First things first: these are legitimate numbers (What Paul Krugman tweeted was insane and he’s now apologized). They don’t seem to square with the weekly unemployment claims numbers, which puts those collecting unemployment benefitshigher than the unemployment rate for the first time in history. You can get unemployment benefits through the CARES Act’s Pandemic Unemployment Assistance program even if you work part-time, but that doesn’t explain this discrepancy.
However, in a long note at the bottom of the BLS report, the bureau explains their difficulties with data collection, as well as a quirk in the data: “there was also a large number of workers who were classified as employed but absent from work.” Those were supposed to be marked as on temporary layoff, but they’re listed as employed. If that was corrected, “the overall unemployment rate would have been about 3 percentage points higher than reported.” BLS didn’t change that because they have a strict rule to accept the data as recorded.
Long story short, BLS is telling us that we’re at 16 percent unemployment. And while that’s better than the nearly 20 percent (if you include the misclassified) in the April jobs report, it means we’ve only brought a small sample of those workers back. The level of employment remains sharply reduced from the pre-pandemic months; we’ve maybe brought back a little over 10 percent of the jobs.