Research by Brown, Chabris, and Wai shows that quality of students is strongly correlated to other quality measures of a college. (Thanks to a reader for sending the link!) See also this global analysis of university quality rankings.
Of course, causality is complex: schools with strong reputations, large endowments, etc. can attract top applicants. But how did those schools acquire those reputations and endowments in the first place?
Salon: ... Though there is often public controversy over the value of standardized tests, research shows that these tests are quite robust measures to predict academic performance, career potential, creativity and job performance.
Critics of the SAT say it tests for students’ wealth, not caliber. While it is true that wealthier parents tend to have students with higher test scores, it turns out the research robustly shows that test scores, even when you consider socioeconomic status, are predictive of later outcomes.
We first found high correlations between our test score rankings and U.S. News national university rank – 0.892 – and liberal arts college rank – 0.890 – even though U.S. News weights these scores only about 8% in their formula. ...
See also Universities Ranked By SAT Score (2013):
Schools with the strongest students (e.g., as measured by SAT) produce graduates who make outstanding contributions at per capita rates easily 10x or 100x higher than others: see Where Nobel winners get their start (Nature) and Colleges ranked by Nobel, Fields, Turing and National Academies output.