Labor supply and wages are a weird genre of discourse wherein people come out of the woodwork to explain ways that increasing the available pool of labor, somehow and through some magical means that we may never fully understand, does not have any effect on wages. It’s just absolutely crazy. You do not need some wildly complicated multivariate analysis to understand the effects. This was standard fare economic understanding in this country right up until the 1990s when, I suppose, we all got put back in a laboratory where labor supply and demand do not matter anymore.