In the summer of 2008, Baylor University made an enticing offer to incoming freshmen. The Baptist university in Texas, which is now led by one-time Clinton prosecutor Kenneth Starr, said it would offer admitted students a $300 credit for the campus bookstore if they agreed to retake the SAT. Students who raised their scores by at least 50 points were guaranteed an additional $1,000 merit scholarship. Those who increased their scores even further could qualify “for a higher-level merit based Baylor Gold Scholarship,” according to an e-mail message the school sent students.

“People do pay attention to test scores,” Reagan Ramsower, Baylor’s vice president of finance, told The Lariat, the campus newspaper, which broke the story. “The university does benefit from higher average scores, and students benefited from book credits. It’s a win-win situation.”

The people that Baylor was trying to impress were the editors of U.S. News & World Report, who factor in SAT scores when compiling the magazine’s infamous annual rankings of colleges. Since 2002, Baylor has been trying to climb up those rankings. It has mostly succeeded, in part by doling out substantial sums of merit aid to attract top students to the campus—many of whom happen to be wealthy. According to data released to the College Board, 34 percent of freshmen at Baylor have no financial need and receive an average of $13,000 in merit-based aid per year. Low-income students at Baylor haven’t fared as well. While recipients of Pell Grants (federal financial aid for low-income students) make up 24 percent of the school’s student body, the university covers the full financial need of only 13 percent of aid recipients. And families making $30,000 or less are left on the hook, on average, for about $21,000 per year, after all grant and scholarship aid is taken into account.

Unfortunately Baylor’s institutional aid spending strategy is becoming increasingly common at both public and private non-profit four-year institutions. Low-income students are increasingly paying for policies that prioritize prestige over opportunity.

How did we get here? Nearly 50 years ago, when Congress first passed the Higher Education Act, the federal government vowed to remove the financial barriers that prevented low-income students from enrolling in and completing college. The Pell Grant program, which spent about $32 billion in the 2013 fiscal year to help more than nine million financially needy students pay for college, is the primary vehicle for such assistance. For years, colleges complemented the government’s efforts by using their financial aid resources to open their doors to the neediest students.

But those days appear to be mostly in the past. Over the last several decades, colleges have learned how they can strategically use their institutional aid dollars to increase both their prestige and revenue. With the exception of the most elite schools, nearly all private, nonprofit colleges provide merit aid, often to the detriment of the low-income students they enroll. Many less well-endowed schools provide deep discounts to affluent students because they believe they must do so to survive, while other fairly wealthy colleges use their aid as a competitive weapon, to try to break into the top echelon of schools, as defined by publications such as U.S. News.

While the situation is better in the public four-year college sector, it is deteriorating fast. As public institutions deal with decreasing state funding and fierce competition, particularly for out-of-state students, they are increasingly using their institutional aid dollars to buy the best and the brightest students and those who can otherwise afford to pay full freight. While many college leaders recognize the futility of engaging in such an arms race, few are willing to disarm for fear of putting themselves at a competitive disadvantage.

Change is going to have to come from outside academe. We need a federal solution that takes a carrot-and-stick approach.

The carrot would help schools that simply don’t have the resources to suppress the net prices of the low-income students they serve. Congress could eliminate the costly and inefficient federal tuition tax credit programs, like the American Opportunity Tax Credit, which provide tax breaks to students and their families to help pay for college, and use some of the savings to offer Pell bonuses to financially strapped public and private four-year colleges. There would be conditions for these bonuses: The schools should serve a substantial share of Pell Grant recipients and graduate at least half their students school-wide. The schools would use this money to boost their institutional aid budgets and reduce the prices they charge the neediest students. Colleges could also use this additional money to create support programs to further increase the retention and graduation rates of low-income students on their campuses.

The stick is for wealthier colleges—those that have chosen to divert their aid to high-achieving students as a way to rise up the U.S. News rankings and increase their net revenues. These schools, which generally enroll a relatively small share of low-income students (less than 25 percent of their student body) but charge them high net prices, would be required to match at least a share of the total amount of Pell dollars they receive. Colleges would be expected to use the match to boost the amount of need-based aid a low-income student can receive—a student with a $5,000 Pell Grant would get up to an additional $5,000 from the school—or to increase the share of Pell Grant recipients they enroll.

If this country is still dedicated to ensuring that all students have an equal opportunity to attend college, the federal government cannot continue to do it alone. Colleges, which receive hundreds of billions of dollars in federal financial aid from students each year, must do their fair share. Together, the Pell matching and Pell bonus proposals are aimed at ensuring that colleges live up to their commitments to serve as engines of opportunity, rather than as perpetuators of inequality.