Well the National Academy of Sciences did perhaps the largest study of this back in the mid-late 90s, and it put the net effect of immigration (not sure if it included illegal w/ legal) as a positive, though only to the tune of about one tenth of one percent of GDP (which today would be about ($10 billion in a $10 trillion economy), hardly the picture presented by some who put forth the notion that the economy would collapse w/o large-scale immigration.
I don't think the premise that most of the benefits of immigration are captured by the immigrants themselves would be seriously disputed by most academics.
They lost me right there. The authors should have said they were too damn lazy to separate legal and illegal immigration for their study.
The typical legal immigrant (A group) will (a)have a police background check, (b)possibly be married to a U.S. Citizen, (c)possess a marketable skill and (d)a desire to adapt to American society. I say typical because there are idiotic legal immigration programs (B group) such as the diversity visa lottery or refugees from third world countries which, only by sheer luck (or a first-hand experience with and loathing for communism in action), might meet one or more of the foregoing criteria.
Then there are the illegal immigrants (C group) who have even less chance at clearing even one of the basic (a), (b), (c) or (d) hurdles.
It is idiotic to study all three such immigrant groups as a monolithic group. It is equally idiotic to state that the costs and benefits of inviting all three groups to live in America cannot be separated.
A sane immigration policy would exclude those in the C group, maximize those in the A group and winnow those in the B group into those likely and those not likely to make a net contribution to American society. Sometimes, such a distinction is impossible, but not nearly so much as the open border crowd claims. In these cases, B group immigrants could be admitted on a slot available, probationary basis-- i.e., one year residence and work permit renewable if the immigrant shows themself to be productive and adaptable to American society, after 5 years or so, extendable for three years at a time, then eventually leading to permanent residence.
Japan has such a sane immigration policy in place. They also have a small number of illegal immigrants and minority groups demanding that the majority reshape society to fit them.