Those facts are not in dispute. The notion that unemployment compensation factors into the calculation of the unemployment rate is utterly false. It's not
even in dispute. (And people who repeat it embarrass conservatism in general).
There absolutely is no way to defeat a liberal in an argument regarding economics if one comes out of the box looking like an idiot about the subject.
Some people think that to get these figures on unemployment, the Government uses the number of persons filing claims for unemployment insurance (UI) benefits under State or Federal Government programs. But some people are still jobless when their benefits run out, and many more are not eligible at all or delay or never apply for benefits. So, quite clearly, UI information cannot be used as a source for complete information on the number of unemployed. Other people think that the Government counts every unemployed person each month. To do this, every home in the country would have to be contacted—just as in the population census every 10 years. This procedure would cost way too much and take far too long. Besides, people would soon grow tired of having a census taker come to their homes every month, year after year, to ask about job-related activities.
Link: How the Government Measures Unemployment