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Appendix A

HIGHWAY CAPITAL AND PRODUCTIVITY GROWTH

by
M. Ishaq Nadiri, New York University and NBER
Theofanis P. Mamuneas, University of Cyprus
June, 1996

Recent discussions have emphasized inadequate growth of infrastructure capital as a cause of the slowdown in productivity at the aggregate and industry levels. Numerous studies have been undertaken to clarify the relationship between productivity growth and public infrastructure capital. These studies can be broadly classified as those which estimate a neoclassical production function augmented to include the publicly financed infrastructure capital stock as a factor of production, and those which utilize the dual approach to production function analysis by estimating cost or profit functions. The level of aggregation used in estimating production and cost functions varies considerably among the different studies. Some studies use highly aggregate national or international data and others use regional or state level data. Some studies use cross-section-time series data covering metropolitan SMSAs, while others employ industry-level data. Studies often differ in their coverage of industries, geographic regions, modeling methodology and use of econometric estimation techniques. Because of such analytical differences and data limitations, the statistical results reported in the literature measuring the effects of infrastructure capital on the economy are often quite diverse and sometimes contradictory. Clearly, no consensus has yet emerged on the precise causes of the productivity growth slowdown and the specific contribution of public infrastructure capital in this process.

To provide a context for this study, a literature review is included in the following section. The analytical framework used in this study possesses several advantages over existing models reported in the literature:

A unique feature of this study is its comprehensiveness.1 This study estimates a model which encompasses both demand and supply factors that may influence industry and total economy productivity growth and uses data on 35 industries that covers the entire U.S. economy for the period 1950-1989. The focus of the study is to identify the contribution of highway capital to productivity growth. Two measures of highway capital are used: total highway capital including roads under federal, state, and local government jurisdiction; and the stock of upper level roads excluding local government investments in roads and streets.2 Since the results of our study did not change much except with respect to the magnitude of some elasticities whichever of these two measures of highway capital are used, the discussion here after will focus on total highway capital. The major changes in the results when non-local highway system (NLS) capital stock is used as a measure of highway capital will be noted at the concluding section.

The relevant policy questions addressed in this research are as follows:

Literature Review

A brief review of the literature on the contribution of public infrastructure (highway) capital suggest that:3

  1. Estimates based on aggregate production function analyses are likely to have overstated the magnitude of the effects of public infrastructure capital on output and productivity growth;
  2. Early estimates based on state level data indicate a relatively smaller contribution of infrastructure and that the composition of infrastructure capital matters; some types of infrastructure may have a greater effect on productivity than others;
  3. There are serious estimation problems in both aggregate national level time series studies and state and regional level studies that lead to highly disparate results; and
  4. Overall, it seems that the recent studies point to a positive but lower elasticity of output with respect to public infrastructure capital of about 0.20 to 0.30 at the national level and possibly a lower range at the regional level.

Similarly, from the view of cost and profit function studies4 the following statements may be in order:

  1. There is a preponderance of evidence that suggests that infrastructure capital contributes significantly to growth in output, reductions in cost and increases in profitability. The magnitude of these contributions, however, vary considerably from one study to another because of differences in econometric methodology and level of data aggregation.
  2. There appears to be a convergence toward a much lower estimate of the magnitude of the contribution of infrastructure capital to output and productivity growth than suggested in earlier studies. Output elasticity estimates of infrastructure capital at the national level in the range of 0.16 to 0.25 appear to be in order. Estimates based on state and metropolitan level data suggest elasticities of approximately 0.06 to 0.20.
  3. Most studies indicate an under-investment in public infrastructure capital, the degree of which varies among different studies. Most of the cost function studies suggest a substitutional relationship between private capital and infrastructure capital, although some studies report a complementary relationship.
  4. The available studies are either too aggregate or partial in their coverage of the economy. Most of these studies, particularly those at the national level, use real GDP, a value added measure, as the dependent variable. However, the appropriate measure for an analysis of the contribution of infrastructure (highway) capital is gross output. Gross output includes purchases of intermediate inputs, along with primary inputs private capital and labor. Because highways are used to transport intermediate inputs, the relationship between public capital and intermediate purchases can be taken into account.5
  5. Studies at the industry level are generally confined to the manufacturing sector or a specific subset of this sector. Infrastructure capital, however, may have important effects on other industries outside the manufacturing sector as well. It is very important to undertake a comprehensive study that includes all sectors of an economy in order to study the role and degree of externalities generated by publicly financed infrastructure capital such as highway capital.

Most of the studies of both production function or cost function have been challenged on conceptual and econometric grounds.6

Estimation Framework and Descriptive Data

The approach developed in our study explicitly incorporates demand and supply forces, including the contribution of highway capital, that may affect industry productivity performance. For each industry, cost and demand functions are estimated separately and the parameter estimates of the model used to decompose Total Factor Productivity (TFP) growth. The critical estimates for decomposition of TFP are the price and income elasticities of output demand and the degree of scale and input substitution derived from the cost function. In formulating industry output demand, changes in quantity demanded in an industry are related to its own price movement in comparison to the GNP deflator and changes in the level of aggregate income and population of the economy. The estimates show that the price elasticity of output demand is negative and statistically significant in almost all industries, and with few exceptions, less than one.

The parameters of the underlying cost function are estimated by using a system of input-output equations which include a labor to output equation, a capital to output equation and an intermediate input to output equation. These input-output ratios functionally depend on private input prices, level of industry output, industry's capacity utilization rate, time trend, and level of total highway capital stock. In order to capture industry specific effects we introduce industry specific intercept terms and a limited number of slope dummy variables.7 There are of course other more elaborate ways to take account of interindustry differences that could be undertaken in future research.8

Previous studies have been criticized on modeling and econometric estimation issues. This study has responded to these criticisms by accounting for several estimation problems in the estimation process. We examine the possibility of spurious correlation by estimating our model in first difference form. A flexible form for the cost function is used to allow interaction between highway capital and private sector output and inputs. No a priori restrictions, such as constant returns to scale are imposed, on the parameters of the cost function. The issue of simultaneity is addressed by estimating the model using appropriate econometric estimation techniques. Extensive hypothesis testing was also carried out to test the specification of the model and the stability of its results.

The data used in this study covers the entire U.S. economy for the period 1947-1989. The industry coverage is derived from a detailed 80 industry classification that Jorgenson, Dollop and Fraumeni carefully aggregated into 35 larger categories.9 Data for the value of gross output and costs of labor, capital services and intermediate inputs as well as their price indices for all industries are from Jorgenson, Gallop and Fraumeni.10 Data on capacity utilization rate for the manufacturing industries for the period 1950 - 1966 have been obtained from Klein and Summers (1966) and for the period 1967 - 1989 from the WEFA group (1992). Data on real GNP and population, used to estimate the demand functions, are obtained from the Bureau of Economic Analysis and the Bureau of the Census, respectively.11

Data on net highway capital stock are from Apogee Research, Inc., which was constructed using Federal Highway Administration's investment expenditure data on highways from 1921 to 1990. Total net highway capital and non-local net highway capital (NLS) are constructed using the perpetual inventory method with an assumed economic rate of depreciation of 0.9. Capital expenditures are distributed in the following way; 52 percent to paving, 26.5 percent to grading, and 21.5 percent to structures. The average lives of paving, grading, and structures are assumed to be 14, 80, and 50 years, respectively.

An examination of the data indicate substantial diversity among the 35 industries examined in the study. The size of the industries, measured by total cost, vary considerably among industries. Factor cost shares also vary considerably across industry sectors. For example, labor's share ranges from a low of about 0.06 in petroleum refining to a high of 0.51 in trade. Capital's share of total cost ranges from 0.04 in apparel and other textile products to 0.38 in crude petroleum and natural gas. Generally, capital's share in total cost, with few exceptions, is less than labor's share. Material inputs, on the other hand, have the largest share in total cost in almost all sectors or industries, ranging from 0.86 in petroleum refining to 0.25 in other transportation equipment.

Figure 1 Growth Rate of Highway Capital (%) 1950-1989

Line chart plotting growth rate of highway capital in percent over the years 1950 through 1989. The trend starts at about 2.8 in 1950 and drops to about 2.1 in 1951, then climbs rapidly to 7.0 in 1956. The trend climbs slowly to 7.8 by the year 1958, then begins a steady drop, reaching 1.0 by the year 1974. The trend climbs to about 1.1 in 1975, then drops to nearly zero in 1978 through 1981, and trends slowly upward to about 2.0 by the year 1989.

Table 1: Cost Function Elasticities Averages: 1950 - 1989
Industry Code Industry Title Cost Elasticities
hcs
Cost Elasticities
h
Cost Elasticities
h*
1Agriculture, Forestry and Fisheries0.05310.95731.0122
2Metal Mining0.04580.80490.8484
3Coal Mining0.04880.92710.9775
4Crude Petroleum and Natural Gas0.06150.93020.9953
5Nonmetallic Mineral Mining0.05910.92310.9843
6Construction0.06830.82800.8889
7Food and Kindred Products-0.16770.92040.7911
8Tobacco Manufactures-0.22450.98010.8040
9Textile Mill products-0.15020.97420.8494
10Apparel and Other Textile Products-0.14630.97430.8521
11Lumber and Wood Products-0.16400.97580.8401
12Furniture and Fixtures-0.15850.96390.8334
13Paper and Allied Products-0.16780.96420.8273
14Printing and Publishing-0.20240.95620.7972
15Chemicals and Allied Products-0.15580.95570.8295
16Petroleum Refining-0.17400.94800.8096
17Rubber and Plastic Products-0.16250.95850.8262
18Leather and Leather Products-0.16760.90950.7805
19Stone, Clay and Glass Products-0.17710.96070.8174
20Primary Metals-0.21640.91660.7544
21Fabricated Metal Products-0.17280.95610.8169
22Machinery, Except Electrical-0.15530.94640.8206
23Electrical Machinery-0.15200.95340.8297
24Motor Vehicles-0.18970.93410.7872
25Other Transportation Equipment-0.16580.95990.8248
26Instruments-0.18760.89410.7528
27Miscellaneous Manufacturing-0.14690.96860.8464
28Transportation and Warehousing0.02870.93180.9593
29Communication0.02640.96070.9870
30Electric Utilities0.03540.95590.9916
31Gas Utilities0.02090.94520.9672
32Trade0.02090.73030.7431
33Finance, Insurance, and Real Estate0.02420.75300.7689
34Other Services0.03150.75480.7762
35Government Enterprises0.02400.96980.9940

The growth rate of total highway capital is shown in Figure 1. After an initial decline between 1950 and 1951, the growth rate of highway capital surged, growing at the average rate of 6.2 percent during 1952-1959. From 1960 onward, the growth rate declined continuously until 1979. It grew very little during 1979-1981. Since 1982 the highway capital stock has been growing at an average rate of 1.2 percent per annum.

Results at the Industry Level

The model used in this study builds up from industry-level estimates to obtain appropriate results for the economy as a whole. Therefore, the careful estimation of the structure and properties of the disaggregated industries plays a critical role in the design of this research. The following sections present some of the basic industry-level results before describing the contribution of highway capital to the aggregate economy. These results include the impact of highway investments on industry cost reductions and economies of scale; effects upon labor, capital and material inputs; the marginal benefits of highway capital to industries; and the analysis of growth in total factor productivity (TFP).

Cost Reduction and Degree of Scale - The first column in Table 1 shows the elasticity of cost with respect to highway capital (hcs). The magnitudes of the cost elasticities vary among the industries. The cost elasticities in manufacturing industries range from -0.146 to - 0.220 while in the non-manufacturing industries they range from +0.02 to +0.06. Positive cost elasticities imply that the demand for highway capital services in these industries is less than the available supply at the price the industries are willing to pay. This does not mean that these industries do not demand highway capital services. What is implied is that these industries face "excess capacity" in highway capital, a situation similar to the notion of excess capacity in private capital stock in a private firm. If the firm cannot freely dispose of this capacity and is instead required to keep its capital stock fully utilized, regardless of changes in demand for its product, the cost to the firm will rise. In the case of highway capital, the entire capital stock enters the cost function of each industry. The optimal level of these services can be estimated from the model which is the level at which the marginal benefit of highway capital is equal to an industry's marginal cost or willingness to pay. As noted later, these estimates imply a set of national subsidies and taxes that would allow industries to use the optimum amount of highway capital services.

The cost elasticities h and h* shown in column 2 and 3 of table 1 have a returns to scale interpretation. The inverse of h represents internal returns to scale, or the effect on output of an equal proportional increase in all inputs except highway capital. Similarly, the inverse of h* represents total returns to scale, meaning that an equal proportional increase in all inputs, including highway capital, yields a 1/h* proportional increase in output. The results show that both 1/h and 1/h* are greater than one for all industries except agriculture, indicating increasing internal and total returns to scale. The degree of internal returns to scale in each industry is smaller, as expected, compared with the degree of total returns to scale which accounts for the contribution of highway capital.

Effects on Labor, Capital and Materials - Highway capital has both direct and indirect effects on the productivity of the private sector. The direct effect of infrastructure capital is measured by the magnitude of the cost reduction due to an increase in highway capital. The indirect effect is given by the magnitude of its effect on the demand for private sector factors of production.

Conditional input demands refer to the demand for labor, capital, and intermediate inputs holding output constant. Elasticities of employment, private capital and intermediate inputs with respect to highway capital vary considerably across industries.12 The general conclusion that arises from the empirical results is that changes in total highway capital have significant effects on the demand for private sector inputs in all industries. The conditional demand for labor, private capital and material inputs in the manufacturing industries will decline when investment in highway capital is increased. In the non-manufacturing industries, however, demand for labor and material is increased while demand for private capital is decreased in response to an increase in highway capital. However, if the level of output is free to change, the demand for employment, capital and materials inputs in each industry will increase as a consequence of an increase in highway capital. This arises because the direct cost reduction effect of highway capital will in turn lead to the expansion of output. This expansion in output will require more inputs which will likely offset the substitutional effects at a given level of output.13

Marginal Benefits - Table 2 reports the average marginal benefit (MB) of highway capital in current dollars for each industry over the sample period. The marginal benefits indicate how much each industry is willing to pay for an additional unit of highway capital services. The magnitudes of the marginal benefits vary considerably across industries and over time. After taking into account price changes, however, the marginal benefits in real terms appear to increase from 1950 to 1969 but decrease from 1970 to 1989 in each industry. Another interesting feature is that all manufacturing industries have positive marginal benefits, i.e., they would be willing to pay a positive amount for additional highway capital services, the amounts ranging from 0.002 in the leather and leather products industry to 0.029 in primary metals. Non-manufacturing industries, on the other hand, are willing to pay negative amounts, i.e., require a subsidy, to use the entire stock of highway capital. That is, the estimated demand for highway capital services in these industries at a price they are willing to pay, falls short of the available supply.

Table 2: Marginal Benefits (MB) of Highway Capital Mean Values 1950 - 1989
Code Industry MB Tax(+) / Subsidy(-)
1Agriculture, Forestry and Fisheries-0.01174-0.01518
2Metal Mining-0.00041-0.00061
3Coal Mining-0.00125-0.00163
4Crude Petroleum and Natural Gas-0.00483-0.00681
5Nonmetallic Mineral Mining-0.00071-0.00092
6Construction-0.03465-0.04384
7Food and Kindred Products0.044640.03936
8Tobacco Manufactures0.003390.00295
9Textile Mill products0.007350.00639
10Apparel and Other Textile Products0.010590.00927
11Lumber and Wood Products0.008160.00721
12Furniture and Fixtures0.004140.00367
13Paper and Allied Products0.013090.01168
14Printing and Publishing0.016240.01448
15Chemicals and Allied Products0.022280.02007
16Petroleum Refining0.020520.01858
17Rubber and Plastic Products0.013010.01178
18Leather and Leather Products0.00200.00164
19Stone, Clay and Glass Products0.009040.00791
20Primary Metals0.028500.02413
21Fabricated Metal Products0.018870.01667
22Machinery, Except Electrical0.025820.02308
23Electrical Machinery0.020730.01870
24Motor Vehicles0.027110.02382
25Other Transportation Equipment0.017260.01519
26Instruments0.010160.00919
27Miscellaneous Manufacturing0.003980.00353
28Transportation and Warehousing-0.00718-0.01080
29Communication-0.00348-0.00472
30Electric Utilities-0.00468-0.00627
31Gas Utilities-0.00275-0.00400
32Trade-0.02178-0.03594
33Finance, Insurance, and Real Estate-0.02331-0.03530
34Other Services-0.02805-0.03873
35Government Enterprises-0.00219-0.00328

The implied taxes and subsidies for various industries are shown in Table 2. These refer to the differences between the amount an industry is willing to pay for highway capital services and the actual price required to use the entire amount of available capital. These estimates are calculated at the optimal level of highway capital services demanded for both manufacturing and non-manufacturing industries. The magnitudes of taxes and subsidies vary considerably. The largest taxes in manufacturing are in food and kindred products, chemicals and chemical products, primary metals, machinery (except electrical), and motor vehicles. Construction, trade, finance, insurance, real estate, and other services require relatively large subsidies to encourage them to use the entire highway capital. Those that would "pay" the lowest taxes are tobacco manufacturing and leather and leather products. The lowest subsidies are in three industries: metal mining, coal mining and nonmetallic mineral mining.

Table 3: Decomposition of Total Factor Productivity Growth Mean Values: 1951 - 1989
Industry Code Industry Title Exogenous Demand Relative Input Price Highway Capital Adjusted

TFP

TFP
1Agriculture, Forestry and Fisheries0.002-0.052-0.1071.5101.353
2Metal Mining0.2340.058-0.060-0.432-0.200
3Coal Mining0.0300.010-0.0981.1201.060
4Crude Petroleum and Natural Gas0.015-0.021-0.123-1.243-1.372
5Nonmetallic Mineral Mining0.098-0.005-0.1050.8830.856
6Construction0.4530.162-0.158-0.3450.092
7Food and Kindred Products0.399-0.1690.430-0.1260.577
8Tobacco Manufactures0.1170.0220.558-0.4210.209
9Textile Mill products0.292-0.1030.3530.7461.293
10Apparel and Other Textile Products0.082-0.1410.3900.8411.282
11Lumber and Wood Products0.330-0.3210.4060.2060.621
12Furniture and Fixtures0.409-0.3470.5030.0350.639
13Paper and Allied Products0.589-0.4260.420-0.3000.280
14Printing and Publishing0.684-0.5620.649-0.808-0.048
15Chemicals and Allied Products0.729-0.5920.3840.3860.904
16Petroleum Refining0.518-0.1210.4270.1110.933
17Rubber and Plastic Products0.827-0.5080.4290.1730.938
18Leather and Leather Products-0.4410.2370.4740.2580.537
19Stone, Clay and Glass Products0.419-0.2680.445-0.2870.310
20Primary Metals0.196-0.1460.667-0.956-0.285
21Fabricated Metal Products0.444-0.2460.440-0.1720.460
22Machinery, Except Electrical0.792-0.4270.4000.2981.072
23Electrical Machinery0.752-0.4090.4060.7221.512
24Motor Vehicles0.635-0.3550.645-0.7480.368
25Other Transportation Equipment0.973-0.4800.420-0.3640.548
26Instruments1.543-0.7500.469-0.2790.989
27Miscellaneous Manufacturing0.263-0.1960.4120.8241.280
28Transportation and Warehousing0.1050.056-0.0430.9271.060
29Communication0.0750.356-0.0382.0792.457
30Electric Utilities0.0560.041-0.0481.1681.222
31Gas Utilities0.125-0.2080.014-0.188-0.256
32Trade1.0710.301-0.026-0.3861.005
33Finance, Insurance, and Real Estate1.0330.118-0.028-0.8940.218
34Other Services0.7680.086-0.098-2.1690.091
35Government Enterprises0.034-0.802-0.044-0.330-1.144

More careful analysis is required to examine further the size and pattern of these implied taxes and subsidies. It is important to note that the benefits of highway capital vary across industries. Demand for highway services are likely to diverge over time and the degree of benefits of any new highway capital expansion may differ considerably among industries. That is, there is an important distributional effect of the public highway capital across industries

Industry TFP Growth Decomposition- The decomposition of TFP growth estimates at the industry level are provided in Table 3. These estimates reflect the effects of:

Exogenous Demand: This refers to increased demand due to growth of real national income, aggregate population and changes in the utilization rate.

Relative Input Price: This factor captures the growth of input prices.

Highway Capital: This factor captures the combined direct and indirect effects of the growth of highway capital.

In general, changes in exogenous demand contribute over half of TFP growth, mainly in the manufacturing industries. Its contribution in agriculture, extractive and mining industries and government enterprises are rather small. In construction, instruments, transportation equipment and trade and finance, the contribution of an increase in demand is relatively large. The contribution of relative input prices could be positive or negative depending on whether industry factor price changes exceed those of the general economy. When an industry's rate of input price inflation exceeds the national inflation rate, productivity growth is hampered. Generally, growth in relative input prices contributes negatively to TFP, and the magnitude of its effect varies across industries. Compared to the contribution of exogenous demand, the effects of relative input prices on TFP growth are small.

Table 4a: Effect of Total Highway Capital, S, on Cost and Factors of Production, Sum of Marginal Benefit, Cost Elasticities Average Values
Total Highway Capital hCS hLS hKS hMS h h* F
∑ME
E-1
"Aggregated" -.044 -.083 -.122 -.013 .862 .826 .18

The contribution of highway capital to TFP growth is positive in all the manufacturing industries. In some of these industries its contribution is relatively large, accounting for almost one-third of TFP growth. In non-manufacturing sectors, growth in highway capital contributes negatively to productivity growth. As explained earlier, this indicates that the supply of highway capital exceeds the demand at the prices these industries are willing to pay. When the effects of exogenous demand, relative input price changes, and highway capital are accounted for, the rate of technological change is much smaller than conventionally calculated. In general, the main causes of TFP growth in the manufacturing industries are exogenous shifts in demand, relative price changes, and highway capital, while in the non-manufacturing industries the dominant factor is the scale effect, or exogenous technological change. Highway capital plays only a minor role in the acceleration or deceleration of TFP growth at the industry level.14 The evidence supports the notion that total highway capital contributes at varying degrees to the long term growth of TFP in different industries, and its contribution to the short run acceleration or deceleration of industry TFP growth over the sub-periods is negligible.

Contribution of Highway Capital at the Total Economy Level

To calculate the contribution of highway capital stock to the total productivity of the aggregate economy, we explored two different approaches: (1) the individual industry elasticity estimates were averaged (using industry input and output shares as weights) to obtain the "aggregated" estimates; (2) the industry level data were summed to the national level and the model was re-estimated with the aggregate data to obtain the "aggregate" estimates for the cost and demand equations. The results were quite similar. In what follows we present the results based on the "aggregated" estimates.

Table 4b: Output Elasticities of Factor Inputs, Total Highway Capital, Utilization Rate, Rate of Technical Change
Model Labor Capital Materials Highway capital output Utilization rate Technology
"Aggregated" .384 .185 .605 .051 .142 .001

Aggregate Output and Cost Elasticities - Table 4 presents the effect of the total highway capital stock, respectively, on aggregate private sector cost and aggregate input demand functions. The "aggregated" cost elasticity is about -.044, which is considerably smaller than estimates from previous studies. The elasticity of labor with respect to highway capital is negative, which suggests that any increase in highway capital is labor-saving at the aggregate economy level when the level of output is held constant. The elasticity of private capital with respect to total highway capital is also negative and slightly higher than that of labor. The elasticity of intermediate inputs with respect to total highway capital is negative and very small. Cost elasticities (h and h*) suggest increasing returns to scale and the sum of marginal benefits (SMB), shown in last column is approximately 0.18. The output elasticities of inputs, the utilization rate, and the rate of technical change at the aggregate economy level show that the output elasticity of material inputs is large (around 0.60 to 0.70), followed by that of labor (approximately 0.40 to 0.45), and private capital (approximately 0.20). The rate of autonomous technical change is comparatively small (about 0.001). The output elasticity of highway capital is also relatively small compared to materials, labor, and private capital, averaging 0.051 for the period as a whole.

Figure 2 Net Rate of Return of Highway Capital, Private Capital, and Private Interest Rate (1951-1989)

Line chart showing rate of return values in percent for three categories over the years 1951 to 1989. The value for return on interest rate begins at about 2.5 and rises to nearly 15 percent by 1981, then falls to about 9 percent by 1989. The value for return on capital investment begins slightly above 15 percent in 1951 and fluctuates up and down about the 13 percent mark to about 1980, and remains near that value through 1989. The value for return on highway capital starts at about 32 percent in 1951, trends up to 45 percent in 1955, and drops to nearly 30 percent in 1958. It rises to about 40 percent in 1965, begins a steep drop to about 11 percent by 1975, and swings up and down to reach a final value of about 5 percent by 1989.

Compared to the results reported in the literature, this estimate of output elasticity of highway capital is very small. In fact, the elasticity estimates originally reported in Aschauer (1989), Holtz-Eakin (1991) and Munnell (1990) are about eight times as large as our estimates for the national economy. Our estimates are more comparable to output elasticities of public capital reported in Duffy-Deno and Eberts (1989) and Eberts (1986) for the highly disaggregate level of the Metropolitan Area. In particular, the output elasticity of private sector capital is clearly larger than the output elasticity of highway capital. The results indicate that a one percent change in private capital stock contributes almost four times as much to economic output as a one percent change in highway capital stock to growth of output of the economy.

Net Social Rates of Return - Past literature has questioned whether public capital is over- or under-supplied. One way to determine whether public capital is provided optimally is to compute the rate of return to highway capital and compare it with the rate of return to private capital for the whole economy. The optimal provision of public capital requires that the rates of publicly provided and private capital be equalized. Thus, if the rate of return of highway capital is higher than that of private capital, highway capital is under-supplied and an increase of public investment is necessary. The net social rate of return of highway capital can be derived as the ratio of the sum of industry marginal benefits to cost minus the depreciation rate of highway capital. This calculation assumes that the user cost of highway capital includes the acquisition price, the relative discount rate, the depreciation rate of highway capital, and the price distortion effect of taxes levied to finance highway capital.15

Table 5 Net Rate of Return from Total Highway Capital, Private Physical Capital, and Interest Rates
Net Social Rate of Return 1950-1959 1960-1969 1970-1979 1980-1989 1950-1989
Total Highway Capital.352.348.161.100.281
NLS Capital.479.474.238.161.338
Private Capital Stock.134.14.120.110.133
Interest Rate.04.05.08.110.07

Table 6 The Ratio of Optimal to Actual Stock of Highway Capital (S*/S)
Ratio of S*/S 1950-1959 1960-1969 1970-1979 1980-1989 1950-1989
Total Highway Capital3.0571.6781.1120.9951.710
NLS Capital3.8311.8511.1861.0431.978

Table 5 presents the net social rate of return to total highway capital, the net rate of return to private capital stock and interest rates for four different sub-periods. The social rate of return on total highway capital was very high during the 1950's and 1960's, reflecting the shortage of highway capital stock during the 1950's when the Interstate Highway System was under construction. This rate has declined continuously since the late 1960's and in 1989 it is barely above the level of the long term interest rate.

The time profile of the net social rate of return for total highway capital is presented in Figure 2. The rate begins at a relatively high level, rises to its maximum level in 1955, and fluctuates around 37 percent until 1968. Thereafter, the rate starts to decline and falls from 10 percent in 1985 to about 5 percent in 1989. When the net rate of return is compared to the long-term interest rate on government securities from 1950 to 1989, the gap between the two is very large until the 1970s. The gap narrows considerably and almost disappears in the 1980s. The net rate of return on private capital averaged approximately 14 percent from 1950 to 1969, and then declined in the 1970s and 1980s. However, it exceeded the interest rate over most of period, as shown in Figure 2.

Table 7
Aggregate

TFP
Decomposition
Total Highway Capital Mean Values

TFP
Exogenous Demand Relative Price Highway Capital Capacity Utilization Adjusted

TFP
0.6783.596-.0571.1767.0069-.0484

Aggregate

TFP
Decomposition
NLS Capital Mean Values

TFP
Exogenous Demand Relative Price Highway Capital g1 Highway Capital g2 Capacity Utilization Adjusted

TFP
0.67830.6029-0.05710.16490.00180.0069-0.0411

g1 = highway capital stock NLS
g2 = other than NLS highway capital

Our estimates of the rate of return on highway capital are much lower than reported in previous literature. Recently, Fernald (1992) estimated the rate of return to investment in roads using essentially the same set of data as used In this study. He concluded that "a conservative statement — is that the data strongly supports the view that roads investments are highly productive, offering rates of return of 50% to 100%, perhaps more."16 Our results suggest rates of return well below Fernald's lower bound estimated rate of return. Our average rate of return for the period of 1950 to 1989 is 28 percent, about half of his rate of return of 50 percent. The rate of return over the postwar period has still been quite impressive, although in recent years the returns to highway capital are more similar to those estimated for private capital stock.

Optimal Highway Capital Stock - The optimal level of highway capital is obtained by comparing the industry marginal benefits for each year to the actual level of highway capital. The average ratio of optimal highway stock to actual highway capital is reported in Table 6. The striking result that emerges from this comparison is that the ratio is very high during the 1950s, then declines dramatically thereafter until 1989, when the ratio is approximately one. This suggests that there was significant underinvestment in highway capital immediately after World War II but the gap between optimal and actual capital stocks narrowed between 1959 and 1969 as the Interstate Highway System and other road systems were completed. The ratio of optimal to actual stock of highway capital declined by about 50 percent from 1960 to 1969 and further decreased from 1970 to 1979. Interestingly, in the 1980s there is no significant evidence of overall under- or over-investment in the highway capital stock.

Figure 3 Ratio of Optimal to Actual Highway Capital 1950-1989

Line chart plotting values for the ratio of optimal to actual highway capital for the years 1950 through 1989. The trend begins at about 3.6 in 1950 and swings gradually downward to the year 1974 when it reaches nearly 1. After a slight increase to 1.1 by 1976, the trend tracks along 1 from the year 1979 through 1989.

The decline in the ratio of optimal to actual highway capital shown in Figure 3 is due in part to public investment decisions and to economic and demographic changes. Growth in the stock of highways and streets, as shown in Figure 1, rose sharply from 1955 to 1975, the period when the U.S. Interstate Highway System was under construction, and leveled off since that time as construction of the Interstate slowed and previously built highways depreciated. The net stock of total highway capital grew at an annual rate of approximately 5 percent from the mid-1950s to the late 1960s. It began to decline in the 1970s, reaching a minimum growth rate of 0.7 percent in 1983. Since then it has gradually increased, but the growth rate of 2.3 percent in 1993 is still less than half the average growth rate of the mid-1950s to late 1960s period.17

Decomposition of Aggregate Total Factor Production (TFP) Growth - The results in Table 7 indicate that growth in exogenous demand is the most important contributor to aggregate TFP growth between 1950 and 1989, as almost 87 percent of TFP growth is accounted for by changes in aggregate demand. Input price movements contribute negatively to TFP growth (about 8 percent) while highway capital contributes positively (about 25 percent) to TFP growth. The contribution of the capacity utilization rate is very small (about 1 percent). Table 8a and 8b demonstrate that the same patterns are evident over different sub-periods. The contribution of highway capital to TFP growth was much larger in the early periods, but has declined significantly since 1972. This reflects two sets of factors: the pattern of marginal benefits of highway capital stock; and, more importantly, the growth rate of highway capital stock exhibited in Figure 1. Highway capital's contribution to TFP growth was less than 0.18 until 1953 when the investment in Interstate Highway System started; its contribution rose to almost twice as much during the period of 1954 to 1967. After 1967, the contribution declined considerably until reaching about .001 in 1981. After 1981, the contribution of highway capital to TFP growth grew to about 0.06 in 1989.

A central issue in the debate on the role of infrastructure or highway capital is its contribution to the deceleration of TFP growth in the period 1975-1979. Aschauer (1989), Munnell (1990a) and others claim the decline in this period was mainly, if not exclusively, due to the decline in growth of infrastructure capital. Hulten and Schwab (1991a), Gramlich (1994) and others have argued for minimal contribution of infrastructure capital to productively slowdown.

When TFP growth is decomposed into trend and deviation from the trend, the trend TFP growth is highly correlated with the trend contribution of highway capital, trend exogenous demand and trend in relative factor prices. The deviation from trend of TFP growth is correlated with deviation of the exogenous demand and relative prices from their trend. The conclusion to be drawn is that highway capital stock contributes to growth of total factor productivity; its contribution is much smaller in comparison of the contribution of exogenous demand.

Table 8a
Average growth rate of

TFP
and contributions of exogenous demand,
total highway capital and relative prices 1952-1989 and sub periods
  1952-1989 I
1952-1963
II
1964-1972
III
1973-1979
IV
1980-1989

TFP
.68.941.03.13.42
EXD.60.30.60.75.84
TGG.17.30.26.03.03
PFP-.06-.06-.10-.17.07

Table 8b
Average growth rate of

TFP
and contributions of exogenous demand,
NLS highway capital, other highway capital and relative prices 1952-1989 and sub periods
  1952-1989 I
1952-1989
II
1964-1972
III
1973-1979
IV
1980-1989

TFP
0.67830.94021.0340.13270.4255
EXD0.60290.31850.59450.73920.8563
TGI0.16490.29660.24630.01950.0353
TGO0.01180.01880.01210.0080.0058
PFP-0.0571-0.0566-0.1089-0.16980.0678

EXD: Exogenous Demand
TGG: Total Highway Capital
TFP: Relative Input Prices
TGI: NLS Highway Capital
TGO: other than NLS Highway Capital

Most of the contribution of highway capital to productivity growth occurred in the 1950s and 1960s. Since 1973, highway capital has made a small contribution to trend TFP. Highway capital, whether measured by total highway capital or NLS (non-local system) capital, does not contribute much to the acceleration or deceleration of TFP growth.

These results stands in contrast to those reported by Aschauer, Munnell and other proponents of large contributions to infrastructure and also to those reported by researchers who have denied any role for infrastructure in enhancing the growth rate of productivity. Our analysis suggests that highway capital stock has contributed to the expansion of the productive capacity of the economy. It has contributed to total TFP growth of the US economy, although its contribution has been much smaller than has been claimed in the production function research. Expansion of highway capital has had significant effects on the pattern of, and demand for, labor, capital and material inputs in different industries.

Summary and Policy Implications

Summary of Main Results - The specific quantitative results of this report can be briefly summarized as follows:

Policy Considerations - The results of this research suggest a number of policy implications:

Future Research

This study raises a number of important issues which should be addressed in future research. These issues include: adjustments for additional variables not included in this research; examining the productivity effects of highway capital under varying levels of output; estimated depreciation rates; further detail about industry types; and the welfare benefits of highway capital to groups other than private sector industries.

Omitted Variables - One of the most important issues to consider in future research is the effect of omitted variables on our results. Two types of adjustments are desirable: one related to quality changes in highway capital stock and the other is the contribution of infrastructure capital other than highway capital. The quality adjustments can take different dimensions. For example adjustments are needed to account for the effects of congestion and other environmental factors such as noise, smog, etc. The highway capital stock needs to be adjusted for quality of roads, degree of maintenance and intensity of use. Besides these types of adjustments, the effects of infrastructure capital other than highway capital should be specifically introduced in our model. Clearly there is considerable evidence that other types of public infrastructure contribute to growth of output and productivity. Including the "other" infrastructure capital may affect the magnitudes and even sign of the elasticities and marginal benefits of highway capital (or NLS) reported in this study.

Allowing Output to Vary - In this study we have evaluated the productivity effect of highway capital and its effect on demand for labor, capital and materials under the assumption that the level of output is given. This assumption needs to be relaxed to take account of output expansion induced by investment in highway capital. Highway capital investment reduces costs, i.e. the average cost shifts downward (productivity effect). This in turn, given a downward sloping output demand curve, leads to a decline in output prices and an increase in quantity demanded. The induced output expansion leads to increases in demand for each of the private sector inputs. This indirect expansion effect of highway capital investment will likely to offset any potential substitution effects on demand for labor, capital and materials. This issue is an important challenge to be taken up also in future research.

Depreciation of Highway Capital. - Another issue is to examine more closely the depreciation rate estimates that are used to generate the total highway or NHS capital. If the depreciation rate is not an accurate measure of the decline in production services then the results on marginal benefit, net social rate of return and productivity contribution of highway capital reported here will be affected. Analytical models are available to estimate the depreciation rate from available investment data. Also, availability of data on maintenance expenditures and other relevant data may allow estimating a more precise measure of the depreciation rate and thus better measures of total highway and NHS capital stocks.

Further Industry Detail - In this study, industries were divided into three broad categories. A more refined classification such as that used by Fernald may be necessary to capture the industry variations in demand for highway capital services. As a result, our measures of industry marginal benefits, social rate of return and contribution to productivity at the industry and aggregate level are likely to be affected. Also, we need to improve our estimation of the output demand function. Furthermore, the demand and cost functions are estimated separately. What is required is to jointly estimate the two functions and allow for the effect of highway capital on the demand for output of an industry.

Benefits to Other Groups - Finally, in this study we have concentrated on the benefits of highway capital to private sector industries. The welfare benefits of highway capital services to the consumers have not been addressed. To do so requires modeling the consumption sector of the economy and integrating it with the production sector in a general equilibrium model. Such an attempt, though extremely important, at present remains outside the scope of our current research.

REFERENCES

Aschauer, David Alan (1989), "Does Public Capital Crowd Out Private Capital?" Journal of Monetary Economics 24, 171-188.
Duffy-Deno, K.T. and R.W. Eberts (1991), "Public Infrastructure and Regional Economic Development: A Simultaneous Equations Approach," Journal of Urban Economics 30, 329-43.
Eberts, Randall W. (1986), "Estimating the Contribution of Urban Public Infrastructure to Regional Growth," Federal Reserve Bank of Cleveland Working Paper 8610, December.
Fernald, John (1992) "How Productive Is Infrastructure" Distinguishing Reality and Illusion with a Panel of US Industries." mimeo.
Gramlich, E. (1994) "Infrastructure Investment: A Review Essay," Journal of Economic Literature, September, 1176-1196.
Holtz-Eakin, D. (1991), "New Estimates of State-Local Capital Stocks by State," Syracuse University, mimeo.
Jorgenson, D., F. Dollop and B. Fraumeni (1987) Productivity and U.S. Economic Growth, Cambridge, MA: Harvard University Press.
Jorgenson, D. (1990) "Productivity and Economic Growth," in Berndt, E. and J. Triplett, (eds) Fifty Years of Economic Measurement, NBER Studies in Income and Wealth Volume 54, Chicago: The University of Chicago Press.
Jorgenson, D.W. and Kun-Young Yun (1990) "The Excess Burden of Taxation in the U.S.," Harvard University Discussion Paper #1528.
Klein, L. and R. Summers 91966) "The Wharton Index of Capacity Utilization," Studies in Quantitative Economics, No. 1, University of Pennsylvania.
Munnell, A. H. (1990), "Why Has Productivity Growth Declined? Productivity and Public Investment," New England Economic Review, Jan./Feb., 3-22.
Hadirl, M. Ishaq and Theofanis P. Mamuneas (1993), "The Effects of Public Infrastructure and R&D Capital on the Cost Structure and Performance of U.S. Manufacturing Industries," C.V. 5tarr Center RR #91-57.

REFERENCES

______(1996), "Contribution of Highway Capital Infrastructure to Industry and Aggregate Productivity Growth," March, a report prepared (Apogee Research Inc.) for the Federal Highway Administration Office of Policy Development, Work Order No. BAT-94-008. WEFA Group, (1990), Industrial Analysis Quarterly Review, July.

1 For a full description see Hadiri and Mamuneas, "Contribution of Highway Capital Infrastructure to Industry and Aggregate Productivity Growth," March 1996, a report prepared (Apogee Research Inc.) for the Federal Highway Administration Office of Policy Development, Work Order No. BAT-94-008.
2The latter includes the federal-aid highway system, with the exception of expenditures on secondary rural roads, and represents approximately 70 percent of total highway capital stock. It is referred to in this paper as the non-local highway system, or NLS.
3 See Nadiri and Mamuneas, (1996) "Contribution of Highway Capital to Industry and National Productivity Growth," opt. cit, for a more comprehensive survey of substantive and technical issues.
4 Opt. Cit.
5 Use of value-added data can be justified if there is no substitution between intermediate inputs such as materials and energy and the primary factors of production like capital and labor. If intermediate input prices are relatively stable, the use of value added in productivity analysis can be justified on practical grounds. However, oil price shocks substantially affected the course of the U.S. economy in the 1970s and 1980s. Similar effects to a lesser extent were associated with price increases in other intermediate inputs. Therefore, it is important to explicitly include energy and material inputs in the productivity analysis.
6 See Nadiri and Mamuneas, "Contribution of Highway Capital Infrastructure to Industry and Aggregate Productivity Growth," opt.cit., 1996 for further discussion.
7 In principle, we could introduce a full set of slope dummy variables (102 additional parameters) but it not possible in an already complicated model. Rather, we classified the 35 industries into three groups - manufacturing (industry codes 7 through 27), service industries (industry codes 28 through 35), and other industries (industry codes 1 through 6).
8 An interesting approach is suggested by Fernald (1992). He uses "vehicle intensity" as a proxy for use of road infrastructure. It is measured as the ratio of the stock of trucks and cars in an industry to its total output. If an industry is vehicle-intense, then presumably it receives a lot of direct productive services from roads.
9 See Nadiri and Mamuneas, "Contribution of Highway Capital Infrastructure to Industry and Aggregate Productivity Growth," opt. cit. for further details.
10For a description of data construction, see Jorgenson, Gallop, and Fraumeni (1987). Also see Jorgenson (1990).
12 The magnitudes of the labor elasticity ranges generally from 0.06 in industry 29 to a high of 0.97 in industry 16. The elasticities are generally small in industries 28 through 35 except for industry 31. The elasticities of private capital with respect to total highway capital are larger in magnitude in the manufacturing industries than in non-manufacturing industries. The magnitudes of elasticities of intermediate inputs with respect to total highway capital are generally small, particularly in industries 1 through 6. They are relatively larger and positive in transportation, trade, and services. The pattern that emerges from these elasticities is that highway capital is a substitute for private capital in all industries, a substitute with labor in all manufacturing (industry codes 7-27) and services (industry code 28-35) while it is a complement to labor in other industries (industry codes 1-6). Finally, highway capital and intermediate inputs are complements in non-manufacturing industries and substitutes in the manufacturing industries.
131n the next phase our study the level of output will be allowed to vary and the new set of results will separate the likely substitutional and expansion effects on private sector inputs of a given increase in highway capital.
14 The sample period was divided into four sub-periods: period I, 1952-1963; period II, 1964-1972; period III, 1973-1979; and period IV, 1980-1989. In a few industries, the contribution of highway capital to the deceleration of TFP growth between periods II and III was fairly large, but in the majority of industries, there was little or no systematic relationship. The magnitudes of the contribution of highway capital between to the rate of change of TFP periods III and IV were generally very small.
15See Jorgenson and Yun (1990)) This distortion effect arises because no country relies extensively on head taxes to finance infrastructure capital. Distortionary taxes (e.g., an income tax) are often used to fund public investments. Therefore, the social cost of additional public capital is the sum of the direct burden of the taxes needed to pay for the infrastructure and the dead weight cost associated with these taxes. The issue of an appropriate cost of investment of highway system require a careful analysis in future research.
16 Fernald (1992) p. 26
17 One factor contributing to the growth pattern in highway capital was the sharp rise in the price of gasoline in the 1970s that increased the cost of travel significantly.

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