Point Estimation in Multiplicative Models - Evans, I. G.; Shaban, S. A. (Econometrica, 1976)
In a multiplicative model it is usual to assume that the logarithm of the disturbance variable is normally distributed with unknown variance a2 and with a mean which is either zero or - la2 according to the viewpoint taken of the object of the model. It is shown that, for each of several estimation criteria, the two assumptions lead to precisely the same point estimators of the exponents of the explanatory variables in the model and of the conditional mean, median, and mode of the dependent variable for specified values of the explanatory variables. An improved form is also given of the estimator of the conditional mean proposed by Teekens and Koerts [8]. A MULTIPLICATIVE MODEL is one in which a dependent variable is hypothesized to be proportional to the product of powers (unknown) of two or more explanatory variables. Such models arise in many areas; an important example of such a model in econometrics is the Cobb-Douglas production function. Observations will deviate from the theoretical model because of the presence of a disturbance variable. It is customary to include this variable as a multiplicative factor in the model and to assume that its logarithm is normally distributed with a mean which may be either zero or minus half its variance, the choice being dependent upon the viewpoint taken regarding the purpose of the model. We show that the choice does not affect the standard point estimators of the exponents (elasticities) of the explanatory variables in the model nor the standard estimators, including that proposed by Teekens and Koerts [8], of the conditional mean, median, and mode of the dependent variable.