Trading Places

by Harry on July 26, 2006

I just finished reading Julian Betts’s essay “The Economic Theory of School Choice” in his (excellent and remarkably inexpensive) edited collection Getting Choice Right. For the most part I don’t expect to find really new ideas about school choice in what I read, so it was a thrill to find something I hadn’t encountered before. The contributors all assume (correctly in my view) that school choice is an inevitable feature of the education system, so the issue is how to get it right — in other words, how to make it as efficient and equitable as possible (self-styled opponents of school choice tend to support the de facto status quo, a school choice system riddled with inefficiencies and inequities).

The most obvious barrier to a school choice being efficient and to it being equitable is the fact that in a choice system schools get to choose students, leading, one presumes, to a concentration of advantaged students into popular schools. Defenders of choice usually offer three solutions to this problem; lotteries (preventing schools from choosing); quotas (allowing them to choose but limiting their ability to select for advantage) and weighted student funding (allowing them to choose, but giving them incentives to choose disadvantaged children, and compensating schools which get landed with high concentrations of disadvantage). (I suggest a combination of these in my proposal at the end of School Choice and Social Justice).

So what’s new in Betts’s paper?

He suggests a fourth solution, adapted from energy and communications deregulation, which incidentally deals with a difficulty in the third solution. The problem with weighted student funding is figuring out how to set the weights — the idea is that a central planner decides how to compensate for disadvantage, but the truth is that no-one really knows how much weight to give (the proposals are mostly off-the-top-of-our-heads). Betts suggests this: first fund the schools equally on a per-student basis. Then distribute trade-able rights to admit highly advantaged students; and allow schools to auction those rights. Schools would then be forced to figure out how much they valued the money they were spending relative to the highly advantaged children they wanted. We don’t know what the outcome would be. At one end of the spectrum you’d have schools with high concentrations of advantage and not much money; at the other end of the spectrum high concentrations of disadvantage and loads of money. It would probably take a few years for administrators to work out what the real costs of disadvantaged children were; but they would have a powerful incentive to work it out.

There are numerous pitfalls in the proposal, including the incentives for administrators to mislabel kids, and for sellers of rights to collude, but Betts provides plausible solutions to these. He only proposes it at the district level, but of course it is more attractive as a regional or statewide proposal (imagine the suburban districts around Milwaukee having to buy the rights to admit highly advantaged children from Milwaukee public schools). As a public proposal, I imagine that its dead in the water, but that’s ok — that’s what I was told about admissions lotteries in the UK when I first suggested them in 2000.

Anyway, just thought I’d share my enthusiasm about a new idea.



eweininger 07.26.06 at 9:00 am

Schools would then be forced to figure out how much they valued the money they were spending relative to the highly advantaged children they wanted. We don’t know what the outcome would be.

Granted the current system in the US, in which residential proximity largely determines schooling options, is particularly insane–especially when coupled with a funding system that partly depends on self-imposed taxation.

Nevertheless, this makes me a bit queasy. What happens when the officials in charge of “figuring it out” do a lousy job? In theory, I guess the “market” that’s been created will eventually “correct” errors, but there will inevitably be a lag.

Also, we would need a new stratum of professional traders, no? Definitely a weird occupation.


Daniel 07.26.06 at 9:09 am

errrm … would this not leave you with a system in which the schools in the richest areas were able to buy the best students from other schools, while schools in the poorest areas quite literally sold their best students to raise money to cover running costs. Surely in order to work, this tradeable permits system needs the assumption of no other sources of funds for the schools, which seems unworkable to me.


Daniel 07.26.06 at 9:14 am

(for example, I can easily see a situation in which one of my local schools, with a mixed catchment area, raised money from the middle class parents to buy the right to send all the working class children and asylum seekers to the sink down the road and drag their middle class children here. True, the sink school would get a bundle of cash, but one of the things we know about education is that there isn’t much of a production function linking money and results.)

Actually thinking about it (without seeing the paper) I would guess that an implicit assumption of a linear relationship might be doing quite a lot of work. If you have one problem kid already, you aren’t going to want another one. I would be surprised if this market cleared.


dearieme 07.26.06 at 9:54 am

Why is the quality of a school routinely viewed as a one-dimensional phenomenon? If it does, indeed, approximate well to parents’ current beliefs, must it? It’s not their view of cars, or shops or many other things.


Matt 07.26.06 at 10:21 am

Is there any idea how large a portion of the resources will be spent on running this sort of thing? Don’t those who are good at this sort of valuation get paid quite a lot to do it, and even then do it only imperfectly? I worry that it would either be done very badly or else be done modestly badly but very expensively.


SamChevre 07.26.06 at 11:29 am

Wouldn’t an auction system accomplish the same thing more understandably?

In other words, let the schools bid on students–the government will pay the lowest tuition someone bids, and private sources can add on if they want to change schools.

Actually, Daniel, grouping problem students can be a huge help. If you can get 6 bouncy children in one room, and assign a teacher who deals well with them, they will do fine–but if you put one bouncy student in each of 6 classrooms of 20 students, often neither the bouncy student not anyone else gets taught.


mcd 07.26.06 at 11:43 am

There should be as little “choice” as possible in schools. And indeed as little to choose between in schools as possible. “Choice” by nature will never be equitable, because equitableness is not what Americans want to “choose”. Parents don’t “choose” the “best” education for children. They choose to get their children much better education than anyone else’s children (when they can afford it), so their children will beat out others’ children in the competition for scarce well-paying slots in the economy.

Energy and communications deregulation? So you look forward to Enron as your model of schools?


Daniel 07.26.06 at 11:44 am

I see what you mean. It strikes me, though, that it could go either way and that the least likely possibility is that the decision maker’s preferences over children will be independent of the hand he has already been dealt. This is highly disanalogous to telecoms minutes or kilowatts, where it makes sense to assume monotonic and independent preferences. I would be really interested to see if someone’s actually checked the conditions under which a market like this might clear, but my Bayesian prior would be that there is no guarantee that there would be any market equilibrium at all and most likely there wouldn’t.


leederick 07.26.06 at 11:44 am

Why not just auction school places to parents directly? With the money collected going to the schools of children who lost the auction.


jim 07.26.06 at 11:59 am

I’m sorry, but I don’t understand the mechanics. How do schools get paid? Is there some kind of NFL draft going to happen? where school A buys draft picks from school B? If so, what happens to student choice? If a student picks an undersubscribed school, he/she gets in but if he/she picks an oversubscribed school he/she goes into the draft? That would incentivise advantaged students (who think to game the system) to chose the second or third school in the league table, rather than the first, so they stay out of the draft. Then the “top” school and the sink schools end up dividing the disadvantaged students between them.


Daniel 07.26.06 at 12:03 pm

As I understand it, in order to allow in a student with parental income above $x, you need a permit. So if you are a rich kid and apply to school A, they can be full in two ways 1) actually physically full and 2) not having any more permits and not willing to buy one in order to let you in. As I say, my guess is that this market doesn’t necessarily clear with the price mechanism alone and ends up having a whole lot of horse-trading going on without much obvious benefit.


mkl 07.26.06 at 12:19 pm

If this did work, it’s not clear how the funding incentive will affect the school administrators making the choice between a high revenue / disadvantaged student body and a low revenue / advantaged one. If the revenue difference is significant and if the parents of the advantaged kids can’t be hit up for the difference, administrators would be best compensated for running sinks.


jim 07.26.06 at 12:36 pm

Thank you, Daniel. So, to work through a simple example, suppose there’s two schools, A and B, A much “better” than B, so everyone puts A as their first choice. To fix ideas, suppose each has ten places. There are 20 applicants, ten of whom are rich. So both schools get 5 permits to admit rich kids. A uses its five permits to admit the smartest of the rich kids. It now has five places left. It can admit the five smartest of the poor kids or it can buy permits from school B and admit more rich kids. Why would it spend that money? If it admits the five smartest of the poor kids then it will still start out ahead of school B (it has the five smartest rich kids and the five smartest poor kids; school B gets left with the five dumbest rich kids and the five dumbest poor kids, among whom are likely the disruptive ones) and therefore end up, all other things being equal, ahead of school B and still be regarded as the better school next time through the cycle. Which is all it needs to make sure it’s solidly oversubscribed.

So, yes, no trades happen.


Andrew 07.26.06 at 12:55 pm

This idea is clever, but it won’t work in many places where it’d be most useful. In the South Bay (where I work now) or in East King County (where I used to work) there are small cities such as Cupertino, Los Gatos, Medina and Mercer Island that are much wealthier than their neighbors such as Santa Clara or Renton and have no incentive to play this game. Swapping different levels on income around Seattle (where I used to live) or San Francisco (where I live now) seems more useful, but large cities like this have far fewer school-age children than the suburbs do. These two cities have the lowest children per capita in the US.


Essjay 07.26.06 at 1:09 pm

Define “highly advantaged student”, please.


Essjay 07.26.06 at 1:18 pm

Don’t the race academies in the South already do this? They forego public money, in exchange they get to limit admissions to “highly advantaged” (a.k.a. white) children.


Barry 07.26.06 at 1:18 pm

Note that this idea fails in the perfect world of CT; it hasn’t even been dragged through several years of politics, lobbying, lying, bribery and BS. Imagine what would come out on the other side, and shudder.


jim 07.26.06 at 2:32 pm

On further thought, if “advantaged” is defined very broadly, so that there are only a few “disadvantaged”, but they’re fairly horrible specimens, then trades can occur.

Consider the toy version above (#13), but instead of ten advantaged, ten disadvantaged, make it 18 advantaged and two disadvantaged. Then each school gets permits to admit nine advantaged. If there’s no trades, each school would have to take one disadvantaged student, guaranteed to disrupt classes. So it’s worth it for school A to offer to buy a permit from school B to avoid picking up the disrupter. School B will have to take a disrupter anyway. Enough extra money might enable it to manage both.

The way to make such a scheme work is there needs to be no disadvantaged students that are acceptable to the oversubscribed schools. If there are, then the oversubscribed schools can admit them and retain their standing and thus continue being oversubscribed. Schools will pay rather than take disadvantaged students only if disadvantaged really does equate to undesirable.

I don’t see this happening. I suspect, if this scheme were to be adopted, large groups would be labelled disadvantaged, which is what’s implied by the use of the term “highly advantaged” after all. All minority children, perhaps, would be labelled disadvantaged, for who can deny the existence of racism? But there are many minority children who can do just fine in school. Better to figure out which ones they are and just admit them rather than give away some of your budget.


Ben M 07.26.06 at 4:04 pm

Daniel (#11) and subsequent comments seem to assume that the “advantage/disadvantage” boundary has to be defined by statute. However, I don’t see why this needs to be the case—#10’s mention of a sports draft may be closer to workable. Consider the following procedure:

1) Students submit a ranked set of school preferences.
2) A computer optimization (the sort used for university dorm assignments) randomly sorts students into schools in an attempt at preference-maximizing, but paying no attention whatsoever to income, academics, discipline issues, etc.
3) School officials look at the pool of student they’ve been assigned, look at the pools available in other schools, and bargain amongst themselves, with full discretion to consider income, behavior, academics, sports, etc., and the school’s already-fixed budget.

Thus you have auction exchanges like this:
CCS: “Dear UrbanBlightAcademy, you were assigned Jessica Topstudent, but we’d like to have her here at CountryClubSchool. Will you accept Eddie Misbehavior and $3000 in exchange?”

UBA: “Jeez, we’d need extra teacher’s aides to handle Eddie. Would you do it for $4500/yr?”

WWCS: [stepping in] “WellRunCharterSchool has effective discipline in place already, but we need cash. We’ll trade a top-ten-percentile academic for Eddie and $3000/yr.”

The initial use of student preferences might serve as an important anti-corruption/anti-sinkhole tool. If a school descends into an academic and disciplinary basket-case—say, by trading away good students for money, then blowing the money—next year’s top students will carefully select themselves away from that school. In the next year’s selection lottery, they won’t pick up any trade bait, and their trade income dries up. Similarly, you can imagine that a school could thrive on its ability to spot diamonds in the rough, or suffer due to a racist policy of trading unquestioningly for rich whites.


Brett Bellmore 07.26.06 at 4:19 pm

I think there’s something just a bit oblivious about saying, “let’s have a system of choice, and how can we rig the incentives so it produces the exact same behavior as we’d command if we didn’t have a system of choice?

Just learn to let go; Choice isn’t about producing the outcome YOU desire, it’s about people getting to chose for themselves.


nelziq 07.26.06 at 4:44 pm

Choice isn’t about producing the outcome YOU desire, it’s about people getting to chose for themselves.

Amen. There are two parts to school choice. First is that students get to choose schools so they won’t be forced to attend schools that are incompetant at teaching. But the other aspect is also important. Why should schools be forced to teach students that don’t want to be there, are disruptive, violent, or otherwise problematic? School choice should let kids and their parents choose schools that have teachers who are serious about learning and should also let them choose schools where the students are serious about learning, too.


harry b 07.26.06 at 4:47 pm

Brett — the problem with “letting people just choose for themselves” is that in actual educational markets the imperfections are such that some people (those whose children have desireable characteristics) get what they want, and others don’t get what they want (they might, sometimes, get what they choose, having chosen not what they wanted but what they thought they could get. Suppose Mr. Smith and Mr. Patel both choose St. Edmunds for their kid, but Lincoln High, being oversubscribed, gets to select which kid it wants to enter the school; Mr. Smith’s kid. They both chose, and one of them got what he wanted, but the other didn’t. Surely, you are not in favour of agents of the state choosing which kid’ll get to attend the better school.

Of course, complete privatisation (withdrawal of any government involvement in education whatsoever) is your preferred alternative. Me, I don’t see that as feasible (and would reject it even if I did, for reasons to do with justice, though I know they won’t carry much weight with you!)

All the mechanisms I mention in the post are efforts NOT to curtial choice, or to achieve a prescribed outcome, but to render choice more equal (and much more equal than in the status quo that many self-styled opponents of choice defend, one in which the government colludes with the most advantaged parents in giving them a great deal of choice, and deprives less advantaged parents of any effective choice).

The rest of you — keep going, this is incredibly interesting to me!


Jack 07.26.06 at 5:30 pm

Setting up a market like this might allow flexibility but it is still set up to allow schools to maximise their utility. The utility of the school is not of much value and without implausibly strong school institutions is only weakly connected with the interests of students, even those of the future when some kind of equilibrium might have been reached.

There is also a problem with spot markets when investment is required if the system prevents commitment. Most markets don’t operate by spot market alone.

I’m also not sure about lotteries. They may achieve the objective of denying advantage to the advantaged but at a cost of reducing incentives to students to do well — what can a student do to get into the school they want to?


Brett Bellmore 07.26.06 at 6:02 pm

“In actual educational markets the imperfections are such that some people get what they want, and others don’t get what they want”

That’s not a property of free markets as contrasted with controlled ones, that’s a property of reality as contrasted with fantasy. It’s never possible for everybody to get what they want. And that’s as true of any of the above proposals as it is of an unregulated market.

I’ll stick by my position: Anybody who insists that a system of “choice” has to incorporate incentives and rules to make sure the outcome is to their liking, doesn’t want choice. They want control. And they ought to have the honesty to admit it.


mythago 07.26.06 at 6:07 pm

Surely in order to work, this tradeable permits system needs the assumption of no other sources of funds for the schools

Yes. Which is a huge, huge problem for this model. The wealthy schools are in high-income neighborhoods, where residents are far more able to raise supplementary funds.

I used to live in the south SF Bay, which andrew mentions in his post. The PTA in wealthy Palo Alto was able to raise $1 million a year in additional funds for their schools. Adjoining school districts with far less wealthy families were not going to match that. And, of course, the ‘official’ numbers get trotted out to suggest that wealthy Palo Alto can educate students on $X per student a year, so why can’t Sunnyvale?


harry b 07.26.06 at 6:45 pm


ok, I’ll just say that almost no-one involved in the school choice debate pretends that they are not interested in policymakers exercising control over the way that children are allocated to schools. They differ as to how much choice to allow, and how it should be distributed. A handful of people believe in complete privatisation. A large number say that they oppose choice (but don’t make proposals that would eliminate it). The rest of us may not, by your definition, care about school choice in any fundamental sense. But that’s where the debate is.


William 07.26.06 at 10:13 pm

The problem with trading rights to admit desirable students is that it misses the real issue . . . the right to exclude undesirable students. That’s the real problem with choice. Who chooses? If you are talking about a system where *schools* have more choice, that probably isn’t going to win over parents.

Just as a thought experiment, what would happen if a student became more desirable over the course of their career? Would they be put in a position where (for example) their senior year Mom wins the Lotto, so they can’t stay at their high school? They have a growth spurt and become a power forward instead of a shooting guard? They buckle down and get a great SAT score? Or what about a kid that develops a drug problem and falls off? How exactly and how often would desirability be evaluated?


Dan 07.26.06 at 10:25 pm

People already have a choice. They can and do move to a different school district if they don’t like the one they are in. I know people who put down Grandma’s address if it is in a better district. If you want to discuss how to make our schools better, I think you have to talk about other things.
People might argue that poor people can’t move. I would argue that many poor people couldn’t get their kids across town to the “better” schools.


mythago 07.27.06 at 1:54 am

I know people who put down Grandma’s address if it is in a better district.

Then you know people who better have lawyers on speed-dial.

Pretending that poor people can ‘just move’ to a school district where the mortgage on a home is more than their monthly income is a pretty severe case of denial of the problem.


Daniel 07.27.06 at 5:05 am

with regard to #19, I think that this demonstrates why I’m suspicious of this one. Professional sports teams’ trading is not meant to achieve an optimal allocation (it’s not even obvious what an optimal allocation would be) and I don’t think that there are many sports economists who would argue that the market for players clears in any meaningful way. It might not be death for the idea (market clearing isn’t the be-all and end-all, and nobody with their head screwed on would ever have thought that the theorems of welfare economics were going to be any help here). But I think that sports teams and draft picks would be a better analogy than emmissions permits.


Ben M 07.27.06 at 10:09 am

daniel (#30),

I think you’re dead right to wonder whether the allocation will, in the end, be optimal, or even good. It’s not obvious what the allocation will be, nor whether that’s good, nor even what “good” actually is. The thing that intrigues me about this proposal is not its “optimalness” or even its “choice”, but simply the fact that it creates incentives within the context of universal, public, free education. At a glance, those incentives seem to push teachers/administrators in the direction of improving their own schools. The manner of improvement (Fiscal efficiency? Teacher quality? Class size?) is wholly up to the schools, and the assay of the improvement is mostly up to the students and parents, rather than test-score-analysts or bureacrats. The presence of re-sorting, while eye-catching, is just the gimmick which makes these incentives possible—it’s not so important that the sorting be in any way optimal. (Given that the status quo is “sorting by cost of parents’ home”, almost any change is an improvement, no?)

In every other scheme I’ve seen, there are either a) no incentives at all, b) “avoid wrath from above based on test scores” incentives, a la No Child Left Behind, or c) some arcanely-engineered profit motive. I’ve never quite figured out what the incentive structure is under “students go to any school they want”, given that there’s finite capacity at each school.


Dan 07.27.06 at 2:20 pm

my point is:
1. choice is already happening for the rich and middle class.
2. poor people wouldn’t have the choice even if given a choice. They can’t afford to get across town.

This whole discussion on choice is strange because it totally sidesteps the real (alleged) problem of bad schools.

People already have choices. Homeschooling, alternative schooling, moving, using someone elses address, applying for other districts (You can do that in some states, certainly in CA).

The only people who really don’t have a choice are the poor.


harry b 07.27.06 at 2:32 pm

2. poor people wouldn’t have the choice even if given a choice. They can’t afford to get across town.

Depends on the design of the choice scheme, population densities, and school size. London (in which schools have powers to select) has free public transport for kids, and most kids are withint reaosnable distance of a reasonable number of secondary schools. Some schemes pay for transport.


mythago 07.27.06 at 3:27 pm

dan, I understand what you’re saying about the poor having just about zero choice. But school choice is really available only to the wealthy. “Using someone’s address” is illegal; homeschooling is not legal, or practical, everywhere; and ‘alternative’ meaning ‘private’ is certainly not available to the poor.

The discussion on choice doesn’t really sidestep the problem of bad schools; you have to assume there are bad schools or there’s no substantial reason for choice.


Terry 07.28.06 at 1:12 am

Re “advantaged” versus “undesirable” students.

The fear with charter schools was that they
would skim off the best students. The reality
has been just the opposite. Parents of the
cream of the crop students don’t want to mess
with success, while parents of those who are
struggling are more motivated to try something

Also, I want to make the point that school choice
isn’t just about getting your child into a better
school. It’s also about getting your child into
a school whose philosophy you agree with.

For example a school which had a strong program
against bullying would hold a lot of appeal for
some parents. But a lot of parents would not care
one way of another what the school’s policy on
bullying was.


britta 07.28.06 at 1:50 am

I went to school in a school district where a) all public high schools were magnet schools and b) public transportation was subsidized by the city for students, making choice very achievable for students. Moreover, funding was roughly inversely proportional to the success of the school (with some exceptions). The highest performing school, which had an international baccalaureate curriculum and sent 95% of its students to university had the lowest per student funding, whereas the worst off school, which had less than a 30% graduation rate, had one of the highest student funding ratios. The rationale was that the highest performing school did well because of the IB curriculum, caliber of students (predominantly white upper middle class), and quality of its teachers, all of which were not that expensive after an initial investment, and also that sending more money to the worst performing school might create an incentive for students to go there. The result was interesting in that it ended up with a very high performing school with overcrowded classrooms (There were 50 students in my calculus class, and in some classes the last students had to sit on the windowsill or stand. Indeed, some teachers asked their students to attend class in rotating four day shifts and then skip on the fifth day to relieve crowding); substandard classrooms; and worn out/photocopied books. In contrast, the worst performing school had extremely small class sizes, motivated teachers, and was in a beautifully renovated building. It did not have the intended effect of reducing inequality however, and despite the extra funding, the school remained underperforming, with about 40% of neighborhood students choosing not to attend.
While funding is certainly important for good schooling, the correlation between money and quality of a school seems not to be as strong as many people are assuming, especially if it’s a superficial amount. It may not be as strong as the correlation between type of students and school, or perhaps administration and school quality. Of course, if a school could provide to disadvantaged students all the resources available out of school to privileged students (trips to museums and libraries, one-on-one tutoring, music lessons, healthy balanced meals, behavior altering drugs, etc.), which are expensive, funding could neutralize student performance inequalities. This would take a very large amount of funding as well as talented teachers and administrators, not necessarily a given.

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