotes

• (1) Taken from special data series produced by Statistics Canada in September 2006 and commissioned by Infrastructure Canada. The data focuses on public and private investments and stock in capital assets, which offer collective benefits in the environmental, social, economic and institutional fields.
• (2) Aschauer, David Alan. 1989. “Is Public Expenditure Productive?” Journal of Monetary Economics, Vol. 23: 177-200.
• (3) Infrastructural capital refers to any physical means of production or means of protection beyond that which can be gathered or found directly in nature. Public infrastructure is typically defined as any infrastructural capital under public ownership - that is, any infrastructure capital assets that are not firm-specific infrastructure. Core public infrastructure encompasses the portion of public capital stock that can directly facilitate private production. While there is no consistent definition of public infrastructure, it can be defined as a set of assets that underpin the economic, social, cultural, institutional and environmental well being of society by enabling activities that provide collective public benefit. These assets are publicly owned or privately owned and regulated by governments to ensure adequate quality, quantity and price.
• (4) Productivity is measured as a ratio of the amount of output created (in terms of goods produced or services rendered) per unit input used in production. For example, labour productivity is typically measured as output per worker or output per hour. Total factor productivity or multifactor productivity, also includes both labour and capital goods in the denominator.
• (5) Neoclassical economics is a school of thought in economics that emerged towards the end of the 19th century. The focus of analytical attention in neoclassical economics is on the process through which a market system allocates an economy's resources.
• (6) The production function may take other forms, depending on how A, K, L and G enter the equation.
• (7) More specifically, f represents the state of technology in an economy and specifies what is possible in combining inputs to produce output.
• (8) Public capital is typically defined as a sum of all state owned assets and all construction or engineering projects carried out by the state. Some authors make a distinction between public capital, which includes items like fire trucks and police cars, and public infrastructure, which does not. Others use the terms synonymously.
• (9) Elasticity of output is a measure of the percentage response of output to a 1 percent change in input.
• (10) An estimator is a formula for representing an unknown parameter, and an estimate is the numerical value obtained when sample data are substituted into the formula.
• (11) Ordinary least squares (OLS) is a simple linear regression procedure that estimates parameters using sample data and a linear model.
• (12) The logarithm is the mathematical operation that is the inverse of exponentiation (i.e. raising a constant to a power). The natural logarithm, denoted “ln”, is the logarithm to the base e, where e is approximately equal to 2.7.
• (13) Aschauer, David Alan. 1989. “Is Public Expenditure Productive?” Journal of Monetary Economics, Vol. 23: 177-200.
• (14) Total-factor productivity (TFP) addresses any effects in total output not caused by inputs or productivity. The higher the TFP of an economy, the more output a given amount of capital and labour could produce.
• (15) See: Tatom J.A. 1991. “Public Capital and Private Sector Performance.” Federal Reserve Bank of St. Louis Review, Vol. 73, No. 3; Tatom, J. A. 1993. "Is an Infrastructure Crisis Lowering the Nation's Productivity." Federal Reserve Bank of St. Louis Review (November-December): 3-21; Hulten, C. and R. A. Schwab. 1991. “Is There Too Little Public Capital?” Infrastructure and Economic Growth, American Enterprise Institute; Hotz-Eakin, D. 1994. "Public Sector Capital and the Productivity Puzzle." Review of Economics and Statistics, Vol, 76: 12-21.
• (16) See: Tatom J.A. 1991. “Public Capital and Private Sector Performance.” Federal Reserve Bank of St. Louis Review, Vol. 73, No. 3.
• (17) See: Aaron, H.J. 1990. Discussion of "Why is Infrastructure Important?" in A. Munnell, ed. Is There a Shortfall in Public Capital Investment? Federal Reserve Bank, Boston: 51-63; Eisner, Robert. 1991. "Infrastructure and Regional Economic Performance: Comment." New England Economic Review, Sept./Oct.: 47-58.
• (18) Estimating a production function implicitly assumes that public capital "causes" output or growth. However, the direction of causality could be the other way around. As a society becomes wealthier it may spend more on public infrastructure so an increase in output, which leads to greater wealth, may in fact cause greater spending on public capital.
• (19) Aaron, H.J. 1990. Discussion of "Why is Infrastructure Important?" in A. Munnell, ed. Is There a Shortfall in Public Capital Investment? Federal Reserve Bank, Boston: 51-63.
• (20) When two data series, such as output and public capital, are both drifting upwards over time, a regression of one series on the other can lead to a statistically significant positive coefficient even if there is no real relationship between the two variables. This is known as the spurious regression problem.
• (21) See: Tatom J.A. 1991. “Public Capital and Private Sector Performance.”  Federal Reserve Bank of St. Louis Review, Vol. 73, No. 3.; Hotz-Eakin, D. 1994. "Public Sector Capital and the Productivity Puzzle." Review of Economics and Statistics, Vol. 76: 12-21.
• (22) A multiple equations production model is based on the statistical principle of multivariate statistics, which involves observation and analysis of more than one statistical variable at a time.
• (23) Zegeye defines infrastructure as any public capital outlays at the state and local levels.
• (24) Zegeye, Aklilu A. 2000. “U.S. Public Infrastructure and its Contribution to Private Sector Productivity.” U.S. Bureau of Labour Statistics, Working Paper 329.
• (25) If a technology exhibits constant returns to scale, then increasing input by some proportion would lead to an increase in output by exactly the same proportion (i.e. doubling input would double output).
• (26) When working with panel data (i.e. data that has both time series and cross-sectional features), the problem of correlated omitted effects arises. Fixed effects models are used with panel data to correct this problem and to obtain unbiased estimates of the parameters of interest.
• (27) Wylie, Peter. 1996 “Infrastructure and Canadian Economic Growth 1946-1991.” Canadian Journal of Economics, Special Issue, Vol. 29, S350-355.
• (28) Goods value added production function is a production function that examines the relationship between production output in the goods sector and technical change, private capital stock and the stock of public capital.
• (29) Translog production function is a second order derivative of the production function in equation one. Marginal products are assumed to add to one.
• (30) Kemmerling, Achim and Stephan Andreas. 2002. “The Contribution of Local Public Infrastructure to Private Productivity and its Political Economy: Evidence from a Panel of Large German Cities.” Public Choice, Vol. 113, Issue 3-4: 403-24.
• (31) Maximum likelihood estimation is a statistical method used to make inferences about parameters of the underlying probability distribution of a given data set.
• (32) Andreas Stephan. 2000-02. “Regional Infrastructure Policy and its Impact on Productivity: A Comparison of Germany and France.” Wissenschaftszentrum Berlin, CIC Research Unit, Working Paper No. FS IV 00-02.
• (33) Log-linear model approach describes a model in which the effect of one unit change in any independent variable will tend to change, but the elasticity of demand is assumed to be constant.
• (34) When using statistical techniques such as ordinary least squares, one of the assumptions that is made is that the error term has constant variance. If the variance of the error term is not the same at all points, the condition is called heteroscedasticity.
• (35) Bonaglia, Federico, Eliana La Ferrara and Massimiliano Marcellino. 2000. “Public Capital and Economic Performance: Evidence from Italy.” IGIER, Bocconi University, Working Paper No. 163.
• (36) A Hausman test is a way of verifying that the model is not misspecified.
• (37) Investment in water includes river planning, electric grids and power plants.
• (38) Delgado, Maria Jesus and Inamculada Alvarez. 2001. “The Effect of Public Infrastructure on Private Activity: Evidence from the Spanish Regions.” Universidad Complutense de Madrid, Working Paper 0103.
• (39) Fixed effects include effects that affect productivity of each region that are outside the production model like weather conditions and the use of technology.
• (40) Increased investment into public capital is thought to increase the demand for private capital.
• (41) First differences are the changes in the series between adjacent observations.
• (42) The authors define productive infrastructure stock as infrastructure that plays an important role in private production such as transport, communication and energy infrastructures.
• (43) Puig-Junoy Jaume. 2001. “Technical Inefficiency and Public Capital in U.S. States: A Stochastic Frontier Approach.” Journal of Regional Science, Vol. 41, No. 1: 75-96.
• (44) Technical efficiency is a measure of productivity based on concepts of total factor productivity and its components.
• (45) Estimates presented are not comparable to previous studies in this section because the author is looking at inefficiencies and not output. We nevertheless include this study because the findings do have important implications for policymakers.
• (46) Wang, Eric. 2002. “Public Infrastructure and Economic Growth. A New Approach Applied to East Asian Economies.” Journal of Policy Modelling, Vol. 24, Issue 5: 411-435.
• (47) Public capital consists of large core infrastructure. Core infrastructure includes public utilities, public works and the transportation sector.
• (48) The exceptions are Malaysia and Taiwan. This might be because the two countries had ratios of public to private capital that were more than double that of other countries.
• (49) The estimate for Singapore is 0.8 % and that for Thailand is 1.08%.
• (50) BIN DONG Lauren (2005). “The Private Benefits of Public Capital: Evidence for Canada, 1987 to 2002”. Economic Analysis Research Paper Series September 2005, Statistics Canada.
• (51) Aggregate studies tend to use a single equation model, whereas the regional studies tend to use multiple equation models. Perhaps this is the reason why there are differences in the results of these two types of studies.
• (52) Returns from core infrastructure will be highest in regions that are lacking major infrastructure like roads and highways and lowest in regions that have too much infrastructure.
• (53) Some economists (e.g. Aaron, 1990) have stated that the production function approach produces estimates that are over inflated and that, as a result, the cost approach produces more realistic estimates. Other economists (US Department of Transportation: http://www.fhwa.dot.gov/policy/gro98ch2.htm) argue that the Cobb- Douglas production function imposes parameter restrictions, such as constant returns to scale, and that these should be tested because innovations, for example, often result in increasing returns to scale. Increasing returns to scale means that when factors of production like labour increase, output will increase by more than the increase in labour.
• (54) Albala-Bertrand, Jose Miguel and Emmanouel C. Mamatzakis. 2001-02. “The Impact of Public Infrastructure on the Productivity of the Chilean Economy.” Queen Mary, University of London, Department of Economics, Working Paper No. 435.
• (55) See note 34.
• (56) A variable cost function is a function that describes the relationship between costs and the various factors and prices of those factors of production. The function is considered variable because factors of production such as capital are split between their variable and fixed costs.
• (57) Unlike the production approach where essential the decision is what combination of factors of production are needed to maximize production the duality approach is to decide what combination of factors of production are needed to minimize costs.
• (58) Ezcurra, Roberto, Carlos Gil, Pedro Pascual and Manuel Rapún. 2005. “Public Capital, Regional Productivity and Spatial Spillovers.” The Annals of Regional Science, Vol. 39: 471-94.
• (59) This may not be sufficient justification to rule out the endogeneity problem. The authors could have used the Hausman test to check if endogeneity is present.
• (60) Moreno, Rosina, Enrique López-Bazo and Manuel Artís. 2002. “Public Infrastructure and the Performance of Manufacturing Industries: Short- and Long-Run Effects.” Regional Science and Urban Economics, Vol. 32, Issue 1: 97-121.
• (61) Cohen, Jeffrey P. and Catherine J. Morrison Paul. 2004. “Public Infrastructure Investment, Interstate Spatial Spillovers, and Manufacturing Costs.” The Review of Economics and Statistics, Vol. 86, Issue 2: 551-560.
• (62) Full information maximum likelihood estimator technique is an econometric technique is used to derive estimates for parameters of the cost share equations.
• (63) Cohen, Jeffrey P. and Catherine J. Morrison Paul. 2004. “Public Infrastructure Investment, Interstate Spatial Spillovers, and Manufacturing Costs.” The Review of Economics and Statistics, Vol. 86, Issue 2: 558.
• (64) SATYA Paul, BALBIR S. Sahni and BAGALA P. Biswal (2004). “Public Infrastructure and the Productive Performance of Canadian Manufacturing Industries”. Southern Economic Journal, 70 (4): 998-1011
• (65) The estimates of rates of return in terms of cost savings found in the research of Bagala et al. are lower than those reported in the study of Demetriades and Mamuneas (2000), “Intertemporal output and employment effects of public infrastructure capital: Evidence from 12 OECD economies”. The Economic Journal 110; 687-712. Demetriades and Mamuneas estimate these rates for Canada in the range of 17% in the short run, 17.6% in the intermediate run, and 23.3% in the long run. It is the same for estimates of rates of return in terms of output. The Bagala et al. ones' are lower than those reported for United States, which vary from 60% to 146%.
• (66) Brox, James A. and Christina A. Fader. 2005. “Infrastructure Investment and Canadian Manufacturing.” Applied Economics, Vol. 37: 1247-56.
• (67) The CES-TL is a log linear cost function that examines the relationship between costs and factors and factor prices of production.
• (68) Constrained coefficient means that the coefficient value can only take on a certain range of numbers.
• (69) Structural equations are equations with a defined structure.
• (70) In econometric estimations, the equation will not be completely defined by the given equation. There will always be random influences that impact the equation being estimated. This random component of the equation is called an error component and the error structure is the structure of that component. Some economists believe that the random component can be modeled and included in the estimation.
• (71) Cost estimates are not comparable to previous studies in this review.
• (72) Morrison Paul, Catherine J. and Schwartz, Amy Ellen, (1992-01-01) "State Infrastructure and Productive Performance". NBER Working Paper No. W3981
• (73) Tarek M. Harchaoui and Faouzi Tarkhani (2003). "Public capital and its contribution to the productivity performance of the Canadian business sector" Statistics Canada Catalogue no. 11F0027MIE - No.017
• (74) Public capital was defined as the engineering construction component of public administrations' capital stock (federal, provincial and territorial, and local) and includes primarily transportation systems, such as subways and highways, mass transit, water supply, and wastewater treatment facilities.
• (75) The authors translate the industry benefit estimates into a dollar value of cost reduction in each industry for a given amount of public capital spending.
• (76) Wylie, Peter (1995),“Infrastructure and Canadian Economic Growth.” Canadian Business Economics, Winter: 40-52.
• (77) See: Aschauer (1989) and followers; Tatom J.A. (1991).
• (78) The cross elasticity between all model inputs is the degree to which public and private capital are complements or substitutes.
• (79) The differences between Solow and Kendrick indexes have to do with the forms of production function used. The Kendrick index is based on a linear production function that uses arithmetic weighted procedure of the factor; that is, output is a function of the sum of the factors of production multiplied by their estimated shares. On the other hand, Solow uses a Cobb-Douglas production function where the weighted procedure of factors is geometric. The Divisia-Törnquist model is defined as a weighted average of rates of growth in which the components are weighted in proportion to their total value share.
• (80) Constant returns to scale means that for a 1% increase in a factor of production there will be a 1% increase in output. With technological innovations often a 1% increase in capital, for example will lead to a more than 1% increase in output.
• (81) Since there are assumed to be constant returns to scale, TFP can only be equal to changes in output.
• (82) Aguayo, Eva, Pilar Expósito, Xose Anton Rodríguez and Emilia Vázquez. “Human Capital and Other Factors of the Total Productivity in Spanish Regions.” University of Santiago de Compostela, Faculty of Economics, Working Paper No. 45.
• (83) A unit root is present if |b|=1 in the equation yt = a + byt-1 + et, where t is time, b is the slope coefficient and e is the error term.
• (84) Autocorrelation is a problem that arises with time series analysis.  It means that the observations are not independent, and so each observation will tend to be close in value to the next, which is common in panel data as a result of repeated observations on the same variable across time. These are two series issues that may impact the validity of the estimates.
• (85) When comparing observations across multiple categories (regions, sectors, attributes etc) there are often effects that will influence total productivity that are more likely in one sector for example than an other. If the effect is the same through time then, the effect is known as a fixed effect; if the effect is dependent on time, then the effect is a random effect.
• (86) See note 34.
• (87) Canning, David and Peter Pedroni. 2004. “The Effect of Infrastructure on Long Run Economic Growth.” Williams College, Department of Economics, Working Paper.
• (88) Granger causality tests are statistical tests used to determine if there exists a causal relationship between two variables, and co-integration tests are used to determine if a long run relationship exists between two variables.
• (89) Estimates from this study are not comparable to others because the author is not examining total factor productivity but is examining the impact of infrastructure on income.
• (90) Martin, Philippe. 1999. “Public Policies, Regional Inequalities and Growth.” Journal of Public Economics, Vol. 73: 85-105.
• (91) Improvement in public infrastructure implies that infrastructure is more efficient, e.g. better transportation systems.
• (92) Reduced cost of innovation can lead to higher growth, lower monopolistic profits (more competition) for capital owners and more even spatial distribution of incomes and economic activities.
• (93) See: Holtz-Eakin and Lovely (1995); Rioja (1999); Haughwout (2000).
• (94) The general equilibrium model aims to describe the economy by aggregating the behaviour of individuals and firms and by assuming that traditional supply and demand analysis is the best approach to understanding the market. In the model, the individual is assumed to be the basic unit of analysis and these individuals will make choices that reflect their unique tastes, objectives, and preferences. It is assumed that individuals' wants typically exceed their ability to satisfy them. It is further assumed that individuals will eventually experience diminishing marginal utility. Finally, wages and prices are assumed to be elastic.
• (95) Input-output analysis considers inter-industry relations in an economy, depicting how the output of one industry goes to another industry where it serves as an input, thereby making one industry dependent on another both as customer of output and as supplier of inputs. An input-output model is a specific formulation of input-output analysis.
• The Input-output model of economics uses a matrix representation of a nation's or a region's economy to predict the effect of changes in one industry on others and by consumers, government, and foreign suppliers on the economy.
• (96) Haughwout, Andrew F. 2000. “Public Infrastructure Investments, Productivity and Welfare in Fixed Geographic Areas.” Federal Reserve Bank of New York.
• (97) Spatial general equilibrium models are able to model economies of scale, external economies of spatial clusters of activity, continuous substitution between capital, labour, energy and material inputs in the case of firms, and between different consumption goods in the case of households. The spatial equilibrium approach emphasizes the importance of infrastructure in altering the distribution of economic activity across regions, and re-establishes the household sector to its joint roles as consumer of infrastructure services, supplier of labour and competitor in the land market.
• (98) Localized public goods refer to regional or municipal infrastructure.
• (99) Haughwout, Andrew F. 2000. “State Infrastructure, the Distribution of Jobs, and Productivity.” Federal Reserve Bank of New York.
• (100) This refers to the assumption that workers will move from large established urban centres to newly developed areas.
• (101) Economies of agglomeration is related to the idea of economies of scale and network effects. It is used to describe the benefits that firms obtain when locating near each other - the more related firms that are clustered together, the lower the cost of production as firms have competing multiple suppliers, greater specialization and division of labour result and the greater the market that the firm can sell into.
• (102) Holtz-Eakin, Douglas and Mary E. Lovely. 1995. “Scale Economies, Returns to Variety, and the Productivity of Public Infrastructure.” National Bureau of Economic Research (NBER), Working Paper No. W5295.
• (103) Rioja, Felix K. 1999. “Productiveness and Welfare Implications of Public Infrastructure: A Dynamic Two-Sector General Equilibrium Analysis.” Journal of Development Economics, Vol. 58, Issue 2: 387-404.
• (104) The two sectors are households and firms.
• (105) The model assumes that there exists an external input in production, public infrastructure, which is provided by the government. The government finances infrastructure investment by taxing output at a flat rate, and it has to balance its budget constraint every period.
• (106) These seven countries are Argentina, Brazil, Chile, Colombia, Mexico, Peru, and Venezuela.
• (107) Rudd, Jeremy B. 2000. “Assessing the Productivity of Public Capital with a Locational Equilibrium Model.” Federal Reserve Board, Working Paper No. 2000-23.
• (108) Based on Roback's locational-equilibrium model of public-goods pricing, cross-sectional data from the Census of Population and Housing, and standard metropolitan statistical areas (SMSA)-level estimates of public capital stocks in order to examine the productive contribution of public capital.
• (109) In this paper, public capital includes infrastructure and non-infrastructure. Infrastructure is broken-down into several subcategories, including water, highway and sewer infrastructure.
• (110) Growth models are only partial equilibrium models.
• (111) Granger causality testing is a technique for determining whether one time series is useful in forecasting another. A time series X is said to Granger-cause Y if it can be shown, usually through a series of F-tests on lagged values of X and with lagged values of Y also known, that those X values provide statistically significant information on future values of Y.
• (112) VAR is an econometric model used to capture the evolution and the interdependencies between multiple time series, generalizing the univariate AR models. All the variables in a VAR are treated symmetrically by including for each variable an equation explaining its evolution based on its own lags and the lags of all the other variables in the model. This feature allows the use of VAR models as a theory-free method to estimate economic relationships, thus being an alternative to restricted structural models.
• (113) Mittnik, Stefan and Thorsten Neumann. 2000. “Dynamic Effects of Public Investment: Vector Autoregressive Evidence from Six Industrialised Countries.” Empirical Economics, Vol. 26: 429-46.
• (114) These six countries are Canada, France, UK, Japan, Netherlands and Germany.
• (115) Lau, S-H P. and C.Y. Sin. 1997b. “Public Infrastructure and Economic Growth: Time Series Properties and Evidence.” The Economic Record: 125-35.
• (116) Pereira, Alfredo M. and Oriol Roca Sagalés. 2006. "Public Infrastructures and Regional Asymmetries in Spain.”
• (117) Sturm, Jan-Egbert, Jan Jacobs and Peter Groote. 1995. “Productivity Impacts of Infrastructure Investment in the Netherlands 1853-1913.” University of Groningen, Research Institute, Research Report No. 95D30.
• (118) Basic infrastructure investments consist of main railways, roads, canals, harbours and docks, the electromagnetic telegraph, drainage, dikes, and land reclamation. Complementary infrastructure sectors include light railways, tramways, gas, electricity, water supply, and local telephone networks.
• (119) Assuming that public investment today is mainly directed towards complementary infrastructure.
• (120) The authors do not report estimations of individual coefficients because links between the equations in the model make interpretation of individual coefficients difficult.
• (121) Karadag, Metin, A. Ozlem Onder and Ertugrul Deliktas. 2005. “Growth of Factor Productivity in the Turkish Manufacturing Industry at Provincial Level.” Regional Studies, Vol. 39, No. 2: 213-223.
• (122) Zhang, Xiaobo and Shenggen Fan. 2001. “How Productive is Infrastructure? New Approach and Evidence from Rural India.” International Food Policy Research Institute, Discussion Paper, No. 84.
• (123) The method of moments is a method of estimation of population parameters by equating sample moments with unobservable population moments and then solving those equations for the quantities to be estimated. The generalised method of moments is a generalization of the method of moments. The method is closely related to the classical theory of minimum chi-square estimation.
• (124) Given a time series of data, the auto regression is a tool for understanding and, perhaps, predicting future values in this series. The model consists of two parts, an autoregressive part and a moving average part.
• (125) Model estimated using actual time series values.
• (126) Model estimated using time series transformed into first differences by calculating changes in the series value between adjacent observations.
• (127) See Delgado, Maria Jesus and Alvarez , Inamculada. 2001. “The Effect of Public Infrastructure on Private Activity: Evidence from the Spanish Regions.” Universidad Complutense de Madrid, Working Paper 0103; Holtz-Eakin, Douglas and Mary E. Lovely. 1995. “Scale Economies, Returns to Variety, and the Productivity of Public Infrastructure.” National Bureau of Economic Research (NBER), Working Paper No. W5295.
• (128) Calderon, Cesar A. and Luis Serven. 2004. “Trends in Infrastructure in Latin America, 1980-2001.” World Bank - Office of the Chief Economist, World Bank Policy Research Working Paper, No. 3401.
• (129) Quality of existing infrastructure assets was measured as a proxy of the percentage of power losses and the proportion of paved roads, as well as subjective aggregate indicators from surveys.
• (130) Model was estimated using infrastructure quantity series only and also using aggregated quality and quantity series.
• (131) Gramlich E.M. (1994), Infrastructure Investment: A Review Essay, Journal of Economic Literature, Vol. 32, No.3, September, pp. 1176-1196.; Tatom J.A. (1991), Public Capital and Private Sector Performance, Federal Reserve Bank of St. Louis Review, Vol. 73, No. 3.; Morrison C.J., Schwartz A.E. (1996), State Infrastructure and Productive Performance, American Economic Review, Vol. 86, No. 5, December, pp. 1095-1111.
• (132) Rosik, Piotr. 2006. “Transport Infrastructure, Public Capital and Regional Policy - Review of Studies.” International Conference on Shaping EU Regional Policy: Economic Social and Political Pressures, Belgium.
• (133) Zhang, Xiaobo and Shenggen Fan. 2001. “How Productive is Infrastructure? New Approach and Evidence from Rural India.” International Food Policy Research Institute, Environment and Production Technology Division, Discussion Paper, No. 84.
• (134) Tatom J.A. (1993), “The Spurious Effect of Public Capital Formation on Private Sector Productivity,” Policy Studies Journal, Vol. 21, No. 2, p. 391-395.
• (135) Fernald J.G. (1999), “Roads to Prosperity? Assessing the Link Between Public Capital and Productivity,” American Economic Review, Vol. 2, June, pp. 619-638.
• (136) Stationarity occurs when time series analysis methods are used.
• (137) See: Wylie (1996), Harchaoui and Tarkhani (2003), Bagala et. al (2004), Brox and Fader (2005), Bin Dong (2005).
• (138) The authors translate the industry benefit estimates into a dollar value of cost reduction in each industry for a given amount of public capital spending.
• (139) (Models based on cost function, production function, or growth approached have predetermined relations between variables.
• (140) This data was only available previously at the national aggregate level.
• (141) A high level of aggregation also means that there will not be enough variation in the investment and capital stock data to disentangle the effect of public capital from the province-specific effect. This problem is known as multicollinearity. A high degree of multicollinearity in the data can lead to poor or imprecise estimates.
• (142) Further analysis would be required to understand whether principle component analysis is actually useful in this case.