Okun's Law is the empirical rule of thumb linking the business cycle to the labour market: when output runs below its potential, unemployment rises above its natural rate, roughly in proportion.
Output gap (AR-1): gap_t = ρ·gap_(t-1) + ε_t, ε_t ~ N(0, σ²)
Growth deviation: g_t = gap_t − gap_(t-1)
Real GDP growth: Y_t = g* + g_t (g* = 2.5% potential growth)
Okun's Law (gap): U_t = U* − c·gap_t
Each simulated quarter, a random demand shock ε (controlled by σ) hits the economy; ρ sets how much of last quarter's gap persists — high ρ means long, sticky recessions and booms instead of noise that vanishes in one period. The Okun coefficient c (empirically ≈ 2 for the US) sets how strongly a 1-point output gap moves unemployment in the opposite direction: a positive gap (boom) pushes growth above potential and unemployment below U*; a negative gap (recession) does the reverse.
- Recession / Boom shock — injects a large one-off demand shock so you can watch the economy propagate and decay through the cycle.
- Bars — each column is one quarter: the left/green row is the GDP-growth deviation from potential, the right/red row is the unemployment gap. Because Okun's Law is a negative relationship, the two rows should move as mirror images of each other — that's the law visualised directly.
Real-world relevance: this "gap version" of Okun's Law is exactly what central banks and forecasters use for quick recession/unemployment sanity checks — e.g. "growth is running 2 points below potential, so expect unemployment roughly 1 point above natural" (with c ≈ 0.5 in the more common growth-rate formulation, or c ≈ 2 in this gap formulation).