I'm unabashedly pro-immigration, and I mean all kinds: high-skill or low-skill, I think everybody has something to add to the American melange. For high-skill immigration specifically, everywhere I have ever worked has suffered from a labor shortage, in the sense that we've always had open job positions that we couldn't fill. When I say this to my less pro-immigration friends, they reply “if labor is so tight, how come wages haven't gone up?”
It's a reasonable question. According to the BLS, private sector “Information” compensation went from 85.8 to 125.1 from 2001 to 2014, which is respectable but not gargantuan compared to other industries (e.g., “Professional and business services” went from 87.6 to 124.4 during the same interval; “Leisure and Hospitality” went from 87.1 to 119.6; and “Utilities” went from 87.9 to 130.7).
One possibility is that compensation has gone up, but they aren't measuring correctly. That table says “total compensation”, which the footnote says “Includes wages, salaries, and employer costs for employee benefits.” So I suspect (hope!) obvious stuff like stock options and health care plans are factored in, but there are a bunch of costs that a corporation could classify as something other than employee benefit (e.g., to prevent alarming shareholders, or for tax purposes), but which nonetheless make the job much nicer. That awesome new building on the beautiful campus you work on probably looks like a capital asset to an accountant, but it sure feels like part of my compensation. How are travel expenses (i.e., attending fun conferences in exotic places) categorized? And there are intangibles: flexible work hours, ability to choose which projects to work on and whom to work with, freedom of implementation technique, less meetings, etc. My personal experience is that these intangibles have greatly improved since I started working. Possibly that is that an artifact of seniority, but I suspect not, since many of my similarly situated coworkers are much younger than me.
I'm partial to this explanation because of personal experience: my current job is not my highest paying job ever, but it is my best job ever.
This explanation still leaves open the question: “why don't employers just skip all that stuff, have dumpy offices without grass-fed beef hamburgers, and pay people a lot more?” I think startups actually do this, although they employ nondeterministic compensation, so it's difficult to reason about. Therefore, let's just consider larger companies. I can imagine several possible explanations (e.g., aversion to skyrocketing labor costs; or to a realization that, past a certain point, a nice campus is more effective than a salary increase), but I don't know the answer. I can say this: while every company I've ever worked at has had a plethora of open positions, I've never heard anybody say “let's fill these open positions by raising the posted salary range.” One explanation I reject is that employers don't want to offer larger salaries because they can't assess true productivity during the job interview process. The assessment problem is real, but bonus-heavy compensation packages are an effective solution to this problem and everybody leverages them extensively.
It's possible that information sector workers are not very good (or very interested) at converting their negotiating power into more compensation. Perhaps at the beginning of the industrialization of computing the field just attracted those who loved computers, but 40 years later when many of the famous titans of industry are computer geeks, I suspect many young people are majoring in computer science in order to earn coin. So this doesn't seem reasonable.
Anyway, it remains a mystery to me, why wages haven't gone up faster. However my less pro-immigration friends then proceed to the next phase of the argument: that (greedy!) corporations just want high-skilled immigration to import large-scale cheap intellectual labor and displace American workers. Well I have news for you, all the majors employ tons of people overseas; they don't need to import cheap intellectual labor since they have access to it already. Furthermore when they engage overseas labor markets, they build buildings and pay taxes, and their employees buy houses and haircuts in their local area. If those employees lived here, America would get those benefits.
America needs to wake up and realize that traveling halfway across the globe and leaving all your friends and family is an imposition, one that becomes less attractive every year as global labor opportunities and governance improve. Since the incentives to immigration are decreasing, we should look for ways to reduce the frictions associated with trying to immigrate.