Unhindered immigration and effects on US per capita GDP

Peterson has just graduated from college and is now a junior member of the staff of a U.S. senator. He has been asked to draft a statement detailing the senator's position on the economic growth implications of immigration. His research on the topic has uncovered the following facts. First, more than a fifth of scientists actively involved in research at the US universities are immigrants. Second, foreign-born scientists residing in the United States write about 60 percent published research studies in the physical sciences and about 30 percent of research publications in the life sciences. Third, nearly a forth of the founders or chief executives of U.S. biotechnology firms that have become publics companies since the early 1990s were born abroad. Peterson knows that in the past the senator who employs him has generally been opposed to permitting unhindered immigration. Nevertheless, the senator also strongly favors policies that promote economic growth. Peterson's task, given what he has learned, is to compose a draft statement reconciling the senator's two positions.

1. Why might unhindered immigration have uncertain effects on US per capita GDP even though immigrant scientists contribute so much to the nation's stock of knowledge and expertise?

2. How might Peterson draw on the insights of new growth theory to draft a position statement ruling out unhindered immigration but proposing greater openness to "targeted immigrants"?