Expectations, Output & Policy

Expectations in the IS–LM Model

coreExam · high

Private spending depends on current and expected future output, taxes, and interest rates: A = A(Y, T, r, Yᵉ', Tᵉ', rᵉ'). The IS relation becomes Y = A(·) + G. A pure current-rate cut with unchanged expectations has a weak effect; a persistent / credible rate cut (which lowers rᵉ' as well) has a much larger effect. Monetary policy works through expectations.

Derivation

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Adding Expectations to IS

Start from the standard IS relation with private spending $A$ :

A(Y, T, r) \equiv C(Y-T) + I(Y, r+x), \quad Y = A + G

Extend $A$ to include expected future variables:

A = A(Y, T, r, Y'^e, T'^e, r'^e), \quad Y = A + G

The Signs

| Variable | Sign in $A$ | Mechanism | |----------|-------------|-----------| | $Y$ | + | Higher income → higher $C$ , $I$ | | $T$ | − | Higher taxes → lower $C$ | | $r$ | − | Higher rate → lower $I$ | | $Y'^e$ | + | Higher expected income → higher $C$ (via human wealth) | | $T'^e$ | − | Expected future tax → lower lifetime wealth → lower $C$ | | $r'^e$ | − | Higher expected rate → lower $V$ → lower $I$ |

Temporary vs Persistent Policy

A temporary rate cut changes only $r$ . A persistent rate cut changes both $r$ and $r'^e$ , so both channels of $A$ operate. This makes persistent shocks far more powerful.

ZLB and Forward Guidance

When the current rate is stuck at zero, the CB cannot lower $r$ further. But it can still shift $r'^e$ by promising to keep rates low for longer — forward guidance. This raises $A$ even though $r$ is unchanged.

QE operates similarly: by holding longer-maturity assets, the CB compresses the term premium and pushes expected future rates lower.

Fiscal Expectations

Forward-looking households respond to both $T$ and $T'^e$ . Austerity that raises both compresses lifetime wealth and contracts $C$ strongly. This is why "expansionary austerity" claims rarely hold up empirically — the expectations channel amplifies rather than offsets the direct tax effect.

Worked Example

A(Y, r, r^e) = 500 + 0.6Y − 200r − 200r^e (simplified, constant T). G = 200.

Current rate cut only: Δr = −1 pp → ΔA = −200·(−0.01) = +2. Multiplier: ΔY = 2/(1-0.6) = 5.
Persistent cut: Δr = Δr^e = −1 pp each → ΔA = +2 + +2 = +4. ΔY = 4/(1-0.6) = 10. Double the effect.
Forward guidance only (current r unchanged, Δr^e = −1 pp): ΔA = +2 → ΔY = 5. Even at the ZLB this can move Y.

Temporary cut: ΔY = 5. Persistent cut: ΔY = 10. Forward guidance alone (at ZLB): ΔY = 5. Expectations channel doubles the impact of a persistent monetary shock.

Common Mistakes

—Treating r and r^e as independent — a rate-setting CB with inertia moves them together in practice.
—Ignoring that expectations channels dominate at the ZLB — why forward guidance matters.
—Forgetting the fiscal version: future tax credibility (T^e) is as important as current T.
—Confusing the level of r with the path of r — it is the whole path that prices assets and drives spending.

Exam Cues

→IS with expectations: Y = A(Y, T, r, Y^e', T^e', r^e') + G.
→Temporary vs persistent rate cuts: persistent much more powerful because r^e' channel activates.
→ZLB: current-rate tool is gone; only forward guidance and QE work — both target r^e'.
→Austerity can be contractionary: T and T^e both rise, shrinking lifetime wealth.