Q:

What incentives do professors have to increase the PhD completion rate in their department?

In other words:

How do professors profit if a larger (rather than smaller) proportion of entering PhD students in their department complete their degree?

(At my department at least, it seems like the only benefit is "warm-glow altruism". A professor gains no more from having more students at her department complete their PhDs than I do by having fewer stray dogs in my town getting killed by traffic. A professor's career prospects does not seem in any way affected by whether 80% rather than just 50% of PhD students complete their degree. Not surprisingly, the completion rate, at least at my department, is closer to the latter.)
Note:  I am not asking whether it is a good idea to give professors stronger incentives to increase PhD completion rate. Neither am I asking for suggestions as to how PhD completion rates can be increased. Rather, I am asking what the incentives at present are (granting of course that this varies from place to place).

A:

In the United States, the National Research Council (http://www.nap.edu/rdp/) regularly ranks university departments. One of the criteria by which departments (and thus universities) are ranked is the "Average of Median Time to Degree" with the presumption that lower is better. 
In my university, this results in the provost's office putting pressure on us to reduce our time to degree through a number of measures, some coercive and punitive. Most of the time, the coercion and punishment is directed towards the graduate students (i.e., after the sixth year they lose their rights to certain fellowships, they have to pay more for their gym and library memberships, etc.). 
But the department as a whole gets some attention. Our chair has been regularly sending out lists of our orphaned and missing ABD candidates (some now in their 12th year) and asking us to find and terminate them (either through graduating them, or formally asking them to leave the program). 
I've also been putting some pressure on my peers through the admissions system by suggesting (since they are my colleagues, I have no power) that people with many students on the books should refrain from taking on new students until they clear their backlog more a bit.
I should note that I'm in anthropology where: 1) students tend to go into the field and disappear for quite sometime; 2) doctoral students are mostly useless to faculty for slave labor as most of us work individually and not in labs (with the exception of some of our archaeological / biological colleagues). 

A:

If an advisee leaves without completing a Ph.D., then the advisor can end up feeling like the whole process was a waste of time, since the goal of strengthening the research area by training a future contributor was not achieved.  That's not fair or reasonable: the education and experience may be useful for the advisee despite not culminating in a Ph.D., and the opportunity to try was itself valuable regardless of how it worked out.  However, these feelings are relatively common, and the advisor's investment of time and effort becomes an incentive towards higher completion rates.
This personal investment begins only when the student chooses an advisor, so the corresponding incentive is not relevant before that stage.  On the other hand, spaces in graduate school are a limited and therefore valuable resource, so there is still an incentive for faculty not to waste them, even at the coursework stage.
What makes this issue tricky is that nobody can agree on what the ideal completion rate should be.  To a first approximation higher is better, but this isn't a universal principle, and a 100% completion rate would arguably mean you're doing something wrong.  Over the course of a difficult five-year program aimed at a narrow career, some people will legitimately discover that there's something else they'd rather do instead, and others will be prevented from finishing by factors beyond their or the university's control.  The only way to enforce a perfect completion rate would be to refuse to admit anyone who seemed like they might not finish and then bully all the students into finishing regardless of whether or how their circumstances had changed.  For example, you would never take a risk by admitting someone who seemed like they deserved a chance, and you would never gracefully accept a student's change of plans.  Ultimately, the fundamental difficulty is that we can't necessarily distinguish between reasonable attrition and inappropriate attrition caused by unsupportive practices, and this makes the whole issue contentious.

A:

In France, labs are assessed by the AÉRES (mirror)  (~= Department of Evaluation of Research and Higher Education).
The evaluation criteria (mirror)  show that the AÉRES prefer labs where PhD students don't drop out too often.
Since the AÉRES evaluation has an important impact, e.g. to get funding, professors have an incentive to increase the PhD completion rate (and they also have an incentive not to turn PhDs into some ever-lasting position: labs typically to try to graduate students in 3-4 years).

In the US - at least in my university - I'm not aware of any incentive, except that new PhD students will avoid professors who have the reputation of taking a while to graduate their students.

