Journal Issue
Share
Article

Recent Developments in Monetary Models of Exchange Rate Determination

Author(s):
International Monetary Fund. Research Dept.
Published Date:
January 1979
Share
  • ShareShare
Show Summary Details

In their seminal contributions to the monetary approach to the balance of payments, both Mundell (1968, Ch. 8) and Johnson (1976) suggested that the approach, which had been applied almost exclusively to countries operating under fixed exchange rates, was equally applicable to flexible exchange rate regimes. This view is well expressed by Frenkel and Johnson:

In a floating rate world, the theory commonly misapplied to a fixed rate world—that the monetary authority controls the money supply and the price level—again becomes valid; but for the monetary approach this merely shifts the focus of analysis from the determination of the balance of payments to the determination of the exchange rate. This is an easy switch of emphasis; it was certainly clear enough to Gustav Cassel, who saw purchasing power parity as determining either a nation’s price level via its exchange rate under a fixed rate system, or its exchange rate via its domestic money supply under a floating rate system.1

It is worthwhile to begin with a formal statement of this view, since it forms the foundation upon which more recent monetary models have been constructed. One simple specification is contained in the following three equations:

where M = the money supply; P = price level; i = the nominal rate of interest; Y = level of real income; and an asterisk denotes the foreign country. S is the exchange rate, expressed in units of domestic currency per unit of foreign currency. In these equations, the demand for real money balances—K(i, Y)—is negatively related to the nominal rate of interest and positively related to the level of real income. The third equation—the purchasing power parity (PPP) condition—relates the exchange rate to the ratio of the nominal price levels. Under a pure dollar standard, the foreign (U. S.) price level is determined by the second equation. The exchange rate is fixed by the commitment of the domestic central bank to exchange domestic currency for U. S. dollars at the fixed parity. This commitment implies that the domestic price level is determined by the PPP condition, so that the first equation determines the size of the domestic money supply through balance of payments surpluses or deficits. Under flexible exchange rates, the first two equations determine the domestic and foreign price levels, thus leaving the third to determine the exchange rate. The particular exchange rate regime determines the set of market-clearing variables without fundamentally altering the underlying structure of the model.

The reduced form solution for the exchange rate from this simple model is

This equation clearly illustrates the position taken by Frenkel (1976), Mussa (1976), and others that the exchange rate, as the relative price of two monies, is determined by the relative supply and relative demand for the two currencies. As Frenkel demonstrates in his doctrinal analysis, this view of the determination of the exchange rate has a long history in classical economics. In contrast, the analysis of the exchange rate through the components of the balance of payments is of relatively recent origin.

It is, of course, true that in a fully specified general equilibrium system any excess supply of money is balanced by an offsetting excess demand for goods and nonmonetary assets, so that the balance of payments components approach and the monetary approach are equivalent in a fully specified model. It is, however, equally true that the predictions that arise from restricted versions are often conflicting. Equation (4) predicts that an increase in domestic interest rates will depreciate the exchange rate by decreasing the demand for the domestic currency. This result runs counter to the capital account analysis, which suggests that higher interest rates appreciate the exchange rate by creating an incipient capital inflow into the domestic economy. The conflict may be resolved by a full specification of the determinants of the interest rate. In the monetary approach, capital markets are generally assumed to be fully integrated, so that nominal interest rate differentials reflect primarily differences in expected inflation rates or, again through the PPP condition, expectations of a depreciation of the domestic currency. In this approach, high interest rates consequently reflect easy monetary policies by the domestic central bank. In contrast, the capital account approach assumes some degree of capital market segmentation, at least in the short run, so that monetary policy may have an independent influence on the real rate of interest. In this approach, high interest rates therefore reflect tight monetary policies. This example illustrates both the similarity of the two approaches in a general equilibrium setting and the differences that arise in restricted applications of the models.

Another apparent conflict arises in the relationship between the exchange rate and the level of real income. An analysis based upon the current account would suggest that higher levels of real income would depreciate the exchange rate by increasing the demand for imported goods. The monetary model, on the other hand, stresses that higher levels of real income will increase the demand for money and create an incipient balance of payments surplus and an appreciation of the exchange rate. The argument is not that higher levels of real income will not create a current account deficit but that any current account deficit will be dominated by an incipient capital account surplus brought about by the increase in the demand for money. In this case, a complete general equilibrium analysis would require a specification of how the increase in the level of real income was brought about. The monetary model would appear to be correct if the increase was due to real factors, such as population growth, capital accumulation, or deficit-financed government expenditure. The current account model would be correct if the central bank offset the effect of higher real income on the capital account through a policy of monetary expansion.

Finally, the approaches differ in their description of the adjustment process. Current account models stress that the exchange rate “works” by influencing relative prices—if the domestic and foreign price levels are fixed, a depreciation of the exchange rate will increase the domestic price of imported goods and lower the world price of domestic exports, thereby leading to a current account surplus if the Marshall-Lerner conditions are satisfied. This approach has led to concern over the effectiveness of the exchange rate as an instrument of adjustment in a world of flexible prices. If prices are completely flexible, an exchange rate change will not improve the competitive position of the economy, and will not have any influence on the current account. In many of the industrial countries, the linkage between prices and exchange rates is strong and direct: the cost of imported inputs is related directly to the exchange rate, and indexation agreements lead to rapid pass-through from commodity prices to labor costs. This analysis may be extended to incorporate the J-curve effect, whereby the inelasticity of demand in the short run results in the failure of the Marshall-Lerner condition in the period immediately following a change in the exchange rate. The combination of flexible prices and inelastic demand have led to the conclusion that the exchange rate is not an effective instrument for balance of payments adjustment, and that the exchange rate may, under certain conditions, exhibit patterns of dynamic instability.

In the monetary model, price adjustment is the core of the equilibrating mechanism. Even if domestic prices fully and instantaneously reflect exchange rate changes, the exchange rate will still be an effective instrument for balance of payments adjustment. Higher prices eliminate incipient balance of payments deficits by decreasing the real value of the domestic money supply, thus eliminating the excess supply of money, which is the root cause of the deficit.

I. The Monetary Approach in the Short Run

Although there is little dispute over the validity of the monetary model as a long-run description of the determinants of the exchange rate, the current experience with flexible exchange rates has pointed to three major deficiencies of the model as a short-run theory of exchange rate behavior. First, many studies—including Isard (1977), Dornbusch and Krugman (1976), and Kravis and Lipsey (1971)—have demonstrated that the PPP condition does not hold in the short run. This failure is particularly evident when aggregate price indices, such as the consumer price index or the gross domestic product (GDP) deflator, are used in the calculation. The failure of PPP with aggregate price indices is particularly damaging to the monetary approach, since these indices are typically considered to be the appropriate deflators for nominal money balances. Second, although the money supply may be assumed to be an exogenous policy instrument under flexible exchange rates, and although the level of real income may be plausibly argued to be independent of the current value of the exchange rate, the assumption that the nominal rate of interest is exogenous is clearly unjustified, even in the classical world of full employment and price flexibility. The lack of emphasis on the endogenous determination of the interest rate in fixed exchange rate monetary models presumably arose from the arbitrage condition that domestic interest rates be equal to world rates in an economy with an immutably fixed exchange rate and a high degree of capital mobility. However, under flexible exchange rates, nominal interest rates will be strongly influenced by exchange rate expectations, which will, in turn, be strongly influenced by the current movement in the actual rate. Unless this link between exchange rates, interest rates, and the exogenous variables is accounted for, the usefulness of the monetary model for policy and forecasting purposes is extremely limited. Finally, the monetary models appear to be incapable of explaining the volatile behavior of exchange rates during the current float. This volatility may be measured relative to price level movements (Artus and Crockett (1978)), money supply movements (Dornbusch (1976); Frenkel (1976)), or forecasted movements from the forward exchange rate (Bilson and Levich (1977)).

International monetary theorists have responded to the challenge of the recent experience by extending and modifying the approach described by Mundell (1968) and Johnson (1976). While the original model emphasized the interaction between commodity and money markets through the PPP condition, and assigned a relatively passive role to nonmonetary assets through the fixed interest rate assumption, the interaction between the asset markets occupies a central place in much of the recent literature. 2 This emphasis has led to a deeper analysis of the role of speculation and of temporal and spatial arbitrage in assets, and to problems of portfolio selection. Within the general asset market approach, a number of different models have been developed, each of which attempts to account for the characteristics of the current experience that are not well described in the original monetary model. In the remainder of this paper, three of these approaches are reviewed, and an attempt is made to indicate how empirical researchers could implement a general approach that includes features of all of them. 3

The first variant to be considered is the equilibrium rational expectations (ERE) version of the monetary approach.

II. The Equilibrium Rational Expectations Model

The main contributors to the ERE approach are Barro (1978), Bilson (1978 b), Frenkel (1976), Hodrick (1978), and Mussa (1976). These models are based upon the concept of PPP as theoretical construct, although they often recognize that published price indices may not satisfy the condition. One argument that has been used to justify this procedure is that published price indices may not be good indicators of transactions prices because of contractual and recording conventions. In addition, there is always a difficulty in deciding which price index is the appropriate deflator for nominal money balances. On these grounds, one can argue that the “true” price index is an unob-servable variable whose ratio is defined to be the exchange rate—the exchange rate is, by definition, the correct relative price with which to measure the relative purchasing power of two currencies. Frenkel (1976) argues:

In retrospect it seems that the translation of the theory from a relationship between moneys into a relationship between prices—via the quantity theory of money—was counterproductive and led to a lack of emphasis on the fundamental determinants of the exchange rate and to an unnecessary amount of ambiguity and confusion. It is noteworthy that the originators of the theory (although not in its present name)—Wheatley (1803) and Ricardo—stressed the monetary nature of the issues involved as well as the irrelevance of commodity arbitrage as determining the equilibrium rate.4

The argument is that it is better to start with a relative money demand function like equation (4), which directly relates the exchange rate to relative money supplies and demands, rather than to pursue the circuitous route through aggregate price indices.

The ERE model still requires a theory of the behavior of interest rate differentials and an explanation for the volatile behavior of exchange rates. This theory begins with the interest rate parity condition that relates the nominal interest rate differential to the forward premium on the exchange rate. 5 Denoting the forward premium by ln(F/S), where F is the forward exchange rate of one-period maturity, the interest rate parity condition may be written as 6

Equation (5) does not close the model because it explains the interest rate differential by introducing an additional endogenous variable—the forward exchange rate. In the ERE model, the forward exchange market is assumed to be dominated by well-informed, profit-maximizing (i.e., risk neutral) speculators who purchase all forward contracts at a price that is equal to the expected future spot rate. 7 Finally, the rational expectations assumption is used to close the model by relating the market’s expected future spot rate to the rate predicted by the model itself. This assumption is specified in equation (6):

In equation (6), Et(St+1) is the expected value of the spot rate in period t+1, conditional upon the information available in period t.

The implications of the ERE model may be best seen by introducing a specific form for the relative money demand function. This form, which is related to the money demand function used by Cagan (1956), offers a particularly simple reduced form equation for the exchange rate. The derivation of this reduced form is due to Sargent and Wallace (1973). The particular functional form is

Equation (7) may be expressed in logarithms as

where m = ln(M/M*), s = ln(S), k = In(K), and y = ln(Y/Y*). Substituting in equations (5) and (6) yields

where zt = mtktηyt, and γ = ϵ/1+ϵ. Through equation (9), the expected value of the exchange rate in any future period t+j may be found to be

Substituting this result back into equation (9) for all values of t+j yields the final reduced form equation for the exchange rate:

Equation (11) illustrates the central lesson to be learned from the ERE model: that the exchange rate depends upon the current and expected future values of the exogenous variables. In a sense, an efficient foreign exchange market discounts future changes in demand and supply into the current spot rate in the same way that an efficient equity market discounts changes in expected future earnings into the current equity price. The discount factor, γ, is related directly to the interest elasticity of the demand for money.

Since equation (11) is in fact a general description of asset price behavior that is equally applicable to the prices of bonds or equities, or of commodities that are traded in organized spot and forward markets, the ERE explanation for the erratic behavior of the exchange rate is closely related to the existing literature on the random behavior of asset prices. The extent of the discounting depends crucially upon the holding cost of the asset: if the holding cost is low, expected future developments will be almost entirely discounted into the current spot price. On the other hand, commodities with significant holding costs will tend to respond more gradually to monetary shocks. Since the holding cost of money is very low, it is perfectly reasonable that exchange rates behave like the prices of other assets with low holding costs rather than like consumer prices.

This point may be clearly understood by completing the model with a specification of the time series process that generates the composite exogenous variable. A simple illustrative model is sufficient for this purpose. Assume, for example, that the change in z is generated by a first-order autoregressive process:

where Δ = the difference operator, ρ = the first-order autoregressive parameter, and ut = an independently distributed random error. Equation (12) may be used to forecast the composite exogenous variable in all future periods:

Substituting equation (13) in equation (11) and taking the limit as j tends to infinity leads to the following expression for the exchange rate:

Equation (14) demonstrates why the exchange rate may exhibit an elastic response to changes in money supply or demand. An increase in the domestic money supply, for example, influences the exchange rate through two channels: the direct proportional relationship stressed in the simple monetary model, and the indirect influence through its effect on expected future monetary growth, hence nominal interest rates, and hence the exchange rate. This second “speculative” influence may aid or disrupt the exchange rate policies of the central bank. If the central bank follows a strict monetary rule, then rational speculators will tend to enforce the equality between the actual exchange rate and the equilibrium rate defined by the monetary rule. On the other hand, if the exchange rate is fixed at a level that conflicts with the domestic monetary policies of the central bank, then rational speculators will appear to be destabilizing with respect to the parity, although they will not be destabilizing with respect to the equilibrium exchange rate.

This appears to be the correct light within which to view the “destabilizing speculation” debate. By construction, the speculative influence under rational expectations is stabilizing with respect to the equilibrium exchange rate. Tests for destabilizing speculation are therefore exactly the same as tests of market efficiency and rational expectations. This does not imply that rational speculators will aid central banks in setting exchange rate targets; such aid will be forthcoming only if the exchange rate targets are based upon a rational model of the equilibrium determinants of the exchange rate. Exchange rate targets will be of value if central banks are prepared to support the targets by adjusting the supply of the domestic currency to the level of demand that is consistent with the target exchange rate. The targets will be of particular value in situations in which there are sharp short-term movements in the demand for the currency.

III. Currency Substitution Models8

The currency substitution (CS) models constructed by Girton and Roper (1976), King, Putnam, and Wilford (1978), and Miles (1978) constitute a second approach to the stylized facts of the floating rate period. These models emphasize that money may be held in a portfolio of currencies. The real value of any of the currencies in the portfolio is measured in terms of its purchasing power over a standard bundle of goods, thus avoiding any need to invoke the PPP condition. For the same reason, the appropriate scale variables are likely to be world wealth or income rather than the national incomes in the countries involved. Expressed within the structure of the previous model, the demand functions for the two currencies may be written as follows:

and

These demand functions differ from the preceding ones in two important respects: (a) the real value of the foreign money is expressed in terms of its purchasing power over domestic (world) goods; and (b) the transactions variable is the level of domestic (world) income in both demand functions. Taking the ratio of equation (16) to equation (15), the following expression for the exchange rate is derived:

where K=K0*/K0. The only difference between this equation and that derived from the ERE model is the absence of the relative real income term. In fact, there are no country-specific elements in equation (17): the equation could very well describe the evolution of the exchange rate between greenbacks and silver dollars in the United States in the 1870s when two currencies were issued by the same central bank. The fundamental determinants of the exchange rate are assumed to be the relative supplies of the two currencies and the relative holding cost as measured by the interest rate differential. A natural extension of this approach would be to also consider the differential risk associated with holding the two assets.

The solution to the CS model with endogenous interest rates is similar to the solution to the ERE model, since both approaches typically make use of the rational expectations hypothesis. In the single-country analysis, it is possible to extend the analysis of the money supply process by explicitly introducing a function determining the supply of foreign currency coming into the domestic economy through the balance of payments. 9 In this paper, more attention is given to the global monetarist variant in which the supplies of the two currencies are determined exogenously by the respective central banks. If the first-order autoregressive process described in equation (12) is taken to be the generating process, the solution for the exchange rate will be exactly the same as the solution described in equation (14). It is useful, however, to write this solution in a slightly different form in order to illustrate some of the more characteristic features of the CS approach.

Two forms of the solution are given in equations (18) and (19).

In these equations, zt = k + mt, and ut = the current innovation in zt. Although the structure of the ERE and CS models are essentially the same, there is a distinctly different emphasis on the factors responsible for the erratic behavior of the exchange rate. In equation (18), the deviation of the current spot rate from the lagged forward rate is shown to depend upon three factors: ρ, γ, and ut. Of these factors, the ERE model suggests that the dynamic instability in the zt variables, as measured by ρ, and the unpredictability of zt, as measured by the variance of ut, are the primary reasons for the poor forecasting performance of the forward rate, as measured by the large variance of the forecast errors. The CS models, on the other hand, are far more likely to stress the γ parameter, which is a measure of the elasticity of substitution between the two currencies. This parameter was previously defined to be

From this expression, it is clear that γ ranges over the interval from zero to unity as ϵ ranges between zero and infinity. If the two currencies are close substitutes, a slight increase in the nominal rate of interest will induce a large shift in demand out of the domestic currency. It is important to notice, in this respect, that it is not possible to really distinguish a high degree of substitut-ability between the currencies from a high degree of substitut-ability between either currency and a third asset. In either case, increases in ϵ, and hence in γ, will be associated with increases in the variance of the forecast error of the forward rate in its prediction of the future spot rate.

The same point is expressed in a slightly different way in equation (19), which derives the widely regarded proposition that exchange rates follow a random walk in the extreme case of perfect currency substitution. In this equation, the change in the spot rate reduces to a function of the current innovation in the case in which γ is equal to unity. This result follows directly from the fact that if the currencies are perfect substitutes, asset holders will be unwilling to hold any currency that is expected to depreciate relative to any other currency. Hence, for the two currencies to coexist, it must be true that the expected rate of depreciation is zero, since instantaneous changes in the spot rate are required to equate the holding costs of the two currencies. These results are again analogous to the efficient market’s view of equity markets wherein instantaneous movements in equity prices are required to equate the expected returns on the assets in the portfolio.

IV. The Dornbusch Exchange Rate Dynamics Model10

The exchange rate dynamics (ERD) model presented in Dornbusch (1976) differs from the preceding models in that it allows explicitly for deviations from PPP, and allows the interest rate parity condition to be the primary link between international financial markets. The interest rate parity condition may be expressed as

In this approach, equation (21) summarizes the two fundamental determinants of the exchange rate—expectations about the future value of the rate, as measured by the forward exchange rate, and the nominal interest rate differential. The forward rate, which is still considered to be a rational forecast of the future spot rate, may be shown to be equal to a weighted average of the equilibrium exchange rate, s, and the current spot rate, s.

Substituting this result back into equation (21) yields an equation relating the exchange rate to the equilibrium rate and the interest rate differential:

This negative relationship between the exchange rate and the interest rate differential is graphically represented in Figure 1 as the XX line. The relationship embodied in the line may be explained in the following way. For a given value of s, a decline in domestic interest rates will decrease the yield on domestic bonds relative to that on foreign bonds, and will induce domestic bond holders to move out of these instruments into foreign bonds. This reaction will result in an incipient capital account deficit that will be eliminated by a depreciation of the exchange rate. The depreciation eliminates the deficit because the forward rate does not depreciate by as much as the spot rate. The depreciation therefore results in a premium on the domestic currency that equates the covered yields on domestic and foreign assets.

Figure 1

This analysis leaves open the question of how the interest rate is determined. In the ERD model, it is the interest rate differential, rather than the exchange rate, that is the immediate equilibrating mechanism in the money market. The relative money market equilibrium condition may be derived directly from equations (1) and (2) to be

Equation (24) may be viewed as determining the interest rate differential in the short run because prices are assumed to not adjust instantaneously. For this reason, it is useful to rewrite the equation as

where zt = mtktηyt. Substituting equation (25) in equation (23) yields

In deriving this equation, the assumption is made that the expected value of the equilibrium exchange rate is equal to the current value of the composite exogenous variable, zt. This assumption essentially abstracts from trends in the exchange rate by assuming that all changes in z are unanticipated. The emphasis on unanticipated changes in the exogenous variables as the cause of the volatile movement in the exchange rate is consequently a central feature of all the theoretical models considered. Equation (26) demonstrates that a change in zt will influence the exchange rate through two channels: (a) through the proportional increase in the equilibrium exchange rate, and (b) through the liquidity effect brought about by the short-run rigidity of prices. Through the second effect, an increase in zt will result in a fall in domestic interest rates relative to foreign rates while the interest rate parity condition is maintained through the induced premium on the domestic currency. As prices adjust through time, the liquidity effect will be eliminated, and a proportional relationship between zt and st will exist in the long run.

The important point is that the exchange rate will overshoot its equilibrium value in the short run. This behavior is illustrated in Figure 1. The AA curve, derived from equation (26), combines the price level and exchange rate points that maintain equilibrium in the money market. An increase in z to z’ will shift the AA curve to A’A’ and the XX curve to X’X’. Since prices are fixed, and since asset market equilibrium must be maintained continually, the exchange rate must immediately depreciate to s0 to accommodate the decline in domestic interest rates to x0. As prices adjust, the economy will move up the AA curve. Higher prices will decrease the real value of the domestic money stock, and will therefore require an increase in the domestic interest rate in order to maintain money market equilibrium. This increase in interest rates will be associated with an appreciation of the exchange rate. The ERD model therefore not only rejects the PPP condition but also demonstrates that prices and exchange rates may move in opposite directions during the adjustment period.

To complete the model, it is necessary to specify the price adjustment mechanisms. In the short run, a depreciation of the exchange rate will lower the relative price of domestic goods and create an excess demand for domestic output. This excess demand will be greater if the decline in domestic interest rates also leads to increased expenditure on domestic goods and if Keynesian multiplier mechanisms are present. In addition, rational consumers should recognize that the rate of inflation will be greater than the nominal rate of interest during the period of adjustment to a monetary shock, and that consequently capital gains may be made from intertemporal substitution in consumption. Although these effects are important, the description here is restricted to the simple relative price effect. 11 In equation (27), the relative rate of inflation is assumed to be proportional to the difference between the exchange rate and the ratio of commodity prices:

The locus of combinations of relative prices and exchange rates that is consistent with commodity market equilibrium is defined in Figure 1 as the = 0 line. At point b, the immediate depreciation of the exchange rate has created an excess demand for domestic goods relative to that for foreign goods. This excess demand results in an inflation of domestic prices and, possibly, a deflation of foreign prices. In the money market, the higher relative inflation decreases the real value of domestic currency relative to that of foreign currency, thus creating an appreciation of the exchange rate. This process will continue until the new long-run equilibrium is reached at point c.

The ERD model consequently accounts for the sensitivity of exchange rates and interest rates to financial market conditions through the differential speed of adjustment between commodity and asset markets. The slow adjustment of commodity prices forces the auction market prices to bear all the burden of the short-run adjustment. The characteristic feature of the Dornbusch model is the use of aggregate price indices as the appropriate deflator for the relative supplies of money. It is this feature that gives the important predictions that the exchange rate will overshoot its equilibrium value in response to a monetary disturbance, and that expansionary monetary policies cause nominal interest rates to fall even in a world of complete capital mobility.

V. Conclusion

Each of the preceding models provides internally consistent explanations of the central features of the current experience with flexible exchange rates. Each accounts for the slow adjustment in commodity prices, the sensitivity of exchange rates and interest rates to financial market conditions, and the observed efficiency of international capital markets. In addition, there is much in common between the models: the emphasis on the stability of the relative money demand function, on the interest rate parity condition, and on the rational formation of expectations about future exchange rates. For these reasons, the models should not be considered as competing hypotheses but as specialized accounts of particular aspects of the adjustment process.

The role of the applied economist is consequently to integrate these attempts into a general model that is capable of being applied empirically to the data from the recent float. Because of the lack of available data, early attempts to explain the exchange rate movements that occurred during the recent float have had to utilize extremely simple econometric models. 12 However, as the number of observations has increased, the justification for these procedures has declined, and the need to test simultaneous equations models empirically with rational expectations mechanisms has become more pronounced. 13

Despite their obvious similarities, there are a number of tests that could be used to distinguish between the various models discussed in the text. One of the most important differences between the Dornbusch model and the ERE and CS models is that the appropriate deflator for the relative money supplies is assumed to be the relative price index rather than the exchange rate. This difference may be incorporated into an empirical analysis through the construction of an aggregate price index that is a (geometrically) weighted average of the relative price index and the exchange rate. The money market equilibrium condition may then be written as

If the weight, α, is equal to unity, equation (28) reduces to the Dornbusch model. On the other hand, a weight of zero reduces equation (28) to the ERE formulation of the relative money market equilibrium condition. Finally, a combination of α equal to zero and η equal to zero reduces equation (28) to the equation specified in the global monetarist variant of the currency substitution approach.

The second important difference between the models is in the behavior of interest rates. In the Dornbusch model, a depreciation (increase) in the exchange rate leads to a fall in domestic interest rates. The ERE and CS models suggest, on the other hand, that the relationship between exchange rates and interest rates cannot be specified without specifying the process generating the exogenous variables. This second approach is, of course, extremely difficult to implement, since market forecasts are based, to a large extent, on subjective judgments and policy announcements that are difficult to describe in a regression equation. However, if the volatile behavior in the exchange rate is due to positive serial correlation in the exogenous variables, then one simple ad hoc model that provides a basis for distinguishing between the models is the two-part expectations hypothesis developed by Frenkel (1975) and estimated by Lahiri (1976; 1977) in two applications. The two-part expectations hypothesis is described in equation (29)

In equation (29), x is the long-run expected rate of depreciation. In an empirical application, a good proxy for this variable is the 12-month forward premium or the difference between long-term bond rates. Through the first (regressive) element, a positive rate of depreciation will lead to a decline in the expected rate of depreciation as market participants expect the actual rate to return to the long-run rate. This is the type of behavior that occurs in the Dornbusch model, where a depreciation of the exchange rate leads to expectations of an appreciation in the subsequent periods. Through the second (adaptive) element in the expectations mechanism, a rate of depreciation that exceeds the current expected rate leads to upward revisions in the expected rate of depreciation. The adaptive element therefore reproduces the explanation for overshooting found in the ERE model of exchange rate determination.

To complete the model, a price adjustment equation is required. In equation (7), the relative rate of inflation is related to the deviation from PPP:

Equation (30) reflects the view that the exchange rate, as an auction price, adjusts more rapidly to money market conditions than does the relative price index.

The specification contained in these equations reflects many of the recent developments in monetary models of exchange rate determination. The failure of the PPP condition in the short run is accounted for, and, in its place, the exchange rate is allowed to have a direct influence on the relative demand for the two currencies. In addition, an attempt is made to specify the factors determining interest rate differentials in terms of expectations about future exchange rate developments. As demonstrated in the main body of the paper, the exact form of the expectations equation reflects the form of the process generating the relative supply of and demand for money, in addition to the speed of price adjustment.

The importance of these theoretical models lies in their ability to reconcile the main features of the current experience with floating exchange rates with recent developments in monetary theory. In particular, the models explain why exchange rates and interest rates adjust rapidly to changes in expected future conditions, and why the exchange rate may “overshoot” its equilibrium value in response to changes in the demand for and supply of money. The models therefore provide an interesting guide to empirical research on the behavior of exchange rates. Econometric research on the monetary approach has proceeded rapidly. Following the initial study by Frenkel (1976) of the hyperinflation in Germany in the early 1920s, similar models have been estimated for the deutsche mark/dollar rate during the current float by Bilson (1979), Hodrick (1978), and Suss (1979). In addition, monetary models have been estimated for the deutsche mark/pound exchange rate by Bilson (1978 a) and for the French franc/dollar, pound/dollar, and French franc/pound exchange rate during the 1920s by Frenkel and Clements (1978). On the currency substitution model, Miles (1978) provides estimates of the elasticity of substitution between Canadian and U. S. dollars, and Brillembourg and Schadler (1979) have estimated a general substitution matrix for all the major currencies. Finally, Driscoll (1978) provides estimates of a model of exchange rate and price level determination that is quite similar to the model described by Dornbusch.

All these models support the general predictions of the monetary approach. In particular, most find that a monetary expansion results in a proportional depreciation of the exchange rate. In addition, increases in real income, for given rates of monetary growth, lead to an appreciation of the exchange rate, and higher levels of nominal interest rates, again for given levels of monetary growth, tend to depreciate the exchange rate. At the moment, however, insufficient empirical work has been done to determine which of the particular models discussed in this paper offers the most apt description of the current floating rate experience.

REFERENCES

    AliberRobert Z.The Interest Rate Parity Theorem: A Reinterpretation,Journal of Political Economy Vol. 81 (November/December1973) pp. 145159.

    ArtusJacques R.Exchange Rate Stability and Managed Floating: The Experience of the Federal Republic of Germany,Staff Papers Vol. 23 (July1976) pp. 31233.

    ArtusJacques R. and Andrew D.CrockettFloating Exchange Rates and the Need for Surveillance Essays in International Finance No. 127 International Finance SectionPrinceton University (May1978).

    BarroRobert J.A Stochastic Equilibrium Model of an Open Economy under Flexible Exchange Rates,Quarterly Journal of Economics Vol. 92 (February1978) pp. 14964.

    BilsonJohn F.O. (1978a) “The Monetary Approach to the Exchange Rate: Some Empirical Evidence,Staff Papers Vol. 25 (March1978) pp. 4875.

    BilsonJohn F.O. (1978b) “Rational Expectations and the Exchange Rate,Ch. 5 in The Economics of Exchange Rates: Selected Studiesed. byJacob A.Frenkel and Harry G.Johnson (Reading, Massachusetts1978) pp. 7596.

    BilsonJohn F.O. (1979) “The Deutsche Mark/Dollar Rate: A Monetary Analysis.” (It is scheduled for publication in the next volume of the Carnegie-Mellon Conference Series on Public Policy.)

    BilsonJohn F.O. and Richard M.LevichA Test of the Forecasting Efficiency of the Forward Exchange Rate” (mimeographedNew York UniversityGraduate School of Business AdministrationJune1977).

    BransonWilliam H.The Minimum Covered Interest Differential Needed for International Arbitrage Activity,Journal of Political Economy Vol. 77 (November/December1969) pp. 102835.

    BrillembourgArturo and Susan M.SchadlerA Model of Currency Substitution in Exchange Rate Determination 1973–1978” (unpublishedInternational Monetary FundFebruary231979).

    CaganPhillipThe Monetary Dynamics of Hyperinflation,in Studies in the Quantity Theory of Moneyed. byMiltonFriedman (University of Chicago Press1956) pp. 25117.

    CalvoGuillermo A. and Carlos AlfredoRodriguezA Model of Exchange Rate Determination under Currency Substitution and Rational Expectations,Journal of Political Economy Vol. 85 (June1977) pp. 61725.

    CornellBradfordSpot Rates, Forward Rates and Exchange Market Efficiency,Journal of Financial Economics Vol. 5 (1977) pp. 5565.

    DornbuschRudigerExpectations and Exchange Rate Dynamics,Journal of Political Economy Vol. 84 (December1976) pp. 116176.

    DornbuschRudiger and PaulKrugmanFlexible Exchange Rates in the Short Run,Brookings Papers on Economic Activity: 3 (1976) pp. 53775.

    DriscollRobertExchange Rate Dynamics, Asset-Market Equilibrium, and Stock/Flow Interaction” (unpublishedOhio State UniversityMarch1978).

    FrenkelJacob A. (1975) “Inflation and the Formation of Expectations,Journal of Monetary Economics Vol. 1 (October1975) pp. 40321.

    FrenkelJacob A. (1976) “A Monetary Approach to the Exchange Rate: Doctrinal Aspects and Empirical Evidence,Scandinavian Journal of Economics Vol. 78 (No. 21976) pp. 20024.

    FrenkelJacob A. and Kenneth C.ClementsExchange Rates in the 1920’s: A Monetary Approach” (unpublishedUniversity of ChicagoMay1978).

    FrenkelJacob A. and Harry G.Johnsoneds. (1976) The Monetary Approach to the Balance of Payments (London1976).

    FrenkelJacob A. and Harry G.Johnson (1978) The Economics of Exchange Rates: Selected Studies (Reading, Massachusetts1978).

    FrenkelJabob A. and Richard M.Levich (1975) “Covered Interest Arbitrage: Unexploited Profits?Journal of Political Economy Vol. 83 (April1975) pp. 32538.

    FrenkelJabob A. and Richard M.Levich (1977) “Transaction Costs and Interest Arbitrage: Tranquil versus Turbulent Periods,Journal of Political Economy Vol. 85 (December1977) pp. 120926.

    GirtonLance and DonRoperTheory and Implications of Currency Substitution” (unpublishedUniversity of UtahAugust1976).

    HodrickRobert J.An Empirical Analysis of the Monetary Approach to the Determination of the Exchange Rate,Ch. 6 in The Economics of Exchange Rates: Selected Studiesed. byJacob A.Frenkel and Harry G.Johnson (Reading, Massachusetts1978) pp. 97116.

    IsardPeter (1977) “How Far Can We Push the’ Law of One Price’?American Economic Review Vol. 67 (December1977) pp. 94248.

    IsardPeter (1978) Exchange-Rate Determination: A Survey of Popular Views and Recent Models Princeton Studies in International Finance No. 42 International Finance SectionPrinceton University (May1978).

    JohnsonHarry G.The Monetary Approach to Balance-of-Payments Theory,Ch. 6 in The Monetary Approach to the Balance of Paymentsed. byJacob A.Frenkel and Harry G.Johnson (London1976) pp. 14767.

    KingDavid T.Bluford H.Putnam and D. SykesWilfordA Currency Portfolio Approach to Exchange Rate Determination: Exchange Rate Stability and the Independence of Monetary Policy,Ch. 14 in The Monetary Approach to International Adjustmented. byBluford H.Putnam and D. SykesWilford (New York1978) pp. 199214.

    KnightMalcolm D.Output, Prices and the Floating Exchange Rate in Canada: A Monetary Approach” (unpublishedInternational Monetary FundDecember301976).

    KohlhagenStephen W.The Behavior of Foreign Exchange Markets—A Critical Survey of the Empirical LiteratureNew York UniversityMonograph Series in Finance and Economics No. 1978–3 (New York1978).

    KouriPentti J.K.The Exchange Rate and the Balance of Payments in the Short Run and in the Long Run: A Monetary Approach,Scandinavian Journal of Economics Vol. 78 (No. 21976) pp. 280304.

    KravisIrving B. and Robert E.LipseyPrice Competitiveness in World TradeNational Bureau for Economic Research (Columbia University Press1971).

    LahiriKahil (1976) “Inflationary Expectations: Their Formation and Interest Rate Effects,American Economic Review Vol. 66 (March1976) pp. 12431.

    LahiriKahil (1977) “A Joint Study of Expectations Formation and the Shifting Phillips Curve,Journal of Monetary Economics Vol. 3 (1977) pp. 34757.

    McCormickFrankCovered Interest Arbitrage: Unexploited Profits: Comment.” (It is scheduled for publication in the Journal of Political Economy in1979.)

    MilesMarc A.Currency Substitution, Flexible Exchange Rates, and Monetary Independence,American Economic Review Vol. 68 (June1978) pp. 42836.

    MundellRobert A.International Economics (New York1968).

    MussaMichaelThe Exchange Rate, the Balance of Payments and Monetary and Fiscal Policy Under a Regime of Controlled Floating,Scandinavian Journal of Economics Vol. 78 (No. 21976) pp. 22948.

    NiehansJürg (1975) “Some Doubts About the Efficacy of Monetary Policy under Flexible Exchange Rates,Journal of International Economics Vol. 5 (August1975) pp. 27581.

    NiehansJürg (1977) “Exchange Rate Dynamics with Stock/Flow Interaction,Journal of Political Economy Vol. 85 (December1977) pp. 124557.

    SargentThomas J. and NeilWallaceRational Expectations and the Dynamics of Hyperinflation,International Economic Review Vol. 14 (June1973) pp. 32850.

    StockmanAlan C.Risk, Information, and Forward Exchange Rates,Ch. 9 in The Economics of Exchange Rates: Selected Studiesed. byJacob A.Frenkel and Harry G.Johnson (Reading, Massachusetts1978) pp. 15978.

    SussEstherA Short-Run Model of the Trade-Off Between Exchange Rate and Reserve Changes” (unpublishedInternational Monetary Fund1979).

    UjiieJunichiA Stock Adjustment Approach to Monetary Policy and the Balance of Payments,Ch. 10 in The Economics of Exchange Rates: Selected Studiesed. byJacob A.Frenkel and Harry G.Johnson (Reading, Massachusetts1978) pp. 17992.

    WilsonCharles A.The Impact of Anticipated Shocks in Professor Dornbusch’s Model of ‘Expectations and Exchange Rate Dynamics’.” (It is scheduled for publication in the Journal of Political Economy in1979.)

Mr. Bilson, economist in the External Adjustment Division of the Fund’s Research Department when this paper was prepared, is Assistant Professor of International Economics in the Graduate School of Business at the University of Chicago. He was formerly an Assistant Professor in the Economics Department at Northwestern University. He is a graduate of Monash University, Melbourne, and the University of Chicago.

This paper is an extended version of a paper entitled, “The Current Experience with Floating Exchange Rates: An Appraisal of the Monetary Approach,” which was delivered at the 1978 meetings of the American Economic Association.

Many of the papers on these topics were published in the Scandinavian Journal of Economics, Vol. 78 (No. 2, 1976) and in Frenkel and Johnson, eds. (1978). In addition, the papers by Artus (1976), Bilson (1978 a), Dornbusch (1976), Knight (1976), and Niehans (1977) present asset market approaches to the exchange rate.

It should be stressed that no attempt is made to provide an exhaustive survey of the literature on monetary models. The aim of the paper is to integrate three particular strands of a wider literature into a simple model with immediate empirical applicability. In particular, larger econometric models based upon monetary principles are not discussed nor are small monetary models that consider currency substitution within a small open economy, that is, Kouri (1976) and Calvo and Rodriguez (1977). Surveys of recent literature on exchange rate determination are provided by Isard (1978) and Kohlhagen (1978).

The empirical evidence on the interest rate parity condition is examined in Aliber (1973), Branson (1969), Frenkel and Levich (1975; 1977) and McCormick (1979).

Equation (5) is an approximation to the complete form of the interest rate parity condition that includes an interaction term. The approximation will be very close for short maturities.

For empirical evidence on the relationship between the forward rate and forecasted future spot rates, see Bilson and Levich (1977), Cornell (1977), and Stockman (1978).

The term “currency substitution” has been used in two different senses in the literature. In the papers by Barro (1978), Calvo and Rodriguez (1977), and Kouri (1976), currency substitution refers to substitution between domestic and foreign currencies within a single small economy. These models typically assume the absence of capital flows, so that importation of currency takes place through current account surpluses. The second approach is the one discussed in this paper, in which currency substitution is assumed to occur in a world of integrated capital markets.

Some features of the Dornbusch (1976) model may be found in Niehans (1975). Niehans (1977) and Wilson (1979) have also contributed to the development of the ERD model.

Dornbusch (1976) does consider the influence of real income and interest rates on the rate of price inflation.

Early attempts at estimating a relative money demand function include those by Frenkel (1976), Bilson (1978 b), and Hodrick (1978). Other papers examined the issues of interest rate parity, purchasing power parity, and the speculative efficiency of the forward market. To the author’s knowledge, there still has been no attempt to empirically estimate a complete monetary model with rational expectations.

One of the difficulties in implementing the rational expectations approach is the need to specify the reaction function of the central bank. Artus (1976) and Ujiie (1978) contain reasonably successful estimates of the reaction functions of the Bundesbank and the Bank of Japan, respectively. These reaction functions could be used in conjunction with forecasting equations for the exogenous variables to construct a simultaneous model of the spot and forward exchange rates.

Other Resources Citing This Publication