The IS–LM Model

The Size of the Fiscal Multiplier

coreExam · medium

The fiscal multiplier (ΔY/ΔG) varies with the state of the economy and monetary response. Textbook 1/(1−c₁) ≈ 2.5. Reality 0.5–2.0 depending on slack, CB response, and openness. Large at ZLB and in recessions; small at full employment or with Taylor rule response. Open economy reduces multiplier via import leakage.

Derivation

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The Textbook Multiplier

\frac{\Delta Y}{\Delta G} = \frac{1}{1 - c_1}

Derived from closed economy, flat LM (no crowding out). With $c_1 = 0.6$ , multiplier = 2.5.

Reductions

| Factor | Effect | |--------|--------| | Openness | Divide by $(1 - c_1 + m)$ — imports leak out | | Taylor rule response | CB raises $i$ , crowds out $I$ | | Full employment | No idle resources to mobilise |

Amplifications

| Factor | Effect | |--------|--------| | ZLB | Full multiplier — no CB response | | Slack | Mobilises unemployed resources | | Long-horizon credibility | Permanent ↑G raises expectations → multiplier |

Empirical Estimates

Pre-2008 consensus: multipliers around 0.5–1.0 — underwhelming. Post-2008: 1.0–2.0, especially at ZLB. The IMF (2012) admitted its austerity-era forecasts used too-low multipliers, leading to worse-than-expected GDP contractions.

Tax vs Spending

\left|\frac{\Delta Y}{\Delta T}\right| = \frac{c_1}{1 - c_1} = c_1 \cdot \text{spending multiplier}

With $c_1 = 0.6$ : tax multiplier = 1.5, spending multiplier = 2.5.

Why This Matters for the Austerity Debate

If multiplier > 1 in recessions, austerity contracts GDP more than it reduces the deficit → debt/GDP rises. This was the core finding of the 2010s austerity backlash and underpins the post-2020 "fiscal-support-first" consensus.

Worked Example

c₁ = 0.6, m = 0.2. Compare: (a) closed economy, (b) open economy, (c) open economy at ZLB, (d) open economy with Taylor rule.

(a) Closed: 1/(1−0.6) = 2.5.
(b) Open, flat LM: 1/(1−0.6+0.2) = 1.67.
(c) Open, ZLB: same as (b), no reaction — 1.67.
(d) Open with Taylor: CB raises i after ↑G, crowds out I — multiplier ≈ 1.0–1.2 empirically.

Multiplier depends on regime: 2.5 (closed, flat LM) → 1.67 (open, flat LM) → 1.0–1.2 (open, Taylor). At ZLB, stays near 1.67.

Common Mistakes

—Using textbook 1/(1−c₁) as the actual multiplier — real-world is typically lower.
—Forgetting state-dependence — multipliers vary with slack, ZLB, openness.
—Treating G and T multipliers as identical — T multiplier is smaller by factor c₁.
—Ignoring the 2012 IMF WEO evidence that multipliers were underestimated during austerity.

Exam Cues

→Textbook multiplier: 1/(1−c₁). Open-economy: 1/(1−c₁+m). Taylor response reduces further.
→ZLB raises multiplier (no crowding out). Slack raises multiplier.
→Tax multiplier smaller: c₁/(1−c₁) vs 1/(1−c₁).
→Austerity debate: if multiplier > 1, austerity can worsen debt/GDP.