From Short to Medium Run (IS-LM-PC)

Okun's Law

coreExam · medium

Okun's law is an empirical regularity linking output growth to changes in unemployment. Theoretical form: u − u₋₁ ≈ −g_y. Empirical (US): u − u₋₁ = −0.4(g_y − 3%). Two slippages: normal growth ≠ 0 because of labour-force and productivity growth; coefficient < 1 because of labour hoarding.

Derivation

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Two Forms of Okun's Law

Okun's law appears in two related forms. The growth form links changes in unemployment to output growth:

u_t - u_{t-1} \approx -g_{y,t} \quad \text{(theoretical)}

u_t - u_{t-1} = -0.4(g_{y,t} - 3\%) \quad \text{(empirical, US)}

The level form appears in the IS-LM-PC model:

Y - Y_n = -L(u - u_n)

Why the Coefficient Is Less Than 1

The theoretical coefficient is 1 (one worker = one unit of output). The empirical coefficient is ~0.4 because of labour hoarding and discouragement. Firms keep workers during short slowdowns; during deep downturns, some workers leave the labour force entirely.

The Normal-Growth Threshold

The 3% intercept in the US reflects structural growth drivers:

| Source | Typical contribution | |--------|---------------------| | Labour-force growth | ~1% | | Productivity growth | ~1.5–2% | | Other (capital deepening) | ~0.5% |

Only growth above ~3% actually lowers unemployment.

Role in IS-LM-PC

Okun's law is the bridge between the goods market (output gap) and the Phillips curve (inflation):

IS curve: Y depends on r
Okun: Y − Y_n translates to u − u_n
Phillips: $\pi - \pi_{-1} = -\alpha(u - u_n) = (\alpha/L)(Y - Y_n)$

Worked Example

US output grew at 4.5% last year. Baseline Okun: u_t − u_{t-1} = −0.4(g_y − 3%). (a) Predict the change in u. (b) Now suppose potential growth rose to 4%. Predict Δu.

(a) Δu = −0.4(4.5% − 3%) = −0.4 × 1.5% = −0.6 pp. Unemployment falls 0.6 pp.
(b) With 4% normal growth: Δu = −0.4(4.5% − 4%) = −0.4 × 0.5% = −0.2 pp. Smaller drop — less excess growth.

(a) Δu = −0.6 pp. (b) Δu = −0.2 pp. Higher normal growth → same g_y produces less unemployment reduction.

Common Mistakes

—Using the coefficient 1 instead of 0.4 — the empirical relation is not one-for-one.
—Forgetting the 3% normal-growth threshold: g_y = 2% produces Δu = −0.4(2% − 3%) = +0.4 pp (u rises).
—Mixing the level form (Y − Yn = −L(u − un)) with the growth form — related but distinct.
—Assuming the coefficient 0.4 is universal — it varies by country (EU closer to 0.2–0.3).

Exam Cues

→Know both forms: growth (Δu = −a(g_y − ĝ)) and level (Y − Yn = −L(u − un)).
→Δu = −0.4(X% − 3%) is the workhorse prediction formula.
→In IS-LM-PC: level form translates output gap to unemployment gap, then Δπ via Phillips.
→Labour hoarding + discouragement explain the sub-1 coefficient.