Abstract
I consider educational signaling of inherent ability that facilitates sorting of individuals between sectors. More able individuals are more productive in the primary sector, and less able individuals are more productive in the secondary sector. I find signaling may increase but never maximizes welfare, and is more likely to increase welfare the greater is productivity in the secondary sector, and, possibly, the lower is productivity in the primary sector. Consistent with recent increased undergraduate enrollment in the U.S, excessive signaling occurs by less able individuals. If education increases human capital, total welfare likely increases although more individuals may over-invest in education.
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Notes
In a new book, The Case Against Education (2018), Caplan argues that 80% of the effect of education is signaling.
Becker (1993, p.8).
At least one National Football League team, the Eagles under coach Chip Kelly, asked potential draftees many questions about their college academics (why a player chose his major, what was his hardest class, etc.). The team believed that college graduation is more than proof of intelligence, and is a signal that an individual is committed to achieving goals (Clark 2014).
Some claim evidence of fairly rapid employer learning of skills implies a low value of educational signaling (Altonji and Pierret 1998; Lange 2007). However, Habermalz (2011) shows such a conclusion is unwarranted. Habermalz demonstrates that signaling is not necessary with very rapid employer learning. With very slow employer learning, signaling would not likely be worthwhile due to the short period for which ability would be revealed. With an intermediate length of employer learning, the value of the signal increases with the speed of learning. Estimated returns to education are consistent with theoretical results that imply that signaling occurs. Waldman (2016) combines educational signaling with signaling to other firms by promotion decisions. He argues that studies such as that by Lange (2007) underestimate the returns to signaling because of the assumption such returns are low late in an employee’s work life. Waldman finds that educational signaling has potential returns later in individuals’ careers when there is asymmetric learning (other firms know less about productivity of a worker than does the worker’s employer) and promotion signaling. For simplicity, I ignore different jobs at the same employer.
Source: US Bureau of the Census Current Population Reports.
The Region (1995, p. 8).
With a continuum of ability and a continuous signal, all but the least able over-invest in education when it is only a signal and there is no sorting gain from education (Riley 2001). Such a model requires all to invest more in education if, say, the difference in education costs between ability levels is reduced. It is hard to reconcile that result with the large recent increase in enrollment in the U.S., which suggests that only some individuals have increased the level of their educational signal.
In a reactive equilibrium, agents consider possible reactions by other agents before the former take actions.
Wolpin (1977) considers the use of signaling (more precisely, screening) by firms to reduce misallocation between and within firms in a model in which a larger variance in skill of labor inputs reduces expected output. He argues too much or too little screening could occur. There is only one occupation in his model, so there is no gain from assigning individuals to different types of jobs. An individual is equally valuable at any firm, given the skill variance at that firm.
For example, a man who signals imposes a negative externality on lower quality men since the latter have one less high quality woman with whom to match. Conversely, a man who signals presents a positive externality for women by his presence.
Typically, when individuals incur cost to identify themselves it is called signaling. Firms incurring such cost is called screening.
Waldman (2016) has a model that is similar to mine in that there is one education level, there are two wages (for those with and without education, the former hired in the primary sector, and the latter in the secondary sector in my model), signaling cost is inversely related to ability, and too much signaling occurs by those who are less able. Waldman is interested in how signaling affects job assignment when said assignment is a signal to alternative employers of individual ability, and when education is directly productive. In particular, in his model, educational signaling reduces the distortion in the promotion decision when promotion is also a signal. I assume no promotions, and that education is generally not directly productive. I am concerned with the welfare effects of signaling which depend on in which sector individuals would be if educational signaling did not occur.
One criticism of signaling models is the assumption that signaling cost and ability are inversely related (Weis 1983; Regev 2012). I believe such an assumption is reasonable. More able individuals require less effort to obtain a given level of education. Also, less study time required for the more able to obtain education implies lower foregone earnings for them. In a paper that assumes education simply increases human capital, Becker et al. (2010) focus on what they consider nontraditional costs of college such as the difficulty involved. They emphasize the variation in these costs across individuals, and argue that individuals with greater ability have lower costs of schooling.
Other equilibria are possible. For example, if all are in the secondary sector, those with the highest ability have an incentive to deviate from this equilibrium, provided primary sector firms have out-of-equilibrium beliefs that the most able would be the most likely to deviate from the old equilibrium. Those with x = xmax who applied to the primary sector without signaling would then be paid vxmax, which exceeds ω. However, if primary sector firms offered a wage of vxmax to all who applied, then all would apply, and the new equilibrium would not be stable.
Suppose individuals incorrectly estimate the number who would signal, and thereby understate or overstate what the wage would be in the primary sector. Depending on the direction of the estimation error, welfare could be higher or lower than with no error. For analysis of when individuals misjudge what wages or prices will be, see Akerlof and Tong (2013), Akerlof and Shiller (2015), and Perri (2016).
Bickhchandani et al. (2013) consider a model with a primary job and an outside opportunity that pays more than the expected productivity of individuals in the primary job. They assume two types of individuals and a continuous signal so, as is usually the case, any excessive investment in education is by the more able. I consider a continuum of types and a discrete signal.
Interestingly, although the output gain from signaling in this case is from moving less able individuals from the primary sector to the secondary sector, the condition for welfare to be improved via signaling depends on the difference between average productivity in the two sectors.
With xmax = 1, C(1) = 0. This is not important. I could assume some additional fixed cost of signaling for all. As long as v−C(1) > ω, some will signal.
These cases are example 7 versus example 3, example 10 versus example 9, example 18 versus example 15, and example 19 versus example 16.
These cases are example 15 versus example 7, example 16 versus example 8, example 17 versus example 9, example 20 versus example 10, example 21 versus example 11, and example 22 versus example 12.
These are example 4 versus example 1, example 5 versus example 2, and example 6 versus example 3.
I find that \( \tilde{x}* > x* \) if \( z > \frac{\omega - c - v}{v} \). With v > ω, \( \tilde{x}* > x* \).
Similar results occur if the increase in productivity due to education is proportional to x. Note, from Eq. (12), if \( z > \frac{\omega + c}{v} \), \( \tilde{x}* = 0 \): all should and would invest in education.
Recent research offers differing views of the effect of education on productivity. Eble and Hu (2015) analyze educational reform in China that extended the length of primary school by 1 year. They find large signaling effects of education. More relevant for my model, which implicitly assumes further education implies a baccalaureate degree, Arteaga (2016) considers the leading Colombian university, which reduced the amount of coursework required for a degree in either economics or business. She finds that human capital accounts for essentially the entire return to education. In contrast, Caplan (2018) claims that 80% of the return to higher education in the U.S. is due to signaling. Finally, Bostwick (2016) considers whether field of study in college serves as a signal of ability. She finds that access to elite schools affects individuals’ choice of major at non-elite schools, which is consistent with signaling.
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Acknowledgements
I wish to thank the editor, Giacomo Corneo, and two anonymous referees for comments on previous versions of this paper.
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Appendix: Proof of Proposition 6 part A
Appendix: Proof of Proposition 6 part A
This is the case when all would be in the secondary sector absent signaling, so education only as a signal improves welfare. Intuitively, if education also is productive, welfare should be even greater. However, more over-invest in education when education is productive, so it remains to be shown that welfare does increase as education is more productive.
Again, let total welfare with signaling be denoted by Ω. Using Eq. (2), and adding the productivity effect of education, z:
Equation (A1) can be rewritten as:
However, x* is determined by:
Using Eqs. (A2), (A3) becomes:
Using Eq. (A4), differentiating Ω w.r.t. z:
With a greater return to investing in education as z increases, clearly \( \frac{\partial x*}{\partial z} < 0 \). Also, those with more ability, x, have lower education cost by assumption, so C (x*) > E(C|x ≥ x*),\( \frac{{\partial \left( {E\left( {C|x \ge x*} \right)} \right)}}{\partial x*} < 0 \), and \( \frac{{\partial \left( {C\left( {x*} \right)} \right)}}{\partial x*} < 0 \).
Thus the {•} term in Eq. (A5) is unambiguously negative and \( \frac{\partial \varOmega }{\partial z} > 0 \) if \( \left| {\frac{{\partial \left( {E\left( {C|x \ge x*} \right)} \right)}}{\partial x*}} \right| < \left| {\frac{{\partial \left( {C\left( {x*} \right)} \right)}}{\partial x*}} \right| \).
With the uniform distribution of x in the text, \( \frac{{\partial \left( {C\left( {x*} \right)} \right)}}{\partial x*} = - c \), and \( \frac{{\partial \left( {E\left( {C|x \ge x*} \right)} \right)}}{\partial x*} = - \frac{c}{2} \), so \( \frac{\partial \varOmega }{\partial z} > 0 \).
