Or is it vice-versa. The 538 website has an interesting post on explanations for tuition increases, here:
All of those trends add to the cost of college, but not by that much. At most, about a quarter of the increase in college tuition since 2000 can be attributed to rising faculty salaries, improved amenities and administrative bloat. By comparison, the decline in state support accounts for about three-quarters of the rising cost of college.