Can the augmented Solow model with migration explain the Italian internal brain drain?

We extend the Dolado et Al. (1994) model to both inflows and outflows of migrants and assume that they have a human capital endowment that contributes to increase/decrease the stock of human capital in the receiving/sending economy. We derive the conditional convergence equation in which the impact of migration flows on the growth rate is disentangled in a pure quantity effect and in a quality or composition effect of immigration and emigration rates that accounts for the relative human capital endowment of migrants with respect to resident population. Next, we test the model with Italian regional data for the 1970-2005 time period. We find that the model provides a good explanation of the Italian experience. The quantity effect is negative for the immigration rate and positive for the emigration rate, while the composition effect is positive for immigration and negative for emigration. Finally, we separate the centre-north from the south and find that the composition effect of emigration is stronger for the latter. We interpret these results as a clear evidence of a brain drain from the Mezzogiorno to the centre-northern regions.