Lesson M17.L05: Medium-Run Equilibrium and Policy Stabilisation

Module: From Short to Medium Run: The IS-LM-PC Model Level: intermediate Duration: 30 minutes Learning Objective: Characterise the medium-run equilibrium in the IS-LM-PC model where output equals potential and inflation is stable. Data as of: 2024 Provenance: RBA Inflation Targeting | MIT OCW 14.02

Explanation

The medium-run equilibrium is the economy's resting point after all short-run adjustments have played out. In the IS-LM-PC framework, it is defined by three simultaneous conditions:

Medium-Run Equilibrium Conditions:

(1) Y = Yₙ           (output equals potential — zero output gap)
(2) π = πᵉ = π*      (inflation equals expectations equals target)
(3) i = i_neutral     (nominal rate at the neutral level)

Neutral nominal interest rate:

i_neutral = r* + π*

Where r is the neutral real rate (consistent with Y = Yₙ when inflation is at target) and π is the inflation target.

Notation: - All variables as in previous lessons - r = neutral real interest rate (Australia: historically ~2.5% per M17.L04; revised down to ~0.75–1.0% post-COVID as global r fell — this lesson uses the post-COVID estimate for the current equilibrium) - i_neutral = nominal neutral rate (Australia: approximately 3.0–3.5% post-COVID)

Why is this a stable equilibrium?

1. If Y > Yₙ: PC shows π > πᵉ → expectations rise → CB tightens → Y falls back toward Yₙ
2. If Y < Yₙ: PC shows π < πᵉ → expectations fall → CB eases → Y rises back toward Yₙ
3. If π > π: CB raises i above i_neutral → aggregate demand falls → gap closes → π returns to π*

The economy converges to medium-run equilibrium IF two conditions hold: - The central bank credibly commits to π - Inflation expectations are anchored (do not drift permanently away from π)

Barro-Gordon intuition (time inconsistency): Without commitment, a CB has an incentive to create surprise inflation to boost output above Yₙ. Rational agents anticipate this → πᵉ rises → CB must deliver higher inflation to keep its "promise" → inflation escalates without output gain. The solution: institutional commitment to a target (e.g., the RBA's legislative mandate and Statement on the Conduct of Monetary Policy, in place since 1993).

RBA inflation targeting (1993–present): Australia adopted formal inflation targeting in 1993. The 2–3% target band has been in place since. The 2022–23 episode was the first serious test of credibility since the 1990s recession. Long-run inflation expectations (5-year ahead market-implied) remained close to 2.5–3% throughout the inflation surge, suggesting the RBA's credibility was largely maintained.

Medium-run vs. long-run: In the IS-LM-PC framework, the "medium run" assumes Yₙ is fixed. In the very long run (growth models), Yₙ itself grows via capital accumulation and technological progress — the subject of Module M18.

Worked Example

Setup: Economy is initially at medium-run equilibrium. Then a fiscal stimulus (G increases) creates a demand shock in period 1.

Initial equilibrium (period 0):

Y₀ = Yₙ = 100, π₀ = πᵉ₀ = π* = 2.5%, i₀ = r* + π* = 1.0% + 2.5% = 3.5%

Period 1 (demand shock):

G↑ → IS shifts right → Y₁ = 103, gap₁ = +3%
π₁ = πᵉ₁ + β × gap₁ = 2.5% + 0.5 × 3% = 4.0%
CB raises i above 3.5% to cool demand

Period 2 (CB response, partial gap closure):

CB raises i₂ = 5.0% → Y₂ = 101, gap₂ = +1%
πᵉ₂ = π₁ = 4.0%  (adaptive)
π₂ = 4.0% + 0.5 × 1% = 4.5%

Period 3 (gap closes, but inflation elevated):

CB holds i₃ = 5.0% or higher → Y₃ = 100 = Yₙ, gap₃ = 0%
πᵉ₃ = π₂ = 4.5%
π₃ = 4.5% + 0 = 4.5%

The new "stuck" equilibrium: Y = Yₙ but π = 4.5% ≠ π = 2.5%. This is NOT medium-run equilibrium because π ≠ π. To complete the return:

Period 4 (active disinflation — CB must create negative gap):

CB raises i above i_neutral, pushing Y below Yₙ. Require: π₄ = π* = 2.5%. If πᵉ₄ = 4.5%:

2.5% = 4.5% + 0.5 × gap₄
0.5 × gap₄ = 2.5% − 4.5% = −2.0%
gap₄ = −4%   → Y₄ = 96

Period 5 (medium-run equilibrium restored):

Once π₄ = 2.5%, πᵉ₅ = 2.5%, and CB can reduce i back to i_neutral = 3.5%, Y returns to 100.

Y₅ = 100, π₅ = πᵉ₅ = π* = 2.5%, i₅ = 3.5% = r* + π*

Medium-run equilibrium is restored. The path required a painful period of Y < Yₙ to wring out the elevated inflation expectations built up during the adjustment.

Common Misconception

Misconception: "Medium-run equilibrium means the economy never changes — it's a long-run steady state."

Correction: Medium-run equilibrium in the IS-LM-PC model is a conditional resting point, not a permanent state. It holds Yₙ, r, and the structure of the economy fixed. In reality, Yₙ grows over time (via capital, labour, and technology — the subject of growth theory). Structural shocks can shift r (e.g., the post-GFC "secular stagnation" lowered r* globally; COVID further compressed it). The medium-run equilibrium is the gravitational centre toward which short-run fluctuations are pulled, given a fixed structure — but that structure itself evolves.

Practice Prompts

1. Conceptual: What are the two necessary conditions for the IS-LM-PC model to converge to medium-run equilibrium, and what historical examples show each condition failing? → Answer: Condition 1 — Central bank commits credibly to π. Failure: the 1970s, when many central banks (including the RBA's predecessor) accommodated supply shocks, allowing πᵉ to drift upward. Result: stagflation, inflation entrenched at 10%+. Condition 2 — Inflation expectations anchor at π. Failure: hyperinflation episodes (e.g., 1920s Germany, Zimbabwe 2000s) where πᵉ became de-anchored and self-reinforcing. Convergence to medium-run equilibrium requires both institutional commitment and rational/adaptive expectations that respond to credible policy.

2. Numerical: Given r = 1.0%, π = 2.5%, compute i_neutral. Then, if actual π = 4.0% and gap = +2%, calculate the Taylor rule prescribed rate (α_π = α_Y = 0.5) and the gap between it and i_neutral. → Answer:
   i_neutral = r + π = 1.0% + 2.5% = 3.5%
   Taylor rule: i = r + π + 0.5(π − π) + 0.5 × gap
   i = 1.0 + 4.0 + 0.5(4.0 − 2.5) + 0.5 × 2.0
   i = 1.0 + 4.0 + 0.75 + 1.0 = 6.75%
   Gap above neutral = 6.75% − 3.5% = 3.25 pp
   The CB must hold rates 3.25 pp above the neutral rate to stabilise the economy. This corresponds to a contractionary stance until inflation returns to target and the output gap closes.

3. Application: The RBA's Statement on the Conduct of Monetary Policy establishes the 2–3% target band and emphasises that "on average, over time" inflation should be within the band. How does this forward-looking formulation support convergence to medium-run equilibrium? → Answer: The "on average, over time" formulation gives the RBA flexibility to temporarily allow inflation outside the band (e.g., due to supply shocks) without sacrificing long-run credibility. This is consistent with the Barro-Gordon insight: as long as agents believe the CB will eventually return inflation to target, πᵉ stays anchored near 2.5%. Anchored expectations flatten the adjustment path — small output gaps suffice to return inflation to target. If the CB instead committed to hitting 2.5% every period, it would have to create large output gaps in response to every supply shock, producing excessive volatility.

Further Resources

• 📺 Macroeconomics: The IS-LM-PC Model — Academic Macro Channel (12 min)
• 📺 The IS-MP-PC Model — Macro Lectures (15 min)
• 📚 RBA Statement on the Conduct of Monetary Policy — The RBA's formal commitment to the 2–3% inflation target band