Real Exchange Rate Dynamics in a Small, Primary-Exporting Country

Although the nominal exchange rate is often used as a policy instrument in small, primary-commodity-exporting countries, the real exchange rate is an endogenous variable that responds to both exogenous and policy-induced shocks. This paper examines the dynamic effects on the real exchange rate of various shocks, such as devaluation, fiscal and trade policies, and changes in the terms of trade and foreign real interest rates. Because the path of the real exchange rate differs for different types of shocks, nominal exchange rate policies to achieve a target real exchange rate must take these differences into account.

Abstract

Although the nominal exchange rate is often used as a policy instrument in small, primary-commodity-exporting countries, the real exchange rate is an endogenous variable that responds to both exogenous and policy-induced shocks. This paper examines the dynamic effects on the real exchange rate of various shocks, such as devaluation, fiscal and trade policies, and changes in the terms of trade and foreign real interest rates. Because the path of the real exchange rate differs for different types of shocks, nominal exchange rate policies to achieve a target real exchange rate must take these differences into account.

THERE IS GENERAL AGREEMENT among economists that the real exchange rate is a key relative price in the economic system.1 Changes in the real exchange rate have a wide-ranging influence on the economy, affecting foreign trade flows, the balance of payments, the structure and level of production and consumption, employment, and the allocation of resources. Although the nominal exchange rate is typically a policy instrument in small, primary-commodity-exporting countries—including most developing countries—the real exchange rate is an endogenous variable that responds to both exogenous and policy-induced shocks. It is obviously important, therefore, to understand how such shocks affect the real exchange rate if one is to design adjustment programs that will improve international competitiveness and shift resources toward the production of tradable goods.2

In the past decade or so, developing countries have experienced a series of external shocks that have had direct effects on their real exchange rates.3 Worsening terms of trade, falling growth rates in industrial countries, and sharp changes in the availability of foreign financing that were accompanied by dramatic increases in real interest rates on external borrowing made economic management in general, and exchange rate management in particular, very difficult for policymakers in these countries. Furthermore, in many cases the adverse effects of these external shocks were compounded by inappropriate domestic policies. The adoption of expansionary demand-management policies combined with rigid exchange rate policies resulted in inflationary pressures, steady losses in international competitiveness, and inefficiencies in the allocation of resources arising from distortions in relative prices.

The need for macroeconomic adjustment was not perceived to be pressing as long as foreign financing was readily available. As is now well known, however, in 1982 the private international credit markets reached the conclusion that recent financing trends were no longer sustainable. The flow of new credits to many capital-importing developing countries suddenly evaporated, making external adjustment the prime objective of economic policy. Such adjustment typically involved fiscal and monetary restraint to control both public and private spending, trade policies to create the incentives for an increased supply of tradables, and the implementation of more flexible exchange rate policies to achieve and maintain international competitiveness.

Taking the view that getting the real exchange rate “right” is a central element in the adjustment effort, in this paper we address the following question: What are the dynamic effects of external shocks and domestic policy actions on the real exchange rate of a small, primary-exporting country? Previous analyses of the effects of external shocks on the real exchange rate—for example, by Dornbusch (1985) and Khan (1986)—have used an essentially comparative static approach. For policymakers, however, it is often equally important to understand the transition path the real exchange rate follows after a shock as it is to know what the value of the real exchange rate would be in the long run. The dynamics of real exchange rate behavior need to be examined, therefore, if useful advice on exchange policies is to be given.

In Section I of the paper we outline a simple theoretical model for the study of real exchange rate behavior in a small, primary-exporting economy. The advantage of this model is that it allows us to examine the dynamic effects of a variety of shocks on the real exchange rate within a single consistent framework. In Section II we examine the effects on the real exchange rate of a nominal devaluation, changes in the terms of trade, fiscal policies, trade policies, and increases in foreign real interest rates. The concluding section summarizes the main issues covered in the paper and highlights the policy implications of the study.

I. The Model

The model we specify to analyze the dynamic adjustment of the real exchange rate is an expanded version of the model proposed by Montiel (1986), which has been modified here to incorporate a three-good structure—importables, exportables, and nontradables—and to allow for instantaneous nominal wage and price flexibility. The model has its roots in the familiar two-good dependent economy model popularized by Dornbusch (1974), Rodriguez (1978), and Liviatan (1979), among others.

The focus of our analysis is on the dynamic behavior of the real exchange rate that is induced by asset accumulation; thus real private financial wealth is the key predetermined variable, as in Calvo and Rodriquez (1977) and Khan and Lizondo (1987).4 Given the current value of real private financial wealth, the real exchange rate and the real wage adjust continuously to ensure equilibrium in the labor market and in the market for nontraded goods. The model assumes perfect foresight on the part of all agents, and consequently the values of the real exchange rate and the real wage that will clear these markets at any instant depend on the future evolution of the economy.5

This section is divided into four subsections. The supply side of the model is described in the first, followed by a description of the demand side. The third subsection analyzes the implications of equilibrium in the market for nontraded goods, and the final subsection presents the solution.

Supply

Consider an economy producing three goods—exportables (X), importables (Z), and nontraded goods (N)—using a single variable factor of production (labor). Production functions for all goods take the form

yi=yi(Li);yi>0,yi<0,(1)

where yi, denotes output of good i, Li is the amount of labor employed in the ith sector, and i = X, Z, N. A prime signifies a derivative, yi = dyi/dLi.

Labor is assumed to be homogeneous and instantaneously mobile among sectors. Labor therefore earns the same nominal wage in each sector. This wage is assumed to be perfectly flexible, so that labor market equilibrium holds continuously:

Lx(w/ρ)+Lz(w)+LN(we)=L¯.(2)

Here w is the wage measured in terms of importables (that is, W/Pz, if W is the nominal wage and Pz is the domestic currency price of importables), and ρ is the terms of trade, given by ρ = Px/Pz, where Px is the domestic currency price of exportables. The variable e is the real exchange rate, defined as the ratio of the domestic currency price of importables (Pz) to that of nontraded goods (PN); that is, e = Pz/PN.6 An increase (decrease) in e represents a real depreciation (appreciation). The demand for labor in each sector is derived from the profit-maximizing condition yi (Li) = Wi, where Wi is the product wage in sector i, so that the labor demand functions satisfy Li = 1/yi < 0. The aggregate supply of labor is assumed to be inelastic and is given by L¯. Equation (2) permits us to solve for the value of w that clears the labor market as a function of the terms of trade and the real exchange rate:

w=w(ρ,e)w1=(Lxw/ρ2)/(Lx/ρ+Lz+LNe)>0w2=LNw/(Lx/ρ+Lz+LNe)<0(3)

where w1 and wz are the partial derivatives of the function w(ρ, e). An improvement in the terms of trade brought about by an increase in the price of exportables, for example, increases the demand for labor in the exportables sector, which causes the nominal wage to be bid up in all sectors, thereby releasing labor from the importables and nontradables sectors to be absorbed in the expanding export sector. In contrast, given ρ, a real exchange rate depreciation (increase in e) must be brought about through a relative decrease in PN. This causes the demand for labor to decrease in the nontraded-goods sector. The nominal wage is thus bid down, causing the traded-goods sectors to absorb the labor released by the nontraded-goods sector. It is easy to verify from the expressions for w1 and w2 that the elasticities of w with respect to ρ and e are both less than unity in absolute value—so that an increase in ρ reduces the product wage (w/ρ) in the exportables sector, and an increase in e increases the product wage in the nontraded-goods sector:

d(w/ρ)/dρ=(w1w/ρ)/ρ=[Lx/(Lx+Lzρ+LNρe)+1]w/ρ2<0d(we)/de=w2e+w+w=[1LNe/(Lxρ+Lz+LNe)]w>0.

substituting the sectoral labor demand functions into the respective production functions and using Equation (3) permits us to write the sectoral supply functions for exportables, importables, and nontradables as

yxs=yx{w(ρ,e)/ρ]}dyxs/dρ=yxLx(w1w/ρ)/ρ>0dyxs/de=yxLxw2>0(4a)
yzs=yz{Lz[w(ρ,e)]}dyzs/dρ=yzLzw1<0dyzs/de=yzLzw1>0dyzs/de=yzLzw2>0(4b)
yNs=yN{LN[w(ρ,e)e]}dyzs/dρ=yNLNw1e<0dyzs/de=yNLN(w2e+w)<0(4c)

The supply of output in each sector is thus a function only of the terms of trade and the real exchange rate. An improvement in the terms of trade shifts labor from the importables and nontraded-goods sectors to the exportables sector, causing output of exportables to expand and output of the other two goods to contract. By contrast, a real exchange rate depreciation moves labor from the nontraded-goods sector into the production of both tradable goods. Output of exportables and importables expands, while that of nontradables contracts.

Demand

For the case of a small country, the law of one price implies that the foreign component of demand for tradable goods is perfectly elastic, so that domestic currency prices of these goods are given by

Px=sPx*(5a)
Pz=sPz*(5b)

where Px* and Pz* are the foreign currency prices of exportables and importables, respectively, and s is the nominal exchange rate (the domestic currency price of a unit of foreign currency). By definition there is, of course, no foreign demand for the nontraded good.

Turning to the domestic component of demand, we assume that the exportable good is not consumed at home. We have in mind, therefore, a small country that is specialized in the export of some primary commodity.7 Importables and nontraded goods are consumed by the private sector and by the government.

The Private Sector

With regard to the private sector, we assume that the representative household possesses a Cobb-Douglas utility function, with share θ for consumption of nontraded goods (cN) and 1 – θ for consumption of importables (cz), where 0 ≤ θ ≤ 1.8 This means that the private sector has constant expenditure shares θ and 1 – θ on nontraded and importable goods, respectively. The price of the consumption basket, denoted P, can therefore be written as

P=PNΘPZ1Θ=PzeΘ(6)

From equation (6), we can write the relative prices Pz/P and PN/P in the form

Pz/P=eΘ(7a)
PN/P=eΘ1(7b)

Letting c denote total real consumption, measured in units of the consumption basket, constant expenditure shares imply that PNCN = èPc and that Pzcz = (1 – θ)Pc. Therefore, private sector demand for importables and nontraded goods can be expressed, using equations (7a) and (7b), as

cz=(1Θ)eΘc(8a)
cN=Θe1Θc.(8b)

Real household consumption c is taken to depend on real factor income y (net of real taxes paid to the government tp), on the real interest rate r, and on the private sector’s real financial wealth, all measured in terms of the consumption basket. For later convenience, we write the last of these variables as eθap, where ap is real private financial wealth measured in terms of importables. Therefore, real consumption is given by

c=c(ytp,r,eΘap);0<c1<1,c1<0,c3>0,(9)

where c1, c2, and c3 are the partial derivatives of the function c). Increases in real factor income net of taxes and in real private financial wealth increase real consumption, whereas an increase in the real interest rate will reduce consumption.

Real factor income is simply nominal output divided by the price of the consumption basket; that is,

y=(Pxyx+Pzyz+PNYN)/P,

which, by using equations (6) and (7), can be written as

y=eΘ(Pxyx+Pzyz+PNYN)/Pz=eΘ(ρyx+yz+yN/e).

Because sectoral output levels, according to supply equations (4a)–(4c), depend only on the terms of trade and the real exchange rate, y likewise depends only on ρ and e. Therefore we can write

y=y(ρ,e)(10)

Choosing units so that initially ρ = e = 1, and using the expressions for w1 and w2 derived in Equation (3), we have

y1=dy/dρ=yx(Lx+Lz+LN)w1yxLxw+yx=yxy2=dy/de=ΘyyN+yN(Lx+Lz+LN)w2yNLNw=ΘyyN.

Thus, an improvement in the terms of trade increases real income by an amount that depends on the initial level of exports. To interpret the effect of a real exchange rate depreciation on real income, note that we will assume below that the composition of government spending initially mirrors that of the private sector and that the market for nontraded goods is in continuous equilibrium. This means that θy can differ from yN only to the extent that real domestic absorption differs from real output—that is, to the extent that the trade balance is initially in surplus or deficit. If the trade balance is in equilibrium (θy = yN), a real exchange rate depreciation will have no effect on real income. If the trade balance is in surplus (θy > yN), the value of domestic production exceeds that of absorption. Because production and absorption of nontraded goods must be equal, output of traded goods must exceed absorption of traded goods, implying that the share of traded goods in production must exceed the share of tradables in absorption—that is, in the consumption basket. Thus an increase in the relative price of traded goods (a real depreciation) must increase the real value of domestic output measured in terms of the consumption basket (dy/de >0). These arguments are reversed if the trade balance is initially in deficit. Because long-run equilibrium will be shown to require a zero current account balance, assuming that the home country is a net international debtor requires a trade surplus in the initial long-run equilibrium. In what follows, therefore, we assume that y2 > 0.

Real household financial wealth consists only of real financial assets (which comprise real money balances, M/P, and the real value of foreign securities, sFp/P) minus real liabilities (which consist of the stock of credit extended to the private sector by the banking system DP/P):

eΘap=(M+sFpDp)/P.(11)

Money pays no interest, whereas foreign securities earn the nominal interest rate i*. The nominal rate charged on bank loans is denoted i. We assume that portfolios are in continuous equilibrium, that domestic and foreign interest-bearing assets are perfect substitutes, and that expectations are characterized by perfect foresight. Under these conditions, uncovered interest parity holds continuously:

i=i*+E(ŝ)=i*,(12)

where E(ŝ) is the expected rate of depreciation of the domestic currency (a circumflex over a variable denotes a proportional rate of change), which is zero under fixed exchange rates and perfect foresight. These conditions also imply that the money market is always in equilibrium. Letting the real demand for money (L) depend, in conventional fashion, on real income and the nominal interest rate, we have, using Equation (12) to replace i by i*,

M/P=L(i*,y);L1<0,L2>0,(13)

where L1 and L2 are the partial derivatives of real money balances with respect to i* and y. Finally, because the real interest rate is the nominal interest rate minus the expected rate of inflation, r = i – E(P), we can use the log-differentiated versions of equations (5b) and (6) to write

r=[i*E(P̂z*)]+ΘE(ê)=r*+Θê,(14)

where r* = i* – E-E(P^z*) is the external real interest rate.

To conclude our description of private sector behavior, we can derive private accumulation of real financial wealth from the private sector’s budget constraint. With a dot over a variable denoting a time derivative, this constraint takes the form

(Pz.ap)=Py+i*(sFDp)PtpPc.

Solving for åp by using Equation (9) and writing out the expression for L, we obtain

ap=¨eΘ(ytpc)+i*(apeΘL)P̂z*ap=eΘ(ytpc)+r*ap(r*P̂z*)eΘL=eΘ{y(ρ,e)tpc[y(ρ,e)tp,r*+Θê,eΘap]}+r*ap(r*+P̂z*)eΘL[r*+P̂z*,y(ρ,e)].

We can summarize the properties of private saving behavior as follows:

a¨p=a(ap,e,ρ,tρ,r*,êP̂z*)a1=r*c3<0a2=(r*c3)Θap+[1c1(r*+P̂z*)L2]y2=?a3=[1c1(r*+P̂z*)L2]y1>0a4=(1c1)<0a5=apL(r*P̂z*)L1c2>0a6=Θc2>0a7=[L+(r*P̂z*)L1]=?,(15)

where all derivatives are evaluated at e = 1 and ap = 0. The signs of these partial derivatives reflect the following assumptions.

First, an increase in real financial wealth reduces household saving (c3 > r*). This assumption is not very restrictive, since the propensity to consume out of nonhuman wealth will exceed the real interest rate in a life-cycle context with finite household horizons (see Ravin (1985)).

Second, the marginal propensity to save remains positive even after one allows for the loss of interest income caused by the instantaneous portfolio shift into money that is induced by an increase in household income, 1 – c1 – (r* + P^z*)L2>0.

Third, real household financial wealth exceeds the real value of money holdings (ap > L).

The Public Sector

The public sector in the model consists of the government and the central bank. The government is assumed to hold no money, so that its net worth is given by

eΘaG=(sFGDG)/P,(16)

where aG is the government’s net worth measured in terms of importables, FG is the government’s stock of foreign securities, and DG is the stock of credit extended to the government by the central bank. The government consumes current output, collects taxes, receives transfers of profits from the central bank, and accumulates assets. Its actions are subject to the budget constraint:

Pza¨G=P(tptB)/i*PzaGPNgNPzgz,

where tB is real transfers received from the central bank, and gN and gz are government consumption of nontraded goods and importables, respectively. Defining g as total government spending, measured in units of the consumption basket, we assume that initially gN = θe1 – θg and gz = (1 – θ) e–θg. Solving the budget constraint for å we have

a¨G=eΘ(tp+tB)/r*aGeΘ1gNgz.(17)

The government’s policy variables are tp, gN, and gz. Transfers from the central bank tB are endogenous (see Equation (20) below), and aG is predetermined. The surplus å is determined residually. The behavior of the surplus, however, is subject to the intertemporal constraint:9

limtaG(t)er*t0.(18)

By solving the differential Equation (17), it can be shown that this condition will be violated unless the long-run values of tp, gN, and gZ, are such that å = 0.10 Because this condition pegs the long-run value of, one of the policy variables tp, gN, or gZ must move to the residual role. We will suppose for now that gz does so (this will change in Section II), In the long run, then, Equation (17) becomes

gz=eΘ(tp+tB)+r*aGeΘ1gN,(17a)

which implies that changes in tp or gN must be offset by changes in gz that leave the (inflation-adjusted) budget in balance.

The balance sheet of the central bank is given by

M=(sFB+Dp+DG)(19)

With the stock of foreign-exchange reserves, FB, being held in the form of foreign securities, bank profits are

tB=i*(sFB+Dp+DG)/P(20)

The central bank controls the stocks of credit extended to the private sector and to the government. Credit policy is assumed to take the form of growth in these stocks at the constant rate D^ Because the exchange rate is fixed, the money stock and the stock of foreign exchange reserves are endogenous variables. The stock of foreign exchange reserves will evolve according to

(sF̂B)sFBM=M̂D̂DM,=M̂D̂(1sFB/M).(21)

A necessary condition for avoiding a balance of payments crisis is that the ratio of foreign exchange reserves to the domestic money stock, sFB/M, be bounded from below.11 It can be seen from Equation (21) that this condition requires that D^M^. It can also be shown that, unless D^M^, the private sector will be unable to satisfy its demand for money in the long run. Thus, the central bank has no long-run discretion over D. Short-run deviations from the long-run value of D will be reflected in changes in the long-run equilibrium value of sFB/M.

Equilibrium in the Markets for Labor and Nontraded Goods

The price of nontraded goods is assumed to be flexible in this model, so that the market for nontraded goods is always in equilibrium:

yN = cN + gN

Substituting for yN from equation (4a) and for cN from equations (8b) and (9), we have

yN{LN[W(ρ,e)e]}=Θe1Θc[y(ρ,e)tp,r*+Θê,eΘap]+gN.(22)

Notice that, since w(ρ, e) is the value of w that clears the labor market, Equation (22) imposes simultaneous equilibrium in the markets for labor and nontraded goods. Equation (22) can be written in the form of an equation for the evolution of the real exchange rate:

ê=ϕ(ap,e,ρ,gN,tp,r*),(23)

with

ϕ1=c3/Θc2>0ϕ2=[yNLN(w2+w)Θc1y2Θ2c3apΘ(1Θ)c]/Θ2c2>0ϕ3=(yNLNw1Θc1y1)/Θ2c2>0ϕ4=1/Θ2c2>0ϕ5=c1/Θc2<0ϕ6=1/Θ<0,(23)

where the partial derivatives are evaluated at e = 1, and the sign of φ2 assumes that the substitution effect of a change in the real exchange rate, θ(1 – θ)c, dominates the income effect, θc1 y2. Equation (23) describes the rate of real exchange rate depreciation that will clear the market for nontraded goods for given values of the variables on the right-hand side. An increase in the rate of depreciation of the real exchange rate implies, given P^z* an increase in the domestic rate of deflation and, thus, an increase in the domestic real interest rate. Such an increase induces a reduction in the excess demand for nontraded goods and becomes necessary whenever excess demand for such goods is created by an increase in household wealth, a real depreciation (that is, a decline in PN), an increase in real income caused by a favorable terms of trade shift, or an increase in government spending on nontraded goods. This explains the first four partial derivatives above. The rate of real depreciation must decrease to lower the domestic real interest rate and stimulate increased demand for nontraded goods, when such demand has been depressed by increased taxation or an increase in international real interest rates. This justifies the signs of the two remaining partial derivatives.

Solution of the Model

Solving the model requires ascertaining values of ê and e. But since the equilibrium value of e depends on the contemporaneous value of ap—a predetermined variable—it follows that future values of e will depend on future values of ap. Thus the dynamics of the real exchange rate and the accumulation of private financial wealth must be worked out jointly (see Khan and Lizondo (1987)). This can be done by using the private sector saving Equation (15) and the equilibrium condition for the nontraded-goods market (23). These equations are repeated here for convenience:

a¨p=a(ap,e,ρ,tp,r*,ê,P̂z*)(15)
ê=ϕ(ap,e,ρ,gN,tp,r*).(23)

Since private asset accumulation depends on the rate of depreciation of the real exchange rate, substituting for e in Equation (15) from Equation (23) produces

a¨p=Ψ(ap,e,ρ,tp,r*,ê,P̂z*),(24)

with

Ψ1=r*>0Ψ2=r*Θap+(1Θ)c+[1(r*+P̂z*)L2]y2yNLN[w2+w]/Θ>0Ψ3=[1(r*+P̂z*)L2]y1yNLNw1/Θ>0Ψ4=1/Θ>0Ψ5=1<0Ψ6=apL(r*+P̂z*)L1>0Ψ7=[L+(r*+P̂z*)L1]=?.(24)

Equations (23) and (24) are a system of differential equations in e and ap. Linearizing this system around the equilibrium e˙ = e˙ = 0, we have

[a¨pe¨]=[Ψ1Ψ2ϕ1ϕ2][dapde]+[Ψ3Ψ4Ψ5Ψ6Ψ7ϕ3ϕ4ϕ5ϕ60][dρdgNdtpdr*dP̂z*].(25)

The determinant of the 2 × 2 matrix on the right-hand side of Equation (25) is

Ψ1ϕ2ϕ1Ψ2=(r*c3Θc2)[(1Θ)c+c1y2yNLN(w2+w)/Θ]+c3Θc2[1c1(r*+p̂z*)L2]y2<0.(26)

Thus the equilibrium e˙ = e˙ = 0 is a saddle point. The phase diagram for the system (25) is depicted in Figure 1. From Equation (24), the condition e˙ = 0 traces out a locus in (e, ap) space. Its slope is

dedap|a¨p=0=Ψ1/Ψ2<0

Similarly, the locus traced out by e˙ = 0 has the slope

dedap|e¨=0=ϕ1/ϕ2<0.

From Equation (25), however,

dedap|e¨=0dedap|ap=0¨=(Ψ2ϕ2)1(ϕ1Ψ2)<0,

so the locus e˙ = 0 is steeper than e˙ = 0, as shown in Figure 1. The direction of the arrows in Figure 1 follows from the fact that ψ1 and φ2 are both positive. The saddle path to the equilibrium point A, labeled SS′, therefore must lie in the second and fourth quadrants—that is, it must have a negative slope.

II. Effects of Shocks on the Real Exchange Rate

To study the dynamics of adjustment to long-run equilibrium, we consider the time path of the response of the real exchange rate to a variety of exogenous and policy-induced shocks. The specific shocks examined are

  • a nominal devaluation

  • a terms of trade improvement

  • a change in the composition of government spending

  • a tax-financed increase in government spending on importables

  • imposition of import and export taxes

  • increases in international real interest rates.

Figure 1.
Figure 1.

Effects of a Devaluation

Citation: IMF Staff Papers 1987, 003; 10.5089/9781451930719.024.A004

The model described by equations (23) and (24) is sufficiently general to handle these six shocks. Although the list is selective, we nevertheless believe that the shocks examined are representative of the actual shocks that developing countries have experienced in recent years.

Nominal Devaluation

Consider the effects of a nominal devaluation that is announced and implemented simultaneously.12 Because none of the exogenous and policy variables in equations (23) and (24) is affected by this shock, the loci e˙ =0 and e˙ = 0 do not move. The devaluation will increase the domestic currency price of importables, however, and, because the nominal domestic currency value of a portion of private wealth is pre-determined, the real value of private wealth measured in terms of importables decreases—that is, ap falls, say, to ap0 in Figure 1.13 The reduction in wealth creates an excess supply of nontraded goods, causing the real exchange rate to depreciate. The real depreciation cannot, however, be sufficient by itself to clear the nontraded-goods market—this would be the case at point C—because to the right of e˙ = 0 the private sector is saving, and this increase in private wealth is associated with a continuous appreciation of the real exchange rate. Because this future appreciation is foreseen, the real interest rate drops on impact, and this decrease combines with the real depreciation to absorb the initial excess supply in the nontraded-goods market. The economy moves to B on the saddle path SS′.

After the initial impact, the economy moves to the southeast along the segment BA in Figure 1 until the initial real equilibrium is restored. It can readily be shown that along this path domestic inflation exceeds the world inflation rate, and the current account is in surplus. The first part of this statement follows simply from the fact that the real exchange rate appreciates continously along BA. To show the second part, define the (inflation-adjusted) current account, measured in terms of importables, as

ca=eΘ(yc)(eΘ1gN+gz)+r*sF/Pz;

that is, the current account is the excess of real income (including interest receipts from abroad) over real domestic absorption. Summing the budget constraints for the private and public sectors and using equations (17a) and (2), we have

ca=a¨p.(27)

Because e˙ > 0 along BA devaluation induces a current account surplus until the original level of real assets is restored.

Notice that, although a nominal devaluation has no long-run real effects in the model in the sense that the long-run equilibrium at point A is undisturbed by devaluation, this does not imply that the initial real equilibrium will tend to re-establish itself after a nominal devaluation, other things being equal. The initial real configuration of the economy will never be restored after a nominal devaluation unless that configuration happens to be one of long-run equilibrium. From an initial position such as point D in Figure 1, for example, a nominal devaluation that reduces wealth by an amount equal to (1 – e˙/ap1) would move the economy directly and permanently to A. Real-world devaluations should therefore be expected to move the economies concerned permanently away from their initial real configurations.14

As a corollary, note that, because a nominal devaluation can often by itself move the economy permanently away from its initial real configuration, it is not always true that the effectiveness of devaluation depends on the implementation of restrictive aggregate demand policies. Such policies may not be necessary even when—as in our model—nominal wages are completely flexible. We show below that such policies will indeed affect the long-run equilibrium level of the real exchange rate, but they do so independently of the level of the nominal exchange rate. As argued by Khan and Lizondo (1987), adjustments in the latter affect only the path of adjustment to the eventual equilibrium.

Improvement in the Terms of Trade

Consider now an improvement in the terms of trade; that is, an increase in p. From equations (23) and (24), we have

dedρ|e¨=0=ϕ3/ϕ2<0
dedρ|ap¨=0=Ψ3/Ψ2<0;

in other words, both e˙ = 0 and e˙ = 0 shift down to e and , respectively, in Figure 2. It can be shown, however, that if the initial trade surplus is small, the downward shift in e˙ = 0 must exceed that in e˙ = 0. To see this, note that

ϕ3ϕ2=yNLNw1Θc1y1yNLN(w2+w)Θc1y2Θ2c3apΘ(1Θ)c
ϕ3ϕ2=Ψ3Ψ3=yNLNw1Θ[1(r*P̂z*)L2]y1yNLN(w2+w)Θ[1(r*+P̂z*)L2]y2Θ2r*apΘ(1Θ)c.

Because 1c1(r*+P̂z*)L2>0,c3>r*, and y2 is approximately zero when the initial trade surplus is small, the result that ψ32 > φ32 follows. Thus the situation is as depicted in Figure 2.

When the improvement in the terms of trade is brought about by an increase in export prices, the economy’s short-run equilibrium will be at point B in Figure 2. The improvement in the terms of trade creates an excess demand in the market for nontraded goods, so that the real exchange rate appreciates. But the appreciation will not be such as to leave e˙ = 0, since the new higher real income from the terms of trade improvement will induce the private sector to save, and this accumulation of wealth is associated with a further real appreciation. In the new long-run equilibrium, private real wealth is higher, and the real exchange has appreciated. Once again, during the period of adjustment from B to C, domestic inflation will exceed the world level, and the current account will be in surplus.

Figure 2.
Figure 2.

Effects of an Improvement in the Terms of Trade

Citation: IMF Staff Papers 1987, 003; 10.5089/9781451930719.024.A004

Because the real exchange rate has appreciated at point C, the price of nontraded goods has to have risen in absolute terms (recall that the price of importables is constant in this case). It remains to investigate the magnitude of the increase in the price of nontradables relative to the increase in the price of exports. To do so, we use Equation (25) to calculate de/dp across long-run equilibria:

dedρ=Ψ1ϕ3Ψ3ϕ1Ψ1ϕ2Ψ2ϕ1.

Substituting for the partial derivatives from equations (23) and (24), we have

dedρ=yNLNw1{r*[1(r*+P̂z*)L2]c1r*c3}Θc1y1yNLN(w2+w)Θ(1Θ)cΘc1y2.(28)

Because w1 + w > w1 and θ(1 – θ)c > – c1y2, this expression must be smaller than one in absolute value if the second term in the numerator is sufficiently small. The magnitude of this term depends on the size of the income effect of the change in the terms of trade on consumption of nontradables (θc1y1). If the terms of trade improvement has a sufficiently large income effect, demand for nontradables could rise sufficiently to cause PN to increase more than in proportion to Px (therefore, de/dρ < –1). Otherwise the increase in PN will be smaller than that of Px, and the real exchange rate will appreciate when defined as e = PZ/PN but depreciate when defined as PX/PN.15

The analysis for the case in which the improvement is the result of a reduction in the price of importables is quite similar. Notice first (from equations (23) and (24)) that, since all exogenous variables take on the same values whether a change in ρ is brought about by an increase in Px* or by a reduction in Pz* the economy’s long-run equilibrium is the same in both cases, as one would expect. In particular, whether a reduction in Pz* is associated with a decrease or an increase in the equilibrium price of nontraded goods will again depend on the magnitude of income effects, as shown by Edwards and van Wijnbergen (1985). The dynamics, however, may be quite different. When the improvement in ρ is brought about by a reduction in Pz*, the domestic price level falls on impact. As a result, the real value of private financial wealth measured in terms of importables, ap, rises to a value such as ap0 in Figure 2 (assuming, as in Section I, that (MDp) > 0). It follows that, when the improvement in the terms of trade results from a reduction in Pz*, the economy’s short-run equilibrium will move on impact to a point such as D, located to the southeast of B on the stable path SS′. The magnitude of the real appreciation on impact must exceed that which results from a rise in ρ caused by an increase in Px*.

The qualitative features of the short-run dynamics in this case will depend crucially on whether ap0 > ap**. If this inequality holds, point D will be located to the southeast of the long-run equilibrium at point C. If so, ap will fall and e will rise during the period of adjustment—that is, the current account will be in deficit, and the domestic rate of inflation will fall short of the world level. Because ap0 rises in proportion to the increase in ρ times the share of M – Dp in private financial wealth on impact, the relationship between ap* and can be examined by calculating the elasticity of ap* with respect to p. Using Equation (25), we obtain

dap*dρ1ap*=(ϕ2Ψ3Ψ2ϕ3Ψ1ϕ2Ψ2ϕ1)1ap*=ΘyNLNw1yNLN(w2+w)Θ(1Θ)c1y2+ΩΘc1y1,(29)

where

Ω=11+(r*+P̂z*)L2c1(r*c3)ΘapΘr*1(r*P̂z)L2c1(r*c3)[yNLN(w2+w)Θ(1Θ)cΘc1y2]>0.

The first term in Equation (29) is positive and less than unity. Because the second term is also positive, the size of the elasticity will depend on the income effect of the terms of trade change on consumption of nontradables (θc1 y1). If the income effect is sufficiently large, this elasticity will exceed unity, in which case ap0 will fall short of its long-run equilibrium value ap** (D lies above Con SS‣, as in Figure 2). The current account goes into surplus in the short run, and domestic inflation exceeds the world level. If the income effect is small, however, it is possible that ap0 > ap**.

Change in Composition of Government Spending

Consider an increase in government spending on nontraded goods that is offset by a reduction in spending on importables.16 For a given ap, the increased spending on nontradables requires a real appreciation to restore equilibrium in the nontraded-goods market. Thus the e˙ = 0 locus shifts down, as in Figure 2. Similarly, at the original ap, the increase in gN induces an increase in the domestic interest rate to maintain equilibrium in the nontraded-goods market. Because the higher domestic interest rate increases private saving, a real appreciation is required to induce the private sector to desist from the accumulation of financial assets. Thus e˙ = 0 shifts down as well to a. These shifts are given by

dedgN|e¨=0=1c3Θ2aρ+Θ(1Θ)c+Θc1y2yNLN(w2+w).
dedgN|a¨p=0=1r*Θ2ap+Θ(1Θ)c+Θc1y2yNLN(w2+w).

Because c3 > r*, the downward shift in e˙ = 0 is dominant, and—qualitatively at least—the dynamics resemble those of Figure 2. The real exchange rate appreciates to a point such as B on impact, by more than enough to restore equilibrium in the market for nontraded goods. The domestic real interest rate falls as domestic inflation accelerates, whereas the nominal interest rate remains at international levels. During the adjustment period, domestic inflation exceeds the world rate; the current account is in surplus (recall that government spending on importables has fallen apace); and financial assets are accumulated by the private sector.

Tax-Financed Increase in Government Spending on Importables

An increase in taxes used to finance increased government spending on importables would, at the original a*p, reduce private saving and depress private demand for nontraded goods. A real exchange rate depreciation is required both to restore the original level of private savings and to clear the market for nontraded goods. These conclusions follow from

dedtp|a¨p=0=Θr*Θ2ap+Θ(1Θ)c+Θc1y2yNLN(w2+w)>0
dedtp|e¨=0=1c3Θ2aρ+Θ(1Θ)c+Θc1y2yNLN(w2+w)>0.

Because c1 < 1 and c2 > r*, it follows that the real depreciation required to clear the nontraded-goods market falls short of what is needed to restore the original level of private savings—that is, the e˙p = 0 curve shifts upward further than the e˙ = 0 curve in Figure 3. The economy jumps to the new saddle path at point B and moves gradually to a new long-run equilibrium at C, with a lower value of private wealth and a depreciated real exchange rate. The transition period combines relatively low domestic inflation with current account deficits. The relatively low level of domestic inflation is the means whereby the further required real exchange rate depreciation is accomplished.

Figure 3.
Figure 3.

Effects of a Tax-Financed Increase in Government Spending on Importables

Citation: IMF Staff Papers 1987, 003; 10.5089/9781451930719.024.A004

Commercial Policies

Consider now the effects on the real exchange rate of the implementation of commercial policies—a subject that has received considerable attention recently in the literature (see, for example, Obstfeld (1986), Mussa (1986), and Edwards and van Wijnbergen (1985)). We define commercial policies here as the imposition of taxes on exports or imports.17 Note that, because such taxes will increase government revenues, an explicit assumption is necessary with respect to the disposition of such additional revenues. Equation (17a) would imply that such revenues are used to finance additional government spending on importables. It is more illuminating, however, to abandon this assumption for the present and to suppose instead that the additional funds collected by the government are used to finance a lump-sum transfer to the private sector, so that total net tax receipts are unaffected.

The imposition of a tax on exports is then equivalent to an adverse movement in the terms of trade that has the same effect on domestic producer prices, except that the loss of real income associated with the reduction in producer prices (given by τYx, where τ is the rate of the ad valorem export tax) is exactly offset by the subsidy paid to the private sector out of the proceeds of the tax. It follows that the effects of the imposition of an export tax are similar to those of an adverse movement in the terms of trade brought about by a fall in export prices. The analysis of Figure 2 would in this case be conducted in reverse—that is, the loci e˙ = 0 and e˙ = 0 would both be displaced vertically upward, and the real exchange rate would depreciate on impact as at point B in Figure 4. A further depreciation would accompany a current account deficit during the adjustment to long-run equilibrium.

Figure 4.
Figure 4.

Effects of Export and Import Taxes

Citation: IMF Staff Papers 1987, 003; 10.5089/9781451930719.024.A004

Although qualitatively the situation is analogous to that of an adverse terms of trade shock, the quantitative effects on the real exchange rate of an adverse terms of trade shock and an export tax, which have the same effect on domestic producer prices, are different because of the absence of an income effect in the latter case. By setting y1 = 0 in the expressions for φ3 and ψ3 in equations (23) and (24), it can be shown that, for a given effect on domestic producer prices, the shifts in the e˙ = 0 and e˙ = 0 loci will be smaller for the case of a reduction in domestic producer prices of exportables that is brought about through the imposition of an export tax. It follows that both the initial and the final real depreciations, as well as the cumulative current account deficits during the period of adjustment, will be smaller in this case.

The analysis of the imposition of a tax on imports proceeds along similar lines. In qualitative terms the long-run analysis is similar to that of an adverse movement in import prices of an equal amount brought about by higher world prices of importables. The quantitative effects, however, will again be muted in the long run, in this case because of the absence of income effects. There will be a real depreciation and a reduction in the real value of private financial wealth on impact, but the former will fall short of what would have been observed had the change in domestic prices of importables been brought about by higher world prices. The effects of import liberalization are also fairly clear—a reduction in tariffs will lead to a real appreciation.18

Moreover, in the case of tax-financed commercial policies, although the real long-run equilibrium generated by an export tax is the same as that produced by an import tariff at the same ad valorem rate, the short-run dynamics are again different. By setting y1 = 0 in equations (28) and (29), we can show that a reduction in the internal terms of trade will cause the real exchange rate to depreciate less than in proportion to the change in ρ, and that the elasticity of ap with respect to ρ is less than unity. The latter finding implies that, if net foreign assets are a sufficiently small fraction of private wealth, the new short-run equilibrium when an import tariff is imposed must be at a point such as D in Figure 4, since real private financial wealth falls in proportion to the change in the internal terms of trade times the share of net domestic assets in private financial wealth on impact. It follows that the imposition of an export tax gives rise to a current account deficit and domestic inflation below world levels in the short 9run, whereas an import tariff generates a current account surplus and inflation rates above world levels during the period of adjustment.

Increases in International Real Interest Rates

Because of the uncovered interest parity condition, an increase in the external real (and nominal) interest rate is immediately transmitted to domestic interest rates. Private saving increases, but the rise is due in part to a reduction of private spending on nontraded goods. Thus an incipient excess supply exists in the nontraded-goods market. On the one hand, this excess supply must be eliminated by a real exchange rate depreciation. On the other hand, a real appreciation is called for to restore domestic saving to its original level. It follows that the e˙ = 0 locus shifts upward, whereas the e˙ = 0 locus shifts downward. Formally, we can write

dedr*|e¨=0=Θc2c3Θ2ap+Θ(1Θ)c+Θc1y2yNLN(w2+w)>0
dedtp|a¨p=0=Θ[apL(r*+P̂z*)L1]r*Θ2ap+Θ(1Θ)c+Θc1y2yNLN(w2+w)<0.

The dynamic adjustment process is depicted in Figure 5. The new long-run equilibrium exhibits a lower value of e and higher private wealth than the original one. During the period of adjustment the current account must be in surplus, and the inflation rate must exceed the world level. Thus the domestic real interest rate only gradually rises to the new level of the external rate.

The impact effect of the interest rate change is ambiguous, however. The new saddle path may lie either above (as in Figure 5) or below the original long-run equlibrium at point A, depending on the relative magnitudes of the shifts in e˙ = 0 and e˙ = 0 (as is apparent in Figure 5). The larger is the effect of the increase in real interest rates on the excess supply of nontradables relative to its effect on private saving, the larger will be the vertical displacement of the e˙ = 0 locus relative to that of the e˙ = 0 locus. In this case the need for a real depreciation on impact to restore equilibrium to the nontraded-goods market is likely to outweigh the need for a real appreciation to restore the original level of private saving, and the saddle path is likely to pass above the original equilibrium at A. Note that this situation is more likely when private spending is highly sensitive to the real interest rate (c2 is large in absolute value) and when real private financial wealth is initially low.

Figure 5.
Figure 5.

Effects of an Increase in the Foreign Real Interest Rate

Citation: IMF Staff Papers 1987, 003; 10.5089/9781451930719.024.A004

Before leaving the discussion of the effects of real interest rate shocks, it may be worth observing that the results described here are not as counterintuitive as they may seem. It may be thought that, in countries that are net international debtors, an increase in real international interest rates would require a real depreciation to generate the trade surplus required to service the debt. Nothing has been said here about the country’s net international position. Suppose now that the country is a net debtor, in that the government’s net financial assets are sufficiently negative so as to offset a positive level of private financial wealth. Because the argument above did not need to refer to the government’s real financial wealth, nothing would change. The reason is that the government is assumed to adjust to its larger interest obligations by curtailing government spending on importables (recall equation (17a)), so that adjustment in its accounts can be achieved without moving resources. Suppose, in contrast, that the government’s larger interest payments are financed by some combination of higher taxes on the private sector and reduced government spending on nontraded goods. In this case the analyses of the third and fourth subsections above (“Change in Composition of Government Spending” and “Tax-Financed Increase in Government Spending on Importables”) would apply, and the real exchange rate could quite easily depreciate both on impact and in the long run. Thus the counterintuitive result is generated by the assumption about the mode of financing the government’s external interest obligations.

III. Conclusions

The question of how the real exchange rate responds to external and domestic shocks in small countries with fixed nominal parities has received increasing attention in recent years. The studies that have examined this question, however, have in general been restricted to considering only equilibrium movements in the real exchange rate and have not analyzed the underlying dynamics. If one is to understand properly the behavior of the real exchange rate over time, it is obviously important to have an idea of both the short-run and long-run effects of shocks, and thus the dynamics become central to the analysis.

This paper has focused on the dynamic responses of the real exchange rate to a variety of exogenous and policy-induced shocks in a small, primary-commodity-exporting economy. Taking the case of external shocks first, we showed that an unanticipated worsening of the terms of trade would, other things being equal, lead to a short-run depreciation of the real exchange rate. This result is, of course, quite familiar. We also showed, however, that the short-run real depreciation will not be sufficient to restore current account equilibrium. The exchange rate will continue to depreciate, and the current account will continue to be in deficit during the transition to long-run equilibrium. The response to an unanticipated increase in the external real interest rate, in contrast, depends on the fiscal reaction of the government. If the government offsets the budgetary impact of the interest rate change by altering its spending on traded goods, then the long-run exchange rate will tend to appreciate, contrary to what is conventionally assumed. Nevertheless, a real depreciation is quite plausible on impact. Depreciation may also be the result in the long run if increased interest payments are financed by the imposition of higher taxes, reduced spending on nontraded goods, or a combination of both.

The effects on the real exchange rate of alternative types of fiscal measures are not well appreciated in the literature. Even with an unchanged fiscal deficit, variations in the level and composition of government spending were shown to have both short-run and long-run effects on the real exchange rate. A tax-financed increase in government expenditures on importables, for example, would depreciate the real exchange rate, whereas an increase in public spending on nontradables financed similarly would cause a real appreciation in both the short run and the long run. Furthermore, a change in the composition of government expenditures with unchanged taxes would also affect the real exchange rate in both the short run and long run. If the government increased spending on nontradables at the expense of importables, the real exchange rate would tend to appreciate. By contrast, a change in the composition of government spending toward importables would lead to a real depreciation.

In the area of trade policy, a liberalization of imports and exports through reductions in tariffs and export taxes would result in an appreciation of the real exchange rate. Reducing import tariffs, however, would be associated with a current account deficit, whereas reducing export taxes would mean a surplus during the transition to the new long-run equilibrium. Finally, a devaluation would depreciate the real exchange rate relative to its initial value in the long run if the initial current account deficit exceeds its long-run level, even with flexible wages and prices and perfect foresight. Although this result is certainly well known, it is often ignored and can only be demonstrated clearly in an explicitly dynamic framework.

In conclusion, the analysis here has shown that the real exchange rate will respond differently to different types of shocks, and in certain instances the short-run response will not necessarily be the same as the long-run response. These results have important implications for policies aimed to alter the real exchange rate. Such policies must be designed to take the dynamics of real exchange rate adjustment into account, although—as this paper has shown—that is by no means an easy task. Nevertheless, simple theoretical models of the type developed here can offer broad guidelines to policymakers in their efforts to achieve an appropriate level for the real exchange rate over time.

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*

Mr. Khan is Assistant Director in the Research Department. He is a graduate of Columbia University and the London School of Economics and Political Science. Mr. Montiel is an economist in the Developing Country Studies Division of the Research Department. He is a graduate of Yale University and the Massachusetts Institute of Technology. The authors are grateful to Miguel Kuguel and Saul Lizondo for helpful comments on an earlier version of this paper.

1

For an extensive discussion of the theoretical and empirical aspects of real exchange rates in developing countries, see the papers contained in Edwards and Ahamad (1986), in particular Harberger (1986).

2

Policies to alter the real exchange rate are often the centerpiece of adjustment programs; see International Monetary Fund (1985).

3

For a description of the role of external factors that affected developing countries, see Khan and Knight (1983) and Balassa (1986).

4

The model here generalizes the Khan-Lizondo model to incorporate a third good, full capital mobility, intertemporal substitution in consumption, and perfect foresight.

5

For an analysis of real exchange rate dynamics induced by changes in the sectoral allocation of capital, see Edwards (1986). Alternative approaches to the question of dynamics are taken by Mussa (1986) and Obstfeld (1986).

6

Note that, as long as ρ is unchanged, this formulation is equivalent to defining e as the ratio of the price of tradables to that of nontradables. When ρ changes, however, this definition becomes ambiguous. We examine effects of such changes on both Pz/PN and PX/PN in Section II.

7

This is strictly a simplifying assumption. It has no effects on the basic results of the paper. What it implies in the analysis here is that exports and exportables are one and the same.

8

We utilize this formulation for reasons of simplicity.

9

This intertemporal constraint allows us to rule out Ponzi schemes.

10

The intertemporal constraint (18) will be violated for the domestic government if åG < 0, and for the government of the rest of the world if åG > 0.

11

This condition is not sufficient, since a crisis will ensue if sFB/M is foreseen to fall below a threshold value. These conditions are obtained in models of balance of payments crises; see Krugman (1979), Obstfeld (1984), and Blanco and Garber (1986).

12

There is now a broad literature on the effects of nominal exchange rates on the real exchange rates; see Khan and Lizondo (1987) and the references cited therein.

13

This will be true as long as M – Dp>0, which we take to be the normal case.

14

Although this point is well known, it is frequently lost sight of and has recently been re-emphasized by Edwards (1985).

15

As Harberger (1986) has stressed, this ambiguity limits the usefulness of the conventional definition of the real exchange rate as the price of tradables measured in terms of nontradables. See also Khan and Zahter (1985).

16

Experiments relating the real exchange rate to changes in the structure of government spending are described in Montiel (1986) and Khan and Lizondo 1987).

17

The analysis holds equally for the case of tariff reductions and removal of export taxes.

18

A similar result is obtained by Khan and Zahler (1985) and by Edwards and van Wijnbergen (1985).

IMF Staff papers: Volume 34 No. 4
Author: International Monetary Fund. Research Dept.