For a general summary of the NAS study, I recommend George Borjas's blog series. (Borjas was my advisor in graduate school.) And for a discussion of the long-term fiscal effects, please see my piece for National Review.
Though I was pleased with the quality of the NAS study, I was displeased to see the media attribute conclusions to it that it never actually drew. Specifically, some media outlets are claiming that the study found no significant wage or employment effects on natives. I first saw this claim in an ABC News "fact check" of Donald Trump. (Regular readers already know how I feel about the fact-check movement.) Here's part of my response that I wrote for the Center for Immigration Studies:
The study's authors are very open to the idea that immigration depresses wages. For example, the fourth chapter of the study is devoted to an economic model in which immigration improves efficiency by reducing the wages of native-born workers by $494 billion. The next chapter lists nine different studies that find at least some negative wage effects, mostly on lower-skilled workers. "While many studies conclude that, economy-wide, the impact of immigration on average wages and employment is small, a high degree of consensus exists that specific groups are more vulnerable than others to inflows of new immigrants," the study says. It goes on to name prior immigrants and low-skill natives as examples of groups hardest hit.
The "little to no negative effects" on wages is not even a quote from the study itself, but rather from a press release accompanying it. And ABC's fact-checker leaves out a crucial qualifier in that press release: "little to no negative effects...in the long term" (emphasis added). It is true that as capital adjusts over time to accommodate a new group of immigrants, wages should revert to pre-immigration levels. This is actually an assumption built into some immigration models. Efficiency gains as well as wage effects disappear in those models in the long run, leaving natives no better off than they were without immigration. But, more importantly, if we keep taking in over a million immigrants every year, then new short-run wage losses are suffered over and over, and the long run never comes!
The National Academies study simply does not say, either literally or in spirit, that immigration has no effect on wages. Furthermore, the conceit that such a sweeping and decisive "fact" could be derived from the study's chapter-length, much-caveated review of a complex literature is implausible.