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||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 it’s 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?