Tuesday, May 2, 2017

College Costs, Part II

Turns out the previous post on college costs omitted some important accounting. This (shorter) post will fill that hole, and then we’ll finally be ready to talk economics. This post will start off right where the previous post left off: decreasing student/faculty ratios.

Decreasing student/faculty ratios mean at least one of three things:
  • Individual faculty are teaching fewer classes
  • Individual students are taking more classes
  • Classes are smaller
In principle, any of these scenarios could be identified with the right data. In practice, data on e.g. class size in college is hard to come by, but many answers can be found just from historical course catalogues. Berkeley is particularly helpful; their course catalogues are available online going back to 1870.

If I really wanted my data to be perfect, I’d go through the course catalogues and count the number of classes (or hire someone else to do so). But for now, I’m just looking for a rough estimate, so I’ll use the number of pages in the course catalogue as a stand-in for the number of classes. Berkeley’s catalogue has kept a pretty consistent three-column format since the mid-70’s, so hopefully this estimate won’t be too far off the mark.

Anyway, looking at the number of pages in Berkeley’s course catalogue by year gives a very satisfying graph:
These numbers line up neatly with the numbers from the previous post. From 2003-2012, the length of the course catalogue increased by 11.0%; last post mentioned that faculty per student increased by 12% from 2003-2013. Similarly, over this whole period, the length of the course catalogue almost doubled; a chart from the previous post suggests that the number of faculty per student has almost doubled over roughly the same period (at least for law schools).

The course catalogue also lists all of Berkeley’s professors. Again, I didn’t count them all, but I searched for “Ph.D.” and counted the hits. This is definitely a noisy measure, since “Ph.D.” doesn’t just appear after professors’ names in the catalogue, but it should suffice for a quick-and-dirty check. In the 1980-81 catalogue, there were 2139 hits for “Ph.D.” and the catalogue was 239 pages, a ratio of 8.9. In the 2011-2013 catalogue, there were 4132 hits and the catalogue was 414 pages, a ratio of 10.0. So if anything, there are fewer professors per class - professors are teaching slightly more courses on average. But the main takeaway is that the number of courses taught per professor has remained roughly constant even though the number of faculty per student has roughly doubled.

Going back to our original list of possibilities:
  • Individual faculty are teaching fewer classes -> nope.
  • Individual students are taking more classes
  • Classes are smaller
I doubt there’s any statistics on how many classes students take, but… sanity check. Are students today taking twice as many courses as students thirty years ago? No way. Maybe there’s been some change, but there’s no way it’s the lion’s share of the effect.

That just leaves one possibility: classes are smaller.

Great! So, colleges could cut their costs in half by trading small sections for large lecture halls, right?

Not really.

If the number of classes offered at a typical college has roughly doubled - as seems to be the case for Berkeley - then it’s not just twice as many sections of Math 101. After all, we measured the growth in courses offered by looking at number of pages in the course catalogue… and multiple sections of the same course usually go under a single entry in the catalogue.

Classes aren’t just half the size; there are twice as many different classes now compared to thirty years ago. If the data and assumptions here generalize, then there’s been a cambrian explosion in diversity of academic subjects, creating a proliferation of new courses and specialties. Anyone who’s been in academia should be able to confirm that this matches experience. At Harvey Mudd, for instance, this period saw two new departments created (biology and computer science), along with more specialties within the existing departments.

This finally gives us a satisfying answer to our original accounting question: where does all the money go? As the previous post showed, growth in college cost has practically all gone to more faculty and staff per student. But more qualitatively, the growth in faculty and staff per student has fed a cambrian explosion in academic specialties, as shown by a proliferation of new courses.

That tells us what all the extra money has been spent on, but we still don’t know why so much money has been spent. Why aren’t most colleges offering a narrower selection of courses for half the price? With that question, we’re finally ready to talk economics. That will be the subject of the next post.

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