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Statistically speaking, it means that the average time unemployed is infinite. Even if you consider the median instead of the average, it is still infinite: this is is worse than during the Great Depression, where the median time unemployment was finite.
Of course, these statistics don't make much sense. Officially, even the average time unemployed in U.S. is finite, according to the BLS. But how is this average time measured? If it is measured on people who eventually found a job when the survey took place, obviously the average will always be finite, but it will be biased and way too optimistic. In particular, official statistics are biased because anyone who's been unemployed for more than 2 years is not accounted for anymore (in the past, very very few people stayed unemployed so long in U.S.)
Between these 2 extremes (average median time unemployed being infinite / average time unemployed being finite depending on how the metric is computed), we have statistical tools (survival analysis) to better represent what the true reality is. First, if someone who is 55 years old and unemployed never gets a new job in his entire life, you could argue that his unemployment time is 12 years (retirement age of 67 minus 55). Even if this worker can't get any retirement benefits and must look for a new job till he dies, and say he dies at age 84, at worst you can say his unemployment time is 29 years. In any case, it is finite.
So in order to better measure average unemployment time, you need a statistical model. Typically, you could say that the unemployment time is modeled by a truncated one-dimensional parameterized exponential distribution. Estimating the average time then consists of estimating the model parameter. The reason I'm talking about a truncated exponential distribution (rather than a regular one) is because we must assume that unemployment ends whenever one of the following happens:
We need to be careful, when doing computations (e.g. based on survey results) because a number of unemployed people are still in U.S., but very difficult to reach because they have reached the ranks of a growing homeless population. They can't be ignored, as they create pressure (crimes) on the economy.
If we use the model that I have described, what would be the average unemployment time? How does BLS compute the average unemployment time?
Actually, you can define the "restricted mean", sometimes called Irwin's restricted mean.
I'm sure the BLS has a technical statistical report on-line somewhere which defines how they calculate the mean.
It appears that BLS is not trying to predict the end of a spell of unemployment. They are simply measuring the length of time that those currently meeting their definition of unemployed have been in that state. (In fact, until this month, those values have been truncated to 2 years, if they are more than that - http://www.bls.gov/cps/duration.htm) With these restrictions, there are no infinite spells of unemployment. (Definitions of "unemployed" and "duration of unemployment" from BLS glossary pasted below.)
It does look like they have grappled with this type of question though. Here is a (very dated) article on a similar topic that might interest you. (http://www.bls.gov/opub/mlr/1987/07/art1full.pdf)
Duration of unemployment (Current Population Survey)
The length of time in weeks (through the current reference week) that persons classified as unemployed had been looking for work. For persons on layoff who are counted as unemployed, duration of unemployment represents the number of full weeks they had been on layoff. The data do not represent completed spells of unemployment.
Unemployed persons (Current Population Survey)
Persons aged 16 years and older who had no employment during the reference week, were available for work, except for temporary illness, and had made specific efforts to find employment sometime during the 4-week period ending with the reference week. Persons who were waiting to be recalled to a job from which they had been laid off need not have been looking for work to be classified as unemployed.