Module 08 · Chapters 8

The Phillips Curve

Inflation, expectations, and the unemployment-inflation trade-off.

“From the original 1958 fit to the modern expectations-augmented version.”

~35 min· 4 sub-skills·5 exercisesExam frequency · high0% mastered

The Phillips curve links inflation and unemployment. It started as a stable empirical relationship (Phillips, 1958: lower u → higher π). The 1970s broke that. We now use the expectations-augmented version, which respects three decades of evidence: in the long run there's no trade-off; in the short run there is.
Expectations-augmented Phillips curve
$\pi_t \;=\; \pi^e_t \;-\; \alpha\,(u_t - u_N)$
$\pi_t$
actual inflation
$\pi^e_t$
expected inflation
$\alpha$
slope of the PC (responsiveness)
$u_t - u_N$
unemployment gap
When u = u_N, π = π^e. Below u_N, inflation accelerates above expectations.
Tip·Three expectations regimes
1. Static (π^e = π_{t-1}): Phillips curve is the change in inflation vs unemployment gap. NAIRU=u_N.
2. Adaptive (π^e adjusts gradually to recent π): similar to static.
3. Anchored (π^e = target π̄ = constant): PC is in levels, π = π̄ − α(u − u_N). Disinflation has no medium-run cost.
Figure · Phillips curve under different expectations
Loading Phillips curve…
Static/adaptive: vertical long-run PC. Anchored: stable downward-sloping PC.
Common misconception
Central banks can permanently raise GDP by accepting higher inflation.
Actually**No long-run trade-off.** With adaptive expectations, sustained u < u_N means π keeps accelerating. Eventually credibility breaks. The long-run PC is vertical at u_N.
Okun + Phillips chained
$\pi_t \;-\; \pi_{t-1} \;=\; -\alpha\,(u_t - u_N) \;\;\Rightarrow\;\; \pi_t \;-\; \pi_{t-1} \;\approx\; \alpha\,\beta\,(g_{Y,t} - \bar g_Y)$
Combining adaptive PC with Okun: the change in inflation is proportional to the output gap. Hawkish CBs use this directly.
Exercise · multiple choice · +8 XP
Original PC interpretation
The original Phillips curve (1958) plots:
Exercise · numerical · +12 XP
Compute π given gap
π^e = 2%, α = 1.0, u = 4%, u_N = 5%. Compute π_t.
Your answer (% per year)
Exercise · multi step · +18 XP
Adaptive expectations dynamics
π^e_{t} = π_{t-1}. α = 1, u = 4%, u_N = 5%. Initial π_0 = 2%. Compute π_1, π_2, π_3.
Context: With u below u_N for three years and adaptive expectations, π drifts upward each year by α·gap = 1%. This illustrates accelerating inflation.
(a)π_1:
(b)π_2:
(c)π_3:
Exercise · true false · +10 XP
Anchored expectations
If the CB has perfect credibility and π^e = π̄ (target) regardless of recent inflation, then disinflation costs nothing in the medium run.
"If the CB has perfect credibility and π^e = π̄ (target) regardless of recent inflation, then disinflation costs nothing in the medium run."
Exercise · numerical · +14 XP
Sacrifice ratio
α = 0.5. To bring inflation down by 4pp via adaptive expectations, what cumulative percentage-point-years of unemployment above u_N is needed?
Your answer (pp · years)

Mastery check

5 questions · pass with 80%

Answer all five to confirm you've internalised the module. A passing run unlocks the next module.

Q1
The expectations-augmented Phillips curve is:
Q2
"With adaptive expectations, the long-run Phillips curve is vertical at u_N."
Q3
Volcker's 1980-83 disinflation came at a high output cost. Why?
Q4
α = 0.4. Cut π by 2pp. PP·years of u above u_N required?
Q5
The original (1958) Phillips relationship broke down in the 1970s because:

0 / 5 answered

Exam pitfalls

Treating the PC as a stable downward-sloping curve in the long run. With adaptive expectations it is vertical at u_N.
Confusing actual u with u_N. The PC is about the *gap*, not the level.
Forgetting expectations channel: what matters is π − π^e.
Mis-computing sacrifice ratio: it is 1/α, not α.