In this paper we address two relevant issues among those characterising the macroeconomic literature on migration. (a) We evaluate which impact is produced by the immigration flows coming from the enlargement countries on the EU-15 labour market. (b) We draw clues on the migrant characteristics as for their skill levels. We adopt an insider/outsider model inspired by that of Amisano and Serati (2003), but enlarged in order to model the migration flows and fit to wage, participation and employment differentials between skilled and unskilled workers. We identify the structural shocks of the reduced VAR form of the model through sign restrictions imposed to the Impulse Response Functions, leaving unconstrained only the impact multipliers of relative (skilled to unskilled) wage, employment and labour force with respect to a migration shock. This is equivalent to adopt an agnostic approach, letting emerge freely the signals coming from the data: combining them with theoretical suggestions we derive at least weak indications on the fact that the skill mix of migrants is either biased towards high or low qualified labour. It does emerge that migration from Eastern European countries towards the EU-15 is mainly constituted by skilled workers and generates effects of reduction of the employment gap; on the other side, it enlarges the skilled to unskilled relative wage gap. The whole picture suggests the adoption of policies aimed at attract skilled migration through economic but also social and environmental incentives.