1 More comprehensive surveys of the production function approach may be found in Aschauer (1993a, b) and Federal Highway Administration (1992).
2 Specifically, the elasticity is defined as .
3 For a cogent discussion, see Gramlich (1994).
4 For a review of the literature, see Aschauer (1993a, b).
5 In the production function context, estimation of the elasticities of substitution requires that the matrix of production coefficients be inverted. This exaggerates the estimation errors and reduces the statistical precision of the computed elasticities of substitution (Nadiri and Schankerman (1981a, b)).
6 See Aschauer (1989a, b).
7 We require the system of equations (3) to satisfy the usual regularity conditions. In particular, for the cost function to be concave in price inputs, its Hessian matrix of second-order derivatives with respect to variable input prices should be negative semi-definite. Also, the cost function should be nondecreasing in output and linearly homogenous in input prices. Finally, in order for public capital to have a meaningful context, the cost function should be nonincreasing in .
8 Similar expressions can be obtained for other infrastructure capital, . Since the main focus of this report on effects of highway capital, the results for other infrastructure capital are not presented.
9 See Table A and B in Appendix 1.
10 For a description of the data construction, see Jorgenson, Gallop, and Fraumeni (1987). Also see Jorgenson (1990).
11 After several discussions with Professor Jorgenson's staff, it was confirmed that the differences were mainly due to recomputation and reclassification of the underlying data.
12 Total highway stock is based on capital outlays by all levels of government. The non-local component is an estimate of the federal aid highway system from 1921 through 1992, excluding secondary rural roads.
13 Federal structures include industrial, educational, hospital and other buildings, highways and streets, construction and development, and other structures. State and local structures include educational, hospital and other buildings, highways and streets, construction and development and other structures. "Other buildings" consists of electric and gas facilities, transit systems, airfields, etc.
14 The numbers in parentheses refer to the SIC code for the industry.
15 Fernald (1992) suggests an interesting approach. He uses "vehicle intensity" as a proxy for the 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 many direct productive services from roads.
16 The elasticities with respect to increases in public infrastructure other than highways can be derived in a similar way.
17 For the derivation of this equation, see Appendix 2.
18 For further explanation of this point, see the discussion in the 1996 report, "Contribution of Highway Capital to Industry and National Productivity Growth," pp. 75-76.
19 These estimates are almost all close to zero and therefore are not reported separately.
20 Under cost minimization the Lagrangian is given by
Applying the envelope theorem, we have
where and is the Lagrangian multiplier. By multiplying the second condition by and using the third, the relationship between public capital output elasticity and public capital cost elasticity is given by
which provides the linkage between the production function approach and cost function approach. This condition can be used to recover the public capital output elasticities from the public capital cost elasticities.
21 Note that figure of 0.2943 is a gross marginal benefit inclusive of the depreciation rate of highway capital stock.
22 Fernald (1992), p. 26.
23 To keep the focus of this report on contribution of highway capital, we have not discussed the contributions of other infrastructure capital.
24 See Nadiri and Prucha 1996.
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