# Overshooting

**DOI:**https://doi.org/10.1057/978-1-349-95189-5_1662

## Abstract

An economic variable may ‘overshoot’ its steady-state value in many different contexts. In recent economic theory the term has assumed a more specific meaning, describing a characteristic relationship between current returns and capital gains on financial assets.

An economic variable may ‘overshoot’ its steady-state value in many different contexts. In recent economic theory the term has assumed a more specific meaning, describing a characteristic relationship between current returns and capital gains on financial assets.

*i*, consists of the current return,

*r*(rental, dividend, coupon), and the capital gain, \( \dot{p} \) both expressed as a proportion of its market price,

*p*:

*p*= 0 and

*i = r/p*. Suppose arbitrage sees to it that

*i*is always equal to the yield on other assets,

*j*, regarded as given and constant. Suppose further that there is some new information indicating that r will be above its steady-state level for a limited period. As a consequence, there will be an instantaneous increase, or ‘jump’, in the asset price reflecting the present value of the extra returns. From then on, the temporary gain in

*r*will be continuously matched by a capital loss, so that \( \dot{p} \)/

*p*< 0. The expectation of a limited period of extra returns will thus produce an instantaneous appreciation of the asset followed by gradual depreciation. This saw-tooth pattern of the asset price is what is called overshooting. While overshooting in a general sense may well be due to speculative excesses, ‘bubbles’ and mistaken expectations, it is important to note that in the more specific sense described here it is not only consistent with, but an implication of, the correct anticipation of the consequences of unexpected disturbances.

While overshooting, as such, is a commonplace feature of asset markets, it is particularly important in foreign exchange markets, where it was observed by Gustav Cassel around 1920. The excess supply of German marks, he argued, had depressed their foreign exchange value so far below its longer-term equilibrium that the expectation of future appreciation attracted speculators, even at relatively low interest rates. Unfortunately, since Cassel did not bother to provide an analytical elaboration, his insight was lost for more than half a century, to be rediscovered around 1974. It was first developed into a theoretical model by Dornbusch (1976). A compact, up-to-date survey of overshooting theory is provided in Obstfeld and Stockman (1985). A somewhat less technical overall perspective is given in Niehans (1984).

Overshooting has to be defined with reference to an equilibrium exchange rate. For a purely monetary disturbance (and in the absence of government debt), the appropriate reference point is purchasing-power parity. PPP relates to the parallel effects of an exogenous increase in the supply of fiat money on exchange rates and prices. It postulates, specifically, that these effects are proportionally equal, which implies that exchange rates and prices move in step. The proposition clearly relates to the comparison of steady states. In the short run, the effects of money on exchange rates can deviate very considerably from those on commodity prices. These deviations are the main subject of overshooting theory.

The difference between the change in the exchange rate and the contemporaneous change in the international commodity price ratio is often called the change in the real exchange rate. In the steady state, an exogenous increase in the money supply has no effect on the real exchange rate. Overshooting implies, however, that there may be sharp fluctuations in real exchange rates in the short run.

*t*

_{0}(see Fig. 1).

With sticky prices, this will be reflected in an immediate increase in real balances and thus a decline in the rate of interest. As prices gradually move upward, the interest rate will rise again toward its equilibrium level. Since international arbitrage equalizes foreign and domestic yields, low domestic yields must be accompanied by a declining price of foreign exchange (with the slope of the exchange rate curve reflecting the interest differential). Under perfect foresight, a gradual decline during the adjustment process is achieved by an instantaneous overshooting of the exchange rate relative to its steady-state level derived from purchasing-power parity. The dynamic properties of such a system were analysed by Gray and Turnovsky (1979); they generally involve saddle-point instability. The size of the initial overshooting has to be determined by reckoning ‘backward’ from the steady state.

Instead of a step-like increase in the money supply, the underlying disturbance may be an increase in the rate of monetary expansion (Frankel 1979). In this case, because of continuing inflation, overshooting cannot be defined with reference to a steady state of the nominal exchange rate. Nor is it certain that the nominal exchange rate will temporarily decline after the instantaneous increase. However, there will still be overshooting of the nominal exchange rate relative to PPP and thus in the real exchange rate. A reversal of direction may also be absent if the market takes time to recognize a change in monetary policy (Moser 1983). Econometric estimates by Driskill (1981) indicate overshooting by a factor of 2.3 in the dollar price of the Swiss franc. Moser’s work suggests that this estimate may be too high because not all changes in the Swiss money supply during the period in question could legitimately be regarded as exogenous. Generally, overshooting seems to be quite sensitive to variations in conditions and model specification. It would not be surprising, therefore, if econometric estimates differed widely.

Besides interest arbitrage, there are other causes of overshooting exchange rates. Of particular importance is the fact that an economy cannot acquire (net) foreign assets overnight, but only over a period of current-account surpluses. This type of portfolio mechanism was first investigated by Kouri (1976) and further developed by Calvo and Rodriguez (1977) and Branson (1979). An exogenous increase in the money supply, with sticky prices, results in an increased demand for international assets. Since the stock of such assets cannot be immediately increased, there is an instantaneous depreciation of the domestic currency, implying overshooting relative to PPP. As domestic prices creep upward, again reducing real balances, the composition of portfolios gradually returns to the initial situation, overshooting subsides, and the exchange rate approaches purchasing-power parity. The nominal exchange rate may also overshoot its equilibrium level, but this is not certain. The sequence of current-account surpluses and deficits during the adjustment process is even more uncertain (Frenkel and Rodriguez 1982; Niehans 1984). Even for small open economies, the overshooting mechanism thus turns out to be quite complicated. In interdependent economies, the taxonomy of dynamic patterns becomes yet more complex (Niehans 1977).

After other than purely monetary disturbances, overshooting of exchange rates may occur even with perfectly flexible prices (Dornbusch and Fischer 1980; Kouri, 1983). In the case of a spontaneous increase in the domestic demand for foreign assets, the additional assets can only be provided through current-account surpluses. These, in turn, require a temporary rise of the exchange rate above its equilibrium level, which means overshooting. Asset arbitrage will see to it that the gradual re-appreciation of the domestic currency following the instantaneous depreciation is associated with an interest differential in favour of foreign rates. But low domestic interest rates result in an increased demand for real balances, which can only be satisfied at domestic prices below their equilibrium level. The overshooting of the exchange rate is thus associated with an undershooting of interest rates and prices, followed by a gradual return to equilibrium. During this process, a depressed, but gradually appreciating, currency is accompanied by a current account surplus and thus a capital outflow. In general, however, there is no clearcut correspondence between exchange overshooting and capital flows.

Since the collapse of the gold-exchange standard in 1973, exchange rates seem to have fluctuated more than their underlying determinants (like money supplies or incomes), and also more than leading monetary theorists had expected. The theory of overshooting suggests that this may be due to the way asset markets work even under perfect foresight. As already realized by Cassel, the resulting fluctuations in real exchange rates may be the source of potentially serious disturbances in the trade, output and employment of the countries concerned. Indeed, overshooting turned out to be the principal policy problem of floating rates.

This raises the question whether overshooting could be dampened or even eliminated by suitable monetary and foreign exchange policies. Various methods have been proposed or debated. The most radical is the return to fixed exchange rates. This would eliminate overshooting by suppressing any movements in exchange rates, thus depriving countries of their monetary autonomy. Other proposals would limit exchange rate movements to a slow ‘crawl’ (Williamson, 1981), but it is doubtful that they would be workable without exchange control and international policy coordination. The so-called OPTICA proposal (CEC, 1977) postulated that foreign exchange interventions be used to keep exchange rates at purchasing-power parity even in the short run. This may make it impossible for central banks to follow a non-inflationary course and also raises serious stability problems. At the present time there seem to be no tested techniques whereby central banks could confidently expect to dampen overshooting without compromising other objectives. It may be better, therefore, not to rely on automatic schemes and to meet each case of serious overshooting on its merits. The most basic policy rule surely is to avoid abrupt shifts in the course of monetary policy.

## See Also

## Bibliography

- Branson, W.H. 1979. Exchange rate dynamics and monetary policy. In
*Inflation and employment in open economies*, ed. A. Lindbeck. Amsterdam: North-Holland.Google Scholar - Calvo, G.A., and C.A. Rodriguez. 1977. A model of exchange rate determination under currency substitution and rational expectations.
*Journal of Political Economy*85(3): 617–625.CrossRefGoogle Scholar - Cassel, G. 1921.
*The world’s monetary problems: Two memoranda to the league of nations*. London: Constable.Google Scholar - Commission of the European Communities (CEC). 1977.
*Inflation and exchange rates: Evidence and policy guidelines for the European community*. OPTICA Report 1976, Brussels.Google Scholar - Dornbusch, R. 1976. Expectations and exchange rate dynamics.
*Journal of Political Economy*84(6): 1161–1176.CrossRefGoogle Scholar - Dornbusch, R., and S. Fischer. 1980. Exchange rates and the current account.
*American Economic Review*70(5): 960–971.Google Scholar - Driskill, R.A. 1981. Exchange-rate dynamics: An empirical investigation.
*Journal of Political Economy*89(2): 357–371.CrossRefGoogle Scholar - Frankel, J.A. 1979. On the mark: A theory of floating exchange rates based on real interest differentials.
*American Economic Review*69(4): 610–622.Google Scholar - Frenkel, J.A., and C.A. Rodriguez. 1982. Exchange rate dynamics and the overshooting hypothesis.
*IMF Staff Papers*29(1): 1–30.CrossRefGoogle Scholar - Gray, M.R., and S.J. Turnovsky. 1979. The stability of exchange rate dynamics under perfect myopic foresight.
*International Economic Review*20(3): 643–660.CrossRefGoogle Scholar - Kouri, P.J.K. 1976. The exchange rate and the balance of payments in the short run and in the long run: A monetary approach.
*Scandinavian Journal of Economics*78(2): 280–304.CrossRefGoogle Scholar - Kouri, P.J.K. 1983. Balance of payments and the foreign exchange market: A dynamic partial equilibrium model. In
*Economic interdependence and flexible exchange rates*, ed. J.S. Bhandari and B.H. Putnam. Cambridge, MA: MIT Press.Google Scholar - Moser, B. 1983.
*Der frankenkurs des dollars 1973–1980: Ein test der kaufkraftparitätentheorie*, Berner Beiträge zur Nationalökonomie, vol. 43. Bern: Haupt.Google Scholar - Niehans, J. 1977. Exchange rate dynamics with stock/flow interaction.
*Journal of Political Economy*85(6): 1245–1257.CrossRefGoogle Scholar - Niehans, J. 1984.
*International monetary economics*. Baltimore: Johns Hopkins University Press.Google Scholar - Obstfeld, M., and A.C. Stockman. 1985. Exchange-rate dynamics. In
*Handbook of international economics*, vol. II, ed. R.W. Jones and P.B. Kenen. Amsterdam: North-Holland.Google Scholar - Williamson, J. 1981.
*Exchange rate rules: The theory, performance and prospects of the crawling peg*. New York: St Martin’s Press.CrossRefGoogle Scholar