Education as a signal

A signal is a costly, observable action whose cost differs across people and so reveals a trait others cannot observe. In Spence’s model of the labour market, education does not raise productivity at all: able workers acquire it because it is cheaper for them, and employers pay more for it because it identifies them.¹ Education separates workers only if it is costly and its cost differs by ability; otherwise workers pool and everyone is paid the average.

The intuition

An employer hiring a new graduate cannot observe how productive she will be. It can observe whether she finished a demanding program. If finishing takes less effort, or less time, for able and persistent people, then only they will find it worth finishing, and the credential tells the employer who they are even if nothing taught in the program matters for the job. Pay then rises with education for a reason that has nothing to do with skills learned in school. This is the alternative to the human capital view, in which schooling pays because it raises productivity.

Spence’s model

Assumptions:

• There are two types of worker. Low-productivity workers produce $250,000 over a career and high-productivity workers $350,000 (present values). Employers cannot observe a worker’s type.
• Education, measured in years $y$, does not change productivity.
• A year of education costs a low type $40,000 ($c_L$) and a high type $20,000 ($c_H$), in effort, tuition and time.
• Employers are competitive and pay $350,000 to anyone with at least $\bar{y}$ years of education and $250,000 to everyone else.

Each worker chooses either no education or exactly $\bar{y}$ years: any amount between zero and $\bar{y}$ costs something without raising pay, and any amount above $\bar{y}$ costs more for the same pay. A low type skips the credential when its cost exceeds the $100,000 raise, and a high type gets it when its cost does not:

$$40\,\bar{y} > 100 \;\Rightarrow\; \bar{y} > 2.5, \qquad 20\,\bar{y} \le 100 \;\Rightarrow\; \bar{y} \le 5 \quad(\text{thousands of dollars}).$$

In general, with a raise of $w_H - w_L$, a separating equilibrium, in which only high types acquire the credential and each type is paid its productivity, requires

$$\frac{w_H - w_L}{c_L} < \bar{y} \le \frac{w_H - w_L}{c_H}.$$

This band exists only if $c_L > c_H$. If education were free, everyone would get it; if it cost both types the same, low types would clear any threshold that high types clear. Employers’ beliefs are then confirmed: everyone with $\bar{y}$ years is in fact a high type.

Credential threshold ȳ (years)

3.50

Low type's net gain from getting ȳ: 100 − 40ȳ

−$40k

High type's net gain from getting ȳ: 100 − 20ȳ

$30k

Open in Graph Lab

Figure 1. Pay jumps from $250,000 to $350,000 at the credential threshold $\bar{y}$; the red and purple lines are the costs of education for low and high types. At $\bar{y} = 3.5$ low types would pay $140,000 for a $100,000 raise and high types $70,000, so only high types get the credential; any threshold in the shaded band, above 2.5 and up to 5 years, separates the types.

Pooling

In a pooling equilibrium both types make the same education choice, so education reveals nothing and employers pay everyone the average productivity of the pool. With a share $q$ of high types, the pooling wage is

$$\bar{w} = q \times 350 + (1 - q) \times 250 = 250 + 100\,q \quad(\text{thousands of dollars}).$$

Separation helps high types only if their pay net of the credential’s cost beats the pooling wage, $350 - 20\bar{y} > 250 + 100q$. Low types always lose from separation, falling from $\bar{w}$ to 250.

Credential threshold ȳ (years)

3.50

Share of high-productivity workers (q)

0.40

Pooling wage w̄ = 250 + 100q, everyone

$290k

High type, separating, net of 20ȳ

$280k

Low type, separating

$250k

Resources spent on signals per worker, 20ȳq

$28.0k

Open in Graph Lab

Figure 2. Pay net of education costs by the share $q$ of high-productivity workers: pooling pays everyone $\bar{w} = 250 + 100q$, while separation pays low types $250,000 and high types $350,000 minus the cost of the credential. With $\bar{y} = 3.5$, high types gain from separation only if $q$ is below 0.3, and low types always lose.

Because education produces nothing in this model, separation does not raise total output. It redistributes pay toward high types and uses up resources on the signal: the smallest separating threshold, just above 2.5 years, wastes least.

Key idea

A signal works only if it is costly and cheaper for the able. Then pay rises with education even if school teaches nothing useful, and the earnings-schooling correlation cannot by itself tell signalling from human capital.

Worked example

Use the model above, with 40 percent high types.

1. Value of the credential. It raises pay from $250,000 to $350,000, a gain of $100,000.

2. Low types. At $\bar{y} = 3.5$ the credential costs $40{,}000 \times 3.5 = 140{,}000$ dollars, more than the gain, so low types choose no education and earn $250,000.

3. High types. The credential costs them $20{,}000 \times 3.5 = 70{,}000$ dollars, less than the gain, so they get it: $350,000 gross, $280,000 net.

4. Check the band. $100/40 = 2.5$ and $100/20 = 5$, so any $\bar{y}$ above 2.5 and up to 5 years separates; 3.5 qualifies.

5. Compare with pooling. Pooling pays $0.4 \times 350 + 0.6 \times 250 = 290$ thousand dollars to everyone. Under separation high types net $280,000 and low types $250,000, so both are worse off. Output is the same in both cases, and separation burns $0.4 \times 70{,}000 = 28{,}000$ dollars per worker on credentials.

Testing signalling against human capital

Both models predict that more educated workers earn more, so the raw correlation cannot separate them. Two tests can.

Sheepskin effects. If schooling only built skills, the year that completes a diploma would pay about the same as any other year. A sheepskin effect is an extra jump in earnings at the year that completes a credential. With data recording actual degree receipt, Jaeger and Page found that estimated sheepskin effects for high school and college degrees in the United States are noticeably larger than estimates based on years of schooling alone.² In Canada, Ferrer and Riddell found substantial credential effects for high school, community college or trade school, and university, accounting for about 30 percent of the return to 16 years of schooling.³ Sheepskin effects fit signalling but do not prove it: finishing may mark persistence, or the final year may teach the most valuable material.

Diploma bonus (log points)

0.12

Return to an ordinary year

6.0%

Return to the year that completes a credential

18.0%

Sheepskin effect

12.0%

Open in Graph Lab

Figure 3. Log wages when an ordinary year of school adds 6 percent and completing a high school diploma (12 years) or a bachelor's degree (16 years) adds a further 12 percent. With no credential effect the profile would be the straight dashed line; the jumps are sheepskin effects.

The GED. The General Educational Development credential lets American high school dropouts earn a high school equivalency by passing a battery of tests, and each state sets its own passing standard. Two dropouts with the same scores, and so similar skills, can end up one with the credential and one without, depending on their state. Tyler, Murnane and Willett used this to measure the credential’s signalling value from the 1995 earnings of dropouts aged 16 to 21 who took the tests in 1990.⁴ One of their comparisons sets New York and Florida, which required a higher minimum score, against a group of states that required a lower one:

1995 earnings, white dropouts	Low-standard states	New York and Florida	Difference
Low scorers (a GED only in low-standard states)	$9,628	$7,849	$1,779
High scorers (a GED everywhere)	$9,981	$9,676	$305
Difference-in-differences			$1,474

The first row mixes the effect of the GED with any difference between the two groups of states. High scorers hold a GED everywhere, so the second row measures the state difference alone. Subtracting it leaves about $1,474 a year ($1,473 in the paper, from unrounded means), roughly 19 percent of the comparison group’s earnings. Across their comparisons the GED raised the earnings of young white dropouts by 10 to 19 percent; they found no statistically significant effect for nonwhite dropouts. Low scorers acquired little further education, so the estimate mainly captures the credential’s signalling value. Since 2024 the GED has been replaced in Canada by the Canadian Adult Education Credential, which is also earned by passing tests in reading, writing, mathematics, science and social studies.⁵

Private and social returns

The private rate of return is the percentage increase in a person’s earnings from another year of schooling. The social rate of return is the percentage increase in national income, net of all costs including public spending on schools.

If education is a pure signal, the private return can be large while the social return is zero or negative: the credential redistributes pay without raising output, and the resources spent acquiring it are lost. Public funding of education would then subsidise sorting. Sorting can still have social value if it places able workers in the jobs where ability matters most, such as surgery or air traffic control.

The social return can also exceed the private return. Moretti found that a one-point rise in a city’s share of college graduates raises the wages of high school dropouts by 1.9 percent and of high school graduates by 1.6 percent.⁶ Lochner and Moretti found that schooling reduces crime, with savings from male high school graduation worth 14 to 26 percent of its private return.⁷ Doctors and engineers clearly learn valuable skills in school, while credentials from demanding programs also signal ability; both models are probably partly right.

Common mistakes

Traps on exams

• Requiring only that education be costly. Separation also needs the cost to differ by ability, $c_L > c_H$.
• Reversing the inequalities. Low types must find the credential not worth it ($c_L\bar{y} > w_H - w_L$); high types must find it worth it ($c_H\bar{y} \le w_H - w_L$).
• Saying pay differs by education in a pooling equilibrium. Everyone makes the same choice and earns the average.
• Stopping at the first difference. In the GED study, the raw gap of $1,779 credits the GED with differences between states.
• Treating sheepskin effects as proof of signalling.

On the exam

Draw the wage schedule as a step at $\bar{y}$ and the two cost lines from the origin, the low type’s steeper. Compare, for each type, pay minus cost at $y = 0$ and at $y = \bar{y}$, and state the band of thresholds that separates.

Check yourself

1.

Which conditions are needed for a separating equilibrium in the signalling model?

1Education must be costly, and a year of it must cost high-productivity workers less than low-productivity workers2Education must raise the productivity of high-ability workers more than that of low-ability workers3Education must be free, so that every worker can afford to signal4Employers must be able to observe each worker's productivity before hiring

Check answer

2.

High-productivity workers are worth $350,000 and low-productivity workers $250,000, and 40 percent of workers are high-productivity. In a separating equilibrium high types acquire a credential of $\bar{y} = 3.5$ years at $20,000 a year. Compared with a pooling equilibrium in which nobody invests, who gains from separation?

Credential threshold ȳ (years)

3.50

Share of high-productivity workers (q)

0.40

Pooling wage w̄ = 250 + 100q, everyone

$290k

High type, separating, net of 20ȳ

$280k

Low type, separating

$250k

Resources spent on signals per worker, 20ȳq

$28.0k

1Neither type: high types net $280,000 instead of $290,000, and low types fall from $290,000 to $250,0002High types only, because they are paid their full productivity of $350,0003Both types, because sorting raises total output4Low types only, because they no longer pay for education

Check answer

3.

In the GED study, why subtract the earnings gap between low-standard and high-standard states among high scorers?

1High scorers hold a GED in every state, so their gap measures differences between the states' labour markets, which would otherwise be credited to the GED2High scorers have more education, so subtracting them removes ability bias among low scorers3High scorers are the treatment group, so their gap is the effect of the GED4It converts the earnings gap from dollars into percentages

Check answer

Practise more questions on this topic

Sources

1. Spence, M. (1973). Job market signaling. Quarterly Journal of Economics, 87(3), 355 to 374. ↩

2. Jaeger, D. A. and M. E. Page (1996). Degrees matter: New evidence on sheepskin effects in the returns to education. Review of Economics and Statistics, 78(4), 733 to 740. ↩

3. Ferrer, A. M. and W. C. Riddell (2002). The role of credentials in the Canadian labour market. Canadian Journal of Economics, 35(4), 879 to 905. ↩

4. Tyler, J. H., R. J. Murnane and J. B. Willett (2000). Estimating the labor market signaling value of the GED. Quarterly Journal of Economics, 115(2), 431 to 468. The table is from Table 6 of the working paper version, NBER working paper 6391. ↩

5. Government of Alberta, Canadian Adult Education Credential. ↩

6. Moretti, E. (2004). Estimating the social return to higher education: Evidence from longitudinal and repeated cross-sectional data. Journal of Econometrics, 121(1–2), 175 to 212. ↩

7. Lochner, L. and E. Moretti (2004). The effect of education on crime: Evidence from prison inmates, arrests, and self-reports. American Economic Review, 94(1), 155 to 189. ↩