Linear and Nonlinear Estimation of Production Functions

TLDR: In this article, a generalized production function (GPFGF) was proposed to provide variable returns to scale as well as a variable elasticity of substitution (VES) of substitution, where the elasticity is linearly dependent on the input ratio.

Abstract: Theoretical and empirical works dealing with production functions have found it convenient, if not a necessity, to work with specific parametric forms. Beginning with the early Leontief and Cobb-Douglas forms, successive generalizations of the form of a production function first allowed constant elasticities of substitution (CES) other than zero or unity (K. J. Arrow, H. Chenery, B. S. Minhas, R. Solow [1]) and then introduced the variable elasticity of substitution (VES) form in which the elasticity of substitution is linearly dependent on the input ratio (Y. Lu and L. B. Fletcher [7]) or on time (R. Sato and R. F. Hoffman [12]). A generalized production function (GPF) modification by use of a composite function approach provides variable returns to scale as well as a variable elasticity of substitution (A. Zellner and R. S. Revankar [14]). Recently K. R. Kadiyala [6] has pointed out a direct generalization of the familiar CobbDouglas and CES functions which contains both as special cases. In addition, the KRK function allows for a more general variable elasticity of substitution and thus provides added flexibility to earlier VES modifications. Aside from its theoretical features the KRK function presents the possibility for a