The Impact of Monetary and Fiscal Policy Under Flexible Exchange Rates and Alternative Expectations Structures

During the 1960s, a number of notable economists including Friedman (1953), Sohmen (1961), Machlup (1972), and Johnson (1973) argued that the speculative crises and sharp exchange rate changes of the Bretton Woods system could be avoided by a switch to a system of floating exchange rates. They suggested that such a change would yield a gradual adjustment process that would help to insulate economies from external disturbances. The actual experience with flexible rates has not, however, been as favorable as anticipated. For instance, McKinnon (1976, p. 100) has asserted that the current system of floating exchange rates has been characterized by: 1

Abstract

During the 1960s, a number of notable economists including Friedman (1953), Sohmen (1961), Machlup (1972), and Johnson (1973) argued that the speculative crises and sharp exchange rate changes of the Bretton Woods system could be avoided by a switch to a system of floating exchange rates. They suggested that such a change would yield a gradual adjustment process that would help to insulate economies from external disturbances. The actual experience with flexible rates has not, however, been as favorable as anticipated. For instance, McKinnon (1976, p. 100) has asserted that the current system of floating exchange rates has been characterized by: 1

During the 1960s, a number of notable economists including Friedman (1953), Sohmen (1961), Machlup (1972), and Johnson (1973) argued that the speculative crises and sharp exchange rate changes of the Bretton Woods system could be avoided by a switch to a system of floating exchange rates. They suggested that such a change would yield a gradual adjustment process that would help to insulate economies from external disturbances. The actual experience with flexible rates has not, however, been as favorable as anticipated. For instance, McKinnon (1976, p. 100) has asserted that the current system of floating exchange rates has been characterized by: 1

  • (1) movements in the spot exchange rate of up to 20 per cent on a quarter-to-quarter basis, or 5 per cent on a week-to-week basis, that are not secular trends but are movements that generally reverse themselves;

  • (2) a significant widening of the bid-ask spreads in the spot markets over those of the 1960s;

  • (3) an even larger increase in the bid-ask spreads in the forward markets;

  • (4) forward rates that have been poor predictors of spot rates; and

  • (5) official intervention that has continued at as high a level as, or higher than, under the old fixed rate system.

While it is still unclear whether these exchange rate movements reflect the influence of endogenous shocks, such as the oil crisis, the lack of speculative capital (as suggested by McKinnon (1976, p. 101)), or the influence of government intervention in the foreign exchange market, it is nevertheless clear that the adjustment process has not been as smooth as anticipated and that flexible rates have not succeeded in insulating economies from external disturbances.

Recently, a number of economists have argued that, in order to understand exchange rate movements, one must examine the process by which exchange rate expectations are formulated. One is immediately confronted with the fact, however, that there are a variety of potential hypotheses that can be used to describe the formation of exchange rate expectations. A traditional hypothesis derived from inflation theory is that the formation of expectations can be described by an adaptive process. Under this expectations structure, the expected exchange rate adjusts gradually to changes in the actual exchange rate. As pointed out by a number of economists, however, the adaptive expectations hypothesis creates the prospects of unrealized profits in the forward markets. Kouri (1975) and Dornbusch (1976) have therefore argued that one should assume that exchange rate forecasts are “efficient” or “rational”—that foreign exchange market participants use all available information to forecast future exchange rate movements. While “efficient” forecasts do not mean that the forward rate will always be an accurate estimate of the actual future exchange rate in stochastic models, rational expectations are equivalent to perfect foresight in deterministic models.2 Feige and Pearce (1976) and Knight (1976) have argued, however, that rational expectations are economically inefficient. They claim that it would be efficient for market participants to gather complete information about the determinants of market prices only if the marginal cost of acquiring such information is zero—something they regard as unlikely. These authors have therefore proposed two alternative expectations structures. Feige and Pearce suggest that “economically” rational expectations can be formed by applying the Box-Jenkins (1976) forecasting technique.3 Their empirical analysis of inflationary expectations in the United States indicates that economically rational expectations will in general differ from both adaptive and rational expectations and will be independent of innovations in monetary and fiscal policy. In contrast, Knight argued that while individuals might have some understanding of the long-run effects of a change in a policy parameter or an external shock, they will be uncertain about the exact path the economy will follow to the new long-run equilibrium. He therefore suggested that the formation of exchange rate expectations could be described by a “semirational” structure. This involves combining an initial change in expectations that reflects the private sector’s best estimate of the long-run effects of a change in a policy parameter or external shock with a learning (or adaptive) component that reflects the uncertainties about the actual path.

This paper attempts to compare the economy’s response to monetary and fiscal policy under the adaptive, rational, and semirational expectations structures. In examining the economy’s response to policy changes, we are especially interested in considering whether each expectations structure implies a unique response to a policy change. To compare the adjustment process generated under different expectations structures, the rest of our paper is divided into four sections. In Section I, the basic model of a small, open economy with a flexible exchange rate is developed. This model is based on Dornbusch’s (1976) rational expectations model but is modified to allow for a more general definition of the aggregate price level, the use of real rather than nominal interest rates in the expenditure function, and the possibility of either rational, adaptive, or semirational expectations. Then, in Section II, this model is used to contrast the exchange rate, interest rate, and price level movements generated by an increase in the money supply under the alternative expectations structures. It is shown that, in the context of this model, one can distinguish between the adjustment processes under the alternative expectations structures only by examining the behavior of the domestic interest rates relative to the world interest rates during the period immediately following the increase in the money supply. Section III examines the adjustment process generated by an increase in government spending. In general, the economy’s response to an increase in government spending cannot be used to differentiate between the different expectations structures. It is shown that the adjustment processes produced by an increase in government spending under rational and semirational expectations not only are almost identical but also differ only slightly from the process under adaptive expectations. Section IV presents the limitations of the model and conclusions.

I. The Basic Model

To facilitate a comparison between our results and those derived in the literature, the model is similar to that developed by Dornbusch (1976). Consider a small economy that exists in a world of perfect capital mobility. Capital mobility will ensure that the domestic interest rate will differ from the exogenous world interest rate only by the expected rate of depreciation of the exchange rate. If we let r(r*) be the domestic (world) interest rate and εe be the expected rate of change of the exchange rate, then capital mobility implies that4

r=r*+ε˙e(1)

In the model, it is assumed that asset markets clear much more quickly than do goods markets. In the asset markets, continuous portfolio equilibrium is maintained by interest rate and exchange rate movements that will immediately offset any asset market disturbances. In contrast, goods market prices will adjust much more slowly to any excess demand or supply. In the goods market, one must also distinguish between the behavior of the prices of the imported and domestic (or exported) goods. The imported good can be purchased at fixed world prices, but this good is viewed as an imperfect substitute for the domestic good. These assumptions mean not only that domestic demand and supply considerations will determine the absolute and relative prices of the domestic good but also that the price of this good will respond only gradually to any disturbances in the goods market.

the money market

The demand for real balances is taken as a function of the level of real income (y) and the domestic nominal interest rate (r). In log-linear form, the money market is in equilibrium when the supply of real money (mαp – (1 – α)p* – (1 – α)ε) equals the demand for real balances (–λry), or

mαp(1α)p*(1α)ε=λr+Φy(2)

where m, p, p*, ε, and y denote, respectively, the logs of the nominal quantity of money, the price of the domestic good, the price of the imported good, the exchange rate, and real income.5 The supply of real balances equals the level of nominal money divided by the “price” level. Since there is a domestic good and an imported good, the price level that is relevant for portfolio owners must reflect the effects of changes in the prices of both goods. For simplicity, it has been assumed that the true price level can be represented by a log-linear, fixed-weights index that depends on the price of the domestic good and the domestic equivalent of the price of the imported good (which will equal the exchange rate multiplied by the price of the imported good). The price index is thus given by αp + (1 – α)ε+ (1 – α)p* where α represents the weight that the price of the domestic good receives in the general price index.

the goods market

The demand for the domestic good (D) is taken as a function of the relative price of the domestic good, the level of real income, and the real interest rate. Thus,

InD=δ(ε+p*p)+γy+σ[rαp˙e(1α)ε˙e](3)

where e is the expected rate of change in the price of the domestic good. The real interest rate has been defined to equal the nominal interest rate less the expected rate of inflation as measured by our price index. Since the foreign price of the imported good is fixed, the expected rate of price change depends only on the expected rates of change in the price of the domestic good and the exchange rate.

The rate of increase in the price of the domestic good () is assumed to depend on the excess demand for the domestic good. Thus,

p˙=πln(D/Y)=π[δ(ε+p*p)+(γ1)yσ[rαp˙e(1α)ε˙e]](4)

expectations

To examine the influence of expectations on the adjustment process, it is assumed that there are three possible expectations structures—rational, adaptive, or semirational. In a deterministic system, rational expectations are equivalent to perfect foresight, which means that the expected rate of change of either the price of the domestic good (e) or the exchange rate (ε˙e) will equal the actual rate of change. In contrast, with adaptive expectations, market participants are assumed to adjust their expectations gradually. Actual and expected price or exchange rate movements can therefore diverge for extended periods of time. Under this expectations structure, it is assumed that a partial adjustment mechanism can be used to describe the manner in which the private sector relates actual and expected price and exchange rate movements. Thus,

p˙e=θ(ppe)(5)
ε˙e=β(εεe)(6)

The semirational expectations structure is based on the hypothesis that market participants may have some estimate of the long-run effects of a change in a policy instrument but are uncertain about the exact path that the economy will follow to the long-run equilibrium. In this situation, one must differentiate between the initial and medium-term changes in expectations. To illustrate the nature of this difference, let Xe be the expected value of any price X. Given a change in a policy instrument, the initial movement in Xe will reflect (1) whether or not the private sector regards this change in the policy instrument as permanent or transitory, and (2), to the degree that the policy change is regarded as permanent, the private sector’s best estimate of the long-run effect of this policy change on X. If it is assumed for the moment that the levels of government spending (g) and the money supply (m) are the only policy parameters, then the private sector’s best estimate of the long-run value of X will naturally be defined as some function (j(g, m)) of the policy instruments. Under semirational expectations, the long-run expected change in the value of X will thus equal

dXe=dEX=jgdg+jmdm

We refer to dEX as the extrapolative component of semirational expectations.

Once this initial change in expectations has taken place, however, the subsequent behavior of the expected value of X will be dominated by the belief that X will ultimately move toward the new value of EX. The expected change in X during this period will be some positive function of the gap between the long-run value (EX) and the actual value. Thus,

X˙e=a(EXX)

We refer to this as the “learning” component of the semirational expectations structure.

The relationship between the actual and expected values of p and ε under semirational expectations will thus be given by

dpe=dEp=fmdm+fgdg(7)

(long-run expected change in pe owing to change in m or g)

Ep=f(m,g)fm>0,fg>06(8)
p˙e=a(Epp)(9)

(medium-term relationship between pe and p)

dεe=dEε=hmdm+hmdg(10)

(long-run expected change in εe owing to change in m or g)

with

Eε=h(m,g)hm>0,hg<0(11)
ε˙e=b(Eεε)(12)

(medium-term relationship between εe and ε)

The adjustment processes generated under these different expectations structures can be compared if we first consider an increase in the money supply.

II. An Increase in the Nominal Money Supply

Given an increase in the nominal money supply, a stable economy will eventually achieve a new steady state equilibrium with a higher price for the domestic good and a depreciated exchange rate.8 But let us examine how the economy will move from the initial equilibrium to its new long-run equilibrium by first considering rational expectations.

rational expectations

Under rational expectations, equations (1)-(4) can describe the adjustment process if we substitute and ε˙ for e and ε˙e. These relationships can then be reduced to two differential equations in the exchange rate (ε) and the price of the domestic good (p), which are given by 9

ε˙=[mαp(1α)ε(1α)p*]/λr*Φy/λ(13)
p˙={λδπ(ε+p*p)ασπ[mαp(1α)ε(1α)p*}/(1ασπ)(14)

The adjustment process implicit in the preceding relationships can be described with the aid of Figure 1. The = 0 curve represents the combinations of p and ε that will yield a stable price for the domestic good. Any point to the right (left) of this line will yield a rising (falling) price of the domestic good. The ε˙ = 0 curve portrays the combinations of p and ε that will generate a stable exchange rate. Any point to the right (left) of this curve will produce a depreciation (appreciation) of the exchange rate.10

Figure 1.

Adjustment Process Under Rational Expectations

Citation: IMF Staff Papers 1977, 003; 10.5089/9781451969450.024.A001

As illustrated by the arrows in Figure 1, not all exchange rate and price level movements will drive the economy back toward the steady state equilibrium (point A) following any disturbance. In fact, as shown in Appendix II, there is a unique saddle point path (illustrated by the dotted line in Figure 1) that the economy must follow if (a) perfect foresight is to be maintained and if (b) the economy is to return to the steady state equilibrium. Along this saddle point path, the money market will be in continuous equilibrium, and the goods market will follow the path described by equation (4).

The presence of this saddle point path implies a Harrod-Domar “knife-edged” adjustment process. The basic problem is that any point that is not on the saddle point path will generate portfolio and price adjustments that will lead to a continuous movement away from any stable steady state. At a point such as B in Figure 1, for example, asset and goods market adjustments will interact to produce a steady, continuous increase in both the exchange rate and the price of the domestic good. Since random shocks could frequently produce departures from the saddle point path, it appears that a perfect foresight economy would find it difficult to achieve a stable steady state equilibrium. To deal with this problem of instability, the advocates of the perfect foresight hypothesis implicitly assume that market participants will always formulate their plans so that the economy will be inherently stable. This means that the adjustment path generated by the private sector’s behavior will always be identical with the saddle point path. What is left unspecified, however, is exactly what incentives or mechanisms exist to ensure that the saddle point path will be selected. In our analysis of the perfect foresight case, we nonetheless accept this assumption of stability. To understand the implications of this structure, let us consider how the economy will respond to an increase in the money supply.

A permanent increase in the nominal money supply will create an initial excess supply of real money that portfolio owners will seek to eliminate by buying bonds. These bond purchases will result in not only a decline in the domestic interest rate but also a capital outflow that will lead to an initial discrete depreciation of the exchange rate. In terms of the analysis developed in Figure 1, an increase in m will shift the ε˙ = 0 curve to the right but will leave the ṗ 0 curve unchanged. (See Figure 2.) The shift in the ε˙ = 0 curve reflects the fact that a higher m will create an excess supply of money that will have to be offset by a higher ε for each given value of p. The initial increase in « that is required to maintain money market equilibrium is given by the move from A to D in Figure 2. It must be remembered, however, that the domestic interest rate can fall below the world interest rate only if there is the expectation that the exchange rate will appreciate over time. (See equation (1).)11 This means that the initial depreciation of the exchange rate must be large enough to create the anticipation of a future appreciation. However, an appreciation will be expected only if the exchange rate initially depreciates by more than the increase in the money supply. The initial depreciation of the exchange rate thus restores instantaneous equilibrium to the money market not only by reducing the real money supply (via a higher price for the imported good) but also by creating the conditions that will allow the domestic interest rate to decline below the world rate, thereby stimulating the demand for money. And, while these exchange rate and interest rate movements will restore money market equilibrium, they will also create an excess demand for the domestic good. The final movement to the new equilibrium (at point E) must therefore involve a gradual increase in the price of the domestic good and a gradual appreciation of the exchange rate. Thus, the adjustment process under rational expectations will be characterized by an initial depreciation of the exchange rate coupled with no change in the price of the domestic good, and then an appreciation of the exchange rate associated with a rising price of the domestic good. Purchasing power parity relationships will therefore not be maintained during most of the adjustment process.

Figure 2.

Impact of an Increase in the Money Supply Under Rational Expectations

Citation: IMF Staff Papers 1977, 003; 10.5089/9781451969450.024.A001

adaptive expectations

To describe the impact of an increase in the money supply under adaptive expectations, one must allow for the fact that actual and expected movements in the exchange rate and the price of the domestic good may diverge for extended periods of time. To draw a comparison with the adjustment process under rational expectations, we can once again distinguish between the initial and medium-term effects of a change in m. However, there is a subtle but important distinction between the nature of the initial period under rational expectations and that under adaptive expectations. Under both expectations structures, the initial effects will be those that occur during the period in which the price of the domestic good does not respond to any excess demand or supply. Under rational expectations, price and exchange rate expectations are nonetheless free to vary during this period. Under adaptive expectations, however, both the expected price of the domestic good and the expected exchange rate will be fixed during the initial period. This reflects the assumption that expectations respond only slowly to actual price movements. The analysis of the medium-term effects naturally relaxes this assumption and allows for the feedback between changes in the actual and expected levels of the exchange rate and the price of the domestic good.

To illustrate the initial effects generated by an increase in the money supply under adaptive expectations, we can use Figure 3. Although this figure looks similar to Figure 1, there are a number of important differences.12 The = 0 curve now represents the combinations of p and ε that will yield goods market equilibrium given the expected exchange rate and the expected price of the domestic good. The slope of the = 0 curve is unity, which reflects the fact that if pe and εe are held constant, there must be equal changes in ε and p in order to keep the goods market in equilibrium (ṗ = 0).13 The EE line in Figure 3. represents the combinations of ε and p that will yield money market equilibrium given a fixed expected exchange rate.14

Figure 3.

Adjustment Process Under Adaptive Expectations

Citation: IMF Staff Papers 1977, 003; 10.5089/9781451969450.024.A001

An increase in m will again create an initial excess supply of money. To eliminate this portfolio imbalance, the private sector will buy bonds and generate capital outflow. In contrast to the rational expectations case, however, these initial portfolio adjustments cannot lead to a change in the domestic interest rate. As long as the expected exchange rate remains fixed, asset market arbitrage will tie the domestic interest rate to the world interest rate. The private sector can therefore initially purchase bonds in the world market at a fixed nominal interest rate. This capital outflow will nonetheless lead to a discrete depreciation of the spot exchange rate by an amount that exceeds the increment in the money supply. A depreciation of this size is required to restore equilibrium to the money market with an unchanged real money supply. Since the level of real income is fixed and the domestic interest rate is initially tied to the world interest rate, the demand for real money will not be affected by the increase in the money supply. Money market equilibrium can therefore be maintained only if exchange rate movements increase the general price level sufficiently to offset the increase in the nominal money supply and to leave the real money supply unchanged. Since the price of the imported good carries the weight 1 – α in the aggregate price index, the exchange rate must depreciate by = dm/(1 – α) > dm.

In terms of the analysis developed in Figure 3, the increase in the money supply will initially shift the EE curve to the right but will leave the = 0 curve unchanged. (See Figure 4.) The initial increase in ε that is required to maintain money market equilibrium is given by the move from A to B in Figure 4. Thus, just as under rational expectations, the initial exchange rate response to an increase in the money supply will involve an overshooting of the ultimate exchange rate level.

Figure 4.

Initial Impact of an Increase in the Money Supply Under Adaptive Expectations

Citation: IMF Staff Papers 1977, 003; 10.5089/9781451969450.024.A001

While the initial overshooting of the exchange rate will therefore occur under both adaptive and rational expectations, the amount by which the exchange rate overshoots its long-run value will be different under the two alternative expectations structures. As has been shown, the overshooting of the exchange rate is part of the process by which instantaneous equilibrium is restored to the money market following an increase in the money supply. The size of this initial depreciation will be determined by whether this exchange rate movement is required to offset just the increase in the money supply (as under adaptive expectations) or the increase in the money supply and the effects of an initial interest rate movement (as under rational expectations). Since the depreciation of the exchange rates helps to restore money market equilibrium by raising the prices of the imported good and thereby reducing the real supply of money, less overshooting will occur under rational expectations than under adaptive expectations. This reflects the fact that, under rational expectations, part of the initial portfolio disequilibrium will be eliminated by the increase in the demand for money that is generated by the decline in the domestic interest rate. Thus, while the largest initial interest rate movements will occur under rational expectations, the largest initial exchange rate movements will take place under adaptive expectations.

The medium-term effects of an increase in the money supply under adaptive expectations are somewhat more complex to analyze. The initial depreciation of the exchange rate will lead the private sector to increase its estimate of the expected exchange rate (ε˙e > 0). As the expected exchange rate increases, however, asset market arbitrage will force the domestic interest rate above the world interest rate.15 The initial depreciation of the exchange rate will also create an excess demand for the domestic good that will drive up the price of that good. Thus, for at least some period, we will see a rising price level and a rising domestic interest rate.

The interaction between changes in actual and expected exchange rate and price level movements means that the economy can follow either a cyclical or direct path to its new long-run equilibrium involving a higher p and ε.16 If the approach to the long-run equilibrium is cyclical, then the exchange rate may overshoot its long-run value not only at the beginning but also during the later stages of the adjustment process. Figure 5 contrasts the adjustment processes for the exchange rate, the price of the domestic good, and the domestic interest rate under rational and adaptive expectations. In Figure 5, panel A portrays the adjustment process under rational expectations; panel B illustrates a direct approach to equilibrium under adaptive expectations; and panel C describes one potential cyclical path under adaptive expectations. Under rational expectations, an increase in the money supply will produce an initial decline in the domestic interest rate and a depreciation of the exchange rate. This will be followed by a gradual decline of the exchange rate to its long-run level, a gradual rise in the price of the domestic good to its new steady state value, and a gradual increase of the domestic interest rate to equality with the world interest rate.

Figure 5.

Adjustment Processes Generated by an Increase in the Money Supply Under Rational Expectations, Adaptive Expectations (Direct Approach), and Adaptive Expectations (Cyclical Approach)

Citation: IMF Staff Papers 1977, 003; 10.5089/9781451969450.024.A001

Under adaptive expectations, a direct approach to the new equilibrium (panel B) will generate paths for the exchange rate and the price of the domestic good that are quite similar to those under rational expectations. However, under adaptive expectations, the domestic interest rate will temporarily rise above rather than fall below the world interest rate.

If there is a cyclical approach to equilibrium under adaptive expectations, then the behavior of r, p, and ε will be quite different from the rational expectations case. (See panel C.) In this situation, the exchange rate and the price of the domestic good may overshoot and undershoot their long-run equilibrium values a number of times. Thus, under adaptive expectations, it is much more likely that the adjustment process will show much greater price, exchange rate, and interest rate fluctuations than under rational expectations. But the key to whether adaptive or rational expectations best characterize the expectations structure of the economy will be the behavior of nominal interest rates following an increase in the nominal money supply. Under rational expectations, the initial decline in the interest rate will be followed by a gradual return to equality with the world interest rate. In contrast, under adaptive expectations, the domestic interest rate will gradually rise above the world interest rate before returning to an equality.

semirational expectations

Under semirational expectations, market participants will have some understanding of the long-run effects of a change in monetary or fiscal policy, but they will be uncertain about the exact path that the economy will follow from the initial equilibrium to the long-run equilibrium.

In this situation, an increase in the nominal money supply will create not only an excess supply of money but also the expectation of a long-run depreciation of the exchange rate and a long-run increase in the price of the domestic good. This initial change in expectations represents the influence of the extrapolative component of the semirational structure.17 Since market participants will anticipate a long-run depreciation of the exchange rate, the domestic interest rate will rise above the world interest rate by the amount of the anticipated depreciation. This is represented by the movement of the interest rate from A to B in Figure 6. 18 This initial increase in the domestic interest rate will reduce the demand for money (by – λdεe), which will work to further increase the initial excess supply of money. To restore equilibrium in the money market, the exchange rate must therefore initially undergo a discrete depreciation (which will raise the price level and reduce the supply of real money) by an amount that is larger than the initial depreciations under either adaptive or rational expectations. The initial depreciation must be larger under semirational expectations because it must offset the excess supply of money created by both the increase in the nominal money supply and the decline in the demand for money induced by the rise in the domestic interest rate. In contrast, the initial depreciation (under adaptive expectations) has to offset only the increase in the nominal money supply, since the domestic interest rate will initially be tied to the world interest rate. And under rational expectations, the realization that the exchange rate will initially overshoot its long-run value creates the anticipation of a long-run appreciation of the exchange rate that drives down the domestic interest rate. Since a lower interest rate will increase the demand for money, however, a smaller initial depreciation is required to restore money market equilibrium.19

Figure 6.

Impact of an Increase in the Money Supply Under Semirational Expectations

Citation: IMF Staff Papers 1977, 003; 10.5089/9781451969450.024.A001

To calculate the medium-term effects of the increase in the money supply, one must allow for the feedback effects associated with the learning component of the semirational structure. It has been shown that the increase in the money supply interacted with the extrapolative component of the semirational structure to initially create the expectation of a long-run depreciation of the exchange rate. This expectation not only pushed the domestic interest rate above the world rate but also forced the exchange rate to overshoot its long-run value (to point D in Figure 6). It must be recognized, however, that this extrapolative effect has only a once-and-for-all impact that occurs at the instant in time when the money supply is increased. During the rest of the adjustment process, the behavior of expectations will be determined by the learning component of the semi-rational structure.20 This means that, once the initial changes in r and ε have taken place, the private sector will find itself faced with a situation where the exchange rate lies above its long-run value but the price of the domestic good is below its long-run value. It will thus be expected that the price of the domestic good will rise over time, whereas the exchange rate will appreciate. This expectation will influence the adjustment process in both the goods and asset markets.

In the goods market, both the depreciation of the exchange rate and the realization that the price of the domestic good must rise over time will work to create an excess demand for the domestic good. This excess demand will drive up the price of the nontraded good.

In the asset market, the realization that the exchange rate must appreciate to reach its long-run equilibrium will lead to a sharp decline in the domestic interest rate, to a level that is below the world interest rate. In Figure 6, this interest rate change is reflected by the move from B to C. This decline in the domestic interest rate will raise the demand for real money balances. At the same time, however, the rising price of the domestic good will be reducing the real supply of money. Thus, to maintain continuous money market equilibrium, the exchange rate must appreciate to lower the price of the imported good and to increase the real money supply. It should be emphasized, however, that the sharp initial changes in the interest rate reflect the assumption that asset markets clear instantaneously. If asset markets adjusted more gradually, then one would see a gradual upswing of the interest rate followed by a gradual decline, instead of the discrete changes described in this paper.

As shown in Figure 6, these price, exchange rate, and interest rate movements will interact to produce a smooth asymptotic path to the long-run equilibrium. (See Appendix IV for an analysis of this path.) During this part of the adjustment process, the interest rate will gradually rise to equality with the world interest rate, the price of the domestic good will increase to its long-run value, and the exchange rate will appreciate to its new steady value.

What then are the basic differences and similarities between the adjustment processes under the three different expectations structures following an increase in the money supply? The major difference between the various adjustment processes lies in the behavior of the domestic interest rate. Under rational expectations, a sharp initial decline is followed by a gradual return to equality with the world interest rate. Under adaptive expectations, in contrast, the interest rate may gradually rise above the world level and then return to its initial level, or there may be a series of cycles with a rising and falling interest rate. And under semirational expectations, the interest rate will undergo a sharp rise, then a sharp decline, and finally a gradual recovery to the initial value. A second difference between the adjustment processes is that only the adaptive expectations structure can possibly involve a cyclical adjustment process. Under either rational or semirational expectations, the initial discrete adjustments will be followed by an asymptotic movement to the long-run equilibrium. However, one element that is shared by all three adjustment processes is an initial exchange rate depreciation that is larger than the increase in the money supply. This discrete depreciation is required to restore money market equilibrium, and the existence (but not the size) of this overshooting is independent of the expectations structure.

III. An Increase in Government Spending

To incorporate fiscal policy into this analysis, we must allow for the impact of government spending and taxation on asset and goods market behavior. To simplify the analysis, it is assumed (1) that government spending can be expressed as a proportion (g) of private spending (D), (2) that government tax revenues are raised via a lump-sum tax and a tax on income, and (3) that all government deficits or surpluses are financed by issuing or retiring bonds. The government budget constraint can therefore be written as 21

dBGdt=gPD+rBGt0t1PY

where BG = the stock of government bonds

t0 = lump-sum taxes

t1 = income tax rate

The presence of taxes means that the demand for goods and for assets will depend on disposable rather than gross income. Nominal disposable income (YD) equals factor income (PY) plus earnings on private holdings of domestic (rBD) and foreign (rBF) bonds, and less any taxes (t0 + t1PY). Thus,

YD=PY+rBD+rBFt0t1PY

In the asset markets, the impact of fiscal policy will be generated via the issuance of bonds and the effects of changes in taxes on disposable income and thereby on asset demands, whereas the effects of fiscal policy on the goods market will be produced by changes in government spending and the impact of changes in taxes on disposable income and thereby on consumption demands. The conditions for money market equilibrium will be identical with those described in equation (2). We are thus assuming that the level of output (rather than disposable income) is still the best indicator of the transactions demand for money. Since it has been assumed that government spending (G) can be expressed as a proportion of private spending on the domestic good, the total demand for the domestic good will be G + D = gD + D = (1 + g)D. Equation (4) must therefore be rewritten as

p˙=π(ln(1+g)+δ(ε+p*p)σ(rαp˙e(1α)ε˙e)+γyDy),or,usingr=r*+ε˙e˙
p˙=π(In(1+g)+σ(ε+p*p)σ(r*+αε˙eαp˙e)+γyDy)(17)

Given these changes, consider the effects of an increase in the level of government spending (via an increase in g) under the assumption of either rational, adaptive, or semirational expectations.22

Before we consider the actual adjustment paths generated under the alternative expectations structures, it must be emphasized that there are two general characteristics of the model that strongly influence the nature of the adjustment process. First, since the goods market is assumed to adjust slowly, the initial impact of an increase in government spending must be generated via its impact on expectations. If a higher level of government spending is going to have an immediate impact on the domestic interest rate, for example, then it must be able to affect the expected rate of depreciation of the exchange rate, or asset market arbitrage will tie the domestic interest rate to the fixed world interest rate. As will be shown, this characteristic often means that fiscal policy will have only a very limited initial impact on the domestic economy. Second, the impact of fiscal policy is further restricted by the assumptions of perfect capital mobility and a given world interest rate. The nature of these restrictions can best be illustrated if we consider why the capital mobility assumption will interact with the conditions for money market equilibrium to ensure that an increase in government spending financed by the issuance of bonds will ultimately lead to a higher price of the domestic good and an appreciation of the exchange rate.23

An appreciation of the exchange rate must be combined with a higher price of the domestic good because this is the only combination of price and exchange rate movements that will ensure long-run money market equilibrium following an increase in government spending. In the long run, the real demand for money (which depends on the level of real income and the nominal interest rate) will be independent of the level of government spending. This independence reflects the fact that the level of real income will be fixed at the full employment level, and the nominal interest rate will be tied to the international interest rate. With a given real demand for money, however, long-run money market equilibrium can be attained only with a fixed real supply of money. And if the higher level of government spending is financed solely by issuing bonds, then the nominal money supply will not be affected by this expansionary policy. A fixed real money supply can therefore be achieved only if price and exchange rate movements combine to leave the overall price level unchanged. Since an increase in government spending on the domestic good will drive up its price, a stable overall price level will require a fall in the price of the imported good. Given the fixed international prices of the imported good, the prices of imported goods can decline only if the exchange rate appreciates. These constraints on the long-run effects of expansionary fiscal policy will naturally have an important impact on the short-run adjustment process.

rational expectations

To illustrate the adjustment path produced by an increase in government spending, let us first consider rational expectations. To finance its purchases of the domestic good, the government must increase its issuance of bonds. Since a significant proportion of these bonds will be sold on the world bond market, the resulting capital inflows will create the expectation of an appreciation of the exchange rate. This expectation will generate portfolio adjustments that will initially drive the domestic interest rate below the world interest rate, thereby stimulating the demand for money. With a fixed nominal money supply, however, this excess demand for money can be satisfied only if the general price level declines in order to increase the real money supply. Since the price of the domestic good will not respond immediately to a change in demand, the general price level will decline only if there is a discrete appreciation of the exchange rate. In the goods market, the initial rigidity of the price of the domestic good means that the higher level of government spending will merely be added to the backlog of excess demands. The initial impact of an increase in government spending is therefore generated through expectations in the sense that the initial exchange rate and interest rate movements reflect changes in expectations regarding future exchange rate movements.

The initial impact of an increase in g can be illustrated using the graphical analysis developed in Figures 1 and 2. As shown in Figure 7, an increase in g will raise the = 0 curve but will leave the ε˙ = 0 curve unchanged. This shift reflects the fact that a higher level of government spending will create an excess demand for goods that can be eliminated only by a higher value of p for each value of ε. The initial appreciation of the exchange rate is given by the movement from A to B in Figure 7.

Figure 7.

Impact of an Increase in Government Spending Under Rational Expectations

Citation: IMF Staff Papers 1977, 003; 10.5089/9781451969450.024.A001

While the initial appreciation of the exchange rate will reduce private spending on the domestic good, the higher level of government spending will still be sufficient to create an excess demand for the domestic good that will eventually force up its price.24 As this price rises, it will work to continuously reduce the real supply of money. During this period, money market equilibrium can therefore be maintained only if the exchange rate appreciates and thereby reduces the price of the imported good. This continuous exchange rate appreciation will keep the domestic interest rate below the world rate during the move to the long-run equilibrium.

Figure 8 portrays the movements of ε, p, and r during the adjustment process. It is interesting to note that, following the initial discrete decline in the interest rate and the appreciation of the exchange rate, the adjustment process will involve increases in both the price of the domestic good and the domestic interest rate at the same time that the exchange rate is appreciating. As we shall see, this is fairly similar to the behavior under adaptive expectations.

Figure 8.

Adjustment Process Generated by an Increase in Government Spending Under Rational Expectations

Citation: IMF Staff Papers 1977, 003; 10.5089/9781451969450.024.A001

adaptive expectations

Under adaptive expectations, one must again distinguish between the initial and medium-term effects of an increase in government spending. Three factors play a crucial role in determining the initial impact of an increase in government spending under adaptive expectations. First, since the price of the domestic good cannot immediately respond to changes in aggregate demand, the exchange rate and the domestic interest rate are the only variables capable of adjusting in the short run. Second, domestic interest rate adjustments are limited by the fact that the interest rate can deviate from the world interest rate only if the exchange rate is expected to change. And, finally, as has just been shown under rational expectations, the initial effects of an increase in government spending must be generated via a change in expectations. Under adaptive expectations, however, the expected exchange rate and the expected price level will initially be fixed and independent of any actual exchange rate or price level movements. Thus, other than to create an excess demand for goods, the announcement of an increase in the level of government spending will have no initial impact on the level of the exchange rate, the price of the domestic good, or the domestic interest rate.

To illustrate why this is true, one can use the graphical analysis described in Figures 3 and 4. It must be remembered that in these figures the EE curve represents the combinations of ε and p that will yield money market equilibrium given the expected exchange rate, the price of the domestic good, and the stock of money. As shown in Figure 9, an increase in g will push the = 0 curve up to the left but will leave the EE curve unchanged. Since the goods market adjusts slowly, the price of the domestic good will not respond instantaneously to the new excess demand. The demand for and supply of money will also not be affected by any increase in government spending financed by issuing bonds, because the domestic interest rate will initially be tied to the world interest rate. Thus, if any initial appreciation of the exchange rate did take place, it would create an excess supply of real balances by lowering the price of the imported good. The effects of an increase in government spending will therefore necessarily be felt somewhat more gradually under adaptive than under rational expectations.

Figure 9.

Initial Impact of an Increase in Government Spending Under Adaptive Expectations

Citation: IMF Staff Papers 1977, 003; 10.5089/9781451969450.024.A001

The medium-term effects of an increase in government spending reflect the feedback between changes in the actual and expected levels of both the exchange rate and the price of the domestic good. The initial excess demand for the domestic good will drive up the price of that good and will thereby reduce the real supply of money. To maintain money market equilibrium, the exchange rate must therefore begin to appreciate to lower the domestic price of the imported good. This appreciation of the exchange rate will also lower the expected value of the exchange rate and will lead to a decline of the domestic interest rate below the world interest rate. From this point on, however, exactly what path the domestic variables will follow to the new steady state will depend on whether the adjustment path is direct or cyclical. In Figure 10, we have illustrated the paths that will be followed by ε, p, and r if there is a direct approach to equilibrium. A comparison with the rational expectations paths (Figure 8) indicates that the economy’s response to an increase in government spending will be quite similar under both adaptive and rational expectations.25 The initial changes in r and ε provide the only differences between the two adjustment processes. The behavior of the domestic interest rate following an increase in government spending may once again provide the best evidence of whether expectations are rational or adaptive. Under rational expectations, one will see a sharp initial decline in the interest rate followed by a gradual recovery to equality with the world interest rate, whereas under adaptive expectations, one will see a gradual decline and a gradual recovery of the domestic interest rate.

Figure 10.

Adjustment Process Generated by an Increase in Government Spending Under Adaptive Expectations

Citation: IMF Staff Papers 1977, 003; 10.5089/9781451969450.024.A001

semirational expectations

Under semirational expectations, the initial effects of an increase in government spending are again generated via a change in expectations. Market participants will recognize that in the long run an increase in government spending will lead to an increase in the price of the domestic good and an appreciation of the exchange rate. The domestic interest rate will therefore initially drop below the world rate to reflect the expected appreciation of the domestic currency. Since this decline in the domestic interest rate will create an excess demand for real balances, portfolio adjustments will force an exchange rate appreciation to lower the price of the imported good and to increase the real supply of money.

Unless the demand for money is highly sensitive to interest rate changes, however, the initial appreciation of the exchange rate will be less than the long-run expected appreciation.26 Since market participants will thus anticipate an additional appreciation of the exchange rate, the domestic interest rate will gradually increase but will remain below the world interest rate until the new equilibrium is reached. As shown in Figure 11, the initial discrete changes in the exchange rate and interest rates will be followed by a gradual rise in the price of the domestic good, and a gradual recovery of the domestic interest rate to equality with the world interest rate.

Figure 11.
Figure 11.

Adjustment Process Generated by an Increase in Government Spending Under Semirational Expectations

Citation: IMF Staff Papers 1977, 003; 10.5089/9781451969450.024.A001

Thus, in contrast to the situation following an increase in the money supply, the adjustment paths generated by an increase in government spending are quite similar under rational and semirational expectations and only slightly different under adaptive expectations. All paths will involve (1) an initial discrete appreciation (except under adaptive expectations) followed by a further gradual appreciation to the new steady state value for the exchange rate, (2) a gradual increase in the price of the domestic good, and (3) a temporary decline of the domestic interest rate below the world interest rate. The only really distinguishing difference between the various adjustment paths is that the domestic interest rate will not undergo an initial discrete decline under adaptive expectations.

IV. Limitations of the Model and Conclusions

It is clear that our model of the effects of monetary and fiscal policy under floating exchange rates is based on a number of assumptions that not only simplify the analysis but also limit its generality. The most important restrictions are imposed by the assumptions of a small country and perfect capital mobility. The small-country assumption implies that the economy faces a fixed world price for the imported good and a given international interest rate. And the perfect capital mobility assumption means that the domestic interest rate can differ from the world interest rate only by the expected rate of depreciation of the exchange rate. Thus, apart from exchange risks, domestic bonds are viewed as perfect substitutes for international bonds. As has been shown, these assumptions are especially important for analyzing the effects of expansionary fiscal policy, for they imply that the authorities can issue any quantity of bonds that they desire without affecting the international interest rate. A more complete analysis would make the international interest rate sensitive to the quantity of bonds issued. In this situation, a higher level of debt-financed government spending would raise the international interest rate applied to domestic bonds. This means that one would see a smaller appreciation than in the small-country case, or possibly even a depreciation of the exchange rate. The incorporation of these effects will be an important part of future work.

It is usually argued that the manner in which the private sector formulates the expectations will play a crucial role in determining the economy’s response to monetary and fiscal policy. Table 1 summarizes the nature of the adjustment processes generated by either an increase in the nominal money supply or an increase in government spending for a small, open economy with a floating exchange rate. What is surprising about Table 1, however, is the rather similar qualitative nature of the adjustment processes under the different expectations structures. Perhaps the only way to establish which expectations structure best describes the economy’s actual expectations structure is to examine the behavior of nominal interest rates following an increase in the money supply. An increase in the nominal money supply will initially force the interest rate to decline if expectations are rational, and to first rise sharply and then decline sharply if expectations are semirational; it will have only a gradual impact on the interest rate if expectations are adaptive. Unfortunately, even these criteria cannot be used to distinguish between the different expectations structures if one is concerned with the economy’s response to an increase in government spending. Only under adaptive expectations is the behavior of the interest rate qualitatively different from that under either rational or semirational expectations.

Table 1.

Small, Open Economy with Floating Exchange Rate: Adjustment Paths Generated by Increase in Nominal Money Supply and in Government Spending

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If direct approach to equilibrium.

There are, however, some important quantitative differences between the behavior of exchange rates and interest rates under the alternative expectations structures. Following an increase in the money supply, the largest initial interest rate changes will occur under semirational expectations, and the smallest under adaptive expectations. The initial depreciation of the exchange rate produced by an increase in the money supply will be larger under adaptive expectations than under rational expectations.

APPENDICES

I. Notation

Unless otherwise noted, each variable represents the log of the original variable (a capital letter denoting the nonlog value):

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II. Rational Expectations

Under rational expectations, the adjustment process will be described by

r=r*+ε˙(18)
mαp(1α)p*(1α)ε=λr+Φy(19)
p˙=π[δ(ε+p*p)+(γ1)yσ[rαp˙(1α)ε˙]](20)

These three relationships can be reduced to two differential equations in ε and p of the form

p˙={λπ[δ(ε+p*p)+(γ1)yσr*]σαπ[mαp(1α)p*(1α)ε+λr*Φy]}/Aε˙=[mαp(1α)p*(1α)ε+λr*Φy]/λwithA=λ(1σπα)

For this system to have a stable saddle point path, one must have

p˙p+ε˙ε=π[λδ+σα2]/[λ(1απσ)]+(1α)λ<0(21)
|p˙pp˙εε˙pε˙ε|=πδ/A>0(22)

This condition will be satisfied only if A>0 or 1 – σπα > 0.

The slopes of the ε˙ = 0 and ṗ=0 curves given in Figure 1 will therefore equal

dpdε|ε˙=0=ε˙/εε˙/p=(1α)α<0dpdε|p˙=0=p˙/εp˙/p={δλσα(1α)}{δλ+σα2}>0ifp˙ε>0

The saddle point path that will allow the economy to return to a stable equilibrium and still maintain perfect foresight will be given by

dpdε=p˙ε˙={λπ[δ(ε+p*p)+(γ1)yσr*]σαπ[mαp(1α)p*(1α)ε+λr*Φy]}/A[mαp(1α)p*(1α)ε+λr*Φy]/λ

Since both the numerator and denominator go to zero as the steady state equilibrium is approached, one can evaluate the slope of the preceding expression by using L’Hôpital’s rule. Thus,

dpdε=π{λδ(1dpdε)+σα[αdpdε(1α)]}1σπα{αdpdε(1α)}

The solutions for dpdε are given by

(dpdε)S.P.=[(1α)(1σπα)+πλδ+πσα]2α(1σπα)±[(1α)(1σπα)+πλδ+πσα]2+4(1σπα)α[πλδ(1α)πσα]2σ(1σπα)

If p˙ε>0, then this system has two roots—one positive and one negative. One can show that the positive root implies a path that has a slope greater than the = 0 curve—an unstable path. The negative root is thus the stable path.

III. Adaptive Expectations

Under adaptive expectations, the adjustment process will be described by

r=r*+ε˙e(23)
m=αp(1α)p*(1α)ε=λr+Φy(24)
p˙=π[δ(ε+p*p)+(γ1)yσ[rαp˙e(1α)ε˙e]](25)
p˙e=θ(ppe)(26)
ε˙e=β(εεe)(27)

These five relationships can be reduced to three differential equations in p, εe, and pe. Thus,

p˙={πδ[mαp(1α)p*+λr*Φy](1α)σαπβεe(1α)π[δ(p*p)+(γ1)yσr*+σαπθ(ppe)]+λρδβεe+βσαπ[mαp(1α)p*+λr*Φy]}/Aε˙e={β[mαp(1α)p*+λr*Φy]+(1α)βεe}/Ap˙e=θ(ppe)

with A = –(1–αβλ)

Sufficient conditions for this system to be stable are

p˙p+ε˙eεe+p˙epe=δπ+παθσπα(δβσα)1αβλ(1α)βθ<01αβλ(28)
|p˙pp˙εep˙peε˙epε˙eεeε˙pep˙epp˙eεep˙epe|=θσπβ1αβλ<0(29)

Condition (29) will be satisfied only if 1—α—βλ >0

IV. Semirational Expectations

Since the extrapolative component of semirational expectations affects the adjustment path only at the initial instant of time when the policy change is announced, the stability of the adjustment process is determined by the behavior of the economy under the learning component. Using the condition for money market equilibrium (equation (2)), the definition of the learning component of semirational expectations (equations (7)(12)), and the conditions for goods market equilibrium (equation (14)), one can show that the adjustment paths for all the endogenous variables can be derived from the path for p. The differential equation describing the path for will be given by

p˙={π[δ+σαb][mαp(1α)p*+λr*ΦyλbEε](1α+λb)π[δp+(γ1)yσr*σαbEε+σαa(Epp)]}/(1α+λb)

This system will be stable if

p˙p=π{α(δ+σab)+(1α+λb)(δ+σaα)}/(1α+λb)<0

which will be true if 1—α+λb>0

BIBLIOGRAPHY

  • Box, George E. P., and Gwilym M. Jenkins, Time Series Analysis: Forecasting and Control (San Francisco, 1976).

  • Daniel, Betty C., “Analysis of Stabilization Policies in Open Economies under Conditions of Inflation and Inflationary Expectations” (unpublished doctoral dissertation, University of North Carolina, 1976).

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  • Dornbusch, Rudiger, “Expectations and Exchange Rate Dynamics,” Journal of Political Economy, Vol. 84 (December 1976), pp. 116176.

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  • Friedman, Milton, “The Case for Flexible Exchange Rates,” in his Essays in Positive Economics (University of Chicago Press, 1953), pp. 157203.

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  • Isard, Peter, “The Process of Exchange-Rate Determination: A Survey of Important Models and Major Issues,” Board of Governors of the Federal Reserve System, International Finance Discussion Paper No. 101 (January 1977).

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  • Johnson, Harry G., “The Case for Flexible Exchange Rates, 1969,” in his Further Essays in Monetary Economics (Harvard University Press, 1973), pp. 198228.

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  • Knight, Malcolm, “Output, Prices, and the Floating Exchange Rate in Canada: A Monetary Approach” (unpublished, International Monetary Fund, December 30, 1976).

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  • Kouri, Pentti J. K., “The Exchange Rate and the Balance of Payments in the Short Run and in the Long Run: A Monetary Approach” (unpublished, International Monetary Fund, December 17, 1975).

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  • Machlup, Fritz, The Alignment of Foreign Exchange Rates: The First Horowitz Lectures (New York, 1972).

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  • McKinnon, Ronald I., review of Fritz Machlup, The Alignment of Foreign Exchange Rates: The First Horowitz Lectures, in Journal of International Economics, Vol. 5 (February 1975), pp. 99101.

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  • Shafer, Jeffrey Richard, “The Macroeconomic Behavior of a Large Open Economy with a Floating Exchange Rate” (unpublished doctoral dissertation, Yale University, 1976).

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  • Sohmen, Egon, Flexible Exchange Rates: Theory and Controversy (University of Chicago Press, 1961).

*

Mr. Mathieson, economist in the Financial Studies Division of the Research Department, holds degrees from the University of Illinois and Stanford University. He has taught at Columbia University.

This paper has benefited from comments by colleagues in the Fund, who are naturally not responsible for any remaining errors.

1

For a detailed discussion of recent exchange rate movements, see the International Monetary Fund’s Annual Report, 1976.

2

The presence of stochastic variables means that the forward rate could differ from the actual future exchange rate whenever there are “surprise,” or unanticipated, occurrences between time t and t + 1.

3

The Box and Jenkins time series methodology assumes that the current value of any variable (e.g., the rate of inflation—Pt) can be represented as a function of past values of the variable and a stochastic term. One could thus write the current rate of inflation as

Pt = π1 Pt−1 + π2Pt−2 + … + at

or as π(B) Pt = at

where Pt = inflation rate at time t

Π(B) = polynomial in the lag operation B (i.e., BiXt = Xt-i)

at = random error with E(at) = 0, E(at. at-s) = σ2I

Note that in such a series, the current rate of inflation is independent of policy variables. To identify and estimate the underlying process, Box and Jenkins first express each time series as a mixed autoregressive moving average process. The resulting time series models are referred to as autoregressive integrated moving average (ARIMA) models. Box and Jenkins have derived techniques for estimating these ARIMA models.

4

See Appendix I for a summary of notation. The symbols are generally the same as those used by Dornbusch (1976). The exchange rate is defined as domestic currency/foreign currency.

5

It is assumed that real income is fixed at the full employment level.

6

Footnotes 8 and 23 explain why the price of the domestic good rises with an increase in the money supply and falls with an increase in government spending.

7

Footnotes 8 and 23 explain why the exchange rate rises with an increase in the money supply and falls with an increase in government spending.

8

In the long run, the conditions for steady equilibrium are given by

mαp − (1 − α)ε − (1 − α)p* = −λr* + Φy

y = δ(ε + p* − p) − σr* + γy

The equilibrium ε and p will thus equal

ε = [δ(m + λr* − Φy) − δp* + σαr* + α (γ − 1)y]/δ

p = [−(1−α)σr* + (1−α)p* + (1−α)(γ − 1)y + δ(m + λr* − Φy)]/δ

Thus,

dp = = dm > 0

These results also explain why fm>0 (in equation (8)) and hm>0 (in equation (11)).

9

In Appendix II, it is shown that the adjustment process described by equations (13) and (14) will be stable only if 1 – ασΠ>0. This condition is required to ensure that the goods market is stable. Any disturbance in the goods market that generates an increase in the price of the domestic good (ṗ>0) will also reduce the real interest rate (by – αṗ). A decline in the real interest rate, however, will stimulate spending on goods and will lead to a further increase in the price of the domestic good (by σαπṗ). If the price level is ultimately to converge to a stable steady state value (i.e., the goods market is to be stable), then the induced change in must be smaller than the initial change, which means that 1 −πασ must be greater than zero.

It is also assumed that ∂ṗ/∂ε = π[δλ − (1 − α)σα]/(1 − σπα)>0. This essentially requires that the relative price effect generated by a change in the exchange rate outweigh the real interest rate effect. One could reverse the sign of this expression and still derive the same qualitative conclusions as described in the text.

10

The slopes of the two curves are given by

dpdε|p˙=0=p˙/εp˙/p=(δλ(1α)σα)δλ+σα2>0ifp˙ε>0(seefootnote0.)dpdε|ε˙=0=ε˙/εε˙/p=(1α)α<0

The arrows in Figure 1 describe the movement of p and ε when they are off the ṗ=0 and ε˙ = 0 curves.

11

This reflects the assumption that there is perfect capital mobility, which implies that the yields on all bonds will be equalized across countries (after allowance is made for expected exchange rate movements).

12

When combined with the adaptive expectations mechanisms described in equations (5) and (6), the adjustment processes in the money and goods markets are given by

mαp(1α)ε(1α)p*=λr+Φy=λ(r*+ε˙e)+Φy(15)

and

p˙=π[δ(ε+p*p)σ(rαp˙e(1α)ε˙e)+(γ1)y]or,usingr*+ε˙e=r,
p˙=π[δ(ε+p*p)σ(r*+αε˙eαp˙e)+(γ1)y](16)

These four relationships describe the adjustment process for the actual and expected price of the domestic good (p and pe) and the actual and expected exchange rate (ε and εε). As shown in Appendix III, this set of relationships can be reduced to a system of three differential equations in p, pe, and εe. A necessary condition for this system to be stable is that 1—α—βλ>0. This is equivalent to the condition that a depreciation of the exchange rate will work to reduce any excess supply of real money. An increase in ε will reduce the real money supply by −(1 – α) (where 1 – α is the weight that the price of the imported good receives in the overall price index). At the same time, however, an increase in ε will raise the expected rate of depreciation of the exchange rate by dεedε (equation (6)), which will thereby increase the domestic interest rate by an equivalent amount. As the domestic interest rate rises, however, the demand for money will decline by −e = −λβ. Thus, a depreciation of the exchange rate will reduce any initial supply of real balances as long as 1 − α>βλ or 1—α –βλ>0.

13

This reflects the fact that the behavior of the price of the domestic good is given by

p˙=π[δ(ε+p*p)σ(r*+αε˙eαp˙e)+(γ1)y]ifε˙e=p˙e=0,thendpde|p˙=0=1
14

If e=0 initially, then continuous equilibrium in the money market will be maintained if ε=[λr*—Φy-αp]/(1 − α). The EE curve thus has a negative slope equal to −(1—α)/α.

15

One would usually expect an increase in the money supply to drive down the domestic interest rate initially. This cannot happen in our model as long as we maintain the assumption of perfect capital mobility. In this situation, the domestic interest rate can differ from the world rate only by the expected rate of depreciation. If one were to assume that there was less than perfect capital mobility, then it is possible that one could see both a rise in the expected rate of depreciation and a fall in the domestic interest rate.

16

In the long run, the percentage increases in the exchange rate and the price of the domestic good will exactly equal the percentage increase in m. The cyclical nature of the adjustment paths will be determined by the characteristic roots of the three differential equations that describe the behavior of the economy under adaptive expectations. (See Appendix III.)

17

The learning component of the semirational structure will initially be fixed.

18

Figure 6 portrays both the initial and the medium-term movements in r, e, and p. Appendix IV examines the stability of the actual adjustment path.

19

Using equations (10)-(12), it can be seen that the initial response of semi-rational expectations to an increase in m equals

dεe=dEe=hmdm>0

This increase in the expected exchange rate will raise the domestic interest rate by an equivalent amount. In the money market, equilibrium will be maintained if the exchange rate depreciates (dε > 0) by

dm(1α)dε=λhmdmordελdm(1+λhm)/(1α)>0.
20

This analysis is based on the assumption that expectations are formulated at the beginning of the trading “day” and are revised only at the beginning of the next “day,” once market participants have observed the trading prices that have prevailed during the current “day.”

21

It has been assumed implicitly that all government spending is on the domestic good.

22

To simplify the analysis, assume that the government always changes the income tax rate so as to offset any changes in interest earnings on private holdings of bonds. This assumption will allow one to abstract from the effects of changes in interest income on asset and goods demands and will fix the level of disposable income.

23

The long-run effects of an increase in government spending can be shown to equal

= −αdg/δ < 0

dp = (1 − α)dg/δ > 0

In a recent survey of models of exchange rate movements, Isard (1977) noted that both Shafer’s (1976) simulation model and Daniel’s (1976) theoretical model also yield the result that an increase in government spending financed by debt insurance will lead to an appreciation of the exchange rate.

24

This is the movement from B to C in Figure 7.

25

This assumes that there is a direct rather than a cyclical adjustment process under adaptive expectations.

26

The relationship between the initial appreciation of the exchange rate and the long-run expected appreciation can be described as follows. The long-run expected appreciation is given by

dEε=hgdg<0

To maintain money market equilibrium, we must have

(1α)dε=λdEε=λhgdgordε=λdEε1α

After this appreciation, Eε < ε if λ < 1 – α.

IMF Staff papers: Volume 24 No. 3
Author: International Monetary Fund. Research Dept.
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    Adjustment Process Under Rational Expectations

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    Impact of an Increase in the Money Supply Under Rational Expectations

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    Adjustment Process Under Adaptive Expectations

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    Initial Impact of an Increase in the Money Supply Under Adaptive Expectations

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    Adjustment Processes Generated by an Increase in the Money Supply Under Rational Expectations, Adaptive Expectations (Direct Approach), and Adaptive Expectations (Cyclical Approach)

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    Impact of an Increase in the Money Supply Under Semirational Expectations

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    Impact of an Increase in Government Spending Under Rational Expectations

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    Adjustment Process Generated by an Increase in Government Spending Under Rational Expectations

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    Initial Impact of an Increase in Government Spending Under Adaptive Expectations

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    Adjustment Process Generated by an Increase in Government Spending Under Adaptive Expectations

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    Adjustment Process Generated by an Increase in Government Spending Under Semirational Expectations