Some Statistical Implications of the Log Transformation of Multiplicative Models

An attempt is made to set out the implications of the log transformation on the stochastic properties of the model, which are postulated in the original multiplicative relationship. The estimation of the mean of the dependent variable, given some vector of explanatory variables, is accomplished by minimizing the mean square error within a certain class of estimators allowing for biased estimators, assuming known variance. The resulting estimator is modified in order to face the problem of unknown variance. This modified estimator turns out to dominate (in MSE) the least-squares, the ML, and the MVU Bradu and Mundlak estimator.