Output, Interest Rate & Exchange Rate (Mundell–Fleming)

Dornbusch Overshooting

extensionExam · medium

Dornbusch's (1976) result: because prices are sticky in the short run but exchange rates move instantly, a permanent monetary expansion causes the nominal exchange rate to overshoot its new long-run value. Immediate depreciation overshoots the long-run PPP level, then the currency appreciates back to equilibrium over time.

Derivation

Step 1 / 7

1Press Space or click Reveal next
(hidden)
2Press Space or click Reveal next
(hidden)
3Press Space or click Reveal next
(hidden)
4Press Space or click Reveal next
(hidden)
5Press Space or click Reveal next
(hidden)
6Press Space or click Reveal next
(hidden)
7Press Space or click Reveal next
(hidden)

Two Time Scales

Long run: PPP and money neutrality. $\bar{E} = \bar{P}^*/\bar{P}$ .
Short run: $P$ is sticky (contracts, menu costs). Only $E$ adjusts in asset markets.

The Overshooting Mechanism

A permanent monetary expansion:

Long run: $P$ rises proportionally with $M$ → $\bar{E}$ depreciates.
Short run: $i$ falls (CB target), $P$ sticky.
UIP forces: $i = i^* + (\bar{E} - E)/E$ . Lower $i$ → expected appreciation.
Solution: $E$ jumps past $\bar{E}$ — overshoots — so there is expected appreciation back to $\bar{E}$ .

The exchange rate depreciates more in the short run than in the long run. Over time, as $P$ adjusts, $E$ appreciates from its overshoot to the new PPP level.

Numerical Illustration

Starting from $E_0 = 1.0$ , long-run $\bar{E}_{new} = 1.10$ , CB cuts $i$ by 1 pp:

Short-run overshoot: $E_{SR} \approx 1.11$
Over time: $E \to 1.10$ as $P$ adjusts
During the transition: expected appreciation $\approx -1\%$ , matching the interest differential

Why It Matters

Volatility puzzle: Observed FX volatility far exceeds what macro fundamentals alone predict. Overshooting is one explanation.
Policy trade-offs: Large overshoots complicate imports/exports in the short run even if long-run effects are neutral.
Forward guidance: Communicating future rate paths smooths expected appreciation, reducing overshoot magnitude.

Worked Example

E₀ = 1.0 (foreign/domestic). i = i* = 3%. CB permanently cuts i to 2%. Long-run neutrality implies Ē rises to 1.10 (10% depreciation).

UIP: i = i* + (Ē − E)/E → 0.02 = 0.03 + (1.10 − E)/E → (1.10 − E)/E = −0.01 → 1.10 = 0.99E → E ≈ 1.111.
Short-run E_SR ≈ 1.111 — currency depreciated past the long-run 1.10.
Expected appreciation = (1.10 − 1.111)/1.111 ≈ −1%, matching the −1 pp interest differential.
Over time, P rises, Ē moves to 1.10, E appreciates from 1.111 back to 1.10.

Short-run E = 1.111 (overshoot). Long-run E = 1.10. Overshoot ≈ 1 pp. Currency appreciates from its immediate depreciation back to the PPP level.

Common Mistakes

—Confusing the direction: a rate cut causes depreciation (E rises under foreign/domestic quoting); a hike causes appreciation.
—Missing the overshooting: without sticky prices, E would jump directly to Ē with no overshooting.
—Applying Dornbusch to temporary shocks — it is about permanent monetary changes.
—Confusing nominal and real exchange rates — overshooting is a nominal-rate phenomenon; the real rate returns to PPP.

Exam Cues

→Sticky prices + flexible exchange rates → overshooting.
→Permanent ↑M: E overshoots its new long-run Ē, then appreciates back to PPP.
→Magnitude of overshooting is proportional to |i − i*| divided by the rate of price adjustment.
→Empirical evidence: short-run FX volatility vastly exceeds what PPP would predict — overshooting is one explanation.