Generally, no, universities classify graduate students as students, not employees. Stanford additionally classifies postdocs as students and charges their funding source a nominal tuition fee.
> A Stanford postdoctoral scholar is a non-matriculated trainee, in graduate student status, in residence at Stanford University pursuing advanced studies beyond the doctoral level in preparation for an independent career.
This makes doing taxes as a postdoc extremely irritating as the stipend is not earned income, which of course benefits Stanford's tax situation considerably.
It depends on the source of the funds and the nature of the postdoc’s duties. If the postdoc is on a “fellowship”, either paid by the university or by something like an NIH trainee fellowship, then they are not employees. If the employee is hired to do work for a project, on the other hand, which is typical when funded on an NSF or DARPA grant, then they are employees. This is MIT’s info page, which I believe is reasonably representative: https://postdocs.mit.edu/postdoctoral-position/defining-post...
Science had an article on that in 2002 that went into more detail on how this system came about (basically, vague laws that have ended up interpreted through a series of IRS rulings). I think but am not 100% sure that even though this article is about 20 years old, the current situation is still similar. https://www.science.org/content/article/postdocs-and-law-par...
> A Stanford postdoctoral scholar is a non-matriculated trainee, in graduate student status, in residence at Stanford University pursuing advanced studies beyond the doctoral level in preparation for an independent career.
This makes doing taxes as a postdoc extremely irritating as the stipend is not earned income, which of course benefits Stanford's tax situation considerably.