In their new book "Crossing the Finish Line," former Princeton University President William Bowen and former Macalster College President Michael McPherson look at the high college dropout rate that is plaguing higher education in America -- and explore some possible remedies.

They also have some intriguing data: Even after adjusting for high school GPAs and SAT scores, students who attend less selective schools are more likely to drop out.

For instance, students who graduate with a GPA of 3.5 or higher and combined SAT scores over 1,200 have an 89% graduation rate when they attend colleges ranked "most selective." That graduation rate falls to just 59% when they attend college ranked "least selective." Check out this graphic from the New York Times to see more numbers.

But before you follow US News & World Report's interpretation of that data ("Thousands of bright, qualified students apply only to lower-ranked schools where their grades and tests scores are above those of the average student. But the new study finds that those who attend such "safety" schools are far more likely to drop out than those who get into "reach" schools."), think about it a little bit more.

Why would someone with a GPA over 3.5 and SAT scores over 1,200 attend a college ranked "least selective"? In the vast majority of cases, I would argue, it would be because of financial considerations. A student with a stellar academic record in high school attending a third-rate school most likely comes from a family with limited financial means.

Similarly, what kind of students with low GPAs are likely to attend highly selective schools, where they won't receive any merit-based financial aid? Kids from wealthier families.

And oh, by the way, study after study has shown that students from low-income backgrounds are less likely to graduate from college -- regardless of their past record of academic success -- and vis versa for kids from high-income backgrounds. So this data corrects for one glaring selection bias problem (highly selective college attract students who are unlikely to dropout) but exacerbates another one: What kind of students are most likely to attend schools two or three tiers below the ones they could get into?

A couple more problems with following the authors' advice of going to the "best college" (whatever the heck that even means):

• Colleges generally award merit aid to students who will be at the top of their class. If your child applies and gets accepted to a college where he's in the bottom 20% of applicants (i.e. a reach school), he's extremely unlikely to be awarded a merit-based scholarship. Merit money will come from schools where your child will be a standout.
• Attending an elite school will result in a lower class rank -- and studies have shown that class rank has a strong correlation with future earnings.

On the other hand, all other things being equal, attending a more selective college is probably a good idea. Every state has a flagship university and nearly every flagship university has an honor's program with admissions standards comparable to more selective private colleges. Best of all, the affordability of public research universities guarantees that they'll attract a large number of "overqualified" students that your similarly overqualified student can interact with.

But what of the data suggesting that students who attend less selective schools are more likely to drop out? I hate to be flippant but here's a good solution: just don't drop out.

I don't doubt that Bowen has valuable ideas for public policy -- the dropout epidemic is a serious problem, and he's clearly a brilliant guy. But please, please, please: Don't encourage your kid to take out student loans so he can attend a more selective college with a higher graduation rate. Just tell him not to drop out.