Arnold Kling  

The Hockey Game of Life?

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Robert H. Frank writes,


[Nobel Laureate Thomas] Schelling observed that by skating without a helmet, a player increases his team's odds of winning, perhaps because he can see and hear a little better, or more effectively intimidate opponents. The down side is that he also increases his odds of injury. If he values the higher odds of winning more than he values the extra safety, he will discard his helmet. Yet when others inevitably follow suit, the competitive balance is restored - everyone faces more risk and no one benefits. Hence the attraction of helmet rules.

As in hockey, many of the most important outcomes in life depend on relative position. Because a "good" school is an inescapably relative concept, each family's quest to provide a better education for its children has much in common with the athlete's quest for advantage. Families try to buy houses in the best school districts they can afford, yet when all families spend more, the result is merely to bid up the prices of those houses. Half of all children will still attend bottom-half schools.


Sports are inherently zero-sum games. Because economics looks at positive-sum games, such as trade and growth, sports can be a dangerous metaphor for economics.

In the case of schools and house prices, I would make several remarks.

1. If we have vouchers and a market for schools, then the money that parents are willing to spend to get their children into better schools would be spent on schools, not houses. Assuming that this produces a supply response, the result would be some overall increase in education quality.

2. It could be that with markets and vouchers, the better schools would get more expensive and the poor would not be able to afford them. I call this a "segregation equilibrium," and I suspect that it explains some of what we observe in higher education today. Affluent parents want to send their children to "good schools," meaning schools that are attended primarily by other affluent children, which means that demand is a positive function of price.

3. If "segregation equilibrium" is a problem, then voucher programs should include a "luxury tax" on high-tuition schools, with the money used to boost vouchers for low-income families. In the worst case, if low-income parents continue to get priced out of the market for high-end schools, they at least can use their larger vouchers to procure better teachers and facilities for the schools that their children do attend.


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TRACKBACKS (3 to date)
TrackBack URL: http://econlog.econlib.org/mt/mt-tb.cgi/387
The author at Asymmetrical Information in a related article titled We will drive ever forward until all our children are above average! writes:
    Arnold Kling has some incisive thoughts about education: Families try to buy houses in the best school districts they can afford, yet when all families spend more, the result is merely to bid up the prices of those houses. Half of all children will sti... [Tracked on October 27, 2005 11:47 AM]
COMMENTS (17 to date)
Timothy writes:

It could be that with markets and vouchers, the better schools would get more expensive and the poor would not be able to afford them. I call this a "segregation equilibrium," and I suspect that it explains some of what we observe in higher education today. Affluent parents want to send their children to "good schools," meaning schools that are attended primarily by other affluent children, which means that demand is a positive function of price.

Making higher education a Giffen good? That seems pretty strange.

Marshall Clow writes:

Having moved (to put my kids in better schools), I believe that a lot of what makes "good schools" is parental involvement. This works in many ways.
The first (and most obvious) way is that the parents teach their children, and insist that they work at their schoolwork.
Secondly, the parents get involved at the school - they volunteer time for teaching and as classroom aides, they organize events/fundraisers, they pressure the school (or district) to improve.

This leads to what The Economist calls a "virtuous cycle" (opposite of vicious). A school gets a "good reputation". Families that value this move there, get involved, and improve the schools. Repeat.

John Thacker writes:

[Nobel Laureate Thomas] Schelling observed that by skating without a helmet, a player increases his team's odds of winning, perhaps because he can see and hear a little better, or more effectively intimidate opponents. The down side is that he also increases his odds of injury.

I think that this might be a bad example. There are more and more severe fights when people wear helmets. It's similar to the argument that safety features make people drive more recklessly-- when everyone is wearing protective gear, they feel more free to behave recklessly, knowing that the helmet will protect them. I've seen some interesting studies analyzing just this for hockey. Does American football really have fewer injuries, for all its armor, than rugby or Australian football?

spencer writes:

So in the end your final solution is to throw public money at the problem?

Pat writes:

This is a bad example - not having your best players getting sent to the hospital also improves your chances of winning. Protecting good players from injury helps you win.

Slocum writes:

One of the obvious ways to prevent this problem is to require that schools that accept vouchers must accept them as full payment for the student. That is exactly how it works in my state for charter schools and open-enrollment districts. The charter school or neighboring district gets the standard per-pupil funding. You get choice without any possibility of a bidding war.

(A comment I also left at 'Asymmetrical Information' that linked to your entry)

Bernard Yomtov writes:

Pat is right.

Besides, the goal is win a high percentage of games, not (usually) just this game. Increased chance of injury may help you win today, but a good player hurt reduces the team's chances in future games.

Also, unless I misunderstand, the claim here is that the value of education is purely relative. But that is not right. Surely if we improve all schools 10%, say, we have improved education.

FXKLM writes:

Here are two more reasons why that housing prices and schools aren't likely to be a zero-sum game:

1. As housing prices rise, property taxes also rise and property taxes are often used to fund schools. Rising housing prices will tend to increase funding to schools, which may result in an absolute improvement in school quality.

2. If housing prices are largely a function of the quality of local schools, the entire community, even those without children attending public schools, will have a much stronger incentive to improve the quality of local schools.

Robert writes:

At least at the K-4, and maybe even the K-8 level, an open voucher system presents a very interesting small business opportunity: the one-room schoolhouse. The enterprising educator will consider that 25 students, each supplying a $7000 voucher (the states pay something more than this per student today), provide a $175,000 annual budget, and they will be able to pay themselves better than most public school districts, even after paying rent and buying all of their own supplies.

Dan Landau writes:

Kling's analysis includes an assumption that the key to better schools is spending more money. That is what the teachers' union wants us to believe. However, it is contrary to the whole point of vouchers.

The point of vouchers is that different privately owned schools can try different ways of educating. The innovator that comes up with a way to provided better education without costing more will win the competition and attract more and more students.

If better education requires more money rather than different approaches to education, the voucher wouldn't help much.

dearieme writes:

Are you assuming that the value of a voucher would be treated as taxable income, so that it's worth more to someone with a lower marginal tax rate?

superdestroyer writes:

Robert,

You have identified one of the biggest problems to vouchers. The entry barriers for starting a private kindergarten are small. The entry barriers for starting a private junior high are huge. The barriers for starting a private high school are enormous.

If a voucher for everyone system is started, the number of private elementary schools will spike but, I predict, few new private high schools will open. Thus, the existing private high schools will have huge increases in the number of applicants without any additional space. Thus, wait lists, insider deals, and legancies will become the dominate barriers to entry.

Image trying to move to a new metropolitan area where the "good" science and technology school has a 2000 student wait list and a two year admissions process but that the ethnic studies high school is the only school with open admissions and open seats. What will parents do? A voucher system could cause the price of housing to decrease due to the unavailability of seats in good schools for the children of new home buyers.

Boonton writes:

Actually the flaw in Kling's argument is that he forgets spending your own money is a lot different than spending someone else's money. It isn't the parents' money that they receive with a voucher but the taxpayers. In essense today responsibility for education is shared; parents must send their kids to school (private, public, or home school w/verification) and taxpayers fund public schools. Vouchers alters the equation by taking taxpayers even more out of the oversight function but still sticking them with the bill.

John F. Opie writes:

Hi -

I must beg to differ with your intial proposition: that sports are inherently zero-sum games.

This is empirically not true for European football, what the US calls soccer.

First, games may end in a tie, and indeed there is a significant portion of games that end in ties.

Second, and this is the reason for having ties, two teams can basically do the statistics and decide that there should be a certain outcome for both teams in order for them to both improve their prospective standings: this can even happen in world cup games (the infamous match between Germany and Austria in 1980-something is a perfect example of this).

Empirically, this means that European soccer is, up to the very final game of the world cup - where one team must indeed win, but may well do so in 15-meter shots - a non zero-sum game.

John

Robert Book writes:

The notion that "a 'good' school is an inescapably relative concept" is an assertion of fact that remains unproven. I personally suspect that it's incorrect: If all schools could increase (say) math test scores by 10%, students would be better off because they know more, in the same sense that if productivity of all workers increases by 10%, all will be richer, and will share in the 10% per-capita increase in GDP. Even with school tuitions "paid" in the housing market, it's not necessarily a zero-sum game.

Furthermore, parents do not differ only in their income; they may also differ in there preferences for (public) schooling. At any given level of income, some parents care more about school quality relative to (say) house quality than others. Under the current system, these parents would rather live in a smaller/older/worse house in a better school district; parents with the opposite preference would rather live in a better house in a worse school district. In the extreme case, parents with the highest preference for schools pay tuition to private schools and would benefit from living in a good house in a bad school district, since the public school quality doesn't affect their kids' education.

It's true that "half of all children will still attend bottom-half schools" -- but this is only relevant if the distribution of schools by quality is constant. If the top half of schools increase in quality by 10% and the bottom half stay the same (or even get worse), children in the top half get better educations, both in absolute and relative terms, than those in the bottom half.

Also, I'd suggest using the more standard term "separating equilibrium" rather than "segregating equilibrium." Not only is "separating" more standard in the literature, but "segregating" is a loaded word when it comes to schools.

James writes:

Robert writes

"The notion that "a 'good' school is an inescapably relative concept" is an assertion of fact that remains unproven. I personally suspect that it's incorrect:"

And the argument is,

"If all schools could increase (say) math test scores by 10%, students would be better off because they know more, in the same sense that if productivity of all workers increases by 10%, all will be richer, and will share in the 10% per-capita increase in GDP."

But the selected counterexample to the suspect claim is an improvement equal to 1/10th of the prior quality, which is strictly a relative measure.

Steve Sailer writes:

The obvious implication is to use immigration policy to improve the quality of students. Enforce the laws against illegal immigration and the quality of students would be much higher -- most illegal immigrants have never been to high school and they don't give their children academic motivations.

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