We investigate the welfare implications of two pre-crisis immigration waves (1991–2000 and 2001–2010) and of the post-crisis wave (2011–2015) for OECD native citizens. To do so, we develop a general equilibrium model that accounts for the main channels of transmission of immigration shocks – the employment and wage effects, the fiscal effect and the market size effect – and for the interactions between them. We parameterize our model for 20 selected OECD member states. We find that the three waves induce positive effects on the real income of natives; however, the size of these gains varies considerably across countries and across skill groups. In relative terms, the post-crisis wave induces smaller welfare gains compared to the previous ones. This is due to the changing origin mix of immigrants, which translates into lower levels of human capital and smaller fiscal gains. With a few exceptions, differences across cohorts explain a tiny fraction of the highly persistent, cross-country heterogeneity in the economic benefits from immigration.