Dornbusch Overshooting Model

Dornbusch Overshooting Model is a foundational dynamic open-economy macroeconomic model demonstrating that differential speeds of adjustment between sticky goods-market prices and flexible financial asset prices cause the nominal exchange rate to overreact—or overshoot—its long-run Purchasing Power Parity equilibrium in response to an unanticipated permanent change in Monetary Policy. Published by Rudiger Dornbusch in the Journal of Political Economy in 1976 ("Expectations and Exchange Rate Dynamics") shortly after the collapse of the Bretton Woods fixed-rate system, the model bridged the short-run Keynesian Mundell–Fleming extension of the IS–LM Model and the long-run monetary model of exchange rates. Within Business & Economics Theory, Dornbusch's synthesis provided the primary theoretical explanation for why floating nominal and real exchange rates exhibit far greater short-run volatility than underlying national price levels or monetary aggregates.

Consider a small open economy integrated into global financial markets under the Impossible Trinity regime of free capital mobility and a floating exchange rate. Throughout the analysis, lower-case letters denote natural logarithms of variables (except for interest rates): m is the log nominal money supply, p is the log domestic price level, y is log real output (with long-run potential output y^*), and e is the log spot nominal exchange rate defined as the domestic currency price of one unit of foreign currency (so an increase in e represents a depreciation of the domestic currency). The foreign price level is normalized to unity (p^* = 0 in logs), and the foreign nominal interest rate i^* is exogenous.

The Dornbusch system rests on four core structural building blocks that separate instantaneous financial-market equilibrium from gradual goods-market price adjustment:

1. Asset Market Equilibrium: UIP and Money Demand

Domestic and foreign government bonds are assumed to be perfect substitutes, and international capital mobility is costless and instantaneous. Consequently, portfolio arbitrage enforces Uncovered Interest Rate Parity (UIP) at every instant t:

where i(t) is the domestic nominal interest rate and E_t[de(t) ÷ dt] is the expected instantaneous rate of depreciation of the domestic currency. Under rational expectations (perfect foresight in the deterministic case), the expected rate of depreciation equals the actual rate of change de ÷ dt, which agents relate to the gap between the long-run equilibrium exchange rate e_LR and the current spot rate e(t):

Simultaneously, the domestic money market clears at every moment via a log-linear Baumol–Tobin Model or Cagan-style money demand schedule:

where φ > 0 is the income elasticity of money demand and λ > 0 is the interest semi-elasticity of money demand.

2. Goods Market Demand and Sticky Price Adjustment

Unlike asset prices (e and i), which jump instantaneously in response to news, the domestic goods price level p(t) is sticky (predetermined) in the short run. Aggregate demand for domestic output y^d(t) depends positively on the real exchange rate (e(t) − p(t)), negatively on the domestic interest rate i(t), and positively on potential income:

Whenever aggregate demand exceeds potential output (y^d(t) > y^*), excess demand pushes domestic prices upward over time according to a Phillips-type gradual adjustment equation with speed parameter π > 0:

In the long-run steady state (dp ÷ dt = 0 and de ÷ dt = 0), the domestic interest rate equals the world rate (i_LR = i^*), real output equals potential (y = y^*), and neutrality of money holds: a permanent, unanticipated increase in the log money supply by Δm > 0 raises the long-run price level p_LR and the long-run nominal exchange rate e_LR by the same proportion:

Why, then, does the spot exchange rate e(0) jump on impact by more than Δm when the monetary expansion occurs at time t = 0?

1. Short-Run Liquidity Effect on Interest Rates: At impact (t = 0), the nominal money supply increases by Δm > 0, while the sticky domestic price level p(0) cannot jump. Therefore, the real money supply (m − p(0)) increases by Δm. With output fixed at y^* in the baseline version, clearing the money market requires the domestic nominal interest rate i(0) to fall below the world interest rate i^* by Δi(0) = −Δm ÷ λ < 0.
2. Arbitrage Condition in the Foreign Exchange Market: Because the domestic interest rate is now lower than the foreign interest rate (i(0) < i^*), international investors would refuse to hold domestic bonds unless they are compensated by an expected future appreciation of the domestic currency (E₀[de ÷ dt] < 0) equal to the interest differential i(0) − i^* < 0.
3. Instantaneous Overshooting Beyond Long-Run PPP: How can rational investors simultaneously know that the currency will be permanently weaker in the long run (by Δe_LR = Δm) and yet expect it to appreciate from time t = 0 onward? The only way both conditions can hold is if the spot exchange rate e(0) depreciates instantaneously at t = 0 to a level above its new long-run equilibrium (e(0) > e_LR).

Substituting Δi(0) = −Δm ÷ λ and Δe_LR = Δm into the UIP relation i(0) − i^* = θ(e_LR − e(0)) yields the explicit Dornbusch Overshooting Equation:

Because λ > 0 and θ > 0, the impact depreciation multiplier 1 + 1 ÷ (λθ) exceeds unity. The smaller the interest semi-elasticity of money demand (λ) or the slower the speed of goods-market price adjustment (which lowers θ), the larger is the magnitude of initial exchange-rate overshooting.

In the (p, e) phase plane, the Dornbusch system is governed by two differential equations: one for predetermined goods prices (dp ÷ dt) and one for the forward-looking jump variable (de ÷ dt). The resulting 2 × 2 Jacobian matrix has a negative determinant, implying one negative (stable) eigenvalue (−θ) and one positive (unstable) eigenvalue. Consequently, the equilibrium is a saddle point with a downward-sloping stable manifold (the saddle path SS of slope −1 ÷ (λθ)):

• At t = 0, an unanticipated permanent monetary expansion shifts the steady-state intersection (p_LR, e_LR) outward along the 45-degree ray by (Δm, Δm), shifting the downward-sloping saddle path SS upward and to the right.
• Because p(0) cannot jump horizontally, the economy must jump vertically onto the new saddle path S′S′ at e(0) > e_LR to avoid explosive hyperinflationary or deflationary bubbles.
• For t > 0, the depreciated real exchange rate and low interest rate stimulate excess demand (y^d > y^*), causing p(t) to rise gradually. As p(t) rises, real balances (m − p(t)) shrink, driving i(t) back up toward i^* while the exchange rate e(t) appreciates smoothly down the saddle path toward e_LR.

Variable Output and the Undershooting Case

In Section IV of his 1976 paper, Dornbusch extended the model to allow short-run real output y(t) to respond endogenously to aggregate demand (y = y^d). If output rises strongly on impact, the resulting surge in transactions money demand (φΔy) increases the demand for liquidity. If φ × δ > 1, the income effect on money demand outweighs the liquidity effect of Δm, causing the domestic interest rate i(0) to rise above i^* on impact and inducing exchange-rate undershooting (e(0) < e_LR).

Empirical Legacy and Exchange-Rate Puzzles

Kenneth Rogoff's (2002) retrospective on the 25th anniversary of Dornbusch's paper highlighted both its enduring theoretical influence—serving as the ancestor of the Obstfeld–Rogoff (1995) Redux New Open Economy Macroeconomics framework—and two empirical challenges: the Meese–Rogoff (1983) random-walk forecasting puzzle and the "delayed overshooting" pattern estimated in structural vector autoregressions by Eichenbaum and Evans (1995), where the peak depreciation occurs several quarters after a monetary shock rather than instantaneously at t = 0.

Why does an announced future monetary expansion cause an immediate depreciation before the money supply changes?

Because the nominal exchange rate e(t) is a forward-looking asset price governed by rational expectations, foreign exchange traders price in future monetary expansions as soon as the policy announcement becomes credible at t = 0. The spot exchange rate jumps instantaneously to an intermediate depreciated level at the announcement date and then continues depreciating smoothly so that no predictable discrete jump (which would offer an infinite risk-adjusted arbitrage return) occurs on the actual implementation date T.

What determines the speed of convergence (θ) along the Dornbusch saddle path?

Rational expectations require that the expected rate of appreciation parameter θ equal the absolute value of the negative stable eigenvalue of the dynamic system. Solving the characteristic equation gives θ = π(δ + σ ÷ λ) ÷ 2 + √{[π(δ + σ ÷ λ) ÷ 2]² + πδ ÷ λ}. Thus, convergence is faster when goods prices are more flexible (larger π) and when net exports are more responsive to the real exchange rate (larger δ).

How does the Dornbusch model explain real exchange rate volatility?

Because the log real exchange rate is q(t) = e(t) − p(t), and the domestic price level p(0) is sticky on impact while e(0) overshoots by Δm[1 + 1 ÷ (λθ)], monetary shocks generate one-for-one changes in both the nominal and the real exchange rate in the short run, explaining why real exchange rates co-move closely with nominal exchange rates under floating regimes.

1. Dornbusch, R. (1976). "Expectations and Exchange Rate Dynamics." Journal of Political Economy, 84(6), 1161–1176. https://doi.org/10.1086/260506
2. Rogoff, K. (2002). "Dornbusch's Overshooting Model After Twenty-Five Years." IMF Staff Papers, 49(Special Issue), 1–34. https://doi.org/10.5089/9781451845846.001
3. Obstfeld, M., & Rogoff, K. (1995). "Exchange Rate Dynamics Redux." Journal of Political Economy, 103(3), 624–660. https://doi.org/10.1086/261997
4. Eichenbaum, M., & Evans, C. L. (1995). "Some Empirical Evidence on the Effects of Shocks to Monetary Policy on Exchange Rates." Quarterly Journal of Economics, 110(4), 975–1009. https://doi.org/10.2307/2946646
5. Meese, R. A., & Rogoff, K. (1983). "Empirical Exchange Rate Models of the Seventies: Do They Fit Out of Sample?" Journal of International Economics, 14(1–2), 3–24. https://doi.org/10.1016/0022-1996(83)90017-X90017-X)