Vouchers Drain the Public Schools, and the Answer Is in the Arithmetic

The most abused phrase in school finance is "the money follows the child." Supporters of choice say it like a hymn. Opponents say it like a diagnosis. Both are talking about the same sentence and neither of them has opened a spreadsheet. Which is a shame, because the spreadsheet is where the argument is won or lost, and it turns out to be a more interesting spreadsheet than either side lets on.

So let us open it. I am going to state the case against vouchers as strongly as its smartest defenders would, build a small invented school district, and push the numbers through. Then I will show you the one figure that decides whether a district gains or loses, and I will tell you where the honest evidence runs out. If you finish this post, you will be able to win this argument with someone who has memorized all the slogans and none of the subtraction.

The best version of the objection

Here is the opposing case at full strength, in language its supporters would sign.

A school district has costs that do not move when a few children leave. The building still needs heat. The buses still run the same routes. The teachers are on contracts, and the district still owes pension contributions and payments on the bonds that built the gym. When a child departs with a voucher, the district loses the per-pupil funding attached to that child, but it does not save the per-pupil cost, because the per-pupil cost was an average, and the real saving from one fewer child is tiny. A classroom with twenty-six children costs nearly the same as one with twenty-five. So the district loses real money and sheds almost no real expense. The children who remain, who tend to be the ones with the greatest needs and the fewest options, pay for it in larger classes and thinner programs. And on top of that, vouchers also go to families who were already paying for private school, so the state spends new money without moving a single child.

That is a serious argument. It contains four separate claims: stranded fixed costs, a mismatch between average and marginal cost, harm to remaining students, and spending on children who were already in private school. Let us test each one, starting with an invented district.

Meet Maple Valley, a hypothetical district

Maple Valley is made up. Every number is invented for the exercise, and it should not be mistaken for any real district. It has 5,000 students and spends $12,000 per student, so its budget is 5,000 times $12,000, which is $60,000,000. The money comes from three places:

• State aid: $5,000 per student, or 5,000 times $5,000, which is $25,000,000.
• Local property taxes: $6,000 per student, or $30,000,000.
• Federal programs: $1,000 per student, or $5,000,000.

Check the addition: $25 million plus $30 million plus $5 million is $60 million. Good.

Now a voucher program arrives. The state offers a voucher worth $6,000 to any child who leaves for a private school. In the first year, 100 of Maple Valley's students take it. That is 2 percent of enrollment, since 100 divided by 5,000 is 0.02.

Answer one: count what actually leaves

The objection says "the money follows the child." So ask exactly which money. In most states the voucher is funded by the state, and the state does it by reducing the state aid that would have gone to the district for that child. It does not usually reach into the local property tax. The local taxes were levied on the homes and businesses in Maple Valley, and they are collected whether or not a child lives in any particular house.

So here is the first year, in this simplified version where only state aid follows the child:

• State aid lost: 100 students times $5,000, which is $500,000.
• Local property tax lost: zero. The $30,000,000 still arrives.
• Federal funding: assume unchanged in the short run. (Some federal aid is tied to poverty counts rather than enrollment, so it would not shift immediately. That is an assumption, and I label it as one.)

Maple Valley's revenue falls from $60,000,000 to $59,500,000. A decline of $500,000 is less than one percent of the budget, to be exact 0.83 percent, because 500,000 divided by 60,000,000 is about 0.0083.

Meanwhile the state pays 100 times $6,000, which is $600,000, in vouchers. It saves the $500,000 of aid it would have sent to the district. So the state's net added cost for these 100 children is $100,000.

Pause on that last number, because it is the one the objection leaves out. The district does not lose the full $6,000 per child. It loses $5,000, the state aid, and the remaining $1,000 comes from the state's pocket, not the district's.

Answer two: the break-even number

Now the part about costs. The objection says that Maple Valley sheds almost no expense when 100 children leave. Let us grant a good deal of that. Suppose the district can trim only $2,000 per departing child, from things like supplies, a few hours of aides and some food service and transportation. That is 100 times $2,000, which is $200,000.

• Revenue lost: $500,000.
• Costs saved: $200,000.
• Net loss: $300,000.

That is real money. It is 0.5 percent of the budget (300,000 divided by 60,000,000 is 0.005), or $61.22 for each of the 4,900 children who remain (300,000 divided by 4,900 is 61.22). The objection is right that this hurts. It is not right that it is a catastrophe.

Now the figure that decides everything. Do the algebra in plain words: the district comes out ahead whenever the cost it can shed per departing child is more than the state aid that leaves with that child, and it comes out behind whenever it can shed less. In Maple Valley the state aid that leaves is $5,000. If the district can trim $5,000 of cost per departing child, it breaks even. If it can trim only $2,000, it is $3,000 per child short, and 100 children times $3,000 is the $300,000 we found.

That is the entire argument, reduced to one subtraction. Everything else is a debate about how big the two terms are.

Answer three: fixed costs are fixed in the short run only

The objection is strongest in year one. Over five years it weakens, and here is why.

Suppose that over five years 1,000 students leave Maple Valley, which is 20 percent of its enrollment. Under the state-aid-only rule it loses 1,000 times $5,000, which is $5,000,000 in state aid. Its revenue falls from $60,000,000 to $55,000,000, spread across 4,000 students. That is $13,750 per remaining student (55,000,000 divided by 4,000), compared with $12,000 before, an increase of $1,750.

Can the district also cut its costs? When 20 percent of the children are gone, it can consolidate classrooms, retire a building, and let staffing shrink through ordinary attrition. If it manages to shed more than $5,000,000 in annual costs, which is 8.3 percent of its $60,000,000 budget (5,000,000 divided by 60,000,000), it comes out ahead on the state-aid-only formula. If it cannot, because it holds on to every building and every position, it runs a deficit.

Is that realistic? Think about how districts handle other enrollment drops. When the birth rate falls or families move away, school systems close buildings and consolidate attendance zones all the time. Nobody calls a falling birth rate theft. A district that loses students to any cause has to adjust to the new reality, and the question for the voucher debate is whether it adjusts at the speed of the enrollment change or slower. Debt service and pension contributions are the sticky ones, because they are obligations that run for decades regardless of enrollment, and that is where an honest critic should press.

What about the classroom? The objection says remaining students get larger classes. Test it with Maple Valley's invented numbers. Spread 5,000 students over thirteen grades, kindergarten through twelfth, and you get about 385 per grade. Put those 385 in 15 classrooms and each class holds about 25.6 children (385 divided by 15). Now remove 100 students from the whole district, about 7.7 per grade. Each grade has about 377 children, and in the same 15 classrooms that is about 25.1 per class (377 divided by 15). The average class got slightly smaller, by about half a child, because no principal can cut a teacher in half. That is the objection's own point turned around: the fixed costs are fixed, which means the children who stay are not squeezed in year one. The squeeze comes later, if the district refuses to adjust and the budget finally runs out, which is a management question as much as a voucher question.

The harsher variant: when local money follows the child too

I promised a fair test, so here is the version that hurts the district more. Some programs reduce the district's local revenue as well as its state aid. Suppose the $6,000 voucher is taken as $5,000 of state aid and $1,000 of local revenue.

• Revenue lost: 100 times $6,000, or $600,000.
• Costs saved: still $200,000.
• Net loss: $400,000, which is 0.67 percent of the budget (400,000 divided by 60,000,000 is about 0.0067) or $81.63 per remaining student (400,000 divided by 4,900).

Every design choice in a voucher law moves those numbers. Whether local property taxes follow the child is one of the biggest. So the first question to ask about any specific program is not "does it drain the schools?" but "what does the formula take, and from which pocket?" Look up your own state's funding formula, and for a template on reading a district's budget, see A Worksheet for Reading Your School District's Budget Line by Line.

The concession: children already in private school

Now to the objection I think has the most force. If a voucher is open to every family, then some of the children who receive it were already in private school. For them, the state is spending money without any child changing schools.

Here is an invented state-level example. Suppose 1,000 children receive $6,000 vouchers, for a total of 1,000 times $6,000, which is $6,000,000. Suppose 400 of those children really did switch from public schools, and 600 were already in private schools. The state saves the $5,000 of aid on the 400 switchers, which is $2,000,000. Its net added cost is $6,000,000 minus $2,000,000, which is $4,000,000.

That is a real cost to the taxpayer, and anyone who tells you vouchers "pay for themselves" has not run this subtraction. The right reply is not to deny it. It is to say what the extra $4,000,000 buys: it recognizes that families who already pay twice, once in taxes and once in tuition, deserve some of their own money back, and it makes the option available to families who could not afford to leave on their own. That is a value judgment, and I am happy to make it openly. But the voter deserves to know the price. For the account-based version of this arithmetic, see Four Families, One Education Savings Account, and the Math of Choice.

Where the evidence is honestly contested

Let me mark the edge of what I can claim.

1. Whether competition improves district schools. Some studies of programs have found that district schools facing competition improved modestly. Others found little or no effect. The literature is not unanimous, and anyone who says it is, in either direction, is overclaiming.
2. Whether the students who stay are worse off. It depends on the formula, the district's ability to adjust and how many students leave. The honest answer is that it varies.
3. What happens to student achievement for those who leave. Studies of different programs have reached different conclusions, and they deserve their own careful treatment, not a one-line summary.
4. The long-term fiscal effect on a state. It depends on the share of voucher users who were already in private school, which differs by program design and eligibility rules.

If you want a quick run through the other popular claims, Seven School Choice Myths Your Neighbor Believes and What the Record Shows tests seven of them against the record.

How to argue it without overclaiming

My advice is to win the argument on the ground you can hold.

Say this: a voucher does not take the full per-pupil figure out of the district, because the local tax base stays in place in most designs. Say this too: the district is not harmless to change, because some costs are fixed in the short run, and a state should write the formula to cushion the transition. Concede that a universal program costs the state more if it serves families already in private school. And then make the case on principle. The child is the point of the system. The building is the means. A system that works for children when it is convenient for the building is not a system anyone should defend.

The bottom line

• "The money follows the child" is not the same as "the district loses everything." In most designs the state aid leaves, the local property tax stays, and the voucher is worth less than the full per-pupil figure.
• The deciding number is simple: does the district shed more cost per departing child than the aid that leaves with the child? If yes, it gains. If no, it loses. Ask your own district for both numbers.
• Fixed costs are real in the short run and shrink in the long run. Debt service and pension obligations are the stubborn ones, and a fair law cushions the transition.
• A program open to everyone costs the state more if it covers families already in private school. Say so out loud, and defend it on principle rather than pretending it away.
• Press your legislator on the formula: what is taken, from which pocket, and what cushion exists for a district that loses students quickly.