WASHINGTON (MarketWatch) — Companies are ramping up their hiring, and more workers are willing to quit, according to government data released Thursday that points to continued improvement in the jobs market.

The job-openings level actually got worse in September — falling to 4.74 million from 4.85 million, according to the Labor Department. But the details of the job-openings report were nearly universally positive. And the job-openings level in September was the second highest in 13 years.

“Job openings have surged in recent months, and despite edging back in September, are up 20% from a year earlier,” said Sarah Watt House, an economist at Wells Fargo Securities.

Companies hired 5.03 million people in September, which is the highest number since December 2007, just as the Great Recession started.

That took the hiring rate to 3.6% from 3.4% in August. Though the hiring rate is only at a two-month high, it ties a rate last seen in December 2007.

One of the big questions as job openings began moving higher in the spring was when hiring would follow. The answer appears to be: now.

A related side of that story is the increased willingness of Americans to quit. The 2.8 million people who quit in September constituted the highest number since April 2008, taking the quits rate to 2% from 1.8%.

Quits are an important measure of worker confidence in that they suggest a capacity to secure a better job, or even to start a company.

Federal Reserve Chairwoman Janet Yellen has explained the significance this way: “The quits rate is important” because an increase “would signal that workers perceive that their chances to be rehired are good — in other words, that labor demand has strengthened.”

See: The Janet Yellen dashboard — how the Fed chief views the jobs market

Another measure of an improving jobs market is that the competition for positions keeps declining. At 1.96 unemployed per opening, the competition for jobs is at its lowest mark since March 2008.