It’s a familiar scene, a high-school student anxiously opening an email or letter that hopefully contains good news: admission to his or her college of choice. The ritual has become a recognizable part of American culture, one that plays out in movies and hyper-emotional commercials. Economists agree that going to college matters a lot for future earnings. But does the sender of that envelope matter?

That depends—for certain majors, going to a top-tier institution is invaluable. But for many career paths, it just doesn’t matter where a person got his or her education, according to a recent study from Eric Eide and Mark Showalter of Brigham Young University and Michael Hilmer of San Diego State University. The researchers compared the earnings of individuals from schools with different selectivity rankings, controlling for their majors and their level of degree attainment (e.g. those with solely bachelor’s degrees were compared to other’s with solely bachelor’s degrees) 10 years after they completed undergrad.

According to their results, school choice matters the most for business majors. Those who attended top schools earn 12 percent more than their peers who went to schools that were in the middle of the pack. And grads from those mid-tier institutions earned 6 percent more than their peers who went to the least-selective schools. For social science and education majors there was also a significant boost that came from attending a better-ranked school.

By contrast, engineers who went to the most selective schools enjoyed only a marginal earnings benefit over their peers at mid-tier institutions. And while humanities majors at the most elite schools enjoyed higher earnings than peers at the least selective schools, there was virtually no difference between top-tier and mid-tier earnings. For science majors, the prestige of a school mattered least of all. The authors found that the sciences exhibited the “statistically weakest earnings differences for a given major across college selectivity types."

Though they don’t provide conclusive reasoning for these discrepancies, the researchers do share a few thoughts. For instance, they suspect that business majors at the most prestigious schools may benefit from better internship opportunities and more robust networks than their peers at lower-ranked schools. And sciences may involve more standardized major requirements, meaning that the core competencies taught are essentially the same no matter where a student winds up. That can mean that for many careers, majors trump alma mater when it comes to earnings.

So should Americans just forget about their entrenched beliefs about prestigious colleges?  It’s not quite that simple. Ten years out, those who graduated from highly-ranked schools earn more than their peers who went to less selective schools. That’s because there are lots of other factors at play. For instance, those who go to high-ranking schools are also more likely to obtain advanced degrees. Though a student who graduates with a degree in chemistry at Harvard would probably wind up earning about the same as someone majored in chemistry at a lower-ranked  state school, the Harvard grad is more likely to go on to obtain a Master’s or Ph.D., pushing their future earnings higher. And attendees of the nation’s top-ranked schools are more likely to graduate in the first place, according to Anthony Carnevale, the director of the Georgetown University Center on Education and the Workforce.

For those headed toward careers where elite networks rule, school choice is more important since selective schools provide access to the companies and individuals necessary to further one’s career.  Who attends these schools? Largely, wealthy kids who’ve had better access to the types of education, test preparation, and extracurricular activities that help them gain entry, says Kim Weeden, a sociology professor at Cornell University. Rich kids also have the ability to build their resumes via unpaid internships, an easier proposition for students whose families can help support them.

These are important considerations especially given the rising cost of a college education, and the increasing amount of debt young people are taking on to graduate. Carnevale says that while more elite schools can boost a student’s standing in a particular region or industry, for most people just graduating from a college is what matters most.