The Medium Run & Labour Market

Labour-Market Flows & Steady-State Unemployment

extensionExam · low

The unemployment rate is determined in steady state by the balance of inflows (job separations) and outflows (job findings). With separation rate s and job-finding rate f, steady-state u = s/(s+f). Countries with high separation or low finding rates (Europe) have higher u than countries with low separation and high finding (US). Structural policies target s and f — not just the natural-rate formula.

Derivation

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Stocks and Flows

At any moment, the labour force is $L = N + U$ (employed + unemployed). Each period:

\text{separations: } s \cdot N \quad \text{hires: } f \cdot U

Steady State

Balance of flows gives the unemployment rate:

s \cdot N = f \cdot U \iff u = \frac{U}{L} = \frac{s}{s + f}

Average unemployment duration is $1/f$ . US unemployed find jobs in ~3 months ( $f \approx 0.3$ /month); EU unemployed take 6+ months ( $f \approx 0.15$ /month).

Cross-Country Patterns

| Country | $s$ (monthly) | $f$ (monthly) | Steady-state $u$ | |---------|---------------|---------------|-------------------| | US | ~2% | ~30% | ~6% | | EU (avg) | ~1% | ~10% | ~9% |

Europe's higher $u$ is driven mostly by lower $f$ — long durations rather than high turnover.

The Beveridge Curve

Plotting $u$ against $v$ (vacancy rate) gives a downward-sloping curve. Outward shifts signal matching-efficiency deterioration:

2008–12 US: curve shifted out (housing-tied workers stuck, skill mismatch).
Post-COVID: curve shifted out again as industries reshuffled.

Policy Levers

Activation (training, job-search requirements) raises $f$ .
Employment-protection legislation (↑ EPL) lowers $s$ and $f$ — ambiguous on $u$ , but raises duration.
Unemployment insurance (↑ generosity $z$ ): lowers $f$ (longer search) but may increase match quality.

Worked Example

Labour force L = 1000. Separation rate s = 0.02/month. Job-finding rate f = 0.30/month.

Steady-state u = s/(s+f) = 0.02/0.32 = 6.25%.
U = 62.5 workers, N = 937.5.
Check flows: Job losses = sN = 0.02 × 937.5 = 18.75; Hires = fU = 0.30 × 62.5 = 18.75. ✓
Average duration = 1/f = 1/0.30 ≈ 3.3 months.

Steady-state u = 6.25%, with average unemployment spells of ~3.3 months. 18.75 workers flow between employment and unemployment each month in each direction.

Common Mistakes

—Treating s and f as fixed — they vary with the business cycle and with structural policy.
—Using u = s − f instead of u = s/(s+f).
—Equating high u with high separation rates — often it is low f that explains the difference.
—Ignoring the Beveridge curve: u can rise without ↑s if v falls (recessionary demand).

Exam Cues

→Steady-state formula: u = s/(s+f).
→Duration formula: 1/f.
→Cross-country: high Euro u driven mostly by low f (long spells).
→Beveridge curve shifts: outward → matching has worsened (skills, geography, UI).