Independent economists say immigration reform will grow our economy
... with ...
[B]ut also, obviously, our population: the phrase “per capita” mean anything?
Yes! That grow-the-economy factoid is one of the hoariest vacuities—or, possibly, hoariest bits of intentional misdirection—in the entire immigration "debate."
It pops up over and over and over and over, year after year, decade after decade. For another recent example, Commerce Secretary Penny Pritzker was babbling about it in Los Angeles a few weeks ago. According to L. A. Times reporter James Barragan
Immigration reform under a Senate-passed bill would boost the U.S. economy by $1.4 trillion over the next 20 years, [Pritzker] said.[Immigration reform must be top priority, Commerce secretary says, January 9, 2014]
Such claims about immigration economics are quite familiar. And the claims are plausible, but merely because increasing the population will generally yield more economic activity, which was Derb's point.
As far as benefit to the nation—especially to us native-born citizens—goes, Pritzker's statement is a non sequitur: True but irrelevant. That's because nearly 100% of the increased economic output goes to the immigrants (and illegal aliens who would be legalized) themselves.
Harvard labor economist George Borjas made this point clear in his 1999 book Heaven's Door: Immigration Policy and the American Economy. From pp. 92 - 93:
Although this economic model underlying the calculation of the immigration surplus is widely accepted — and, in fact, forms the underlying framework for the calculations contained in the widely cited report by the National Academy of Sciences — many participants in the immigration debate often confuse the calculation of the gains and losses. In 1997, for instance, Senator Spencer Abraham [R-MI], chair of the Subcommittee on Immigration, wrote a Wall Street Journal editorial that quoted the economist who headed the National Academy of Sciences panel as saying that "due to the immigrants who arrived since 1980, total gross national product is about $200 billion larger each year." In a dizzying display of beltway arithmetic, Senator Abraham then inferred that "recent immigrants will add $2 trillion to the nation's GNP over the course of the 1990s."
This conclusion is quite surprising since the immigration surplus is less than $10 billion a year. The "trick" is that the senator forgot to mention that most of that $2 trillion increase in GDP goes to the immigrants themselves in the form of wages and salaries. Many participants in the immigration debate might welcome the fact that immigrants make substantial economic gains by being in the United States. But many other particpants might also want to know exactly what is in it for the "average" native. And the answer is short and simple: not much.
Borjas defines the "immigration surplus" as the gain in national income accruing to natives as a result of immigration. Generally speaking, native capital significantly benefits (several hundred $billion per year), and native labor loses big time; the immigration surplus is the relatively inconsequential difference (Peter Brimelow calls it "nugatory") between the two, something like $10 billion to $20 billion/year.
But a landlord like Pritzker—member of the humongous-bucks Pritzker family of Chicago — would naturally think it's terrific.
Given Borjas's point, the essential irrelevance of Pritzker's claim is obvious: If economic well-being is the criterion, then it's per-capita income that matters, as Derb implied.
For an example that makes this point vividly, India's year-2000 GDP was $510 billion, and Switzerland's was $286 billion. But their respective per capita GDPs were $500 and $39,000. See link here. There are probably reasons some would prefer living in India over Switzerland, but the average person's material comfort wouldn't be one of them. (And in the U.S., the present mass influx of predominantly poorly-educated and low-skilled aliens actually lowers per-capita GDP.)