The paper, by Raj Chetty and John N. Friedman of Harvard and Jonah E. Rockoff of Columbia, all economists, examines a larger number of students over a longer period of time with more in-depth data than many earlier studies, allowing for a deeper look at how much the quality of individual teachers matters over the long term. “That test scores help you get more education, and that more education has an earnings effect — that makes sense to a lot of people,” said Robert H. Meyer, director of the Value-Added Research Center at the University of Wisconsin-Madison, which studies teacher measurement but was not involved in this study. “This study skips the stages, and shows differences in teachers mean differences in earnings.” The study, which the economics professors have presented to colleagues in more than a dozen seminars over the past year and plan to submit to a journal, is the largest look yet at the controversial “value-added ratings,” which measure the impact individual teachers have on student test scores. It is likely to influence the roiling national debates about the importance of quality teachers and how best to measure that quality. Many school districts, including those in Washington and Houston, have begun to use value-added metrics to influence decisions on hiring, pay and even firing. Supporters argue that such metrics hold teachers accountable and can help improve the educational outcomes of millions of children. Detractors, most notably a number of teachers unions, say that isolating the effect of a given teacher is harder than it seems, and might unfairly penalize some instructors. Critics particularly point to the high margin of error with many value-added ratings, noting that they tend to bounce around for a given teacher from year to year and class to class. But looking at an individual’s value-added score for three or four classes, the researchers found that some consistently outperformed their peers. “Everybody believes that teacher quality is very, very important,” says Eric A. Hanushek, a senior fellow at the Hoover Institution at Stanford and longtime researcher of education policy. “What this paper and other work has shown is that it’s probably more important than people think. That the variations or differences between really good and really bad teachers have lifelong impacts on children.” The average effect of one teacher on a single student is modest. All else equal, a student with one excellent teacher for one year between fourth and eighth grade would gain $4,600 in lifetime income, compared to a student of similar demographics who has an average teacher. The student with the excellent teacher would also be 0.5 percent more likely to attend college. Perhaps just as important, given the difficulty of finding, training and retaining outstanding teachers, is that the difference in long-term outcome between students who have average teachers and those with poor-performing ones is as significant as the difference between those who have excellent teachers and those with average ones, the study found. In the aggregate, these differences are potentially enormous. Replacing a poor teacher with an average one would raise a single classroom’s lifetime earnings by about $266,000, the economists estimate. Multiply that by a career’s worth of classrooms. “If you leave a low value-added teacher in your school for 10 years, rather than replacing him with an average teacher, you are hypothetically talking about $2.5 million in lost income,” said Professor Friedman, one of the coauthors. To do the study, the researchers first tackled the question that has swirled controversy in so many school districts, including New York City’s: whether value-added scores are in fact a good measure of teacher quality. Mr. Jones might regularly help raise test scores more than Ms. Smith, but maybe that is because his students are from wealthier families, or because he has a harder-working class — factors that can be difficult for researchers to discern.