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Appendix A: A Summary of Contributions of Highway Capital to Output and Productivity Growth in the U.S. Economy and Industries

Arthur Jacoby, Federal Highway Administration
September 1998

Background

A number of research studies by and for the Federal Highway Administration (FHWA) Office of Policy Development document the effects of public highway capital on logistics system and commercial sector economic performance. A notable example is Professor M. lshaq Nadiri's 1996 study,1 which examined the contributions of total highway capital and nonlocal highway capital to the output growth and productivity of 35 industry sectors comprising the U.S. economy. His 1996 econometric analysis provides empirical evidence of the positive impacts of public highway capital on private-sector costs of production. It also (1) evaluates the effects of highway capital investment on the production sector's demand for labor, private capital formation, and materials; (2) estimates the marginal commercial benefits of road system investments; (3) calculates the net social rate of return on highway infrastructure spending; and (4) identifies the contribution of highway capital and other economic factors to the productivity growth rate in the U.S. economy between 1950 and 1989.

The Current Study

Professor Nadiri's most recent effort reflects several extensions and improvements to his 1996 study.2 First, underlying economic data are extended to include the period 1947 to 1991 and take into account recent revisions in national income accountin industry reclassifications. Second, other types of public infrastructure capital ar introduced into the analysis to address concerns about the effects of omitted explanatory variables. Third, assessments of highway capital's impact on the private sector's demand for labor, capital, and intermediate goods are broadened to consider the output expansion effect of public road investments.3 Finally, detailed estimates of the effects of highway capital during the subperiod 1981 to 1991 are provided to enhance contemporary policy discussions.

The main goal of this research is to measure the historical impacts of publicly provided highway capital on the production sector of the U.S. economy. Empirical assessments of the relationships between highway investment spending and industry economic performance are aggregated to produce national economic measures. It is important to note that the benefits of infrastructure to the consumer sector are not considered in the current work. Although some interactions between the producer and consumer sector benefits are likely, consumer benefits are largely additive to the commercial-sector benefits estimated in the current study.

The sophisticated nature of the analysis, the relatively large number of interrelated economic measures, the comprehensiveness of the industry sectors considered, the long time frame of the study, and the variations in empirical estimates across industries and over time make a succinct statement of research findings in a nontechnical manner very difficult. Therefore, this summary of Professor Nadiri's 1998 research for the FHWA is organized in the form of brief answers to several basic questions about the economic impacts of road investments on the commercial sector of the economy.

  1. What are the effects of highway capital on private-sector production costs; level of output, and demand for labor, capital, and intermediate goods?

A principal conclusion of this research is that an increase in the stock of U.S. highway capital has an initial direct productivity effect on business: It reduces the total cost of producing a given level of output in almost all industries. The cost-reducing "productivity effect" of highway capital varies in magnitude across industries and over time. The size of the highway capital productivity effect on each of the the 35 industry sectors that make up the U.S. economy is indicated by the "cost-elasticity" measure.4 Cost reductions due to highway capital investment are relatively large (i.e., cost elasticities greater than -0.08) in such industries as agriculture, food and kindred products, transportation and warehousing, trade, construction, and other services. In most manufacturing industries cost elasticities range between -0.04 to -0.06.

To obtain a national-level estimate of the initial cost-reducing impact of highway capital investment, industry cost-elasticity measures are weighted by the industry's share of total national output and summed. The average cost elasticity with respect to total highway capital for the U.S. economy during the period 1950 to 1991 is about -0.08. This is approximately double the -0.04 estimate reported in Nadiri's 1996 study.

The economic impact of highway investment on the various industry sectors does not stop with the direct productivity effect. Cost reductions permit products to be sold at lower prices, and lower prices can be expected to lead to output growth. This is termed the "output effect" of highway capital investment. The size of industry output expansion depends on the nature of the demand for products and, therefore, varies across industry sectors. Of course, at higher production levels, a producer's total costs will increase because of the additional labor, capital, and materials required to make the additional output. An important empirical finding of the current research is that the higher total production costs associated with the output expansion effect are "financed" almost entirely by the cost-saving productivity gains of highway capital investments.

Given the cost-reducing and output-expanding impacts of highway capital, it is not surprising that road investments have a significant effect on the production sector's demand for labor, capital, and materials. The magnitude of the effect, which is termed conditional factor demand, varies among the three inputs (labor, capital, materials) and across industries, and depends on whether we are examining industry's demand for resources in the context of the "productivity effect" alone (i.e., when output level is held fixed) or after allowing for the "output effect" (i.e., when the level of output is allowed to increase in response to the cost-saving/price-reducing effects of highway investment).

The study indicates that highway capital's initial "productivity effect" results in a reduction in the demand for labor and materials but an increase in the demand for private capital in all industries. However, the current work also evaluates changes in the production sector's demand for labor, capital, and materials when industry production levels vary (increase) due to the "output effect" of highway capital. While the direction of the impacts on business demand for labor, capital, and materials remain the same as under the productivity effect alone (i.e., highway capital increases result in reductions in demand for labor and materials but increases in demand for private capital), the magnitude of the change in demand for labor and materials is substantially reduced while the demand for private capital increases significantly. That is, the output effect of highway capital investment leads to an even larger "crowding in" of private capital formation. We can generally conclude that the productivity and output effects of road investment substantially change the input ratios of the production function in all industries, point toward an important role for public capital spending in contributing to investment-led economic expansions, and imply that highway capital may be a prerequisite for growth in private capital investment.

  1. What are the marginal benefits to industry sectors and the aggregate economy of an increase in highway capital?

The marginal benefit of highway capital is measured in terms of its initial cost-reducing impact (i.e., the productivity effect). The magnitude of cost reduction depends on the industry's elasticity of cost with respect to highway capital and the industry's total costs of production relative to the size of the highway capital stock. The current research indicates the marginal benefits of highway capital are positive in all but three fairly small industries. Marginal benefit estimates can be interpreted as a measure of producer's "willingness to pay" for an additional unit of highway capital and vary considerably across industries and over time. For most industries, particularly manufacturing industries, the marginal benefits of a $1.00 increase in highway capital range between 0.20 and 0.60. Industry marginal benefit estimates can be translated into a dollar value of cost reduction in each industry for a given amount of highway capital spending. The simplest way to do this is to multiply the measure of marginal benefit in each industry by the net increase in highway capital for a particular year or period.

The calculation of the marginal benefit of highway capital investment at the national economy level assumes that the use of the road system by one industry does not preclude or reduce the value of its use by any other industry (i.e., we assume nonrival consumption of the highway public good). Therefore, industry marginal benefits are additive across the 35 sectors. The average sum of marginal benefits across all industries is about 0.294. That is, a $1.00 increase in the net capital stock generates approximately 300 of "cost-saving" producer benefits per year. Assuming highway spending covers the depreciation charges required to maintain the net capital stock value, benefits can be thought of as continuing over the design life of the underlying road improvements. The 300 aggregate marginal benefit estimate for total highway system spending is somewhat larger than the amount reported in the 1996 study, which estimated a marginal benefit of 180 for total highway system capital. It also exceeds the 240 estimate given in the earlier study for nonlocal highway system capital.

  1. What is the contribution to productivity growth of highway capital, and what is the overall social rate of return on road investments?

The contribution of highway capital to productivity growth is positive in all industries. In the previous study, highway capital increased productivity mainly in manufacturing industries but not in nonmanufacturing industries. Although the current results show a more pervasive influence of highway capital on industry productivity growth, the magnitudes of the contribution of highway capital vary across industries. In some industry sectors, the effect can be quite large. At the aggregate economy level, highway capital's contribution to total productivity growth is about 25 %. This contribution is somewhat larger than the 18 % reported in the 1996 work. Nevertheless, the current study confirms the previous finding that the main contributor to productivity growth, both at the industry and aggregate economy levels, is exogenous demand (representing the effects of aggregate income and population growth).

Nadiri calculates the net social rate of return to total highway capital as the sum of industry marginal benefits divided by the cost of highway capital, minus the depreciation of public capital. The estimated cost of highway capital is adjusted to account for the price distortion effect of taxes levied to finance highway capital, which effectively raises the cost of highway capital approximately 46 % above the combined government long-term bond rate and highway capital depreciation rate. As in the previous study, current results indicate that the net social rate of return on total highway capital was very high during the 1950s and the 1960s, but declined considerably during the 1970s and 1980s. The average net rate of return on total highway capital investment for the 1950 to 1991 analysis period was 32 % per annum. Although net rates of return on total highway capital investment are generally larger in the current study than in the 1996 effort, the trend since the 1970s remains downward. In the 1980s, the rate of return on highway capital and private-sector capital appear to have converged at approximately 16 % per annum.

The declining rates of return on highway capital investment since the 1970s are likely to be an important concern of policymakers. No doubt the rates of return on highway capital during the 1950s and 1960s were very high indeed. These high returns can be interpreted as signaling a severe shortage of highway capital during the early stages of the Interstate highway construction era. One view of the declining rate of return trend since the late 1970's is simply that as interconnective, upper-level roads were put in place, commercial transportation needs were addressed, and subsequently the rates of return on highway capital from the production side of the economy declined to more normal and sustainable levels. That is, over time, real reductions have occurred in the flow of commercial benefits from further additions to the public highway capital stock. Alternatively, declining returns may reflect the economic effects of relative disinvestment in road capital during this period. Crumbling roads and bridges were of great concern to transportation policy makers in the 1980s and the extent of the "infrastructure crisis" was documented in several important studies.5 If the rate of public-capital investment during this period slipped relative to private-sector investment and growth in the economy, increasing demands placed on the available quantity and quality of public-capital stock would be manifest by a declining performance contribution. In terms of Professor Nadiri's econometric approach, the ratio of total highway capital stock to production-sector total cost and output levels is very important, because it is a component of industry cost elasticity, and thus affects the value of the industry's marginal benefits and the rate of return.

  1. What evidence is there of over- or under-supply of highway capital in the postwar period?

An important public policy question is whether public highway capital is over- or under-supplied. Economic efficiency requires an amount of publicly provided highway capital such that the sum of the marginal benefits to producers and consumers from one more unit of highway capital is just equal to the marginal cost of providing the additional unit of highway capital. Since consumer marginal benefits are not known at this time, an alternative method for determining whether public capital is optimally provided is used. That method is to compare the rate of return to highway capital with the rate of return to private capital for the whole economy. If the rate of return on highway capital investment is higher than that of private capital, highway capital is under-supplied. An increase in public highway investment is therefore desirable when the economic benefit of an additional unit of highway capital exceeds its cost and the rate of return that is available from alternative uses of the required resources.

In the current study, net social rates of return for total highway capital are compared to those of private capital for several time periods. Although the average rate of return for the entire analysis period (1950–1991) is 32%, as previously noted, it has declined continuously since the 1970s. For example, the average net rate of return fell from 54 % in 1960–1969, to 27% in 1970–1979, and to 16 % for the period 1980–1991. The net social rate of return in the 1980s is approximately equal to the average rate of return on private capital in the 1980s, implying a close-to-optimal amount of total highway capital. However, two points that bear on this fording should be noted. First, the equality between public and private capital rates of return is only a partial macroeconomic assessment because it does not consider consumer-sector benefits of the road system. Consumer benefits may be considerable. Second, Nadiri's previous study indicates the rate of return on nonlocal highway capital, the main focus of federal-aid highway program spending, are approximately 5 % to 7 % greater than those for the total highway capital.

  1. How do results for the 1980–1991 period differ from those for earlier decades and the entire 1950–1991 analysis period?

Examination of industry economic data for the 1980s indicates a pattern of input usage, output growth rates, and costs that are similar to previous periods. The effects on industry output from additional amounts of labor, private capital, and materials are basically of the same magnitude as the averages for the entire study period. However, it is noticeable that industry internal and total returns to scale for the 1980s are larger in most industries than the modest increasing returns to scale observed over the entire 40-year analysis period.

The pattern of the distribution of highway benefits across industries for the 1981–1991 subperiod is also similar to that for the entire analysis period. The initial effect of an increase in highway capital investment on producer's demand for inputs is similar to that observed in earlier periods—highway capital substitutes for labor and materials, but private capital and highway capital are complements (i.e., the demand for private capital increases when investment in highway capital rises).

When an accounting is made for the output expansion effect induced by the productivity gains from highway capital, we also see ostensibly similar results. In the 1980s, the induced increase in total costs associated with higher output levels is approximately of the same magnitude as the cost reduction or "productivity effect" of highway capital. This phenomenon, which is observed at both the industry and aggregate economy levels, is due to the size of the output cost elasticities (the reciprocal of the degree of returns to scale noted above), which suggest that a 1 % increase in output generates almost the same increase in cost. That is, the productivity gain of highway capital offsets the increased cost associated with the induced output expansion.

The most significant change in analysis results between the 1981–1991 period and the rest of the study period involves the elasticity of cost with respect to highway capital. The average percentage change in producer total cost associated with a 1 % change in the net highway capital stock for the 1981–1991 is much smaller. The average cost-elasticity value is about -0.039 in the 1980s, compared to an average value for all periods of about -0.08 (see above). Furthermore, the economic impact of highway capital on producer cost continues to decline during the 1980s. To illustrate, while the average rate of return on highway capital for the period 1981–1991 is about 16 %, the rate of return declines to approximately 10 by the end of the period (i.e., in 1991).

Concluding Comments

In this study, Nadiri concentrates on calculating the commercial benefits of highway capital to the production sector of the economy. The welfare benefits of highway capital to consumers are not addressed. However, the magnitude of consumer benefits, including employment-related trips that are not directly included in the production-sector analysis, are likely to be significant. Efforts to account for the total effect of highway capital on the economy will require modeling the consumption-sector impacts and ultimately integrating these results with the production sector in a general equilibrium model framework. Work in this area has just begun and is expected to continue for some time.

A careful analysis of the size and pattern of industry marginal benefits is needed. The needs of different industries for highway services diverge over time and the degree of benefits of new highway capital differ considerably across industries. Because public highway capital creates important distributional effects across industries, further analysis of the sign and magnitude of industry marginal benefits at a more desegregated level is highly desirable from a transportation policy standpoint.

Finding measures to account for quality changes in the highway capital stock and intensity of use of the capital stock are another consideration for future research. Efforts to differentiate between wealth- and productivity-based assessments of the public capital stock are now under way in collateral research.6 Nevertheless, the challenge to find ways of converting productive potential capital stock measures into service flow measures remains. This requires adjustments for utilization of highway capital, taking into account congestion, intensity of use by different industries, and the overall level of business activity.

Your comments and inquiries are welcome and should be directed to
Dr. Arthur Jacoby
Office of Policy Development, HPP-10
Federal Highway Administration
400 Seventh Street, SW
Washington, DC 20590
Phone: (202) 366-9248
Fax: (202) 366-7696
e-mail: arthur.jacoby@fhwa.dot.gov

Endnotes

1 Nadiri, M. Ishaq and Theofanis Mamuneas, Contributions of Highway Capital to Industry and National Productivity Growth, September 1996, Final Report, FHWA Work Order BAT-94-008. The report is available online at www.fhwa.dot.gov/reports/growth.pdf or from the FHWA homepage at www.fhwa.dot.gov. Select "Publications and Statistics" and click on the above title.
2 Nadiri, M. Ishaq and Theofanis Mamuneas, Contributions of Highway Capital to Industry and National Productivity Growth, September 1996, Final Report, FHWA Work Order BAT-94-008. See recommendations in Directions for Future Research, pp. 116–118. Also, the main results of the 1996 study are presented in section III of the current work to provide a context for evaluating new modeling techniques and the effects of extended and revised data.
3 In Nadiri's 1996 study, industry output levels were held fixed when calculating the productivity benefits of highway investment. The overall substitution of highway capital for private inputs initially produces a "productivity effect" in firms and industries by reducing the cost of producing a given level of output. However, highway capital investment can also be expected to induce an output expansion effect that will further affect producer demand for labor, capital, and materials. That is, the downward shift in production cost leads to a reduction in product price. At the lower price, more of the product is demanded. The resulting increase in the quantity of the product demanded is termed the "output effect" of highway capital. Firms require greater quantities of labor, capital, and materials to produce the additional output. Therefore, the total impact of highway capital investment on the private sector's demand for labor, capital, and materials must reflect both the initial productivity effect and the subsequent output effect. Changes in industry output due to an increase in highway capital investment were not considered in the 1996 model.
4 Industry measure of "cost elasticity with respect to highway capital" is one basic empirical result of Professor Nadiri's econometric model. Econometric studies can generate a number of different cost and output elasticity measures. This can be a source of confusion. The simplified term "cost elasticity" is used in this summary when the source of the effect on total production cost is unambiguously attributable to highway capital investment. The cost-elasticity value indicates the percentage change in the total cost of producing a given level of output that is associated with a 1 % change in the value of the highway capital stock. It is mathematically derived from the econometric estimation of the industry cost function by taking the first partial derivative of the total cost function with respect to highway capital. A negative signature (sign) indicates that an increase in highway capital results in total cost reduction.
5 See, for example, Fragile Foundations: A Report on America's Public Works, National Council on Public Works Improvement, February 1988, and High Performance Public Works, U.S. Advisory Commission on Intergovernmental Relations (ACIR), Report SR-16, November 1993.
6 The Quality Adjustment of Public Capital Stock research is under the direction of Professor Barbara Fraumeni, Northeastern University. A pro forma "productive" highway capital stock assessment for use in future econometric studies was produced in February 1999.

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