When Luke Greiner quizzes high school students about Minnesota's labor market, there's one question that always stumps them: What college major--and type of degree--leads to the highest salary two years after graduation?

"Students pick chemical engineering, anything with computers," said Greiner, who works for the Minnesota Department of Employment and Economic Development (DEED).

The correct answer? A specialized plumbing and water supply program.

Many states, driven partly by people's anxiety over whether a college degree is worth the cost, now track the early career wages of residents who went to college in the state.

Minnesota is one of the few states that goes beyond...

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