Abstract

This study investigates several key parameters of the production process for the manufacturing sector of the United States. Attention is focused on the behavior as well as the magnitude of the elasticity of substitution, neutral and nonneutral technical progress (in a Hicksian sense), and the returns to scale. Several papers have been concerned with one or a combination of several of these parameters at the two-digit level of aggregation [7; 14; 16; 25]. However, this paper attempts a more comprehensive approach to production function estimation. By hypothesizing five relations in which the marginal rate of technical substitution is functionally dependent on the capital-labor ratio and nonneutral technical progress (i.e., the cost minimizing relation), a set of production functions is derived that includes the Cobb-Douglas and CES as well as four VES production functions. Estimating all five relations yields not only results on the elasticity of substitution and nonneutral technical progress, but it also enables us to determine the descriptive ability of each of the competing specifications. By incorporating the property of homotheticity, a set of transformations is introduced that allows for returns to scale to be constant or vary with the level of output. Homotheticity has been used in this context [3; 25]. However, estimation of an explicit homothetic transformation that allows us to determine the behavior of the returns to scale is an advancement. Estimation is based on time series data, * The author is an assistant professor of economics at Tulane University. I acknowledge the advice and criticism received from John R. Moroney, David B. Humphrey and an unknown referee. In addition, I thank Mark Schupack for making the data available. 1949-65, for the U. S. manufacturing sector aggregated according to the two-digit classification. Because the time series ends in a strong expansionary period, the problems associated with slack terminal years (and the resultant disequilibria) are avoided. In addition, the homothetic transformations are estimated twice; once with data adjusted for capacity utilization rates and again for unadjusted data.l A potentially significant source of measurement error is measurement of capital in existence (as is usual) when capital in use is required. By using both series, an estimate of the bias in estimating the homothetic transformation due to the capital data misspecification is obtainable. The plan of the paper is as follows. The theoretical relations are presented in Section I. Section II contains the econometric specifications as well as a discussion of the estimation procedure. Section III comprises results and analysis, and some concluding remarks appear in Section IV.

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