The OLS estimator of the intergenerational earnings correlation is biased towards zero, while the instrumental variables estimator is biased upwards. The first of these results arises because of measurement error, while the latter rests on the presumption that the education of the parent family is an invalid instrument. We propose a panel data framework for quantifying the asymptotic biases of these estimators as well as a mis-specification test for the IV estimator. Using US data we estimate the bias of the OLS estimator to be in the order of 10% to 20%, and that of IV to vary between 40% and 60%. Supporting evidence that the IV estimator is inconsistent, in face of the specification test, is however limited, and results are shown to be sensitive to the assumptions underlying the serial correlation in transitory incomes. [Author]