As David Leonhardt revealed in September, almost half of all students who enter college in the U.S. don't graduate. Cutting this number down should be a national priority, but even a determined effort is likely to leave many students short of a bachelor's degree. Instead, what they'll be leaving school with is a sizable debt burden.

Is there a way to protect these students? Philly Fed's Satyajit Chatterjee and Colgate's Felicia Ionescu argue that there is -- a government-backed insurance program. Such insurance would increase the value of going to school which, in turn, would likely encourage graduation rates and encourage more high school students to enroll in college.

Examining U.S. data, Chatterjee and Ionescu estimate that:

the optimal insurance offered in case of non-completion ranges from 10 to 40 percent of total college cost, depending on the ability of the student and the time when insurance is offered. The insurance scheme induces an increase in enrollment rate of 5.4 percentage points and an increase in college graduates of 5.4 percentage points. Although insurance draws in students with a high risk of failure, completion rates rise because fewer students drop out voluntarily from college. The leaving rate declines by more than three times.

But there's a real-world problem that could make any effort to create this type of insurance futile. In order for it to work as intended, the amount students are insured for should be based on their abilities. Chatterjee and Ionescu use SAT data as a proxy for this. But, like proposals for taxing people based on gender or height, basing insurance (even if only partially) on aptitude is unlikely to pass the egalitarian test.