this doesn't talk about anything regarding wages.
> illegal immigration from Mexico has a minimal impact on wages in U.S. border areas.
That seems narrowly scoped to "US border areas" whereas the parent comment is talking about America in general. Likewise how do you provide a control factor for a study like that?
I think the evidence is pretty much obvious and doesn't require a study to conclude. The market wouldn't prefer illegal immigration (which it does - ask any restaurant operating in the US) if it didn't reduce labor costs for businesses. So the opposite must be true - citizens and legal immigrants would increase labor costs.
The other factors are simply true by careful observation. How is it not obvious that a labor class that has no legal rights of citizenship is also not going to have legal rights in the labor market? (i.e. ability to legally fight wage fraud, depressed benefits, etc.)