Dornbusch Overshooting

The puzzle the model solved

When Bretton Woods collapsed in 1971-73 and major currencies began to float freely, economists faced a puzzle. Floating exchange rates moved far more than the fundamentals — money supplies, inflation differentials, current accounts — that the textbook models said should drive them. The Deutsche Mark moved 20 percent against the dollar in 1973-74; the yen swung 30 percent in single years; the pound's volatility tripled between 1971 and 1976. The volatility looked far greater than the implied changes in underlying purchasing power or productivity. Standard Mundell-Fleming, which predicted clean jumps to new long-run equilibria, gave no account of what was happening.

In 1976 Rudiger Dornbusch, then a 33-year-old assistant professor at the University of Chicago shortly to move to MIT, published 'Expectations and Exchange Rate Dynamics' in the Journal of Political Economy. The paper proposed a unified framework that combined three ingredients: (1) free international capital mobility imposing uncovered interest parity, (2) money-market equilibrium with the demand for money depending on the interest rate, and (3) goods prices that adjust only gradually rather than instantaneously. The model predicted that exchange rates should overshoot their long-run equilibrium on monetary shocks and slowly return. The volatility puzzle had a structural explanation.

The paper has been cited more than twelve thousand times. It became, in the words of Stanley Fischer, 'the canonical model of exchange-rate dynamics' for a generation. Dornbusch's contribution, on Fischer's summary, was 'to put rational expectations into Mundell-Fleming'.

The model in three equations

Let e be the log nominal exchange rate (domestic per foreign), p the log domestic price level, m the log money supply, i the domestic nominal interest rate, i* the foreign rate, y output, and time index t. The model is:

(1)  Money market:  m − p = φy − λi
(2)  UIP:           i − i* = E[Δe]
(3)  Price adjust:  Δp = π(y_demand − ȳ),  with  y_demand = δ(e − p) + γy

Equation (1) is standard money-market equilibrium. Equation (2) is uncovered interest parity — the no-arbitrage condition that links interest-rate differentials to expected exchange-rate changes. Equation (3) is the goods market: output demand depends on the real exchange rate e − p; if demand exceeds capacity prices adjust upward over time. The crucial assumption is that p moves slowly through (3) rather than jumping instantaneously.

Suppose at time zero the central bank permanently expands the money supply by 10 percent. What happens?

Variable	Long-run change	On-impact (t=0)	Explanation
Money supply m	+10%	+10%	Policy shock, both periods
Price level p	+10%	0% (sticky)	Prices adjust slowly
Real money m − p	0%	+10%	Real money rises on impact
Interest rate i	0 (back to i*)	−x% (must fall)	Money-market equilibrium with sticky p
Exchange rate e	+10% (depreciate)	+(10+overshoot)%	Must depreciate enough to subsequently appreciate
Expected Δe (going forward)	0	negative (appreciation expected)	UIP requires negative E[Δe] to match i below i*

The mechanism is elegant. Sticky prices mean real money rises 10 percent on impact, requiring a fall in the domestic interest rate to clear the money market (equation 1). The fall in i below i* means UIP (equation 2) requires an expected appreciation of the domestic currency. But long-run neutrality says the long-run exchange rate must depreciate by the same 10 percent as the money supply. The only way the currency can both end up 10 percent weaker and be expected to appreciate going forward is to depreciate by more than 10 percent on impact. That excess depreciation is the overshoot. Then, as goods prices rise over time, the interest rate climbs back toward i*, the currency appreciates along the UIP path, and both converge to the new long-run equilibrium.

How big is the overshoot?

The size of the overshoot depends on the parameters of the model — particularly on how sticky prices are (lower π means larger overshoot) and how interest-elastic money demand is (higher λ means smaller overshoot for a given interest-rate fall). Dornbusch's algebra gives an explicit formula. With typical values for advanced economies, the on-impact exchange-rate response is roughly 1.2 to 1.5 times the long-run response — that is, a 20 to 50 percent overshoot beyond the long-run target.

The empirical literature is broadly consistent. Martin Eichenbaum and Charles Evans's 1995 QJE paper used vector-autoregression identification on US monetary-policy shocks to trace out the implied path of the trade-weighted dollar; they found significant overshoot at horizons of one to three years, with a peak excess depreciation of roughly 20-30 percent above the long-run level. Faust and Rogers (2003), Scholl and Uhlig (2008) and more recent work using high-frequency monetary surprises (Gertler-Karadi 2015) all find similar patterns. The half-life of the overshoot — the time for half of the excess depreciation to be undone — typically runs six months to two years.

Worked example: a 10 percent monetary expansion

Let the long-run equilibrium exchange rate be 1.00 USD/EUR. The central bank announces a permanent 10 percent expansion in money supply. By long-run neutrality, the new equilibrium is 1.10 (the domestic currency has depreciated by 10 percent). What happens on impact, and how does the path play out?

Suppose the foreign interest rate is fixed at 4 percent and the parameters of the model imply an on-impact domestic interest rate of 2 percent (a 200-basis-point fall). UIP requires an expected appreciation of 2 percent per year. Starting from the eventual long-run rate of 1.10 and working backward, the spot rate on impact must be:

e(0)  =  e_LR / (1 − E[Δe per period])
      =  1.10 / (1 − 0.02 × half-life-in-years)

With a half-life of, say, two years, the on-impact overshoot is around 4-6 percent — so the spot rate jumps to roughly 1.16 USD/EUR. Over the subsequent two years it appreciates from 1.16 toward 1.10, exactly tracing the UIP-implied path. The annualised expected appreciation along that path equals the 200 basis-point interest differential. The mechanics are tight: every variable in the model is determined simultaneously and the path is rationally expected.

Time	e (USD/EUR)	i (domestic)	p (price level)	Comment
t = 0⁻ (pre-shock)	1.00	4.0%	100	Equilibrium
t = 0 (impact)	1.16	2.0%	100 (sticky)	Massive depreciation; rate falls
t = 6 months	1.135	2.6%	102	Prices rising, currency appreciating
t = 1 year	1.12	3.1%	104	Convergence in progress
t = 2 years	1.11	3.7%	108	Approaching new long-run
t → ∞ (long run)	1.10	4.0%	110	New steady state

Empirical tests — what survived

Dornbusch's model has been tested intensively for nearly fifty years. The picture is mixed but largely supportive of the qualitative prediction.

• Qualitative overshooting — confirmed. Eichenbaum-Evans (1995), Faust-Rogers (2003), Scholl-Uhlig (2008), Bouakez-Normandin (2010), Gertler-Karadi (2015), Inoue-Rossi (2019) all find that monetary surprises produce on-impact exchange-rate moves larger than long-run moves, in the predicted direction. Robust across identification strategies and countries.
• UIP at high frequency — rejected. The 'forward premium puzzle' of Hansen-Hodrick (1980) and Fama (1984): currencies with higher interest rates do not subsequently depreciate as UIP predicts — they tend to appreciate, generating positive excess returns to carry trades. This contradicts the basic Dornbusch UIP equation at horizons under a year.
• UIP at long horizons — partially confirmed. Chinn-Meredith (2004), Engel (2014) and others find UIP holds far better at 5-10-year horizons than at quarterly. The long-run prediction of Dornbusch is consistent with the data even if the high-frequency dynamics are not.
• PPP convergence — too slow. Dornbusch's model has prices converging to long-run equilibrium relatively quickly. Empirically, the half-life of real-exchange-rate deviations from PPP is 3-5 years — much slower than basic price-stickiness assumptions imply. Modern models add layers of friction (local-currency pricing, distribution costs, durables) to explain the persistent real-exchange-rate volatility ('PPP puzzle' of Rogoff 1996).
• Disconnect puzzle — partial. Meese and Rogoff (1983) showed that random-walk forecasts beat structural models at one-month and one-year horizons. The Dornbusch model is no exception — its forecasting performance is mediocre. The model is useful for understanding mechanisms, not for predicting next month's rate.

Variants and modern extensions

• Frenkel-Rodriguez extensions. Add real shocks (productivity, terms of trade) and richer goods-market dynamics. Show that overshooting can run in either direction depending on shock origin.
• Obstfeld-Rogoff redux (1995, 2000). Build microfounded open-economy models with sticky prices, optimising households, and rational expectations. Confirm the qualitative overshooting prediction in a fully optimising framework.
• Open-economy New Keynesian models. Galí-Monacelli (2005), Adolfson et al. (2007), Justiniano-Preston (2010) embed Dornbusch dynamics in DSGE models used by central banks. Modern policy modelling at the Bank of Canada, Sveriges Riksbank and Bank of England all incorporate sticky-price overshooting as a core feature.
• Term-structure models. Bansal (1997), Backus-Foresi-Telmer (2001) integrate UIP with the term structure of interest rates, showing how overshooting interacts with bond-market expectations.
• Disconnect literature. Devereux-Engel (2002), Engel-West (2005) embed Dornbusch-style mechanics in models with discounting and asset-pricing dynamics to explain why exchange rates appear largely disconnected from fundamentals at high frequency.
• Heterogeneous-agent extensions. Itskhoki-Mukhin (2021) and others build models where exchange-rate dynamics are driven by both fundamentals and noise traders, generating overshooting alongside the empirical persistent excess volatility.

Policy implications

• Monetary policy moves exchange rates aggressively in the short run. A 25-basis-point Fed cut can move the trade-weighted dollar by far more than the long-run textbook prediction suggests. Central banks should expect — and communicate around — outsized short-run reactions.
• Foreign-currency debt creates balance-sheet risk. The overshoot means borrowers with un-hedged dollar liabilities can take large balance-sheet hits from monetary surprises. Emerging-market companies and sovereigns are particularly exposed. Latin American and Asian crises in 1994-2002 illustrate the channel vividly.
• Tradables sectors bear disproportionate adjustment. Because exchange rates move more than prices in the short run, tradable goods producers see their competitive position swing dramatically. Hedging is rational; building a tradables business assuming long-run exchange rates can be lethal.
• Co-ordinated intervention can work — partially. The Plaza Accord (1985) and Louvre Accord (1987) explicitly co-ordinated G5/G7 monetary signals to move the dollar. The model's policy implication is that announcement effects can shift expectations, and through expectations the spot rate. Reverse-engineering an overshoot in the desired direction is feasible if the signal is credible.
• Inflation targeting helps stabilise expectations. Credible inflation anchors reduce the policy-shock variance that feeds overshooting. Countries with explicit inflation targets (Canada from 1991, UK from 1992, Brazil from 1999) tend to have smaller exchange-rate responses to monetary surprises than countries without.

Common pitfalls and counterarguments

• "Overshooting requires irrationality." The opposite — Dornbusch's model is the rational-expectations equilibrium. The overshoot happens precisely because forward-looking agents must agree on a UIP-consistent path, and the only consistent path involves overshooting.
• "Sticky prices have to be assumed away." Empirically, prices ARE sticky — Bils-Klenow (2004) and Nakamura-Steinsson (2008) document median price-stickiness of 6-12 months in US data. The assumption is grounded.
• "UIP fails, so the model fails." UIP fails at short horizons but holds better at long ones. Modern overshooting models (Itskhoki-Mukhin 2021) include forces beyond UIP — risk premia, noise traders — while preserving the core overshooting mechanism.
• "Random walks beat the model in forecasting." True — Meese-Rogoff. But forecasting performance isn't the test of a structural model; understanding mechanism is. The model explains why exchange rates are volatile, not predicts their next move.
• "Modern models with floating prices give the same result." No — without sticky prices the overshoot disappears. The dynamics depend on the asymmetric speed of asset-market vs goods-market adjustment.
• "Overshooting was an artifact of 1970s data." Subsequent samples through 2024 confirm the pattern across the Volcker disinflation, the Plaza/Louvre era, the 1990s currency crises, the 2008 financial crisis, and the 2022-23 Fed tightening cycle. The mechanism remains operative.