Human capital model

The foundation of the drive to increase educational attainment across the board is the human capital model of education, which began with the research of Gary Becker.^[2] The model suggests that increasing educational attainment causes increased prosperity by endowing students with increased skills. As a consequence, subsidies to education are seen as a positive investment that increases economic growth and creates spillover effects by improving civic engagement, happiness, health, etc.

Present value of learning, adjusted for forgetting

The simple human capital model tends to assume that knowledge is retained indefinitely, while a ubiquitous theme in educational interventions is that "fadeout" (i.e., forgetting) reliably occurs.^[3] To take a simple example, we may compute the present value of a marginal fact ${\displaystyle F}$ that increases a person's productivity by ${\displaystyle V}$ as:

$${\displaystyle PV(F)=\int _{0}^{\infty }e^{-rt}Vdt={V \over {r}}}$$

where ${\displaystyle r}$ is the discount rate used to compute the present value. If ${\displaystyle V}$is $100 and ${\displaystyle r}$ is 5%, then the present value of learning ${\displaystyle F}$ is $2,000. But this is at odds with the concept of fadeout. To correct for this, assume that the probability density function for retaining ${\displaystyle F}$ follows an exponential distribution—with the corresponding survival function ${\displaystyle S(t)=e^{-\lambda t}}$. Then the present value of learning ${\displaystyle F}$, accounting for fadeout, is given by:

$${\displaystyle PV(F)=\int _{0}^{\infty }e^{-rt}S(t)Vdt=\int _{0}^{\infty }e^{-(r+\lambda )t}Vdt={V \over {r+\lambda }}}$$

Since the expected value of an exponential distribution is ${\displaystyle \lambda ^{-1}}$, we may tune this parameter based on assumptions about how long ${\displaystyle F}$ is retained. Below is a table showing what the present value is based on and the expected retention time of the fact:

Present Value of Learning ${\displaystyle F}$, with Fadeout

3 Months	6 Months	1 Year	2 Years	3 Years	5 Years	10 Years
$24.69	$48.78	$95.24	$181.82	$260.87	$400.00	$666.67

Regardless of the retention time assumption, the present value of learning ${\displaystyle F}$ is significantly reduced.

Signaling model

The main alternative to the human capital model of education is the signaling model of education. The idea of job market signaling through educational attainment goes back to the work of Michael Spence.^[4] The model Spence developed suggested that, even if a student did not gain any skills through an educational program, the program can still be useful so long as the signal from completing the program is correlated with traits that predict job performance.

Throughout the book, Caplan details a series of observations that suggest a significant role for signaling in the return to education:

• Intelligence^[5][6][7] and conscientiousness^[8] are known predictors of educational and occupational success, and are relatively stable^[9][10] throughout a person's life
• International estimates of the effect of an additional year of education on national income are much lower than those estimating the impact of an additional year of education on personal income^[11] (p. 114-118^[1])
• Many students forget material over the summer and after the end of a class (p. 39-40^[1])
  • Adults tend to forget much of the information they learned in school (p. 39-50^[1]). This builds on Caplan's earlier book The Myth of the Rational Voter.^[12]
• Students look to take courses that offer easy As, instead of more difficult courses
• The sheepskin effect seems to be fairly large (p. 97-102^[1])
• Transfer of learning to other disciplines appears to be low or nonexistent (p. 50-59^[1])

Given the above signs of signaling, Caplan argues in ch. 5–6^[1] that the selfish return to education is greater than the social return to education, suggesting that greater educational attainment creates a negative externality (p. 198^[1]). In other words, status is zero-sum; skill is not (p. 229^[1]).

Cost-benefit analysis of going to college

For many students, Caplan argues that most of the negative social return to pursuing further education comes from the incursion of student debt and lost employment opportunities for students who are unlikely to complete college (p. 210-211, ch. 8^[1]). He suggests that these students would be better served by vocational education.

Positive

• Robin Hanson at Overcoming Bias^[17]
• Naomi Schaefer Riley in The Wall Street Journal^[18]
• Gene Epstein in City Journal^[19]

Mixed

• Stephen L. Carter in Bloomberg Opinion^[20]
  • "I'm not sure he's right, especially about education being almost entirely for the purpose of signaling, but goodness does he make a strong case. Agree with him or not, you'll never look at the schools and colleges in quite the same way."
• Tyler Cowen in Marginal Revolution^[21]
• Ilya Somin at Reason^[22]

Negative

• Sarah Carr in The Washington Post^[23]
• Sean Illing at Vox^[24]
• Joshua Kim at Inside Higher Ed^[25]