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The analytical framework of the present study is similar to that of our 1996 study. The main difference is that in this study we adapt a translog functional form instead of a Normalized Symmetric MacFadden functional form to approximate an industry's cost function. After some experimentation it became clear that the translog functional form permitted to more easily incorporate some of the new features of the model, such as the inclusion of two public infrastructure capital stocks as separate arguments of the cost function. When we compared the results of the cost models with translog and Normalized Symmetric MacFadden functional forms, the overall results were not very different.
We estimated the demand function (1) for each industry. Initial estimation revealed that in a few industries the price elasticities had incorrect signs. A different formulation of the demand functions was attempted by estimating the model with the industry panel data; we also formulated alternative specifications of equation (1), introducing other variables in the demand function such as interest rate, unemployment rate, and the price of imports. The results of these alternative specifications did not differ much from those reported in Table 5. The results indicate that the price elasticities of demand and the per-capita income elasticities of demand vary across industries. The price elasticity of output demand is negative, less than one, and statistically significant in almost all industries. In two industries, SIC 34 and SIC 35, the price elasticities are positive but statistically insignificant. We then set these coefficients to zero and t re-estimated the demand equation. The magnitude of the price elasticity varies across industries, but generally they are very small. Unfortunately, there are not many recent studies available to provide a basis for comparison. Houthakker and Taylor (1966) calculated price elasticities for different industries based on product classification, as opposed to the industry classification used here. However, in cases where our frameworks are comparable, their estimated price elasticities are similar to ours.
The parameters of the underlying cost function are estimated using the cost
function (3) and the share equations (4). These equations depend on private
input prices, the level of industry output 
, the time trend 
,
the level of total highway capital stock 
, and the level of other infrastructure
capital 
. Hulten (1990) argues that the
intensity of public capital usage fluctuates over time. There are variations
in the utilization of highways, evidenced for example, by the ratio of vehicle
miles traveled to the capital stock of roads. Also, public capital is a collective
input which firms must share with others and therefore is subject to congestion
(see Deno (1988)). Firms might have some control over the use of the public
stock (see Shah (1992) and Fernald (1992)). For instance, a firm may have no
influence on the level of highways provided by the government, but it can vary
its use of existing highways by choosing routes. Adjustment for utilization
of highway capital could indeed affect both the magnitudes of industry marginal
benefits and the time pattern of the rates of return to highway capital stock.
However, it is difficult at present to obtain a reliable and appropriate measure
of highway usage by each industry over the period 1950-91.15
Therefore, at this stage of our analysis, we have not made any adjustment for
utilization of the public capital stocks 
and 
.
The sample consists of pooled time-series cross-section data for 35 two-digit
industries during the period 1950 - 1991. In order to capture industry specific
effects, we assume the parameters 
are industry specific.
Thus, we assume 
, where the parameters are normalized
with respect to the k-th industry 
,
is an industry dummy
variable taking values either 1 or 0, and 
is an industry identification index. We estimate the model using an iterative
seemingly unrelated regression approach (ISUR). Initial estimation revealed
serial correlation in the residuals. Therefore, the equations were re-estimated
with a correction for first order serial autocorrelation.
Moreover, in order to account for the effect of infrastructure capital other
than total highway capital in the model, we assume that the two types of public
capital are complements. Therefore, we add an auxiliary equation of the form
where 
and 
are highway capital and other public capital, respectively. The equation fit
extremely well and the coefficient 
was statistically significant and robust with a magnitude of about 0.37. Other,
more complicated forms of this equation were also estimated but the estimates
did not change much. We have estimated the overall model assuming different
values for 
, but the most sensible results
were obtained when 
was close to the estimated
value of 0.37.
In Table 6, we present parameter estimates for the translog
cost function (3). The estimated factor demand system satisfies all the required
regularity conditions: the estimated cost function is shown to be nondecreasing
in output, linearly homogeneous in input prices, and concave in factor prices.
The results show that the cost model is well specified and that the parameter
estimates are statistically significant. Coefficients of the industry dummy
variables, not shown in Table A in Appendix 1, are also
statistically, which suggests significant differences in the cost structure
across industries. The squares of the correlation coefficients between the actual
and predicted values are high, and the standard errors of each equation are
small in both versions of the model. The estimated value of the autocorrelation
parameter, 
, was very high—about
0.9. Since the estimate of 
was so close to unity
we re-estimated the model, setting 
=1. Furthermore, we carried
out a number of tests, similar to those in our 1996 report to test the sensitivity of our results.
To estimate the effect of an increase in highway capital stock on industry
cost and demand for factors of production, we need estimates of the cost elasticity
with respect to highway capital, 
, and the cost elasticity
of output for each industry. The indirect or "factor bias effect"
of 
can
be measured by its impact on private sector input demand functions. Furthermore,
we can derive the "induced" output effect of cost reduction due to
an increase in highway capital. This occurs because the reduction in cost (due
to an increase in highway capital investment) induces a price decline, which
in turn leads to an output increase. To produce the extra output, however, will
require demand for inputs to increase, thus leading to higher costs of production.
From the estimates of the demand and cost functions, we derive the critical demand and cost elasticities that are necessary to measure the impact of highway capital on the cost structure and productivity growth of each industry. The critical elasticities are the following:16
represents
the private cost elasticity with respect to total highway capital. It is defined
as 
and is obtained by simply differentiating the cost function (3) with respect
to 
,
the total highway capital stock.
.
is obtained by differentiating
the cost function (3) with respect to the level of output, 
.
The marginal cost is 
and is derived from the cost function using the expression.
is the cost elasticity of output when all inputs, including highway capital
and other infrastructure capital are included. It is defined as 
.
; that is the cost elasticity of
highway capital multiplied by the estimated internal degree scale for each industry.
Total factor productivity growth, 
, can be decomposed as17
(8) 
where 
.
We obtain the relevant parameter estimates from the estimates of the industry
demand and the cost functions. The parameters of equation (8) are defined as
follows. 
is the output elasticity of demand, 
is the income elasticity of output
demand, 
is the markup over cost, 
and 
are respectively the growth of GNP and population, and 
and 
are respectively the growth rates of the industry output prices and the GNP
price deflator. 
is the change in degree of scale, 
is the ratio of output price, 
,
to average cost. Finally, the 
are the cost elasticities with respect to highway capital and other infrastructure
capital, 
the changes in these two types of public capital and 
is the change in level
of technology.
According to equation (8) TFP growth can be decomposed into the following components:
(i) an exogenous demand effect,
;
(ii) a factor price effect, 
;
(iii) a public capital effect, 
; and
(iv) disembodied technical change 
.
The parameter estimates of both the demand function (1) and the cost function
(3) are critical for the decomposition of 
. In particular, 
,
the price and income elasticities of demand, and 
and 
,
the output cost elasticity and elasticity of cost with respect to an increase
in highway capital,
,
play critical roles in the decomposition of total factor productivity growth.
The public capital and disembodied technical change effects can be decomposed
further into direct and indirect effects. For example, the direct effect of
infrastructure 
, is given by 
while its indirect effect is given by 
. Thus, an increase in public infrastructure
initially increases total factor productivity by reducing the private cost of
production, which in turn leads to a lower output price and higher output growth.
Changes in output growth in turn lead to changes in TFP growth.
The important parameters in (8) are the price and income elasticities of demand
and the cost elasticities of the private cost function. Note that if the demand
function is completely inelastic (
= 0), then shifts in the cost function
due to real factor price changes, public capital, or disembodied technical change
have no effect on output and hence no indirect effect on TFP. In addition, if
the technology exhibits constant returns to scale with respect to all inputs,
including public capital inputs, (i.e.
), then equation (8) collapses to
.
