In other words, the statement that "but [once] people no longer receive unemployment they are no longer carried on the rolls of the unemployed . . . therefore, they are no longer counted," is factually incorrect.
I think that you are the only one in the entire galaxy who sees it that way. UE IS a factor in the calculation, that is the entire point! If you don’t collect it, you are not counted. If you do collect it you are counted. This is not rocket science. Your own post says this and you are denying your own evidence.
If they are counted, I would like to see how. Your own post states that if someone no longer recieves benefits they are no longer counted.
“These data are not used to measure total unemployment because they exclude several important groups. To begin with, not all workers are covered by UI programs. For example, self-employed workers, unpaid family workers, workers in certain not-for-profit organizations, and several other small (primarily seasonal) worker categories are not covered. In addition, the insured unemployed exclude the following:
Unemployed workers who have exhausted their benefits- Shouldn’t they be counted?
Unemployed workers who have not yet earned benefit rights (such as new entrants or reentrants to the labor force- shouldn’t they be counted? They are not working...
Disqualified workers whose unemployment is considered to have resulted from their own actions rather than from economic conditions; for example, a worker discharged for misconduct on the job. Again, are they working?
Otherwise eligible unemployed persons who do not file for benefits” Do they now have a job?
What about all of those small business owners who lost their business? They are not eligible to file most likely. Are they employed? The people above, are they employed?
People who worked commission only jobs who lost them. They are not eligible but are they somehow not worty of being counted?
The only thing I can think of is that you are saying that the Unemployment numbers are only one figure used to determine those who are unemployed but they are not the entire picture. If you are saying that then I can agree. But if you are saying that we currently have 7.8% unemployment right now because of these numbers then I would have to call BS on that one and refer you to the Workforce Participation Rate.