Fun with education funding and ROI, historically

As I wrote in the entry from March 10 on manipulated charts,1 there’s a legitimate discussion to be had about investments in education, returns on investment, and so forth, but not if we start with manipulated presentations. What sorts of questions are relevant? I’m a little hesitant to dive in, as I have published exactly one piece on the topic (and that one an historical perspective on Florida’s education finance system). But since Matthew Ladner is clamoring for us to look at forests rather than trees, and there is relatively little research on long-term perspectives, I’ll try for something historical.


First, let me rescue the one point of Andrew Coulson that’s interesting: in summing inflation-adjusted expenditures on education per pupil over a “typical” school career (13 years), in essence he is arguing for a long-term moving average as a better measure of expenditure changes than year-to-year or two-year averages. Is there a substantive difference when you do that? To get a long-term view on per-pupil expenditures, before 1970 you have to work with the biennial reports of the old Office of Education. From the 2009 Digest of Education Statistics Table 182 (supplemented by 2007-08 data from the 2010 Digest), I used the current expenditures per fall enrollee, adjusted for inflation for every other year from 1929-30 to 2007-08,2 and calculated change in two ways:

  • Annualized change from the prior date (two years before)3
  • Annualized change across the 13-year moving average, calculated as the average of the central year and 2, 4, and 6 years before and after the central year.4

With a 13-year moving average, the comparison with the biennial change lops off the biennial changes at the beginning and end of the time series, but you still end up with a very interesting pattern that I bet will be familiar to education finance researchers:

As you should have expected, the moving average eliminates the substantial noise you see in short-term expenditure changes, which are noticeable even when calculated at the national level. The large-scale feature when you use the very-long-term moving average is the difference between the first few decades with substantial per-pupil expenditure growth, generally over 4% (beyond inflation) when annualized, and the last few decades, where per-pupil expenditure growth drops below 3% and generally stays around 2% over inflation. (Addition: See Bruce Baker’s comments on inflation adjustments.) What happened at the transition point, in the early 1970s? Remember that for the 13-year moving average, the reference year would normally be about the 6th-grade year for a cohort. A 1970 sixth-grade year translates into a late-1950s birth cohort, or just after the peak of the Baby Boom. You’d see somewhat different features with a 3- or 5-year moving average, a slightly-later peak in the 1960s and deeper troughs corresponding to inflation in the late 1970s and the early-90s recession, but the 13-year moving average captures the longer-term change coinciding with the end of the Baby Boom. Over 80 years, per-pupil expenditures have averaged about 2% or above (beyond inflation) when you look at the whole country and a student’s career (not single years or states/small areas). And that average long-term expenditure increase was higher for children born during the upswing of the Baby Boom than since.

There are three fundamental questions I have on the spending side:

  • What other large patterns of social spending also rose at a 2% or higher annualized rate on a per-unit basis?
  • What explains the substantial drop in annualized long-term spending increases on education after the end of the Baby Boom?
  • How does this national picture change if you disaggregate it by region or state? Addendum: See Bruce Baker’s notes on spending and more.
  • How does this national picture change if you look at private school spending?

This longer-term picture undermines the stories told either by folks such as Coulson who focus on supposedly low productivity increases in education in the past 40 years or by those who rely on a 1970s broadening of educational rights (including the rights of individuals with disabilities) and mandates (such as health education, drivers ed, etc.) as a driver of spending. There is something more complicated going on.5

Return on investments in education

The “productivity” side of the question is more complicated because most of the putative outcome measures for schooling are at best proxies for the broader social value the majority of Americans attach to public schooling. We cannot measure the return on the investment in the area of “better citizenship,” but we can look at test scores or attainment data. As long as one understands that we cannot measure everything we expect from schools, we can see the proxies as small slices. In some areas, it looks like we’re standing still since the late 1960s: NAEP trend data for 17-year-olds, well-defined high school graduation rates. In other areas, we have some noticeable improvement over 40 years: school access for students with disabilities, NAEP trend data for younger children, college attendance and completion. And in some areas, the time of greatest improvement was also the time of highest annualized expenditure increases: high school graduation (but not because of the acceleration of spending at the time0.

The better research on educational return on investment is attainment or exposure related: economists’ and psychologists’ research on long-term outcomes from high school graduation, college, early childhood, and so forth. But that is generally on a micro level: the value of investment by individual students and children. It does not mean we’ve gotten our “bang for the buck” at the national level. It also doesn’t mean we haven’t. I am not persuaded that we can answer that return-for-the-investment question with something as complicated as schooling with as little trustworthy data sources over the long term.


  1. Yes, there’s a new addition there in response to Andrew Coulson. []
  2. Smoothing the other three series across 13 years ends up with very similar profiles over the years. []
  3. I annualized by taking half the natural log of the ratio of expenditures. []
  4. Annualization of the change in moving average is calculated the same way as for the biennial expenditure figures. []
  5. Yes, I’ve done the obvious cursory check to see if I could find an analysis of education spending that started before 1970, and at least for the search terms I tried, no dice. []

3 responses to “Fun with education funding and ROI, historically”

  1. Hemi-Sync Peter

    Ola! Sherman Dorn,
    I was wondering on a similar note,, Title I of the Elementary and Secondary Education Act (ESEA) calls for the distribution of federal grants to local education agencies (LEAs) and schools with high numbers or percentages of children from low income families. The hope is that these funds will encourage all children to meet their state’s academic standards. Four statutory formulas based largely on the census and state education costs help to determine which LEAs should receive which of four grant types, if any.
    Nice One!

  2. CCPhysicist

    First, something that might interest you as a historian. There is a systematic analysis of CPI data that bridges the gaps due to changes in base year and the “market basket” formula that might interest you:

    Second, as mentioned in a past comment, there are some separate construction price indices (some proprietary maintained for the past century by those in the construction business, some from the govt as part of the PPI) that tend to run higher than the CPI. If your data includes capital costs as well as operating costs, factoring that in could be relevant to the “investment” side of this discussion.

  3. CCPhysicist

    Now my answer to your bulleted questions about spending:

    *) Housing construction for all of those families with all of those kids likely matched that, just as I suspect school construction made up a big part of that higher expenditure growth rate between 1950 and 1970. I went to a brand new middle school.

    *) New schools were not needed at nearly the rate as in the past. They also could not keep up with the huge rates of inflation during the “stagflation” era.

    *) I predict it would be different in growing sunbelt states if compared directly to the rust belt states where schools are now being closed due to a drop in the number of children.

    *) No idea.

    And I would add another question, which concerns some measure of teacher quality (SAT scores?) with some measure of their pay relative to the median for persons with a college education.