In estimating heteroscedastic error models, researchers usually hypothesize what they think may be the approximate functional structure of the error term. Since very little is known about the impacts of this approximation on the efficiency of estimators, further investigation of the role of the assumption that the functional structure of heteroscedasticity is known seems warranted. Monte Carlo study results reveal that in estimating heteroscedastic error models, the exponential modelling of the true unknown underlying error structure may produce more attractive estimation results. Based on this result, further suggestions are made for estimating heteroscedastic error models.