SEATTLE – Every year, American schools pay more than $8.6 billion in bonuses to teachers with master’s degrees, even though the idea that a higher degree makes a teacher more effective has been mostly debunked.

Despite more than a decade of research showing the money has little impact on student achievement, state lawmakers and other officials have been reluctant to tackle this popular way for teachers to earn more.

That could soon change, as school districts nationwide grapple with shrinking budgets.

Just last week, U.S. Education Secretary Arne Duncan said the economy has given the nation an opportunity to make dramatic improvements in the productivity of its education system and to do more of what works and less of what doesn’t.

Duncan told the American Enterprise Institute on Wednesday that master’s degree bonuses are an example of spending money on something that doesn’t work.

On Friday, billionaire Bill Gates took aim at school budgets and the master’s degree bonus.

“My own state of Washington has an average salary bump of nearly $11,000 for a master’s degree — and more than half of our teachers get it. That’s more than $300 million every year that doesn’t help kids,” he said.

Gates also took aim at pensions and seniority. “Of course, restructuring pay systems is like kicking a beehive,” he acknowledged.

As of 2008, 48 percent of public school teachers in this country had a master’s degree or above, and nearly every one of them got a bonus of between $1,423 and $10,777 each year, according to research from the University of Washington.

Michael Podgursky, an economics professor at the University of Missouri, said the economic downturn may force payroll reform in some places where the political will has been lacking.

“We’re experimenting now,” he said, noting pay-for-performance experiments in New York City, Houston and Nashville.

Ninety percent of teachers’ master’s degrees are in education, not subjects such as English or math, according to a study by Marguerite Roza and Raegen Miller for the Center on Reinventing Education at the University of Washington.

Their colleague, research professor Dan Goldhaber, explained that research dating back to a study he did in 1997 has shown that students of teachers with master’s degrees show no better progress in student achievement than their peers taught by teachers without advanced degrees.