Lesson M16.L04: The Expectations-Augmented Phillips Curve

Module: The Labour Market and Phillips Curve Level: intermediate Duration: 30 minutes Learning Objective: Derive the vertical long-run Phillips curve from the expectations-augmented model. Data as of: 2024 Provenance: Reserve Bank of Australia | OpenStax Macroeconomics 3e

Explanation

Milton Friedman (1968) and Edmund Phelps (1968) independently showed that the stable, exploitable Phillips curve of the 1960s rested on a crucial assumption: that workers and firms had fixed (non-adaptive) inflation expectations. Once expectations are allowed to adjust, the long-run trade-off between inflation and unemployment disappears.

Derivation from the WS-PS framework:

Starting from the nominal wage-setting (WS) and price-setting (PS) relations:

\[W = P^e(1 - \alpha u + z)\]

\[P = (1 + \mu)W\]

Substitute WS into PS:

\[P = (1 + \mu)P^e(1 - \alpha u + z)\]

Taking percentage changes (approximation for small changes):

\[\pi \approx \pi^e + \text{(percentage change in } [1 - \alpha u + z] \times (1 + \mu)\text{)}\]

In the linearised version commonly used at intermediate level:

\[\pi = \pi^e - \alpha(u - u_n)\]

where: - π = actual inflation - π^e = expected inflation - α = slope of PC (sensitivity of inflation to unemployment gap) - u − u_n = unemployment gap (negative when labour market is tight)

Key results:

Short run (π^e fixed): standard downward-sloping PC — lower u → higher π. Same as the original PC for a given π^e.
Long run (π^e = π): substituting into the EAPC: $$\pi = \pi - \alpha(u - u_n) \Rightarrow 0 = -\alpha(u - u_n) \Rightarrow u = u_n$$ The long-run PC is vertical at u = u_n. In the long run, output cannot be permanently held above (or below) the natural rate.

Adaptive expectations: Friedman assumed agents update expectations based on past inflation:

\[\pi^e_t = \pi_{t-1}\]

(simple adaptive expectations)

This means any inflationary shock (or policy-induced fall in u below u_n) eventually shifts the short-run PC upward.

Australia 1990: The RBA deliberately caused a recession (cash rate reached 17.5% in January 1990) to break entrenched high inflation expectations. Unemployment rose to ~10.8% (1992) — well above u_n — shifting inflation expectations sharply downward. By 1993, inflation was below 2% and the RBA introduced its 2–3% target band. Anchored expectations are the legacy of this painful adjustment.

Notation: π = actual inflation; π^e = expected inflation; u = unemployment; u_n = NAIRU; α = PC slope.

Worked Example

Setup:

EAPC: π = π^e − 0.5(u − 5) [α = 0.5, u_n = 5%]
Adaptive expectations: π^e_t = π_{t-1}
Policy: government holds u = 3% indefinitely starting in Period 1

Period 0 — Baseline (u = 5%, stable inflation):

π^e₀ = 2% (initial anchored expectations)
π₀ = 2 − 0.5(5 − 5) = 2%
u = u_n: stable equilibrium.

Period 1 — Expansionary policy drives u = 3%:

π^e₁ = π₀ = 2%  (adaptive: expect last period's inflation)
π₁ = 2 − 0.5(3 − 5) = 2 − 0.5(−2) = 2 + 1 = 3%

Output is above potential, inflation rises to 3%.

Period 2 — Expectations catch up:

π^e₂ = π₁ = 3%  (expectations adjust upward)
π₂ = 3 − 0.5(3 − 5) = 3 + 1 = 4%

Inflation rises again to 4%, even though u is still at 3%.

Period 3 — Expectations adjust again:

π^e₃ = π₂ = 4%
π₃ = 4 − 0.5(3 − 5) = 4 + 1 = 5%

Inflation is now 5% — and accelerating. As long as u < u_n, inflation keeps rising.

Summary table:

Period	u (%)	π^e (%)	π (%)
0 (baseline)	5	2	2
1	3	2	3
2	3	3	4
3	3	4	5

Interpretation: Holding u below u_n causes accelerating inflation. The only way to stabilise inflation is to return u to u_n (the NAIRU), which is why the NAIRU is the Non-Accelerating Inflation rate. The short-run PC shifts upward each period as π^e adjusts.

Long-run result: If the government eventually abandons the policy and u returns to 5%, inflation will stabilise at 5% (not back to 2%) — disinflation requires a period of u > u_n.

Common Misconception

Misconception: Because the long-run PC is vertical, monetary policy has no effect on output even in the short run.

Correction: The vertical long-run PC only says that permanently holding u < u_n is infeasible — it generates accelerating inflation. In the short run, while expectations are adjusting, monetary expansion does reduce unemployment and raise output. The EAPC framework says nothing about the speed of expectation adjustment. If expectations are slow to adjust (sticky), monetary policy has real effects for an extended period. This is the Keynesian-monetarist synthesis: real effects in the short run, purely nominal in the long run.

Practice Prompts

Conceptual: Using the EAPC diagram with multiple short-run Phillips curves, show what happens to inflation and unemployment when the central bank maintains u < u_n for three consecutive periods. → Answer: Start on SRPC₁ at (u_n, π̄). Period 1: move left along SRPC₁ to (u < u_n, π₁ > π̄). Expectations adjust: SRPC shifts up to SRPC₂. Period 2: at the same u, we are now on SRPC₂ at a higher inflation rate (π₂ > π₁). SRPC shifts up again to SRPC₃. Period 3: inflation rises further to π₃ > π₂. Each period, the SRPC shifts upward by the amount π^e increases. Inflation is continuously rising — consistent with the numerical example above.
Numerical: Using the EAPC π = π^e − 0.5(u − 5) with adaptive expectations (π^e_t = π_{t-1}), suppose the government drives u to 4% starting from a stable equilibrium at π₀ = π^e₀ = 3%. Compute π₁, π₂, and π₃. → Answer:
```
Period 1: π^e₁ = 3%
π₁ = 3 − 0.5(4 − 5) = 3 + 0.5 = 3.5%

Period 2: π^e₂ = 3.5%
π₂ = 3.5 − 0.5(4 − 5) = 3.5 + 0.5 = 4.0%

Period 3: π^e₃ = 4.0%
π₃ = 4.0 + 0.5 = 4.5%
```
Inflation accelerates: 3% → 3.5% → 4.0% → 4.5%. Each period inflation rises by 0.5 pp.
Application: The RBA raised the cash rate to 17.5% in 1990, causing unemployment to rise above 10% and anchoring inflation expectations. Using the EAPC, explain the disinflation mechanism and why anchored expectations are now seen as a key advantage for central banks. → Answer: By pushing u > u_n, the 1990 recession moved the economy right along the SRPC. With u − u_n > 0, the EAPC gives π < π^e: actual inflation falls below expected. With adaptive expectations, π^e adjusts downward each period. The SRPC shifts down until expectations stabilise at the new lower inflation rate. Once inflation expectations are anchored near 2–3%, the short-run trade-off becomes much more favourable: small rises in unemployment produce proportionately larger reductions in inflation. The 2022–23 RBA tightening cycle benefited from this anchoring — even with 13 rate hikes, long-run inflation expectations remained near 2.5–3%, limiting the SRPC upward drift.

Visual — Expectations-Augmented Phillips Curves and the Vertical Long Run

Figure: With fixed expectations, each short-run Phillips curve is downward sloping. If policymakers keep unemployment below the natural rate, expectations rise, the SRPC shifts upward, and inflation accelerates while the long-run Phillips curve remains vertical at the NAIRU.

Further Resources

📺 Video Tutorial: Expected Inflation and the Phillips Curve — Macroeconomics Tutorials (11 min)
📺 The Expectations Augmented Phillips Curve Ousts the Keynesian Consensus — Economics in Context (13 min)
📚 RBA Explainer: Inflation Target — History and rationale for Australia's 2–3% inflation target