Most low-income students who have top test scores and grades do not even apply to the nation’s best colleges, according to a new analysis of every high school student who took the SAT in a recent year.

The pattern contributes to widening economic inequality and low levels of mobility in this country, economists say, because college graduates earn so much more on average than nongraduates do. Low-income students who excel in high school often do not graduate from the less selective colleges they attend.

Only 34 percent of high-achieving high school seniors in the bottom fourth of income distribution attended any one of the country’s 238 most selective colleges, according to the analysis, conducted by Caroline M. Hoxby of Stanford and Christopher Avery of Harvard, two longtime education researchers. Among top students in the highest income quartile, that figure was 78 percent.

The findings underscore that elite public and private colleges, despite a stated desire to recruit an economically diverse group of students, have largely failed to do so.