This is sort of the reverse of a Slatepitch, but Benjamin Castleman and Bridget Terry Long have a piece of research showing that giving kids financial aid makes them more likely to finish college, not just more likely to enroll. The doubt you might have about this is that college completion rates are often quite bad for low socioeconomic status kids, so you might think that high-motivation aid recipients would have found some other way to pay even absent aid while low-motivation aid recipients don't finish school anyway.
But that's not what happens in Florida, at any rate:
Gaps in average college success among students of differing backgrounds have persisted in the United States for decades. One of the primary ways governments have attempted to ameliorate such gaps is by providing need-based grants, but little evidence exists on the impacts of such aid on longer-term outcomes such as college persistence and degree completion. We examine the effects of the Florida Student Access Grant (FSAG) using a regression-discontinuity strategy and exploiting the cut-off used to determine eligibility. We find grant eligibility had a positive effect on attendance, particularly at public four-year institutions. We also extend the literature by investigating the impact of aid on college success and find that eligibility for FSAG increased early persistence and the cumulative number of college-level credits students earned in their first four years. Most importantly, we find that FSAG increased the likelihood of bachelor’s degree receipt within six years at a public college or university by 4.6 percentage points, which translates into a 22 percent increase among students near the eligibility cut-off. The results are robust to sensitivity analyses.
There's a pretty strong consensus at this point that an agenda for improving college completion and college afforability at this point has to include more than just "more money," but we do continue to see evidence that money helps.