I could look up economic studies of statistical correlation for you that show/"prove" these points but, equally, I could almost certainly find more that demonstrated the exact opposite. This is, after all, economics.
Unsurprisingly then, most attempts to overview such macro-economic studies come out on the side of immigration not having profound impacts on aggregate wage levels. The cynic in me suggests that, of course they would, if they expect to retain research funding from the neoliberal state.
The more focused studies do tend to examine the negative wage impacts of immigration in certain sectors of employment, particularly those where much of the labour cost falls on the neoliberal state via it's out-sourced neoliberal corporations, care being a well known example.
Without providing you with the examples you really wanted I would, in response, pose the question that, if these macro-economic outcomes were not the reasons why neoliberal states effected high rates of net in-migration, why would they do that? I think we know it's not out of the goodness of their hearts.