The Forward Exchange Market and the Effects of Domestic and External Disturbances Under Alternative Exchange Rate Systems1

Victor E. Argy; Michael Porter

doi:10.5089/9781451969290.024.A001

The Forward Exchange Market and the Effects of Domestic and External Disturbances Under Alternative Exchange Rate Systems¹

Author: Mr. Victor E. Argy¹ and Michael Porter

¹ 0000000404811396https://isni.org/isni/0000000404811396International Monetary Fund

Publication Date:: 01 Jan 1972

eISBN:: 9781451969290

Language:: English

Keywords:: SP; exchange rate; exchange rate regime; interest rate differential; forward rate; exchange rate expectation; equilibrium interest rate; Exchange rates; Personal income; Exchange rate flexibility; Exchange rate arrangements; Monetary base; exchange rate system

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THIS PAPER explicitly incorporates the forward exchange market into a model of a small open economy under perfect capital mobility. It is shown that the degree to which the forward rate responds to movements in the spot exchange rate is important in determining the qualitative and quantitative impacts of monetary and fiscal policies.2 Additionally, the effect of exogenous disturbances both to the demand for money and to the capital and current accounts in the balance of payments is examined. The analysis is applied to three foreign exchange regimes: rigidly fixed, completely flexible, and dual—the last system being one in which the commercial exchange rate is fixed and the financial exchange rate is flexible. Although we are not convinced that it will be administratively possible to have divergent exchange rates in the current and capital accounts,3 we believe it a useful exercise to examine the properties of an “ideal” version of a dual exchange rate system. In a final section, the implications of the analysis for a regime intermediate between fixed and flexible rates, one entailing wider bands, are discussed briefly.

Abstract

THIS PAPER explicitly incorporates the forward exchange market into a model of a small open economy under perfect capital mobility. It is shown that the degree to which the forward rate responds to movements in the spot exchange rate is important in determining the qualitative and quantitative impacts of monetary and fiscal policies.² Additionally, the effect of exogenous disturbances both to the demand for money and to the capital and current accounts in the balance of payments is examined. The analysis is applied to three foreign exchange regimes: rigidly fixed, completely flexible, and dual—the last system being one in which the commercial exchange rate is fixed and the financial exchange rate is flexible. Although we are not convinced that it will be administratively possible to have divergent exchange rates in the current and capital accounts,³ we believe it a useful exercise to examine the properties of an “ideal” version of a dual exchange rate system. In a final section, the implications of the analysis for a regime intermediate between fixed and flexible rates, one entailing wider bands, are discussed briefly.

The paper focuses particular attention on the effects of monetary and fiscal policies in a regime of flexible exchange rates under perfect capital mobility. In general, the literature has shown that under completely flexible exchange rates monetary policy is very powerful, while fiscal policy has no effect on economic activity. Assuming that the forward rate is determined entirely by speculators’ expectations, it is shown that the conventional results have to be modified according to the assumptions made regarding the relationship of the expected future spot rate to changes in the current spot rate. When expectations are inelastic (that is, a change in the spot exchange rate provokes expectations of some return toward its original level), monetary policy is shown to be somewhat weaker than in the conventional analysis. The magnitude of the change in the results depends on the size of the elasticity of expectations; the more inelastic the expectations, the weaker are the effects of monetary policy on economic activity. When, however, expectations are elastic (that is, an exchange rate change provokes expectations of a further change in the same direction), a given injection of money into the system generates an effect even stronger than in the conventional analysis.

For fiscal policy, inelastic expectations will enable fiscal expansion to generate some increase in income in contrast to the zero multiplier of the conventional literature. On the other hand, when expectations are elastic, fiscal expansion may actually reduce income.

A much more extensive and detailed summary, including a discussion of a larger range of disturbances under alternative exchange rate regimes, is given in the last section of the paper.

The Model

Symbols

Note: All variables are expressed in terms of domestic currency value.

	Relationship	Equations	Signs of Partial Derivatives
(1) Income determination		Y = A + X - M
(2) Domestic expenditure		A = A(Y, R, g)	A_y > 0, A_r < 0, A_g > 0
(3) Exports		X = X(K, h)	X_k < 0, X_h > 0
(4) Imports		M = M(Y, K)	M_y > 0, M_k > 0
(5) Foreign indebtedness		$B = B (R - R * + \frac{K_{f} - K}{K}) B_{d} > 0 †$
(6) Forward exchange rate		K_f = K + λ(K - K_-1), or $[\frac{K_{f} - K}{K} = λ (\frac{K - K_{- 1}}{K})]$
(7) Money supply		Mo_S = D + F‡
(8) Money demand		Mo_D = L(Y, R, q)	L_y > 0, L_r < 0, L_q > 0
(9) Money equilibrium		Mo_S = Mo_D
(10) Foreign exchange		F - F_-1 = X - M + B - B_-1
	(10a) Flexible rates	F - F_-1 = 0
	(10b) Fixed rates	K - K_-1 = 0
	(10c) Dual rates	B - B_-1 = 0, (K - K_-1)_com = 0

	Relationship	Equations	Signs of Partial Derivatives
(1) Income determination		Y = A + X - M
(2) Domestic expenditure		A = A(Y, R, g)	A_y > 0, A_r < 0, A_g > 0
(3) Exports		X = X(K, h)	X_k < 0, X_h > 0
(4) Imports		M = M(Y, K)	M_y > 0, M_k > 0
(5) Foreign indebtedness		$B = B (R - R * + \frac{K_{f} - K}{K}) B_{d} > 0 †$
(6) Forward exchange rate		K_f = K + λ(K - K_-1), or $[\frac{K_{f} - K}{K} = λ (\frac{K - K_{- 1}}{K})]$
(7) Money supply		Mo_S = D + F‡
(8) Money demand		Mo_D = L(Y, R, q)	L_y > 0, L_r < 0, L_q > 0
(9) Money equilibrium		Mo_S = Mo_D
(10) Foreign exchange		F - F_-1 = X - M + B - B_-1
	(10a) Flexible rates	F - F_-1 = 0
	(10b) Fixed rates	K - K_-1 = 0
	(10c) Dual rates	B - B_-1 = 0, (K - K_-1)_com = 0

Where K_com refers to the (commercial) exchange rate in the trade equations, K_{f in} is the financial exchange rate used in equations (5) and (6).

† Note that B_d is the partial derivative of B with respect to the covered differential. For example:

B_d = ∂B/∂d, where $d = R - R * - (\frac{K_{f} - K}{K}) .$

‡ A simplification here is that the money multiplier is 1.

The major features of the model are as follows: Domestic expenditure is a function of income, interest rates, and a shift parameter (fiscal policy or changes in domestic expenditure). Exports are a function of the exchange rate and a shift parameter, while imports are a function of both income and the exchange rate. The stock of net foreign debt is explained in equation (5) by the level of the covered interest differential, where K_f-K/K is the forward premium on the domestic currency.⁴ The forward rate in turn is assumed to be a function of the change in the exchange rate. (A detailed discussion of this aspect of the model is given below.) The money supply has a domestic component (D) and a foreign component (F), while the demand for money is a function of income, the domestic interest rate, and a shift parameter (q).⁵ An increase in q represents an increase in liquidity preference. Equation (10a) represents the flexible exchange rate model, in which the change in net foreign assets of the central bank is zero, with the exchange rate equilibrating the demand and supply of foreign assets. Equation (10b) represents the fixed exchange rate model, in which an excess supply of foreign assets at this rate is absorbed by the central bank and an excess demand is accommodated by a reduction in the net foreign assets of the monetary authorities. These changes in reserves are reflected in corresponding changes in the money supply, as represented in equation (7). Equation (10c) represents the dual exchange rate regime, in which the exchange rate that enters into the export/import equations is assumed to be fixed while the exchange rate in the equation for foreign indebtedness is allowed to fluctuate freely, so that in this model the capital account is, by definition, always balanced. It is assumed that all the functions are linear.

The unique feature of this model is the explicit introduction of the forward rate in equations (5) and (6). Equation (5) has already been explained. In equation (6) λ represents the response of the forward rate to changes in the spot exchange rate. Since λ will be shown to be critical in evaluating the effects of a number of exogenous disturbances under flexible exchange rates, we need to explore in some detail the factors that may enter into the determination of the size of λ.⁶

We make the simplifying assumption that the only operators in the forward market are pure arbitrageurs, who cover all spot transactions and assume no foreign exchange risk, and pure speculators, who take an open position by buying and selling only in the forward market and who are assumed to have certain and uniformly held expectations concerning the future spot rate. In the absence of constraints on the amount of forward commitments, this means that the demand for foreign currency forward at the expected future spot rate will be infinitely elastic. In this case speculators dominate the forward market, the forward rate being determined solely by speculators’ expectations of the future spot rate, with arbitrageurs playing no part in influencing this forward rate. Then

\begin{matrix} (a) & K_{f} = K_{t + 1}^{e} \end{matrix},

that is, the forward rate is the same as the speculators’ expected future spot rate $(K_{t + 1}^{e}) .$ The expected future spot rate, in turn, may be explained by the following function:

\begin{matrix} (b) & K_{t + 1}^{e} \end{matrix} = K_{t} + λ (K_{t} - K_{t - 1}),

where λ is the coefficient of expectations, reflecting the degree of response of the expected future spot rate to current changes in the spot rate. With λ assuming values between -1 and +1, the expectation function (b) accommodates a whole range of possibilities. A coefficient of -1 represents perfectly inelastic expectations, where the future rate is expected to return to its original level. Here the forward premium will rise (fall) by the same percentage as the depreciation (appreciation) in the spot rate. A value of λ between 0 and −1, representing inelastic expectations, means that the future spot rate is expected to be at a level intermediate between the original spot rate and the currently prevailing rate. Here the forward premium will rise (fall) by less than the depreciation (appreciation) in the spot rate. Where λ = 0, as with neutral expectations, the expected future spot rate is always equal to the existing spot rate, so that the forward premium is totally insensitive to changes in the spot exchange rate. This is the traditional case implicit in the literature, which has tended to disregard the forward market.⁷

When λ > 0, that is, when expectations are elastic, a depreciation in the spot rate is assumed to provoke expectations of a further depreciation in the next period. Hence, a depreciation of the spot rate will now generate a forward discount. When λ = 1, expectations are perfectly elastic. It can be shown that the model is necessarily unstable once A rises above a certain value, λ*, where λ* > 0.⁸ However, as long as the “true” λ is small enough for the model to be stable, then it can be shown that these elastic expectations are sufficient to change the sign of some of the key multipliers in the model, for example, the sign of the expenditure multiplier.

The model will be manipulated for five exogenous disturbances: (1) changes in the domestic component (D) of the money supply (the monetary policy instrument); (2) changes in autonomous expenditures (g), including both discretionary fiscal policy and shifts in private demands for goods and services; (3) changes in external interest rates (R*); (4) changes in export demand (h); and (5) changes in the demand for money (q). A simplifying assumption is that domestic and foreign prices are constant over the period of the model. In addition, it is assumed throughout that there is perfect capital mobility, which in this model implies that the covered interest differential (R - R* + K_f - K/K) approaches zero in equilibrium (B_d, in other words, approaches infinity).

The model is restrictive in that it only considers impact multipliers and abstracts from the dynamic repercussions of developments in the forward market, in particular from the effects of maturing forward contracts. We also assume no intervention by the authorities in the forward or spot exchange markets. The model also suffers from the usual stock-flow problem mentioned in footnote 4, a problem that can be resolved only by a complete specification of a dynamic system.

Evaluation of Effects of Exogenous Disturbances

The relative income multipliers for alternative exchange rate systems are given in Table 1. The multipliers for the rigidly fixed exchange rates are given in column (2). The conventional results for flexible exchange rate models that disregard the forward market (that is, where λ = 0) are shown in column (4). Columns (3), (5), and (6) show how the results are modified by the explicit introduction of the forward exchange market. Appendix I contains the complete solutions, including the effects of the disturbances on interest rates as well as on foreign reserves (for the fixed exchange rates) and on exchange rates (for the flexible and dual market regimes).

Table 1.

Income Multipliers for Alternative Exchange Rate Systems and Values of the Coefficient of Exchange Rate Expectations λ ¹

^¹The approximate relative magnitude of particular multipliers within each disturbance category is given by the number of + or − signs. The actual multipliers, expressed in terms of partial derivatives, are set out in Tables 2, 3, and 4, in Appendix I.

^²The value of λ for which the model becomes unstable is designated by λ*.

^³The multipliers, dY/dD, for flexible and dual exchange rates are, respectively, $\frac{M_{k} - X_{k}}{λ L_{r} (1 - A_{y} + M_{y}) + λ A_{r} M_{y} + L_{y} (M_{k} - X_{k})} and \frac{A_{r}}{L_{r} (1 - A_{y} + M_{k}) + A_{r} L_{y}} .$ It is possible that if |M_k - X_k| is small, relative to |λ| and |A_r|, dY/dD will assume a larger value under dual rates.

^⁴As in footnote 3, it is possible, although unlikely, that |M_k - X_k|, |λ|, and |A_r| will assume such values that fiscal policy has greater impact under flexible rates than under dual rates. The relative magnitude of the fiscal multipliers in columns (2) and (6) is ambiguous.

^⁵Again, as in footnotes 3 and 4, it is possible that |M_k - X_k|, |λ|, and |A_r| will assume such values that export fluctuations generate greater income fluctuations under flexible rates than under dual rates.

Table 1.

Income Multipliers for Alternative Exchange Rate Systems and Values of the Coefficient of Exchange Rate Expectations λ ¹

Exogenous Disturbance		Rigidly Fixed Exchange Rates	Flexible Exchange Rates ²			Dual Exchange Rates
Exogenous Disturbance		Rigidly Fixed Exchange Rates	λ < 0	λ = 0	0 < λ < λ*	λ < 0
(1)		(2)	(3)	(4)	(5)	(6)
			Inelastic	Neutral	Elastic
Monetary policy ³
	dY/dD	0	++	+ + +	+ + + +	+
External interest rates
	dY/dR*	–	+	+ +	+ + +	0
Fiscal policy,⁴ or changes in domestic expenditure
	dY/dg	+ +	+	0	–	+ +
Export fluctuation ⁵
	dY/dh	+ + +	+	0	–	+ +
Liquidity preference ³
	dY/dq	0	––	–––	––––	–

^²The value of λ for which the model becomes unstable is designated by λ*.

Table 1.

Income Multipliers for Alternative Exchange Rate Systems and Values of the Coefficient of Exchange Rate Expectations λ ¹

Exogenous Disturbance		Rigidly Fixed Exchange Rates	Flexible Exchange Rates ²			Dual Exchange Rates
Exogenous Disturbance		Rigidly Fixed Exchange Rates	λ < 0	λ = 0	0 < λ < λ*	λ < 0
(1)		(2)	(3)	(4)	(5)	(6)
			Inelastic	Neutral	Elastic
Monetary policy ³
	dY/dD	0	++	+ + +	+ + + +	+
External interest rates
	dY/dR*	–	+	+ +	+ + +	0
Fiscal policy,⁴ or changes in domestic expenditure
	dY/dg	+ +	+	0	–	+ +
Export fluctuation ⁵
	dY/dh	+ + +	+	0	–	+ +
Liquidity preference ³
	dY/dq	0	––	–––	––––	–

^²The value of λ for which the model becomes unstable is designated by λ*.

Monetary policy and fluctuations in liquidity preference

It is now an accepted dogma that under a regime of rigidly fixed exchange rates (with a zero band) and perfect capital mobility, monetary policy is ineffective in controlling the level of economic activity, as is shown in Table 1, column (2). The reason is simple. An expansionary monetary policy, represented by an increase in the domestic assets of the central bank, will lead to temporarily lower domestic interest rates relative to foreign rates. However, in equilibrium, domestic interest rates cannot diverge from the foreign rate, and this equilibrium will be achieved by a flight of capital and a depletion of reserves equal to the initial expansion in central bank assets. In these conditions, the equilibrium money supply, interest rate, and level of economic activity will be unaffected by monetary policy.

It might be thought that as long as capital mobility is less than perfect, independent monetary policies are always feasible under fixed exchange rates, provided that the authorities are prepared to continually neutralize the domestic liquidity effects of capital movements. For example, as long as the first multiplier (dY/dD) is positive, however low, the monetary authorities can always bring about the desired change in the level of income by some change, however large, in their domestic assets. There are, however, constraints on this. Most important is the foreign reserve constraint. If the multiplier is very low, achievement of a given change in income may entail an unacceptable loss of (or acquisition of) foreign exchange reserves. Continuation of independent monetary policies becomes particularly hazardous at the point at which, as a result of these reserve movements, speculation sets in. In general, it will be difficult to predict both the sensitivity of capital flows to domestic monetary actions and the point at which the level of reserves will generate speculative flows. Accordingly, an independent monetary policy under conditions of high capital mobility proves difficult to manage and imposes severe strains on the authorities.

Under flexible exchange rates, monetary policy comes into its own as an effective instrument of stabilization. Consider the conventional analysis (which omits the forward market) of monetary policy under perfect capital mobility, defined as requiring an uncovered interest rate differential of zero. A “pure” flexible exchange rate system requires that the central bank not transact in foreign assets; hence, there is no change in the balance of payments and no change in the money supply originating from external sources. An expansionary monetary policy will therefore raise the money supply by the amount of expansion in the central bank’s domestic assets (or a multiple of that change if the expansion of deposits is allowed for) with no offset from changes in its net foreign assets. Since the equilibrium interest rate cannot be different from the foreign rate, we obtain a familiar quantity theory result with a multiplier (change in income over change in domestic assets) equal to marginal velocity.⁹ The adjustment process to the higher level of income is that initial monetary expansion induces a transitory fall in interest rates, which induces capital outflow. The resultant depreciation of the exchange rate improves the trade balance, which then generates a multiplier effect on income. Summarizing the conventional results then, on the one hand, under fixed exchange rates monetary policy has no leverage on income, and, on the other hand, under flexible rates monetary policy has the maximum leverage represented by the quantity theory.

When the forward market is explicitly introduced to the flexible exchange rate system, that is, when A is not zero, the impact of monetary policy under flexible rates is affected. If we assume that expectations are inelastic (λ < 0), then monetary policy is weakened in its effect on income. The basic reason for this is that under flexible exchange rates monetary policy gains its impact by affecting the exchange rate and, as a result, the trade balance. To the extent that expectations are inelastic, the amount of capital outflow, and hence exchange rate depreciation produced by monetary expansion, is reduced, since the capital outflow that is generated because interest rates are below foreign levels is partially offset by the speculative inflow that is induced because the forward rate (that is, the expected future spot rate) is above the spot rate. In other words, if λ < 0, the initial depreciation of the exchange rate generates a forward premium and the net capital outflow is smaller than if λ = 0. While it remains true that monetary policy is effective in controlling the level of income with flexible rates, the fact that exchange rate expectations are inelastic weakens this effectiveness, since the quantity theory result no longer holds. However, here the weaker monetary policy is accompanied by a more stable exchange rate.

If we assume that expectations are elastic, that is, λ > 0, but that they are not sufficiently elastic to destabilize the system, then it turns out that monetary policy is strengthened in its efficacy under flexible rates. This is so because the depreciation of the spot rate that is induced by monetary expansion is accompanied by expectations of a further depreciation. Hence, there are speculative outflows that depreciate the exchange rate further and help to improve the trade balance. The intuitive reason for this result is that an expansion in the money supply will now actually raise the domestic interest rate above the foreign rate, reflecting the forward discount on the domestic currency that results from the fall in the spot rate. By contrast, where expectations are inelastic the domestic interest rate will settle sufficiently below the foreign rate to exactly offset the forward premium that results from the fall in the spot rate.

Under the dual exchange rate system (as specified above), monetary policy is effective as long as the forward premium or discount is allowed to vary. If λ = 0, then under conditions of perfect capital mobility there is no way in which monetary expansion can affect income, since interest rates will be tied to the world level and the exchange rate that applies to trade is not allowed to vary. It can be shown that monetary disequilibrium will prevail under a dual system with λ = 0, since the system then becomes overdetermined.¹⁰

If expectations are inelastic under dual exchange rates, then monetary expansion will depress the financial exchange rate to the point at which the domestic interest rate is consistent with the new money supply. The equilibrium value of the spot financial exchange rate will be such that the implied forward premium (for a given λ) is just equal to the gap between the foreign and domestic interest rates. The new, lower, interest rate is consistent with a higher level of income. The expansionary effect will be less than under completely flexible exchange rates, since in the latter system the trade exchange rate would also depreciate, thereby stimulating the economy. In this dual system any expansion in income must worsen the trade account, leading to some loss of reserves by the central bank; hence, some of the original money supply injected into the economy will escape overseas.

It is useful at this juncture to consider briefly the consequences of fluctuations in liquidity preference, since the effects are analogous to those for discretionary monetary policy. For example, with fixed exchange rates, either an expansionary monetary policy or a reduction in liquidity preference will have no effect on income or interest rates, and either will be offset by a loss of foreign reserves. Again, under flexible rates, a reduction in liquidity preference will have powerful effects on income, paralleling those for monetary expansion. These effects will tend to be weakened, as shown earlier, by the presence of the forward market.

The importance of these conclusions lies not in the technical results obtained but in the fact that shifts in liquidity preference are outside the control of the authorities; hence, for evaluating alternative exchange rate regimes, these shifts have implications that are exactly opposite to those for monetary policy. A regime, such as flexible exchange rates, under which monetary policy is very powerful is also a regime in which those shifts alone will have particularly disturbing repercussions on domestic income.

Fluctuations in the external interest rate

Consider first neutral expectations, that is, λ = 0. Fluctuations in R*, the external interest rate, manifest themselves in domestic income fluctuations in all except the dual exchange rate system, although the effects are dissimilar. Under fixed rates a rise in R* causes a capital outflow, a drop in the money supply, and an equal rise in the domestic interest rate, which induces a fall in the equilibrium level of income. Under flexible rates, a rise in R* also causes a capital outflow; however, this now induces a depreciation of the exchange rate. The rise in domestic interest rates and the induced depreciation of the exchange rate have opposing effects on income, but it can be shown (see Appendix I) that the exchange rate effect will dominate, so that income actually increases. Intuitively, the reason is that since the money supply cannot change and the interest rate must rise to the foreign level, equilibrium income must rise in order to remove an excess supply of money. In summary then, whereas a rise in the foreign interest rate depresses domestic income under fixed exchange rates, it expands domestic income under flexible rates.

If expectations are inelastic, the capital outflow and resultant exchange rate depreciation associated with a given rise in R* are reduced, since a forward premium is generated by the fall in the exchange rate. Accordingly, the more inelastic are expectations, the less sensitive is domestic income to external fluctuations in interest rates. When expectations are elastic, λ > 0, a rise in R* generates a larger depreciation in the spot rate, and this leads to a more substantial rise in the domestic income level in response to monetary restrictions abroad. In both situations, the domestic money supply cannot change as a result of a rise in the foreign interest rate; with inelastic expectations, a forward premium will open up and the domestic interest rate will settle below the new foreign rate, whereas with elastic expectations a forward discount is generated, which means that the domestic interest rate will be pulled up above the foreign rate by the substantial increase in income.

Under our version of the dual exchange rate system incorporating the forward market, a rise in the foreign interest rate will induce purchases of spot foreign currency, which in turn will depress the financial exchange rate and open up a forward premium (discount), given that expectations are inelastic (elastic). Since, by assumption, there can be no net flows of foreign capital, there can also be no reduction in the money supply resulting from a rise in R*. Consequently, the domestic interest rate cannot change, and the financial market is equilibrated by such changes in the forward premium (discount) as will exactly match the difference between the foreign and the domestic interest rates. In the special case where λ = −1, the forward financial exchange rate remains stationary, so that the whole of the adjustment is borne by the financial spot rate.

Fiscal policy¹¹ and changes in private expenditure

In the conventional analysis of fixed exchange rate systems under perfect capital mobility, fiscal expansion must bring about a net improvement in the balance of payments, the induced net inflow of capital exceeding the induced deterioration in the current account.¹² Intuitively, the explanation for this is that with the rate of interest constrained to foreign levels an increase in income can be satisfied only through an increase in the money supply, which can originate only in the foreign sector—given that domestic assets of the central bank are assumed to be fixed. In this case the leverage on income is strengthened by the fact that interest rates do not rise in response to the rise in income, since the fiscal expansion is accompanied by an induced rise in the money supply.

Under flexible rates and perfect capital mobility, the stimulative effect of fiscal expansion is offset by the appreciation of the exchange rate that results from the capital inflows induced by the upward pressure on the interest rate. The transitory rise in the domestic interest rate is generated by the increased demand for money owing to the rise in income. The money supply is fixed under truly flexible rates, and, with λ = 0, domestic interest rates are, in equilibrium, forced back to the level of external interest rates. Accordingly, equilibrium in the money market will be possible only at the original level of income, and the exchange rate will appreciate to the point at which the fall in trade balance owing to the appreciation of the exchange rate exactly offsets the effect on income of increased government spending.

When expectations are inelastic, fiscal expansion becomes effective as the appreciation of the exchange rate is moderated, since the volume of capital inflow is reduced as a result of the forward discount generated by the appreciation. Thus, we obtain the result that as expectations become more inelastic fiscal policy becomes more effective and monetary policy becomes less effective.¹³ However, monetary policy never becomes completely ineffective despite highly inelastic expectations, whereas fiscal policy is quite ineffective as expectations become neutral. When expectations are elastic, we obtain the unusual result that an act of fiscal expansion induces a fall in the level of income. This is so because a forward premium is generated by the rise in the spot exchange rate following the inflow of capital that results from fiscal expansion. Thus, the appreciation of the exchange rate is reinforced by speculative inflows, and the net effect of the appreciation is sufficient to reduce the equilibrium level of income. In this case the domestic interest rate will actually settle below the given foreign level.

Under a dual exchange rate regime, an expansionary fiscal policy will initially raise income as well as domestic interest rates. With a fixed commercial exchange rate, there will be an adverse effect on the current account, which in turn will result in some loss of central bank reserves and hence some reduction in the money supply. The reduction in the money supply, through its effects on interest rates, will dampen the increase in income. Nevertheless, fiscal expansion will have some positive effect on income. The size of λ in this case determines only the magnitude of adjustment in the spot and forward financial exchange rates that is necessary to generate a forward discount (premium) sufficient to exactly offset the interest rate differential in favor of (against) the domestic economy. Since the commercial exchange rate is fixed, there is no way in which a change in the financial exchange rate can influence the current account or the level of income.

Export fluctuations

If λ = 0, then a perfectly flexible exchange rate system will completely stabilize domestic income in the face of exogenous fluctuations in exports. This is so because a rise in exports, for example, induces an appreciation of the domestic currency, which induces a rise in imports and a fall in the endogenous component of exports.¹⁴ The money supply does not change and, with perfect capital mobility, neither does the interest rate. Accordingly, monetary equilibrium constrains the level of income to its value prior to the export fluctuation. If expectations are inelastic (elastic), an exogenous increase in exports is now consistent with some increase (decrease) in domestic income. The increase in exports will lead to an appreciation of the domestic currency, which in turn will open up a forward discount (premium). In equilibrium, with the covered differential equal to zero, this requires that the domestic interest rate be above (below) the foreign rate. A higher (lower) domestic interest rate in conjunction with an unchanged money supply generates a potential excess supply of (demand for) money, which is eliminated by a higher (lower) level of income. Exchange rate fluctuations in response to fluctuations in exports will be reduced or increased, depending on whether expectations are, respectively, inelastic or elastic.

Under the dual exchange rate regime, an exogenous rise in exports will have the same positive effect on income regardless of the elasticity of expectations vis-à-vis the financial rate, since this rate does not affect the real sector of the economy. With a fixed commercial rate, the increase in exports will affect income directly and reserves of the central bank will also rise, thereby expanding the domestic money supply. At the same time, the interest rate will be pulled up by the rise in income,¹⁵ inducing a capital inflow that will cause adjustment of the spot and forward financial rates to the point at which the forward discount (premium) exactly matches the interest rate differential.

Under rigidly fixed exchange rates, an increase in exports will have the strongest impact on income.¹⁶ There will be direct effects on income as well as money supply effects through the improvement in the balance of payments. Whereas interest rates rose in the flexible and dual exchange rate systems (differential interest rates being matched by forward discount), in this case the domestic interest rate cannot rise, being constrained to the foreign level by the assumption of perfect capital mobility. Hence, there will be an additional expansionary stimulus to income through the lower interest rate.

Wider bands

The preceding conclusions have obvious application to the question of the degree of independence in monetary policy that it may be possible to achieve with wider bands. Clearly, the wider the intervention band, the closer the approximation to the flexible exchange rate case. The central bank will have to support the rate at the lower end by supplying reserves, or at the upper end by buying reserves. At this point, some of the features of a fixed exchange rate system become relevant. However, our model requires modification when a band is introduced, since the “permissible” movements in the spot rate depend on the direction in which the exchange rate is expected to move. As an illustration, suppose that there is confidence in the par value and the forward rate is near its lower limit while the spot rate is around par. In this situation, a downward movement in the spot rate will constrain the magnitude of expected downward changes in the future spot rate. Accordingly, the element of expectation in the model, and hence the size of λ, is a more complicated issue than can be dealt with adequately in this paper.

Despite the above-mentioned inadequacy in the model, it is possible to make some general remarks. For example, as long as the par value of the currency is not expected to change, then it follows that the width of the band dictates the maximum value by which the exchange rate may be expected to change, if it is at the ceiling or the floor, and this in turn dictates the maximum interest rate differential that will be consistent with the corresponding forward discount or premium. The more inelastic (elastic) are expectations, the smaller (larger) the change in the spot exchange rate associated with all the exogenous changes discussed in the sections above. Accordingly, the elasticity of expectations is important in determining whether or not a particular band will be wide enough to contain the movement of the equilibrium value of the exchange rate in response to exogenous shocks.

Consider first a regime in which the band is sufficient to absorb movements in the spot rate owing to changes in monetary policy (the flexible rate case). As shown, a given dose of monetary policy becomes weaker, the more inelastic are expectations. Now suppose that the band may be insufficient to absorb the movements in the spot rate resulting from monetary expansion, so that intervention by the monetary authorities may be required. In this instance, expansionary monetary policy will push spot rates to their lower limits, at which point the authorities will sell some foreign currency, which in turn will attenuate the expansion in the money supply. In equilibrium, domestic and foreign interest rates will be the same, and there will be some expansion in the money supply and some increase in income (induced by the fall in the spot rate). Given the same band, a rise in the inelasticity of expectations has two opposing effects on income: (1) the fall in the spot rate will be weaker, removing the need for the authorities to intervene to supply reserves and thereby increase the money supply; and (2) the weaker fall in the spot rate implies a smaller rise in the trade surplus. In equilibrium, then, the money supply will be larger, the more inelastic are expectations, but at the same time the trade surplus will be lower; hence, it remains ambiguous, in conditions where the band is inadequate, whether the efficacy of monetary policy is increased or weakened by highly inelastic expectations.

Summary and Conclusions

This paper has integrated the forward market and speculative exchange rate expectations into a macromodel of an open economy. It has examined the effects of a number of exogenous disturbances on income, interest rates, exchange rates, and central bank reserves under fixed, flexible, and dual exchange rate systems. Throughout the discussion perfect capital mobility was assumed, since this is a useful reference point, given the trend to financial integration that is now particularly evident in the industrial world. In evaluating the results, it is useful to distinguish two types of disturbance: those originating in the government sector (stabilization policies) and those that are outside the control of the government (although, of course, governments can and do attempt to offset these disturbances). The latter may originate externally, for example, when foreign interest rates change or the demand for exports increases, or internally, when private expenditures increase or liquidity preference shifts. In all, two stabilization policies (monetary and fiscal) and four disturbances outside the direct control of governments are discussed.

Analysis without forward market

Consider first the conventional results when the forward market is disregarded, in other words, where it is assumed that the disturbances in question have no effect on the difference between the forward and the spot rates. In these conditions, monetary policy is totally ineffective in influencing income under fixed exchange rates but very powerful under completely flexible rates.¹⁷ In contrast, fiscal policy is very powerful under fixed rates but totally ineffective under flexible rates. The contrast, then, between the two stabilization instruments under fixed and flexible exchange rate regimes is extremely sharp.

In the second type of disturbance, the contrast between these two regimes is also very sharp. Under fixed rates, fluctuations in private expenditure or changes in export demand have powerful effects on income; a change in the foreign interest rate will also have strong effects on income—a rise in the foreign rate lowering domestic income—but shifts in liquidity preference (as with monetary policy, whose effects are identical) will leave income and interest rates unchanged. Under fixed rates, then, the economy is completely sheltered only from shifts in liquidity preference; other disturbances outside the control of the government have substantive effects on economic activity.

Under pure flexible rates, by contrast, the income level of the economy is immune to fluctuations in expenditure, whether these originate domestically or from abroad (in the form of export demand). Shifts in liquidity preference, however, will have powerful effects on income, and changes in foreign interest rates will also provoke changes in it—a rise in external rates inducing an increase in domestic income. Expenditure disturbances, then, tend to be completely neutralized, while monetary disturbances (originating domestically or overseas) continue to have effects on income.

In terms of our analysis then, fixed rates have an advantage over flexible rates only in that they increase immunity to shifts in liquidity preference, while flexible rates have an advantage in respect of all shifts in expenditure. If undesired shifts in private expenditure were more significant than shifts in liquidity preference, this would tend to create some presumption in favor of flexible rates.¹⁸ Additionally, if monetary policy is easier to administer than fiscal policy, the fact that monetary policy has a strong comparative advantage in a flexible exchange regime would give some advantage to flexible over fixed rates. Also, under flexible rates the balance of payments target is automatically taken care of, whereas under fixed rates the target needs to be met by allowing central bank reserves to fluctuate and/or by taking additional measures (for example, exchange rate changes, appropriate monetary/fiscal mixes, special restrictions, or deflationary policies) that complicate the task of policy making.

Even within the framework of conventional analysis, this is not intended to be a complete evaluation of fixed as against flexible exchange rate regimes. Some of the broader considerations that are highly relevant in evaluating flexible rates include the effects of exchange rate risk and uncertainty on trade and international investment; the possibility of destabilizing expectations; the possible inflationary bias and the absence of monetary discipline; the possibility that random fluctuations in exchange rates will provide false indicators to resource reallocations. Of course, a more complete evaluation of exchange rate regimes would need to take account of these broader and very important considerations.

Analysis with forward market

Once we depart from conventional analysis and allow explicitly for forward markets, the preceding conclusions regarding flexible rates are modified. When exchange rate expectations are inelastic—that is, a change in the spot rate provokes expectations of a return to its original level—monetary policy becomes weaker, while fiscal policy assumes some potency.

Monetary policy was shown to be weakened under flexible rates as exchange rate expectations became more inelastic; however, to the extent that expectations regarding the exchange rate are elastic, monetary expansion is found to be more powerful than in the conventional analysis, since the fall in the spot rate following monetary expansion is reinforced by the capital outflows induced by the forward discount that results from elastic expectations.

With inelastic expectations under flexible rates, increases in private or government expenditure will have some positive effect on income, while shifts in liquidity preference have weaker effects on it. When expectations are elastic, however, increases in expenditure have contractionary effects on income, while shifts in liquidity preference have even stronger effects on it. It remains true, in general, that if shifts in expenditure are more significant than those in liquidity preference a flexible exchange rate regime will perform better (in reducing the sensitivity of income to disturbances) than a fixed regime.

One important finding is that a rise in the foreign interest rate under flexible exchange rates will raise domestic income by less when exchange rate expectations are inelastic; however, when expectations are elastic, the increase in domestic income is still larger and the domestic interest rate rises above the foreign level.

In sharp contrast to the flexible rate case, allowance for the forward market under a dual market regime (that is, a regime with a flexible financial rate and a fixed commercial rate) will not in any way affect income or interest rates. In other words, in this regime income and interest rates are determined independently of the sensitivity of the forward premium or discount to changes in the spot exchange rate.¹⁹ The role of the forward market in this regime is to facilitate the forward premium or discount necessary to accommodate the interest rate differential. The larger the sensitivity of the forward premium/discount to changes in the spot rate, the smaller needs to be the fluctuation in the spot financial rate to accommodate a given interest rate differential.²⁰ In a dual market regime, changes in the financial spot rate do not affect the money supply and hence do not influence either income or interest rates.

APPENDICES

I. Solutions to the Model

The solutions to the model in the text are set out below. We solve for the total derivatives of income, interest rate, and exchange rate or foreign reserves with respect to changes in (i) the domestic assets of the central bank (or, equivalently, shifts in liquidity preference); (ii) the shift parameter in the domestic expenditure equation (say, fiscal policy); (iii) external interest rates, R*; and (iv) the shift parameter in the export equation. In other words, we are testing the sensitivity of the equilibrium values of this comparative statics model to exogenous changes, dynamic considerations being explicitly excluded. The solutions are all limiting values as the degree of capital mobility approaches infinity. The results in Table 1 in the text are obtained from Tables 2, 3, and 4 in this Appendix.

Table 2.

Income Multipliers for Flexible Exchange Rates

^¹Perfect capital mobility implies that B_d → ∞. Accordingly, all these solutions are limiting values as B_d → ∞.

Table 2.

Income Multipliers for Flexible Exchange Rates

di		Multipliers, di/dj, for Perfect Capital Mobility ¹
dj		Income	Interest rate	Exchange rate
		dY	dR	dK
Monetary expansion, or reduction in liquidity preference
	dD	$\frac{λ A_{r} + M_{k} - X_{k}}{D a} > 0$	$\frac{(1 - A_{y} + M_{y}) λ}{D a} \frac{>}{<} 0$	$\frac{- (1 - A_{y} + M_{y})}{D a} < 0$
Fiscal expansion
	dg	$\frac{L_{r} λ}{D a A g} \frac{<}{>} 0$	$\frac{{- L}_{y} λ}{D a A g} \frac{<}{>} 0$	$\frac{L_{y}}{D a A_{g}} > 0$
Rise in external interest rates
	dR*	$\frac{- L_{r} (M_{k} - X_{k})}{D a} > 0$	$0 < \frac{L_{y} (M_{k} - X_{k})}{D a} \leq 1$	$\frac{L_{r} (1 - A_{y} + M_{y}) + A_{R} L_{y}}{D a} < 0$
Unit increase in exports
	dh	$\frac{L_{r} λ}{D a} \frac{<}{>} 0$	$\frac{{- L}_{y} λ}{D a} \frac{<}{>} 0$	$\frac{L_{y}}{D a} > 0$

^¹Perfect capital mobility implies that B_d → ∞. Accordingly, all these solutions are limiting values as B_d → ∞.

Table 2.

Income Multipliers for Flexible Exchange Rates

di		Multipliers, di/dj, for Perfect Capital Mobility ¹
dj		Income	Interest rate	Exchange rate
		dY	dR	dK
Monetary expansion, or reduction in liquidity preference
	dD	$\frac{λ A_{r} + M_{k} - X_{k}}{D a} > 0$	$\frac{(1 - A_{y} + M_{y}) λ}{D a} \frac{>}{<} 0$	$\frac{- (1 - A_{y} + M_{y})}{D a} < 0$
Fiscal expansion
	dg	$\frac{L_{r} λ}{D a A g} \frac{<}{>} 0$	$\frac{{- L}_{y} λ}{D a A g} \frac{<}{>} 0$	$\frac{L_{y}}{D a A_{g}} > 0$
Rise in external interest rates
	dR*	$\frac{- L_{r} (M_{k} - X_{k})}{D a} > 0$	$0 < \frac{L_{y} (M_{k} - X_{k})}{D a} \leq 1$	$\frac{L_{r} (1 - A_{y} + M_{y}) + A_{R} L_{y}}{D a} < 0$
Unit increase in exports
	dh	$\frac{L_{r} λ}{D a} \frac{<}{>} 0$	$\frac{{- L}_{y} λ}{D a} \frac{<}{>} 0$	$\frac{L_{y}}{D a} > 0$

^¹Perfect capital mobility implies that B_d → ∞. Accordingly, all these solutions are limiting values as B_d → ∞.

Table 3.

Income Multipliers for Fixed Exchange Rates¹

^¹Limiting values where B_d → ∞ and Db = 1-A_y+M_y > 0.

Table 3.

Income Multipliers for Fixed Exchange Rates¹

di		Multipliers, di/dj, for Perfect Capital Mobility
dj		Income	Interest rate	Foreign reserves
		dY	dR	dF
Monetary expansion, or reduction in liquidity preference
	dD	0	0	-1
Fiscal expansion
	dg	$\frac{1}{A_{g} D b} > 0$	0	$\frac{L_{y}}{A_{g} D b} > 0$
Rise in external interest rates
	dR*	$\frac{A_{r}}{D b} < 0$	1	$\frac{L_{r} (1 - A_{y} + M_{y}) + A_{r} L_{y}}{D b} < 0$
Unit increase in exports
	dh	$\frac{1}{D b} > 0$	0	$\frac{L_{y}}{D b} > 0$

^¹Limiting values where B_d → ∞ and Db = 1-A_y+M_y > 0.

Table 3.

Income Multipliers for Fixed Exchange Rates¹

di		Multipliers, di/dj, for Perfect Capital Mobility
dj		Income	Interest rate	Foreign reserves
		dY	dR	dF
Monetary expansion, or reduction in liquidity preference
	dD	0	0	-1
Fiscal expansion
	dg	$\frac{1}{A_{g} D b} > 0$	0	$\frac{L_{y}}{A_{g} D b} > 0$
Rise in external interest rates
	dR*	$\frac{A_{r}}{D b} < 0$	1	$\frac{L_{r} (1 - A_{y} + M_{y}) + A_{r} L_{y}}{D b} < 0$
Unit increase in exports
	dh	$\frac{1}{D b} > 0$	0	$\frac{L_{y}}{D b} > 0$

^¹Limiting values where B_d → ∞ and Db = 1-A_y+M_y > 0.

Table 4.

Income Multipliers for Dual Exchange Rates¹

^¹Limiting values where B_d → ∞ and Dc = λL_r(1-A_y+M_y) + A_rλL_y > 0.

Note: If λ = 0, the model is overdetermined for reasons set out in footnote 10.

Table 4.

Income Multipliers for Dual Exchange Rates¹

di		Multipliers, di/dj, for Perfect Capital Mobility
dj		Income	Interest rate	Financial exchange rate
		dY	dR	dK_{f in}
Monetary expansion, or reduction in liquidity preference
	dD	$\frac{A_{r} λ}{D c} > 0$	$\frac{λ (1 - A_{y} + M_{y})}{D c} < 0$	$\frac{- (1 - A_{y} + M_{y})}{D c} < 0$
Fiscal expansion
	dg	$\frac{L_{r} λ}{A_{g} D c} > 0$	$\frac{{- λ L}_{y}}{A_{g} D c} > 0$	$\frac{L_{y}}{A_{g} D c} > 0$
Rise in external interest rates
	dR*	0	0	$\frac{1}{λ} \frac{<}{>} 0$
Unit increase in exports
	dh	$\frac{L_{r} λ}{D c} > 0$	$\frac{- λ L_{y}}{D c} > 0$	$\frac{L_{y}}{D c} > 0$

^¹Limiting values where B_d → ∞ and Dc = λL_r(1-A_y+M_y) + A_rλL_y > 0.

Note: If λ = 0, the model is overdetermined for reasons set out in footnote 10.

Table 4.

Income Multipliers for Dual Exchange Rates¹

di		Multipliers, di/dj, for Perfect Capital Mobility
dj		Income	Interest rate	Financial exchange rate
		dY	dR	dK_{f in}
Monetary expansion, or reduction in liquidity preference
	dD	$\frac{A_{r} λ}{D c} > 0$	$\frac{λ (1 - A_{y} + M_{y})}{D c} < 0$	$\frac{- (1 - A_{y} + M_{y})}{D c} < 0$
Fiscal expansion
	dg	$\frac{L_{r} λ}{A_{g} D c} > 0$	$\frac{{- λ L}_{y}}{A_{g} D c} > 0$	$\frac{L_{y}}{A_{g} D c} > 0$
Rise in external interest rates
	dR*	0	0	$\frac{1}{λ} \frac{<}{>} 0$
Unit increase in exports
	dh	$\frac{L_{r} λ}{D c} > 0$	$\frac{- λ L_{y}}{D c} > 0$	$\frac{L_{y}}{D c} > 0$

^¹Limiting values where B_d → ∞ and Dc = λL_r(1-A_y+M_y) + A_rλL_y > 0.

Note: If λ = 0, the model is overdetermined for reasons set out in footnote 10.

By successive substitutions in equations (1)-(10a) in the text, we may express the model as follows: ²¹

\begin{matrix} [\begin{matrix} 1 - A_{y} + M_{y} & - A_{r} & M_{k} - X_{k} \\ M_{y} & - B_{d} & - α \\ L_{y} & L_{r} & 0 \end{matrix}] [\begin{matrix} \begin{matrix} d Y \\ d R \end{matrix} \\ d K \end{matrix}] = [\begin{array}{l} \begin{matrix} X h d h + A_{g} d g \\ - B_{d} d R * + X h d h \end{matrix} \\ d D - L_{q} d_{q} \end{array}] & (11) \end{matrix}

The solution to this system is as follows:

{[\begin{matrix} \begin{matrix} d Y \\ d R \end{matrix} \\ d K \end{matrix}]}^{\frac{1}{D}} = [\begin{matrix} L_{r} α & L_{r} (M_{k} - X_{k}) & A_{r} α + B_{d} (M_{k} - K_{k}) \\ L_{y} α & L_{y} (M_{k} - X_{k}) & (1 - A_{y} + M_{y}) α + M_{y} (M_{k} - X_{k}) \\ M_{y} L_{r} + B_{d} L_{y} & - L_{r} (1 - A_{y} + M_{y}) - A_{r} L_{y} & A_{r} M_{y} - B_{d} (1 - A_{y} + M_{y}) \end{matrix}] [\begin{array}{l} \begin{matrix} X h d h + A_{g} d g \\ - B_{d} d R * + X h d \end{matrix} \\ d D - L_{q} d_{q} \end{array}

where D = L_r(1-A_y+M_y)α + A_rL_yα + (M_k-X_k)(L_rM_y+L_yB_d)

and $α = X_{K} - M_{K} - \frac{λ B_{d} K_{- 1}}{K^{2}} < 0.$

D = determinant of matrix on left-hand side of equation (11).

We then solve for the limiting values of the respective multipliers as B_d → ∞, obtaining the results given in Table 2; the income multipliers are set out in Table 1, columns (3), (4), and (5).

The solutions for the other exchange rate systems are obtained by using the alternative relationships in equation (10) in the text. The results for flexible and dual exchange rate regimes are discussed briefly in the following sections.

Flexible rates

The main result is that λ is important in determining the size of the respective multipliers. If λ = 0, fiscal policy is ineffective in regulating income, and export fluctuations do not affect income. The relative strength of monetary and fiscal policy may be expressed as follows:

d Y / d G / d Y / d D = \frac{L_{r} λ}{A_{g} (M_{k} - X_{k})} .

In other words, under flexible rates the efficacy of fiscal policy relative to monetary policy increases as expectations become more inelastic; increases as L_R, the interest sensitivity of the demand for money, increases; and decreases, the higher the sensitivity of real exports and imports to exchange rate changes. As long as expectations are not neutral, interest rates may diverge from foreign levels, and this explains the results in the second column.

Stability and the value of λ

Although we avoid a complete analysis of the conditions for stability of the system given above, we can make some general remarks. It can be shown that a necessary condition for stability is that the determinant, Da, be positive. With perfect capital mobility this requires

λ < \frac{L_{y} (X_{k} - M_{k})}{L_{r} (1 - A_{y} + M_{y}) + A_{r} L_{y}} .

It is evident by inspection that the right-hand side of the inequality is positive. Hence, we know that a necessary condition for stability is that λ be less than a certain positive magnitude, which we call λ*.²² However, it does not follow that λ < λ* is sufficient for stability. In order to determine sufficient conditions for stability, a more complete analysis is clearly required.

Dual rates

The essential features of our particular version of a dual system are evident in the row of results for dR* in Table 4. The domestic money supply is independent of capital flows, and the real volume of trade is independent of the financial exchange rate, the commercial rate being fixed. Changes in R* are offset by changes in the forward premium/discount, with the magnitude of the change in K_{f in} depending solely on λ. If λ = -1, that is, if expectations are perfectly inelastic, then all the adjustment is in the spot rate, with the forward rate remaining stationary despite the change in the spot rate. The equilibrium domestic interest rate cannot change, since neither the domestic money supply nor the level of income changes in response to a shift in R*.

As an example, consider the fiscal multiplier, $d Y / d G = \frac{L_{r} (X_{k} - M_{k} + λ B_{d})}{D}$ [from equation (11)].

If we divide the numerator and the denominator of the right-hand side of this equation by B_d, and then solve for the limit as B_d → ∞, the limiting value of dY/dG is $\frac{L_{r} λ}{D a},$ that is, $d Y / d G = \frac{L_{r} (X_{k} - M_{k} + λ B_{d})}{B_{d}} / \frac{D}{B_{d}} .$ Now $\frac{L_{r} (X_{k} - M_{k} + λ B_{d})}{B_{d}} \to L_{r} λ as B_{d} \to \infty,$ and $D a = \frac{D}{B_{d}} \to λ L_{r} (1 - A_{y} + M_{y}) + λ A_{r} L_{y} + L_{y} (M_{k} - X_{k}) as B_{d} \to \infty .$ Hence, $d Y / d G \to \frac{L_{r} λ}{D a} as B_{d} \to \infty .$

II. The Model Interpreted as Embodying a Situation in Which Speculators Hold Uncertain Expectations

The model can be interpreted to embody the case in which speculators hold uncertain expectations, which are reflected in a less than infinitely elastic demand for forward funds at a given expected future spot rate. For example, speculators may be willing, at a given expected future spot rate, to acquire a larger amount of forward foreign exchange only if they can obtain it at a lower price. In this case, arbitrageurs will play a role in determining the equilibrium forward rate (and hence λ in our model), since changes in the amount of their demands and supplies for forward exchange will be satisfied only by changes in the forward rate. For example, if speculators’ expectations regarding the future spot rate are independent of the current spot rate, it no longer indicates that λ = -1 (that is, that the forward rate remains constant in the face of changes in the spot rate, with the result that a depreciation in the spot rate of x per cent generates a forward premium of x per cent). This can be seen by considering the consequences of outward arbitrage generated by a rise in the foreign interest rate, R*. The arbitrageurs will acquire foreign currency spot in order to lend at the rate R* and they will cover by selling foreign currency forward. These forward sales will be possible only if the forward rate has depreciated by an amount sufficient to induce speculators to reshuffle their portfolio to absorb the increased forward commitments. Accordingly, the forward premium will rise by more than x per cent, and, in terms of our model, λ will be less than −1, although its absolute value will be larger than 1. In general, as long as the speculators’ function is not perfectly elastic, the value of the coefficient λ will tend to be smaller than when the forward rate is determined solely by the speculators.

A more complete analysis would also allow for the fact that the forward rate would be determined not only by the joint actions of pure arbitrageurs and pure speculators but also by uncovered arbitrage, by traders, and by the possibility of intervention by the monetary authorities. Pure outward arbitrage entails the purchase of foreign currency spot and the sale of an equivalent amount of foreign currency forward. It is likely, however, that with the spot rate falling and the forward rate appreciating, or falling by less than the spot rate, arbitrageurs will be induced to transact without forward cover; that is, as long as they expect the future spot rate to be below the prevailing forward rate, they will refrain from covering forward. Traders will also operate in the forward market. If the forward rate appreciates, this may encourage imports and discourage exports where payments for these transactions are expected to be made in the future. Alternatively, given imports and exports and hence expected receipts and payments, the incentive to cover in the forward market may be a function of the forward rate. An appreciation of the forward rate will induce some net purchase of foreign currency forward. In these situations arbitrageurs and traders behave more like speculators, since they would in effect be taking an open position. This increases the elasticity of supply of foreign currency forward, which tends to lower the absolute size of λ. Finally, the monetary authorities may also operate in the forward market; in an extreme case, they may wish to maintain the forward rate and buy foreign currency forward at the existing rate. Here they would be operating in ways identical to speculators where the latter have firm, uniform expectations that are independent of the spot rate.

Le marché des changes à terme et l’incidence des perturbations intérieures et extérieures sous différents régimes de taux de change

Résumé

Les auteurs de la présente étude intègrent dans un modèle macroéconomique d’une économie ouverte le marché des changes à terme et les anticipations des spéculateurs en ce qui concerne le futur taux de change au comptant. Ils examinent l’incidence d’un certain nombre de perturbations exogènes sur le revenu, les taux d’intérêt, les taux de change et les réserves de la banque centrale, lorsque sont appliqués tour à tour un régime de taux de change fixes, de taux de change flexibles et un système de change double. Tout au long de l’étude, il est admis comme hypothèse que les capitaux sont parfaitement mobiles. En évaluant les résultats, les auteurs distinguent deux espèces de perturbation: celles qui émanent du secteur public (mesures de stabilisation) et celles qui échappent au contrôle du gouvernement. Ces dernières peuvent provenir soit de l’extérieur, par exemple lorsque les taux d’intérêt étrangers varient, ou que la demande d’exportations augmente, soit de l’intérieur, quand les dépenses du secteur privé s’accroissent, ou que se produit un déplacement de la préférence pour la liquidité. Les auteurs étudient en tout deux types de politiques de stabilisation (monétaire et budgétaire) et quatre perturbations qui échappent au contrôle direct du gouvernement.

Lorsqu’il n’est pas tenu compte du marché à terme, la politique monétaire est totalement dépourvue d’influence sur le revenu quand les taux de change sont fixes, mais elle a sur lui une très forte incidence si les taux sont totalement flexibles. En revanche, la politique budgétaire est un instrument très puissant lorsque les taux sont fixes, mais absolument inefficace lorsqu’ils sont flexibles.

Lorsque les taux sont fixes, les fluctuations des dépenses du secteur privé ou les variations de la demande d’exportations ont une forte incidence sur le revenu; une variation du taux d’intérêt étranger aura également de fortes répercussions sur le revenu—une hausse du taux étranger entraînant une diminution du revenu intérieur—mais les déplacements de la préférence pour la liquidité (de même qu’un réaménagement de la politique monétaire, dont les effets sont identiques) ne modifieront ni le revenu ni les taux d’intérêt.

Lorsque les taux de change sont flexibles, le niveau du revenu de l’économie est à l’abri de toutes fluctuations des dépenses. Des déplacements de la préférence pour la liquidité auront une forte incidence sur le revenu, et les variations des taux d’intérêt étrangers provoqueront également des variations du revenu—une hausse des taux d’intérêt étrangers induisant une augmentation du revenu intérieur. Les perturbations dues aux variations des dépenses auront alors tendance à être entièrement neutralisées, tandis que les perturbations monétaires (d’origine locale ou étrangère) continueront d’avoir une incidence sur le revenu.

Lorsqu’il est tenu compte explicitement du marché à terme, les conclusions relatives aux taux de change flexibles sont modifiées. Quand les anticipations de variation des taux de change sont inélastiques—c’est-à-dire quand une variation du taux de change au comptant incite les spéculateurs à penser que le taux pourrait revenir plus ou moins à son niveau initial—l’incidence de la politique monétaire s’affaiblit, mais lorsque les anticipations sont élastiques, l’expansion de la masse monétaire s’avère un instrument plus puissant que ne l’indique l’analyse conventionnelle.

Lorsque les anticipations sont inélastiques sous un régime de taux de change flexibles, la progression des dépenses privées ou publiques aura certaines répercussions positives sur le revenu, tandis que les déplacements de la préférence pour la liquidité ont sur le revenu une incidence plus faible. Toutefois, lorsque les anticipations sont élastiques, l’accroissement de dépenses a sur le revenu un effet de contraction, alors qu’un déplacement de la préférence pour la liquidité a sur lui une incidence encore plus forte.

Il en résulte, entre autres, qu’une hausse du taux d’intérêt étranger sous un régime de taux de change flexibles augmentera le revenu intérieur dans une moindre mesure si les anticipations relatives aux taux de change sont inélastiques; toutefois, lorsqu’elles sont élastiques, l’augmentation du revenu intérieur est encore plus importante, et le niveau du taux d’intérêt intérieur est supérieur à celui du taux étranger.

Il ressort également de l’analyse que, si un pays applique un double régime des changes, son économie intérieure a tendance à être complètement protégée des perturbations extérieures résultant de variations de taux d’intérêt étrangers. Par exemple, étant donné que, par hypothèse, il ne peut y avoir de flux nets de capitaux étrangers, il ne peut pas non plus se produire de réduction de la masse monétaire par suite d’une hausse du taux d’intérêt; en conséquence, le taux d’intérêt intérieur ne peut pas changer, et le marché financier se trouve équilibré par des variations de la prime de change à terme (déport) égales à l’écart entre le taux d’intérêt étranger et le taux d’intérêt intérieur.

El mercado de divisas a plazo y los efectos de las perturbaciones internas y externas bajo distintos sistemas de tipos de cambio

Resumen

El estudio integra el mercado a plazo y las expectativas especulativas sobre los tipos de cambio en un macromodelo de economía abierta. Se examinan los efectos de algunas perturbaciones exógenas en el ingreso, los tipos de interés, los tipos de cambio y las reservas del banco central, en sistemas de tipos de cambio fijos, flexibles y dobles. En todo el análisis se supone una movilidad perfecta del capital. Al evaluar los resultados se distinguen dos clases de perturbaciones: las que se originan en el sector del gobierno (políticas de estabilización) y las que están fuera de su control. Estas últimas pueden ser de origen externo, por ejemplo, cuando varían los tipos de interés extranjeros o aumenta la demanda de exportación, o de origen interno, cuando aumenta el gasto privado o cambian las preferencias por la liquidez. En total, se estudian dos políticas de estabilización (monetaria y fiscal) y cuatro perturbaciones que quedan fuera del control directo de los gobiernos.

Cuando no se tiene en cuenta el mercado a plazo, la política monetaria es completamente ineficaz para influir en el ingreso en un sistema de tipos de cambio fijos, pero muy potente cuando los tipos de cambio son totalmente flexibles. En cambio, la política fiscal es muy potente con tipos de cambio fijos, pero totalmente ineficaz con tipos flexibles.

Con tipos fijos, las fluctuaciones del gasto privado o las variaciones de la demanda de exportación tienen un gran efecto en el ingreso; una variación del tipo de interés extranjero tendrá también un gran efecto en el ingreso—un aumento del tipo extranjero disminuye el ingreso interno—pero con las variaciones de la preferencia por la liquidez (al igual que con la política monetaria, cuyos efectos son idénticos) no se alterarán en absoluto el ingreso ni los tipos de interés.

Con tipos flexibles, el nivel de ingreso de la economía es inmune a todas las fluctuaciones del gasto. Las variaciones de la preferencia por la liquidez tendrán potentes efectos en el ingreso, y las variaciones de los tipos de interés extranjeros también causarán variaciones del ingreso—un aumento de los tipos de interés externos induce un aumento del ingreso interno. Así, las perturbaciones debidas al gasto tienden a quedar totalmente neutralizadas, mientras que las perturbaciones monetarias (de origen interno o externo) siguen afectando al ingreso.

Si se tiene en cuenta explícitamente al mercado a plazo, se modifican las conclusiones referentes a los tipos flexibles. Cuando las expectativas sobre los tipos de cambio son inelásticas—es decir, cuando una variación del tipo a la vista da lugar a la expectativa de que tenderá a volver a su nivel original—se debilita la política monetaria, pero cuando las expectativas son elásticas, la expansión monetaria resulta más potente que en el análisis convencional.

Con expectativas inelásticas y tipos flexibles, los aumentos del gasto privado o del gobierno tendrán cierto efecto positivo en el ingreso, mientras que las variaciones de la preferencia por la liquidez tendrán efectos más débiles. No obstante, cuando las expectativas son elásticas, los aumentos del gasto causan una contracción del ingreso, mientras que los cambios de la preferencia por la liquidez tienen efectos aún más fuertes en el ingreso.

Una de las consecuencias en un sistema de tipos de cambio flexibles consiste en que un aumento del tipo de interés extranjero causa un aumento menor en el ingreso interno cuando las expectativas sobre los tipos de cambio son inelásticas; sin embargo, cuando son elásticas, el aumento del ingreso interno es aún mayor y el tipo de interés interno se eleva a un nivel más alto que el extranjero.

Otra consecuencia, en régimen de mercado doble, consiste en que la economía interna tiende a estar totalmente protegida contra las perturbaciones externas debidas a variaciones de los tipos de interés extranjeros. Por ejemplo, dado que, por hipótesis, no puede haber flujos netos de capital extranjero, tampoco puede haber reducción alguna en la oferta monetaria al aumentar el tipo de interés externo; por consiguiente, no puede variar el tipo de interés interno y el mercado financiero se equilibra mediante modificaciones de la prima (descuento) de las operaciones a plazo, que coinciden exactamente con la diferencia entre el tipo de interés extranjero y el interno.

Mr. Argy, Chief of the Financial Studies Division of the Research Department, is a graduate of the University of Sydney, Australia. He has been a lecturer at the University of Auckland, New Zealand, and a lecturer and senior lecturer at the University of Sydney. He has contributed several articles to economic journals.

Mr. Porter, a graduate of the University of Adelaide (Australia) and Stanford University (California), was an economist in the Financial Studies Division when this paper was prepared. He is currently on leave to the Reserve Bank of Australia.

The authors are grateful to Stephen W. Kohlhagen of Stanford University for comments on an earlier draft of this paper.

The literature on the effects of monetary and fiscal policies under fixed and flexible exchange rates in conditions approximating perfect capital mobility is now extensive. For early contributions, see J. Marcus Fleming, “Domestic Financial Policies Under Fixed and Under Floating Exchange Rates,” Staff Papers, Vol. IX (1962), pp. 369-80; R.A. Mundell, “Capital Mobility and Stabilization Policy under Fixed and Flexible Exchange Rates,” The Canadian Journal of Economics and Political Science, Vol. XXIX (1963), pp. 475-85; and Rudolf R. Rhomberg, “A Model of the Canadian Economy under Fixed and Fluctuating Exchange Rates,” The Journal of Political Economy, Vol. LXXII (February 1964), pp. 1-31. More recent contributions are by Egon Sohmen, “Fiscal and Monetary Policies Under Alternative Exchange-Rate Systems,” The Quarterly Journal of Economics, Vol. LXXXI (1967), pp. 515-23; John F. Helliwell, “Monetary and Fiscal Policies for an Open Economy,” Oxford Economic Papers, New Series, Vol. 21 (1969), pp. 35-55; and Marina von Neumann Whitman, Policies for Internal and External Balance, Special Papers in International Economics, No. 9 (Princeton, 1970).

Since this paper was written, we have become aware of a paper by Robert W. Baguley that incorporates exchange rate expectations into a macromodel. See “The Effectiveness of Monetary and Fiscal Policies under Pegged and Floating Exchange-Rate Systems,” in Richard E. Caves and Grant L. Reuber, Capital Transfers and Economic Policy: Canada, 1951-1962 (Harvard University Press, 1971), Appendix A, pp. 361-96.

For a theoretical discussion of the dual system, see J. Marcus Fleming, “Dual Exchange Rates for Current and Capital Transactions: A Theoretical Examination,” Chapter 12 in his Essays in International Economics (Harvard University Press, 1971), pp. 296-325.

We assume that the stock of financial wealth is exogenous and that the composition of the domestic portfolio varies only on account of shifts in the yields available in the domestic and foreign markets. Our model suffers the same difficulties with stock-flow problems that are found in the papers cited in footnote 2. True stock equilibrium in any comparative statics model requires that the current accounts of the government and foreign sectors be constrained to zero, because if this is not so the stocks of domestic and foreign financial assets cannot be stationary. A model that does apply such a constraint may be found in Ronald I. McKinnon, “Portfolio Balance and International Payments Adjustments,” in Monetary Problems of the International Economy, ed. by Robert A. Mundell and Alexander K. Swoboda (University of Chicago Press, 1969), pp. 199-234. However, complete resolution of the stock-flow problem requires the specification of a fully dynamic model.

A more general version of the model would include a demand function for domestic (government) bonds as well as demand functions for foreign bonds and money. The financial equations would then be

M o_{D} = L (W, Y, R, R *, \frac{K_{f} - K}{K})

B_{d o m} = H (W, Y, R, R *, \frac{K_{f} - K}{K})

B_{f o r} = J (W, Y, R, R *, \frac{K_{f} - K}{K}) .

The financial wealth constraint (Walras’s law) tells us that only two of these equations are independent, viz.,

L_{i} + H_{i} + J_{i} = 0, i = Y, R, R *, \frac{K_{f} - K}{K}

L_{w} + H_{w} + J_{w} = 1.

In the text we assume that changes in financial wealth are zero over the period, although strictly speaking this will be true only if both trade and government deficits are zero. We omit the domestic bond demand function, and we simplify matters by assuming that L_r* = L_k = J_y = 0. This amounts to assuming that H_r* = -J_r*, L_y = -H_y, and H_k = -J_k. Clearly, our results will not be sensitive to this simplification as long as |L_r*|, |L_k|, and |J_y| are sufficiently small. Theoretical reasons for structuring the model in the more general way are given in James Tobin, “A General Equilibrium Approach to Monetary Theory,” Journal of Money, Credit and Banking, Vol. I (1969), pp. 15-29.

Useful references are two Princeton Studies in International Finance (Princeton University Press) by Egon Sohmen, The Theory of Forward Exchange, No. 17 (1966), and Fred R. Glahe, An Empirical Study of the Foreign-Exchange Market: Test of a Theory, No. 20 (1967).

See Appendix II.

A discussion of this point may be found in Appendix I.

See Table 2, in Appendix I, when λ = 0, dY/dD = 1/L_y.

If λ = 0, then it is not possible to separate the equilibrium domestic interest rate from the foreign interest rate, since the assumption precludes any forward discount or premium. The assumption of a flexible financial exchange rate precludes the money supply from changing as the result of capital flows. Accordingly, there is no adjustment mechanism in the money market, and the money supply and the interest rate are determined independently. In other words, the monetary system is overdetermined. When λ ≠ 0, the domestic interest rate may adjust so as to restore equilibrium.

We assume that fiscal policy is represented by a rise in expenditures, with no injection of base money, since this facilitates a clear analytical distinction between “pure” monetary policy and “pure” fiscal policy. Following traditional analysis, it is assumed that the increased government expenditures are financed by additional debt issues. The wealth effects generated by the fiscal expansion are disregarded.

See Table 3, in Appendix I, where it is shown that the effect of fiscal expansion is to unambiguously increase the reserves of the central bank.

Some of these results have been anticipated in earlier literature. See Fleming, “Domestic Financial Policies Under Fixed and Under Floating Exchange Rates” (cited in footnote 2). In the concluding section of his article, he argues that “since the greater relative effectiveness which a floating rate gives to monetary policy, compared with budgetary policy, is attributable to the stronger influence that the former exercises on exchange rates, it is to be expected that equilibrating speculation, by damping down exchange rate effects, will tend to reduce the difference in effectiveness between the two kinds of policy,” p. 376. See also Sohmen, The Theory of Forward Exchange (cited in footnote 6), p. 34, who concludes that “Mundell’s conclusion … that fiscal policy would be inoperative as a tool of employment policy in a frictionless system of flexible exchange rates also does not follow” (where spot and forward rates are no longer assumed to be identical).

Although domestic income is unchanged, resources will move toward the export sector and away from the import-competing sector.

As Table 4, in Appendix I, shows, the income effect will be stronger than the money supply effect and will tend to push interest rates up. The direct effect on income will in itself increase imports, which in turn will attenuate the initial expansion in the money supply. Additionally, the exogenous increase in exports will generate multiplier effects on income.

The income multipliers for flexible, dual, and fixed exchange rate systems for a unit increase in exports are as follows:

flexible d Y / d h = \frac{1}{(1 - A y + M y) + \frac{A_{r} M_{y}}{L_{r}} + \frac{L_{y} (M_{k} - X_{k})}{L_{r} λ}} > 0

dual d Y / d h = \frac{1}{(1 - A_{y} + M_{y}) + \frac{A_{r} L_{y}}{L_{r}}} > 0

fixed d Y / d h = \frac{1}{(1 - A_{y} + M_{y})} > 0.

Very powerful monetary effects are not always an advantage to the authorities. One implication is that errors in monetary policy will also have strong destabilizing effects.

For some empirical evidence supporting this proposition for the United States, see William Poole, “Rules-of-Thumb for Guiding Monetary Policy,” in Open Market Policies and Operating Procedures, Board of Governors of the Federal Reserve System, Staff Studies (Washington, 1971), pp. 135-89.

This is easily seen in Table 4, in Appendix I, where all the solutions for income and interest rates are independent of λ.

This is also seen in the last column in Table 4.

In the solutions, we assume that K_-1/K² approximates unity.

For example, if λ = λ*, then Da = 0 and the multipliers in Tables 1 and 2 approach infinity; in other words, the model becomes unstable.

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IMF Staff papers: Volume 19 No. 3

Author: International Monetary Fund. Research Dept.

Volume/Issue:: Volume 1972: Issue 003

Publisher:: International Monetary Fund

ISBN:: 9781451969290

ISSN:: 1020-7635

Pages:: 202

DOI:: https://doi.org/10.5089/9781451969290.024

Table 4.

Income Multipliers for Dual Exchange Rates¹

di		Multipliers, di/dj, for Perfect Capital Mobility
dj		Income	Interest rate	Financial exchange rate
		dY	dR	dK_{f in}
Monetary expansion, or reduction in liquidity preference
	dD	$\frac{A_{r} λ}{D c} > 0$	$\frac{λ (1 - A_{y} + M_{y})}{D c} < 0$	$\frac{- (1 - A_{y} + M_{y})}{D c} < 0$
Fiscal expansion
	dg	$\frac{L_{r} λ}{A_{g} D c} > 0$	$\frac{{- λ L}_{y}}{A_{g} D c} > 0$	$\frac{L_{y}}{A_{g} D c} > 0$
Rise in external interest rates
	dR*	0	0	$\frac{1}{λ} \frac{<}{>} 0$
Unit increase in exports
	dh	$\frac{L_{r} λ}{D c} > 0$	$\frac{- λ L_{y}}{D c} > 0$	$\frac{L_{y}}{D c} > 0$

^¹Limiting values where B_d → ∞ and Dc = λL_r(1-A_y+M_y) + A_rλL_y > 0.

Note: If λ = 0, the model is overdetermined for reasons set out in footnote 10.

Y	=	national income
A	=	domestic expenditure (including consumption, investment, and government expenditure)
X	=	exports
M	=	imports
R	=	domestic interest rate
R*	=	foreign interest rate
K	=	spot exchange rate (foreign units per unit of domestic currency)
K_f	=	forward exchange rate
D	=	domestic assets of central bank
F	=	net foreign assets of central bank
Mo	=	money supply
B	=	net stock of foreign indebtedness
g	=	shift parameter in domestic expenditure equation
h	=	shift parameter in export equation
q	=	shift parameter in money demand equation

Y	=	national income
A	=	domestic expenditure (including consumption, investment, and government expenditure)
X	=	exports
M	=	imports
R	=	domestic interest rate
R*	=	foreign interest rate
K	=	spot exchange rate (foreign units per unit of domestic currency)
K_f	=	forward exchange rate
D	=	domestic assets of central bank
F	=	net foreign assets of central bank
Mo	=	money supply
B	=	net stock of foreign indebtedness
g	=	shift parameter in domestic expenditure equation
h	=	shift parameter in export equation
q	=	shift parameter in money demand equation

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Abstract

The Model

Evaluation of Effects of Exogenous Disturbances

Monetary policy and fluctuations in liquidity preference

Fluctuations in the external interest rate

Fiscal policy11 and changes in private expenditure

Export fluctuations

Wider bands

Summary and Conclusions

Analysis without forward market

Analysis with forward market

APPENDICES

I. Solutions to the Model

Flexible rates

Stability and the value of λ

Dual rates

II. The Model Interpreted as Embodying a Situation in Which Speculators Hold Uncertain Expectations

Le marché des changes à terme et l’incidence des perturbations intérieures et extérieures sous différents régimes de taux de change

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El mercado de divisas a plazo y los efectos de las perturbaciones internas y externas bajo distintos sistemas de tipos de cambio

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Fiscal policy¹¹ and changes in private expenditure