America had 5 million job openings at the end of November, the most since 2001, according to new government data.

That means the U.S. isn't just back to pre-recession levels, it's humming better than it has in a decade. In fact, last year was the best year for job growth since 1999.

So are we back to normal yet?

CNNMoney polled numerous economists, and they were nearly split on the issue. It's a hot debate at the Federal Reserve as well. The Fed doesn't want to raise interest rates until the job market is solidly better.

The data has been so strong that Barclays economist Michael Gapen predicts the labor market will be back to its average levels by next month, and Sam Bullard of Wells Fargo dubs the current situation "normal-like."

Unemployment, the official barometer for the health of the U.S. job market, fell to 5.6% in December. That's certainly in the range of normal.

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Buzz about new jobs: There's also anecdotal evidence that more Americans are getting jobs. A popular trend on photo-sharing site Instagram is to take a photo of yourself on your first day of work and tag it #newjob.

CNNMoney profiled Joshua Wolfe of Oklahoma who went from being a part-time restaurant worker in November to having a full-time job with benefits by the end of 2014.

His lucky break came when he chatted with a regional sales manager for rental company while he was waiting in line at a fast food restaurant. Their casual conversation led to an interview, which led to a job.

Show me the wage increase: But other economists compare what's going on to a plane taking off -- sure, the front end is tilting up, but what about the back end? When is that truly going to lift off?

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Economist Diane Swonk of Mesirow Financial says America's job market is "nowhere near" normal. She points to the lack of wage growth.

Median weekly earnings in the U.S. are just shy of $800 -- the same as in 2007 after adjusting for inflation. It's hard for a family to feel any better off when their pay isn't keeping up with the cost of living.

"We still have a ways to go before wage growth accelerates and the labor market really looks 'normal,'" says Thomas Simmons of Jefferies. He notes that hiring might be back to 1999 levels, but wage growth is a mere 1.7% a year right now compared to 3.6% in December 1999.

CNN wants to know: Are you expecting a raise this year?

Fewer Americans are working: Another red flag is the number of people who have jobs or are actively looking for one -- the so-called labor force participation rate. It's fallen to 62.7%, the lowest since Jimmy Carter was president.

What that means is nearly four in 10 Americans aren't in the labor force. There are logical reasons for this: They could be disabled or taking care of children. There are also demographic shifts with the Baby Boomers retiring, so we would expect some drop off. But people could be so discouraged that they have given up on finding a job.

Even among those still in the labor force, almost 3 million have been looking for work for about half a year or longer.

"The bottom line is that there are still way too many unemployed people and way too many people working part-time who would prefer full-time employment to call what we saw in December 2014 anything other than nice, but distinctly subpar," says James Smith, chief economist for Parsec Financial in Asheville, NC.

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Is this a 'new normal?' Most economists told CNNMoney they expect the jobs picture to continue to improve. Many were willing to go as far as to say it could be normal by the end of the year, if not sooner, especially if job growth stays so strong.

But a few are beginning to question whether America is in a "new normal" -- a place where jobs are plentiful again, but wages aren't going up as expected. That's a far scarier place to be.

Allen Sinai of Decision Economics believes we are "normal for a situation where companies basically do not want to hire people because they are maximizing shareholder value."

Then there's technological change and the ability for companies to make much faster changes that they once did.

"The point is that change is occurring so fast that equilibrium is impossible," says Bill Watkins, head of the Center for Economic Research and Forecasting at California Lutheran University,