From Short to Medium Run (IS-LM-PC)

Policy Credibility, Rules vs Discretion

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The time-inconsistency problem (Kydland-Prescott 1977): discretionary policy leads to an inflation bias — CB is tempted to surprise-inflate for short-run Y gain, but rational expectations internalise this, raising πe without Y benefit. Solutions: rules (fixed policy), delegation to conservative CB (Rogoff), or inflation targeting with independence. Equilibrium: higher π than optimal, same u.

Derivation

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The Time-Inconsistency Problem

Kydland-Prescott (1977): a policy that is optimal ex ante can be suboptimal ex post. For monetary policy:

Ex ante, the CB wants low inflation. Ex post — after $\pi^e$ is set — it has an incentive to surprise-inflate to push $u$ below $u_n$ . Rational agents anticipate this, setting $\pi^e$ higher, and in equilibrium $\pi$ is high with no output gain.

The CB's Loss Function

L = (\pi - \pi^*)^2 + \beta (u - k u_n)^2, \quad k < 1

The crucial parameter: $k < 1$ means the CB aims at below-natural unemployment. This creates the incentive to surprise-inflate.

Two Equilibria

| Regime | $\pi$ | $u$ | Loss | |--------|-------|-----|------| | Rules | $\pi^*$ | $u_n$ | minimum | | Discretion | $\pi^* + \text{bias}$ | $u_n$ | higher |

The inflation bias exists with zero output benefit — a pure welfare loss.

Three Solutions

Rules. Commit to a policy function. The Taylor rule is a semi-rule that has reduced discretion.
Delegation (Rogoff 1985). Appoint a conservative central banker with $\beta_{\text{CB}} < \beta_{\text{society}}$ . Reduces bias at the cost of flexibility.
Reputation. Repeated games allow the CB to build credibility through consistent behaviour.

Modern Practice

Central-bank independence + inflation targeting has become the dominant institutional solution:

ECB (1999): inflation mandate only (recently broadened).
Bank of England (1997): operational independence, 2% target.
Fed (1977): dual mandate but strong operational independence.

Empirically, these institutional changes reduced inflation and sacrifice ratios across OECD in the 1990s–2010s.

Worked Example

CB loss: L = (π − 2)² + 0.5·(u − 4)², with un = 5 (so k = 0.8). Adaptive PC: π − π₋₁ = −α(u − un), α = 0.5.

Under rules: CB commits to π = 2, u = un = 5. Loss = 0 + 0.5·(5 − 4)² = 0.5.
Under discretion: take πe as given, minimise. FOC yields π = πe + (kα·β)/(1 + βα²)·(un − k·un).
In equilibrium πe = π, so π_disc = 2 + positive bias ≈ 3 for these parameters.
Discretionary loss: (3 − 2)² + 0.5·(5 − 4)² = 1 + 0.5 = 1.5. vs rules loss 0.5.

Rules dominate discretion: L_rules = 0.5 < L_disc = 1.5. The inflation bias of 1 pp costs society in higher average inflation without any output gain.

Common Mistakes

—Thinking the inflation bias gives the CB any output benefit — in equilibrium u = un under both regimes.
—Treating rules as obviously better without accounting for flexibility — rules are rigid to genuine shocks.
—Confusing delegation (Rogoff) with full commitment — conservative CB reduces but doesn't eliminate bias.
—Ignoring reputation effects — in repeated interactions, the CB can build credibility.

Exam Cues

→Time inconsistency: optimal ex-ante plan differs from optimal ex-post action. Creates inflation bias.
→Three solutions: rules, delegation (independent CB), reputation.
→Rogoff conservative CB: β_CB < β_society reduces bias.
→Post-1990s: CB independence + inflation targeting anchored expectations.