MINNEAPOLIS—In U.S. cities with the tightest labor markets, workers are finding something that’s long been missing from the broader economic expansion: faster-growing paychecks.

Workers in metro areas with the lowest unemployment are experiencing among the strongest wage growth in the country. The labor market in places like Minneapolis, Denver and Fort Myers, Fla., where unemployment rates stand near or even below 3%, has now tightened to a point where businesses are raising pay to attract employees, often from competitors.

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