Public higher education is often thought of as a way to help level the playing field between Americans of all stripes, but there’s evidence that flagship public colleges aren’t the engines of mobility we think.

These schools are often thought a way to provide students from a variety of backgrounds with a high-quality education at an affordable cost. But a new study adds to the growing body of evidence that these schools increasingly serve wealthier students.

Between 1972 and 2007, the share of applicants to the University of Wisconsin-Madison from the bottom fifth of the income distribution stayed roughly the same at less than 5%, according to a study published last week in the Russell Sage Foundation Journal of the Social Sciences. During the same period, the share of applicants from the second-lowest income quintile declined from at least 20% or more to just 11.5% in 2007. But the share of applicants from the top two highest income levels grew from 42.6% to 64.1%.

The university does make efforts to reach more low-income applicants, including through outreach, scholarship programs and transfer agreements with two-year colleges, whose classes typically include a large share of low-income students, according to Meredith McGlone, a University of Wisconsin-Madison spokeswoman. In addition, the school upped its need-based grant aid from $6.6 million during the 2007-2008 academic year to $31.3 million this past academic year, she said.

“UW-Madison is committed to making sure that a high-quality education is not out of reach to students due to their family income,” McGlone wrote in an email.

Barbara Wolfe, a University of Wisconsin professor and one of the paper’s authors, said she found it “very frustrating” that the share of low-income applicants hasn’t budged over several decades, despite these efforts.

“In a broader scheme, it’s tied to this whole question of inequality, it’s tied to the cycle of poverty,” she said. “It does just perpetuate or make worse the current income distribution.”

While this particular research only looks at the University of Wisconsin, the results point to broader concerns about equity in higher education. McGlone noted in her email that “this study speaks to a national trend that affects many universities beyond UW-Madison. Wealthy students are increasingly applying to more and more colleges.”

Wolfe said she hopes the method she and her co-authors developed can serve as a model for researchers in other states to study similar questions. Studies about the income of college applicants typically rely on self-reporting from the applicants themselves, who are teens “if you use what an 18-year-old says is your family income, you’re not doing very well,” Wolfe said.

In order to come up with a more reliable proxy for the income of applicants, Wolfe and her fellow researchers matched the home address listed on a student’s application to her census block and then got the median income of the area.

While the share of low-income students applying to Wisconsin has remained relatively stagnant over the past several decades, the increase in wealthier students applying to the school was fueled in large part by a boost in applicants from out of state. Wisconsin is not alone in this trend: Students with means are increasingly applying to more colleges, including flagship public universities, to boost their chances of admission somewhere.

In some cases, public universities are actively luring these students at the expense of those in their state, as they cope with cuts to state funding. A 2015 report from New America, a Washington-based think tank, found that the share of merit aid—or grants that aren’t based on need — at four-year public colleges grew from 8% to 18%. That indicates that instead of devoting resources to the low-income students who may need them, these schools are using scholarships to draw out of state students who may not need the money, but who will end up paying more than their in-state peers even with the discount, the report claims.

The University of California system came under fire last month after a state audit accused the schools of lowering its standards to admit up to 16,000 out-of-state students who were less qualified on a variety of academic measures than the typical in-state student admitted to the schools. The university system disputed the report’s findings, with its own report, which argued that the schools’ admissions policies favor California residents and noted that the system plans to enroll 5,000 more in-state residents in the upcoming academic year than in the year prior and will add 5,000 more California students on top of that in the next two years.

The state audit “makes inferences and draws conclusions that are supported neither by the data or by sound analysis,” Janet Napolitano, the president of the UC system, said in a statement last week.

The Wisconsin study doesn’t point to any practices at the university that indicate it’s luring wealthier or out-of-state students at the expense of low-income and in-state students. In fact, the chances of a low-income applicant getting into the university increased during the later years of the study. But that’s also true of wealthier applicants. “In considering how this might affect access, we emphasize that applicants from the highest income quintile are far more numerous than those from the lowest,” the authors write in the study.

McGlone noted that Wisconsin does well by the low-income students who do enroll. The school was recognized by the Education Trust, a nonprofit devoted to educational equity, for increasing graduation rates for students from underrepresented backgrounds.

Still, it’s possible things may get more unequal at Wisconsin. For years, the school required that no more than 25% of the freshman class be nonresidents or residents of a state covered by a reciprocity agreement with the school, like Minnesota. That helped to curb the number of wealthy out-of-state students gaining spots over lower income Wisconsin residents, the paper notes. But in 2012, the university’s governing body upped that quota to 27.5% and last year they voted to suspend the limit for four years.

“Because the state contributes a smaller and smaller proportion of UW-Madison’s operating budget, the university administration naturally considers alternative ways of raising revenues, and the many wealthy applicants offer a quick, attractive alternative,” the study authors wrote.

Wisconsin is taking pains to ensure a decent share of students are from the state. The school has committed to enrolling at least 3,600 in-state freshman each year, McGlone said. To give a sense of how that stacks up to the freshman class as a whole, the school enrolled 6,279 freshman in 2013.