Why have so many of us parents, including me, paid a fortune for exclusive private schools or prepped our children strenuously for selective public school entrance exams?

One reason is our belief that in a school that rejects most applicants, the competition and camaraderie of so many great students will ensure our kids too become top scholars. No slacker delinquents will lure them away from their Advanced Placement homework. Ivy League admission and big careers we can brag about will be assured.

Or maybe not. A new study by economists at the Massachusetts Institute of Technology and Duke University suggests that students who qualify for some of the nation’s most selective public high schools do no better academically than similar kids who miss the entrance test cut-off.

Joshua D. Angrist and Parag A. Pathak of MIT and Atila Abdulkadiroglu of Duke wrote the paper “The Elite Illusion: Achievement Effects at Boston and New York Exam Schools,” published last month by the National Bureau of Economic Research. They compared students who just made the cut-off to those who just missed it. They examined the average scores of both samples on later tests that might reflect how much they learned in high school. This included state tests plus PSAT, SAT and Advanced Placement tests.

Most of the students who passed the entrance exams attended one of the six schools studied. Most of those who missed the cut-off did not. The authors say passing the entrance exams had little effect on their later scores. “The intense competition for exam school seats does not appear to be justified by improved learning for a broad set of students,” they said.

In other words, even students edged out for admission to selective schools found that their talent and energy led to academic achievements similar to those of students who made the cut. Perhaps they didn’t need the intense exam school atmosphere to do well. Perhaps they found enough good teachers and competitive classmates at less prestigious schools to get the desired results.

The exam schools in the study are among the best known in the country: Stuyvesant High School, Bronx High School of Science and Brooklyn Technical High School in New York City as well as the Boston Latin School, the Boston Latin Academy and the John D. O’Bryant High School of Mathematics and Science (formerly Boston Technical High) in Boston.

They are not quite as selective as the Thomas Jefferson High School for Science and Technology in Fairfax County, at least as measured by average SAT scores. No school matches Jefferson’s average SAT of 2233 in 2010.

But the study buttresses a widespread belief in Northern Virginia that high-scoring students who don’t attend Jefferson do as well in regular schools with far fewer high-performing classmates. The authors don’t say whether the same principles apply to students rejected by selective private schools, but that question merits further study.

The authors ask an obvious question: Could their results be distorted because “marginal applicants may be ill-positioned to benefit from an exam school education”? That seems unlikely, they say, because the students who just missed the cut-off are still quite bright, with “measured ability far above that of most other urban public school students.”

Test scores are often not the best indicators of school quality. The authors acknowledge that the exam schools have special features, such as Latin instruction at Boston Latin or the top lab equipment at the Boston and New York schools that focus on science. Regular schools often can’t match that.

Still, many of them appear to be holding their own, even when compared with America’s most famous high schools. Those of us with exam school envy might reexamine old assumptions about selectivity being the measure of a school, or even a college. We ought to remember that how much students learn at any school is dependent on their personal talent and effort, and not the name above the entrance or how many smart students it has.