Sources of Exchange Rate Variability: Theory and Empirical Evidence

Four years’ experience with floating exchange rates have revealed a number of troubling and still puzzling aspects of the behavior of flexible exchange rates. To some extent, gaps in understanding about how flexible exchange rates behave are a result of the preponderance of attention focused, before the advent of floating exchange rates, on the fixed versus flexible exchange rate controversy rather than on the issues particular to flexible exchange rates. Models of flexible exchange rate behavior were usually built for symmetrical analyses of policy alternatives under fixed and flexible exchange rate regimes. These generally gave little attention to the problems of how expectations about future exchange rates are formed, reactions of the economy to risk concentrated in the foreign exchange market, and disequilibrium dynamics of the exchange rate. In addition, they rarely considered possible differences between a free float and a managed float. In short, the highly generalized debate on the ease of adjustment under fixed and flexible rates did not permit a rigorous examination of exchange rate dynamics. Of course, the additional disadvantage of being unable to observe flexible exchange rate behavior firsthand also inhibited a thorough study of exchange rate dynamics.


Four years’ experience with floating exchange rates have revealed a number of troubling and still puzzling aspects of the behavior of flexible exchange rates. To some extent, gaps in understanding about how flexible exchange rates behave are a result of the preponderance of attention focused, before the advent of floating exchange rates, on the fixed versus flexible exchange rate controversy rather than on the issues particular to flexible exchange rates. Models of flexible exchange rate behavior were usually built for symmetrical analyses of policy alternatives under fixed and flexible exchange rate regimes. These generally gave little attention to the problems of how expectations about future exchange rates are formed, reactions of the economy to risk concentrated in the foreign exchange market, and disequilibrium dynamics of the exchange rate. In addition, they rarely considered possible differences between a free float and a managed float. In short, the highly generalized debate on the ease of adjustment under fixed and flexible rates did not permit a rigorous examination of exchange rate dynamics. Of course, the additional disadvantage of being unable to observe flexible exchange rate behavior firsthand also inhibited a thorough study of exchange rate dynamics.

Four years’ experience with floating exchange rates have revealed a number of troubling and still puzzling aspects of the behavior of flexible exchange rates. To some extent, gaps in understanding about how flexible exchange rates behave are a result of the preponderance of attention focused, before the advent of floating exchange rates, on the fixed versus flexible exchange rate controversy rather than on the issues particular to flexible exchange rates. Models of flexible exchange rate behavior were usually built for symmetrical analyses of policy alternatives under fixed and flexible exchange rate regimes. These generally gave little attention to the problems of how expectations about future exchange rates are formed, reactions of the economy to risk concentrated in the foreign exchange market, and disequilibrium dynamics of the exchange rate. In addition, they rarely considered possible differences between a free float and a managed float. In short, the highly generalized debate on the ease of adjustment under fixed and flexible rates did not permit a rigorous examination of exchange rate dynamics. Of course, the additional disadvantage of being unable to observe flexible exchange rate behavior firsthand also inhibited a thorough study of exchange rate dynamics.

Now, however, the fixed versus flexible debate has been overtaken by the realization that, imperfect as it may be, floating is necessary to a world that refuses to accept the discipline of policy harmonization. Research effort has correspondingly turned to the task of trying to understand why, contrary to predictions of long-standing advocates of flexible exchange rates, the first four years of floating have been characterized by very large fluctuations in exchange rates, even for relatively stable economies, such as those of the Federal Republic of Germany and the United States.

Bilateral exchange rates between a number of major currencies have shown large fluctuations, although effective exchange rates (the weighted average of exchange rates of one currency against a variety of others) have fluctuated considerably less. For example, during the four years of floating, the rate for the deutsche mark against the U. S. dollar (and, similarly, the exchange rates of snake currencies taken as a whole) experienced four major fluctuations in which, over a period of up to one year, the exchange rate appreciated and then depreciated over a range of 10 to 20 per cent. The Austrian schilling and the Swiss franc have tended to follow the fluctuations of the snake currencies against the dollar. The French franc, sporadically coordinated with the snake, also displayed several fluctuations against the dollar over the period. Fluctuations of the Canadian dollar and the Japanese yen, while far from being negligible, have been milder than those of the major European currencies. Finally, the United Kingdom and Italy have seen their exchange rates on a rather consistent, yet still erratic, trend of depreciation.

This paper is an attempt to collect and critically evaluate various explanations that have been proposed as to why such significant exchange rate variations have persistently characterized the current floating regime. On the surface, the problem of explaining exchange rate variations does not appear to be a difficult task. The traditional monetarist approach, which views exchange rates as the price of one money in terms of another, suggests that not only randomly distributed real shocks but also the commonly observed divergences between countries’ monetary policies would largely explain the variations in bilateral exchange rates. In terms of the familiar Mundellian analysis,1 where capital mobility is infinite, output is at its full-employment level, and the expected future spot rate is identical to the current spot rate, a monetary expansion in one country is illustrated in Figure 1. XX is the locus of combinations of the price level and exchange rate consistent with the domestic goods market equilibrium. LL is the equivalent locus of points consistent with money market equilibrium. XX must be a 45° upward-sloping line, since an increase in prices reduces demand for domestic goods and must therefore be offset by a diversion of foreign demand to domestic goods via an exchange rate depreciation.2 LL is vertical because the equality of forward and spot rates implies that the domestic interest rate must always equal the foreign rate. Prices must, therefore, change in proportion to changes in the money supply to preserve money market equilibrium. The analysis shows that an increase in the domestic money supply produces an increase in prices and a depreciation in the exchange rate, as seen in the movement from P0 to P1, and from S0 to S1.

However, the last four years’ experience with floating rates suggests that there may be more to the adjustment process than the simple monetarist argument implies. There is, for example, concern that variations of floating exchange rates have been larger than those of determining factors.3 Also, changes in exchange rates have often exceeded differences between countries’ rates of inflation. Pigott, Sweeney, and Willett (1976), for example, report that the variability of the dollar exchange rate of several currencies is greater than the variability of those countries’ price levels relative to that of the United States. The explanations of exchange rate dynamics reviewed in the following pages deal explicitly with the possibility of overshooting or “magnification” effects in exchange rate adjustment, that is, greater variations in exchange rates than in their fundamental determinants. The idea underlying this paper is that the explanation for such exchange rate behavior lies in unresolved issues concerning expectations formation, differential speeds of adjustment among markets, the impact of uncertainty on foreign exchange transactions, and the nature of economic policy decisions.

Before turning to this matter, a word about the importance of exchange rate variations will put the problem in perspective.4 The most readily identifiable cost imposed by exchange rate variability is the risk of exchange rate changes during the contract period of any international goods, or capital market, transaction. Even if forward cover can be obtained to eliminate exchange risk, higher bid-ask spreads and other transactions costs can increase the cost of international, relative to domestic, transactions. Frequent and severe exchange rate variations are also likely to produce substantial and prolonged deviations from purchasing power parity (PPP) between currencies. Aside from adding to uncertainty about the relative cost of buying foreign and domestic goods, prolonged deviations from PPP can distort the allocation of resources on an international scale. All these factors can build some reluctance on the part of businesses to become involved in international transactions unless they are properly rewarded for the risks that they assume.

The remainder of this paper is organized into four sections, each covering one aspect of exchange rate adjustment that has been proposed as the source of exchange rate variations. Each of these aspects can be fitted into a general model in which exchange rates are determined by the balancing of supply and demand for each currency and in which expectations play a prime role in determining demand. Section I deals with the various methods by which expectations of future exchange rates may be formed. Section II reviews the exchange rate dynamics postulated by asset market equilibrium models, which assume that, in the short run, exchange rates are determined in asset markets. Section III considers the possibility that the exchange risk accompanying international transactions under flexible exchange rates prevents smooth adjustments to disturbances in exchange markets. Finally, Section IV examines exchange rate movements in a managed float, where official intervention may have a significant impact on deviations of the exchange rate from its equilibrium value.

I. The Role of Expectations in Exchange Rate Determination

The centerpiece in the early debate over fixed versus flexible exchange rates was the question of whether speculation is “stabilizing” or “destabilizing.” 5 Essentially, this aspect of the debate was concerned with whether speculators forming expectations about future exchange rates merely extrapolate from a trend and move funds so as to reinforce that trend, or whether, on the basis of a consistent appraisal of the forces at work in the foreign exchange markets, speculators form some idea of an equilibrium rate and transact in a way that moves the actual rate toward that value. If the former were true, speculators could be accused of destabilizing the market, and large exchange rate gyrations could result from just about any small disturbance that initiated a trend. This debate set the stage for an as yet unresolved controversy over the empirical and theoretical justification for relating exchange rate swings to destabilizing speculation.6

Writing in 1944, Nurkse attributed the exchange rate instability of the interwar years to destabilizing speculation. According to Nurkse, the depreciation of several European currencies in the early 1920s began as a response to shortages of physical capital following World War I and was successful in attracting foreign capital. As depreciation (particularly for the example of France that is cited) persisted with only sporadic periods of relief, however, expectations became increasingly elastic (i.e., sensitive to movements in the current spot rate) and resulting capital outflows hastened further depreciation.7 Nurkse (p. 118) points to this tendency toward destabilizing speculation as evidence that the market was unable “to maintain a stable equilibrium, at any rate in the short run”:

. . . anticipations [of exchange rate depreciation] are apt to bring about their own realization. Anticipatory purchases of foreign exchange tend to produce or at any rate to hasten the anticipated fall in the exchange value of the national currency, and the actual fall may set up or strengthen expectations of a further fall.

Advancing a related argument for the possibility of unstable exchange rate behavior, Nurkse (p. 119) questions whether trade flows react as normally expected to “wide and violent exchange [rate] variations.” In the first place, he argues, demand elasticities may be low, particularly in the short run (i.e., the Marshall-Lerner conditions may not hold), so that a perverse trade balance effect results from exchange rate changes. Second (p. 120), “speculative anticipations dominating the exchange market” may affect commodity traders so that a depreciation of the exchange rate that generates expectations of a further depreciation may encourage an increase in imports by importers hoping to avert further price increases. Both influences would tend to reinforce exchange rate trends, once initiated.

Nurkse denies that domestic credit policies of individual countries induced rational speculators to behave as they did. He concedes that France did experience rapid expansion of domestic credit during the “destabilizing” period, but insists that the withdrawal of funds from French Treasury paper (after the initial exchange rate depreciation set up expectations of further depreciation)necessitated the credit expansion, rather than vice versa.8 Domestic credit policy, he claims (pp. 121-22), is not a sufficient stabilizing mechanism, since the credit system is usually elastic enough to meet excess demand through “previously inactive reserves or out of additional bank credits.” Instead, he believes, direct exchange stabilization measures are required to offset capital flows.

Since Nurkse, the stabilizing versus destabilizing speculation controversy has centered around two issues: (1) Can profits be made from destabilizing speculation? and (2) Does the pattern of exchange rate movements that has emerged during the current floating exchange rate regime differ from one that would have occurred if speculation were destabilizing?

Friedman (1953) seriously challenged the destabilizing speculation theory with the assertion that destabilizing capital flows could not be profitable for the market as a whole. Postulating that market transactors have linear supply and demand functions for foreign exchange and that the foreign exchange market works like any other asset market, he shows that profitable speculation should always drive exchange rates toward their equilibrium values. Destabilizing speculation in this simple context implies that speculators, by collectively buying when the price of foreign exchange is high and selling when it is low, would lose money. Friedman concedes that such behavior could characterize a small, continuously changing group of “amateur” speculators but asserts that “professional” speculators and/or the government should speculate against these “amateurs” and make money. His conclusion is that excessive exchange rate gyrations produced by destabilizing speculation could occur only if most speculative funds were controlled by irrational speculators.

Numerous counterexamples of Friedman’s proposition have been based on the alteration of one or more of his assumptions. Kemp (1964), for example, shows that nonlinear demand functions for foreign exchange can produce multiple equilibria, and that speculators can force the exchange rate to oscillate between two stable equilibria.9 A more interesting attack on Friedman’s thesis deals with the role of expectations in determining speculative demand. Friedman’s analysis admits only the level relative to the expected future value of the exchange rate as an argument in the speculative demand function, but does not explain explicitly how expectations are formed. A Nurksian model, however, introduces a time dimension in the form of past exchange rate movements as a determinant of expectations of the future exchange rate. In this sort of model, a speculator still profits by buying when the price is low and selling when it is high, but it is assumed that he may be able to identify peaks and troughs only ex post, or after a new trend has been established. Baumol (1957) puts this problem in a mathematical framework in an attempt to determine whether maximum speculative sales immediately after the start of a trend of exchange rate depreciation and maximum purchases after the start of a trend of appreciation could both yield profits and aggravate exchange rate swings.

In Baumol’s example, the interaction of nonspeculators, whose demand for domestic currency depends positively on the current level of the exchange rate, and the supplier of currency (presumably the government), who follows a cyclical pattern in supplying currency, is assumed to produce regular, cyclical exchange rate fluctuations in the absence of speculation.10 Introducing speculators whose demand for currency depends on recent trends, as well as the current level of the exchange rate, produces explosive exchange rate oscillations.11 The example can be grasped intuitively by understanding that the speculative excess demand function specifies that speculative sales be greatest when a cyclical depreciation of the exchange rate begins, and speculative purchases greatest when a cyclical appreciation begins. Thus, while speculators’ response to changes in the exchange rate level tends to stabilize the market, their response to changes in trends tends to accelerate downward and upward movements. Baumol’s example is designed to show that the latter influence can outweigh the former so as to produce speculation that is, on balance, destabilizing.

Of course, counterexamples of Friedman’s proposition about speculation had to show not only that there are plausible behavioral postulates that imply destabilizing speculation but also that such speculation could be profitable and, therefore, sustained in a rational world. Baumol presents a rigorous mathematical proof to show that, under certain conditions on the timing of speculative purchases, speculators would make profits by behaving in the way postulated. His model implies that speculative excess demand follows a sinusoidal curve of constant amplitude and that the duration of each cycle is equal to that of the cycle in prices resulting from nonspeculative behavior. These speculative excess demand cycles, however, are inversely related to and lag slightly behind exchange rate cycles. This means that the integral of the exchange rate times excess demand over a cycle is positive (i.e., profits are greater than zero), provided that the lag between price movements and speculative purchases is less than one fourth of the cycle.12

Until Baumol’s analysis is embedded in a more general model of goods, money, and asset market behavior, it is difficult to say whether it merely makes a technical point or actually presents a likely explanation of exchange rate determination. The assumptions behind the model are not without a potential real-world setting. Any country, for example, that has cyclical movements in its prices and interest rates that even partially coincide may experience such exchange rate movements. Given the assumptions made in Baumol’s analysis, exchange rates would vary cyclically in the absence of speculators. Introducing speculators, who concentrate their sales just after the exchange rate begins to depreciate, would, given Baumol’s behavioral functions, produce exchange rate fluctuations that are proportionately greater than changes in the money supply or the interest rate. In this model, however, it is not clear why, when speculators and nonspeculators collectively produce these steadily increasing oscillations, individual speculators do not take advantage of the information contained in the pattern to make larger profits.13 In so doing, speculators would reduce the amplitude and frequency of the cycle to what would be produced by rational speculators in the presence of cyclical interest rate movements. This alternative to the mode of behavior postulated by Baumol suggests that, although it can be proved that speculators as a whole can make profits from destabilizing speculation, individuals do not maximize their profits by behaving that way.

To maximize profits, proponents of rational expectations would say that speculators forming expectations, like economists forecasting future events, must use all information available to them and attempt to interpret it in the context of a systematic understanding of how the economy works. This approach does not imply that speculators must have estimated models that resemble those of economists; rather, it merely requires that, for the same information set, predictions based on theory and speculators’ expectations have the same stochastic distribution.

Muth (1961), to whom the original theory of rational expectations is attributed, asserts (p. 323) that “speculation with moderately well-informed price expectations reduces the variance of prices by spreading the effect of a market disturbance over several time periods, thereby allowing shocks partially to cancel one another out.” On the surface, then, wide fluctuations in exchange rates would appear to indicate that transactors have not formed their expectations rationally. Mussa (1976 a), however, has shown that both wide, systematic fluctuations in exchange rates and movements that are larger than changes in underlying determinants can be consistent with a rational process of expectations formation.14 He illustrates his case with a a simple reduced-form model representative of a broad class of monetarist models in which the exchange rate is determined by the quantity of any currency and the general willingness to hold that quantity.15 This process can be stated simply in the equation


or, equivalently,


where π = E[st+1st] = the expected change of the exchange rate, and

k is the set of other factors (income, interest rates, etc.) that influence the demand for money.16 The assumption of rational expectations implies that individuals forming exchange rate expectations know, or act as if they know, the exchange rate determination process implied by equation (7). Exchange rate expectations are then determined by expectations about the future money supply (mt+j), expectations about all the variables that are included in k, and the parameters (λ and η) that link these variables with the exchange rate.17

The point of this analysis is to emphasize that the behavior of the underlying determinants of the exchange rate is crucial to the behavior of the exchange rate itself. Transactors will use all information available, including knowledge of the stochastic structure of disturbances to underlying variables. Mussa (1976 a), for example, demonstrates that if all variables in k are held constant and the money supply has a fixed mean over time with autocorrelated disturbances, the exchange rate will also be autocorrelated over time. This follows from the fact that rational transactors will expect the long-run exchange rate to be determined by the fixed mean level of the money supply. Following any random disturbance to the money supply, however, the exchange rate will jump to a new level to clear the market as determined by equation (7). Rational transactors should then expect the rate to converge to its long-run level at a rate proportional to the rate at which the money supply is expected to return to its fixed mean level.

Mussa also describes a stochastic structure of the growth rate of the money supply that could generate a larger exchange rate change than the change in the money supply. Specifically, he describes an example in which the growth rate of the money supply does a random walk such that


where αt is the expected long-term growth rate of the money supply


and εt and δt are serially uncorrelated random disturbances with zero mean and variance σ2. Money holders do not have information on anything other than current movements of M, although clearly they need to form expectations about future values of M on which they can base expectations about future exchange rates. The accuracy of exchange rate expectations depends on their ability to distinguish between disturbances to the level of the money supply alone (εt) and those to the rate of growth of the money supply (δt). The distinction is crucial to the behavior of the exchange rate. That is, a positive value of εt forces the exchange rate to change by (1/λ).εt as equation (7) predicts for any once and for all change in the money supply. A positive value of δt, however, forces the exchange rate to change by (1/λ).δt plus enough to compensate for the expected increase in the rate of depreciation that results from the permanently higher money growth rate. This latter amount is proportionately greater than the current disturbance to the money supply.18

How money holders actually sort out whether disturbances are related to δt or εt is a crucial question to exchange rate theory. Mussa (1976 a) suggests an adaptive expectations mechanism as a rational method for money holders to make the distinction. Realistically, judgments on the source of a disturbance are more likely to be made on the basis of the underlying state of the economy and the expected political response to it, in the form of stabilization policy. In his regard, decisions on δ versus ε disturbances may be most accurately tracked with a government policy reaction function. This problem, however, is not crucial to the point being made, which is simply that an unexpected change in the money supply that provokes expectations of a change in the underlying growth rate of the money supply will, in the context of a very basic monetary model, induce a larger change in the exchange rate than in the money supply.

Even though both rational and adaptive expectations may produce exchange rate fluctuations that follow autoregressive patterns and that are greater than concomitant changes in underlying variables, it can be important for policy purposes to distinguish between the two expectations mechanisms. First, if expectations are not rationally formed, a government should be able to make profits from intervening in the foreign exchange market to smooth nonfundamental fluctuations. Second, knowledge of the way in which policy innovations are interpreted by the foreign exchange market is likely to be a crucial factor in determining the success of any policy measure. For example, if it is known that expectations are not formed by a rational process, but rather by extrapolating from current trends, it is possible for governments to use exchange rate policy with greater effectiveness vis-à-vis the real economy than if expectations were formed rationally. Although a number of methods have been used to try to identify the nature of expectations, no consensus has been reached on the issue.

The extent to which market transactors use available information in forming exchange rate expectations, or the efficiency of exchange markets, has been the focus of considerable research.19 Often, tests have been designed that identify efficient markets with random exchange rate changes over time.20 It follows from the foregoing theory, however, that non-random exchange rate behavior is not necessarily an indication of non-rational market behavior. Several authors—in particular, Dooley and Shafer (1976), Cummins and others (1976), and Logue and Sweeney (1977)—have tested whether filter rules (i.e., buy when the rate increases by X per cent, sell when it falls by Y per cent) are profitable as a guide for exchange market transactions.21 Although Dooley and Shafer find profitable filter rules for many major currencies, the preceding theory shows that systematic exchange rate patterns that yield profits could exist when markets are efficient. Cummins and others (1976) and Logue and Sweeney (1977) make a more discerning filter test by comparing filter-rule earnings on forward markets with those from buying and holding forward contracts. The former paper finds that filter rules on the Canadian dollar do not yield significant profits, while the latter paper finds significant profits from filter rules on the French franc.

In tests comparing the forecasting efficiency of the forward rate with that of an alternative forecast of the future spot rate based on information from the history of exchange rate time series, Bilson and Levich (1976) find evidence that exchange markets are efficient. They work on the assumption that exchange rates are generated by discrete linear stochastic processes, so that forecasts generated on the basis of past time-series properties of a particular exchange rate are defined as efficient ones. Estimates of these time-series properties are obtained by using Box-Jenkins techniques to fit a lower-order moving average process to pound sterling and deutsche mark rates against the U. S. dollar. They find that, for these two rates, forecasts that are one month and three months ahead, based on information from the Box-Jenkins analysis, are not statistically superior to the comparable forward rate forecast. Specifically, they find that post-sample forecasts using Box-Jenkins techniques have higher mean errors than do the forward rate forecasts and similar standard errors. The notable aspect of this test is that unlike other tests of market efficiency all efficiency criteria are ex ante; that is, only those forecasts based on information that is available at the time when the forward rate is formed are compared with the forward rate.

An approach that has been used to determine whether speculation has been stabilizing (in the sense defined earlier in this paper) is to identify some equilibrium level for the exchange rate in each period and compare it with the actual rate. Bilson (1976 b), for example, uses results from his estimation of a single equation—embodying the monetary approach to exchange rate determination—to derive proximate monthly equilibrium values for the deutsche mark/pound sterling exchange rate. Comparing the equilibrium rate with the actual rate, Bilson finds that the equilibrium rate appears to be as variable as the actual rate. Kohlhagen (1976 b) uses a different version of this approach in an attempt to distinguish speculative from nonspeculative influences on the exchange rate. Kohlhagen’s working rule is that if an exchange rate time series is more variable than estimates of what it would have been in the absence of speculation, then speculation is destabilizing. To determine the exchange rate that would have resulted from nonspeculative forces alone, a simple monetary model of the form


is estimated for the currencies concerned. The speculative influence is assumed to enter only via the forward premium (equal to the domestic/ foreign interest differential), so that the exchange rate series in the absence of speculation is assumed to be Sβ2 (F-S/S).22 Comparing this non-speculative series with the actual spot rate series for the deutsche mark and the French franc against the dollar, Kohlhagen concludes that speculation has been destabilizing for the franc and stabilizing for the deutsche mark.

Kohlhagen’s results can be misleading in relation to the foregoing discussion of destabilizing speculation. In this paper, destabilizing speculation has been identified with the way that speculators form expectations rather than with the degree of variability that speculation adds to exchange rate movements as measured by Kohlhagen. Thus, it has been argued here that rationally consistent expectations that stabilize the exchange rate at its momentary equilibrium value for each time period may force the rate to change by more than current changes in nonspeculative determinants alone would.

II. The Adjustment Mechanism Under Continuous Asset Market Equilibrium

Several recent models of exchange rate determination have been based on the underlying assumption of continuous asset market equilibrium. Put simply, this assumption means that holders of assets continuously adjust or attempt to adjust their portfolio until the actual value of each asset forms some desired proportion of the whole. If the exchange rate is understood to be the relative price of a domestic and a foreign asset and if the distribution of domestic and foreign assets among countries at any time is fixed, it follows that the exchange rate (as well as the interest rate) is continuously determined so as to produce portfolio balance. This approach stands in contradistinction to a flow equilibrium approach, which assumes that asset holders have a desired flow of assets that would leave their portfolios in balance at the end of the period under consideration.23 Recent interest in the stock approach has lead to conclusions about exchange rate dynamics that are very different from those reached by earlier exchange market theory, which relied on a (slightly inaccurate) version of the flow approach. In this section, assumptions underlying various versions of asset market equilibrium models that describe exchange rate dynamics are clarified and evaluated.

In critically examining asset equilibrium models, it is important to emphasize the rather stringent assumptions underlying them. In particular, the assumption of continuous portfolio balance implies that asset demand functions are stable and that costs of changing the composition of portfolios are not so high as to discourage a high level of activity in the asset market. This latter condition is less likely to hold for small countries with poorly developed capital markets than for larger countries. More important, however, is the question of whether the costs of making decisions about the future value of particular assets are prohibitively high when a large number of national assets, in an uncertain world, are involved.24 Of course, only empirical investigation can generate judgments on the validity of these assumptions, but it is fair to emphasize that the assumptions that determine the rigor of the following arguments are indeed stringent.

Although specifications of the asset equilibrium model have been made at various levels of generality and theoretical rigor, a basic underlying framework can be identified. Specifically, the private sector is typically assumed to hold a stock of assets, the demand for each being a function of rates of return on each asset and an activity and wealth variable. Rates of return on foreign assets typically include expected changes of exchange rates. The trade balance is a flow corresponding to income less the sum of private and government expenditure. This underlying structure can be summarized as follows:


In most theoretical work, this basic framework is qualified by small country assumptions, that is, that the foreign interest rate and foreign currency price of traded goods are determined exogenously for the country under examination. Of particular interest in the following examination of various asset equilibrium models are the assumptions necessary to explain exchange rate variations that are greater than the variations of underlying variables—assumptions that typically concern how exchange rate expectations are formed, the degree of capital mobility among countries, and the response of the trade balance to exchange rate changes. Various combinations of assumptions about these aspects of the model explain larger movements of the actual exchange rate than of the equilibrium exchange rate following certain unanticipated shocks to the system—a phenomenon commonly referred to as “overshooting” in the context of these models.

A good beginning point is a simple model by Kouri (1976) in which only domestic money and noninterest-bearing foreign assets are assumed to be held in domestic portfolios. This implies that the only relevant rate of return in the model is the expected rate of change of the price of domestic currency in terms of foreign currency. Further, Kouri assumes that only traded goods are produced and consumed domestically, so that, with the price of traded goods set on the world market, and normalized to one, the domestic price level equals the exchange rate. Finally, the economy is assumed to be fully employed with output constant.

Kouri’s version of the basic model described earlier is illustrated in Figure 2.25 It is assumed that the central bank acquires all government debt and that the government uses the proceeds, along with tax revenue, to finance its expenditure. With tax revenues and the growth of the money stock used as policy tools, government expenditure is determined residually. Thus, when the exchange rate (or, identically, the price level) rises, the real value of new debt issues falls and government expenditure likewise falls. Although this mechanism is not considered in the following discussion, it tends to increase the slope of the DD curve.

Figure 2 demonstrates how the economy adjusts to an unanticipated shock—namely, a purchase of foreign exchange by the central bank—when expectations of the future exchange rate are static, that is, the expected future spot rate equals the current spot rate. Assuming, for simplicity, that the economy is initially in equilibrium, a reduction in Af to Af and an increase in M shifts the FF curve rightward to F'F' and depreciates the exchange rate. With no change in the expected change of the exchange rate, the exchange rate must increase proportionately more than the increase in the nominal money supply, since a proportionate increase would only return the value of real balances to its original level. With a smaller stock of foreign assets, however, the original level of real balances would leave portfolios out of balance. Thus, a greater depreciation is required to reduce the stock of real balances until it is held in the desired proportion to the new stock of foreign assets. The increase in the exchange rate reduces the real value of wealth and, therefore, absorption, so that with fixed output the trade balance is left in surplus. This surplus increases the domestic holdings of foreign assets while the exchange rate gradually falls to keep portfolios in balance. With the real value of wealth increasing, the DD curve shifts outward while the appreciating exchange rate further increases absorption. Equilibrium is reached at S*, Af0 and E0 = Y when the current account and the portfolio are in balance and real wealth is constant.

Overshooting occurs in this model as a result of two crucial assumptions: first, that asset market equilibrium obtains immediately after a shock while flows of goods in response to the shock occur over a longer period, and, second, that exchange rate expectations are static. To illustrate the importance of the second assumption, consider the introduction of nonstatic (or, more specifically, perfect foresight) expectations into the preceding analysis. Immediately after the official purchase of foreign exchange, asset holders revise their expectations about the future exchange rate to make them consistent with the new equilibrium exchange rate, S*. As in the case of static expectations, the exchange rate begins to change immediately to adjust the relative values of the two assets to their desired levels. As the exchange rate depreciates, relative to S*, however, expectations of a future appreciation dampen the rightward shift of the FF curve that results from the increase in nominal money balances. Final equilibrium is still given by the F'F' curve, where assets are held in their desired proportions and the expected change of the exchange rate is zero. The impact effect of the shock on the exchange rate, however, can be anywhere from S* to S', depending on the degree of substitutability between the two assets. Obviously, within these limits, with perfect foresight and perfect substitutability of foreign and domestic currency, no overshooting occurs at all.

Introducing domestic and foreign interest-earning assets changes conclusions about exchange rate dynamics of the asset equilibrium model, and, needless to say, renders the model more realistic. In most such expansions of the model, assets are aggregated into domestic bonds, foreign bonds, and domestic money, with the former two bearing interest. Genberg and Kierzkowski (1975) have provided an extension of this sort in which they examine the dynamic adjustment of commodity, labor, and financial markets following various shocks to the system. Although the model assumes only the rather uninteresting case of static expectations, it is made considerably richer than Kouri’s model by the inclusion of both traded and nontraded goods and shifts of production and consumption between the two sectors following exchange rate changes. These sectoral effects are considered here, however, only insofar as they affect the adjustment path of exchange rates.

Several features of the basic asset equilibrium model, equations (10)-(12'), stand out when the model includes interest-bearing assets. First, in most versions that include interest-bearing assets, it is assumed that residents of one country do not hold stocks of the currency of another. In fact, in the analysis that follows, foreigners are assumed not to hold domestic assets of any kind. Second, income must include net income, not only from factors of production but also from holdings of assets. Income from holdings of domestic government bonds may or may not be included in the definition of income, depending on whether domestic bond holders are assumed to discount future interest receipts and future tax liabilities (required to finance interest payments) identically. If bond holders do discount the two identically, domestic government bonds are correctly seen as inside assets, they are not included in the definition of real wealth, and interest payments are not included in the definition of income. Finally, the balance of payments must be defined as the sum of the trade balance, new purchases or sales of foreign assets, and net income from holdings of foreign assets. The following simplified version of the Genberg-Kierzkowski model provides the essential framework for an understanding of the exchange rate dynamics hypothesized therein.


This framework can be used to derive two standard conclusions of asset equilibrium models: (1) that the exchange rate overshoots its long-run equilibrium following financial sector shocks, and (2) that it adjusts monotonically to equilibrium following real shocks. The impact effects of an unanticipated open market purchase of bonds comes through equations (16)–(18). The domestic interest rate falls until domestic bonds and money are held in the desired balance. The lower domestic interest rate increases the demand for foreign assets, so that, given a fixed stock of foreign assets held domestically, the exchange rate depreciates until the excess demand for foreign bonds is eliminated. Overshooting occurs if the domestic interest elasticity of demand for money is less than the elasticity of demand for foreign bonds with respect to the domestic interest rate—an assumption easily accepted in the light of recent evidence of high international capital mobility. A more difficult assumption to accept, and one that is not treated with sufficient explicit recognition in the analysis, is that the domestic interest rate may deviate substantially from the (assumed) fixed foreign rate even though exchange rate expectations are static. The assumption, of course, implies that interest parity does not hold continuously, that is, that domestic and foreign assets are imperfect substitutes.26

After the initial exchange rate change, which is required to maintain portfolio balance, the exchange rate adjusts gradually to its long-run equilibrium where actual wealth equals desired wealth and the nontraded goods market is in equilibrium. The difference between the initial and the long-run equilibrium exchange rate, however, is not identical to the initial proportionate change of the money supply as in the Kouri model. The difference arises because Genberg and Kierzkowski (1975) include foreign bonds as an outside interest-earning asset that is not perfectly substitutable for domestic bonds, which, as noted earlier, are inside assets in their model. Since domestic residents are assumed to accumulate foreign bonds durings the adjustment process when the depreciated exchange rate induces a current account surplus, long-run equilibrium interest receipts on foreign bonds must be greater than in initial equilibrium. The trade account must, therefore, settle at a permanent deficit to offset the permanently higher foreign interest receipts. This equilibrium deficit must be induced by a permanent increase (relative to the initial equilibrium) in the relative price of nontraded to traded goods, that is, in the ratio of the price level to the exchange rate.

On the basis of the models examined thus far, it would appear that, in the absence of particular properties of the stochastic process governing determinants of the exchange rate,27 overshooting arises in an asset equilibrium approach if exchange rate expectations are not rational and/or if domestic and foreign assets are not perfect substitutes. Dornbusch (1976 a), however, has attempted to show how overshooting might occur in a model with rational expectations and infinite capital mobility.

By ignoring any consideration of wealth and assuming perfect capital mobility, Dornbusch is able to simplify the asset market equilibrium approach considerably. While the simplification serves to focus attention on the monetary aspects of exchange rate determination, it detracts somewhat from the richness of the model as a whole. Implicitly assuming two assets, bonds and domestic money, Dornbusch specifies a demand function for domestic money


and assumes that interest parity keeps returns on foreign and domestic bonds identical.


with exchange rate expectations expressed in the general form


The absence of any consideration of wealth is particularly important for the demand function for domestic output, which specifies the interest rate and exchange rate as the only links between the financial and real sectors such that


where the price level is assumed to adjust proportionally with excess demand for domestic goods such that


Domestic and foreign-produced goods are not perfect substitutes, since PPP does not hold continuously.

To consider the exchange rate dynamics of the Dornbusch model, a simple diagram developed in his paper is useful. In Figure 3, AA represents combinations of p and s that are consistent with money market equilibrium, and = 0 is the equivalent locus of points consistent with money and goods market equilibrium.29 In the context of this diagram, an unanticipated open market purchase of domestic bonds leaves both the goods market and the money market in disequilibrium at the initial exchange rate and price level, and generates expectations of a long-run depreciation of the exchange rate. Given the assumption that money market equilibrium and interest parity obtain continuously, the interest rate falls immediately to clear the money market, and an incipient capital outflow raises the exchange rate until interest parity is regained. These adjustments are represented by the rightward shift of A A (to A' A') by an amount proportionate to the increase in the money supply. At the same time, the = 0 schedule shifts up to P˙=0, since a higher price level must now be associated with goods market equilibrium. Since adjustment of the goods market to equilibrium is assumed to occur only with a lag, the short-run equilibrium established at B entails excess demand in the goods market, which ultimately forces prices up to their equilibrium level at C. As prices rise, real money balances fall short of desired money balances and force the interest rate up. For interest parity to obtain while interest rates rise, the spot exchange rate must fall. Long-run equilibrium is established when prices and the exchange rate have increased from their initial levels by the amount of the increase in the money supply and the interest rate is again at its original level.

A careful look at this adjustment process reveals the importance and implications of the assumption of slower adjustment of prices in goods markets than in asset markets. To observe exchange rate overshooting following an unexpected monetary shock in this model, variables determined essentially in asset markets must bear the full burden of the initial adjustment to the shock, while the prices of goods adjust only slowly. This implies that, even though asset holders form expectations about the future level of the exchange rate rationally, taking into account, in particular, expectations about the future price level, they either do not or cannot incorporate these price expectations in their determination of the interest rate. Were they able to, they would attempt to switch not only from domestic bonds to foreign bonds after the monetary expansion but also from financial assets to goods or real capital. In fact, the assumption of slow adjustment of goods’ prices means that there are costs (storage costs or costs of breaking contracts, for example) related to an immediate shift into goods following a change in expectations. The exclusion from the model of real assets and, therefore, the opportunity to earn the expected increase in prices, however, could weaken the model and its conclusions concerning overshooting if real assets prove to be an effective hedge against inflation. That is, if wealth holders were able to switch into real assets when prices were expected to increase, an unanticipated open market purchase of bonds that was expected to have a long-run impact on the price level would increase both the expected future exchange rate and the interest rate. The interest parity constraint would require that the spot rate increase less than, or by the same amount as, the expected future rate, and overshooting would not occur.

An interesting variation of the Dornbusch model that deserves mention focuses on exchange rate movements when prices of traded goods adjust more quickly than quantity flows following an exchange rate change. The exchange rate dynamics, given this condition, are formalized by Niehans (1975) and elaborated upon by Dornbusch (1976 b). The model is essentially identical to the previous one but assumes that income, instead of prices, adjusts to clear goods markets. Also, expectations about the future exchange rate are assumed to adjust only gradually as the actual rate moves to maintain portfolio balance. In this framework, an open market purchase of bonds that induces a sudden depreciation of the domestic currency results in an initial worsening of the trade balance, requiring an offsetting capital inflow.30 As long as domestic and foreign assets are perfect substitutes, capital will flow in at the interest parity level of the exchange rate. The extent of exchange rate overshooting thus depends on the size of the initial fall in the interest rate, which itself depends on the change in income during the adjustment period, since money market equilibrium must hold continuously. The behavior of income depends on the reaction of domestic absorption to the change in the terms of trade. The larger deficit that results temporarily from the change in the terms of trade must correspond to an increase in overall absorption (decrease in savings) or a fall in income as expenditure is switched from domestic to foreign goods. Dornbusch argues that symmetrical treatment of expenditure on domestic and foreign goods would imply that residents dissave to finance a constant level of domestic expenditure while temporarily increasing expenditure on foreign goods. If the alternate approach were taken, however, so that the J-curve effect were assumed to divert expenditure from domestic to foreign goods, domestic income might fall and necessitate a larger fall in the nominal interest rate to equate the demand for and supply of money. The larger gap between domestic and foreign interest rates would require a larger depreciation (overshooting) of the exchange rate.

The rather arbitrary nature of the assumptions about savings behavior following exchange rate changes reflects the difficulty of specifying precisely the relationship between the real and financial sectors. Interestingly, each of the three main models examined in this section handles this relationship in a different way. Kouri specifies consumption as a function of real wealth, which, he claims, renders the model consistent with the life cycle model of consumption and results from most empirical studies of consumption. In this formulation, changes in exchange rates affect savings and expenditure decisions by altering the value of wealth held in foreign assets. Cooper (1976) very aptly questions whether changes in the market valuation of wealth resulting from short-run changes in exchange rates should be expected to have any effect on expenditure decisions, as this type of approach suggests. If the expected value of wealth over time were expected to remain unchanged, expenditure decisions might well be unaffected, or, at most, affected only slightly, by most short-run exchange rate changes. Genberg and Kierzkowski (1975) also use a wealth transmission mechanism, but it differs from Kouri’s by specifying consumption as the difference between income and savings and, therefore, assuming rather implausibly that people attempt to stabilize wealth over time and leave consumption to be determined as a residual.

Dornbusch adopts an alternative approach that involves an interest rate transmission between financial and real sectors. This approach posits no necessary or systematic effect of exchange rate changes themselves on total absorption. Rather, an open market purchase of domestic bonds or foreign currency has the (intuitively expected) result of increasing absorption by reducing the domestic interest rate.31 Although the interest rate transmission lends a certain intuitive appeal to models of exchange rate dynamics, in some cases it can leave considerable ambiguity as to the pattern of expenditure and savings decisions after exchange rate changes. Dornbusch’s formulation of Niehan’s model is an example of this ambiguity. To relieve the necessity of making ad hoc assumptions about the link between exchange rate changes and spending, empirical evidence is needed on the validity of different assumptions about the criteria used in savings and expenditure decisions following shocks to the economy that affect the exchange rate.

Empirical evidence on the validity of the asset equilibrium approach and of the various assumptions implicit in the versions just considered is still scanty. Several attempts have been made to test the general applicability of the asset market equilibrium approach on data from the recent floating period. Using monthly data from the period 1971-76 for the deutsche mark/pound sterling rate, Bilson (1976 a) has tested a simple, one-equation monetary model of exchange rate determination against PPP and random walk models of exchange rate determination. On the basis of several statistical criteria that indicate goodness of fit, he concludes that the monetary approach compares favorably with the random walk approach (exchange rate regressed on lagged values of itself) only if lagged values of exchange rates are included on the right-hand side. The introduction of lagged endogenous variables can be rationalized theoretically by assuming either a partial adjustment mechanism in money demand or an adaptive expectations mechanism in the determination of permanent income. Under the former assumption, the importance of the lagged endogenous variable could be evidence against the case for instantaneous adjustment in asset markets. Bilson also finds a higher-than-average interest elasticity of demand for money that may be evidence of the significance of currency substitution in exchange rate determination. Its omission in several theoretical models (as in models by Dornbusch and by Genberg and Kierzkowski) may therefore be a serious distortion.

Artus (1976) has estimated a larger, structural model of the behavior of the foreign exchange market in the Federal Republic of Germany from 1969 to 1975. With real sector variables (i.e., income, commodity prices, and the current account balance) given, Artus specifies a model in which the money market determines interest rates, and the demand for international assets determines the spot rate. His results reveal a slow adjustment of the money market but an extremely rapid adjustment of domestic and foreign asset values in investors’ portfolios following any shock. He also finds that an increase of 1 percentage point in the dollar/deutsche mark interest differential depreciates the exchange rate for the deutsche mark by 2.4 per cent within a month. Without the comparable reaction of the expected future spot rate, this is not necessarily support for the overshooting hypothesis in asset market equilibrium models, although, notably, it is not contradictory.

Knight (1976) has estimated a structural model of the adjustment process under floating exchange rates using data from Canada’s two postwar flexible exchange rate periods. His model combines an asset market exchange rate determination process and long-run neutrality of money with Keynesian aspects of the adjustment of prices, output, and the trade balance in the short run. Of particular interest to the focus of the present paper are Knight’s results that an increase of 1 per cent in foreign real balances appreciated the domestic exchange rate by 1.37 per cent during Canada’s early float and by 2.7 per cent during the current float. This not only is consistent with the overshooting hypothesis but also indicates that overshooting has been greater in the recent floating period. He also finds that the period required to complete 63 per cent of the adjustment of exports, imports, and overall domestic expenditure to a shock is very short, ranging from one to three months. Unfortunately, the speed of adjustment of portfolios is not estimated, so that no comparison of adjustment speeds can be drawn.

Other studies that require mention in connection with the asset market equilibrium approach have investigated more particular aspects of the model. Bilson (1976 a) has attempted to determine the validity of Dornbusch’s assumption of slow price adjustment in the goods market. He uses ordinary least-squares estimation to determine the relationship between the first difference of the log of the ratio of the consumer price index for the Federal Republic of Germany to that for the United Kingdom and the difference between the log of the current deutsche mark/ pound sterling spot rate and the last period’s price ratio. He finds that the long-run existence of PPP is suggested by the failure of the data to turn up a significant constant term, but that the adjustment of the price ratios is considerably less than the change in the exchange rate. This evidence suggests that changes in the exchange rate lead changes in the intercountry price ratios, as hypothesized in the Dornbusch model. It might be added that Dornbusch himself questions the theoretical support for the assumption of differential speeds of adjustment of goods and asset markets. One likely explanation for this phenomenon is that money and bond markets tend to be characterized by extensive and detailed networks for communicating information about changes in prices and quantities, while at least certain goods markets are characterized by spatial monopolies and imperfect information flows. Excess demand is then more susceptible to interpretation as a stochastic event when initially observed in the goods markets, rather than in the asset markets.

Although PPP has often been used as a model of exchange rate determination in itself, many asset equilibrium models (in particular, those of Kouri and Dornbusch mentioned earlier) have postulated PPP as a long-run equilibrium condition. Knowledge of the true nature of PPP would provide a useful piece of evidence in support of one model or the other. Using time-series analysis techniques that help to distinguish whether the relationship between two variables is a causal or an equilibrium one, Brillembourg (1976) finds that unpredictable components of the ratios of domestic to foreign prices and of the corresponding exchange rate have no lead or lag relationship, on a monthly basis for 11 of 13 OECD countries. However, Brillembourg explains that noise in the data may eclipse an underlying equilibrium relationship between PPP and the exchange rate. In an attempt to reduce this noise, a second test using quarterly data pooled across countries is run and reveals strong evidence of an equilibrium relationship between relative prices and exchange rates.

III. Uncertainty and Risk in Exchange Rate Determination

A frequently heard explanation of the high degree of instability of floating exchange rates in recent years attributes exchange rate instability to the instability of the world economy as a whole. What with record rates of inflation in most industrialized countries, the oil price shock, and a major worldwide recession, exchange rate instability, it is argued, is simply a reflection of the instability inherent in the system. Implicit in this argument is the idea that with instability of underlying economic conditions has come uncertainty about how to interpret new events as they occur. Since uncertainty is inevitably reflected in market expectations about future exchange rate changes, it comes to play a crucial role in the determination of actual exchange rates. This argument, then, asserts that great instability of economic conditions contributes to exchange rate instability, not only via the variability of fundamental determinants of the exchange rate but also via the uncertainty about exchange rate expectations that such variability generates.

Actually, there are two closely related issues that should be distinguished in discussing the role of uncertainty and risk in exchange rate determination. The first concerns the increased difficulty of interpreting recent events in order to form expectations about future exchange rate changes. The second concerns the decline in substitutability among assets when the degree of risk attached to holding assets denominated in domestic and foreign currencies differs.

McKinnon (1976 b) has examined these two issues in a Keynesian liquidity preference model quite similar to that used by Dornbusch. One notable difference distinguishes the two models; while Dornbusch assumes that capital flows to eliminate stock disequilibria can take place only as current account adjustment occurs, McKinnon asumes the existence of a group of transactors (which he hypothetically calls foreign exchange dealers) who have no preferred monetary habitat but hold noninterest-bearing working balances in both domestic and foreign currencies. The importance of these dealers lies in their role as currency speculators who provide foreign exchange and forward cover to wealth holders wishing to change the asset composition of their portfolios. It will be shown that the activity of foreign exchange dealers provides the possibility of a much higher interest elasticity of demand for money than that implied by the Dornbusch analysis and, consequently, smaller variations in the exchange-rate after various sorts of shocks. In fact, it is McKinnon’s premise that constraints, imposed either by law or by high risk, connected to taking open positions in foreign exchange have reduced the effectiveness of speculators during the recent period of floating. Without the cushion of sufficient speculative funds, various shocks to the international economy have resulted in excessive variations in exchange rates.

McKinnon illustrates the importance of foreign exchange dealers in cushioning exchange rate variations in the usual case of an unanticipated open market purchase of bonds. For simplicity, his argument is presented here in the diagrammatic framework of Dornbusch’s monetary approach model, since McKinnon, like Dornbusch, bases his model on the assumption of more rapid adjustment of prices in asset markets than in goods markets.

McKinnon emphasizes that, at the moment the monetary shock occurs, foreign exchange dealers must make a judgment about the nature of the policy, that is, whether it is merely a transitory change in the money supply that will be reversed immediately, a once and for all increase in the money supply, or the beginning of a larger overall increase in the money supply. Obviously, the judgment of the market on this question determines expectations about the future level of the exchange rate, or, identically, expectations about where the economy will come to rest on the 45° line in Figure 4. If these expectations are held with certainty—or near certainty—foreign exchange dealers push the forward rate to a level that conforms to their expectations and accept open spot positions in domestic currency, once the spot rate has moved sufficiently to allow dealers a reasonable profit. With speculators active in the adjustment process, the nonspeculative public must absorb a smaller quantity of money than was initially injected into the market, and the interest rate declines by less than it would in the absence of currency speculation. Figure 4 shows the difference between the impact of the monetary expansion on the exchange rate when foreign exchange dealers are active in the market (A'A') and when they are not (B'B').

When domestic economic conditions are quite unstable, however, the initial judgment about implications of the policy for the future can be made with much less certainty. During a period of recession, for example, it becomes extremely difficult to distinguish between a monetary expansion that will succeed in temporarily stimulating demand and one that will have longer-run consequences. Faced with such uncertainty, asset holders run the risk of mistaking a transitory monetary expansion for a continuing one and of basing their expectations about the future value of a currency on the wrong judgment about the nature of monetary policy. Obviously, the greater the tendency for asset holders to believe that policy innovations are signals of a reorientation of policymakers’ objectives, the larger the change in exchange rate expectations and, consequently, in the actual exchange rate, which follows policy changes. Mussa (1976 b, p. 9) has argued that one important difference between credible fixed rate regimes and flexible rate regimes is the “firm anchor for expectations concerning the future spot rate” that exists under a fixed regime. When an exchange rate has varied within a fairly narrow band for some time, firm expectations that the rate will remain in that band evolve. When there is no such “firm anchor” for expectations, Mussa asserts, any event that changes the market’s view of the appropriate level of the current spot rate is likely to change the market’s view of the appropriate level of the future spot rate by approximately the same amount. In other words, in a state of uncertainty about future implications of a policy change, the market is likely to expect neither a reversal nor an intensification of the policy.

Cogent generalizations about the effect of economic instability on the methods by which asset holders form expectations are, of course, very difficult to make. However, the effect of uncertain expectations on the behavior of exchange rates is far easier to pinpoint and is, in fact, the foundation of McKinnon’s (1976 b) hypothesis about why exchange rate fluctuations have exceeded variations in the fundamental determinants of exchange rates. In short, McKinnon argues that when expectations are held with great uncertainty, foreign exchange dealers hold open positions in particular currencies only if they are fully compensated for the risk they bear. The required risk premiums, however, are likely to make foreign exchange dealers’ demand for a particular currency less elastic with respect to an expected appreciation. In Figure 5, the Dornbusch diagram is drawn with BB again representing points consistent with money market equilibrium when foreign exchange dealers’ activity is incorporated in the adjustment process. Now, however, assume that the open market purchase of bonds generates some uncertainty about future monetary policy, so that the locus of points consistent with money market equilibrium after the shock has been absorbed is expected to be somewhere between bb and cc, specifically along B'B'.32 Clearly, foreign exchange dealers who, under perfect certainty, accepted open positions in domestic spot currency, thereby absorbing some of the newly created money, will be reluctant to take open positions with the same expected return but greater risk. Rather, dealers will purchase excess domestic currenly only at s'', so as to allow themselves a risk premium equal to the difference between s' and s''. With the expected value of the future spot rate at se, it can be seen that the risk premium demanded by foreign exchange dealers flattens the BB schedule, that is, it reduces the interest elasticity of demand for money, until the equilibrium schedule is B''B''.

McKinnon emphasizes that high levels of risk associated with foreign exchange dealings have led not only to higher risk premiums for transactors bearing risk but also to the withdrawal from risky foreign exchange dealings of certain transactors who have traditionally borne risk. He argues that long-standing advocates of floating exchange rates, who assumed that banks in particular would smooth unwarranted exchange rate variations by taking open positions in foreign currencies, failed to realize the potential risk posed by commercial bank speculation to the security of domestic residents’ deposits. However, with several bank failures during the early years of the floating regime, governments and commercial banks themselves have moved toward policies restricting banks’ net open positions in foreign currencies. Such self-imposed and legal requirements have obviously limited banks’ ability to smooth exchange rate variations. In short, it appears that banks cannot be induced to bear the high risk associated with speculative foreign exchange transactions by the expectation of higher returns.

McKinnon (1976 a) also argues that the decline in stability of major currencies that might be considered “international” money has made the job of speculation much more difficult and costly. He points out that the existence of at least one currency, whose real value in terms of internationally traded goods and services is constant, serves as a store of value and numeraire for active speculators, and enables them to focus on bilateral speculative transactions that smooth exchange rate variations of individual currencies against the stable international numeraire. Without such a haven for speculative funds, speculation necessarily involves the costs of forming expectations about the future value of two currencies rather than one. This added degree of uncertainty and the higher costs of gathering information may well drive many potential speculators out of the market. McKinnon also points out that the absence of a stable store of value is likely to lead to large flows of money from one currency to another as large international holders of assets—oil exporters or multinational corporations, for example—search for a stable haven for funds. He emphasizes that such capital flows are likely to be defensive rather than speculative, and therefore less related to judgments about the equilibrium value of a currency than to a rather great aversion to risk.

Within the limits, it would appear that levels of risk sufficiently high to drive currency speculators completely out of the market could not produce exchange rate overshooting of a greater magnitude than that postulated in the Dornbusch model, where it is assumed that no currency speculation exists. However, introducing risk and uncertainty is likely to flatten the BB curve in Figure 5 still further under Dornbusch’s assumptions. For example, if a sudden change in the money supply increases uncertainty about the future value of domestic currency, short-run portfolio balance will not be regained until the spot rate has changed by more than it would have with perfect foresight. The increase in uncertainty related to the domestic exchange rate makes domestic residents more uncertain about the future domestic value of assets held in foreign currency. In contrast, foreign residents have more uncertainty about their assets held in domestic currency relative to assets held in other currencies. If the domestic country is a net debtor (creditor), the increase in uncertainty will force the exchange rate to depreciate by more (less) or appreciate by less (more) than if the degree of uncertainty had not changed

Under conditions (enumerated earlier) that give rise to a J-curve effect when goods markets adjust more slowly than do asset markets, the presence of risk in the foreign exchange market may aggravate the inherent tendency to overshoot. For example, if the domestic and foreign assets are imperfect, rather than perfect, substitutes, the exchange rate must overshoot its equilibrium value by a greater amount, following an increase in the money supply, to induce a capital inflow that matches the increase in the trade account deficit. In this case, the exchange rate must depreciate not simply enough to make asset holders indifferent between domestic and foreign assets but, rather, enough to induce asset holders to increase the overall proportion of more risky domestic assets in their portfolios.

These two cases embody two channels by which risk may aggravate exchange rate overshooting: first, changes in the level of risk attached to asset holdings denominated in a particular currency may lead to larger exchange rate changes than under conditions of perfect foresight; and, second, any sort of shock that affects the trade balance and therefore requires an offsetting capital flow into assets denominated in a relatively risky currency requires a larger change in the exchange rate to compensate for a higher overall level of risk in portfolios than when domestic and foreign assets are considered to be perfect substitutes.

IV. Official Intervention in the Foreign Exchange Market

The theoretical models examined thus far have tended to focus on exchange rate dynamics under a pure floating exchange rate regime, that is, one in which the government does not intervene in the foreign exchange market. Although official intervention could be incorporated in any of the models described in Section II, it would be viewed as simply another method of changing the money supply and would therefore affect only the exchange rate in that capacity. Once risk is attached to assets denominated in different currencies, the effects of domestic credit changes and official intervention in the foreign exchange market can be differentiated, since official intervention changes the amount of foreign and domestic currency in circulation while domestic credit creation affects only holdings of domestic currency. In fact, there is evidence that official intervention, particularly during periods of crisis, has had a direct effect on exchange rates. Dooley and Shafer (1976), for example, report that during a 16-day period of consecutive declines of the deutsche mark/dollar exchange rate (the longest run of unidirectional exchange rate changes that occurred among 9 industrial countries during the first 15 months of floating), dollar/deutsche mark intervention was “larger and more sustained” than at any other time during the floating period. They take this evidence as an indication of a successful policy of leaning against the wind, and thereby spreading a potentially abrupt exchange rate change over a month-long period.

If intervention actually has some direct impact on exchange rate changes in addition to its effect via changes in the money supply, might this effect contribute to greater or smaller exchange rate fluctuations? In most cases, of course, governments design intervention policies to reduce fluctuations. In fact, however, there is not uniform agreement that this goal is actually accomplished. McKinnon (1976 a) suggests that the rather large amount of intervention that has marked the floating period might have been interpreted by the market as very unpredictable, and has, therefore, been unconducive to a desirable degree of certainty regarding future levels of various exchange rates. Of course, large-scale intervention would not necessarily be a source of greater exchange rate uncertainty. Provided that intervention is designed to stabilize the rate around a target and that the target is not changed, it would by definition be stabilizing. However, when this target is subject to frequent revisions, intervention policy, like an unstable monetary policy, may well increase uncertainty and aggravate fluctuations of the exchange rate.

This type of argument can be explored most easily by considering a model of managed floating by Artus (1976), which explicitly incorporates the effects of intervention on the exchange rate. As described earlier, the model includes a specification of the money market and the capital account. Of particular interest here, however, are the policy reaction functions, especially the reaction function for intervention that makes changes in official reserves a function of the difference between the actual exchange rate and a target level (determined by the relation of the domestic to the foreign price level) and the current rate of change in the exchange rate.


Since changes in official reserves must equal the balance of payments


and the current account is assumed to be determined exogenously, the capital account must change to equilibrate the system. Given domestic and foreign interest rates and exchange rate expectations, however, this means that the spot exchange rate must adjust to produce the required capital flows. Intervention in this system, therefore, controls the exchange rate by influencing the capital flows to which the spot exchange rate must adjust.

As long as the parameters governing the intervention reaction function are stable, transactors can form expectations with some degree of certainty about official control of the exchange rate. If those parameters are not stable, considerable uncertainty may arise over the process that determines the exchange rate. In particular, official intervention policy may be designed to relieve pressure on the exchange rate in the face of what is believed to be a temporary divergence between domestic and foreign price levels or a short-run speculative run on the domestic currency. When official resistance becomes too costly, however, the target rate may be revised by an amount disproportionate to the current rate of increase in the money supply. This sudden change—in particular in the Artus model, where a lagged value of the exchange rate is an argument in the exchange rate expectations functions—may generate a further change in the same direction, as investors try to assess the extent of the official policy change. Of course, instability of any of the parameters of the system is equally prohibitive of a systematic appraisal of the market. However, because private transactors, whether traders or investors, are likely to be motivated without exception or interruption by profit-maximizing incentives, their behavior is likely to be quite stable. The government, however, guided by transitory political concerns and a particular, yet changing, set of policy objectives, may be more likely to change its behavior in response to changes in particular variables. Nevertheless, Artus (1976) finds that his reaction function describing official intervention behavior by the Federal Republic of Germany during the current floating period is both stable and effective in explaining official behavior. Knight (1976), however, finds that during the early Canadian experience with floating (when the exchange rate was quite stable) the parameters of an official intervention reaction function were not significant. On the other hand, the same reaction function for the more recent Canadian float does exhibit significant explanatory power.

Hodgson (1976) has presented a quite different view of the stability and stabilizing influence of official intervention. He estimates a simple model relating the exchange rates of five major currencies against the U. S. dollar to a number of variables fundamental to exchange rate determination. He then compares simulations of these exchange rates from the model with actual rates during the floating period 1971-74 in an attempt to determine the extent to which actual exchange rate movements reflect movements of fundamental factors. He finds, not unexpectedly, that actual exchange rate movements do largely correspond to movements of fundamental factors. Nevertheless, he does find that, particularly after July 1973, actual rates frequently overshot rates predicted by his simulations. Examining this overshooting more closely (but on a very informal level), Hodgson claims that overshooting frequently occurred just after periods when official intervention to stem natural rate movements was quite heavy. He asserts that this is evidence of a “slingshot effect,” which results from authorities’ efforts to restrain exchange rate movements while fundamental pressures for exchange rate change build up. When these pressures finally force authorities to drop their defense of the rate, a sudden adjustment may involve the exchange rate’s overshooting its equilibrium value. Hodgson examines this possibility by looking at official intervention behavior around periods when his simulated exchange rates differ noticeably from actual rates. The disturbing element of this argument is that it implies that speculators have imperfect expectations, but it does not specify any behavioral hypotheses for speculators that might generate such imperfections. There are, of course, plausible hypotheses that would describe this behavior. For example, if speculators become very uncertain about the equilibrium level of the exchange rate after prolonged deviations of the actual from the equilibrium rate or if expectations are extrapolative, the exchange rate may overshoot its equilibrium following a change under pressure of intervention policy. Tests of these propositions, however, can be obtained only by specifying them rigorously in a structural model.

V. Conclusion

With theoretical and empirical research focused only recently on the issue of short-run exchange rate dynamics, it is not surprising that there is not a conclusive explanation for the unexpectedly large exchange rate fluctuations observed over the past four years. On the whole, each of the models presented in this paper is theoretically plausible. At the same time, most of them are not mutually exclusive; the true explanation of large exchange rate fluctuations is likely to be some combination of several of the arguments presented. On a theoretical level, the consensus seems to be that exchange rate dynamics are best studied in an asset market equilibrium model, and that without appeal to destabilizing speculation, this model does predict exchange rate fluctuations in excess of fluctuations in underlying conditions. On a more realistic level, however, it does not seem likely that the overshooting implicit in asset market equilibrium models is sufficient to account for the magnitude of exchange rate variations observed recently. There seems to be little evidence that conclusively precludes the possibility that, at least over particular periods for certain currencies, destabilizing speculation has contributed to exchange rate variations. Among the more promising channels for further research are the possibilities that changes in the risk attached to assets denominated in certain currencies and general uncertainty related to foreign exchange transactions with a corresponding decline in speculative activity have aggravated erratic exchange rate behavior. Although empirical tests of the influence of risk on exchange rate behavior are difficult to formulate and have consequently been scarce, the appeal, on a purely theoretical level, of risk as a source of exchange rate instability is strong.

Throughout this paper, exchange rate dynamics have been analyzed primarily in the context of a shock to the money supply. This approach reflects a general tendency in much of the theoretical literature to focus on the role of monetary shocks and expectations formed on the basis of monetary policy orientations in exchange rate determination. In part, this bias is a result of the difficulty of constructing models that can incorporate the wide variety of possible real shocks that could affect the exchange rate—each in a slightly different way. In fact, few of the models reviewed in this paper have the proper disaggregation of goods, recognition of risk considerations, or potential for supply-side shocks to allow a meaningful analysis of the effect of real sector shocks on the exchange rate. Nevertheless, the potential importance of such shocks, rooted in events ranging from huge increases in primary commodity and oil prices to the worldwide recession, in the explanation of exchange rate movements seems great. Brittain (1976, p. 16), for example, concludes from very rudimentary tests of interactions of the spot, forward, and interest rates that “monetary explanations [of sources of exchange rate changes], based on changes in the expectations about the future course of monetary variables, can contribute to an understanding of recent experience but must be supplemented by non-monetary considerations before that understanding is complete.”

Often economists are eager to draw conclusions about the implications of one or another hypothesis of exchange rate determination for optimal policy decisions. Although this issue goes beyond the scope of this paper, a word of caution about such conclusions is in order. Generally, policy decisions involve a trade-off between desirable and undesirable effects, and the characteristics of the trade-off lead to different recommendations under different circumstances. For example, the belief that unexpected changes in the money supply cause the exchange rate to overshoot its equilibrium value need not necessarily mean that authorities should announce monetary policies in advance of their implementation or intervene to smooth out fluctuations.33 A decision under these circumstances depends on both the objective function of the government and the tradeoff between the costs of exchange rate fluctuations and the effectiveness of an unannounced change in monetary policy. In the same way, the association of differential risks with assets denominated in different currencies should not in itself be taken as an excuse for official intervention to offset risk.34 Rather, conclusions from analyses of exchange rate dynamics should be viewed as essential information on which to base policy decisions—not general or rigid indicators of optimal policy.

APPENDIX List of Symbols

A = assets held by domestic residents

BOT = balance of trade

CAP = capital account balance

CUR = current account balance

c = constant term

C = consumption (in real terms)

D = demand for domestic output

E =real domestic expenditure

F = forward rate

G = government expenditure (in real terms)

i = nominal interest rate

I = imports (in real terms)

M = money supply

NFA = net foreign assets of the domestic central bank

O = nominal output

P = domestic price level

S = domestic currency price of foreign exchange on the spot market

T = tax receipts of the government

W = domestic real wealth

X = exports (in real terms)

Y = national income (in real terms)

Yd = nominal disposable income

π = expected rate of depreciation of the domestic exchange rate

An e (superscript) denotes the expected future values of a variable.

A d (subscript) denotes the domestic value of a variable.

An f (subscript) denotes the foreign value of a variable.

The expression E ( ) denotes an expected value operator.

An* denotes the desired or target level of a variable.

An N (subscript) denotes nontraded goods.

A T (subscript) denotes traded goods.

Variables symbolized by small letters denote logarithms.

A bar over a variable denotes the long-run or fixed value of the variable.


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Ms. Schadler, economist in the Special Studies Division of the Research Department, holds degrees from Mount Holyoke College and the London School of Economics and Political Science.


Mundell (1968) actually analyzed situations of less than full employment. The following analysis is conceptually identical to his, although the price level, rather than income, adjusts.


Throughout this paper, the exchange rate is defined as the domestic currency price of foreign exchange.


Frenkel (1976) provides evidence that this was true for the Federal Republic of Germany during an earlier floating exchange rate period as well. He finds that during the hyperinflation in that country (1920-23), the elasticity of the current exchange rate with respect to the money supply over the preceding five years exceeds unity.


See Aliber (1976) for a lucid explanation of the costs of exchange rate variability and basic empirical evidence on the importance of these costs.


The terminology in the early part of this debate was, at best, poorly defined. “Speculation” was usually used synonymously with “private short-term capital flows”; more formally, it can be assumed that speculation is the deliberate assumption of a net open position in foreign currency reflecting a judgment on the part of the transactor as to future exchange rate movements. Destabilizing speculation in Nurkse’s context appears to apply to those speculative capital movements that tend to prevent the rate from stabilizing at a unique level. In Friedman’s context, destabilizing speculation refers to speculative capital movements that are not based on judgments about the long-run equilibrium level of the exchange rate as determined by the relative stance of economic policy in the countries concerned.


See, for example, Kindleberger (1976), who attributes large swings in the current floating regime to “destabilizing and profitable” speculation.


Polak (1943) comes to similar conclusions about exchange rate behavior during the hyperinflation in the Federal Republic of Germany (1920-23). Using a small structural model of the foreign exchange market, Polak concludes that in the initial postwar period speculators expected a return to prewar par values. When depreciation continued, speculators “lost all confidence in an eventual recovery” and instead “projected the rate of depreciation into the future.”


Tsiang (1959) offers another interpretation of the franc’s behavior during the 1920s. He analyzes exchange rate developments vis-à-vis both the relative purchasing power of the franc and France’s policy during the period of letting the money supply vary to maintain a fixed interest rate. He argues (p. 271) that the “almost infinitely elastic supply of money and credit” required to hold interest rates constant was primarily responsible for periods of heavy speculation against the franc. Yeager (1966) presents a similar view. For empirical tests of the period, see Aliber (1962).


Kemp’s counterexample is rather academic, however, since the type of nonlinearities required in demand functions for foreign exchange are unlikely to exist in reality.

Algebraically, this phenomenon is shown as follows:

where Q = supply of currency

  • S = domestic currency price of foreign exchange

  • D = nonspeculative demand

  • c1, c2, b1, and b2 are constants

One, two, and three dots represent, respectively, the first, second, and third derivatives of the variable with respect to time.

Equating (1) and (2) and substituting D¨ for Q¨ yields

which implies constant sinusoidal exchange rate movements.

Baumol (1957) postulates an excess demand function for speculators, E8, as

where c3, a, and w are constants.

Equilibrium is given by
so that substituting equations (2) and (4) into equation (5) gives

where K = c2 + c3a, e = b2 + c3

Substituting equation (6) and the second derivative of equation (6) into equation (1) gives the price equilibrium condition

which must have at least one positive real root, since complex roots come in pairs and a negative root cannot satisfy an equation with alternating positive and negative terms.


Actually, this proof has been the focus of considerable controversy. Under certain conditions, the sinusoidal component of the time path of the exchange rate could be dominated by an exponential component, so that speculators behaving as postulated would have to acquire stocks of foreign exchange indefinitely and never be able to cash them in to realize profits. For more on this problem, see Telser (1959), Baumol (1959), and Kemp (1964).


Baumol (1957, p. 270) himself notes that “there is little reason to expect any consistent pattern of cyclical price movement on [foreign] exchanges. Rather, the time path can plausibly be expected to be erratic, responding to the political developments in the countries involved.” He holds, however, that any of the cycles in his examples could be a “never-to-be-repeated erratic individual movement” and that the type of profitable destabilizing speculation he envisions could exist.


Barro (1976) and Bilson (1976 a) have arrived at much the same conclusions via a similar monetarist model with explicit assumptions of perfect efficiency in all markets. Bilson, however, has a more extensive discussion of the connection between innovations in the money supply and income and of their possible offsetting effect on the exchange rate.


Mussa’s reduced-form equation for the exchange rate acually comes from a model by Sargent and Wallace (1973).


See the Appendix for definitions of variables used throughout this paper but not identified in the text.

This can be shown by substituting continuously for E(sui) in equation (7) to get

This can be shown by substituting equations (8) and (9) in equation (7') and equation (7') in equation (7) to get st = 1/λ[mt-k+(η/λ) · Et)]. A disturbance to εt affects only mt, while through δt it affects E(αt) and mt.


A thorough review of empirical studies of market efficiency is beyond the scope of this paper. For more comprehensive overviews of this subject, see Kohlhagen (1976 a) and Levich (1976).


Tests (only some of which relate random exchange rate behavior to market efficiency) of time series properties of exchange rates during the recent float were made by Giddy and Duffy (1975), Levich (1976), Dooley and Shafer (1976), Cummins and others (1976), and Logue and Sweeney (1976). See Poole (1967) for similar tests on earlier floating rate periods.


Tests are generally run on the forward rate or the spot rate corrected for interest differentials, the two being equivalent if interest parity holds as expected.


One problem with relating interest rate differentials to the speculative influence alone is that the effect of changes in interest differentials on the valuation of domestic and foreign assets in the portfolios of wealth holders, which is likely to influence the exchange rate quite apart from speculative pressures, is ignored.


See Foley (1975) for a detailed discussion of the stock versus flow approaches and the appropriateness of each for certain applications.


This point is developed further in the following section.

With domestic and foreign interest rates excluded, Kouri’s asset demand functions can be written

where w ≡ Af + M/P

Substituting the definition of wealth into equation (13) and simplifying gives

which, holding M, Y, and π constant, gives FF in Figure 2. DD is given by a version of equation (10) with desired wealth held constant and actual wealth substituted in BOT = Y - C(Y - T, Af + M/P) - G.


The implications of this assumption are developed further in the following section.


See Section I for a description of these properties.


Rational expectations in this context imply that θ is determined by the model.

A downward-sloping AA curve is derived by substituting equations (23) and (24) in equation (22) to get
Since, in the long run, with a stationary money supply s=s, the long-run equilibrium price will be
Substituting equation (19) in equation (20) gives

Since λ and θ are positive parameters, ds/dp evaluated at equilibrium is negative. This result is perfectly intuitive, since an increase in prices relative to their long-run equilibrium level, when money market equilibrium and interest rate parity hold continuously, decreases money balances and increases the interest rate. Given a constant foreign interest rate and long-run exchange rate expectations, the current spot exchange rate must change sufficiently to fulfill equation (27). The upward-sloping = 0 schedule is derived by setting =0 in equation (26) to fulfill goods market equilibrium, and substituting from equation (22) for id to get P = [δλ/(δλ+σ)]s + [σ(δλ+σ)]m + [λ/(δλ+σ)] (u + (1-γ)y - φσy/λ).


Actually, Dornbusch describes two influences that tend to worsen the trade balance initially after a monetary expansion. First, a fall in the domestic interest rate stimulates expenditure and therefore reduces the gap between income and absorption. Second, if quantities traded depend on the expected exchange rate but trade is effected at the current rate, a monetary expansion that produces a smaller depreciation of the expected rate than of the actual rate worsens the trade balance. Several empirical studies of the effect of exchange rate changes on current balances have indicated initial perverse effects. See Branson (1972) for several member countries of the Organization for Economic Cooperation and Development (OECD), Artus (1975) for the United Kingdom, and Clark (1977) for the United States.


Both Kouri (1976) and Genberg and Kierzkowski (1975) hypothesize that the effect on wealth of an exchange rate change resulting from an open market purchase is to depress absorption.


More formally, bb and cc are possible equilibrium loci, each expected with a 50 per cent probability to be realized loci of combinations of p and s consistent with equilibrium in the money market. The expected equilibrium locus, before accounting for risk, is B'B''.


Branson (1976), for example, has suggested that such an intervention strategy may be beneficial.


See an argument, for example, put forth by Day (1977).