Todd Zywicki notes the growing bloat of university administrations--far faster than the illusory tenure-induced bloat*. He speculates on the cause:
Jay focuses on the role of government subsidies in feeding the bloat of academic bureaucracy. That seems plausible to me. The other factor that strikes me as perhaps relevant is that during most of that period university endowments grew at record rates. This essentially gave university presidents and their minions a huge slush fund to play with without actually having to raise new funds from alumni. This created a growth in agency costs for senior university administrators. Finally, this allowed universities to continue giving raises to faculty while expanding the bureaucracy even more. Thus, the growth in bureaucratic spending was not coming out of a zero-sum pot, so that faculty were not monitoring the growth in the bureaucracy as much.
Finally, I suspect this might also reflect the developing model of university president as CEO. As university presidents have come to be more like CEO's of universities, their entourages have grown as well. Universities have come to take the look of a top-heavy bloated corporation like General Motors, with Vice-Presidents layered one atop the other. In a world of lax budget constraints owing to flush endowments, it is easier to fritter away resources on unproductive bureaucrats and internal empire-building.
I'd note that this bureaucratic bloat is most common, and most dramatic, in industries that are, for one reason or another, protected from competitive forces. Academia in many way resembles those sorts of industries--but it's not clear why. You can't explain all of it with government subsidies.
* Yes, I am critical of tenure, but not for this reason.