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Point Estimation in Multiplicative Models

I. G. Evans
S. A. Shaban

Abstract

In a multiplicative model it is usual to assume that the logarithm of the disturbance variable is normally distributed with unknown variance @s^2 and with a mean which is either zero or -1/2@s^2 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].