The median wage offered to new hires in Minnesota rose by almost a dollar an hour in the past 12 months, bolstered by the increase in the minimum wage, but the majority of open jobs in the state still don’t pay well enough to support a family.

Minnesota has the most job vacancies since 2001, according to new data from the state. Median pay for the openings rose from $12.05 per hour to $12.99 per hour.

“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.

But in the Twin Cities, where two-thirds of the state’s population lives, $12.99 per hour isn’t enough to live on for a family of four with two working parents.

Two working parents with one child must each earn around $14 per hour in the Twin Cities to support their family, according to the state’s cost of living calculator. Families with more children or only one earner must find jobs that pay much more.

The new job vacancy data, released twice a year in Minnesota, is the latest evidence of a difficult problem across the country. The economy has been growing and the stock market until August was setting records, but wages have been stagnant for years and have ground to make up.

In Minnesota, the three types of occupations with the most openings are food preparation and serving, which pays a median wage of $9.11 per hour; sales and related jobs, which pay a median of $10 per hour; and office and administrative support, which pays a median of $12.52 per hour.

Jobs in those fields account for 34,000 of the 98,000 openings in the state.

“There are certainly a lot of jobs that offer very low wages,” Casale said.

One explanation for this is that people are leaving low-wage, low-skill jobs all the time and employers are constantly looking to fill the openings. Low-wage positions always make up a large share of the vacancies. In contrast, people are less likely to leave well-paid jobs, so the number of vacancies will always be lower.

A high job vacancy rate is a sign of a tightening labor market, said Laura Kalambokidis, the state economist, and it’s not clear that people are trying to raise a family on the available low-wage jobs.

New hires in low-skill occupations are always going to start at lower wages, she said, and those who are already in jobs can often demand higher pay to prevent them from leaving their company, which is not reflected in the survey’s data on wages.

“It’s not telling you about the wages of people who are already employed,” Kalambokidis said.

The pay companies offer for professional workers in management, legal and computer science fields rose over the past 12 months, while the median offer for health care practitioners dropped more than $2 to $23.78 per hour.

The biggest shift from a year ago was the increase in pay for workers at the low end of the income spectrum. For workers at the 25th percentile in Minnesota, wages rose 7.5 percent over the past 12 months. Most of those jobs still don’t pay enough to support a family, but the trend is encouraging.

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

The increase was driven by the rise in the minimum wage, Casale said, which rose from $6.15 per hour to $8 per hour in 2014 and rose again to $9 per hour at the beginning of August.