The job market may finally be healing at a more normal pace, with one key indicator—jobless claims at the lowest rate in 8½ years.
Moody's Analytics economists Thursday said they were encouraged more broadly by gains in the job market and now see full employment by late 2015, a year earlier than they previously forecast.
The Moody's economists expect full employment when the unemployment rate hits 5.5 percent by late in the third quarter or early in the fourth quarter of next year. At that point, the long-term unemployed should be rejoining the workforce and part-time workers should be able to move to full-time work. Unemployment was at 6.2 percent in July, up slightly from June.
Weekly jobless claims data Thursday confirmed positive momentum in the jobs market, with claims falling to 289,000 and the four-week average at 293,500—the lowest since February, 2006.
Read MoreJobless claims below 300,000
The four-week average is also at a record low ratio to the labor force, according to MKM Partners.
Mike Darda at MKM also said in a note other labor indicators have improved to cycle highs, including job openings and the National Federation of Independent Business' small-business hiring plans. He says that means a period of faster job growth is likely on the way.
Economists have varied views on when the job market will reach full employment.
"Our forecast for full employment is 6 percent, and we think we'll cross that threshhold at the end of this year," said Carl Riccadonna, Deutsche Bank senior U.S. economist. He expects the unemployment rate to hit 5.5 percent by the first quarter.
"Whether we get there this year or next year is not as relevant as people think. The point is we're poised to get to full employment," he said.
Full employment, however, should signal a more healthy job market, where hiring picks up from its current pace, finding a job becomes easier and workers see higher wages.
"We think at that point, when the unemployment rate gets to 5.5 percent, you're going to see significant upward pressure on wages and that would induce people who are out of the workforce to come back in and look for work," said Marisa Di Natale, Moody's senior economist.
Moody's economists said they have been surprised by the pace of decline in the jobless rate. While job growth has been in line with their expectations, there has not been the increase in labor force participation that economists have been anticipating as workers attempt to rejoin the workforce. The participation rate, at 62.9 percent, represents people in the workforce or looking to join it.
For that reason, they changed their view on when the economy will hit full employment. They also altered their view on the participation rate which they expect to be affected by increasing numbers of retirement age baby boomers.
"There's a huge demographic shift in the population, and we think that contributes to half the decline. The other is the economic cyclical factor," said Di Natale. "We think the participation rate will stabilize where it is right now, but it might move up about a percentage point, as we approach full employment, but after that we expect it to move lower again." The later decline would be a direct result of retiring baby boomers.
Even with six months of 200,000-plus payrolls growth, the rate of job creation has not been contributing to the labor force, as it has in the past.
"If you look at the four-week moving average of initial claims, they've rarely gone below 300,000. The only times they have is in peaks of expansion," said Di Natale. Besides 2006, claims were under 300,000 in 1999, and the unemployment rate was much lower. "Those were very tight labor markets. It's very different now. You have a lot of slack in the labor market."
That labor slack has been a big concern for the Fed, and it shows up in the low participation rate—at 62.9 percent, near a post-recession low. There's also a high number of long-term unemployed, unchanged at 3.2 million people in July.
The Fed's forecast is that unemployment will reach a range of 5.4 to 5.7 percent in 2015 and 5.1 to 5.5 in 2016. The market has been watching the 6 percent level, since the central bank once targeted it as a level where it would begin to consider raising interest rates.
But Fed officials have said they have no target, and Fed Chair Janet Yellen has repeatedly emphasized her concerns about labor slack.
Di Natale said she expects the slack to diminish as full employment gets closer and the job market will achieve better equilibrium. She said data continues to show a mixed picture, where companies are not hiring but also not firing. Di Natale said government data on job openings shows the disparity.
Currently job openings as a share of employment is 3.4 percent, and it was 4 percent before the recession, she said. In 2009, it hit a low of 2.8 percent.
"This is just one side of the equation. On the layoff side it could indicate we get some modest increase in nonfarm payrolls, but the other side is hiring. ... It hasn't come back to where it was before the recession," she said.
July's slower gain of 209,000 nonfarm payrolls showed the economy is chugging along, and the labor market is improving, but economists also do not see it as strong enough to push the Fed to hike rates earlier than expected. Important to the central bank is the number of long-term unemployed, a group that accounts for 32.9 percent of the unemployed, and that number has dropped by 1.1 million over the past year.
A concern in markets has been that stronger data and signs of inflation mean the Fed will raise rates sooner than the second half of next year, the time frame expected by many economists.
The Fed ends tapering of its bond-buying program in October, and there's been lots of speculation about when the central bank would start to raise the fed funds rate.
Employment is one of the most critical components in its decision-making, and if it gets much stronger, economists say the Fed may have to rethink its timing. Some forecasters expect it to, and some Fed officials are calling for a swifter move toward the Fed's first rate hike.
—By CNBC's Patti Domm