MINNEAPOLIS — First, the good news: Minnesota job openings are at their highest since 2001.

Now the bad news: The majority of open jobs don’t pay well enough to support a family.

Those mixed findings come from the latest state data on job vacancies in Minnesota, according to a press relase. And while the median income for job openings has increased in the last year — from $12.05 last year to $12.99 this year — it still falls short of the $14 hourly benchmark for two working parents to support a family of four in the Twin Cities.

“The minimum wage increase is maybe shifting that a little bit,” said Oriane Casale, an analyst at the Minnesota Department of Employment and Economic Development, which publishes the job vacancy data twice a year.

Jobs in sales, administrative support and food preparation and serving industries accounted for more than a third of the 98,000 current openings. Each field pays below the $14 threshold.

State economist Laura Kalambokidis said it’s unclear whether people are trying to raise families on the low-wage jobs that are available. But state officials explained that openings concentrated in low-paying fields are the norm.

People leave low-wage jobs in search of higher pay, opening up those positions, while workers tend to stay in higher-paying fields. Also, new hires in low-skill jobs will always start at lower pay, Kalambokidis said.

Although the stagnant wages are troubling, there was a bright spot: Among the biggest shifts in the last year, wages increased more than 7 percent for Minnesota’s lowest income earners. It’s not enough to meet a family’s cost of living, but an encouraging trend and one that Casale attributes to Minnesota’s recent minimum wage increase to $9 an hour.

“Wages moved up at the lower end, which I think is the most interesting thing here, because it’s so rare,” she said.