The U6 unemployment rate is supposed to cover those who are underemployed. What is usually reported is the U3 unemployment rate which is closest to that used internationally as defined by ILO.
Supposed to, but doesn't. The U6 rate includes two new things: part-time workers, and a very strangely-defined category: people who are NOT working at ALL, AND were looking for work previously, AND have stopped looking for 4+ weeks.
It doesn't capture the common on-the-street definition of the word "underemployment", such as a tech worker flipping burgers at mcdonald's.
Perhaps that category is simply to hard or expensive to measure, or it's specifically being avoided. Either/or really.
Heh, "it's probably tracked somewhere by economists". The more I learn about economics as a "science" the more I balk at the idea of giving them the benefit of the doubt, which people seem really willing to do for some reason. I know, it's scary that the economy might be a complex system that nobody understands, and it's easier to have "faith" that there is some shadowy economic cabal of god-kings who are keeping a watchful eye on it. But,.. yeah, that doesn't seem to be true, honestly.
the only signal I can think of is returns on student debt to measure "employment quality" - i.e how well is my education capital being deployed, but any realistic evaluation of the labor market will be complex and include qualitative data.
https://fred.stlouisfed.org/series/U6RATE