Failing public schools

You might think that I’m going to be talking about the (somewhat) recent cheating scandals plaguing schools around the country. Sorry to disappoint. What I’m more interested in is discussing why there is such a large achievement gap between public schools and private schools. We often read about how the public school system in this country is a mess. We thus have various national initiatives to try to help improve public schools, whether it be No Child Left Behind, or Race to the Top, or whatever. In any case, a lot of work has to be done on the public school system. For example, in New York City, less than half of students met the English standards. Compare this with New York City private schools, many of which are so successful that the state doesn’t even bother to test their students, as their curricula significantly surpass those of the state tests.

I think that a large factor in determining the quality of the public schools is how much the general public (including those with more resources to invest in education) actually are willing to contribute. If the wealthier students are all opting out and going to private school, then the money that these students could have been spending on the public school system is lost. Moreover, since students from a wealthier background will probably have a home environment more conducive to studying (after all, if the parents want to send them to private school, it shows a commitment to their children’s education), there will likely be, on average, more of an atmosphere at school as well of academic seriousness. In short, having the students from more affluent backgrounds attend the public schools would probably improve their quality by quite a bit.

Obviously, things are not so simple to fix – the families whose kids go to private school prefer this option, and are free to choose to pursue it. To illustrate the dynamic of sending children to private schools, we have to consider the incentives of the wealthier families. To simplify things, we reduce the number of agents to two (it makes it easier to see the rationale). We’ll call them the Smiths and the Joneses. As it stands now, their kids are mostly going to private schools, so the equilibrium we are in has both the Smiths and the Joneses choosing this option. The question is, is this the only equilibrium?

Smiths\Joneses Public Private
Public (A,A) (L,H)
Private (H,L) (B,B)

For the aforementioned equilibrium to hold, we require that B>L. Note that I don’t set H=B (though it might be), since it’s possible that private schools aren’t quite as good if there are not as many wealthy people attending; for example, they have the same fixed costs to pay for on less income from tuition, which may make it more difficult to maintain a higher quality.

We can say some more things about this. Given that schools are worse off when the wealthier students leave, we would expect this trend to hold even when only some of them leave. Thus we can stipulate that L<H. This means that everything comes down to H – if it is higher than $A$, then the families have a dominant strategy to send their kids to private school. But if not, then (Public, Public) is also an equilibrium. Thus it might be possible to “shock” the system to get the parents to send their kids to public school instead. I’m no education policy expert, so I don’t have any suggestions as to how to execute this, or whether it’s even desirable: perhaps we just want to pour our efforts into our students with the best chance of succeeding. But it’s a thought worth considering.

Note: This post was originally written in 2011, which is why the references are a little bit out of date, but the point is still valid.

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