Students listen to a substitute teacher, Deborah Pattin, in a temporary classroom in Olympia, Wash. (Ted S. Warren/AP)

Beginning 40 years ago, a series of court rulings forced states to reallocate money for education, giving more to schools in poor neighborhoods with less in the way of local resources. Critics such as Eric Hanushek, an economist at the Hoover Institution, argued these decisions were simply "throwing money at schools."  His research found that there was little correlation between how much schools spent and how well their students performed on tests.

It's a view still held by many politicians today, including Gov. Andrew Cuomo (D-N.Y.). "We spend more than any other state in the country," he said a year ago. "It ain't about the money. It's about how you spend it — and the results."

More recent research, however, has found that when schools have more money, they are able to give their students a better education. A new study on those who went to school during the school-finance cases a few decades ago found that those who attended districts that were affected by the rulings were more likely to stay in school through high school and college and are making more money today.

The authors, Kirabo Jackson and Claudia Persico of Northwestern University and Rucker Johnson of the University of California, Berkeley, released a revised draft of their as-yet-unpublished paper this week. The benefits were most obvious for students from poor families. They found that a 10 percent increase in the money available for each low-income student resulted in a 9.5 percent increase in students' earnings as adults. A public investment in schools, they wrote, returned 8.9 percent annually for a typical pupil who started kindergarten in 1980.

The findings are evidence that public schooling can be a way for children who grow up in poverty to overcome their circumstances, Johnson argued.

"Those increases in instructional expenditures proved to have large dividends, significant economic returns, in the lives of these children," he said. "We're always searching for what can break that cycle of poverty from one generation to the next."

The study used data on incomes for 15,353 people. The oldest subjects will turn 60 this year.

"What I like about this study is that the authors didn't shy away from proving what many of us consider the obvious," wrote Bruce Baker, a professor at Rutgers University and an expert on school funding, in an email. "If you have it, you can spend it, and if you don't you can't."

As for why his group came to a different conclusion than the one reached by Hanushek and other skeptics, Johnson suggested that earlier efforts to find a a connection between school spending and results were simply confounded by the range of factors that affect the kinds of adults that kids become. Lawmakers send additional money to poor districts, but just because their students don't do as well as those in affluent districts doesn't mean that the money was wasted.

The group used the series court rulings to compare students from otherwise similar circumstances in different places around the country, some of whom attended schools where funding was increased, and others who did not.

Another explanation could be that the benefits of a better education might not become apparent for decades. Johnson said that the difference in earnings was more pronounced for adults in their prime, not for younger adults.

Still, the authors don't advocate simply throwing money at the problem of education, either. "Money matters, but it matters how it's spent," said Jackson of Northwestern.

The group found that the increased funding had the greatest effect if it was used to raise teachers' salaries, reduce class sizes or lengthen the school year. That conclusion accords with other research finding that better teachers can have profound effects on how much students learn, since the schools with the smallest classes and the highest salaries can attract the most talented instructors.