The jobs numbers have been terrific lately. Can we believe them?

Lately, we've been getting some genuinely encouraging news on the jobs front. For the past two weeks, the number of initial unemployment claims has been plummeting. A lot. Does that mean the U.S. labor market is rapidly improving? Or is it all just a statistical fluke?

On Thursday, the Department of Labor reported that the number of new people filing for unemployment benefits fell to just 330,000, a huge drop from the previous week and a new five-year low. This is usually a good indicator of the state of the labor market, so that's a healthy sign. What's more, initial jobless claims have been dropping far faster than economists have expected all January:

One theory, offered up by Quartz's Matt Phillips, is that the recent drop might simply be due to a temporary surge of construction hiring as the Northeast tries to rebuild after superstorm Sandy. He points out that New York saw the largest decline in jobless claims last month, some 27,000, thanks to “fewer layoffs in transportation, construction, and educational service industries.”

Another possibility, offered up by the Wall Street Journal's Vincent Cignarella, is that the recent plunge in jobless claims might just be a weird statistical fluke due to the fact that California has failed to report its claims for the past two weeks:

[A] small San Francisco research firm suggests it has more to do with the fact that California, whose 38 million population gives it the biggest workforce in the nation, hasn’t filed its claims numbers for past two weeks.

That meant the state’s bean counters had to come up with a guesstimate — and by Southbay Research’s reckoning, they may have come up with too low a number....

An analyst at the Labor Department confirmed that both California and Virginia provided estimates rather than precise data in their filings and that it the bureau was forced to make its own estimate for Hawaii, which also failed to provide data in the most recent week.

If the California bean-counter theory is right, then we might see the number of initial jobless claims revised back upward again in the weeks ahead, when better data rolls in. If that happens, it would mean we're still stuck with a labor market that's improving only gradually.

Of course, the California theory might be wrong, and it's possible that the labor market really is getting much better, much faster than anyone expected. With the U.S. unemployment rate still at a painfully high 7.8 percent (that's what it was during the worst of the 1991 recession), more improvement would help a lot. Remember, if the recent gradual pace of job growth persists, it will take more than a decade for the United States to get back to full employment.