We show (in confirmation of previous work) using one- and three-dimensional models that extratropical zonal wind anomalies, produced by fluctuating Rossby wave forcing in the troposphere, appear first in the stratosphere, and migrate downward into the troposphere. By systematically eliminating wave reflection and downward control through an induced meridional circulation, it is shown that the downward migration is dependent on neither process. Rather, the mechanism appears to rely on local wave, mean-flow interaction just as in the similar downward migration evident in the tropical quasi-biennial oscillation. In particular, these results imply that the similar downward migration observed in the Arctic Oscillation should not be taken to indicate any controlling influence of the stratosphere on the troposphere.