This paper develops a model of immigration that encompasses different channels through which immigra tion impacts native wages. The framework incorporates a frictional labor market with different outside options for immigrants and natives, local demand conditions captured by relative prices, and capital-labor substitution. The model is calibrated on labor data for the four largest European Union economies, France, Germany, Italy and Spain. Three counterfactual scenarios are explored, where the adjustment speed of the capital stock and the sensitivity of domestic relative prices to immigration differ. Results shows that the impact of immigration on wages and wages inequality depends crucially on the latter factor, i.e. whether relative prices are determined by local vs. global conditions. In the former case, the migration pattern observed in the data has led to a non-negligible increase in native wage inequality. In the latter case, migration skewed towards the low-skilled has led to a (quantitatively small) decrease in native wage inequality, due to the lower wage bargaining power of immigrants who compete with native workers.