An important new book on improving the stagnant graduation rates of the nation's public colleges and universities suggests that one reason so many academically talented students leave college without a diploma may be that they enroll in schools for which they are overqualified. Authors William G. Bowen, Matthew M. Chingos, and Michael S. McPherson propose that counterintuitive idea, which they call "undermatching," in "Crossing the Finish Line," published this month by Princeton University Press. The book's findings are drawn from a new study of 68 public colleges and universities, including 21 flagship schools, in four states. The authors of "Crossing the Finish Line" introduce some empirical evidence into the graduation question by gathering data on hundreds of thousands of students entering public colleges and universities in 1999 in Maryland, North Carolina, Ohio, and Virginia. They focused on public institutions, according to the book, because those schools enroll 80 percent of all students seeking four-year degrees in the United States. The findings on undermatching, though, come from data on North Carolina students. Among the students from that state who presumably would have qualified to enter more-selective schools because of their grades and college-entrance-exam scores, 40 percent chose not to attend the most prestigious schools. They chose the next most-competitive state school, a historically black college or university, a two-year college, or no college at all. The study also found that undermatching was more common among students from families with low incomes and those whose parents did not attend college. The flagship schools in the study drew only 36 percent of the well-qualified students from families with no college-going experience, and 41 percent of those from families whose incomes put them in the bottom quartile of the income distribution. The authors suggest that one barrier for lower-income families may have been the "sticker prices" for the elite schools--possibly because parents may not have had information about the financial-aid opportunities available.