Accounting For College Costs

post by johnswentworth · 2022-04-01T17:28:19.409Z · LW · GW · 41 comments

Contents

  Accounting Data
  Crosscheck: Falling Student/Faculty Ratio
  Why The Falling Student/Faculty Ratio?
  Summary
  Appendix: Stray Graphs
None
41 comments

Why are costs of certain things, most notably education and healthcare, skyrocketing so quickly, with relatively little improvement in quality? A few years ago, SlateStarCodex and Marginal Revolution both had interesting pieces on this "cost disease" phenomenon. I think both of them were coming at it wrong.

Cost disease is really about two questions:

• Costs in education, healthcare, etc keep rising faster than inflation, so where is all that extra money going? This is an accounting question.
• Why is so much money going there? This is an economics question.

Both the SSC and the MR pieces were mostly speculation on the second question. I think that's premature; the first step should be to go look at where all the extra money is going. Don't try to draw a map of a city by sitting in an apartment with the curtains closed; go look at the world, in detail, and let that steer the theorizing.

In this post, we'll dig into the accounting data for college costs, especially for 4-year private nonprofit colleges. The main theory we'll end up at, based on the accounting data, is that college costs are driven mainly by a large increase in diversity of courses available, which results in much lower student/faculty ratios, and correspondingly higher costs per student.

Accounting Data

For any particular college, if you had access to the books, you could simply look through all the expenditures, add it up, and see how expenditures changed over the years. I don’t know of any college which puts its books on the internet for all to see going back to the ‘60’s. But there is the National Center for Education Statistics, which compiles some high-level accounting data on all colleges in the US, and publishes an annual digest.

Let’s start at the beginning: what’s the cost of college, by year?

This is undergraduate tuition & required fees at 4-year colleges. Data separating private nonprofit/for-profit only goes back to 1999, because enrollment in for-profit colleges was negligible prior to the late ‘90’s. Note that all costs in this post, both in the graphs and the discussion, are adjusted to 2013 dollars.

From here on out we’re going to focus only on private, nonprofit 4-year colleges from 1999 to 2013, because that’s what the Digest of Education Statistics has data on. (Again, if anyone can find good data back to the ‘60’s, please let me know!)

We’re going to follow the money on its journey.

From tuition, comes revenue for colleges. Let’s make sure the payments arrive safe and sound…

Well that’s informative! If you’ve been to a private 4-year nonprofit university lately, you probably noticed that most people don’t actually pay the sticker cost. This data makes it pretty clear: actual expenditure on tuition is a lot lower than the sticker cost suggests. More to the point, nominal tuition grows much faster than actual tuition revenue. From 1999 to 2013, nominal tuition grew by 42.0% (about 3% per year), whereas tuition revenue grew by 23.7% (about 1.7% per year).

So roughly half the supposed growth in private college cost comes just from the games colleges play with their sticker-price tuition. If we look at what students actually pay - what colleges actually receive in tuition revenue - growth is lower by a factor of two.

But we’re not done yet! Remember, these numbers are all inflation-adjusted, so the remaining 1.7% annual growth is still 1.7% on top of inflation. So, we still want to know why college costs are growing faster than inflation.

Before we move on to expenses, a little more on revenue. Tuition revenue is less than half the revenue of private nonprofit colleges. Most of the rest comes from a combination of federal/state grants, private gifts, and investments. Key facts:

Grants and gifts cover the lion’s share of non-investment revenue, but they’re roughly flat from 1999-2013. 

Investment revenue is very noisy, and colleges mostly don’t rely on their portfolios to cover costs.

Other than a rise in profits from hospitals, tuition was the only category of revenue to grow significantly and steadily.

I don’t want too much data-clutter, so the relevant graphs are at the end of the post. The important takeaway here is that, even though tuition is less than half of colleges’ revenue, it absorbs pretty much all of the growth in expenses.

With all that in mind, let’s look at non-investment revenue compared to expenditures.

That’s comforting: non-investment revenue is pretty close to expenditures. This is a good justification for ignoring investment revenue. As expected, both non-investment revenue and expenditures are growing steadily.

Now, how do all those expenditures break down?

Again, everything is per FTE per year. So support cost (student services, academic and institutional support) is roughly comparable to instruction cost (teaching), and the two have risen at similar rates in the 1999-2013 window. Research expenditures, meanwhile, have been pretty flat.

Between them, support and instruction expenditures added about $5800 per FTE during this period, while (actual) tuition only increased by about $3900. What about the other $2000? About $1000 of it came from cutting expenses in public service, grant-based financial aid, and other costs. Another $1000 came from net profit in university-owned hospitals, which became quite profitable during this period.

So colleges really have been tightening their belts, cutting back on things like public service and grant-based financial aid, making money off their hospitals… and all the money from that belt-tightening, along with tuition increases, has gone back into paying professors and staff. 

Let’s keep following the money. Next stop, professors and staff. Why are costs for instruction and support increasing faster than inflation, year after year?

Well, as the professors will tell you, it’s not their salaries. Inflation-adjusted average instructor salaries rose from $81500 to $87000 over the period (source). Full professor salaries rose a bit more, and were offset by dramatically increasing numbers of graduate assistants and associate professors and whatnot. Bottom line, average inflation-adjusted salaries increased, but not enough to account for the growth in expenditure.

The bigger factor was a decrease in student-faculty ratio. The Digest only gives numbers for 1993, 2003, and 2013, but from 2003 to 2013, the student-professor ratio dropped from 11.9 to 10.6 at private nonprofit colleges. That’s a 12% increase in professors per student. Combined with the 7% increase in salary, that’s just about right to account for the 18% increase in instruction costs.

The data in the digest does not provide a clear story about the increase in support expenditure; it doesn’t have much information on non-instructional staff other than the expenditures. But it does clearly follow the instructional-faculty costs pretty closely. Based on that, my guess is that institutions generally need to spend a roughly-fixed amount of resources on support per faculty member, so the increase in support cost is driven mainly by the increase in faculty (plus probably a small increase in support salaries, similar to the small increase in faculty salaries).

Crosscheck: Falling Student/Faculty Ratio

Unfortunately, the relevant revenue and expenditures data from the Digest only goes back to 1999, whereas rapid growth in college prices started around 1980. Were student-faculty and student-staff ratios the main source of cost increases all along? I expect the answer is yes, although this data set doesn’t go back far enough to check. One quick sanity check for law schools in particular is provided by the Bar Association:

Sure enough, student faculty ratios at law schools have fallen steadily since the early ‘80’s, by a factor of 2 for the largest schools. So it’s quite plausible that student-faculty ratios have been the main source of cost increase all along.

Why The Falling Student/Faculty Ratio?

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 accounting section. From 2003-2012, the length of the course catalogue increased by 11.0%; the previous section found that faculty per student increased by 12% from 2003-2013. Similarly, over this whole period (starting from 1976), the length of the course catalogue almost doubled; the student/faculty ratio chart for law schools in the previous section 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 that difference is pretty small; 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 list of possible drivers of lower student/faculty ratios:

• 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?

Maybe, but there's a bit more to it than that.

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 my alma mater Harvey Mudd, for instance, this period saw two new departments created (biology and computer science), along with more specialties within the existing departments.

Summary

We started with the sticker price of tuition, and immediately saw that sticker price is much larger and grows much faster than the actual tuition revenue per student (at least at private 4-year nonprofit colleges/universities). So a big part of the growth of cost in college is that colleges play games with the sticker price, which doesn’t really reflect the actual tuition paid. But that only accounts for half the inflation-adjusted growth, so we have to keep looking.

Next, we followed the money: from tuition and other revenue to overall expenditures to expenditures by category and finally to student-faculty ratio, which is the main driver of cost growth over this period (along with its support-staff equivalent).

Then, we compared to some direct data on student/faculty ratios in law schools, confirming that the ratio has fallen by roughly the amount suggested by the accounting data. Finally, we looked at historical course catalogues, and saw that the number of different classes increased in proportion to the number of faculty per student.

This finally gives us a satisfying answer to our original accounting question: where does all the money go? 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.

Appendix: Stray Graphs

All sources for these graphs were linked above. All costs are per FTE per year, for private nonprofit 4-year institutions, adjusted for inflation.

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