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We have discussed the so-called at or near full employment economy that we have today and I have been constantly pushing back on that narrative citing the number of folks taking jobs who were not considered in the labor force before they took that job and therefore not counting towards the unemployment rate before they started working.
Here's a visual from FRED (all graphs courtesy of Warren Mosler at his blog):
Here's the flows of people from employed to out of the labor force (not counted):
Clearly, there is slack in the economy and the U3 unemployment rate is not an accurate reflection of labor tightness.
Someway it became harder to be counted as in the labor force and easier to be counted outside of it when not employed.
I don't work at the BLS so I can't tell you if their methodologies have changed or if estimation errors are the problem, or if the definition of labor force participation has 'narrowed,' but there are clearly a lot of people taking jobs who weren't in the labor force the day before and that means the U3 number is under-counting them, and they may not all be 'captured' by the U6 estimates.
This goes a long way in explaining why we have not seen the expected wage and salary increases that accompany tight labor environments.