Faced with a mounting labor shortage and high employee turnover, restaurant chains have earned plaudits for offering incentives to workers to stay in the job longer — tuition payments, bonuses, even a four-day workweek.

But the shortage of workers also appears to have had a darker effect: a steady drumbeat of labor violations by operators who have cut corners to keep their restaurants fully staffed.

In the latest example, Chipotle Mexican Grill was fined nearly $1.4 million on Monday over accusations that it routinely violated Massachusetts child labor laws, with the authorities estimating more than 13,000 violations from 2015 to 2019, the Massachusetts attorney general’s office said.

The authorities examined the records of six Chipotle locations across the state, finding that the chain regularly let dozens of 16- and 17-year-old employees work more than nine hours per day and more than 48 hours per week, in violation of state law, according to the Massachusetts attorney general. The authorities then used those findings to estimate that Chipotle had violated child labor laws 13,253 times across 50 locations in the state.