Overshooting (Exchange Rates)

Overshooting, in international economics, describes an exchange rate that reacts to a shock by moving beyond the level where it will eventually settle, then gradually moves back. The classic version is the model published by the economist Rudiger Dornbusch in 1976, "Expectations and Exchange Rate Dynamics", in the Journal of Political Economy. It showed that a surprise expansion of the money supply can make a currency fall by more than the eventual rise in prices justifies, even when everyone in the market forms expectations rationally.

The model was written to explain why floating exchange rates, introduced after the collapse of the Bretton Woods system in the early 1970s, proved far more volatile than many economists had expected. It combines sticky prices in goods markets with fast-moving asset markets, and remains a standard teaching model of exchange rate dynamics and of how monetary policy works in an open economy.

Imagine a crowded room in which the thermostat is suddenly turned down. The air near the vents cools almost instantly, but the walls and furniture take hours to change temperature. For a while the air feels colder than the room will be once everything settles. Currency markets are like the air; shop prices and wages are like the walls.

When a central bank surprises markets by cutting interest rates, traders sell the currency immediately. Shop prices, however, barely move for months. Because only the currency can adjust at first, it has to move more than it eventually needs to, and then it creeps back as prices catch up.

The model rests on three assumptions: prices of goods adjust slowly; capital moves freely between countries; and investors expect the exchange rate to return gradually to its long-run value. Capital mobility means uncovered interest parity holds: any gap between home and foreign interest rates must be matched by an expected change in the exchange rate. With expectations that the currency returns towards its long-run level at speed $\theta$, the condition is:

• $i$ and $i^{*}$ are the home and foreign interest rates.
• $s$ is the log of the exchange rate (home currency per unit of foreign currency), so a rise means depreciation.
• $\bar{s}$ is the long-run equilibrium exchange rate.
• $\theta$ is the speed at which the rate is expected to close the gap each period.

A permanent rise in the money supply $\Delta m$ raises the long-run price level and $\bar{s}$ by the same proportion. In the short run, with prices fixed, the extra money pushes the home interest rate down by $\Delta m / \lambda$, where $\lambda$ measures how sensitive money demand is to interest rates. For investors to hold home assets at the lower rate, they must expect the currency to appreciate from here on, which is only possible if it first falls below its long-run value. The initial jump is:

Worked example: the money supply rises by 10%, with $\lambda = 2$ and $\theta = 0.5$, so $\lambda \theta = 1$. The currency immediately depreciates by $10\% \times (1 + 1) = 20\%$, twice its long-run move of 10%. As prices rise and the interest rate returns to normal, the currency regains about half of the initial fall. The smaller $\lambda\theta$, the bigger the overshoot.

Economists have linked overshooting to several episodes. The sharp appreciation of sterling in 1979–1981, when the UK tightened monetary policy and North Sea oil came on stream, was analysed in overshooting terms at the time. The strong US dollar of the early 1980s, under tight Federal Reserve policy, and the fall of the yen after the Bank of Japan's large-scale easing from 2013 are also often discussed in this framework, alongside the Swiss franc jump when the Swiss National Bank removed its euro floor in January 2015.

Formal tests give mixed results. A well-known study by Martin Eichenbaum and Charles Evans (1995) found "delayed overshooting": after a US monetary tightening, the dollar kept appreciating for a year or more instead of jumping at once, which contradicts the timing of the original model. Later work using high-frequency data around central bank announcements finds that currencies react quickly to policy surprises, closer to Dornbusch's prediction. Overall, the model is better at explaining why exchange rates are volatile than at forecasting them, and forecasting currencies remains notoriously hard.

• Expectations. The original model assumes investors know the true model and expect a smooth return to equilibrium. With rational expectations in a richer setting, or with traders who follow trends, the path can look very different, and bubbles can form.
• Output effects. If output responds to the shock, as in later versions, overshooting can be smaller or even reversed.
• Interest parity. The carry trade and the forward premium puzzle suggest that uncovered interest parity often fails in practice, weakening the mechanism. See forward exchange rate for the related evidence.
• Policy relevance. The model implies that monetary shocks can cause large swings in the real exchange rate, hurting export industries temporarily. This has been used both to argue for stable, predictable policy and, by some, to justify capital controls or intervention.

Dornbusch's paper is widely regarded as one of the most influential in international macroeconomics. It sits alongside the Mundell–Fleming framework and the work on optimal currency areas as a foundation of open-economy analysis, and modern central banks still weigh exchange-rate overshooting when judging how fast interest rate differentials feed through to inflation and equilibrium.

• NBER: Eichenbaum and Evans, "Some Empirical Evidence on the Effects of Monetary Policy Shocks on Exchange Rates"