Specification and Estimation of Cobb-Douglas Production Function Models

In this paper we consider the specification and estimation of the Cobb-Douglas production function model.After reviewing the "traditional" specifying assumptions for the model which are based on deterministic profit maximization, we develop a model in which profits are stochastic and in which maximization of the mathematical expectation of profits is posited."Sampling theory" and Bayesian estimation techniques for this model are presented.1. INTRODUCTION IN THIS PAPER we take up the problem of specifying and estimating a model of a profit maximizing firm operating with a Cobb-Douglas production function.Our model differs from the traditional production model considered in the literature, in that we assume that: (a) the production process is neither instantaneous nor deterministic; and (b) entrepreneurs are aware of the stochastic nature of production in their profit maximizing endeavors.This fundamental conceptual difference in our approach leads us to a new model with properties different from that of the traditional model.2Also we develop both sampling theory and Bayesian estimation procedures for the new model.The order of presentation is as follows.In Section 2 we review the traditional model, and then go on in Section 3 to formulate the new model.In Section 4, sampling theory estimation procedures are developed for the new model.In contrast with the traditional model, it is found that classical least squares provides consistent estimators of the parameters of the Cobb-Douglas production function.With a normality assumption, these are also unbiased and maximum likelihood estimators.Finally, in Section 5, a Bayesian analysis of the new model is presented.2. REVIEW OF THE TRADITIONAL MODEL According to economic theory, output, inputs, and profit of a firm are determined by the production function, the definition of profit, and the conditions of profit maximization.If the production function is of the Cobb-Douglas type with two