Averaging methods are routinely used in order to limit biases resulting from the mismeasurement of permanent incomes. The Solon/Zimmerman estimator regresses a single-year measurement of the child's resources on a T-period average of the parents' income while the Behrman/Taubman estimator regresses an S-period average of the child's resources on a T-period average of the parents' income. The latter estimator is shown to be the arithmetic mean of the S slope estimates arising from the Solon/Zimmerman methodology. However, because sampling variation produces yearly changes in the variance of children's incomes, it is shown that the Behrman/Taubman estimator is not efficient in the class of estimators which can be expressed as a weighted sum of the S distinct Solon/Zimmerman estimates. The minimum variance estimator in the above class is thus derived and applied to a US sample. [Author]