How would the unemployment rate be impacted if 2 million formerly unemployed workers decide to return to school full time and stop looking for work?

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The unemployment rate is determined by individuals filing for unemployment assistance from the government or other similar programs, such as disability. If 2 million of those individuals decided to stop looking for work, they would necessarily stop filing unemployment (active job seeking is a requirement for unemployment filing). This would, in turn, significantly reduce the unemployment rate in the country in spite of the total number of unemployed people remaining the same.

This action, while a smart decision for those 2 million people, would artificially deflate the unemployment numbers—which would look like a significant positive gain for the economy, in spite of there being no actual change. When they reentered the workforce, anyone who still could not find a job would have to reapply for unemployment, and the numbers would rise once again.

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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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