Certainly you can't believe there's only two possibilities.
A typical example would be political campaigns and/or advertising in highly competitive sectors - all work done there serves only to cancel out the work done by other people, thus creating a negative feedback loop that can consume infinite amount of resources for little marginal gain. Think about how much time, paper, paint and fuel is wasted printing leaflets and billboards and notice that if everyone collectively agreed not to do this, the results would be the same.
Touché. See, this is why we should all unit test with a fuzzer...
I suppose I would need to amend it to zero-or-less-value-add. This thought intertwines with the other line of discussion, in that these proposed "negative" items would likely be seen as GDP-positive. After all, someone needs to print all those pamphlets, and that's a value-add over paper and ink.
Interesting aside: São Paulo, Brasil has a ban on all outdoor advertising. Of course, that's only a limited subset of possible advertising, but it seems to have gone over well with the general populous.