Healy Hall on the the Georgetown University campus. (Simon Brubaker/The Washington Post)

Selective colleges get plenty of applications from the top-scoring children of affluent parents, including many in this region. What the colleges need, their admissions officers say, are more high-achieving, low-income applicants. Places such as Georgetown and Duke don’t like being called country clubs for the rich. They want more academically talented poor kids. Why aren’t they applying?

Now we know, thanks to remarkable research by economists Caroline Hoxby of Stanford and Sarah Turner of the University of Virginia.

Many analysts have suggested that low-income high-achievers don’t apply to the most famous schools because such places are often far from home and they don’t want to be away from family and friends. Hoxby and Turner discovered a more influential reason: Such students think the prestigious campuses are unaffordable. That is a shame because the opposite is true; the more selective the college, the better their chances are to get financial aid.

High-achieving, low-income students, as defined by the researchers, are in the top 4 percent of all high school students by grades and college aptitude test scores, and in the bottom quarter of high school seniors by family income (no more than about $41,000 a year).

Most of them are non-Hispanic whites. They are mostly urban and suburban kids, like their counterparts who do apply to big-name colleges, but are less likely to be in the big metro areas such as New York, Los Angeles, Houston, Dallas, Chicago, Miami or Washington.

The researchers calculated that 25,000 to 35,000 high-achieving, low-income students are part of each year’s high school graduating class, about 1 percent of the total. A large majority of them are not applying to the 236 most competitive colleges and universities rated by the 2008 edition of Barron’s “Profiles of American Colleges.”

Hoxby and Turner said the students were handicapped by having few, if any, counselors who understood what they were missing. Some high-achieving kids were so ill-advised that they would apply only to Harvard and the local community college, and nowhere else. Seasoned counselors would have told them to apply to two safety schools and five or six selective colleges whose middle range of successful applicants is within 5 percent of their strong SAT and ACT scores and grade point averages.

Hoxby persuaded the U.S. Department of Education and several foundations to fund an unusual experiment. Letters were sent to 40,000 low-income high achievers, revealing the relatively low costs of selective schools compared with the less selective ones they appeared to prefer. Then, after the admission season was over, the researchers asked the students what happened.

The results were startling. Those who received the letters were 53 percent more likely to apply to a college that matched their high achievement level. They were 70 percent more likely to be admitted to one of those schools and 50 percent more likely to attend.

Hoxby said colleges do a better job finding and admitting black and Hispanic students in the high-scoring, low-income category because their race and neighborhood are often a clue to their family income. Smart, poor kids of every race are difficult to identify because they resist disclosing their family income and colleges don’t require the information.

Should all college applicants be required to reveal their family income? Hoxby said no, at least not yet. The College Board has agreed to keep sending letters to low-income high achievers that explain their options. Hoxby wants to see whether that produces enough new applicants to give selective colleges significantly more students whose parents thought they could never afford such an opportunity.