The Math Works for School Choice, in Rhode Island


There seems to be a misperception about school funding that it always costs more to educate more students, but it never costs less to educate fewer.  Or something like that.

The RI Center for Freedom & Prosperity released, this week, a report and district-by-district summary graphics showing the results of a predictive model that I helped to develope, called the Rhode Island District Impact Model of Educational Scholarships (RI-DIMES).  The model began as a concept with Andrew Coulson of the Cato Institute, based on the elasticity of demand for private school, and Providence College Economics Professor Angela Dills adapted it to Rhode Island’s education system.

The Center put in months’ worth of work gathering more granular data and fine-tuning the formulas to make the model applicable at the level of each school district and to better capture how the money would flow upon passage of the legislation currently making its way through the General Assembly (H5790 and S0607).

The Bright Today education savings accounts (ESAs) in the legislation would provide income-adjusted scholarships  up to $6,000 for students whose parents use the opportunity to switch their children to private school (or home school).  Students who are already in private school will receive one-quarter of the scholarships for which they would be eligible if they were switching schools.  All of the money would come from state aid.

Statewide, the model projects that the program would free up $1.9 million in its first year, meaning districts would save that much over the cost of the scholarships.  If the money is simply applied to public education, it would increase per-pupil funding by an average of $316.  Additionally, parents would invest another $17.2 million in order to capture the value of the scholarships.  In the first five years, $289.5 million dollars will be freed up and invested in education in Rhode Island.

The hang-up that the Center has encountered while sharing these results is that people don’t believe the savings are real, and it’s difficult to know where to begin with a response.  The basic concept of variable costs is inarguable.  As enrollment increases, districts have to hire more teachers, purchase more supplies, provide more transportation, and so on.  As enrollment decreases, districts have reduced need for these expenses.  The first question is how big the variable costs are.

The Center has heard estimates ranging from around 60% of all costs’ being variable, determined through regression analysis of district spending, to 73% variable plus 23% semi-fixed, using a high-view analysis of spending categories.  RI-DIMES uses a more-detailed level of spending at the district level, available through the state Dept. of Education’s uniform chart of accounts (UCOA) data.

The UCOA data breaks down spending in different ways: by what “function” money is spent to support (e.g., “instructional teachers”) and by what “object” the money purchases (e.g., “salaries”).  Because, for example, not all “salaries” go to “instructional teachers,” the results are different when dividing spending into fixed, semi-fixed, and variable categories, so the Center averaged these two views.  This method finds that the average district has variable costs of 69.1%, with another 15.5% that are semi-fixed (including such categories as guidance, which serve larger number of students).

The next question is how quickly districts can realize savings from decreases in enrollment, which will vary from district to district and from year to year.  Adding or subtracting one more student will probably not change the district’s costs all that much.  The question is, on average, how many students does it take until a district can realize all of the variable cost savings; it’s a stepped line.  By default, the model uses the statewide student-teacher ratio of 11 students.  That means that the district realizes no savings at all until it has 11 fewer students to educate.  With average state and local spending of $15,945 and 69.1% variable costs, the district saves $121,198, or $11,018 per student, but only when that eleventh student transfers.

Changing the threshold at which the money is realized matters less than one might think.  The model predicts that 102 students will transfer out of the average district in the first year.  With an 11-student threshold, the average district would save $121,198 nine times and save nothing from the remaining three students.  If the threshold turns out to be 25 students, the average district would only hit it four times, but each time, it would save $274,450, with two students remaining.

Keep in mind that the question isn’t, “When can the district subtract a classroom?”  On average, “instructional teachers” are only 48% of the average district’s spending.  The question is, “When can the district save $11,018, which is 69.1% of the money that it spends on each student?”

Obviously, these are only averages, and in some cases the savings will be more difficult to realize.  In other cases, though, they’ll be easier to realize.  Adding one more student to a grade level in a particular elementary school might require a district to split that grade level into more classrooms, but subtracting one student from a grade level in another elementary school might enable it to consolidate.

This is the basic math of school choice.  The numbers and thresholds can always be tweaked and debated, but the RI Center for Freedom & Prosperity now has a model that can show the effect of different estimates in order to help educate the public about the principles involved.

  • guest

    “people don’t believe the savings are real,”…your reputation precedes you, Justin. Most folks are just plain skeptical of the “Katz Math” by now.

    • Justin Katz

      Now, now. There’s no need to match your behavior to the grade level of your numeracy.