When people get more education, they become more productive and help strengthen the entire U.S. economy. So it is discouraging to see that students from wealthy families are increasingly more likely to graduate from college than are those from poor families. This perpetuates inequality from one generation to the next and limits the economic benefits that could come if a wider swath of the population earned college degrees.

The widening gap in college completion rates is documented in a paper by economists Martha Bailey and Susan Dynarski of the University of Michigan. Looking at children born in the early 1960s, the researchers found that only 5 percent of children from families in the lowest-income quartile completed college, while 36 percent of those from families in the highest-income quartile did.

For children born around 1980, the college completion rate among low-income students rose to 9 percent, but among high- income students it jumped to more than half (54 percent). In other words, over two decades, the college income gap widened to 45 percentage points from 31 percentage points. This widening was observed even after the researchers accounted for differences in students’ cognitive skills.

It’s tempting to conclude that the advantages of wealth and income have simply intensified, so the odds are increasingly stacked against poorer students. No doubt that’s true to some extent, but Bailey and Dynarski show that most of the change has been driven by trends among female students. The gap between rich and poor in both college entry and college completion widened by almost twice as much for women as it did for men. (An astonishing 85 percent of girls born in well-off families around 1980 entered college.)

It can’t simply be that wealthy families directly or indirectly buy advantages for their children. If this were the case, why wouldn’t it work as well for sons as for daughters?

So what has happened to widen the college gap and what can we do about it?

Bailey and Dynarski focus on two crucial pieces of the picture: inequality in high school graduation rates and inequality in college completion among students who begin college.

Gaps in high school graduation by income, the researchers find, account for about half of the gap in college entry rates. After all, college entry isn’t an option for people without a high school degree. Among those who do finish high school, though, the percentage who go on to enter college has risen to about 70 percent among those born around 1980 — up from about half of those born around 1960. So raising high school graduation rates among low-income students could make a difference.

One way to do this has been suggested by the Hamilton Project at the Brookings Institution: compulsory schooling. In a September 2012 paper for Hamilton, economists Philip Oreopoulos and Derek Messacar of the University of Toronto note that about half of low-income and minority students don’t graduate with their high school class. They propose that all states require students to stay in school until age 18. This would at least make more low-income students eligible to attend college.

To be sure, a high school degree won’t matter much if the student isn’t adequately prepared for college, which is why Oreopoulos and Messacar couple their suggestion with other reforms to improve educational quality. And as I have written before, to get more students to enroll in college, the financial aid process must be simplified.