The San Francisco branch of the Federal Reserve offers "The Effect of Immigrants on U.S. Employment and Productivity" by visiting scholar Giovanni Peri of UC Davis (Wall Street Journal article here, the brief study at [1]). According to Peri, we're all rich beyond our wildest dreams due to massive immigration:

"There is no evidence that immigrants crowd out U.S.-born workers in either the short or long run... "the economy absorbs immigrants by expanding job opportunities rather than by displacing workers born in the United States." ...Peri's work estimates that an inflow of immigrants equal to 1% of employment boosts income per individual by 0.6% to 0.9%. On a larger scale, "total immigration to the United States from 1990 to 2007 was associated with a 6.6% to 9.9% increase in real income per worker." ...Peri says that gain "equals an increase of about $5,100 in the yearly income of the average U.S. worker in constant 2005 dollars” for a gain that equals “20% to 25% of the total real increase in average yearly income per worker registered in the United States between 1990 and 2007."

For some economics problems with earlier Peri work, start here or here or here.

Note also that he doesn't differentiate between legal and illegal immigration or between, say, low-wage low-skilled workers and Silicon Valley entrepreneurs. Would any benefits to Americans of the latter be masking costs by the former?

Peri also refers to the "average U.S. worker" when the benefits of massive immigration probably skew towards those with higher incomes. Would the gains by, say, construction company owners be masking losses by, say, U.S. citizen drywall workers?

Note that his study only looks at income and not at costs, such as spending on welfare programs, education, and so on for illegal aliens or their children. And, of course, his study doesn't look at the costs of giving the Mexican government even more power inside the U.S. or of political corruption. In fact, that's something that he admitted to me he didn't look at or concern himself with in any earlier study (link).

UPDATE: The commenters here pick apart several things the study got wrong or misled about. Even a good number of commenters at the HuffPost raise issues with the study (link).

[1] frbsf.org/publications/economics/letter/2010/el2010-26.html