Financial Markets & Expectations

Rational vs Adaptive Expectations

coreExam · medium

Two competing theories of expectations. Adaptive: πe = π_{-1} (or weighted past). Rational: πe = E[π | information], equal to the model's prediction. Adaptive makes predictable mistakes after regime shifts; rational uses all info efficiently. Lucas critique: policy rules that work under adaptive expectations fail under rational because agents anticipate them.

Derivation

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Two Theories

| Theory | Formula | Behaviour | |--------|---------|-----------| | Adaptive | $\pi^e_t = \pi_{t-1}$ | Backward-looking, sluggish | | Rational | $\pi^e_t = E_t[\pi_t \mid \Omega_{t-1}]$ | Uses all available information |

The Information Set

Rational expectations means using all available information — including the structure of the economy, central-bank announcements, and anticipated policies. Agents are not always right, but they make no systematic errors.

The Lucas Critique

Reduced-form relationships (like the Phillips curve) embed agents' expectations. Change the policy regime, and the relationship itself changes. You cannot use historical estimates of the trade-off to predict how policy changes will play out.

Sargent's Disinflation

Under rational expectations + full credibility, a disinflation announcement immediately lowers $\pi^e$ , and through the Phillips curve $\pi$ falls without any unemployment cost. The sacrifice ratio collapses to zero.

Why doesn't this happen in practice?

Credibility must be built. New policies are doubted until proven.
Nominal contracts lock in old expectations (multi-year wage deals).
Heterogeneous agents — some adaptive, some rational.

Hybrid Models

Most modern macro uses a blend:

\pi^e_t = \alpha \cdot \pi^e_{\text{rational}} + (1-\alpha) \cdot \pi_{t-1}

with $\alpha \in [0, 1]$ . At $\alpha = 1$ , full rational; at $\alpha = 0$ , pure adaptive. Real economies usually have $\alpha$ around 0.3–0.7.

Worked Example

Year 0: π = 5%, πe = 5%. CB announces credible disinflation target π* = 2%. Compare adaptive vs rational response.

Adaptive: πe_1 = π_0 = 5%. PC gives π_1 = πe_1 − α(u − un); needs large u gap. Sacrifice ratio 1/α.
Rational (fully credible): πe_1 = 2% immediately. PC gives π_1 = 2% at u = un. Zero sacrifice.
Partial credibility (α = 0.5): πe_1 = 0.5·2 + 0.5·5 = 3.5%. Intermediate.

Adaptive: slow, costly disinflation. Rational + credibility: instant, costless. Partial credibility (reality): intermediate. Volcker's disinflation was closer to adaptive.

Common Mistakes

—Treating rational expectations as 'agents are perfect forecasters' — it means no systematic errors, not 'always right'.
—Ignoring the Lucas critique when using estimated relationships to predict policy effects.
—Conflating rational expectations with full credibility — agents can rationally doubt policy announcements.
—Assuming adaptive is always bad — it's a reasonable approximation during stable periods but fails at regime shifts.

Exam Cues

→Adaptive: πe = π_{-1}. Rational: πe = E[π | info].
→Lucas critique: policy changes alter expectations, so estimated relationships change.
→Sargent disinflation: credible + rational → painless. Reality usually closer to adaptive.
→Partial credibility: real-world models use weighted average of both.