Analyzing the Indirect Production Function for U. S. Manufacturing

Abstract

In recent years there has been considerable research conducted in applied production economics to estimate the firm's structure of technology and its production characteristics. The main concept used in this research is the duality principle relating production and cost (or profit) together with the use of flexible-form econometric specifications for estimating production technologies. Under the assumption of cost minimization (or proft maximization), duality implies that for any production function, there exists a cost (or profit) function that provides an equivalent description of the technology. What is less well known, however, is that the firm's technology can be equally well described by the indirect production function, a production analog of the indirect utility function in consumer theory [5; 8; 9]. The indirect production function is based on the firm's output maximization subject to a budget constraint on input costs. Of course, it is evident enough that a firm choosing inputs to maximize output for a given input cost produces that output at the minimum cost. By implication, the indirect production and cost functions are equivalent ways of characterizing the firm's technology and, as will be seen, there exists a unique correspondence between the two functions. In empirical application, however, the choice between the two functions hinges on the exogeneity or endogeneity of output. For the indirect production function, the level of output is an endogenous variable. In the case of the cost function, on the other hand, output is exogenously given. In most situations, it is the indirect production function, not the cost function, that is more compatible with observed behavior of firms and industries. While numerous studies have been conducted recently to estimate the cost (or profit) function in a variety of firms and industries [1; 2; 3; 6], no attempts have been made to employ the indirect production function as a working tool in applied production analysis. This paper attempts to provide empirical evidence from analyzing the indirect production function within the context of an application of the duality principle. Using the well known data set utilized by Berndt and Wood [3] and Berndt and Khaled [2], it reexamines the production structure of U.S. manufacturing, based on a translog specification of the indirect production function for the underlying technology. An important question is how the choice of a model-the indirect production or cost function-