(This question may be specific to US university systems. Also, sorry it is long.)
US universities usually have some provision for students to drop a course. Within the first N weeks of the term, if they decide they don't want to continue with a course they are taking, they can drop out of it. Their official transcript will show no record that they ever took it, and it will have no effect on their GPA. If they are paying tuition per course or per credit, they may get a refund. Usually they have to stay enrolled in some minimum number of courses, so this can probably only be done for one or two courses per term.
Students may have many reasons for dropping a course, but obviously one common reason is that they are not doing well in the course and are afraid they may fail it.
(There may be another option to withdraw from the course up to N+K weeks, but with a note on the transcript saying that they enrolled in the course and later withdrew, maybe listing the pseudo-grade of "W". This usually doesn't affect their GPA but may look bad to prospective employers, graduate schools, etc.)
I realized the other day that there is very wide variation between institutions in the value of N. At Institution A, the medium-sized public university where I currently work, we have N=2. At Institution B, the small private college where I got my bachelor's degree, we had N=11! (I had vaguely remembered that N seemed to be larger at B, but I was still startled when I looked back at an old B calendar to check.)
(One significant difference: at A, students very often pay by the credit, and get a refund if they drop, so the university has a financial disincentive to let them go. At B, most students paid a flat tuition fee per semester, and didn't get any refund if they dropped a course.)
Anyway, it seems like this could have a rather profound effect on student outcomes. When N is small, students have only a short time to commit to their schedule, and can more easily get in over their heads. By the time they've had a midterm exam and realized they are in trouble, N weeks have already passed and they are stuck in a course. Most likely, they end up with an F (or several, if the time they spent trying to pass the hard course hurts their work in their other classes). Their GPA drops, hurting their eventual job prospects. It may drop below the institution's minimum for continued enrollment, in which case they may quit college altogether. I'd expect an overall negative effect on retention and graduation rates, job placement, and other common measures.
On the other hand, if N is large, then by the time the drop date approaches, students may be more than halfway through the course, and may have taken several exams. If they are likely to fail the course, they probably know it by now, and the obvious course of action is to drop it. In an extreme case, the result may be that students hardly ever get D's and F's (because they drop those courses), and grades may inflate.
So I have two questions:
What factors do universities actually consider in choosing or changing their value of N?
Is there any research studying the effect of N on student outcomes?