Public infrastructure and the productive performance of Canadian manufacturing industries.

1. Introduction

While the international literature on the effects of public infrastructure on productivity growth reports controversial results, the Canadian policy makers tend to regard public infrastructure as the key to long-run industrial and economic growth. The public infrastructure investment, as leverage to competitiveness, was the subject matter of the Tenth John Deutsch Roundtable Conference in June 1993, the proceedings published in Mintz and Preston (1993). Most of these contributions deal with broad Canadian policy issues and questions relating to public infrastructure and growth at the aggregate level. Wylie (1996) reports output elasticity of public capital to be around 0.5 for the Canadian goods sector. His study is based on a goods value-added translog production function with two private factors of production, labor and capital, and the stock of public capital. There are other Canadian studies, which focus on the related issues such as the financing of productivity enhancing public investment (Feehan 1998; Feehan and Matsumoto 2000) and the performance of manufacturing industries in terms of labor or total factor productivity relative to their counterparts in the United States and Japan (Fullerton and Hampson 1957; West 1971; Frank 1977; Caves and Christensen 1980; Balwin and Green 1987; Denny 1992; Keay 2000).

The present article examines the effects of public infrastructure on productivity in 12 two-digit manufacturing industries, which contribute about two thirds to the total output of the manufacturing sector. (1) A translog cost function incorporating public capital infrastructure is estimated for each industry separately using annual time-series data for 1961-1995. The cost-function approach facilitates the investigation of productive effects of public capital in terms of both cost-saving and output-augmenting measures. It also enables us to examine public capital's effects on the input demand and derive the rate of return on public investment (pertaining to manufacturing). To the best of our knowledge, this is the first detailed study of the effects of public capital on the productivity of two-digit Canadian manufacturing industries.

Our empirical results provide strong evidence of the important role public infrastructure plays in the productivity of manufacturing industries. The estimates of output-side (primal) measures of productivity effects are higher than the cost-side (dual) measures due to the existence of significant scale economies in production. The public capital has a substitutional relationship with private capital and labor in most industries. The degree of substitutability between private capital and public capital is stronger than that between labor and public capital. The rates of return on public capital are statistically significant and vary over the years.

The rest of the article is organized as follows. Section 2 provides a brief overview of international empirical debate on the relationship between public capital and productivity growth. The cost function approach that forms the basis of our analysis is discussed in section 3. Section 4 describes the data and variables and identifies the Canadian manufacturing industries. The empirical results are discussed in section 5. Section 6 summarizes and brings together the main conclusions.

2. A Review of International Debate

The empirical research on the relationship between public infrastructure and productivity growth originated in an attempt to explain the slowdown of U.S. productivity during the 1970s. The first wave of work by Aschauer (1989) and Munnell (1990a) based on the Cobb-Douglas production function framework provides estimates of output elasticity with respect to public infrastructure in the range of 0.30-0.40 for the aggregate U.S. economy. Given the size of public capital and output, these results imply a rate of return to public infrastructure in the range of 60-146% per year. (2) In contrast, at the state/ regional level, the estimates of output elasticity reported in Duffy-Deno and Eberts (1989), Munnell (1990b), Eisner (1991), and Garcia-Milla and McGuire (1992) are smaller or insignificant (0.04-0.20). (3)

The wide differences in the estimates of production effects of public infrastructure led to questioning the validity of the Cobb-Douglas production function framework. The latter represents a very restrictive technology and ignores the role of input prices in the decision-making process of a firm. Subsequent contributions overcame these issues by replacing the Cobb-Douglas production function with a flexible (translog or generalized Leontief) cost function. The cost-function approach measures productivity effects of public infrastructure in terms of cost saving. The estimates of this cost-side (dual) measure of productivity effects are shown to be smaller. For instance, based on a translog unit cost function, Nadiri and Mamuneas (1994) report the estimates of cost-side productivity (cost-saving) effects to be in the range of 0-0.2 for 12 U.S. two-digit manufacturing industries. Using time series of state-level U.S. data, Morrison and Schwartz (1996) estimate a generalized Leontief cost function for the aggregate manufacturing sector and report a significant cost saving effect of public capital. Based on a translog cost function, Lynde and Richmond (1992) find strong evidence of the important role played by public capital in the productivity of the U.S. nonfinancial corporate sector.

Recently, the data for other economies have been utilized to assess the productivity effects of public infrastructure using a variety of methodologies. The results vary from country to country. Based on a cost-function approach, Shah (1992) reports an output elasticity of public infrastructure as low as 0.05 for the Mexican manufacturing sector. Berndt and Hansson (1992) obtain output elasticity of 0.69 with respect to public infrastructure for the Swedish private business sector. Using a Cobb-Douglas production function, Otto and Voss (1994) report an output elasticity of 0.4 for the Australian aggregate private sector. Their estimates of output elasticity at sectoral levels are quite unstable: positive and high for some sectors and negative and statistically insignificant for others. Using the same data set, Paul (2003) estimates translog cost functions incorporating public capital variable. His study reports an output elasticity of 1.18 for the aggregate private sector and in the range of 0.67 for manufacturing to 1.26 for mining.

Sturm (1998) obtains cost elasticities of public infrastructure for the aggregated, the sheltered, and the exposed sectors in The Netherlands, respectively, of -0.31, -0.28, and -0.2. His study is based on a generalized McFadden cost function. Based on an intertemporal profit function framework, Demetriades and Mamuneas (2000) present for the OECD short-run estimates of output elasticity for the whole manufacturing sector, which range from 0.35 for the United Kingdom to 2.06 for Norway. These estimates do not change much in the intermediate and long runs.

Thus, the empirical results on the productivity effect of public infrastructure vary across countries. These differences seem to have arisen due to differences in data and the model specification. In the following section, we discuss a flexible cost function approach, which enables us to measure the effects of public infrastructure on productivity in terms of both cost-saving (dual) and output-augmenting (primal) measures.

3. The Cost Function Approach

If Q is output, P the vector of prices of private inputs, t the time counter representing technology, then the cost function incorporating public infrastructure services, Z, can be specified as

(1) C = C(Q,P,t;Z),

where C = PX and X is a vector of quantities of inputs. Public infrastructure is freely provided to firms at levels determined by the government. The amount of services a firm receives from public infrastructure is not directly observable. However, the degree of usage of public capital by a firm or industry greatly depends on the level of its activities. For example, as the demand for an industry's output expands, its usage of highways, mass transit, and sewage and water systems is likely to rise. Using industry's capacity utilization rate (U) as a proxy for the degree of usage of public capital, the variable of public infrastructure services can be expressed as Z = UG, where G is the stock of public infrastructure.

Firms achieve cost savings from reduction in private inputs for the same level of output if public infrastructure services are available. This occurs due to the substitutability of public infrastructure facilities with privately purchased inputs. These cost-side productivity effects of public capital are measured by [A.sub.G] = [[eta].sub.CG], where rice = ([[partial derivative]ln C/[partial derivative]ln G) is the elasticity of cost with respect to public infrastructure. If public infrastructure investment is cost saving, [[eta].sub.CG] will be negative. Because cost and output changes are related, the cost-saving measure of productivity effects is related to output elasticity (primal) measure [[eta].sub.QG] calculated in production function-based studies. That is, [[eta].sub.QG] = ([partial derivative]Q/[partial derivative])(G/Q = [-A.sub.G]/[[eta].sub.CQ], where [[eta].sub.CQ] is the elasticity of cost with respect to output. Both the measures are equivalent only under constant returns to scale and instantaneous adjustment when they are evaluated at the same point. Under nonconstant returns to scale, the output-side (primal) measure of productivity effects can be obtained from the cost-function approach. But it is not always possible to obtain accurate values of cost-side measure from the production-function approach. (4)

The cost-function approach also enables us to examine how individual input demand and the cost structure are affected or adjusted if additional public infrastructure facilities are available to the firm. By Shephard's lemma (Diewert 1974), we know that the cost share equation for the ith input, [S.sub.i] = [P.sub.i][X.sub.i]/C = ([partial derivative]C/[partial derivative][P.sub.i])([P.sub.i]/C). The input demand elasticity of public capital can then be written, [[eta].sub.iG] = ([partial derivative][X.sub.i]/[partial derivative]G)(G/[X.sub.i]) = [eta].sub.SiG] + [eta].sub.CG], where the first term on the right-hand side of this expression is the elasticity of input cost share with respect to public capital that measures the biases in input use (as a proportion of cost share) induced by public capital facilities, and the second term is the productivity effect representing the neutral effect of public capital services on demand. Public capital services are biased toward the use of input i if [[eta].sub.SiG] > 0, saving of input i if [[eta].sub.SiG] < 0, or neutral if [[eta].sub.SiG] = 0. The cost structure of a firm remains unaffected if [[eta].sub.SiG] = 0 for all i, and in this case, the value of input demand elasticity is equal to the cost elasticity of public capital. In general, the sign and magnitude of input demand elasticity will depend on the signs and relative strengths of both the nonneutral and neutral effects of public capital facilities. They can reinforce or offset each other. The public infrastructure and input i are substitutes, independent or complementary according to whether [[eta].sub.iG] is less than, equal to, or greater than zero, respectively.

The rates of return to public capital can be calculated by adding the marginal benefits to various industries and dividing the sum by the cost of public capital investment. The cost-function approach enables us to compute marginal benefits in terms of both marginal cost saving, [b.sub.CG] = -([partial derivative]C/[partial derivative]G), and marginal output gains, [b.sub.QG] = ([partial derivative]Q/[partial derivative]G) = -([partial derivative]C/[partial derivative]G)/([partial derivative]C/[partial derivative]Q).

For empirical implementation, we require a functional form for the cost function. Two cost-function specifications, namely the translog and generalized Leontief, are quite flexible and have widely been used to represent production technology. We consider a cost function represented by the following translog functional form:

(2) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.],

where [[gamma].sub.ij] = [[gamma].ji] (symmetry). The price indices for intermediate inputs (energy and materials) for two-digit-level manufacturing industries are not available; hence, the cost function includes input prices for labor and capital only. The total cost C = [P.sub.L] + [X.sub.L] + [P.sub. K] [X.sub.K].

The cost function has to be homogeneous of degree one in input prices. The imposition of this and the symmetric restrictions on Equation 2 leads to

(3) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.].

By applying Shephard's lemma, the following input cost-share equations are obtained:

(4) [S.sub.L] = [[gamma].sub.L] + [[gamma].sub.LL] ln([P.sub.L]/[P.sub.K]) + [[gamma].sub.LQ] ln Q + [[phi].sub.LZ] ln UG + [[beta].sub.Lt]t,

(5) [S.sub.K] = (1 - [[gamma].sub.L]) - [[gamma].sub.LL] ln([P.sub.L]/[P.sub.K]) - [[gamma].sub.LQ] ln Q - [[phi].sub.LZ] ln UG - [[beta].sub.Lt]t.

The cost function of Equation 3 and one of the input cost-share equations can be jointly estimated using Zellner's iterative seemingly unrelated regression procedure. The estimate of the other input cost-share equation can be retrieved from the additivity condition. The cost-side measure of productivity effects of public capital can be computed as

(6) [A.sub.G] = [partial derivative] ln C/[partial derivative] ln G = [[phi].sub.Z] + [[phi].sub.LZ] ln([P.sub.L]/[P.sub.K]).

The output-side measure of productivity effects can be computed as

(7) [B.sub.G] = [partial derivative] ln Q/[partial derivative] ln G = [-A.sub.G]/[[eta].sub.CQ],

where

(8) [[eta].sub.CQ] = [[alpha].sub.Q] + [[alpha].sub.QQ] ln Q + [[gamma].sub.LQ] ln [P.sub.L]/[P.sub.K]

is the elasticity of cost with respect to output. The input demand elasticities of public capital can be computed as

(9) [[eta].sub.LG] = [[phi].sub.LZ]/[S.sub.L] + [[eta].sub.CG] and [[eta].sub.KG] = -[[phi].sub.LZ]/[S.sub.K] + [[eta].sub.CG],

where the first term on the right-hand side of these expressions is the input biased effect and the second term is the productivity effect representing the neutral effect on demand.

In order to represent a cost-minimizing production technology, the cost function must be linear homogeneous and concave in input prices. While the conditions of linear homogeneity are imposed on the cost function, the concavity is to be tested empirically. The latter requires that the Hessian matrix of second-order derivatives with respect to input prices be negative semidefinite.

4. Data, Variables, and Industry Identification

The time series (1961-1995) annual data on all the variables required for the estimation of cost functions for 12 two-digit manufacturing industries are taken from Statistics Canada, CANSIM. The variables are defined as follows. Output is value added measured in 1986 dollars. The stock of public infrastructure capital is measured as end-of-year stock of highways, airports, roads, bridges, marine facilities, pipelines, sewage and water systems in 1986 dollars with a one-year lag to reflect the beginning-of-year stock. (5) Similarly, the stock of private capital is measured as the end of year of privately purchased capital in each industry with a one-year lag to reflect the beginning-of-year stock. The wage rate ([P.sub.L]) is defined as the ratio of total wages and salaries to total number of employees. Following Morrison (1993), the price of private capital is measured in terms of user cost defined as: [P.sub.K] = [p.sub.K](d + r)HT, where [p.sub.K] is the investment deflator (defined as the ratio of current to constant values of privately purchased capital stock), d, the depreciation rate, is total depreciation divided by the value of capital stock, r is 10-year bond rate, and HT = (1 + [iota]), [iota] is the effective rate of taxation. (6) Both the input prices have been normalized to equal one in 1986 before estimating the model.

Table 1 identifies industries and provides some descriptive statistics such as mean levels of output, input cost shares, and growth rates of inputs and output. There are large differences in input cost shares across industries. In most of the industries, the share of labor in cost is considerably higher than that of capital. There is also notable variation among industries in terms of growth rates of output, labor, and capital inputs.

5. An Analysis of Empirical Results

The model consisting of the cost function of Equation 3 and labor cost share, Equation 4, is estimated using Zellner's iterative seemingly unrelated regression procedure for each manufacturing industry and tested for concavity. The Hessian matrix ([partial derivative][C.sup.2]/[partial derivative][p.sub.i][p.sub.j]) is found to be negative semidefinite at all data points for all the industries. This suggests that the estimated model represents a well-behaved (cost-minimizing) production technology.

Table 2 presents the estimated parameters of the model. The high values of [R.sup.2] and low value of standard errors for each equation reveal that estimated models provide reasonably good fit to the data. (7) Most of the estimated parameters of the cost function are statistically significant.

The Productivity Effects

The estimates of both the cost-side and output-side productivity effects of public capital presented in Table 3 show considerable variation across industries. For most industries, the cost elasticities vary in the range between -0.10 and -0.40 and are statistically significant, implying cost savings. (8) The only exceptions are chemical and chemical products, electrical and electronic products, and leather and allied products, where these elasticities are not statistically different from zero. For most industries, our estimates are higher than those of Nadiri and Mamuneas (1994). The latter study reports the cost elasticity in the range between 0 and -0.15 for 12 two-digit U.S. manufacturing industries. The differences between their estimates and ours might have arisen due to differences in model specification. The cost function used in their study assumes constant returns to scale, whereas our model imposes no such restriction.

The output-side measure of productivity effects is defined as the negative of the ratio of cost-side measure to the cost elasticity of output. There are scale economies, neutrality, or scale diseconomies according to the cost elasticity of output: respectively, less than, equal to, or greater than unity. Thus, the output-side measure of productivity effects is higher than, equal to, or lower than the dual cost-saving measure depending on whether there are scale economies, neutrality, or scale diseconomies. For most industries, the estimates of output-side measure vary in the range between 0.26 and 2.65 and are also statistically significant. They are higher than the dual estimates because of the presence of significant scale economies in production (see Table 4). They are quite similar to the short run estimates of Demetriades and Mamuneas (2000) for the manufacturing sector in 12 OECD countries (0.35-2.06) and higher than those reported in Shah (1992) for the Mexican manufacturing sector (0.05).

Input Demand and Public Capital

The effect of public capital on input demand is the sum of input biased effect ([[gamma].sub.LG]/[S.sub.i]) and productivity effect ([[eta].sub.CG]. The input biased effects presented in Table 5 reveal that public capital is biased toward the use of labor and the saving of private capital in five industries (electrical and electronic products, rubber, tobacco, transport, and wood products). The converse holds for clothing and primary metal industries. In most of these cases, the magnitude of biased effects on the demand for private capital is higher than that for labor. In all other industries, the estimates of [[gamma].sub.LG]/[[S.sub.i] are not statistically different from zero, implying neutrality to the use of inputs.

The overall effects of public infrastructure on input demand reported in Table 6 show considerable variation across industries. The elasticity of demand for private capital in most industries is negative (-0.23 to -0.65) and statistically significant, implying that public capital and private capital stock are substitutes. The only exceptions are clothing, leather and allied products, and chemical and chemical products, where the elasticities are statistically insignificant, implying that public infrastructure has no impact on demand for privately purchased capital. The elasticity of demand for labor is negative and statistically significant in clothing, fabricated metal, furniture and fixture, paper and allied products, and primary metal (-0.35 to -0.70), which reveals the substitutability between labor and public capital. In all other industries, these elasticities are not statistically significant from zero, implying independence between the two.

These results suggest that, in most industries, an increase in public infrastructure leads to a decline in demand for both labor and privately purchased capital. The magnitude of decline in private-capital demand seems to be stronger than that in labor demand. In other words, the degree of substitutability between private capital and public capital is stronger than that between labor and public capital. This simply reflects the fact that it is very difficult for a firm to fire labor due to contract rigidities; it is easier to substitute public capital for private capital.

Our results are quite comparable with those of Berndt and Hansson (1992), Lynde and Richmond (1992), and Nadiri and Mamuneas (1994) and opposite to Demetriades and Mamuneas (2000). Nadiri and Mamuneas report estimates of the elasticity of demand for private capital in the range between -0.62 and -1.82 and for labor in the range between -0.10 and -0.50 for 12 U.S. manufacturing industries. Our estimates for private capital are much smaller whereas those for labor are relatively large. Our results are also similar to the estimates of Berndt and Hansson and Lynde and Richmond with respect to labour input. There is, however, one major difference. We find a substitutional relationship, whereas Berndt and Hansson and Lynde and Richmond report complementarity between public infrastructure and private capital stock.

Demetriades and Mamuneas (DM) report positive and significant effects on the demand for both labor and private capital in the manufacturing sectors of 12 OECD economies (including Canada), implying that public capital is a complement to both labor and private capital. It is not clear why this particular result of DM is different from the existing country-specific studies based on the cost-function approach. For the public capital to have a positive impact on productivity (measured in terms of cost saving or increase in profits for a given level of output), it should have a substitutional relationship with at least one of the privately purchased inputs. The DM study utilizes the panel data for OECD relating to 1972-1991. Should the OECD countries with larger public capital have bigger manufacturing sectors (employing larger labor and private capital), then the observed complementary relationship between public capital and private inputs may be a statistical artefact of resource differences between them.

Marginal Benefits and the Rates of Return

The industry-specific marginal cost saving benefits are obtained as [b.sub.CG] = -([partial derivative]C/[partial derivative]G) = -[n.sub.CG](C/ G) and marginal output benefits as [b.sub.QG] = ([partial derivative]Q/[partial derivative]G) = [n.sub.QG](Q/G). Table 7 presents their estimates along with standard errors. All marginal benefits are positive and statistically significant except for four industries (chemical and chemical products, electrical and electronic products, leather and allied products, and transport equipment), where they are not statistically different from zero. The marginal benefits in terms of cost saving are fairly small in magnitude. The output-side marginal benefits are higher than the cost-side benefits. This is understandable in view of the existence of significant scale economies in production.

The sum of marginal cost savings is 0.15 and that of marginal output benefits 0.43 (see Table 8, columns 1 and 4). On dividing these sums by the marginal cost, we can get the estimates of rates of return to public investment. The measurement of the marginal cost of public funds is a very controversial issue. A range of estimates of the cost of public capital that is available for Canada includes a value of 1.25 obtained by Campbell (1975) and another of 1.38 by Dahlby (1994). These two values have gained some degree of acceptance in Canadian literature. The values of rates of return in terms of cost saving based on the Campbell and Dahlby estimates are presented respectively in columns 2 and 3 (Table 8), with the corresponding values of rates of return in terms of output presented in columns 5 and 6. Based on Dahlby's marginal cost of 1.38, the rate of return to public capital is 10.91% per year in terms of cost savings and 31.45% per year in terms of output. Our estimates of rates of return in terms of cost savings are higher than the Nadiri and Mamuneas estimate (7.2%) for the U.S. manufacturing industries and lower than those reported in Demetriades and Mamuneas (2000) for Canada (17% in the short run, 17.6% in the intermediate run, and 23.3% in the long run). But our estimates of rates of return in terms of output are much lower than the range of estimates reported for the United States (60-146%).

The rates of return to public capital vary over the years. The cost-side rates of return increased from 5.26% during 1961-1970 to 17.48% during 1981-1990 and declined to 16.21% during 1990-1995. On the contrary, the output-side rates of return showed a declining trend during the entire period. This is understandable in view of the fact that the magnitude of scale economies (cost elasticity of output) in most of the industries has declined (increased) over the sample period. If the scale economies continue to decline, the two rates of return are likely to converge at some point in the near future.

The rates of return reported above pertain only to 12 manufacturing industries. It is understandable that publicly financed capital stock may have provided some benefits to consumers and other producers not included in our study. To the extent these benefits are not negligible, the rates of return reported here should be taken as the lower bound estimates of economy-wide (social) rates of returns to public capital.

6. Conclusions

The cost function model estimated for 12 two-digit Canadian manufacturing industries imposes no restriction on returns to scale and thus facilitates the investigation of productivity effects of public capital in terms of both cost savings and output elasticity. The empirical results provide strong evidence of the important role public infrastructure plays in the productivity of manufacturing industries.

Some aspects of the evidence deserve special emphasis. First, the productivity effects of public capital vary across manufacturing industries. The estimates of output-side measure of productivity effects are larger than the cost-saving measure because of the existence of scale economies in production. Second, the services of public capital infrastructure appear to be substitutes for both labor and private capital in most of the industries. The degree of substitutability between private capital and public capital is stronger than that between labor and public capital. These results are quite similar to those reported in Nadiri and Mamuneas (1994) for 12 U.S. manufacturing industries and opposite to those reported in Demetriades and Mamuneas (2000) for the OECD economies.

Third, the marginal benefits of public capital are positive and statistically significant in most industries. Fourth, the estimates of rates of return to public capital are quite modest, 11% in terms of cost saving and 31% in terms of output. While making a case for more public infrastructure investment, output-side rates of returns are more relevant than the cost-side rates because the former take into account the scale economies. Fifth, the rates of return presented here are based on the assumption that public infrastructure provides no benefits to consumers and other producers in the economy. Most components of public infrastructure such as highways, roads, sewage, and water pipes are known to generate some benefits to consumers. To the extent these additional benefits to society are not negligible, the social rates of return to public infrastructure should be larger. The computation of benefits to all consumers and producers requires the estimation of a general equilibrium model on the lines suggested in the literature on the optimum provision of public infrastructure capital. (9) This is considered beyond the scope of this article.

Table 1. Descriptive Statistics of Manufacturing Industries (Mean
values: 1961-1995)

Industry Codes Within Parentheses             Q        C     [S.sub.L]

Chemical and chemical products (37)          7020     5032     0.410
Clothing (24)                                2343     1192     0.870
Electrical and electronic products (33)      5713     3210     0.743
Fabricated metal (30)                        6494     3353     0.751
Furniture and texture (26)                   1576      793     0.838
Leather and allied products (17)              613      447     0.592
Paper and allied products (27)               7538     6704     0.423
Primary metal (29)                           6322    17129     0.146
Rubber products (15)                         1224      852     0.587
Tobacco products (12)                         761      365     0.419
Transport equipment (32)                    11330     6595     0.662
Wood products (25)                           4044     2963     0.654
Public infrastructure stock
  Level: 87808 (constant 1986 $
  in millions)
  Growth rate: 3.37%

Industry Codes Within Parentheses         [S.sub.K]   [??]

Chemical and chemical products (37)        0.590      4.61
Clothing (24)                              0.130      2.71
Electrical and electronic products (33)    0.257      5.28
Fabricated metal (30)                      0.249      3.13
Furniture and texture (26)                 0.162      3.13
Leather and allied products (17)           0.408     -1.06
Paper and allied products (27)             0.577      3.29
Primary metal (29)                         0.854      2.52
Rubber products (15)                       0.413      4.84
Tobacco products (12)                      0.581      2.53
Transport equipment (32)                   0.338      7.46
Wood products (25)                         0.346      3.83
Public infrastructure stock
  Level: 87808 (constant 1986 $
  in millions)
  Growth rate: 3.37%

Industry Codes Within Parentheses         [X.sub.L]  [X.sub.K]

Chemical and chemical products (37)         0.83       4.69
Clothing (24)                              -0.35       0.71
Electrical and electronic products (33)     0.99       4.68

Fabricated metal (30)                       1.39       1.95
Furniture and texture (26)                  1.37       2.38
Leather and allied products (17)           -2.81       0.65
Paper and allied products (27)              0.24       4.19
Primary metal (29)                         -0.05       3.15
Rubber products (15)                        0.46       3.95
Tobacco products (12)                      -2.40       1.51
Transport equipment (32)                    2.66       5.28
Wood products (25)                          1.26       3.39
Public infrastructure stock
  Level: 87808 (constant 1986 $
  in millions)
  Growth rate: 3.37%

Q = output (constant 1986 $ in millions); C = cost (constant 1986 $ in
millions); [S.sub.L] = cost share of labor; [S.sub.K] = cost share of
private capital, [??] = percentage growth rate of output; [X.sub.L] =
percentage growth rate of labor, [X.sub.K] = percentage growth rate of
private capital stock.

Table 2. Estimated Parameter of Cost Function Models
(Standard Errors in Parenthesis)

                    Chemical              Electrical
                       and                    and
                    Chemical              Electronic    Fabricated
Parameter           Products   Clothing    Products       Metal

[[alpha].sub.0]      5.0992    17.5595     11.9070       16.0621
                    (2.3500)   (2.0470)    (2.7900)      (3.3248)
[[alpha].sub.Q]      0.2412    -2.4384     -1.0639       -1.7055
                    (0.0599)   (0.5487)    (0.6500)      (0.7843)
[[alpha].sub.QQ]                0.4227      0.2047        0.2892
                               (0.0708)    (0.0815)      (0.0916)
[[gamma].sub.L]      1.3454     0.2689     -0.5233        0.1127
                    (0.7546)   (0.1717)    (0.2479)      (0.3012)
[[gamma].sub.LL]     0.2058     0.0880      0.1084        0.2769
                    (0.0095)   (0.0073)    (0.0125)      (0.0165)
[[gamma].sub.LQ]                0.1634      0.1018        0.0857
                               (0.0120)    (0.0204)      (0.0282)
[[theta].zub.Z]      0.1006    -0.3377     -0.1592       -0.3493
                    (0.2277)   (0.0956)    (0.1315)      (0.0844)
[[theta].zub.LZ]    -0.0689    -0.0535      0.0578       -0.0012
                    (0.0716)   (0.0211)    (0.0254)      (0.0443)
[[beta].sub.t]       0.0220    (0.0091)    -0.0087        0.0059
                    (0.0077)   (0.0026)    (0.0048)      (0.0019)
[[beta].sub.Lt]     -0.0079    -0.0026     -0.0127       -0.0050
                    (0.0024)   (0.0006)    (0.0011)      (0.0010)
Cost Function
[R.sup.2]            0.97       0.98        0.98          0.98
Std. Error           0.0870     0.0255      0.0515        0.0273
Lab. Cost Share
[R.sup.2]            0.92       0.92        0.97          0.83
Std. Error           0.0229     0.0053      0.0091        0.0131

                                Leather
                    Furniture    and      Paper and
                       and      Allied      Allied       Primary
Parameter            Fixture   Products    Products       Metal

[[alpha].sub.0]      7.3191     3.9329     11.0643       10.6942
                    (2.3920)   (2.4166)    (1.1706)      (1.3652)
[[alpha].sub.Q]      0.2478     0.5143      0.1270        0.3676
                    (0.6614)   (0.7101)    (0.0527)      (0.1385)
[[alpha].sub.QQ]     0.0805    -0.0252
                    (0.0922)   (0.1135)
[[gamma].sub.L]      0.4197    (0.6316)    -0.2075       -0.2008
                    (0.1942)   (0.3002)    (0.3387)      (0.1203)
[[gamma].sub.LL]     0.1461     0.2703      0.1266        0.0520
                    (0.0116)   (0.0122)    (0.0133)      (0.0086)
[[gamma].sub.LQ]     0.1085     0.1490      0.0827        0.1017
                    (0.0175)   (0.0202)    (0.0154)      (0.0126)
[[theta].zub.Z]     -0.3974     0.0187     -0.3269       -0.4066
                    (0.0812)   (0.0654)    (0.1188)      (0.1891)
[[theta].zub.LZ]    -0.0271     0.0333      0.0080       (0.0433)
                    (0.0241)   (0.0371)    (0.0344)      (0.0164)
[[beta].sub.t]       0.0055    -0.0089      0.0316        0.0355
                    (0.0021)   (0.0021)    (0.0038)      (0.0051)
[[beta].sub.Lt]     -0.0033    -0.0066     -0.0100       -0.0026
                    (0.0006)   (0.0013)    (0.0011)      (0.0005)
Cost Function
  [R.sup.2]          0.97       0.99        0.98          0.97
  Std. Error         0.0377     0.0226      0.0425        0.0600
Lab. Cost Share
  [R.sup.2]          0.81       0.99        0.98          0.92
  Std. Error         0.0102     0.0108      0.0112        0.0048

                     Rubber     Tobacco    Transport       Wood
Parameter           Products   Products    Equipment     Products

[[alpha].sub.0]      4.6793   -18.1116     13.7835       -3.7197
                    (3.0260)   (4.1733)    (3.1702)      (4.5973)
[[alpha].sub.Q]      0.9767     7.5046     -1.2034        3.0513
                    (0.7580)   (1.2747)    (0.5871)      (1.1044)
[[alpha].sub.QQ]    -0.0932    -1.0787      0.1714       -0.3088
                    (0.1145)   (0.1957)    (0.0732)      (0.1345)
[[gamma].sub.L]     (0.3835)   -0.6383     -1.6115       -1.6924
                    (0.3551)   (0.2186)    (0.2948)      (0.3705)
[[gamma].sub.LL]     0.1956     0.2025      0.0614        0.2972
                    (0.0250)   (0.0167)    (0.0205)      (0.0339)
[[gamma].sub.LQ]    -0.0029    -0.0163      0.0624        0.0122
                    (0.0221)   (0.0298)    (0.0188)      (0.0372)
[[theta].zub.Z]     -0.2129    -0.1184     -0.1145       -0.2556
                    (0.0792)   (0.0825)    (0.1198)      (0.1065)
[[theta].zub.LZ]     0.1136     0.1314      0.1788        0.1359
                    (0.0332)   (0.0288)    (0.0365)      (0.0448)
[[beta].sub.t]       0.0112    -0.0115      0.0166        0.0106
                    (0.0028)   (0.0018)    (0.0035)      (0.0027)
[[beta].sub.Lt]     -0.0130    -0.0122     -0.0156       -0.0125
                    (0.0011)   (0.0012)    (0.0008)      (0.0011)
Cost Function
  [R.sup.2]          0.97       0.97        0.98          0.98
  Std. Error         0.0485     0.0377      0.0561        0.0521
Lab. Cost Share
  [R.sup.2]          0.95       0.77        0.96          0.88
  Std. Error         0.0176     0.0123      0.0147        0.0197

Table 3. Estimates of the Cost-Side (Dual) and Output-Side
(Primal) Measures of Productivity Effects of Public Infrastructure
(at Mean Values; Standard Errors in Parentheses)

                                      Dual Measure      Primary Measure
Industries                            [A.sub.G] =        [B.sub.G] =
                                      [[eta].sub.CG]     [[eta].sub.QG]

Chemical and chemical products        0.1030 (0.2286)  -0.4270 (0.9477)
Clothing                             -0.3308 (0.0935)   0.4032 (0.1140)
Electrical and electronic products   -0.1617 (0.1315)   0.2299 (0.1870)
Fabricated metal                     -0.3493 (0.0845)   0.4189 (0.1013)
Furniture and fixture                -0.3950 (0.0795)   0.4754 (0.0957)
Leather and allied products           0.0177 (0.0643)  -0.0508 (0.1948)
Paper and allied products            -0.3272 (0.1194)   2.6501 (0.9746)
Primary metal                        -0.4039 (0.1885)   1.1180 (0.5217)
Rubber products                      -0.2268 (0.0792)   0.7223 (0.2522)
Tobacco products                     -0.1283 (0.0812)   0.3688 (0.2333)
Transport equipment                  -0.1068 (0.1196)   0.2674 (0.2994)
Wood products                        -0.2629 (0.1073)   0.5414 (0.2210)

Table 4. Estimates of the Elasticity of Cost with Respect to
Output ([[eta].sub.CQ]

                                          At Mean Level

Industries                          [[eta].sub.CQ]  Std. Error

Chemical and chemical products      0.2412          0.1884
Clothing                            0.8203          0.0498
Electrical and electronic products  0.7032          0.1083
Fabricated metal                    0.8338          0.0564
Furniture and fixture               0.8307          0.0591
Leather and allied products         0.3479          0.0335
Paper and allied products           0.1225          0.0530
Primary metal                       0.3613          0.1381
Rubber products                     0.3140          0.0802
Tobacco products                    0.3480          0.0780
Transport equipment                 0.3994          0.1150
Wood products                       0.4856          0.0922

                                      Estimates of [[eta].sub.CQ]
Industries                          1961           1970        1980

Chemical and chemical products      0.2412         0.2412      0.2412
Clothing                            0.5140         0.6528      0.8123
Electrical and electronic products  0.4506         0.5667      0.6749
Fabricated metal                    0.6128         0.7902      0.8572
Furniture and fixture               0.7758         0.7999      0.8199
Leather and allied products         0.4097         0.3874      0.3275
Paper and allied products           0.1074         0.1095      0.0976
Primary metal                       0.2993         0.3220      0.3321
Rubber products                     0.4064         0.3413      0.3183
Tobacco products                    0.9144         0.6192      0.1924
Transport equipment                 0.1410         0.2892      0.3680
Wood products                       0.7105         0.6177      0.4770

                                    Estimates of [[eta].sub.CQ]

Industries                            1990           1995

Chemical and chemical products       0.2412         0.2412
Clothing                             0.9575         0.9591
Electrical and electronic products   0.8063         0.8677
Fabricated metal                     0.8956         0.9194
Furniture and fixture                0.8505         0.8633
Leather and allied products          0.3365         0.3927
Paper and allied products            0.1288         0.1534
Primary metal                        0.3732         0.4016
Rubber products                      0.2944         0.2679
Tobacco products                     0.1431         0.0555
Transport equipment                  0.4781         0.5449
Wood products                        0.4025         0.3778

For all industries, the estimates of [[eta].sub.CQ] are less than
one at 5% or higher levels of significance. Standard errors for
selected years are not presented. These are available from the
authors on request.

Table 5. Input Biased Effects of Public Infrastructure (as a Percentage
of Input Cost Share) (at Mean) Levels; Standard Errors in Parentheses)

Industries                                Labor             Capital

Chemical and chemical products      -0.1680 (0.1746)   0.1167 (0.1213)
Clothing                            -0.0615 (0.0242)   0.4115 (0.1623)
Electrical and electronic products   0.0777 (0.0341)  -0.2249 (0.0988)
Fabricated metal                    -0.0016 (0.0589)   0.2321 (0.1779)
Furniture and fixture               -0.0271 (0.0287)   0.1672 (0.1487)
Leather and allied products          0.0565 (0.0626)  -0.0816 (0.0909)
Paper and allied products            0.0189 (0.0813)  -0.0138 (0.0596)
Primary metal                       -0.2965 (0.1123)   0.0507 (0.0192)
Rubber products                      0.1952 (0.0565)  -0.2750 (0.0803)
Tobacco products                     0.3136 (0.0687)  -0.2262 (0.0495)
Transport equipment                  0.2700 (0.0551)  -0.5289 (0.1080)
Wood products                        0.2078 (0.0685)  -0.3928 (0.1295)

Table 6. Estimates of Input Demand Elasticity with Respect to
Public infrastructure (at Mean Values; Standard Errors in Parentheses)

Industries                               Labor            Capital

Chemical and chemical products      -0.0648 (0.2327)   0.2200 (0.2764)
Clothing                            -0.3923 (0.1130)  -0.0827 (0.1105)
Electrical and electronic products  -0.0839 (0.1359)  -0.3868 (0.1645)
Fabricated metal                    -0.3510 (0.1321)  -0.3445 (0.1353)
Furniture and fixture               -0.4274 (0.1031)  -0.2271 (0.1027)
Leather and allied products          0.0741 (0.1190)  -0.0639 (0.0607)
Paper and allied products           -0.3082 (0.1137)  -0.3412 (0.1538)
Primary metal                       -0.7010 (0.2685)  -0.3532 (0.1784)
Rubber products                     -0.0334 (0.0953)  -0.5020 (0.1151)
Tobacco products                     0.1852 (0.1343)  -0.3547 (0.0649)
Transport equipment                  0.1634 (0.1257)  -0.6353 (0.1702)
Wood products                       -0.0552 (0.1036)  -0.6565 (0.1968)

Table 7. Estimates of Dual and Primal Measures of Marginal Benefits of
Public Infrastructure (at Mean Values; Standard Errors in Parentheses)

Industries                            Dual Measure     Primal Measure
                                      ([b.sub.CG])      ([b.sub.QG])

Chemical and chemical products      -0.0059 (0.0131)  -0.0241 (0.0757)
Clothing                             0.0045 (0.0013)   0.0108 (0.0030)
Electrical and electronic products   0.0059 (0.0047)   0.0034 (0.0121)
Fabricated metal                     0.0133 (0.0032)   0.0309 (0.0075)
Furniture and fixture                0.0035 (0.0007)   0.0085 (0.0017)
Leather and allied products         -0.0001 (0.0003)   0.0000 (0.0013)
Paper and allied products            0.0250 (0.0091)   0.2273 (0.0837)
Primary metal                        0.0788 (0.0367)   0.0805 (0.0134)
Rubber products                      0.0022 (0.0007)   0.0100 (0.0011)
Tobacco products                     0.0005 (0.0003)   0.0032 (0.0007)
Transport equipment                  0.0080 (0.0089)   0.0345 (0.0154)
Wood products                        0.0089 (0.0036)   0.0249 (0.0049)

Table 8. The Rates of Return to Public Infrastructure

                            Dual measure

                             Based on       Based on
               Sum of       Campbell's      Dahlby's
              Marginal        (1975)         (1994)
Period      Benefits (1)   Estimate (2)   Estimate (3)

1961-1995      0.1506         0.1205         0.1091
              (0.0394)       (0.0315)       (0.0285)
1961-1970      0.0726         0.0581         0.0526
1971-1980      0.1365         0.1092         0.0989
1981-1990      0.2412         0.1930         0.1748
1991-1995      0.2337         0.1890         0.1621

                           Primal Measure

                             Based on       Based on
               Sum of       Campbell's      Dahlby's
              Marginal        (1975)         (1994)
Period      Benefits (4)   Estimate (5)   Estimate (6)

1961-1995      0.4340         0.3472         0.3145
              (0.1157)       (0.0925)       (0.0838)
1961-1970      0.6124         0.4899         0.4438
1971-1980      0.5862         0.4690         0.4248
1981-1990      0.5044         0.4035         0.3655
1991-1995      0.3259         0.2607         0.2362

The subperiod estimates are the means of yearly estimates.
Values within parentheses are the standard errors.

The authors are thankful to Urvashi Biswal, James Feehan, and an anonymous referee for useful comments on an earlier draft of this article.

(1) We could not cover the entire sector because the required complete set of data for the remaining two-digit industries is not available.

(2) See Demetriades and Mamuneas (2000, p. 687), Munnell (1992, p.191), and Gramlich (1994, p. 1176).

(3) Holz-Eakin (1994), Evans and Karras (1994), and Tatom (1991) have estimated the production function in the first difference, which yields implausible results showing public capital's effects quite small, sometimes negative, and generally statistically insignificant. As argued in Munnell (1992), the first differencing has problems of its own, which stem from its inability to capture the long-run nature of the relationship between public capital and output. In other words, the first-difference specification destroys long-run relationships in the data, which is exactly what one is trying to capture. It is for this reason that the equations in first difference often yield quite implausible results.

(4) If the production structure is nonhomothetic, then the returns to scale parameter (v) obtained as the sum of output elasticities with respect to inputs from the production function is not equal to the inverse of [[eta].sub.CQ]. Therefore, -([[eta].sub.QG]/v) can only be used as an approximation to the true value of [[eta].sub.CG] (=-[[eta].sub.QG][[eta].sub.CQ]) obtained from the cost function. However, this problem does not arise if the production structure is homothetic.

(5) The data on different components of public capital are not readily available. Hence, we could use only an aggregated public capital variable in our cost function.

(6) In the case of a few industries, the values of effective rate of corporate tax were either missing or were reported negative or very high for a few years. These were replaced by the average value of the adjacent years to smooth out the data series.

(7) For three industries, namely, the chemical and chemical products, paper and allied products, and primary metal, estimates of cost elasticity with respect to output were found to be negative. These turned out to be positive when we reestimated the model with [[alpha].sub.QQ] = 0 in the case of paper and allied products and primary metals and with [[alpha.sub.QQ] = [[gamma].sub.LQ] = 0 in the case of chemical and chemical products. The estimates of these parameters in the respective cost functions were not statistically different from zero. It is also worth noting that the model with zero restrictions on these parameters is still quite flexible and imposes no restrictions on the statistics that are of interest to us. The concavity condition is also satisfied at all data points.

(8) For computing standard errors of elasticities, we have used the following general formula:

Var ([summation over (i)] [beta.sub.i][x.sub.i]) = [summation] [x.sup.2.sub.i]Var([[beta].sub.i]) + 2 [summation over (i[not equal to]j) [x.sub.i][x.sub.j]Cov([[beta].sub.i],[[beta].sub.j]).

All the variables entering this formula, except the parameter estimates, are treated as constants equal to their mean values.

(9) See Feltenstein and Ha (1999) and Rioja (1999).

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Satya Paul, * Balbir S. Sahni, ([dagger]) and Bagala P. Biswal ([double dagger])

* School of Economics and Finance, University of Western Sydney, Campbelltown Campus, Locked Bag 1797, Penrith South DC, NSW 1797, Australia; E-mail [e-mail]; corresponding author.

([dagger]) Centre for International Academic Cooperation, Concordia University, 7141 Sherbrooke Street West, Montreal, Quebec H4B 1R6, Canada; E-mail [e-mail].

([double dagger]) CYSD/ARB/Strategic Policy, Human Resources Development Canada, Phase II, 7th Floor, Place du Portage, 165 Hotel de Ville, Hull (Quebec) K1A 0J2, Canada; E-mail [e-mail].

Received March 2002; accepted April 2003.