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If 2 million people who have been unemployed go back to school full time, the unemployment rate will (all other things being equal) go down.
The reason for this is that people who are in school full time and are not looking for jobs are not unemployed. Instead, they are not part of the labor force. If those 2 million people go back to school, the size of the labor force drops. The rate of participation in the labor force drops. But the unemployment rate also drops because the unemployment rate does not count people who have simply left the labor force.
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