Answer: They didn't. They pulled numbers out of the air.
The other day the morning paper contained a short unsigned Associated Press filler piece titled, "Report: Extending jobless benefits creates jobs" in which AP says the following:
Washington -- Extending the current level of long-term unemployment benefits for another year would add 300,000 jobs to the economy, according to a report from the Congressional Budget Office.
The Washington Post elaborates:
The report notes that extending unemployment insurance is a particularly effective form of stimulus when the economy is still struggling. That’s because jobless workers who receive benefits are extremely likely to spend the money right away. So, the CBO estimates, if Congress extends all the programs, GDP will likely be 0.2 points higher and employment will be 300,000 higher at the end of 2013 than if Congress does nothing at all.
[They are referring to the CBO report of 11/28/2012. Click Unemployment Insurance in the Wake of the Recent Recession to get the CBO summary, and download the full PDF here.]
One not so minor problem: The economy is much too complex to make predictions like that and expect them to come true. And another contributing factor that can't be measured is the rampant fear present today that things will only get worse.
The report says that the CBO estimates that if unemployment benefits are extended the payoff to the GDP will $1.10 for every $1.00 of budgetary cost in 2013. And they don't admit it, but that's just a wild guess. Researchers are all over the map on whether or how much government stimuli influences the GDP.
Valarie Ramey has analyzed the research on the effects of stimuli on GDP, and she reported in a podcast interview by Russ Roberts with her last year that the effect varied from about $0.80 to $1.20 increase in GDP for every $1.00 the government spent. Download or listen to that interview at econtalk.org.
In any event, here's some good news for the unemployed. The CBO currently has four job openings. Go for it. Their standards really can't be very high.