The Phillips Curve
The trade-off between inflation and unemployment — and why it disappears in the long run.
Built and reviewed by Stephen Omukoko Okoth
Mathematical Economist · ex-Morgan Stanley FI · Equilar
Theory
What the model says, and why
A.W. Phillips (1958) plotted a century of UK wage inflation against unemployment and found a striking negative relationship: when unemployment was high, wages grew slowly (or fell); when unemployment was low, wages rose fast. Samuelson and Solow (1960) generalized this to price inflation and proposed it as a policy menu — pick the inflation-unemployment combination you want.
Friedman (1968) and Phelps independently demolished this interpretation. The argument: workers and firms care about real wages. If everyone expects 5% inflation and the central bank delivers 5%, unemployment sits at its “natural rate” (today called NAIRU — Non-Accelerating Inflation Rate of Unemployment) regardless of whether realized inflation is 0%, 5%, or 50%.
The expectations-augmented Phillips curve:
Realized inflation π equals expected inflation πᵉ minus a coefficient β times the unemployment gap (u − u*), plus a supply shock ε. When u = u*, π = πᵉ — inflation equals expectations and there’s nothing to push it either way.
Short run. If the central bank surprises everyone with looser money, π > πᵉ briefly. Workers, fooled by inflation, accept lower real wages; firms hire more; u falls below u*. The Phillips curve appears to slope downward.
Long run. Workers update expectations. Once πᵉ catches up to π, real wages return to where they were, hiring drops back, u returns to u*. The long-run Phillips curve is vertical at u* — there’s no permanent trade-off.
What broke. The 1970s. US unemployment rose sharply and inflation rose sharply — stagflation. The original Phillips curve couldn’t explain it; the Friedman-Phelps version could. Mainstream macro adopted the expectations-augmented form, with refinements: rational expectations (Lucas), NK Phillips curve (Calvo pricing), hybrid forms. The basic insight survives: you can’t systematically buy lower unemployment by accepting higher inflation.
Interactive playground
Move the parameters, watch the equilibrium move
Parameters
The Phillips equation
Equilibrium
At u = u* (5%): π = 2.00%
Long-run inflation
2.00%
Equal to expectations
NAIRU (u*)
5.00%
No-accelerating-inflation rate
In the classroom
How to teach it well
Sequence the history. Phillips’s original empirical paper, Samuelson-Solow’s policy menu, Friedman’s 1968 AEA presidential address, Lucas critique, and the New Keynesian Phillips curve. This is one of the cleanest cases in macro of theory and empirics fighting it out — the 1970s stagflation directly killed the original curve.
The expectations debate. Friedman assumed adaptive expectations (πᵉ updates from past π). Lucas insisted on rational expectations — agents understand the central bank’s rule. The implications are similar (vertical long-run curve) but the policy-effectiveness conclusions differ. Worth a separate lecture if you have time.
Modern relevance. The Phillips curve has flattened in advanced economies since 2000 — unemployment fell to historic lows without much inflation, and 2021-22 saw inflation surge from supply rather than demand. The model isn’t dead, but β is small and ε has been doing more of the work than usual.
African application. NAIRU is harder to estimate in economies with large informal sectors and noisy unemployment data. Use this as motivation for why Africa-specific monetary frameworks (KE, ZA, NG, GH inflation targeters) often look different from textbook prescriptions.