Jobless Benefit Numbers Underestimate Unemploymen
In short: No. Though it likely means that the rate of deterioration is slowing.
The reason why jobless benefit numbers are now falling is that jobless benefits have a time limit. In America, that limit for the regular programmes are 26 weeks (or 6 months). And since we've had very high level of jobless benefits for more than 6 months now, this means that many of those that applied in December 2008 or January 2009 are now seeing their regular benefits disappear, meaning that they are removed from the jobless benefit claims numbers.
However, it should be noted that the actual number that receives jobless benefits is a lot higher than the 6.20 to 6.67 million mentioned above. As Congress has passed legislation enabling people to receive benefits longer than 26 weeks, and as the above numbers excludes people receiving benefits longer than 26 weeks, the actual number of people receiving benefits is even higher. The number of people receiving extended benefits is still rising.
Even so, the drop in the official number has been bigger than the increase in the number of people receiving extended benefits, so the true number of recipients is still falling. However, as is noted here in the New York Times, an increasing number of people are losing even their extended benefits. Some of them might have gotten jobs, but many will remain jobless. We should therefore expect Friday's employment report to show another increase in the unemployment rate.