I recently received this email from a self-styled “anti-school teacher.” Reprinted unchanged with permission of the author, Samuel Mosley.
Dear Professor Caplan,
My name is Samuel Mosley. I studied economics at Beloit College, my advisor was a former graduate student of yours, Laura Grube.
I recently read The Case Against Education and it explained so much of what I see. Like many new graduates who do not know exactly what they want to do but want to do something that helps people, I became a teacher right after college. I have spent the last year teaching math at a high school in Chicago. Observing how unlikely it was that the decisions we make increase our students human capital, I wondered how it could be of benefit to the students. Your book helped me answer that question.
I was swayed to believe that education is overfunded. I began to view every decision made by my boss with the question “is this to add to our students’ human capital or their signaling value?” Looking at the school from this framework, I have come to suspect that education is best understood as a game theory problem. Often, my bosses are faced with options where one option would be better for the students’ human capital and another would help the student send a more functional signal. The school I teach at invests time in signals (like AP Calculus) because it will enrich our students’ lives more than classes that would cultivate their human capital (like AP Statistics). Because every school can choose to signal, we arrive at a Nash Equilibrium where students at none of the schools acquire human capital and the decisions of schools’ to signal cancel each other out.
Assume schools can either set the average grade to B or C. Schools that set the average grade to C have higher standards so students from those schools graduate college at a higher rate. Assume also that college admissions officers do not have perfect information about the standards of each high school so they admit students from schools where a B is the the average grade more often than students from schools where a C is the average grade.
Now, say Theoryville College only admits students from Row High School and Column High School. There are only 1000 spots available. Students from Row and Column only apply to Theoryville. Both schools have 1000 seniors. Theoryville accepts students evenly if they both come from schools with similar standards. If one school chooses lower standards (B), 700 of their students will get in and 300 from the other school. 45 percent of students from low standards schools graduate college while 55 percent of students from high standards schools graduate. Assume the utility function for both high schools is the number of its students who complete college, with no penalty for having students go to college and leave degreeless in debt. So, the game matrix can be expressed:
C | B | |
C | 275, 275 | 135, 315 |
B | 315, 135 | 225, 225 |
This simple prisoners’ dilemma does not seem immediately relevant to the human capital vs. signaling debate and it does not address the question of whether or not college brings human capital. I choose college completion as the utility function for simplicity. Schools of standard C produce graduates who are more ready for college. Schools of standard B produce graduates who appear more college ready. Replace the idea of college readiness with “human capital,” and this becomes relevant. Signaling has become more profitable to schools, so they invest resources in signals when they could invest resources in human capital. This is a different claim from the one that schools cannot produce human capital. My time at this job has convinced me prisoners dilemmas like this one exist for course offering, course placement, pass rates and a number of other decisions schools face.
Do you think its at all likely that schools would be better human capital factories given an incentive structure that accounts for the game theory problem? Do you think game theory is a useful framework for this problem?
Sincerely,
Samuel Mosley
READER COMMENTS
Phil H
May 20 2019 at 9:39am
I like the question at the end: What sort of structure would work better?
Because there are absurdities in all systems. Demonstrating that absurdity exists within the current system does not constitute an argument against it; you also have to demonstrate that some other system would produce less harm and less absurdity. Bad teaching drives out good in this system; why should we think bad teaching would not drive out good in any other system?
Harry Robinson
May 20 2019 at 11:17am
Then we have to deal with the truth and quality of the knowledge being introduced. As I have found only by continuing my education is that the academic texts being offered by public education and I bet even to private and parochial schools, are providing less than a whole true and history of especially in the studies of economics and finance, the law and judiciary and such sociological issues as environmental and biological health studies.
We are even seeing these debates on a mass cultural level with a war on words currently ongoing between the larger hierarchic and commercial institutions and smaller less costly social and alternative media. The plethora of high-quality information on youtube as an example is impressive with studies and other evidence in involved. Whereas the mainstream media seldom even allows “Comments” on the writings and videos.
I like to use the word “contraindications” as the term to mean the negative ramifications of social policies. My favorite example for public education is Ad Volorum taxation; a/k/a property taxes, primarily used to fund public education in most States.
When poor people can’t afford to pay their property taxes, the Counties issue what are called Tax Deeds and sell them off to wealthier investors who pay the taxes. After two years of non-payment by the owners, the investors can start foreclosure proceeding against the homes because of them owning the tax deeds. It’s a pretty big business in many counties and of course, many primarily poor people lose their homes. During the Great Depression and Great Recession, even many middle class people loss their homes to this system.
So we are taking the homes away from poor and middle-class people to pay for education of the children of irresponsible parents who had children even though they knew they couldn’t afford to educate them.
My wife says the reason we must have social welfare is that women are too irresponsible to be parents and will have children knowing they’re poor and won’t be able to afford to raise them without social assistance. We do have a society where women get prenant on purpose because they then can then rely on others for money such as the father(s), parents, charities and government. To suggest that poorly educated women are having children they shouldn’t be, is deemed politically incorrect. It’s a co-dependency issue as well. For some women, their value to society is so low that without a child in their arms, they have little monetary value and therefore survival is more difficult.
This, of course, would be greatly improved for poorer women by eliminating the vast networks of corporate and social welfare dominating our socio-economic system that is causing the increased levels of poverty, low wages and fewer productive jobs. How do you teach that to the poorer women who keep voting for more social welfare?
Matthias Görgens
May 21 2019 at 3:44am
Lowering property taxes helps current land owners, but does nothing for people who are buying only after the tax has been decreased. That’s because land prices will just go up: what they save in taxes, they’ll pay in a higher mortgage.
Similarly, raising taxes on real estate is basically free for anyone but the current owner.
Many countries in Europe have big welfare systems and low birth rates.
Most poor countries have absolutely smaller welfare systems, and some of them have considerably higher birthrates.
Not sure if there’s a systematic relationship between welfare and birth rates. But if there is, it’s not obvious that more welfare leads to more births.
John Hall
May 20 2019 at 12:51pm
Wrt the prisoner’s dilemma, the problem is that GPA is such an arbitrary statistic, especially when different students take different classes (compare the average Engineer or Physics major’s GPA vs. a Liberal Arts major’s GPA).
Instead, I would recommend fitting something akin to an IRT, except to grades instead of test answers, in order to get an estimate of student quality. If the model is done across colleges (and maybe also take into account standardized test scores), then it would be a much better way to assess student quality without caring about GPAs.
Samuel Mosley
May 21 2019 at 6:15pm
I admit that this model is not sufficiently complex to explain everything we see. I intend to expand and generalize it.
To respond to your point on the model as it is:
If in the first round both Row and Column choose B, Theoryville perceives no difference between the two high schools as their students complete college at the same rate.
College completion rates are typically computed 4 or 6 years after the class begins college. Being fair to the argument that colleges will learn, let’s go with 4.
Suppose Theoryville wants to maximize its graduation rate when admitting its class of t by taking into account differences in high school quality. The admissions committee makes the decision in year t-4. The most recent class they have completion data on is the class of t-5. So, when admitting the first 5 classes, Theoryville does not know students from these high schools have different college graduation rates. Short sighted schools will still choose B.
Jeff G.
May 20 2019 at 1:44pm
Won’t the dilemma immediately break down once game is repeated? If Theoryville is trying to maximize it’s graduation rate, then next year it will select 100% of it’s students from the school(s) that chose ‘C’ in the prior period and we’ll jump to the stable equilibrium at (C,C).
Also, small correction. The (C,B) pay-off should be (315,165) and vis-versa.
Matthias Görgens
May 21 2019 at 3:46am
Yes, the model isn’t conplex enough to capture the dynamic we see in practice.
In practice, things are noisier, and there are lots of ways to fudge signalling on the margin.
Samuel Mosley
May 21 2019 at 7:15am
My apologies for a mathematical oversight. The (C,B) payoff should be (165,315) and vis versa. Thank you, Jeff G. for pointing this out.
Joseph e Munson
May 21 2019 at 1:39pm
I’ve found this knowledge of signaling a minor superpower.
They told me I couldn’t do financial services because I majored in English, but armed with signaling theory I actually make the explicit signaling case and get lots of a jobs (I’ve done (a relatively) hard thing X, so I’m likely to be able to do hard thing Y that you will pay me for). I have had great success with this line of reasoning in interviews.
It even seems to fit with normal peoples gut instinct, until you explain the ramifications of the signaling theory on education policy, at which point they become horrified.
I’ve also found that you can game the system a bit by being cross-cultural.
Most Americans assume having a masters degree in English Lit from the University Of Amsterdam means that one has to jump through tons of impressive signaling hoops when admission is actually pretty open to anyone with a BA in English from a research university that is deemed to be equal to an equivalent 3 year (Dutch bachelor’s degrees are 3 years) Dutch degree.
Nonetheless, the university is ranked highly and employers and immigration officials treat it with a very high amount of deference.
Teacher
May 23 2019 at 5:35pm
I believe teachers should be incentivised. There are many theories and researches to consider before implementing them. Bureaucracy kills inventions and proactiveness. It is a tight rope to walk.
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