There's a lot in your post and I think that some of the dots just need to be connected. When you discuss monetary policy Immigration what I think you're implying is that it is a way for the government to assist with long term economic growth. This is true because government does make up a portion of the GDP equation. Earlier you mentioned increases in tax revenue and the connection that should be made here is that this tax revenue will then be used within the GDP equation to increase government expenditure