December 16, 2003

Great ideas, no time

A week ago, more or less, I had one of the clearest epiphanies I’ve ever had in academe, right in the middle of finals week. Do I have time to work on this right now? No! Sheesh. But I can describe it, and it’ll sit until I do have time, or I’ll peck away at it. Here’s the gist:

Dropout and graduation rates are notoriously unreliable. There are decent measures of graduation, if you use population-based data from the Census Bureau (for the U.S.), but numbers from school systems are awful. Part of the reason why they’re bad is because counting dropouts relies on accurate identification of school-leavers as dropouts (as opposed to transferees), something that’s tough even when there isn’t evidence of intentional fraud. Part of the reason is because students transfer between schools at such a high rate that looking at raw numbers longitudinally is seriously problematic. Part of the problem is relying on information by grade when that number is fuzzy as you get to secondary school and when you never know how long someone can stay in a grade, especially with what Robert Hauser has called an epidemic of grade retention (PDF file—look at the figures starting on p. 55 of the file). Demographers like to work with age, because you can generally rely on someone’s age going up by one year for every year of time. (There’s a phenomenon of misestimation called age heaping, but I’ll ignore that for the moment, and it’s considerably less evident at younger ages and in countries where knowing your birthday is common.) But school systems do not publish information by student age.

So here’s my epiphany, inspired by some wonderful work by demographers Sam Preston, Ansley Coale, and Ken Hill: one version of the demographic balancing equation is that the rate of growth in any population is equal to the birth rate minus the death rate plus the net migration rate. That’s pretty simple. Here’s a corollary: if you take any age x, the rate of growth in any population for that age up (from x to infinity) is equal to the “birthday rate” at age x (the rate at which birthday x is happening in the population) minus the death rate for the population from x on up plus the net migration rate for the population from age x on up. Most demographers don’t use this, because you can get good estimates of mortality and fertility directly from birth and death registration systems combined with census figures (estimated or actual full census).

But here’s the application to school systems. For any grade x, the growth rate for students grade x and up is equal to the “first time in grade” rate for grade x minus the graduation rate plus a residual “net flow” rate that includes transfers in and out, student deaths, dropping out, and returning to school. You can calculate all of that for a single year just by knowing the enrollment counts by grade for two successful years (or any two points in time), the number of graduations between the two points in time, and the retention rate for each grade. Or, rather, by a bit of algebraic magic, from that data one can directly calculate the growth rate, the first-time-in-grade rate, and the graduation rate, allowing one to infer the net flow rate.

And if you can calculate the net flow rate for grade x on up for every grade, then you can get the net flow rate grade by grade. Since children of school age move around at a fairly-even rate across the age span, you can take the average net-flow rate for the earlier grades (grades 2-7 look pretty good) and then calculate an adjusted net-flow rate that should be pretty close to the sum of student bodies flowing in and out of schools because of deaths (pretty small), in- and out-flows that are for specific grades (most commonly flowing to public schools in 9th grade), and dropping out.

I’ve done this tentatively for Massachusetts 1996-2001 (skipping 1998) and for Texas for 2000-2001, since the states post grade-by-grade retention rates. But it was pretty simple, there’s a clear dip in the 10th grade net-flow rate for Mass. in the last year that might be attributable to the MCAS graduation requirement, and I can easily imagine how to write grants for this for NICHD and NSF (with an extension to analyzing retention in higher ed). Now, if only I didn’t already have the following on my plate:

  • two edited book projects that are in process
  • Some papers I’m committed to working on as a fellow of ASU’s Ed Policy Studies Unit
  • a book on academic freedom that I should write, given events at USF and my knowledge of them
  • an historiography book tied to the history of education
  • everything else academics typically do

So it’ll sit there until I can figure out how to carve out time. Ideas are welcome!

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Posted in Research on December 16, 2003 9:08 AM |