Abstract
Standard real models predict that a permanent increase in oil prices would result in a current account surplus. The surplus occurs because investment falls while saving remains unchanged. This paper shows that if currency substitution is introduced into the analysis, a permanent increase in oil prices could cause a current account deficit. Furthermore, the greater the dependence of the economy on oil, the larger will be the deficit. The availability of foreign money makes it optimal for the public to decrease saving following the terms of trade deterioration. The fall in saving could more than offset the decline in investment.
THE OIL PRICE increases of 1973–74 and 1979–80 brought about an extensive literature dealing with the response of the current account to supply shocks in the context of intertemporal optimizing real models. In one of the more influential papers on this subject, Sachs (1981) develops a two-period model of an economy producing, consuming, investing, and exporting a final good and importing an intermediary input, oil. A temporary oil price increase induces a current account deficit because of the desire of the household to smooth out consumption over time. In contrast, a permanent oil shock generates a surplus in the current account. This key result follows from the fact that there is no change in saving while investment falls.1
Empirical evidence for oil-importing countries, particularly developing countries, indicates, however, that current account deficits persisted throughout the 1970s and into the 1980s.2 In contrasting the predictions of the model with the empirical evidence, Sachs (1981) argues that since the first oil shock turned out to be permanent, it seems reasonable to assume that in general people anticipated this, thus invalidating as an explanation for the observed current account deficits the argument that economic agents perceived the shock as temporary. Hence, one has to rely on alternative explanations, such as the effects induced by a fall in the world real rate of interest, to generate the possibility of a deficit. Marion and Svensson (1984b) show that the world real interest rate will fall following a permanent rise in oil prices if it is assumed that the marginal propensity of the Organization of Petroleum Exporting Countries (OPEC) to consume is less than that of the rest of the world. If the resulting increase in absorption in oil-importing countries dominates the drop in gross domestic product (GDP), a deficit will arise. When non-traded goods are introduced into the picture, however, Marion (1984) indicates that the direction of the change in the current account following a permanent oil shock depends critically on the relative production technologies in the traded and nontraded goods sectors.3
The constancy of the rate of time preference, which is assumed in all of these models, plays an important role, as suggested by Svensson and Razin (1983). They develop a many-good, two-period model, with no investment, to study the Harberger-Laursen-Metzler (hereafter H-L-M) effect. They show that, given identically homothetically weakly separable preferences, a rate of time preference that is an increasing function of the welfare level, as in Obstfeld (1980, 1982), implies that the current account improves following a terms of trade deterioration.
In contrast, the response of the current account in the context of optimizing monetary models with flexible exchange rates and investment seems to have received less attention. The difficulties encountered by real models in accounting for observed deficits in oil-importing countries suggest that this may be a fruitful line of research insofar as it could point to additional—that is, monetary—channels through which an oil shock could affect a small open economy.
The presence of money in itself, however, does not alter the picture. Fender and Nandakumar (1985) develop a two-period, two-good, Sidrausky-type model to study fiscal policy, the “Dutch disease,” and the effects of oil shocks. They find that a future increase in oil prices could, under some circumstances, generate a current account deficit. From this it follows that a permanent oil shock could also result in a deficit. But this outcome seems to derive from the presence of nontraded goods, along the lines suggested by Marion (1984). In fact, it is simple to show that if money enters separably into the utility function, money is only a “veil” in that the results of standard real models—for instance, Svensson (1984)—are reproduced (Vegh (1987a)). Clearly, this outcome is to be expected, since changes in the stock of real money that result from changes in wealth are brought about by movements in the exchange rate.
This paper shows that allowing for currency substitution substantially affects the results of real or domestic-money-only models. In the presence of currency substitution,4 a permanent oil shock could result in a current account deficit. Furthermore, the greater the economy’s dependence on oil—as measured by the level of pre-shock oil imports—the larger the deficit.5 In real models, the change in the current account does not depend on the initial level of oil imports because consumption drops by the same amount that real income does, thus leaving saving unaffected.6 When there is currency substitution, however, the possibility of a decrease in saving arises, which is financed by running down the stock of foreign money balances. This H-L-M effect depends on the magnitude of the fall in wealth, which in turn is dictated by the initial level of oil imports. The larger the decrease in saving, the more likely that it will offset the fall in investment, thus generating a current account deficit.
If the sign of the change in the current account is left aside, real models can also be interpreted as suggesting that, following a permanent oil shock, variations in investment dominate current account movements. As Fischer (1981) points out, however, the evidence does not bear out this prediction. Fischer (1981) shows that the mean absolute changes in the ratio of saving to GNP have been larger than those in the ratio of investment to GNP for both OECD and developing countries. Hence, an attractive feature of the currency substitution model is that it generates movements in both saving and investment.
The proposition that a terms of trade deterioration leads to a worsening of the current account finds empirical support in Khan and Knight (1983). They provide a formal analysis of the influence of external and internal factors on the current account of non-oil developing countries. Using pooled time-series cross-section data for a sample of 32 countries during 1973–80, they report, among other findings, that the effect of a change in the terms of trade on the current account is positive and statistically significant. More precisely, a 1 percent deterioration in the terms of trade would lead, on average, to a decline of about half a percentage point in the ratio of the current account to exports. Furthermore, changes in the terms of trade turn out to be the most important of the six explanatory variables considered.7
This paper proceeds as follows. Section 1 presents a two-period model of currency substitution. The inclusion of both currencies, which are the only assets, in the utility function is meant to capture the services that money provides other than being a store of value.8 This framework has been used by, among others, Calvo (1980, 1985) and Liviatan (1981). The implicit assumption is that, because of legal restrictions, domestic and foreign money are not perfect substitutes. A condition for the current account to deteriorate following a permanent oil shock is derived from the model. A high level of pre-shock oil imports ensures that this condition holds. In addition, the higher the initial level of oil imports, the larger the current account deficit. Section II, building upon an insight developed in the previous section, presents a study of a fixed-exchange-rate model and concludes that it reproduces the relevant results, even if the household no longer cares about foreign money, because, under fixed rates, domestic money acts as if it were foreign money. The possibility that, under fixed exchange rates, a deterioration in the terms of trade could lead to a deficit has already been pointed out by Michener (1984), in the context of an optimizing version of models of the monetary approach to the balance of payments. The much simpler model of this section isolates this effect and makes the point that, under a constant path of the fixed exchange rate, the workings of the currency substitution model and the fixed rates model are identical. Section III contains some concluding remarks.
I. A Currency Substitution Model
Consider a two-period small open economy that produces a final, tradable good whose world price is given and taken to be unity. Production of the good requires labor, capital, and oil. The latter has to be imported, since there is no domestic production. The price of oil in terms of foreign currency is q, which is also the relative price of oil in terms of the final good. Capital is given in the first period and can be augmented by investing so that
To specify the production side, one may resort to the dual functions (see Dixit and Norman (1980)) and follow the analysis developed by Svensson (1984). It is assumed that there exists a well-behaved concave production function given by
where xt stands for output of the final good, nt for full employment labor, and z, for oil input. Define the domestic product (which, in this model, is identically equal to the national product) in period t, Y t as
with kt and nt given.
The equilibrium level of investment is given by the solution to the following problem:
where et denotes the (flexible) nominal exchange rate and R = e1/e2 is the domestic nominal discount factor.9 If an interior solution is assumed, the optimality condition,
where
with
Under the assumption that oil and capital are cooperative factors, iq, which denotes the partial derivative of the investment function with respect to the price of oil in the second period, is negative (see Svensson (1984)).
The household faces the following maximization problem:10
subject to
where c, stands for consumption in period t, Mt and Ft for foreign and domestic money held in period t, respectively.
At an optimum, the following must hold:
Equations (1)-(6), together with the two money market equilibrium conditions,
If money market equilibnum is imposed on equations (5) and (6), it follows that, given
Substituting equation (4) into equations (1)-(3) and taking into account the money market equilibrium conditions, the following subsystem, which determines F1 F2, and C1, is obtained:
Equation (7) represents the balance of payments equilibrium condition for the first period. With equation (4), which relates second-period consumption and foreign money balances, taken into account, equation (8) can be viewed as the balance of payments equilibrium condition for the second period. equation (9) has a standard interpretation: since one unit of resources can either be held as a unit of foreign money during both periods or consumed in the first one, the utility derived, at the margin, from these two alternative uses has to be the same. Note, for further reference, that equation (9) implies that βσC1 – αF2 < 0 and σC1 – αF1 < 0.
By totally differentiating equations (7)-(9) and taking into account the optimal investment decision and the standard properties of the domestic product function, one can analyze the effects of changes in the price of oil on F1, F2, c1 and—using equation (4)—c2. Since the effects of a permanent rise in the price of oil consist of the added effects of a temporary and a future rise in the price of oil, it proves useful to begin by analyzing the latter two cases.
Temporary Increase in Oil Prices
A temporary oil increase is defined as dq1 > 0 and dq2 - 0. The following results obtain: where
where
It will be assumed that z1 = Z2 = Z; that is, initial oil imports are the same in both periods. equations (11) and (14) indicate that the current account worsens in the first period while it improves in the second. Consumption falls in both periods (equations (10) and (13)) so that the exchange rate depreciates by the same proportion. Since the oil price increase is temporary, the intuition behind these results lies in the desire of the household to smooth out consumption over time. Thus, whereas production falls by z in the first period, consumption decreases only by a fraction of z, as reflected in equation (10). Since investment is not affected, the current account worsens. In the second period, production remains unchanged but consumption decreases, thus generating a surplus.
The presence of currency substitution allows the household to decrease lifetime consumption by less than would otherwise be the case, as can be inferred from the fact that the fall in total consumption, given by the sum of equations (10) and (13), falls short of z—the magnitude by which wealth decreases—by the same amount that second-period foreign money balances fall. Although foreign money balances absorb part of the fall in wealth, the qualitative nature of the results is not affected when compared with those results obtained in real or domestic-money-only models. When the oil price increase is permanent, however, the role of foreign money balances in absorbing part of the fall in wealth becomes a crucial feature, as will be discussed in detail below.
Future Oil Price Increase
An (expected) future oil price increase is defined as dq,=0 and dq2>0. The following expressions obtain:
A future shock causes an improvement in the current account in the present (equation (16)) and a worsening in the future (equation (19)). It reduces future consumption (equation (18)) but has an ambiguous effect on present consumption (equation (15)). In the absence of currency substitution, or in real models, present consumption decreases by a fraction of the fall in wealth, which is given by z. This effect is the second term in equation (15). But now there is an additional effect, as represented by the first term in that equation. Why does iq affect the change in consumption? Note that a higher ? implies that there is a greater dependence on oil so that the negative wealth effect is larger. On the other hand, the magnitude of iq does not affect wealth since, at the margin, investment in physical capital has the same return as that in foreign money, which is zero in this case. Therefore, one has to conclude that some margin is broken in the current model. Indeed, note that, other things being equal, a higher iq would translate itself, on a one-to-one basis, into a higher current account surplus (that is, a higher F1). This is in fact all there is to it in real models. But, in the current model, the rise in F1 breaks the following margin:
Hence, either c1 rises and c2 falls, or c1 rises by more than c2 does. Recall that, by equation (4), c2 always moves in the same direction that F2 does; furthermore, it must be the case that the sum of the changes in c1, c2, and F2 have to add to zero since no wealth effect is involved. The implication is that c1 rises while F2 and c2 fall. In turn, the rise in c1 means that the current account surplus increases by less than on a one-to-one basis with the higher iq. There is now a new channel through which iq affects consumption and therefore the current account. Put differently, the higher current account surplus, which implies higher holdings of foreign currency, decreases their marginal utility and thus affects the above margin relating the marginal utilities of consumption across periods. Naturally, a similar condition holds for domestic money; that is.
This margin, however, is not affected by a higher iq since the stock of domestic money remains the same. The crucial ingredient is the presence of foreign currency. equation (21), however, suggests that under fixed exchange rates—where the stock of domestic money is endogenous and would be affected by a higher iq—consumption would have to adjust to restore the margin, thus affecting saving. In other words, condition (21) would be truly analogous to (20). That this is indeed the case will be proven in Section II.
Permanent Increase in Oil Prices
A permanent increase in oil prices is defined as dq1 = dq2 = dq > 0. The following holds:
A sufficient condition for C-B>0 is β>α/(σ + α), which seems very likely (with equal weights in the utility function, the condition becomes β > 1/2). It is assumed that this relationship holds. Hence, the coefficient of z in equation (22) is positive. As can be easily verified, this same condition is sufficient to ensure that (2B + A)/Γ, the coefficient of z in equation (23), is less than unity. equation (22) indicates that the change in the current account following a permanent rise in oil prices is ambiguous. This ambiguity stems from the fact that the change in present consumption (equation (23)) is affected by the magnitude of iq as discussed above, which implies that consumption declines by less than production falls, thus reducing saving. The reduction in saving is financed by a fall in second-period foreign balances. To see this, combine equations (4), (7), and (8) and differentiate to obtain
which implies, given that
Lifetime consumption declines by less than wealth does. In other words, the household uses part of its foreign currency holdings as a shock absorber. From equation (22), it follows that for the current account to worsen it must be true that
A high level of initial oil imports implies that this condition will hold and thus that the current account will deteriorate following a permanent rise in oil prices.11 (In particular, if the current account is initially balanced, a deficit will follow.) As can be easily checked from equation (22), this condition is also sufficient for present consumption to fall. equation (23) also shows that the deterioration of the current account will be greater the higher the initial level of oil imports. Intuitively, a higher initial level of oil imports implies that the wealth effect of a permanent rise in oil prices is stronger. (Recall that the reduction in wealth equals 2z.) The change in consumption depends on the variation in “permanent” wealth (z), which is also the amount by which production falls, as indicated by the second term in equation (23). The coefficient of ? in that term, however, is less than unity: consumption falls by less than production does, which implies that a higher z means a higher fall in saving. For a given change in investment, this implies a larger current account deficit.
Finally, note that equation (26) indicates that the current account worsens in the second period.12 Since the household has the option of reducing its financial wealth, the current account may in fact deteriorate in both periods.
In this section it has been shown that, in the context of currency substitution, the response of the current account to a permanent oil shock is contingent on oil dependency. This result is due, basically, to a H-L-M effect; namely, saving decreases in response to the terms of trade deterioration. The crucial role played in the model by the foreign currency makes it intuitively clear that similar results would obtain in a fixed-exchange-rate model. This issue is explored below.
II. A Fixed Exchange Rate Model
It was discussed above why equation (21) suggested the possibility that, in a regime of fixed exchange rates, similar results to those obtained under flexible rates in the currency substitution model could be reached. In a world of fixed rates, changes in the exchange rate cannot bring about equilibrium in the domestic money market. Rather the adjustment must come through quantities. The excess supply of real money balances owing to the decline in wealth will have to be “shipped abroad” through central bank reserves. Naturally, this mechanism is very much at the basis of the monetary approach to the balance of payments.13 It seems appropriate, then, to review briefly the results obtained under classical versions of the monetary approach, with money being the only asset.
In the simplest version, assuming there is some domestic production of oil, a rise in the price of any tradable good, in particular an imported input, increases the price level, thus raising money demand, which is assumed to depend on nominal income, and causes a balance of payments or current account surplus in the short run. There has to be some domestic production of oil to get any effect at all because no account is taken of the loss in real income. Now, if brought into the picture, the loss in real income will constitute a force toward a deficit since it decreases money demand. But, as shown by Caves and Jones (1981), if the economy produces any oil, the price effect will still dominate, assuming unitary income elasticity of the demand for money. There would be no effect at all if there is no domestic production because the two effects would exactly cancel each other out.
Rodriguez (1976) provides an early attempt at generating a deficit in the balance of payments. In his model, expenditures respond to permanent income, but the latter is adjusted only with a lag when the shock hits. Real balances, then, play the role of shock absorber in the short run. The mechanism by which the deficit comes about is thus different from the one being discussed, as has been noted by Michener (1984). In optimization models, it is precisely the fact that consumers immediately revise their wealth downward that induces them to reduce their money holdings.
Jones (1979) relies on world equilibrium considerations to bring about a deficit. He argues that, with a given world supply of money, the price level would be unchanged so that we would be left with the terms of trade effect, which calls for a deficit. In the present model, the price level relevant for the household also stays constant since it does not consume oil directly.14 We are then left with a wealth effect, in addition to the investment substitution effect.
Michener (1984) develops an optimizing version of models of the monetary approach to the balance of payments in which he discusses, among other issues, the effect of a change in the terms of trade on the balance of payments. The model includes an exportable, an importable, and a nontraded good. Michener (1984) notes that a sufficiently strong income effect could provoke a fall in the price index, which in turn implies that steady state nominal balances must decline. The model developed here can be viewed as a simpler version of Michener’s and its objective is to isolate the effect of a terms of trade shock. The model does, however, allow for investment and concentrates on an intermediate good. Nevertheless, its main purpose remains that of illustrating the analogy with the currency substitution model.
The model remains the same as before, but now only domestic real balances enter the utility function. The foreign exchange authority is in charge of the transactions with foreigners. As pointed out by Helpman and Razin (1979), the foreign exchange authority, under fixed rates, serves only as an intermediary between the household and foreigners, while, under floating rates, the private sector transacts directly with foreigners. In this way, consistency is achieved in formulating the same problem under alternative exchange rate regimes.
The household faces the following optimization problem:
subject to
where ēt denotes the (fixed) exchange rate,
At an optimum, the following must hold:
Equations (27)-(32) form a system of six equations in six unknowns: M1, M2, c1, c2, F1 and F2. From substituting equations (27) and (28) into equations (29) and (30) and making use of the fact that
Note that if ē1= ē2—that is, the exchange rate is constant over time (as opposed to a crawling peg, for instance)—equations (29), (33), and (34) form the same system as before (with δ in lieu of σ), given by equations (7)-(9). The same system results because when the household uses domestic currency, the fixed exchange rate ensures that its value in terms of foreign currency remains unchanged. If there is a high dependence on oil, a permanent oil shock will result in a worsening of the current account, which will reduce the money supply in both periods. Under fixed exchange rates, domestic real balances act as if they were foreign money balances and are able to perform the shock-absorber role that they cannot under flexible rates.
As suggested earlier, a key difference from standard versions of the monetary approach to the balance of payments is that there is no price level effect in the present model because oil is an intermediate good; only the wealth effect remains. The wealth effect calls for a reduction in real balances and constitutes, therefore, a force toward a current account, or balance of payments, deficit. On the other hand, the fall in investment implies, other things being equal, a shift toward foreign investment, which in this model is equivalent to the acquisition of foreign money since there are no other foreign assets. A large dependence on oil makes it more likely that the former effect will prevail.
III. Conclusions
The response of the current account to supply shocks in the context of models that incorporate saving-investment behavior has received considerable attention in the literature. These real models predict that a permanent supply shock from an increase in oil prices would result in a current account surplus since the terms of trade deterioration does not affect saving while investment falls. The evidence, however, suggests that the current account usually worsens in response to a terms of trade deterioration.
This paper has analyzed whether monetary considerations would alter the standard real-model results. It has shown that, in the context of a monetary model with flexible exchange rates and currency substitution, a current account deficit could now arise following a permanent worsening of the terms of trade brought about by higher oil prices. The availability of foreign money enables the public to absorb part of the loss in wealth in the form of lower foreign money balances.15 As a consequence, consumption does not fall by the full amount that real income does. The terms of trade deterioration leads therefore to a decrease in saving. If the dependence of the economy on oil is high, the fall in saving prevails over the fall in investment, thus causing a current account deficit. Furthermore, the higher the initial level of oil imports, the larger the current account deficit.
It has also been shown that identical results obtain in the presence of fixed exchange rates even if there is no currency substitution. The fixed exchange rate allows domestic money to perform the same shock-absorber role that foreign money plays in the currency substitution model. Under high dependence on oil, then, higher oil prices would lead to a current account deficit. The opposite would happen in standard versions of the monetary approach to the balance of payments.
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Mr. Vegh, an economist in the European Department, was an economist in the Research Department when this paper was written. He holds a doctorate from the University of Chicago.
This paper is based in part on the author’s doctoral dissertation at the University of Chicago. The author would like to thank the members of his thesis committee, Joshua Aizenman, Jacob Frenkel, and John Huizinga, as well as Guillermo Calvo, Pablo Guidotti, Lars Svensson, and colleagues in the Fund for helpful comments and suggestions.
Oil and capital are assumed to be complements, in the sense that their cross derivative is positive. This assumption is supported by econometric evidence as pointed out by Sachs (1981).
See, for instance. Sachs (1981) for evidence.
Ostry (1988; in this issue of Staff Papers) also notes that the presence of nontraded goods causes an ambiguous response of the current account to a permanent deterioration in the terms of trade.
For evidence on currency substitution in small open economies, see, for instance, Ortiz (1983), Ramirez-Rojas (1985), and El-Erian (1988).
Sachs (1981) reports that as far as oil-importing countries are concerned, the change in the current account relative to gross national product (GNP) is negatively correlated with the pre-shock ratio of oil imports to GNP—the correlation coefficient being -0.7—for the period 1968–79. Sachs (1981) also finds that for oil-importing members of the Organization for Economic Cooperation and Development (OECD), a 1 percentage point greater dependence on oil in 1968–73 corresponds to a drop in the ratio of the current account to GNP of 0.9 percentage points in 1974–79. Sachs (1981) claims that these results come primarily from the first years after the shock.
The effect of the initial level of oil imports on the partial derivative of the investment function, which is ambiguous, is disregarded.
As measured by the relevant Beta coefficients. The other explanatory variables are the rate of growth of industrial countries, the level of foreign real interest rates, the change in real effective exchange rates, the ratio of domestic fiscal deficits to GDP, and a time trend.
This setup has been adopted for simplicity. The basic results would not change if bonds were allowed for and both monies were viewed as reducing transaction costs, as in Vegh (1987b), because, for the issues being discussed in this paper, the key ingredient is that money be valued and not why it is valued. When dealing with issues such as the optimal inflation tax, however, the question of why money is valued plays a critical role in determining the outcome of the analysis. Hence, it becomes essential that the analysis be explicit on this point (see Vegh (1987b) for a discussion).
The foreign price level is assumed to be constant.
The logarithmic specification of the utility function is adopted because it simplifies the algebraic manipulations. A general formulation, however, would lead to similar results.
For simplicity, the level of initial oil imports is being treated as a parameter whose value does not affect the initial equilibrium. The implicit experiment one has in mind is that of a change in technology such that, at the initial oil price, the input composition is altered, but the aggregate levels of production and investment remain unchanged. Under these circumstances, the coefficients A, B, and C do not vary with z. Note that it is not necessary that the new technology generates the same investment function but that, at the initial oil price, the level and slope be the same, which also ensures that iq does not vary with z.
The coefficient of ? is taken to be positive. Note that equal weights in the utility function are a sufficient, though not necessary, condition to ensure this result.
The classic collection of papers on the subject is Frenkel and Johnson (1976). See also International Monetary Fund (1977).
In real models, Svensson (1984) makes the point that if oil is consumed directly (heat or gasoline), the effect on the current account of a permanent oil shock becomes ambiguous owing to substitution effects in consumption.
Since one can view the stock of foreign money as being equivalent to a stock of a durable tradable good, the present analysis suggests that a real model with a durable consumption good could generate similar implications concerning the response of the current account to a permanent oil price increase. (I am indebted to Guillermo Calvo for this point.)