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If there's a fun (or depressing) game for college presidents these days, it might be imagining: What could I do with Harvard University's endowment -- or just the earnings on its endowment? With members of Congress and other critics raising questions about why the wealthy institutions need so much, more attention than before is focused on the funds in Cambridge, New Haven, Palo Alto and a few other select locations.

MaryAnn Baenninger, president of the College of St. Benedict, in Minnesota, looked at it this way: With just the $6 billion in last year's earnings on the endowment (not touching a penny of the original), she could pay for tuition, room and board for every one of her 2,000 students -- for the next 85 years. Unlike some in Congress, Baenninger isn't advocating an endowment raid and has no expectation that Drew Gilpin Faust, Harvard's new president, is about to send her a check.

But the fact that earnings alone could cover all costs for enrolling at a small college for so long (admittedly at today's rates) drives home why the endowments look so obscenely large at some institutions. But is the relationship between endowment spending rates and generous financial aid policies as clear as some say it is?

The link is talked about with increasing frequency. When powerful senators asked colleges with large endowments for information about their policies, they suggested that higher spending rates would lead to more generous aid. Sen. Max Baucus, a Montana Democrat who is chairman of the Senate Finance Committee, praised the colleges that have recently made aid more generous and said that he wanted to understand how colleges could "use their endowments to make certain that talented young folks in Montana and across the country aren't left out of the classroom."

And in her higher education platform, Hillary Clinton raised the issue. "Hillary is challenging some of the most selective schools in the U.S. to further expand access for low-income and minority students by spending a greater percentage of their endowment annually on recruiting more low-income students and students of color, supporting them so that they graduate and growing the pipeline of students that are prepared to compete for admission to the most selective schools," the position paper says. "The endowments of the 12 wealthiest universities total $155 billion and in recent years and have gotten tax-free returns of almost 20 percent. These elite institutions benefit tremendously from their tax-exempt status as well as from federal student financial aid and research grants.

A closer look at three colleges -- all of them with endowments large enough to be receiving Congressional scrutiny -- suggests, however, that the relationship between endowment spending rates and access for low income students is limited, if it exists at all.

Arguably one of the most generous financial aid packages in American history's (Harvard University's latest offering) came with a spending rate that is significantly below the level being kicked around as an acceptable minimum (5 percent). An institution that is less wealthy than Harvard (Cornell University) increased its spending rate significantly -- to 5 percent -- in part to offer more generous aid, but will not come close to Harvard's level. And an institution with much less money, less generous aid packages and lower spending rates -- Smith College -- actually enrolls far more low-income students than do wealthier institutions that (as in Harvard's case) adopt policies Congress likes to praise or (in Cornell's case) increases the spending rate on its endowment.

Consider Harvard, whose aid policies have been praised by the same members of Congress who are saying that colleges need to explain why they don't have a 5 percent endowment spending rate. In December, Harvard announced an aid policy under which students from families with incomes of up to $60,000 will pay nothing, while those with incomes of up to $180,000 would be assured of paying no more than 10 percent of family income -- and without loans in aid packages. Harvard's announcement set off a wave of policy shifts from colleges -- but with just a few exceptions, the policies didn't come close to Harvard's level of aid.

So how did Harvard afford that level? With a high spending rate? Actually, the spending rate that produced that largesse was 4.6 percent -- the kind of rate seen as inadequate by the same lawmakers who praise Harvard's aid plan.

Last week, Cornell University became one of the institutions trying to play catch-up with Harvard's aid bonanza. It took Cornell a while, in part because it is much less wealthy than Harvard (their respective endowments are $5.4 billion and $34.6 billion). But Cornell also tends to enroll a greater share of low-income students (not to mention twice the total number of undergrads) and thus any increase in aid promises has greater ramifications. So when Cornell announced its plan, it featured loan caps (but not loan elimination) at the $75,000 and up family income level. But Cornell and Harvard will end up spending about the same on financial aid under their new plans (about $120 million annually).

For Cornell, with its smaller endowment, to spend that amount, it is increasing its spend rate to 5 percent from 4.7 percent -- reaching the level senators want. But is spend rate the relevant factor? Compare the $120 million financial aid cost to the endowment earnings of the two universities in the last year. If the two universities were to finance all of their aid budgets from endowment earnings, that $120 million would make up 2 percent of Harvard's earnings but 11 percent of Cornell's earnings. That suggests that the relevant factor isn't spend rates but wealth to start with.

But the Smith example suggests that equally important may be the question of who gets admitted. More than 13 percent of Cornell undergraduates receive Pell Grants. But at Smith, more than 23 percent of students receive Pell Grants, and the formula used by the college for endowment payout is based on an average of 4.75 percent, with some modest adjustments based on the market. Both Smith's endowment and student body are a fraction of those at Cornell and Harvard.

From an aid policy perspective, not only is Smith not in a position to compete with Harvard, but it isn't able to be need blind in admissions. Each year a small share of the Smith class is admitted on a need-aware basis -- meaning that the final slots go to those who can pay.

So if Smith's spending rate isn't what Congress is demanding and its aid policy doesn't come close to Harvard's or even the places pushing to keep close to Harvard, what is the key to enrolling low-income students in larger numbers? The answer, according to Smith, has nothing to do with endowment spending rates or even aid policies. To enroll more low-income students, you need (this will sound obvious) to recruit and enroll them.

Audrey Smith, dean of enrollment at Smith, said that the success there comes from an institutional commitment and also the idea that "women's colleges have sought talent broadly for a long time."

Ultimately, she said, the key is "thinking more about the potential" of students in admissions decisions and not just going after those with "perfect preparation at the secondary level." In admitting such students -- who may have lower test scores or have never attended prestigious high schools, the college looks for "the ability to take full advantage of an environment like this one," but not at numerical measures.

Smith is able to provide aid that it gives to students based on the "intergenerational equity" of not spending too much of its endowment in any one year, Smith said.

But the key issue is who gets admitted, she said, not the endowment payout rate -- and especially not the endowment payout rate at the places with mega-billions that attract the attention of Congress. Of the public discussion of late linking endowment payout rates to access issues, Smith said: "In all honesty, it just adds to the longstanding frustration that I have that a place like Smith and so many others can do a wonderful job and make a difference in the lives of students, but the spheres of influence in Congress are focused on a small number of institutions and on other issues."

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