Public infrastructure and the productive performance of Canadian manufacturing industries.

• Author: Paul, Satya

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...