LANSING, Mich. — About 19,500 jobs in Michigan were saved or created through the end of September with federal stimulus money, according to the state’s first accounting of how the money was spent.

About 74 percent of the jobs were at schools or related to education, according to a state report released Monday. Many of the jobs were likely teachers or others who would have been laid off without the federal money.

About 17 percent of the jobs were related to work force development, such as summer and fall jobs for people under age 24. Another 6 percent were tied to road, sewer and other construction projects.

Nationwide, education and construction benefited the most from the federal stimulus package, according to preliminary information gathered by The Associated Press. Schools in particular were helped, as federal money supplemented state and local budgets and spared what officials said would have been tens of thousands of teacher layoffs.

“The blow would have been much worse had that money not been there,” said Doug Pratt, a spokesman for the Michigan Education Association, the state’s largest teachers union.

As of Sept. 30, Michigan had spent about $620 million of the $3.7 billion it was allocated in federal stimulus money.

The state’s report covered money it spent or distributed to other agencies for such things as education, road and sewer construction and alternative energy. It did not include stimulus money spent on such programs as Medicaid, food assistance or unemployment.

It also didn’t include money the federal government sent directly to more than 1,300 local governments, universities and other agencies around the state.

Overall, Michigan officials estimate more than $9.3 billion in stimulus funding has been allocated to the state, local governments, residents and tribal governments.

The report doesn’t distinguish the number of jobs saved from the number created by the stimulus package. But it’s likely Michigan’s high unemployment rate — 15.2 percent in August — would be worse if it weren’t for the federal assistance.

The state has lost more than 300,000 jobs in the past year.

All states and local agencies that receive stimulus money were required to report to the federal government over the weekend. The reports cover the period from when the stimulus package was signed into law in February through Sept. 30.

State and local agencies will be required to file reports every three months as the Recovery Act program continues.

“There has been a lot of back and forth between the states and the federal government,” said Leslee Fritz, director of the Michigan Economic Recovery Office established to coordinate and monitor the program in the state. “There’s a learning curve.”

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