Economic Forecasting Simulation — Phillips Curve & Adaptive Expectations

Policy & Shock Inputs

Target money growth μ 4.0%

Expectations speed λ 0.40

Demand volatility σ 0.60

Forecast horizon 8 periods

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Unemployment u

5.0%

Inflation π

2.0%

Expected π^e

2.0%

Forecast RMSE

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How it works

Each period, unemployment moves toward a level implied by Okun's law relative to real output growth g, and inflation is set by a Phillips curve with adaptively formed inflation expectations:

g_t   = g_{t-1} + 0.25(μ − g_{t-1}) + noise(σ)      demand growth drifts toward policy target μ
u_t   = u_n − 0.8·(g_t − g*)                        Okun's law (g* = potential growth, u_n = NAIRU)
π_t   = π^e_t − β·(u_t − u_n) + noise(σ/2)          Phillips curve, β = 0.5
π^e_{t+1} = π^e_t + λ·(π_t − π^e_t)                  adaptive expectations, 0 < λ ≤ 1

Each step the model also projects forward for the chosen horizon with the noise terms set to zero (its best forecast), forming the dashed cone ahead of the current point. When real (noisy) time catches up to a period that was once forecast, the squared error between the forecast and the realized inflation is folded into the running RMSE — a direct measure of how good the model's own forecasts turned out to be.

μ (money growth) — the policy lever; raising it pushes demand growth, and eventually inflation, higher.
λ (expectations speed) — how fast expected inflation chases realized inflation. Low λ = "sticky" expectations, sluggish disinflation. High λ ≈ adaptive-expectations classic ratchet.
σ (demand volatility) — the size of random demand/supply shocks each period; higher σ widens the forecast confidence cone and raises RMSE.
Demand Shock — injects one large one-off shock, visible as a kink in the actual path versus the forecast made just before it landed.

This is the textbook expectations-augmented Phillips curve used to explain why disinflation is costly (the "sacrifice ratio") and why central banks manage expectations, not just the money supply.

Realized path (u, π) Forecast (dashed) Miss (outside 90% band)

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