I. INTRODUCTION

In our 1996 study, "Contribution of Highway Capital to Industry and National Productivity Growth," we examined the effects of highway capital on the costs, production structure and productivity growth of thirty-five US industries. The individual industry estimates were then aggregated to measure the total effect of investment in highway capital on the entire economy during the post-war period. We use the main results of that study (which we report in section III of this paper) as the primary point of departure for the work presented here. In the present study, we use new modeling techniques and an extended and revised data set to test and improve the results of the 1996 report. The modifications that we introduce in our current work are as follows:

1. We address the possibility that omitting variables, such as other infrastructure capital stocks, may bias the magnitude of highway capital's contribution to the output and productivity growth. Clearly, there is considerable evidence that other types of public infrastructure capital beside highway capital contribute to productivity growth. In addition, it is important to take account of the complementarity among the services of highway and transportation capital and other types of infrastructure capital. We need to consider explicitly in our estimation algorithm the fact that the marginal productivities of these types of capital are interrelated.

2. In our previous study, we held the level of output fixed and calculated the productivity gains for each industry as the rate of cost reduction given the level of output. However, investment in highway capital induces an output expansion effect. Highway capital investment initially reduces cost via a productivity effect that shifts the average cost curve downward. This in turn, given a downward sloping output demand curve, leads to a decline in output prices and an increase in the demand for output. To produce the greater output induced by the decline in output price, firms increase their demand for factors of production such as labor, materials and capital. This leads to an increase in total cost. The total impact on the demand for factors of production is the sum of the induced output expansion effect of highway capital investment and initial effect on demand for labor, capital and materials given the level of output. We report in this study the changes in costs, input demands and output due to an increase in highway capital, at a given level of output and when output is allowed to vary.

3. Our previous study covered the period 1950-1989. In this study not only do we extend the sample period to include 1990 and -1991, we re-estimate the contribution of highway capital in a more comprehensive model. This comprehensive model includes two types of public capital, i.e., highway capital and other infrastructure capital as unpaid inputs in the production function. In addition, we use a revised data set on outputs and inputs and their respective prices. Furthermore, the model we use here differs from the one used in the 1996 study. Here, we use a translog cost function instead of the Normalized Symmetric MacFadden functional form we used previously.

The report is organized as follows. Section II briefly summarizes the main results reported in the literature on the contribution of public infrastructure capital to productivity growth using production, cost, and profit function approaches.¹ This discussion is similar to that provided in the 1996 study; it is repeated to provide a context for the findings of our recent results. In section III, we summarize the main findings of the 1996 report. This provides a point of comparison for the findings reported here. Of course, we would expect the new results to be different in certain respects because of revision and re-classification of the data and model specification.

Section IV specifies a general analytical framework of our study specifying demand and cost functions for individual industries. The analytical structure allows estimation of the structural parameters for each industry's output demand and cost functions and provides a framework for decomposing total factor productivity growth into several components including the contribution of highway infrastructure capital. This methodology allows us to trace the effects of growth of aggregate income (GDP) population, real factor price changes, technical change, and highway capital on total factor productivity (TFP) growth in each industry. Section V describes briefly the sources of data, some descriptive statistics and construction of the variables used to estimate the model. The primary data are a cross-section, time series of prices and quantities of output and inputs for 35 industry sectors for the period 1950-1991. Also, data on highway capital stock, other infrastructure capital and some aggregate data series, such as GDP, population and GDP deflator for this period are included. The industries collectively cover the entire US economy and provide a basis to estimate the contributions of various factors to the growth of output and productivity for the overall economy.

In section VI, the estimation approach for the demand and cost functions and the principle concepts, using the parameter estimates of the econometric model, to calculate the characteristics of the industry production structure, marginal benefits of highway capital and other non-highway infrastructure capital and decomposition of TFP growth are discussed.

Section VII presents empirical estimates of the effect of total highway capital on industry production costs, input demand when the level of output is assumed to be given. Estimates of the effect of an increase in total highway capital on the derived demand for inputs such as labor, capital and materials are presented. We also present the results of a decomposition of total factor productivity growth into its various components, including highway capital, by industry. Estimates of the marginal benefits of a change in the level of total highway capital to each industry are also provided. Finally, we present estimates of induced output expansion effects due to an increase in highway capital and calculate the total effects of an increase in highway capital investment on industry cost and demand for labor, materials and capital when the level of output is allowed to vary.

Section VIII provides measures of the contribution of the highway capital stock to the national economy's output and productivity growth by aggregating industry-specific estimates. We provide estimates of the social net rate of return and the net rates of return to highway capital. The net rate of return on highway capital is compared with that obtained by the private sector capital stock and with the long-term interest rate. In this section we also discuss the issue of externalities of the highway capital and provide some estimates for illustrative purposes. We also discuss the decomposition of TFP growth at the aggregate economy level. Since the results pertaining to recent years are of interest for policy purposes, we discuss very briefly in section IX, the contribution of highway capital in recent years, i.e., 1981-91 period to the growth of output, employment, capital formation and productivity growth. These results are based on the parameter estimates of the basic model. Section X provides a brief summary and conclusion followed by the appendixes and references.

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