Education Investments and Signaling

Estimating the returns to education:

Social returns versus private returns:

The signaling theory of education

The general idea is very simple. Suppose you have two types of workers, whose productivities are 1 and 2. Employers cannot distinguish the type-1 workers from the type-2 workers. So in the absence of signaling, they just pay everyone the expected marginal product, say, 1.5. Now assume that individuals can acquire education at a cost. For the sake of argument assume education cannot improve productivity whatsoever, and employers are aware of this. The crucial assumption for signaling to arise is the "single-crossing condition," which basically requires that it is less costly for the more productive types to acquire education. One can think of the type-2 workers are being smarter so that taking exams or listening to lectures is less painful to them. Let's say the cost of each year of schooling is 0.2 for the type-2 workers and 0.5 for the type-1 workers. A "separating equilibrium" occurs when all type-2 workers take 2 years of schooling and all type-1 workers take 0 year. Employers correctly infer that all those with 2 years of schooling are more productive, and they pay them 2 dollars. People with no schooling are less productive, and they receive 1 dollar. Type-2 workers (who receive 2 and pay a schooling cost of 0.4) cannot improve their wellbeing by skipping school. Similarly, type-1 workers (who receive 1 and pay no cost) cannot improve their net earnings by going to school for 2 years (which will yield 2 dollars in wages but will cost them 1 dollar). Obviously the implications of the signaling model of education and the human capital model are very different. Even though both models suggest a positive private return to education, the signaling model suggests that the social returns are lower than the private returns.

To understand this model more formally, let us consider a more general formulation of the problem. Let

C = C(n,z)
where C is the cost of acquiring z years of education and n is ability.

We assume ∂C/∂n < 0, ∂C/∂z > 0. Most importantly we assume

2C/∂n∂z < 0
It says that the marginal cost of education (∂C/∂z) is smaller for people with higher ability (n).

Let's also assume that productivity M is an increasing function in ability and in education level (that is, education is not completely unproductive). We write M = M(n,z). Assume that ∂M/∂n > 0 and ∂M/∂z > 0.

Employers cannot observe workers' ability (at least in the beginning), but they can observe their education level. Let W(z) be the wage paid to workers with education level z. Workers maximize

L = W(z) - C(n,z)

Individuals take the market wage schedule W(z) as given. They choose education level z*(n) to maximize discounted lifetime income L. This is the first equilibrium condition.

The first-order condition for maximization imply that the equilibrium education level z*(n) satisfies

dW(z*(n))/dz = ∂C(n,z*(n))/∂z

If an increase in ability shifts down the marginal cost of education (∂2C/∂n∂z < 0), then the equilibrium level of education z*(n) will be an increasing function of n. So employers expectation that more able workers will get more education will be justified in equilibrium.

Employers do not systematically overestimate or underestimate worker productivity. So in equilibrium we must also have

W(z*(n)) = M(n,z*(n))

By differentiating the informational consistency requirement, we get

dW(z*(n))/dz dz*(n)/dn = ∂M(n,z*(n))/∂n + ∂M(n,z*(n))/∂z dz*(n)/dn
Since ∂M/∂n > 0 and since dz*(n)/dn > 0, we conclude that that
dW(z*(n))/dz > ∂M(n,z*(n))/∂z
which implies that in equilibrium, the private returns to education (dW/dz) exceeds the social returns (∂M/∂z). In other words, signaling considerations lead to "excessive" investments in education.

While signaling is a consistent model of education, is it a reasonable model?

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