Subjective model selection rules versus passive model selection rules

In this paper, the choice of a particular functional form based on the objective of the author is called the subjective model selection rule and the choice of a particular functional form using pre-selected model selection criteria is called the passive model selection rule. The objective of the author is the analysis of equilibrium, an efficient input choice, the study of the returns to scale function, the estimation of the elasticity of substitution, and the evaluation of the technical progress. Depending on the chosen objectives, economic restrictions such as the homogeneity, homotheticity, and regularity condition (positivity, monotonicity, and quasiconcavity) can be imposed. Various well-known functions beginning from the Cobb–Douglas (CD) to a globally well-behaved polynomial series are listed and the performances are compared with respect to the possibility of extracting economic interpretation, usefulness for advanced studies, computational easiness, and the potentiality of extending the given function to a more complex function. The isoquants and three dimensional output surfaces are plotted for a series of production functions using the transportation data of Zellner and Revankar (1969). Barnett and Jonas (1983) imposed the sufficient conditions for quasiconcavity of production functions while Gallant and Golub (1984) imposed the necessary and sufficient conditions. The strength and weakness of the above two methods are discussed. These methods are extended for three input cases using the U.S. electric power industry data of Nerlove (1963) and Greene (2008).