## Abstract

An intertemporal optimizing model of a small open economy is used to analyze how terms of trade changes affect real exchange rates and the trade balance. Temporary current, (expected) future, and permanent changes in the terms of trade are considered. The results suggest that the relationship between the terms of trade and the current account (the so-called Harberger-Laursen-Metzler effect) is sensitive to whether the model incorporates nontradable goods. Thus, the real exchange rate may be an important variable through which terms of trade shocks are transmitted to the current account.

Several developed and developing countries have experienced—in the course of the past fifteen years—what are by historical standards large disturbances in their terms of trade. Such changes in the terms of trade have taken many forms: changes in the relative price of intermediate inputs, in the relative price of final manufactured goods, or in the relative price of some final primary commodity. Along with these developments in the world economy has arisen a renewed theoretical interest among economists about the likely effects of terms of trade shifts on various macroeconomic variables such as spending, saving, investment, and, in particular, the current account balance. Part of this interest is no doubt due to recent historical experience, but it is also due to dissatisfaction with certain aspects of the more traditional approaches to the analysis of the relationship between the terms of trade and the current account that view the latter as being determined in a nonoptimizing, static setting.

Of course the current account—being the difference between saving and investment—is inherently a forward-looking economic variable; hence the question of how various terms of trade changes affect the current account balance requires an explicit intertemporal model. Only in such a setting can the important distinctions about the different effects of current versus future shocks, or of temporary versus permanent shocks, be made clear.

The analysis of the effects of changes in the terms of trade on spending, saving, and the current account has a long history in the open-economy literature. The early papers, which include Harberger (1950) and Laursen and Metzler (1950), were based on nonoptimizing models. Their argument was essentially that a deterioration in the terms of trade would lower real income and hence reduce saving out of any given level of nominal income, both measured in terms of exportables. If investment, fiscal policies, and nominal income are fixed, the lower saving implies a worsening in the country’s current account position. Thus, the Harberger-Laursen-Metzler (hereafter H-L-M) effect states that a deterioration in the terms of trade will cause a reduction in the current account balance.

More recent contributions have viewed the current account in an explicit intertemporal setting in which the spending and saving decisions of forward-looking individuals are derived from the maximization of an intertemporal utility function subject to lifetime budget constraints. Examples include Sachs (1981, 1982), Obstfeld (1982), Svensson and Razin (1983), Greenwood (1984), Persson and Svensson (1985), Bean (1986), Edwards (1987), and Frenkel and Razin (1987).

A central finding in this literature is that a permanent deterioration in the terms of trade will not have a large impact on the current account (assuming that the initial equilibrium is stationary and that trade is initially balanced).^{1} The reason is that, with a permanent increase in the relative price of importables, both real income and real spending are likely to fall by similar amounts (assuming homothetic preferences), and the current account, being the difference between these two magnitudes (assuming no historical debt commitment, so that initial current and trade account balances are identical), will therefore remain unaffected.

In contrast, a temporary deterioration in the terms of trade has an ambiguous impact on the current account. On the one hand, the “consumption-smoothing” motive dictates that agents will maintain spending in the face of a temporary decline in real income. This force favors a worsening in the current account position if the temporary deterioration in the terms of trade occurs in the current period, but it favors an improvement in today’s current account if the shock to the terms of trade is expected to occur in the future.

On the other hand, a temporary current (expected future) deterioration in the terms of trade raises (lowers) the cost of current consumption in terms of future consumption. This rise (fall) in the consumption-based real interest rate associated with a temporary current (expected future) deterioration in the terms of trade encourages (lowers) saving and hence favors an improvement in the current account in the case of a current shock and a worsening in the current account in the case of a future shock. This is the intertemporal substitution effect.

Thus, the net effect on the current account resulting from a temporary change in the terms of trade depends on which of these two influences—the consumption-smoothing motive or the intertemporal substitution effect—is stronger.

One aspect that has been largely ignored in the literature to date concerns the role of nontradable goods.^{2} In general, a change in the terms of trade alters both the level and composition of aggregate real spending, part of which falls on nontradable goods. The result, from an initial position of equilibrium in the home-goods sector, will be either excess demand or supply of nontradable goods. To ensure market clearing, a new relative price structure—a new path of the equilibrium real exchange rate—is required. The new value of the real exchange rate in turn feeds back to affect the real trade balance.

The purpose of this paper is therefore to consider the effect of terms of trade disturbances on the trade balance in a real, intertemporal, optimizing, general equilibrium model of a small open economy in which some commodities are assumed not to be tradable internationally. This allows one to address two related questions. First, how do changes in the terms of trade affect the path of the equilibrium real exchange rate? Second, how do movements in the real exchange rate induced by the change in the terms of trade affect the relationship between the terms of trade and the trade balance? Put differently, how, in models with non-tradable goods, do changes in the terms of trade affect the balance of trade? Distinctions are drawn among temporary current, (expected) future, and permanent changes in the terms of trade. The results are presented both diagrammatically and analytically.

The motivation for extending the two-tradable-good (importable and exportable) model of a small country to allow for a home-goods sector is by now clear. First, at a theoretical level, the terms of trade and the real exchange rate are interesting macroeconomic relative price variables, and identifying whether one expects them to be positively or negatively correlated (as well as the magnitude of the correlation) is a useful task. Second, any expenditure-switching policy that alters the internal terms of trade faced by domestic agents will in general have a nonzero effect on the real exchange rate that policymakers may wish to take into account. Third, the results may shed some light on empirical regularities in the comovement between the terms of trade and the real exchange rate. Finally, as mentioned previously, the real exchange rate is potentially an important variable through which terms of trade shocks are transmitted to the current account.

In this paper, the response of the trade balance to a change in the terms of trade is decomposed into two parts. First, there is a *direct effect*—as discussed in Svensson and Razin (1983) and Frenkel and Razin (1987)—that in the context of this model may be viewed as the effect of a terms of trade disturbance holding constant the path of the real exchange rate. There is also an *indirect effect* operating through the response of the real exchange rate to a change in the terms of trade and the feedback of the real exchange rate to the trade balance.

It will be shown that the indirect effect is in general nonzero, so that, quantitatively, the response of the trade balance to a change in the terms of trade will differ according to whether the model incorporates non-tradable goods. Further, it is shown that, because the direct and indirect effects depend on different parameters of the model, they may be either of the same or opposite sign. Moreover, for certain values of the parameters, the indirect effect may be opposite in sign to the direct effect and may even dominate the latter; thus, qualitatively, the two types of model may differ in their predictions.^{3}

The remainder of the paper is organized as follows. Section I sets out the analytical framework, which is similar to the one employed in Svensson and Razin (1983) and Frenkel and Razin (1987) except that it allows for one of the goods to be nontradable. Section II considers the effects of terms of trade shocks on the path of the equilibrium real exchange rate, and Section III uses these results to determine the *total effect* of a change in the terms of trade on the balance of trade. Section IV reviews the main results of the paper and presents possible extensions. The paper concludes with a brief technical Appendix.

## I. Analytical Framework

Consider a two-period, real model of a small open economy in which there are three goods: an importable, an exportable, and a nontradable good. In this economy, there is a representative agent who maximizes utility subject to the following budget constraints:

where *c _{xt}*, c

_{mt}, and

*c*denote consumption levels of exportables, importables, and nontradables, respectively;

_{nt}*Ӯ*,

_{xt}*Ӯ*, and

_{mt}*Ӯ*denote the endowments of exportables, importables, and nontradables, respectively;

_{nt}*p*and

_{mt}*p*denote the relative price of importables and nontradables;

_{nt}*B*

_{-1}is the level of initial debt (which may be positive or negative):

*B*represents borrowing between periods 0 and 1 (which, if negative, represents net lending) and

_{0}*r*represents the rate of interest (for borrowing and lending) between periods t—1 and t,

_{xt}*t*= 0,1. The numeraire is chosen to be the exportable commodity, so that all assets and liabilities (as well as interest rates) are measured in units of the exportable. There is no loss of generality in this choice of numeraire so long as relative price changes are fully anticipated, since in this case an interest parity relationship will prevail between alternative debt instruments denominated in terms of different commodities. See Frenkel and Razin (1987, pp. 170 and 182) for the consequences of the choice of numeraire in the case of unanticipated relative price movements.

The real exchange rate will, for the purposes of this paper, be defined as the inverse of the relative price of nontradable goods in terms of exportables; that is, 1/*p _{nt}*. A rise in

*p*denotes a real appreciation, and a fall in

_{nt}*p*denotes a real depreciation.

_{nt}In a model with three goods, there are in general two real exchange rates: one in terms of exportables (l//p_{nt}), and the other in terms of importables *(p _{mt}/p_{nt})*. So long as the price of importables relative to exportables,

*p*is constant, the choice of either definition of the real exchange rate is completely innocuous. This is not the case when the shock being considered is a change in the commodity terms of trade; in this case, a change in

_{mt,}*p*will obviously have different effects on

_{mt}*l/p*and

_{nt}*P*In subsequent analysis of the real exchange rate effects of various shocks, only the first definition is considered—that is, the effect on the relative price of exportables in terms of the home good, 1/

_{mt}/P_{nt}·*p*. Simple algebra is then required to determine the effects of these shocks on the alternative definition of the real exchange rate,

_{nt}*p*, or on any weighted average of the two definitions, such as the consumption-based measure of the real exchange rate.

_{mt/}p_{nt}Preferences are defined over the six goods c_{xo}, *c _{mo}, c_{no}, c_{x1}, c_{m1}*, and c

_{n1}, and it will be assumed that the intertemporal utility function is weakly separable through time (see, for example, Goldman and Uzawa (1964) or Deaton and Muellbauer (1980) on separability). Thus, lifetime utility

*U(*c

_{x0},

*c*may be written as

_{m0}, c_{n0}, c_{x1}, c_{m1}, c_{n1})where *C _{0}*(.) and C

_{1}(.) are the subutilities, which are functions of the consumption levels of the three commodities in periods 0 and 1, respectively. In addition, it will be assumed that the subutility functions are themselves homothetic, so that, without any further loss of generality, they may be taken to be linearly homogeneous functions of the consumption vector in each of the two periods.

With these assumptions, the consumer may be viewed as solving a two-stage optimization problem. In the first stage, the consumer chooses levels of c_{xt}, c_{mt}, and *c _{nt}* to minimize the cost of attaining subutility level

*C*. In other words, he solves

_{t}subject to

for *t* =0,1. The solution to this problem yields demands for the three goods, which are functions of the temporal relative prices, *p _{mt}* and

*p*, and of total spending in that period,

_{nt}*P*where

_{t}C_{t,}*P*is the price or marginal cost of a unit of subutility (or real spending), C

_{t}_{t}. The consumption-based price index,

*P*, is a function of the relative prices,

_{t}*p*and

_{mt}*p*.

_{nt}In the second stage, the consumer chooses real spending levels *C _{0}, C_{1}* to maximize lifetime utility subject to an intertemporal wealth constraint. In other words, he solves

subject to

where *P _{0}, P_{1}* are the consumption-based price indices solved for in the first stage and

*W*

_{0}represents wealth (in terms of exportables), defined as the present value of the economy’s current and future endowment net of historical debt commitment. From equations (1) and (2), it is easy to verify that

where α_{x1} is the world discount factor, which is equal to 1/(1 + *r _{x0})*. It is noteworthy that, in the absence of a historical debt commitment

*(B*

_{-1}

*=0)*, the intertemporal budget constraint (with equality) of the representative agent is identical to the condition that, over the lifetime of this economy (that is, during periods 0 and 1), the present value of the sum of the trade account balances equals zero. This condition reflects, therefore, the assumption of perfect capital mobility subject only to the economy’s intertemporal solvency constraint.

Normalizing the intertemporal budget constraint by dividing by *P*_{0} yields the constraint relevant for the second stage of the consumer’s problem:

where α_{c1} = (P_{1}/P_{0})α_{x1}, and *W*_{c0} = *W*_{0}/*P*_{0}. In equation (4), all variables are measured in real terms; that is, in terms of units of period-0 subutility, *C*_{0}. The solution to the second-stage problem yields demands for C_{0} and *C*_{1} as functions of the intertemporal relative price, α_{c1}, and real lifetime wealth, *W _{c0}*.

^{4}

## II. Terms of Trade Shocks and the Real Exchange Rate

There are three main channels through which a change in the terms of trade alters the equilibrium real exchange rate. First, a change in the commodity terms of trade, whether brought about by a change in the world relative price of importables or by policy actions (such as a tariff) affecting the domestic price, leads to substitution among goods within the period. Thus, for example, a deterioration in the terms of trade in period 0 leads to increased consumption of nontradable goods in period 0 if the two goods are net (Hicksian) substitutes or to decreased consumption if they are net complements, all other things being held constant (including the level of utility, or welfare). This is the *intratemporal* or simply *temporal* substitution effect.

Second, if the rise in the relative price of importables is confined to period 0, the real (consumption-based) rate of interest also rises. This is so because a temporary current deterioration in the terms of trade (a rise in *P _{m0})* raises the consumption-based price index,

*P*

_{0}, whereas tomorrow’s price index,

*P*

_{l}, is constant because

*p*is assumed to be constant. Since the ratio P

_{m1}_{0}/P

_{1}rises, the cost of current consumption relative to future consumption has risen. This induces substitution of aggregate spending from period 0 to period 1. This rise in tomorrow’s consumption and fall in today’s consumption, brought about by the change in the intertemporal relative price while other factors are held constant, is the

*intertemporal*substitution effect.

Third, in addition to these intratemporal and intertemporal effects, a rise in *p _{m0}* reduces welfare. The magnitude of this

*welfare*effect depends on the volume of imports at the initial terms of trade.

To gain some insight into the quantitative impact of a change in the terms of trade on the real exchange rate, consider the market-clearing conditions in the market for nontradable goods in each of the two periods:

Equations (5) and (6) state that domestic demand must equal the exogenous endowment of nontradables, in each period. Of course, there are no corresponding conditions for tradable goods because trade account imbalances allow discrepancies between demand and supply of tradables, period by period.

Total differentiation of equations (5) and (6) yields solutions for the endogenous variables, *p _{n0}* and

*p*, as functions of the exogenous variables, the terms of trade, the world rate of interest, and the endowments.

_{n1}Because the focus here is on the first of these three variables, it is assumed in what follows that there are no supply shocks (endowments are fixed) and that there are no shocks to the world rate of interest. A useful diagrammatic apparatus for the interpretation of the effect of terms of trade shocks on the equilibrium real exchange rate is provided in Figure 1.^{5} The N_{0}N_{0} and N_{1}N_{1} schedules represent the loci of combinations of *p _{no}* and

*p*that clear the period-0 and period-1 markets for nontradable goods, respectively. These schedules are drawn for given values of the exogenous variables,

_{n1}*p*and

_{m0}*p*. For convenience, it is assumed that initially

_{ml}*p*. As shown in the Appendix, the two schedules have the following slopes:

_{n0}= p_{n1}where β_{mt}, β_{xt}, and β_{nt} are the period-*t* expenditure shares of importables, exportables, and nontradables. respectively: σ_{ij} is the Allen elasticity of substitution between goods *i* and *j*, and σ is the average saving propensity (defined as the ratio of future spending to lifetime wealth, in present value). It is easily verified that both schedules are positively sloped and that the *N _{0}N_{0}* schedule is necessarily steeper than the

*N*schedule.

_{1}N_{1}The intuition of this result is straightforward. Consider a rise in *p _{no}* from

*A*to

*B*in Figure 1. This creates excess supply for

*c*(through both a temporal and intertemporal substitution effect) and excess demand for c

_{n0}_{n1}(through an intertemporal substitution effect). A rise in

*p*eliminates the excess supply for c

_{nl}_{n0}(through an intertemporal substitution effect) and the excess demand for c

_{n1}(through both a temporal and intertemporal substitution effect). The rise in

*p*required to clear the period-0 market (to point

_{n1}*D*in Figure 1), however, is larger than the rise required to clear the period-1 market (to point C in Figure 1). The reason is essentially that a change in the relative price of nontradable goods in period

*t*always has a larger effect on excess demand in period

*t*than in the other period.

^{6}

### Temporary Current Changes in the Terms of Trade

Consider a temporary current deterioration in the terms of trade—that is, *N _{0}N_{0}* and the

*N*schedules. In the Appendix, it is shown that the horizontal shifts of these loci are, respectively,

_{1}N_{1}where µ_{nt} is the ratio of endowment to consumption of importables in period *t, t =* 0,1.

In equation (9) it can be seen that whether the *N*_{0}*N*_{0} schedule shifts to the right or to the left depends only on whether *p _{m0}* affects the demand for through three separate channels: (1) a temporal substitution effect, since enters directly as an argument in the demand for

*c*function; (2) the price index effect, since a rise in p

_{n0}*raises the consumption-based price index,*

_{mo}*P*, and hence raises the value of spending

_{0}*P*C

_{0}_{0}; and (3) the real spending effect, since a rise in

*p*alters both the real rate of interest and the real value of wealth and hence affects the period-0 demand for real spending,

_{m0}*C*. Each of these three effects will be considered in turn.

_{0}The magnitude of the (gross) temporal substitution effect depends on the elasticity of C_{no} with respect to *p _{mo}* which, by the Slutsky decomposition, is equal to β

_{mo}(σ

_{nm}- 1). Obviously, the gross substitutability or complementarity of the two goods is determined by whether

The price index effect is always positive. A percentage rise in *p _{m0}* raises

*P*, the consumption-based price index, by β

_{0}_{m0}, the expenditure share of importables in period-0 spending. The rise in

*P*raises total spending,

_{0}*P*

_{0}

*C*

_{0}(.), and, by the homotheticity assumption, creates an excess demand for C

_{n0}equal to β

_{m0}times

_{m0}.

^{7}

The real spending effect is always negative; that is, a temporary current deterioration in the terms of trade always reduces current-period real spending. There are two channels at work here: a real wealth effect and an intertemporal substitution effect. First, from the budget constraint, a rise in *p _{m0}*, lowers the real value of wealth,

*W*(and hence the demand for

_{c0}*c*, by the amount β

_{n0})_{m0}[(1—γ)µ

_{m0}—1]. Second, the rise in

*p*lowers the real discount factor, and this reduces the demand for C

_{m0}_{0}by an amount equal to the product of the change in α

_{c1}, which equals -β

_{m0}, and the elasticity of

*C*with respect to α

_{0}_{c1}which equals γ(σ- 1). Summing these two effects yields the real spending effect,

^{—}β

_{m0}[(1 - γ)(1—µ

_{m0})+ γσ], which is unambiguously negative. This result accords with intuition because, in the case of a temporary current deterioration in the terms of trade, real wealth falls and the real rate of interest rises. These two effects are mutually reinforcing as they affect real spending, C

_{0}.

**Effect of a Temporary Current Deterioration in Terms of Trade on Path of Real Exchange Rate**

Citation: IMF Staff Papers 1988, 004; 10.5089/9781451930733.024.A001

**Effect of a Temporary Current Deterioration in Terms of Trade on Path of Real Exchange Rate**

Citation: IMF Staff Papers 1988, 004; 10.5089/9781451930733.024.A001

**Effect of a Temporary Current Deterioration in Terms of Trade on Path of Real Exchange Rate**

Citation: IMF Staff Papers 1988, 004; 10.5089/9781451930733.024.A001

Finally, as is easily verified, the sum of the temporal substitution, price index, and real spending effects yields precisely the numerator of the expression in equation (9). The *N _{0}N_{0}* schedule will shift to the right if σ

_{nm}> [(1 - γ) |(1-µ

_{m0})+γσ]; that is, if the temporal substitution effect dominates the real spending effect, and conversely. Note further that the welfare effect is zero if σ

_{m0}= 1· This is the case in which, at the initial terms of trade, the small country is in the autarky equilibrium. In this case, only the relative magnitudes of the temporal and intertemporal (compensated) elasticities (that is, whether

*N*schedule.

_{0}N_{0}Consider now the market-clearing condition in period-1, equation (6). A rise in *p _{m0}* affects the demand for home goods in the future period only through the real spending effect. In contrast to the period-0 equilibrium condition, there is neither a temporal substitution effect nor a price index effect.

Real spending in period 1, C_{1}, is influenced by way of two separate channels: the rise in *p _{m0}* raises the consumption-based rate of interest, which in turn raises the demand for

*c*(the intertemporal substitution effect), while the negative real wealth effect lowers the demand for c

_{n1}_{n1}. Specifically, the intertemporal substitution effect is equal to the product of the change in the consumption-based discount factor,—β

_{m0,}and the elasticity of period-1 real spending with respect to the real discount factor, -[(1 - γ)σ + γ]. The sum of this intertemporal substitution effect and the real wealth effect, given previously β

_{m0}[(1 -γ)µ

_{m0}- 1], yields precisely the expression in the numerator of equation (10). As can be seen, the real spending effect on the demand for c

_{n1}is ambiguous, reflecting a conflict between the negative wealth and the positive intertemporal substitution effects. If µ

_{m0}= 1 so that, at the initial terms of trade, the economy is in the autarky equilibrium, the

*N*

_{1}

*N*

_{1}schedule necessarily shifts to the left. This is so because, in the neighborhood of the autarky equilibrium, the temporary terms of trade deterioration raises the demand for c

_{n1}through the intertemporal substitution channel alone; there is no mitigating welfare effect.

In Figure 2, two possible equilibria are depicted. In both panels, it is assumed that the terms of trade shock occurs around the autarky equilibrium; that is, µ_{m0} = 1. In panel A, the temporal elasticity is assumed to exceed the intertemporal elasticity. In this case, the rise in *p _{m0}* shifts the

*N*schedule to the right. In panel B, the

_{0}N_{0}*N*schedule shifts to the left, reflecting the assumption that σ

_{0}N_{0}_{nm}< γσ. In both panels, the

*N*schedule shifts to the left. As can be seen in panel A, the equilibrium moves from point

_{1}N_{1}*A*to point

*B*, and a temporary deterioration in the terms of trade necessarily leads to a real appreciation in both periods.

^{8}In panel B, the equilibrium moves from point

*A*to point

*B’*, and there is a fall in

*p*and a rise in

_{n0}*p*. This result is not general, however, as experimenting with the figure will reveal. Finally, note that, although the shock is confined to period 0, part of the adjustment in the real exchange rate occurs in period 1 when there is no change in any “fundamental.”

_{nl}In the Appendix, the following general result is derived for the equilibrium response of *p*_{no} (the inverse of today’s real exchange rate) to a temporary current deterioration in the terms of trade (the result for *p _{nI}* is also given in the Appendix):

where

and Δ_{1} > 0, Δ_{2} > 0. Thus, the following proposition may be stated.

Proposition 1. *The nature of the response of the real exchange rate to a temporary current disturbance in the terms of trade depends on the relative magnitudes of the temporal, intertemporal, and welfare effects. If nontradables and importables are Hicksian substitutes, the temporal substitution effect favors a contemporaneous real appreciation, whereas the (net) intertemporal and welfare effects favor a real depreciation*.^{9}

### An (Expected) Future Change in the Terms of Trade

Consider now the effect that an (expected) future deterioration in the terms of trade would have on the path of the real exchange rate; that is.

*N _{0}N_{0}* and N

_{1}N

_{1}schedules are given by

Consider first equation (12). A rise in *p _{ml}* affects the period-0 equilibrium condition through two channels. By lowering the real interest rate, the future deterioration in the terms of trade causes substitution of aggregate spending (part of which falls on nontradable goods) from period 1 to period 0. The magnitude of this effect is governed by the intertemporal elasticity of substitution, σ, and is positive in terms of its impact on today’s relative price of home goods,

*p*. In contrast, the future deterioration in the terms of trade lowers welfare and hence reduces the demand for home goods today. The magnitude of this effect, which is negative in terms of its impact on today’s relative price of home goods, is proportional to the ratio of imports to consumption of importables in period 1, (1—µ

_{n0}_{m1}). Overall, the

*N*locus shifts to the right if the intertemporal substitution effect outweighs the welfare effect—that is, if σ > (1—µ

_{0}N_{0}_{m1})—and conversely.

Consider now the *N*_{1}*N*_{1} schedule. From equation (13), we see that an (expected) future deterioration in the terms of trade affects the period-1 market for nontradable goods in a way that is analogous to the effect of a current terms of trade shock on the period-0 market for home goods. The only real difference arises from changes in the values of the various elasticities over time, which are in turn functions of the underlying parameters: the expenditure shares, the temporal and intertemporal elasticities of substitution, the average propensity to save, and the ratio of imports to consumption of importables. Accordingly, if importables and nontradables are Hicksian substitutes, the future deterioration in the terms of trade raises the demand for *c _{nl}* through the temporal substitution effect. In addition to the temporal substitution effect, there is a negative effect on aggregate real spending,

*C*

_{1}. that tends to reduce the demand for

*c*, This effect operates through two channels: a negative real wealth effect, which equals—β

_{n1}_{m1}γ(1—µ

_{m1}), and a negative intertemporal substitution effect, which equals—β

_{m1}(1—γ)σ. The latter effect reflects the fall in the real rate of interest caused by the increase in the price of importables that is expected in the future. Thus, the overall shift in the

*N*

_{1}

*N*

_{1}schedule reflects the sum of the positive temporal substitution effect (if the goods are Hicksian substitutes) and the negative real spending effect.

**Effect of an (Expected) Future Deterioration in Terms of Trade on Path of Real Exchange Rate**

Citation: IMF Staff Papers 1988, 004; 10.5089/9781451930733.024.A001

**Effect of an (Expected) Future Deterioration in Terms of Trade on Path of Real Exchange Rate**

Citation: IMF Staff Papers 1988, 004; 10.5089/9781451930733.024.A001

**Effect of an (Expected) Future Deterioration in Terms of Trade on Path of Real Exchange Rate**

Citation: IMF Staff Papers 1988, 004; 10.5089/9781451930733.024.A001

In Figure 3, a benchmark case is depicted in which the economy operates in the autarky equilibrium in period 1, so that ε_{m1} is equal to unity. In this case, the rise in *p _{m1}* necessarily causes the

*N*schedule to shift to the right. The figure shows two possibilities for the

_{0}N_{0}*N*

_{1}

*N*

_{1}schedule. In panel A, the temporal elasticity of substitution is assumed to exceed the (absolute value of the) compensated elasticity of period-1 real spending with respect to the real discount factor. In that case, the rise in

*p*causes excess demand for

_{m1}*c*, and the

_{nl}*N*schedule shifts to the left. In panel B, the opposite case is considered, in which σ

_{1}N_{1}_{nm}< (1 - γ)σ.

In panel A, the equilibrium moves from point *A* to point *B*, and the real exchange rate necessarily appreciates today as well as in the future. In general, however, whether *p _{n0}* rises more or less than

*p*(both cases are possible) depends on the relative magnitudes of σ and σ

_{nl}_{nm}, the temporal and intertemporal elasticities of substitution. Thus, as in the case of a temporary current shock to the terms of trade, the real exchange rate may either over- or undershoot its new long-run value.

^{10}Note also that, even though no “fundamental” has changed in period 0, part of the adjustment of the real exchange rate occurs in that period.

In panel B, the new equilibrium is at point *B’*, at which *p _{n0}* rises and

*p*falls. This result is not general, however, as experimenting with the figure will reveal.

_{n1}Recall now the general case: *µ _{m1}* ≠ 1. In the Appendix it is shown that the equilibrium response of today’s relative price of nontradable goods to a future deterioration in the terms of trade (the response of

*p*is also given in the Appendix) can be given by

_{n1}where

and where Δ_{3} > 0 and Δ_{4} > 0. The analysis of anticipated future shocks to the terms of trade yields Proposition 2.

Proposition 2. *An (expected) future change in the terms of trade will in general alter the real exchange rate in the present; that is, in periods before any “fundamental” has changed. A future deterioration in the terms of trade will cause a real appreciation today if the temporal elasticity of substitution between importables and nontradables*, σ_{nm}, *and the intertemporal elasticity of substitution, σ, both exceed the critical value*, (1 - μ_{m1}). *which equals the ratio of imports to consumption of importables in period* 1. If *both elasticities fall short of the critical value, however, a future deterioration in the terms of trade causes a real depreciation in the present*.

**Effect of a Permanent Deterioration in Terms of Trade on Path of Real Exchange Rate**

Citation: IMF Staff Papers 1988, 004; 10.5089/9781451930733.024.A001

**Effect of a Permanent Deterioration in Terms of Trade on Path of Real Exchange Rate**

Citation: IMF Staff Papers 1988, 004; 10.5089/9781451930733.024.A001

**Effect of a Permanent Deterioration in Terms of Trade on Path of Real Exchange Rate**

Citation: IMF Staff Papers 1988, 004; 10.5089/9781451930733.024.A001

### Permanent Changes in the Terms of Trade

Consider now the effect of a permanent deterioration in the terms of trade; that is, *N*_{0}*N*_{0}, and *N _{1}N_{1}* schedules are

Thus, a permanent deterioration in the terms of trade has two effects. First, by permanently raising the relative price of importables, the change in the terms of trade permanently alters the temporal composition of spending. The magnitude of the temporal substitution effect is governed by σ_{nm} the elasticity of substitution between importables and nontradables. Second, the permanent deterioration in the terms of trade lowers welfare. The magnitude of this welfare effect, which is always negative in terms of its impact on the demand for *c _{n0}* or

*c*is governed by (1 - µ

_{n1}_{m}), the (assumed to be constant) ratio of imports to consumption of importables. The

*N*schedule clearly must shift to the right, and the

_{0}N_{0}*N*schedule to the left, if σ

_{1}N_{1}_{nm}

*>*(1 - µ

_{m}), and conversely.

These two cases are illustrated in Figure 4. In panel A, it is assumed that σ* _{nm} >* (l—µ

_{m}). In that case, a permanent deterioration in the terms of trade leads to a real appreciation in both periods. In panel B, it is assumed that σ

_{nm}< (1 - µ

_{m}), so that the permanent deterioration in the terms of trade leads to a real depreciation in both periods. The intuition of this result is clear: if

*σ*>(1—µ

_{nm}_{m}), the positive substitution effect outweighs the negative welfare effect so that the rise in

*p*raises (permanently) the demand for nontradables. Given the supply, a rise in both

_{m}*p*, and

_{n0}*p*is necessary to clear the home-goods sector. Conversely, if

_{n1}*σ*>(1—µ

_{nm}_{m}), the negative welfare effect dominates, and a permanent deterioration in the terms of trade lowers permanently the demand for home goods, resulting in a real depreciation in both periods.

In the Appendix, it is shown that the equilibrium response of today’s relative price of nontradable goods to a permanent deterioration in the terms of trade (the response of *p _{n1}* is also given in the Appendix) is

where

Note that, from equation (17), the effect of a permanent change in the terms of trade on the real exchange rate is very similar to the effect derived in the context of static (one-period) models (for example, Dornbusch (1974) or Neary (1988)). The analysis of permanent terms of trade changes leads to the following proposition.

Proposition 3. *The effect of a permanent terms of trade disturbance on the real exchange rate depends on the relative magnitudes of the temporal elasticity of substitution between importables and nontradables*, σ_{nm}. *and the ratio of imports to consumption of importables*, (1—µ_{m}). *If the value* of σ_{nm} *exceeds this critical ratio, a permanent terms of trade deterioration causes a real appreciation in both periods, and conversely. That intertemporal considerations are absent from the analysis is* *a consequence of the assumption of constant expenditure shares. Under this assumption, a permanent change in the terms of trade does not alter the (consumption-based) real rate of interest*.

## III. The Harberger-Laursen-Metzler Effect in the Presence of Nontradable Goods

The effect that various shocks to the terms of trade have on the path of the real exchange rate is an important ingredient in the analysis of the H-L-M effect. In particular, the total effect of a terms of trade change on the trade balance can be decomposed into a direct effect (that is, the effect with the real exchange rate held constant) and an indirect effect (operating through changes in the real exchange rates caused by the shock to the terms of trade, which in turn feed back to alter the trade balance). Accordingly, one may write

where *(TA _{c})_{0}* is the consumption-based trade balance in period 0, which is defined as

where

The first term on the right-hand side in each of equations (18)-(20) corresponds to the direct effect, and the terms inside the summation signs represent the indirect effect of a terms of trade change on the balance of trade.

Differentiating equations (21) and (22) yields

where µ_{c0} is the ratio of real gross domestic product (GDP) to real spending in period 0, a positive number that is greater or less than unity as the period-0 trade balance is in surplus or deficit.

As can be seen from equation (23), a temporary current rise in the relative price of home goods, *p _{n0}*, affects the consumption-based trade balance through two separate channels: a real income effect, β

_{n0}(1 - µ

_{c0}), and a real spending effect, β

_{n0}γσ. The real income effect is positive if µ

_{c0}< 1 (that is, if at the initial terms of trade the country has a trade deficit) and is negative if µ

_{c0}> 1 (that is, if initially the country has a trade surplus). The reason is clear: if µ

_{c0}< 1, there is excess demand for tradables in period 0, so that a fall in their relative price (a rise in

*p*raises real income. Conversely, if µ

_{n0})_{c0}> 1, there is excess supply of tradables in period 0, so that a fall in their relative price lowers real GDP.

The only mechanism through which a change in *p _{n0}* affects real spending, C

_{0}, is intertemporal substitution. This is so because of the assumption that the home-goods market clears in each period. Because non-tradable goods are neither in excess demand nor excess supply, there is no aggregate welfare effect from a change in their relative price. However, a rise in

*p*raises the real rate of interest relevant for consumption decisions, and this increase reduces current spending, which corresponds to an improvement in the current-period trade balance.

_{n0}Consider now equation (24). A rise in *p _{nl}* affects the period-0 trade balance only by altering real spending, C

_{0}, because there is no effect of a change in

*p*on current real income, (GDP

_{n1}_{c})

_{0}. Again, and for the same reason as above, real spending is affected only by altering the intertemporal terms of trade. The rise in

*p*raises the discount factor relevant for consumption decisions, which in turn raises current-period real spending. The increase in real spending corresponds to a worsening of the period-0 trade balance.

_{n1}### Permanent Changes in the Terms of Trade

Substituting the relevant expressions into equation (20) and assuming that the expenditure shares and importables production-consumption ratio do not vary over time allow the total effect of a terms of trade change on the period-0 real trade balance to be written as

where

Consider the first term in equation (25), which represents the direct effect. As can be seen, the sign of the direct effect is determined solely by the initial position of the country’s trade balance: the sign is positive if, at the initial relative price structure, the economy runs a trade deficit (µ_{c0} < 1); it is negative if the country has a trade surplus (µ_{c0} > 1), If initially the trade account is balanced, then the permanent rise in the relative price of imports lowers real income and spending by the same amount, and the trade balance is unchanged.

The second term on the right-hand side of equation (25) is the indirect effect, and its sign depends on two factors: first, whether _{nm} - (1 - µ_{m})] determines the sign of the change in the relative price of home goods as a result of the deterioration in the terms of trade. If σ_{nm} > 1 - µ_{m}, the permanent rise in *p _{m}* leads to a permanently lower real exchange rate, and conversely. The term [1 - µ

_{c0}] translates the change in the real exchange rate into a change in the balance of trade.

^{11}

The analysis suggests that if (1 - µ_{m}) > σ* _{nm}*, so that a terms of trade deterioration causes a real depreciation, the direct and indirect effects of the terms of trade change will be opposite in sign. It can be verified that, for certain values of the parameters, the indirect effect may even outweigh the direct effect.

Thus, although the assumption of no nontradable goods (a value of β_{n} close to zero) implies that, from an initial position of trade deficit, a permanent terms of trade deterioration always improves the trade balance, the analysis here suggests that a comovement consisting of (1) deteriorating (improving) terms of trade, (2) a negative and worsening (positive and improving) trade balance, and (3) real depreciation (real appreciation) is a theoretical possibility.^{12} These types of comovement would be difficult to explain in the context of models without nontradable goods. This analysis suggests a fourth proposition.

Proposition 4. *The response of the current account to a permanent disturbance in the terms of trade will be qualitatively similar in models with and without nontradable goods if the elasticity of substitution between home goods and importables*, σ_{nm}, *exceeds the ratio of imports to consumption of importables*, 1—µ_{m}, *or if trade is initially balanced. For values of* σ_{nm} *falling short of this critical ratio, the behavior of the trade balance may differ qualitatively in the two types of model. For example, a deterioration in the terms of trade may lead to a worsened trade balance (from an initial position of deficit), and an improvement in the terms of trade may lead to an increase in the trade surplus. In the first case, the worsened trade balance will be accompanied by a real depreciation, whereas in the second case the larger surplus will be accompanied by a real appreciation*.

### Temporary Changes in the Terms of Trade

To sharpen the analysis, a benchmark case is considered in which, in the initial equilibrium, the trade account is balanced.^{13} Substituting the relevant expressions into equations (18) and (19) yields

where Δ_{7}= β_{m}[β_{m} σ_{nm}+ β_{x} σ_{nx} + β_{n} σ]^{-1} > 0.

Consider first the direct effect (the first term on the right-hand side) in equation (26). A rise in *p _{m0}* has three effects on the period-0 trade balance. First, real GDP falls by the amount β

_{m}(1—µ

_{m}); that is, in proportion to the (assumed to be constant) volume of imports. This is the negative real income effect associated with a deterioration in the terms of trade. Second, the rise in

*p*raises the consumption-based rate of interest, which lowers real spending,

_{m0}*C*

_{0}. The magnitude of this effect is governed by the product of β

_{m}, which equals the fall in the real discount factor, and γσ, the compensated elasticity of

*C*with respect to the discount factor. Third, the rise in

_{0}*p*lowers lifetime real wealth. The proportional fall in lifetime wealth is a fraction, (1 - γ), of the fall in current period real GDP, β

_{m0}_{m}(1—µ

_{m}). The fall in real wealth lowers the volume of spending,

*C*, by the amount β

_{0}_{m}(1—γ)(1—µ

_{m}), given the assumption of homotheticity. Summing these three effects yields precisely the first expression in equation (26).

The direct effect is therefore positive or negative according to whether ^{14} The reason is of course that a terms of trade shock is a particular kind of real income shock. Like a negative supply shock, a deterioration in the terms of trade lowers real income. Unlike a negative supply shock, however, a deterioration in the terms of trade raises the real rate of interest (for this small open economy). The rise in the rate of interest reduces real spending through the intertemporal substitution channel. If this force is sufficiently powerful—that is, if σ >(l—µ_{m})—then a temporary adverse movement in the terms of trade will actually cause the trade balance to move into surplus.

Equation (26) states that the sign of the indirect effect (second term on the right-hand side) of a temporary current deterioration in the terms of trade depends on the relative magnitudes of the temporal and intertemporal elasticities of substitution. The intuition of this result is as follows. A rise in *p _{m0}* induces substitution among goods within period 0. The magnitude of this substitution is governed by σ

*, the temporal elasticity of substitution between nontradables and importables. If the two goods are Hicksian substitutes, the temporal substitution effect raises the real exchange rate ratio,*

_{nm}*p*.

_{n0}/p_{n1}In contrast, a rise in *p _{m0}* raises the consumption-based rate of interest and induces substitution of aggregate spending (part of which falls on home goods) from period 0 to period 1. This intertemporal substitution effect is negative in its impact on the price ratio,

*p*. Its magnitude is governed by a, the intertemporal elasticity of substitution.

_{n0}/p_{n1}Thus, if σ* _{nm} > σ*, so that the temporal substitution effect dominates the intertemporal substitution effect, the rise in

*p*raises the price ratio,

_{m0}*p*

_{n0}/p

_{n1}, and the sign of the indirect effect is necessarily positive. This is the case of equilibrium overshooting, according to which the (absolute value of the) short-run (period-0) change in the real exchange rate exceeds the long-run (period-1) change. Conversely, if a temporary current deterioration lowers the home-goods price ratio, which will occur if σ

_{nm}< σ, then the sign of the indirect effect is negative. In this case of equilibrium undershooting, there is a real appreciation in the long run (period 1) relative to the short run (period 0).

^{15}

The analysis above suggests that the direct and indirect effects of temporary terms of trade disturbances depend on different parameters of the model. Specifically, the sign of the direct effect depends on the relative magnitudes of the intertemporal elasticity of substitution, σ, and the share of imports in the consumption of importables, 1 - µ_{m}. On the other hand, the sign of the indirect effect depends on the relative magnitudes of the temporal and intertemporal elasticities of substitution, σ and *σ _{nm}*. This observation shows that the direct and indirect effects may actually be of opposite sign. Furthermore, for certain parameter configurations, equation (26) reveals that the indirect effect may dominate the direct effect (see the Appendix). Thus, as in the case of permanent shocks, the real exchange rate may be an important variable through which terms of trade shocks are transmitted to the current account.

The preceding analysis has concentrated on temporary current, rather than (expected) future, shocks to the terms of trade. The underlying symmetry between equations (26) and (27) suggests that a separate analysis of future shocks is not required.^{16} One can note briefly, however, that in the case of an (expected) future deterioration in the terms of trade, the direct effect on today’s trade balance will be positive if σ < (1 - µ_{m}). This is the case in which the current account acts as a shock absorber, moving into surplus in anticipation of a real income loss in period 1. If σ > (1—µ_{m}), however, then the direct effect will worsen the trade balance as a result of an (expected) future deterioration in the terms of trade. The intuition here is that the expected rise in *p _{ml}* lowers the real rate of interest, which raises real spending today,

*Co;*this effect dominates the consumption-smoothing motive (or welfare effect), which by itself lowers real spending and hence improves the trade balance. The direct effect is therefore negative if the welfare (or consumption-smoothing) effect is weak relative to the intertemporal substitution effect—that is, if σ > (1—µ

_{m})—and conversely.

The sign of the indirect effect of a rise in *p _{m1}* depends on the response of the time path of the real exchange rate,

*p*. The parameters that influence this time path are the temporal and intertemporal elasticities of substitution. If σ

_{n0}/p_{n1}*σ, then a rise in*

_{nm}>*p*lowers the price ratio, p

_{ml}_{n0}/p

_{n1}, which in turn lowers the consumption-based rate of interest. Real spending, C

_{0}, therefore rises, and the indirect effect contributes to a worsening of the trade balance. In contrast, if

*σ*< σ, a rise in

_{nm}*p*raises the price ratio.

_{m1}*p*, which in turn contributes to a higher real rate of interest. The indirect effect contributes to a fall in C

_{n0}/p_{n1}_{0}, hence to an improvement in the period-0 trade balance. A further proposition is suggested.

Proposition 5, *Temporary terms of trade disturbances will in general have different effects in models with or without nontradable goods. The fundamental reason underlying these differences is that the time path of the real exchange rate (which is a key determinant of the real rate of interest and, hence, of real spending and the trade balance) is an endogenous variable that responds to disturbances in the terms of trade. For certain parameter configurations, a temporary terms of trade shock will lead to a deterioration in the trade balance when the response of the real exchange rate is taken into account even if, with the real exchange rate held constant, the trade balance improves, and conversely*.

Figure 5 illustrates such a result. Real income and spending in period 0 are plotted on the horizontal axis, and the corresponding period-1 variables are shown on the vertical axis. The initial real income and spending points are denoted *I*_{0} and *S*_{0}, respectively. It is assumed, in Figure 5, that the initial trade balance is zero, so that *I*_{0}, *S*_{0} occur at the same point. The solid budget line in Figure 5 represents the lifetime solvency constraint, and its slope is (minus) unity plus the real rate of interest.

Consider now a temporary current deterioration in the terms of trade. This causes the real income point to shift from *I*_{0} to *I*_{1}. At a constant real discount factor, the real spending point shifts from *S _{0}* to

*S*

_{1}. The period-0 trade balance unambiguously turns negative, with the magnitude of the deficit being equal to the horizontal distance between

*I*

_{1}and

*S*

_{1}.

**Harberger-Laursen-Metzler Effect with Nontradable Goods: Effect of a Temporary Current Deterioration in Terms of Trade on the Trade Balance**

Citation: IMF Staff Papers 1988, 004; 10.5089/9781451930733.024.A001

**Harberger-Laursen-Metzler Effect with Nontradable Goods: Effect of a Temporary Current Deterioration in Terms of Trade on the Trade Balance**

Citation: IMF Staff Papers 1988, 004; 10.5089/9781451930733.024.A001

**Harberger-Laursen-Metzler Effect with Nontradable Goods: Effect of a Temporary Current Deterioration in Terms of Trade on the Trade Balance**

Citation: IMF Staff Papers 1988, 004; 10.5089/9781451930733.024.A001

However, in general the real rate of interest will not remain unchanged. First, the current deterioration in the terms of trade tends to raise the real rate of interest, with the real exchange rate held constant. This change is captured by a clockwise pivot of the budget line through point *I*_{1}, where the new slope equals (minus) *S*_{2}. along a new Engel curve (not shown) corresponding to the higher real interest rate. The movement from the pair (*I*_{0},*S*_{0}) to the pair (*I*_{1},*S*_{2}) corresponds to the direct effect in equation (26). Accordingly, it is assumed that the direct effect on the trade balance is negative.

Consider now the indirect effect, and suppose that the temporary terms of trade deterioration results in a steeper time profile of the real exchange rate (that is. *p _{no}/p_{n1}* rises). This effect raises the real rate of interest and causes a further clockwise pivot of the budget line through point

*I*

_{1}. The slope of the new budget line is equal to (minus)

*R”*, and spending moves to a point such as

_{c0}> R’_{c0}*S*

_{3}, at the intersection of a new Engel curve (not shown) and the budget line. At S

_{3}, there is a trade surplus corresponding to the horizontal distance between

*I*

_{1}and

*S*

_{3}. Thus, although the direct effect, which corresponds to the movement from (

*I*

_{0},

*S*

_{0}) to (

*I*

_{1},

*S*

_{2}) lowers the trade balance, the total effect, which corresponds to the movement from (

*I*

_{0},

*S*

_{0}) to

*(I*

_{1},

*S*, yields a trade surplus. The fundamental reason for these different results is the endogenous movement in the time profile of the real exchange rate.

_{3})## IV. Conclusions and Extensions

This paper has used an intertemporal, real model of a small country, in which optimizing agents consume three goods in each period, to determine to what extent the introduction of a nontradables sector alters the relationship between changes in the terms of trade and the balance of trade. An answer to this question required an understanding of how the two temporal relative prices—the terms of trade and the real exchange rate—are linked. Therefore, an analysis of the effects of various terms of trade shocks on the real exchange rate was undertaken. These changes in the real exchange rate represent a separate and distinct channel through which changes in the terms of trade affect a country’s trade balance.

Specifically (and schematically), the effects of temporary shocks to the terms of trade were found to depend critically on two factors: first, the relative magnitudes of temporal and intertemporal elasticities of substitution; second, the relative magnitudes of the intertemporal elasticity of substitution and the ratio of imports to consumption of importables. The first factor determines the effect of the terms of trade change on the time profile of the real exchange rate (which is a key determinant of the real rate of interest and, hence, of real spending and the trade balance), whereas the second determines the effect of the terms of trade change on the trade balance, with the real exchange rate held constant. It was shown that, for certain parameter configurations, the predictions of models that incorporate nontradable goods may differ from those of models that do not.^{17} The real exchange rate is potentially an important transmission mechanism of terms of trade shocks to the current account.

The analysis of permanent shocks revealed that the initial trade balance position and the relative magnitudes of the temporal elasticity of substitution and the ratio of imports to consumption of importables are important factors that determine the behavior of the trade balance. This finding contrasts with previous analysis (not incorporating nontradable goods), which showed that the initial borrowing position of the country was the main factor determining the behavior of the current account as a result of a permanent terms of trade shock.

One possible extension of the model developed here would involve analyzing the role that capital mobility plays in determining the comovement of the terms of trade and the real exchange rate. In this paper, agents were assumed to have perfect access to the world capital market; an assumption of restricted access to world financial markets would be worth examining.

A second extension might involve relaxing the small-country assumption in order to analyze, within the context of a two-country general equilibrium model of the world economy, how various shocks (such as changes in fiscal and commercial policies, or supply shocks) affect the comovements of world real interest rates, real exchange rates at home and abroad, and the terms of trade.^{18}

## APPENDIX

### The Basic Model

This Appendix provides some guide posts to the main derivations for equations contained in the body of the paper.

On numerous occasions in the text, use is made of the relationship between gross elasticities and Hicks-Allen elasticities of substitution. The Allen elasticity of substitution between goods *i* and *j*, σ_{ij} = σ_{ij}, equals

*i*with respect to a change in price

*p*. Using this definition, the Slutsky decomposition of a total elasticity into its corresponding substitution and income effect components, and the homogeneity property of demand functions, one obtains a relationship between gross elasticities and an expenditure-share-weighted average of the elasticities of substitution and total spending (or wealth) elasticities. If, in addition to homothetic subutility functions, one assumes that the intertemporal utility function is itself homothetic, the elasticities of demand with respect to spending and of spending with respect to lifetime wealth will both be equal to unity. The following relationships used in the paper are now readily derivable:

_{j}where σ, the intertemporal elasticity of substitution, is defined as

Note that, since σ>0 and 0<γ<1, η_{c1α} is negative. However, whether *C*_{1}, α_{c1}, raises (lowers) demand for C_{0}, and η_{c0α,} is positive (negative). Note also that, since -[β* _{mt}* σ

*+ β*

_{nm}*σ*

_{xt}*] is a compensated effect, it is nonpositive because of the negative semidefiniteness of the Slutsky substitution matrix.*

_{nx}Many of the expressions in the paper follow from a solution to the system of market-clearing conditions in the nontradable-goods sector:

Totally differentiated, these become

where use has been made of the fact that the elasticity of the price index *P*, with respect to a change in one of the temporal relative prices *(p _{nt}* or

*p*is simply the corresponding expenditure share (β

_{mt})_{NT}or β

_{MT}). It is assumed throughout that there are no supply shocks (endowments are constant) and that the world discount factor, α

_{x1}, is given. In this case, the discount factor relevant for domestic consumption, α

_{c1}, evolves according to

Recalling that real wealth is given by

one can totally differentiate equation (38) to obtain

Substituting equations (28)-(31), (37). and (39) into equations (34) and (35) yields the system

This system underlies the derivation of the slopes of the *N _{0} N_{0}* and

*N*schedules shown in Figures 1–4 as well as their shifts in response to various terms of trade changes.

_{1}N_{1}Using equation (40) allows one to solve for

where

Equations (11) and (14) of the text correspond to the coefficients of

Substitution of the relevant terms in equations (41) and (42) into equations (18)-(20) of the text underlies the main derivations in Section III of the paper.

Finally, some numerical examples are provided to illustrate the claim that the qualitative response of the trade account to a change in the terms of trade may depend on whether the model incorporates nontradable goods. Consider first a permanent change in the terms of trade. Rewriting equation (25) of the text yields

Consider the case in which the economy receives no endowment of importables (complete specialization), so that ³_{m} = 0. Then let σ_{nm} *-* σ_{nx} = a, where 0 < *a* < 1 (all goods are net substitutes). If the share of nontradables. β_{n}, is larger than *a*, the indirect effect will dominate the direct effect.

Consider now a temporary (current) change in the terms of trade. Rewriting equation (26) yields

Suppose again that µ„ = 0 (complete specialization).

Suppose now that the intertemporal utility function is logarithmic. Then the direct effect in equations (26) and (27) of the text is zero. In other words, with the real exchange rate held constant, a temporary (current or future) terms of trade shock has no effect on the trade balance. When home goods are present in the model, however, it is clear that a temporary current deterioration in the terms of trade results in a trade surplus if *σ _{nm} > 1* and in a trade deficit if

*σ*< 1.

_{nm}Consider another example. Maintaining the assumption that *µ _{m}=0*, suppose that σ>1, so that the direct effect is positive in equation (26). Consider the following parameter values: σ

_{mn}=

*σ*, 0 <

_{nx}= a*a <*1,

*σ =*1 +

*a*, and β

_{m}= β

^{x}, = β

^{n}= 1/3. If

*a<*VT/3, then the direct effect is positive, but the total effect is negative.

Finally, consider the following parameter configuration: µ_{m}=0, σ, 0 < a < 1, σ_{nm} = σ_{nx} = 1+a, β_{m} = β_{n} = β_{x} = 1/3. If

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(Cambridge, Massachusetts), Vol. 94, No. 4 (November 1984), pp. 649–72.*Quarterly Journal of Economics*Svensson, Lars E.O., and Assaf Razin, “The Terms of Trade and the Current Account: The Harberger-Laursen-Metzler Effect,”

(Chicago), Vol. 91 (February 1983), pp. 97–125.*Journal of Political Economy*Végh, Carlos, “The Effects of Currency Substitution on the Response of the Current Account to Supply Shocks,”

, International Monetary Fund (Washington), Vol. 35 (December 1988), pp. 574–91.*Staff Papers*

^{}*

Mr. Ostry is an economist in the Financial Studies Division of the Research Department. He holds a doctorate from the University of Chicago, as well as degrees from the London School of Economics and Political Science. Oxford University, and Queen’s University (Canada).

This paper draws on two previous working papers (Ostry (1987, 1988a)) and the author’s Ph.D. dissertation (Ostry (1988b, Chapter 2)). The author thanks Jacob A. Frenkel, John Huizinga, and Assaf Razin, who served on his thesis committee, for their encouragement and helpful comments. He also thanks his colleagues at Chicago, especially Carlos Végh for detailed comments.

^{}1

This is the case in real models that abstract from physical capital and endogenous time preference. For a discussion of this issue in a monetary model with currency substitution, see Végh (1988; in this issue of *Staff Papers)*.

^{}2

Marion (1984) discussed the effect of changes in the price of oil (as opposed to changes in the price of a final consumption good) in the context of a two-sector model with nontradable goods. Greenwood (1984) examined the effect of terms of trade shocks on the real exchange rate and trade balance, but he considered the case of two goods on the production side and two goods on the consumption side rather than the more general three-good model developed here. This accounts for some differences in the conclusions reached in the two papers. The papers by Edwards (1987) and Ostry (1987) were developed independently and deal, in part, with similar issues.

^{}3

The Appendix provides several numerical examples illustrating the reversals that may obtain when nontradable goods are introduced into the model.

^{}4

The consumption-based discount factor, α_{c1}, is related to the (consumption-based) real rate of interest in the usual manner, namely α_{c1} = (1 + r_{c0})-1 where *r _{c0}* is the (consumption-based) real rate of interest. The relationship between the real rate of interest and the exogenous world rate of interest is given by r

_{c0}= (1 +

*r*1. Therefore, a rise in

_{x0})(P_{0}/P_{1}) -*P*

_{0}or a fall in

*P*raises the real rate of interest. (See, for example, Dornbusch (1983) or Frenkel and Razin (1987) on the consumption rate of interest.)

_{1}^{}5

For previous uses of a similar diagram, see Dornbusch (1980) and Edwards (1987).

^{}6

This verbal justification holds precisely for a flat spending profile over the life cycle; that is, γ = 1 - γ. However, it is easy to verify that, algebraically, the slope in equation (7) is always larger than the slope in equation (8), even if γ ≠ 1 - γ.

^{}7

Note that the sum of the gross temporal substitution effect and the price index effect equals β_{m0} σ_{nm}, which is the net or compensated temporal substitution effect. The sign of the net temporal substitution effect depends of course on whether

^{}8

Panel A illustrates the case of equilibrium overshooting, according to which the short-run change in the real exchange rate exceeds the long-run change in absolute value (see Edwards (1987) for further discussion of this issue). As shown below, whether there is equilibrium over- or undershooting is determined by the relative magnitudes of the temporal and intertemporal elasticities of substitution.

^{}9

If σ_{nm} > max {[(l - γ)(l - µ_{m0}) + γσ], (1 - µ_{m0})}, a temporary current deterioration in the terms of trade causes a real appreciation in the current period. If σ_{nm} > min {[(l - γ)(l - µ_{m0}) + γσ], (1 - µ_{m0})}, a temporary current deterioration in the terms of trade causes a real depreciation in the current period.

^{}10

Panel A, for example, illustrates the case of equilibrium undershooting, according to which the long-run change in the real exchange rate exceeds the short-run change (in absolute value).

^{}11

If trade is balanced initially, both the direct and indirect effects are zero in the case of a permanent change in the terms of trade.

^{}12

Note that this is an equilibrium phenomenon and has nothing to do with lags in the adjustment of the current account to relative price changes, which underly the “J-curve.”

^{}13

The role of initial trade account imbalances was discussed in the previous subsection. The ingredients necessary for consideration of the general case in which µ_{c0} ≠ 1 are given in the Appendix.

^{}14

This role of the current account is emphasized in Sachs (1981) and Svensson (1984), among others.

^{}15

As noted earlier, overshooting (undershooting) of the real exchange rate is defined as the short-run *change* being greater (less) than the long-run change (in absolute value), rather than as the short-run *level* being higher (lower) than the long-run level.

^{}16

This symmetry stems from the assumption of constant expenditure shares, constant production-consumption ratio of importables, and initially balanced trade.

^{}17

Further differences arise if trade is initially not balanced, since in this case there are real GDP revaluation effects associated with real exchange rate changes. The direction of these effects was discussed in the subsection on permanent terms of trade shocks; because the revaluation effects operate in essentially the same manner here, they were excluded in the subsection of the paper dealing with temporary disturbances.

^{}18

Ostry (1988b). Chapter 3, examines the effect of government purchases in such a model; Chapter 4 considers commercial policies.