In fact the Bureau of Labour Statistics does measure the number of "discouraged" workers and lots of other things: the U-6 number here includes underutilised labour. It's at 9% or so.
The BLS national figures for unemployment are not based on the numbers collecting unemployment insurance. At the state level that might be true.
Taking US Govt. statistics at any kind of face value is a bit like taking Nazi Party statistics on Jewry at face value.
Perhaps the easiest to breakdown demonstration of statistics in the USA is the Nielson television ratings. A fundamentally manufactured statistic that is incredibly wrong and consistently leads to "incorrect" decisions based on objective data is the accepted standard because THOSE IN POWER TO MAKE THESE DECISIONS HAVE AGREED TO ACCEPT ITS BIAS.
This is a mechanism of control, a method of manufacturing consent and a basic tool of propaganda.
