Signaling and Screening: Labor Market

When employers cannot observe productivity, equilibria arise in which agents strategically convey information through "costly signals." The Spence model is a classic example of equilibrium signaling, demonstrating that education can be valuable not as human capital, but as a pure signal of ability.

Spence Signaling Model (1973)

Structure: Two types of workers: H (productivity θ_H) and L (θ_L < θ_H). The employer does not know the type. The worker chooses the level of education e. Payment = E[θ|e] (expected productivity given observable e). Education costs: c_H(e) = e/θ_H < c_L(e) = e/θ_L. The key condition: education is cheaper for type H—"single-crossing condition."

Separating equilibrium: H chooses e*, L chooses 0. Self-selection conditions: H is rational — θ_H − e*/θ_H ≥ θ_L (profit from signal ≥ zero-choice). L does not imitate — θ_L ≥ θ_H − e*/θ_L. Range: e* ∈ [θ_L(θ_H − θ_L), θ_H(θ_H − θ_L)].

Intuitive Criterion (Cho & Kreps, 1987): Eliminates "excess" equilibria. If e' > e*, only H can rationally deviate (L never benefits). The employer, upon observing e', should believe this is H → best response: pay θ_H → L does not benefit from imitation at e' → equilibrium with e* = θ_L(θ_H − θ_L) (minimum separating signal).

Pooling equilibrium: Both choose e = 0, the employer pays E[θ] = λθ_H + (1−λ)θ_L. Stable when: θ_H − e/θ_H < E[θ] for all small e (H does not want to signal).

Screening via Contract Menu

Alternative: The employer first offers a menu (eⱼ, wⱼ). Self-selection conditions: IC_H: w_H − e_H/θ_H ≥ w_L − e_L/θ_H. IC_L: w_L − e_L/θ_L ≥ w_H − e_H/θ_L. IR_H: w_H − e_H/θ_H ≥ 0. IR_L: w_L − e_L/θ_L ≥ 0.

Screening optimum: IR_L and IC_H are binding. e_L* = e_L^{FB} (undistorted for low type). e_H > e_H^{FB} (education for H is exaggerated). Information rent for H: IR_H not binding → H receives extra. To reduce the rent, e_H is distorted upward.

Human Capital vs Signaling

Theoretical predictions: Human capital: education increases productivity → linear relation between salary and education. Signaling: education does not increase productivity → value of diploma (sheepskin effect).

Sheepskin Effect Test: A worker with e = 4 (diploma) earns significantly more than a worker with e = 3.9 (dropout). This "diploma effect" (≈5–10% premium for the final year) is incompatible with pure human capital accumulation, but compatible with signaling—diploma = signal of completeness, perseverance.

Quantitative assessment (Lam & Schoeni, 1993; Caplan, 2018): according to various estimates, 50–80% of the return to education is signaling, 20–50% is real human capital. If so—education subsidies create an "arms race": everyone spends more on education, equilibrium shifts upward, but no one wins (Caplan: education is "waste").

Numerical Example

θ_H = 2, θ_L = 1, λ = 0.5 (share of H). Range of separating equilibria: e* ∈ [1·(2−1), 2·(2−1)] = [1, 2]. The Intuitive criterion selects e* = 1.

At e* = 1: H spends e*/θ_H = 1/2 = 0.5 on education, receives θ_H = 2. Net gain = 2 − 0.5 = 1.5. L: e = 0, receives θ_L = 1. Net gain = 1.

Alternative: no signal. Mixed salary = 0.5·2 + 0.5·1 = 1.5. H gain = 1.5 (not 2), L gain = 1.5 (more than 1!). Redistribution from H to L.

"Signaling losses": education expenses of H = e*/θ_H = 0.5, as a fraction of θ_H = 25%. Social losses: 0.5·λ = 0.25 per person (resources spent on unproductive education).

Exercise: θ_H = 3, θ_L = 1, λ = 0.4. (1) Find the range of separating equilibria. (2) Find the equilibrium according to the Intuitive criterion. (3) Calculate "signaling losses"—education expenses of H as a fraction of θ_H. (4) Find the optimal screening contract (eH*, wH*, eL*, wL*) in the screening equilibrium. (5) Compare: for what λ is signaling better for society?