Do Full-Time Faculty Help Students Complete College?

This morning I moderated a panel discussion at the Library of Congress focused on college completion. When we came to the Q&A, Cary Nelson, President of the American Association of University Professors, posed a question (I'm paraphrasing from memory):

"One thing nobody on the panel has mentioned is that fact that colleges with higher completion rates also have a larger percentage of their classes taught by full-time professors. So that's one thing we could do: give colleges the resources to employ a stable, full-time faculty."

There are some obvious correlation / causation issues to resolve here. Because full-time faculty are more expensive than contingent faculty, the colleges that tend to employ a lot of them tend to be wealthier than those that don't. Wealthy colleges also tend to enroll a disproportionate number of wealthy, academically well-prepared students, who are more like to complete college. So yes, colleges with stellar college graduation rates are more likely to hire full-time, well-credentialed, tenure-tack professors to teach. But they're also more likely to have lots and lots of other things that also independently improve graduation rates. Resource advantages in higher education tend to be highly co-linear.

So I'm curious: Is there any good research out there that properly explores the relationship between full-time / tenure track status and student outcomes like retention, completion, and learning? Most of what I've seen on the subject only speaks to things like student - faculty interaction and doesn't really get to outcomes. The answer seems non-obvious to me: one the one hand there seem to be obvious advantages to being taught be experienced, knowledgeable professionals who are well-integrated into the university community; on the other hand tenure-track faculty are subject to some pretty severe professional incentives related to publishing that actively push against the time available for helping students learn, earn degrees, etc.

More broadly, given that our vast, world-beating higher education system is populated with many thousands of people who have been highly trained to unravel complex phenomena, and that the subjects in questions aren't located in some distant land nor are they indiscernible without complex scientific equipment but rather are right there on the campuses where all of our researchers live and work, and this is a subject that clearly arouses a lot of strong feelings and is thus in sore need of more empiricism, why isn't there more research in this area?