By means of an endogenous growth model of directed technical change with vertical and horizontal R&D, we study a transitional-dynamics mechanism that is consistent with the changes in the shares of the high- versus the low-tech sectors found in recent European data. Under the hypothesis of a positive shock in the proportion of high-skilled labor, the technological-knowledge bias channel leads to unbalanced sectoral growth with a noticeable shift of resources across sectors. A calibration exercise suggests that the model is able to account for up to from 50 to about 100 percent of the increase in the share of the high-tech sector observed in the data from 1995 to 2007. However, the model predicts that the dynamics of the share of the high-tech sector has no significant impact on the dynamics of the economic growth rate.