The link between migration and wages is complex and confusing – especially when it is often communicated about in different ways (eg are we talking about wage growth now with regards to monetary policy, wages in specific industries due to the changing make-up of the economy, or long-run real wages?). And I can’t be much help here.
However, I think this is one place where carefully using the macroeconomic model taught in ECON101 can help us to think about the issues a little bit – especially if we are narrowing the question to only “what is the monetary policy consequences of changes in migration flows“. Now this model is wrong, assumptions in it are wrong, the outcomes it describes aren’t forecasts – but it clearly articulates tendencies we observe following a change in economic circumstances which will hold in more realistic models, and clarifies assumptions that may make these tendencies false. We have pointed at this before for monetary policy – but lets outline a bit more now.
It is a model for thinking about the potential consequences of something in a critical way – not something that we accept uncritically as truth. To me this is pretty damned useful as a way to start thinking about something, so let’s do it!