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The average elasticities of cost with respect to highway capital for our 35 industries are shown in column 1 of Table 7. They indicate that an increase in highway capital does reduce costs (given the level of output) in all but three industries. The magnitudes of these elasticities vary across industries, and range from -0.0021 for Coal Mining (3), and -0.1125 for Other Services (34). In our previous study, the elasticity of cost with respect to highway capital is positive in a large number of non-manufacturing industries. In addition, the magnitudes of the cost elasticities in the manufacturing industries are fairly large, and range from -0.14 to -0.22. The results reported in Table 7 show that in all except three industries, the elasticities have the expected negative sign. The magnitudes of the elasticities we report here are much smaller than those reported in our previous results. The reason for this change is partly because the basic data has been revised and reclassified and partly because the estimation methodology in the two studies are different.
Overall, there is a wide range in the magnitudes of the elasticities across industries. The elasticities are relatively large in Other Services (34), Trade (32), Finance, Insurance and Real Estate (33), Agriculture (1), Other Transportation Equipment (28) and Motor Vehicle (24). These industries are probably the most intensive users of the highway network. In most of the manufacturing industries, the elasticities are about -0.04 to -0.06. The industries with fairly small elasticities are Tobacco (8), Furniture and Fixtures (12), Instruments (26) and Miscellaneous Manufacturing (27). In Metal Mining (2), Non-metallic Mineral Mining (5) and Leather and Leather Products the elasticities of cost with respect to highway capital are positive. However, much should not be made of this result. These are very small industries and the magnitudes of these elasticities are very small and probably not well estimated. Even if these estimates were correct, all it means is that these industries require a subsidy in order to use the entire highway capital.18
Elasticities 
and 
shown in Table 7 have a returns to scale interpretation.
The inverse of
, or 
,
represents internal returns to scale, or the effect on output of an equal proportional
increase in all inputs except highway capital. That is, an equal proportional
increase in labor, capital, and materials, holding highway capital fixed, yields
a 
proportional increase in output. For example, in Agriculture (1), the degree
of returns to scale to private inputs is approximately 1.017. However, an equal
proportional increase in all inputs, including highway capital, yields a 
proportional increase in output or total returns to scale of 1.237. The results
show that both 
and 
are less than one for all industries, suggesting that except for Tobacco (8)
and Lumber and Wood Products (11), increasing internal and particularly total
returns to scale prevail in all industries. These scale elasticities are robust;
that is, the magnitudes of 
and 
do
not change with different estimation methods. The magnitudes of these scale
estimates vary across industries. The degree of internal returns to scale in
each industry is smaller than the degree of total returns to scale. This is
expected because total returns to scale accounts for the positive contribution
of highway capital. The scale estimates that we obtain are quite different and
much smaller than those Hall (1988) finds. While our estimates suggest reasonable
degrees of internal scale ranging 1.016 to 1.131 Hall's estimates for the
same industries are often quite large.
The cost reduction due to an increase in highway capital may lead to a reduction
in output price. In response to the price decline, given the downward sloping
industry demand function for output as indicated by the demand function (1),
demand for output will increase. The output elasticities in different industries
with respect to an increase in highway capital, 
,
are presented in column 4 of Table 7. The magnitudes of
the elasticities vary considerably across industries. The patterns of these
elasticities are similar, as expected, to those of the cost elasticities of
highway capital shown in column 1 of the table. The output expansion effect
of an increase in highway capital, 
ranges
from approximately 0.121 for Trade (32) to 0.017 for Instruments (26). For three
minor industries, (2), (5) and (18), the elasticity is negative. The industries
with the largest output elasticity with respect to highway capital are some
of the service industries, the transportation industries, the construction sector,
and some manufacturing industries.
When output is allowed to vary, the net impact of an increase in highway capital
on total industry costs is extremely small, if not zero in almost all industries.19
This results from two opposing but equal effects. The first is due to the cost
reduction induced by the highway capital that was noted earlier. The second
is due to the cost increase that results from the expansion of output induced
by the initial cost reduction due to an increase in highway capital. These two
effects need not offset each other. The result depends on the estimates of highway
capital cost elasticity and the cost elasticity of output, 
, in each industry. What our empirical
results suggest is that the cost reduction, given the level of output, shown
in column (1) of Table 6 is offset almost completely by
the cost increase due to the expansion of output induced by the initial cost
saving effect of the highway capital. To meet the induced increase in output,
firms must increase their demand for factors of production which imply increase
in total costs. But this increased cost is offset by the initial cost saving
of highway capital. That is, the cost of the induced increase in output is "financed"
by the productivity gains of highway capital.
Highway capital has both direct and indirect effects on the productivity of the private sector. The direct effect is a consequence of the positive marginal product of public capital, i.e., an increase in public capital services decreases private sector production costs. The indirect effect arises because private and public capital are complements in production, i.e., the partial derivative of the marginal product of private capital with respect to public capital is positive. If private capital and public capital are complements, an increase in public capital raises the marginal productivity of private capital, and, given the rental price of capital, private capital formation increases, further raising private sector output. The same will occur with employment and demand for materials depending on whether they are substitutes or complements with highway capital in the production process.
If all private inputs are substitutes with public capital, then an increase in public capital is always cost saving. The inverse, of course, is not true. The review of available literature on cost functions supports the hypothesis that cost savings are associated with an increase of public capital. Hence, if one of the private inputs is a complement to public capital then cost savings can arise only if the substitution effects of the other private inputs outweigh its own complementary effect (see also Seitz (1994)). It is clear, a priori, that no sign can be assigned to the effect of public capital on the inputs of production. The direction and magnitude of the effect is an empirical question. Estimates in the literature support the hypothesis that labor and public capital are substitutes. However, the relationship between public capital and private capital is not as clear. For instance, Conrad and Seitz (1994), Seitz (1992, 1994) and Lynde and Richmond (1992) find that public capital and private capital are complements, while Shah (1992), Nadiri and Mamuneas (1993), and Morrison and Schwartz (1991) find they are substitutes.
Table 8a presents average values of the elasticities
of conditional input demands with respect to total highway capital for the period
1950-1991.Conditional input demands are the demand for labor, capital, and intermediate
inputs holding output constant. We calculate these elasticities 
according to equation (6). The magnitudes of the elasticities of employment,
private capital and materials with respect to highway capital vary across industries.
They suggest that in all industries, the demand for labor and materials is reduced
as the investment in highway capital is increased. However, private capital
and highway capital are complements in most industries. This complementarity
effect is relatively large in industries such as Crude Petroleum and Natural
Gas (4), Utilities (29, 30), Trade (32), Finance & Real Estate (33), and
Other Services (34). In all but one of these sectors, an increase in highway
capital decreases the conditional demand for all inputs.
Table 8b presents the total effect of an expansion in highway capital on demand for labor, capital and materials in different industries for the period 1950-1991. The total effect is the sum of the effects shown in Table 8a (when the output level is fixed) and the induced output expansion effect. The latter effect measures the increased demand for the inputs in response to the increase in output induced by the initial cost reduction of the highway capital. The output expansion effect on input demands is positive for all three inputs but their magnitudes vary across industries and among inputs. The expansion effect reduces the magnitude of the substitution effect shown in Table 8a for both labor and materials. That is, the effects of an increase in the highway capital on employment and materials are still negative, but the magnitudes of these elasticities are much smaller than the elasticities reported in Table 8a. The magnitudes of these effects vary considerably among industries. The total effect of an increase in highway capital on demand for capital is positive and larger than the elasticities reported in Table 8a.
We can generally conclude that increases in highway capital substantially changes the input ratios in all industries. The effects of these changes vary considerably across industries and among inputs. Increases in highway capital save labor and materials, but these increases also raise the demand for private physical capital in all of the industries that we consider. The net effect on total cost is practically null. This is because the gain, i.e., the cost reduction from the increase in investment in highway capital, offsets the increased cost of producing the expanded output induced by the productivity gains of the infrastructure capital.
Recall that the marginal benefit of highway capital is defined to be the negative
of the partial derivative of the cost function (3) with respect to highway capital
(see
equation (5)). This derivative can be interpreted as the marginal willingness
to pay function. We measure this for each industry using the expression (9).
(9) 
This expression suggests that the marginal benefit of highway capital, 
,
is measured in terms of cost reduction. The magnitude of the marginal benefit
depends on the ratio of an industry's cost to the size of the highway capital
stock, 
.
Other factors that determine the magnitude of the marginal benefit for the industry
are the level of output, 
,
and the relative input prices of labor, capital and materials. The stocks of
highway capital, 
,
and other infrastructure capital, 
, and the level of technology, 
also affect the measure of industry
marginal benefit.
Table 9 lists the average marginal benefits of an increase
in the highway capital using the expression 
(see (9)) for each industry over
the period 1950-1991. These benefits indicate the "willingness to pay"
for an additional unit of highway capital services by each industry. This "willingness
to pay" is exclusive of the income taxes, gasoline taxes, fees and interest
payment on bonds, etc. that are used to construct and operate the highways.
These are measures of the highway system's externality benefits to various industries.
The magnitudes of the marginal benefits of highway capital vary considerably across industries. The largest benefits occur in service industries—Trade (32), Finance, Insurance and Real Estate (33), Other Services (34), Construction (6), Kindred Products (7), Machinery except Electrical (22) and Motor Vehicles (24). The marginal benefits are fairly small and negative in Mining Industries (2,3 and 5). The marginal benefits are very small in Tobacco (8), Leather and Leather Products (18), Furniture and Fixture (12), Instruments (26) and Miscellaneous Manufacturing (27). In all other industries, and particularly in the manufacturing industries, the marginal benefits of an increase in highway capital range approximately between 0.002 to 0.006. These pattern of benefits correspond to a large extent to the Fernald (1992) ranking of industries by their share of motor Vehicles. The measures of marginal benefits can be translated into dollar units of cost reduction in each industry. A simple way to do this is to multiply the measure of marginal benefits to each industry by the net increase in highway capital in a particular year or period.
The estimates of the marginal benefits imply potential taxes that the industries will be "willing" to pay. The magnitudes of the taxes correspond to the size of the benefits received by different industries. The magnitudes of such taxes vary considerably across industries. The largest potential taxes, corresponding to industry's "willingness to pay," in manufacturing are in Food and Kindred Products (7), Chemicals and Chemical Products (15), Primary Metals (20), Machinery except Electrical (22), Other Transportation Equipment (25), Motor Vehicles (24), Construction (6), Trade (32), Finance, Insurance and Real Estate (33), and Other Services (34). These industries are major recipients of the benefits of highway capital and therefore would theoretically be willing to pay sizable taxes to use the highway capital or make additions to the existing stock. Those industries that would "pay" the lowest taxes include Furniture and Fixtures (12) and Leather and Leather Products (18). In three industries: Metal Mining (2), Coal Mining (3) and Nonmetallic Mineral Mining (5), modest subsidies are needed for these industries to use the existing highway capital stock at a rate equal to its marginal benefit.
One of the fundamental goals in analyzing the effect of public infrastructure is to determine its contribution to productivity growth. As indicated at the outset of this report, this issue provides the rationale for much of the literature in this area. For example, in Aschauer's original study (1989b), he attributes almost all of the slowdown in the rate of aggregate productivity growth to the slowdown in the growth of public infrastructure. To examine this issue further, we calculate the contribution of total highway capital to total factor productivity growth at the disaggregated industry level using the parameter estimates of our econometric model.
Table 10 lists the decomposition of TFP growth for each industry based on equation (8). Changes in exogenous demand are large in several industries such as Construction (6), Food and Kindred Products (7), Primary Metals (20), Machinery except Electrical (22), Motor Vehicles (24), Trade (32), Finance, Insurance and Real Estate (33) and Electrical Machinery (23). In other industries, particularly manufacturing industries and utilities, changes in exogenous demand are a major contributor to the TFP growth.
The sign of the contribution of relative input prices to TFP growth depends on whether the changes in an industry's factor price exceeds that of the general price level in the economy. Productivity growth in an industry is hampered when its input price inflation exceeds the national inflation rate, measured by the GDP deflator. As Table 10 shows, the growth in relative input prices contributes negatively to TFP growth in a some industries while contributes positively in others. The magnitude of this effect varies across industries ranging from -0.0631 in Petroleum Refining (16) to 0.0364 in the Textile and Textile Product (9) industry. However, compared to the contribution of exogenous demand, the contribution of changes in the relative input price to TFP growth is very small.
Highway capital's contribution to TFP growth is positive in all industries. In some industries, its contribution is relatively large, accounting for almost 25% of TFP growth, but in most industries its contribution to changes in TFP is fairly modest. When the effects of demand, relative input price changes, and highway capital are taken into account, the rate of technical change is much smaller than conventionally calculated. In general, the main contributors to TFP growth in almost all industries are the exogenous shifts in demand, highway capital and technological change.
