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The terms of trade between oil importers
Journal of International Economics 20 (1986) 99-113. North-Holland
THE TERMS OF TRADE BETWEEN
OIL IMPORTERS
N a n c y Peregrim M A R I O N Dartmouth College, Hanooer, NH 03755, USA
Lars E.O. S V E N S S O N * Institute for International Economic Studies, Stockholm, Sweden
Received April 1983, revised version received May 1985 An intertemporal model of OPEC and two large-country oil importers is used to show that asymmetries between importers cause oil price changes to alter the terms of trade between them in systematic ways. For example, differences in oil dependence, marginal propensities to save, international debt positions, factor substitutability, trade in capital goods and wage setting behavior can all influence the final-goods terms of trade between oil importers in predictable ways when oil prices change.
1. Introduction An oil price change not only alters an oil importer's terms of trade with oil exporters but can also alter its competitive position with fellow oil importers. T h e latter occurs because oil price changes can affect a country's final-goods terms of trade, that is, the price of final-goods exportables in terms of finalgoods importables. In this p a p e r we examine whether oil price shocks lead to predictable changes in the competitive positions of two oil importers. O u r analysis indicates that a knowledge of the asymmetries between oil importers is crucial for predicting the direction of change in their final-goods terms of trade. In the presence of some asymmetries, such as differences in the degree of oil dependence, an oil price change will have no effect on the terms of trade between importers unless c o n s u m e r preferences are biased towards ownproduced goods. In the presence of other asymmetries, such as differences in the degree of substitutability in production, differences in the pattern of trade in capital goods, or differences in wage behavior, the final-goods terms of trade are affected even if c o n s u m e r preferences are not biased. We shall show *This paper is adapted from Marion and Svensson (1983). We are grateful to seminar participants at the National Bureau Of Economic Research, the Institute for International Economic Studies in Stockholm, Hebrew University of Jerusalem, and Tel-Aviv University for their helpful comments. Especially we would like to thank Michael Bruno, Elhanan Helpman, Torsten Persson, Assaf Razin, Michael Schmid and several anonymous referees. Financial support from the Haney Fund is gratefully acknowledged. 0022-1996/86/$3.50 © 1986, Elsevier Science Publishers B.V. (North-Holland)
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that the importer with fewer substitution possibilities then always faces a decline in its final-goods terms of trade if oil prices increase. The oil importer that is a d o m i n a n t supplier of capital goods always faces a change in its terms of trade that is positively correlated with the response of investment d e m a n d to the change in oil prices. The oil importer that has rigid real wages and suffers a fall in e m p l o y m e n t improves its terms of trade if oil prices increase. O u r analysis of the terms-of-trade response is conducted with the aid of an intertemporal model of O P E C and two oil importers. 1 The model and the world equilibrium are set out in section 2. In section 3, the effect of an oil price increase on the final-goods terms of trade is derived. All results are symmetric in that the effect of an oil price decrease merely involves a change in sign. Section 4 shows how the presence of certain asymmetries a m o n g oil importers influences the final-goods terms of trade between them when oil prices change.
2. Three countries and world equilibrium Consider a world of three countries, called the h o m e country, the foreign c o u n t r y and O P E C . There are two dates, indexed t = 1 and 2, which are called the present and the future. Three goods are p r o d u c e d in the present period: (1) h o m e final goods, p r o d u c e d exclusively in the h o m e country; (2) foreign final goods, p r o d u c e d exclusively in the foreign country; and (3) oil, p r o d u c e d exclusively in O P E C . T w o g o o d s are p r o d u c e d in the future: a c o m m o n final g o o d p r o d u c e d in the h o m e and foreign countries, and oil in O P E C . The assumption of a c o m m o n final g o o d in the future greatly simplifies the analysis and is permissible given our focus on the current terms of trade between oil importers. 2 1Three-country world equilibrium models have previously been constructed by Sehmid (1980), Krugman (1983) and Sachs (1983), but they differ considerably from the one developed here. In Schmid's model there is no capital accumulation nor is there a role for the world interest rate. It is also assumed that both oil importers produce the same final goods, so relative price changes induced by oil price increases are ignored. Krugman considers the effect of oil price increases on the exchange rate between two industrial countries. His model combines interesting aspects of a goods-market and an assetmarket view of the exe"hangerate, and examines how OPEC's spending shares and asset-holding shares affect the exchange rate in the short and long run. However, his model relies on very simplitied behavioral assumptions, some of which are not quite consistent with maximizing behavior. Sachs' model of OPEC and two industrial oil importers is intertemporal in nature and gives an important role to capital accumulation and the world interest rate in the adjustment process. However, his model is too complicated to solve analytically, and is instead examined by simulation methods. 2Assuming a common final good in the future essentially means assuming that future home and final goods are perfect substitutes in either consumption or production, so that the future final-goods terms of trade are fixed. Changes in an endogenous relative price between future home and foreign goods seem to have no systematic effect on the present final-goods terms of trade.
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In the present period, the n o n - O P E C countries consume home and foreign goods. They can also use home and foreign goods for investment in order to increase their future capital stocks. In the future, both countries consume final goods. To capture the lag in O P E C consumption of its dramatically increased oil revenues and the corresponding high marginal propensity to save, we invoke the simplifying assumption that all O P E C consumption is confined to the future. None of our results would be changed by allowing O P E C to consume in the present as long as OPEC's marginal propensity to consume home and foreign goods is sufficiently smaller than that of the other two countries) Oil is used as an input in the production of home and foreign final goods. O P E C sets oil prices exogenously according to the Hotelling Rule and supplies whatever quantity is demanded at these prices. Equivalently, O P E C can be considered as controlling the total stock of exhaustible oil and letting it be priced competitively. All three countries can trade goods on the world market at each date. They also have access to a common world credit market, where home and foreign bonds are perfect substitutes. 4 In the present, no country has inherited debt from the past. The model is specified using prices expressed in present-value terms, s The home country's output is chosen as the numeraire in period 1, so its price Ph is set at unity. The price of foreign final goods in terms of home goods is P = Pf/Ph" This is the reciprocal of the home country's final-goods terms of trade. We shall refer to an increase (decrease) in p as a deterioration (improvement) in the home country's final-goods terms of trade. The price of the common final good is chosen as the numeraire in period 2, so p 2 = 1. The present value of future final goods in terms of currently-produced home goods is the discount factor 6, which is identical to the inverse of one plus the (home goods real) rate of interest (6 =(1 +r)-1). The present-value price of oil in terms of home goods is ql =q; its current-value price in period 2 is q2 =q(1 + r ) = q / 6 . Hence, oil prices follow the Hotelling Rule. Let us now examine the behavior of the home country, modeling first its production side. Let x t = f * ( k t, lt, z ~) denote its well-behaved concave production function at date t, where x t is output of home goods, k t the home 3Of course, if OPEC spending in the present was skewed strongly towards one importer, it could influence the terms of trade between oil importers. See Krugman (1983). Also, the assumption of a very high marginal propensity to save for OPEC, while certainly reasonable for the first oil price increase in 1973-1974, is much less reasonable for an analysis of the oil price decreases in the 1980s. 4The assumption that allows asset trade to be suppressed is not merely that all countries have access to a common world capital market, but also that there are no shocks to technology,no threats of repudiation and no dangers of exchange controls which create uncertainty and hence render the liabilities of the differentcountries imperfectsubstitutes. SFor a more extensivediscussion of these kind of intemporal models, see for instance Marion and Svensson (1984).
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country's capital stock, It its employment level, and z t its input (import)- or oil. Firms operate competitively. We can then represent the production side by means of the GDP functions, Yr(1,qt, kt, lt) defined as Yt(1,qt, kt, lt)= max { x ' - q'z':x t = f(k', ~, z')}. Using standard properties of G D P functions, we can express home goods supply and the home country's import of oil as x ' = Y~t and
z'= - Y~,
(2.1)
where Y] and ~ are the partial derivatives of the G D P function (Y~t denotes OYt/OPh). With respect to employment, we assume that labor is fixed in total supply within the home country. Flexible wages ensure a given full employment level,/t, at each date. In section 4 we shall consider rigid wages and variable employment as well. We next specify the home country's investment behavior. Since the home country can increase its future capital stock by investing today, we have k2= k t + i t, where i t is investment in the present and k t is the present capital stock, which is predetermined and exogenously given. Both home and foreign goods are used as investment goods. A simple way to model this is to assume that the capital stock consists of home and foreign goods in the fixed proportions ~, and l - y , respectively (0<~<1). Hence, the cost of a capital good is y +(1-y)p. The home country's investment demand, I I(p, 6, q, k 1,12), is given by the level of investment that maximizes the excess of the present value of future G D P over the cost of present investment. The investment function fulfills the in:st-order condition:
6 y2(1, q/6, k t + It(p, 6, q, k t, lZ), 12)= ), + (1 -),)p,
(2.2)
which says that firms invest up to the point where the present value of the future marginal product of capital (6 Y~) equals the cost of present investment goods. Let us next consider the home country's demand side. We assume that the home country can be represented by a well-behaved utility function U(Ch, Cf, C2), where Ch and cf are the home country's consumption of home and foreign goods in the present and c 2 is its consumption of final goods in the future. We define the corresponding present value expenditure function in terms of home goods as E(1, p, 6, u) = min {% + per + 6c 2: U(%, cf, c 2) > u}. The expenditure function gives the minimum present value of expenditure on consumption required to reach a given utility level at given prices. By standard properties of expenditure functions, the partial derivative of the expenditure function with respect to the price of a good is equal to the Hicksian compensated demand function for that good. That is,
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N.P. Marion and L.E.O. Soensson, Terms of trade between oil importers Ch=E1,
cf=Ep
and
c2--Ea.
(2.3)
The home country's intertemporal budget constraint expressed in home goods can now be written as E(1, p, 6, u) + D' + (1 - y)p] I x(p, 6, q) = Y 1(1, q) + 6 y2(1, q/6,1 l(p, 6, q)), (2.4) where we have suppressed labor inputs and the present capital stock. The budget constraint states that the present value of expenditure on consumption and investment equals the present value of GDP. The budget constraint can alternatively be written as equating the present value of expenditure on consumption to the home country's wealth, W, defined as W = Y l - [ y + ( 1 - y ) p ] I I + 6 Y 2 , which is the sum of present GDP, net of investment, and the present value of future GDP. This completes our discussion of the home country. Let us now briefly examine the foreign country. Its variables and functions will be denoted by an asterisk. The foreign country produces foreign goods in the present period and final goods in the future using capital, labor and imported oil. Let Y*t(pt, qt, k*t,l*t) denote its G D P functions measured in home goods. 6 Its investment demand, l*~(p, 6, q, k *l, /,2), will fulfill: 6 Y~2(1, q/6, k *~ +I*t(p, 6, q, k *~, 1,2), 1,2) = y , +(1 - 7*)p,
(2.5)
where y*(0_<_y*=
(2.6)
where we have again suppressed labor inputs and the present capital stock. Finally, let us briefly examine OPEC, denoting its variables with an 'o' superscript. Since all O P E C consumption is confined to the future, we can write OPEC's intertemporal budget constraint as 6c °2 = qS, (2.7) 6Note that the foreign GDP function Y*~(p,ql,k*~,l*~) gives present GDP in terms of home goods while the function Y*2(l,q2,k*2,1.2) gives future foreign GDP in terms of future l'mal goods. Note also that the first argument in the GDP function Y*~ is the relative price of foreign goods.
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where c°2 is OPEC's consumption of future goods and S is the total stock of oil produced in the two periods. In equilibrium, total oil use equals total production: S t a g 1 ,-[-Z.1 ..}-Z2 -[..Z.2.
(2.8)
Let us next look at a world equilibrium, where the oil market clears and the final-goods markets clear at each date. Due to Walras' Law, we can disregard one of the market equilibria, and we choose to disregard the future final-goods market. Consequently, a world equilibrium can be represented by the three countries' budget constraints, (2.4), (2.6) and (2.7), and by the following set of market equilibria: equilibrium in the oil market, (2.8), equilibrium in the market for currently-produced home final goods, E 1 +E* + y I I + y . i . t = x 1,
(2.9)
and equilibrium in the market for foreign goods. E2 + E~ + (1 - ~,)I~+ (1 - y,)i,1 = x,X,
(2.10)
where world spending on each importer's current output equals the supply. For the exogenous oil price q and given full employment levels in both countries, eqs. (2.4) and (2.6)--(2.10) determine welfare levels in each oil importer, u and u*, the discount factor, 6, the present terms of trade between foreign and home final goods, p, OPEC's future consumption, c02, and the amount of oil extracted, S. 3. The final-goods terms of trade
In this section we examine how an increase in today's oil price alters the competitive position of two oil importers vis-fi-vis each other. We proceed by totally differentiating the market-clearing equations for home and foreign final goods, eqs. (2.9) and (2.10). In the process, we take into account the welfare effects of an oil price increase which can be derived by differentiating eqs. (2.4) and (2.6). We get:
?h, < df~
dfpJ
dp
LSfJ
(3.1)
where on the left-hand side dha is the partial derivative of the world excess demand for home goods with respect to the discount factor, dhp is the partial with respect to the price of foreign goods, and dr~ and dfp denote the corresponding partials of the world excess demand for foreign goods. On the
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right-hand side, Sh is the change in the world excess supply of home goods following the oil price increase, given a constant discount factor and price of foreign goods, and sr is the corresponding change in the world excess supply of foreign goods. The partials in (3.1) are given by cumbersome but easily interpreted expressions which are found in the appendix. The solution to (3.1) is dc~= (dfps h -- dhpSf)/ A ~ 0
(3.2)
dp = (dhrSr-- drrsQ/A ~ O, + + -
(3.3)
and
where A is the determinant A =dh~ do,-dhp df,~. We assume gross substitutability, which is sufficient for stability and makes A <0. 7 An oil price increase generally has an ambiguous effect on the discount factor and the terms of trade between the two oil importers. Now consider the case where an oil price increase leads to an incipient excess supply of both home and foreign goods, implying excess world savings in the present. This outcome occurs if the contraction in home and foreign output is not severe enough to offset reduced world demand for these outputs. In this case, Sh and sr are positive. It follows that the discount factor increases; excess saving in the present period bids down the interest rate. a We shall take a fall in the rate of interest to be the 'normal' case in the discussion that follows. An increase in the oil price still has an ambiguous impact on the terms of trade, however. By rewriting (3.3) and assuming sh, sf > 0, we get: d p = ( Sf / Sh - -
df,~/dh~) dh6Sh/ A .
(3.4)
++-It follows that the sign of the foreign price change is given by sign dp = sign (du/dh, - sf/s~).
(3.5)
VThe assumption of gross substitutability implies that dhp>0 and dfp<0. That is, an increase in the relative price of foreign goods raises world excess demand for home goods and reduces world excessdemand for foreign goods. Similarly,it implies dh~, dr8> 0. SAn excesssupply of both home and foreign goods also leads to a rise in the foreign goods discount factor (~/p) and thus a fall in the foreign goods real rate of interest. Formally, let p'= I/p and 6'=6/p. Then d~5'=(dfp,Sh-d~p.sf)/A'>O if dfp,>0, dhp,<0 and A'=dhr, drp,--dhp,dfv>0 by gross substitutability, and Sh,sf>O by assumption. See Marion and Svensson (1984) for further discussion of the effecton world interest rates of oil price changes.
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This expression can be nicely interpreted. The ratio (dfddhn) gives the relative world excess demand for foreign goods from the change in the discount factor, at constant foreign goods prices. The ratio (Sf/Sh) gives the relative world excess supply of foreign goods from the oil price increase, at constant discount factor and foreign goods price. If the relative world excess demand for foreign goods exceeds the relative world excess supply, the price of foreign goods must rise.
4. Differences across oil importers and the relative price of foreign goods Clearly, if the home and foreign countries are alike in every respect, there will be no change in the relative price of foreign goods, and the two oil importers will have unaltered competitive positions vis-a-vis each other when OPEC raises today's oil price. In this section we look at how differences between the home and foreign oil importer influence the way the foreign goods price responds to an oil price increase. A number of asymmetries can be examined in order to assess their impact on the final-goods terms of trade when there is an oil price increase. We choose to focus on four: (1) the degree of oil dependence; (2) the degree of substitutability in production; (3) the pattern of trade in capital goods; and (4) the employment response. We shall examine the implications of each asymmetry in turn. Our method will be to assume that the home and foreign countries are identical except in one respect at a time. Let the initial situation be one where the relative price of foreign goods equals unity, p = 1.
(4.1)
Suppose that the home country is more oil dependent in each period than the foreign country, in the sense that z t > z *t, for t = 1, 2.
(4.2)
The two countries are alike in other relevant respects. That is, we assume that Exn=E* 6, Epr=E* 6, I6=I'~ 1, I~=I *z,
x q = x *t
and
bZ=b *z. (4.3)
In particular, we assume that in spite of the home country using more oil, the production substitution effects xq and x* are equal. (See also footnote 12 below.) Differences in substitution effects are treated separately below. In addition, we assume that both countries have the same marginal propensities
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to consume their own-produced good and the same propensities to consume the other country's final good, so that
,1 _ , * l
( hW -- ( fW
and
C~w =ch*lw.
(4.4)
Finally, we assume that both countries invest symmetrically in the sense that each uses the same fraction of own-produced output in its capital stock, so that ?,=(1-7*)-
(4.5)
It follows from (4.1)-(4.5) and the appendix that dh,~-- df,~= (c,1h w - C~w)(q/6) (z 2 - z* 2) and .X ,1 .1 Sh--Sf=((h),,--(.V)(-~ ---~_ ~ 1 + Z ""~ --Z*2).
(4.6)
If oil importers consume symmetrically across home and foreign final goods, i.e. if C~w=C~w, then dh,5=df~>0, s h = s f > 0 , and by (3.5) we have d p = 0 ; differences in oil dependence have no effect on the terms of trade between oil importers. The intuitive reason is straightforward. Even if an increase in today's oil price causes a greater welfare loss for the more oildependent home economy, that translates into an equal drop in demand for home and foreign goods if there are no consumption biases. Hence there will be no change in the relative price of final goods. This result is the same as the one in Sachs (1981). He analyzes a model with a single final good, which is equivalent to assuming that the final-goods terms of trade are given. In terms of our model, this would be the case where goods are perfect substitutes in each period and hence there are no biases in consumption. Now consider the case where each oil importer has a bias toward its ownproduced good, so that ~w'l_---*l'--,,t~fwl-~fw_---*l,,hw.This bias could be due to transport costs, for instance. If consumers have such a preference for their own-produced goods, then d h ~ - d f e > 0 , s h - s f > O and thus d p ~ 0 ; differences in oil dependence can affect the terms of trade between oil importers, but the direction of effect is uncertain. The source of the ambiguity arises from the fact that an increase in today's oil price does not necessarily cause a bigger welfare loss for the more oil dependent importer. To see this, we differentiate (2.4) and (2.6), which gives US
E, d u = - ( z l + z Z ) d q + [ b 2 +(q/<~)z2]d¢5-[E~,+(1-y)IX] dp
(4.7)
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and E~*du* = - (z* z + z.2) dq + ['b.2 + (q/6)z .2] d6 + [E,, + ( 1 - 7)I 1] dp, (4.8) where the expressions E,,du and E*du* are wealth-equivalent welfare changes. 9 Examining (4.7) and (4.8), we see that an increase in today's oil price causes a bigger deterioration in the oil terms of trade for the more oildependent importer since ] - ( z z + z 2) dql > l - ( z .1 + z .2) dq]. However, it also raises the discount factor. An increase in the discount factor for a given oil price will, via Hotellings Rule, decrease the future price of oil and hence most benefit the more oil-dependent importer, (q/6)z 2 d r > ( q / 6 ) z .2 dr. N o w if this latter benefit is relatively modest, 1° then on net an increase in today's oil price will cause a bigger welfare loss for the more oil-dependent country. Then, given the o w n - g o o d bias in consumption, there will be a bigger d r o p in c o n s u m p t i o n of h o m e goods relative to foreign goods and the relative price of foreign g o o d s will increase. The m o r e oil-dependent oil importer suffers a loss in competitiveness vis-/L-vis its industrial trading partner. This loss exacerbates the direct welfare cost already imposed by the oil price increase. In summary, differences in oil dependence can cause an oil price increase to alter the terms of trade between importers t h r o u g h differential welfare effects if c o n s u m e r preferences are biased. It can also be shown that certain other asymmetries between oil importers, such as differences in marginal propensities to save or in international debt positions, can also influence the terms of trade between them t h r o u g h the welfare channel if c o n s u m e r preferences are biased.Z z 9The expressions E, and E* in (4.7) and (4.8) are the partials of the expenditure functions with respect to welfare levels; they equal the inverse of the marginal utilities of wealth and are positive. 1°If the two oil importers have the same degree of oil dependence in the future (z2=z*2), this latter effect is eliminated. lZSee the discussion in Marion and Svensson (1983). For example, suppose that two importers are similar except that the home country has a larger (smaller) propensity to consume (save) than the foreign country. This assumption can be represented by Crw--~Chw,*l-J" " Chw--~Cfw,*I _ I . 0<~< 1. It follows that Sh--Sr=(ZZ+ZZ)(1--Ot)(C~w--C~w) and dha-dfa=[b2+(q/6)z"](l-~)(e~w-C~w) and dpX0. Again, the source of ambiguity in the terms-of-trade response is due to the fact that an increase in today's oil price has an uncertain impact on the welfare of the importers. It worsens their oil terms of trade but also lowers the rate of interest, which makes them better off by lowering the future oil price and lessening their debt burden. If on net welfare is reduced by today's oil price increase, then there will be a bigger drop in the consumption of home goods relative to foreign goods because of the home country's higher MPC, and the home country will face a deterioration in its final-goods terms of trade. Consider next the case where two oil importers are similar except for their net creditor/debtor positions. Let the home country have a larger net creditor or smaller net debtor position at present. This implies th~t bI >b .1 and b"0 and dha-dfa=(chw-efw)(b2-b*"). Given biased consumer preferences towards own-produced goods, then dhr-dfa<0 and dp>0. The country
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N o w let us e x a m i n e a n a s y m m e t r y t h a t affects the terms of t r a d e t h r o u g h the p r o d u c t i o n side. S u p p o s e the two oil i m p o r t e r s are similar except for the degree of s u b s t i t u t a b i l i t y in p r o d u c t i o n between oil a n d d o m e s t i c factors. Let the h o m e c o u n t r y have less such s u b s t i t u t a b i l i t y at present. As a result, it will experience a s m a l l e r d r o p in the f u l l - e m p l o y m e n t level of c u r r e n t o u t p u t following an oil price increase: x2 x.I
(4.9)
It follows t h a t d f r = d u ~ > 0 a n d Sh--Se>0, SO t h a t b y (3.5) we have d p > 0 . T h e c o u n t r y with fewer s u b s t i t u t i o n possibilities - - in this case the h o m e c o u n t r y - - suffers a decline in its final-goods terms of trade. T h e r e a s o n is t h a t there is a smaller decline in p r o d u c t i o n of h o m e goods, a n d the relative excess d e m a n d for foreign g o o d s p u t s u p w a r d pressure on p. O u r results here agree with those of Obstfeld (1980). C o n s i d e r next a t h i r d a s y m m e t r y between oil i m p o r t e r s , n a m e l y their p a t t e r n of t r a d e in c a p i t a l goods. U p to this p o i n t we have a s s u m e d t h a t each c o u n t r y uses the s a m e fraction of o w n - p r o d u c e d g o o d s for investment, with y * = l - - y . S u p p o s e we relax this a s s u m p t i o n a n d allow the h o m e c o u n t r y to use a g r e a t e r fraction of o w n - p r o d u c e d g o o d s as capital goods. This implies t h a t y*>(1 -y).
(4.10)
(In the limit y = y * = 1 a n d o n l y h o m e g o o d s are used as c a p i t a l goods; the with the larger net creditor position faces a deterioration in its final-goods terms of trade. This is because the oil price increase lowers the rate of interest, generating a bigger welfare loss for the creditor country. Given biased preferences, there will be a larger fall in the consumption of home goods and hence upward pressure on the relative price of foreign goods. Of course, should there be no consumer biases, then an increase in today's oil price should not affect the terms of trade between two oil importers even if they differ in their marginal propensities to consume or in their international credit positions. 12Assume that date 1 production of home goods is separable between an aggregate of domestic capital and labor, o(k,l), and oil input, z. That is, the production function fulfills x=f(k,l,z)=g(o(k,l),z). Note that if g(.) and 0(.) are constant returns to scale, so is f(.). In particular, with this technology, frequently assumed in the literature, capital, labor and oil are all cooperative in the sense of having positive cross partials. With full employment of labor, only x and z vary. By standard results we have ~2=0~. and ~= - ~ , where ~ denotes the rate of change dx/x, etc., 0 is the cost share of oil in the value of output of home goods, and ~ (defined positive) is the elasticity of demand for oil with respect to the relative oil price. Furthermore, ~ equals or/(1-0), where ¢ is the elasticity of substitution between oil and the domestic aggregate factor o. Hence, we have x=-[0/(l-0)]~r~, and it follows that for a given oil price increase and a given output level, the absolute response in output is smaller the smaller the elasticity of substitution. Note that a difference in oil dependence (4.2) together with the similarity assumption (4.3) is equivalent to assuming that the elasticity of substitution in home-goods production is smaller than that in foreign-goods production.
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home country exports capital goods and the foreign country imports them.) It follows that dh~-- dfn > 0, s h - sf > 0 and that dp ~ 0. An increase in the oil price at constant discount factor will reduce investment demand if capital and oil are cooperative in future production, in the sense that the corresponding cross partial f~, of the production function is positive. At the same time, the induced increase in the discount factor (a drop in the real rate of interest) stimulates investment demand. If on net investment demand is depressed, there will be a bigger drop in demand for home goods relative to foreign goods since the home country is the larger supplier of capital goods. Consequently the relative price of foreign goods rises. The home country faces a deterioration in its final-goods terms of trade. On the other hand, should the home country produce capital goods which are considered to be non-cooperative with oil in future production (fg~ < 0), then investment demand will be stimulated by the oil price rise and the home country will experience an improvement in its final-goods terms of trade. So far we have assumed that both oil importers have flexible wages and full employment in the present and the future. Let us finally examine what happens when the countries differ in their wage behavior. Consider the case where the home country has rigid wages and variable employment in the present period. Suppose that the wage in the home country is presently fixed in terms of home goods, i.e. wages are indexed to the GDP deflator. The level of employment is then given by the condition that the demand price for labor, Y], equals the given wage w1. This condition determines the present employment function L~(w ~, q~, k~), which fulfills:
Y~( I, ql, k 1, L I(w 1, ql, kl)) = w1.
(4.11)
The change in the home country's present employment level in response to an oil price increase is dl I = L~ dq < O.
(4.12)
Employment falls if labor and oil are cooperative. 13'x4 Assuming that the 13We have Lqt = - YtJY~t0 if labor and oil are cooperative factors (f~.>0) and Y]~<0 by the concavity of the G D P function. 14The home country's welfare is directly influenced by this drop in employment. Specifically, its welfare in (4.7) is modified to E, du = w I d/t - ( z I + z 2) dq + ( b 2 +q/~)z 2) d6 - ( E n + ( 1 -~/)I 1) dp. The change in welfare now includes a negative employment effect, w ~ dP, the drop in G D P due to the fall in employment. Note that it is crucial here that leisure is not an argument of the utility function. If it is, and the initial level of wages is the equilibrium one, there is no first-order welfare effect of employment changes.
N.P. Marion and L.E.O. Svensson, Terms of trade between oil importers
111
two oil importers are alike in all relevant aspects except the employment response, we have dh~=drn>0 and Sh--Sf<0. ~5 By (3.4) we can then write dp = dh~ (s r - s h ) / A < O, (+) (+) (_)
(4.13)
which says that the foreign goods price falls. Since the oil price increase causes employment in the home country to fall, there is a greater drop in the production of home goods relative to the production of foreign goods. The relative excess supply of foreign goods puts downward pressure on foreign prices. Consequently with an oil price increase, the oil importer with rigid real wages experiences a welfare loss due to reduced employment but a final-goods terms of trade gain. Now consider a more c o m m o n form of wage indexation, where the wage in the home country is indexed to a consumer price index (CPI) rather than to the price of home goods. ~6 Let co1 denote this given real wage. Let the price index nl(l,p) denote the present C P I in terms of home goods. It is a function of the price of home goods (normalized to unity) and the price of foreign goods. Then the wage in terms of home goods will be a function, wX(1,p, m l ) , defined by wl(1, p, co1) = nl( 1, p)~o t.
(4.14)
It is an increasing function of the price of foreign goods and the C P I wage rate. In this case, the home country's present employment level will simply be given by L l ( w l ( 1 , p , t o l ) , q X , k l ) . It follows that the change in employment will be given by _ 1 1 1 dP - Lq dq + L w w p dp.
(-)
(-)(+)
(4.15)
At first glance, it appears that an oil price increase has an ambiguous impact on employment. While it directly reduces employment, it can also have a positive effect if it reduces the price of foreign goods and hence the wage in JsWith variable employment, the changes in excess supplies of home and foreign goods are modified from those given in the appendix to ,1 sh= [x,.1 Lq1 q_xol + chw( - wI Lq1 + z' + z2)+ c*~,(z*' + z*2) _ rl ~_ ~,.i.,] dq ~ 0 and s r = [.~:*~'+ ctw( - w tL~ + z t + zZ) + c~.,t.(z., + z*2)_ ( 1-),)I~ - ( 1- ~,*)I*'] dq ~ 0. t6Marston (1982) emphasizes the difference between indexing wages to the CPI and to the GDP deflator in a partial equilibrium analysis of a small open economy's adjustment to disturbances.
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terms of home goods. Indeed, it can be shown that the foreign goods price does fall. But the foreign goods price can only fall if the drop in output of home goods exceeds that of foreign goods. This outcome can occur only if home employment falls. Hence, (4.15) is actually negative. Thus whichever indexing scheme is used, the oil importer with rigid real wages experiences a drop in employment but an improvement in its final-goods terms of trade when the oil price increases.
5. Conclusion We have constructed an intertemporal model of O P E C and two largecountry oil importers in order to show that asymmetries between importers cause oil price increases to alter the terms of trade between them in systematic waysJ 7 A country's degree of oil dependence affects its final-goods terms of trade unless consumer preferences for home and foreign traded goods are identical across countries. A country's relative ability to substitute domestic factors for oil, its pattern of trade in capital goods, and its employment response will also influence its terms of trade with other oil importers when oil prices change. The model can also be used to show that other asymmetries between oil importers, such as differences in international debt positions or marginal propensities to save, can influence the terms of trade between them in predictable ways. The analysis therefore increases our understanding of why countries respond differently to the same external shock.
Appendix The partial derivatives of (3.1) are: dha = E16 + C~wEb2 + (q/6)z 2] + E*a + ~hWt"*lrh,2 + (q/6)z,2] +yl~ + y , i , 1 > 0 ,
17In Marion and Svensson (1983), the same sort of model is used to show that changes in the final-goods terms of trade play an important role in determining the relative trade balance response to oil price changes. The results there must be interpreted with caution, however, since the assumption of a single final good in the second period fixes the future final-goods terms of trade. Hence only the effects of temporary changes in the final-goods terms of trade on the relative trade balance are considered. As emphasized by Sachs (1981), Svensson and Razin (1983) and others, temporary and permanent terms of trade changes have very different effects on the trade balance. To be able to analyze both kinds of changes, two separate final goods have to be considered in the future. This transforms the model into a three-country model with six commodities (oil and two final goods in each period) and makes the model intractable.
N.P. Marion and L.E.O. Svensson, Terms of trade between oil importers
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dfa = ep6 + clw[b 2 + (q/6)z 2] + E*6 + c~'#[b .2 + (qfiS)z .2] + ( 1 - ~,)I] + ( 1 - T * ) I ~ a > 0 , dhp = E Ip + clw[ -- Ep -- (I -- T)I I"]"F E*p + c* w [Ep + (I -- 9')II] 1
* .1~
+ t i p + ? Ip ¢~0, dtp=Epp+Cltw[_Ep_(1 _ ),)i 1] +E,p+C,w[Ep+( 1 _ ? ) i , ] +(1-
~,)lp~ + ( 1 - - ? * ) 1 . 1 - x .1 <>0, .1 . 1 +z*2)-Tl~--T*I*l]dq~O Chw(ZI +Z 2 )+Chw(Z
Sh = [Xql .if_ 1
and
sf = [x .1 + c~w(z 1 + z 2) + c~'~(z.1 + z .2) - (1 - ),)I~ - (1 -- ?*)1.1] dq ,~ 0. References Dixit, A., 1981, A model of trade in oil and capital, Woodrow Wilson School, Discussion paper no. 16, Princeton University. Dixit, A. and V. Norman, 1980, Theory of international trade (Cambridge University Press, London). Golub, S., 1983, Oil prices and exchange rates, Economic Journal 93, 576--593. Krugrnan, P.R., 1983, Oil and the dollar, in: J.S. Bhandari and B.H. Putman, eds., Economic interdependence under floating exchange rates (MIT Press, Cambridge) 179-190. Marion, N.P. and L.E.O. Svensson, 1983, Structural differences and macroeconomic adjustment to oil price changes: A three country approach, Institute for International Economic Studies, Seminar paper no. 248. Marion, N.P. and LE.O. Svensson, 1984, World equilibrium with oil price increases: An intertemporal analysis, Oxford Economic Papers 36, 86--102. Marston, R.C., 1982, Real wages and the terms of trade: Alternative indexing rules for an open economy, NBER Working paper no. 1046 Obsffeld, M., 1980, Intermediate imports, the terms of trade, and the dynamics of exchange rate and the current account, Journal of International Economics 10, 461-480. Sachs, J.D, 1981, The current account and macroeconomic adjustment in the 1970s, Brookings Papers on Economic Activity 1, 201-268. Sachs, J.D., 1983, Energy and growth under flexible exchange rates: A simulation study, in: J. Bhandari and B. Putnum, eds., Economic interdependence and flexible exchange rates (MIT Press, Cambridge) 191-220. Schrnid, M., 1980, International adjustment to an oil shock: The role of competitiveness, Board of Governors of the Fedral Reserve System, Mimeo. Svensson, L.E.O. and A. Razin, 1983, The terms of trade, spending and the current account: The Harberger-Laursen-Metzler effect, Journal of Political Economy 91, 97-125.
THE TERMS OF TRADE BETWEEN
OIL IMPORTERS
N a n c y Peregrim M A R I O N Dartmouth College, Hanooer, NH 03755, USA
Lars E.O. S V E N S S O N * Institute for International Economic Studies, Stockholm, Sweden
Received April 1983, revised version received May 1985 An intertemporal model of OPEC and two large-country oil importers is used to show that asymmetries between importers cause oil price changes to alter the terms of trade between them in systematic ways. For example, differences in oil dependence, marginal propensities to save, international debt positions, factor substitutability, trade in capital goods and wage setting behavior can all influence the final-goods terms of trade between oil importers in predictable ways when oil prices change.
1. Introduction An oil price change not only alters an oil importer's terms of trade with oil exporters but can also alter its competitive position with fellow oil importers. T h e latter occurs because oil price changes can affect a country's final-goods terms of trade, that is, the price of final-goods exportables in terms of finalgoods importables. In this p a p e r we examine whether oil price shocks lead to predictable changes in the competitive positions of two oil importers. O u r analysis indicates that a knowledge of the asymmetries between oil importers is crucial for predicting the direction of change in their final-goods terms of trade. In the presence of some asymmetries, such as differences in the degree of oil dependence, an oil price change will have no effect on the terms of trade between importers unless c o n s u m e r preferences are biased towards ownproduced goods. In the presence of other asymmetries, such as differences in the degree of substitutability in production, differences in the pattern of trade in capital goods, or differences in wage behavior, the final-goods terms of trade are affected even if c o n s u m e r preferences are not biased. We shall show *This paper is adapted from Marion and Svensson (1983). We are grateful to seminar participants at the National Bureau Of Economic Research, the Institute for International Economic Studies in Stockholm, Hebrew University of Jerusalem, and Tel-Aviv University for their helpful comments. Especially we would like to thank Michael Bruno, Elhanan Helpman, Torsten Persson, Assaf Razin, Michael Schmid and several anonymous referees. Financial support from the Haney Fund is gratefully acknowledged. 0022-1996/86/$3.50 © 1986, Elsevier Science Publishers B.V. (North-Holland)
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that the importer with fewer substitution possibilities then always faces a decline in its final-goods terms of trade if oil prices increase. The oil importer that is a d o m i n a n t supplier of capital goods always faces a change in its terms of trade that is positively correlated with the response of investment d e m a n d to the change in oil prices. The oil importer that has rigid real wages and suffers a fall in e m p l o y m e n t improves its terms of trade if oil prices increase. O u r analysis of the terms-of-trade response is conducted with the aid of an intertemporal model of O P E C and two oil importers. 1 The model and the world equilibrium are set out in section 2. In section 3, the effect of an oil price increase on the final-goods terms of trade is derived. All results are symmetric in that the effect of an oil price decrease merely involves a change in sign. Section 4 shows how the presence of certain asymmetries a m o n g oil importers influences the final-goods terms of trade between them when oil prices change.
2. Three countries and world equilibrium Consider a world of three countries, called the h o m e country, the foreign c o u n t r y and O P E C . There are two dates, indexed t = 1 and 2, which are called the present and the future. Three goods are p r o d u c e d in the present period: (1) h o m e final goods, p r o d u c e d exclusively in the h o m e country; (2) foreign final goods, p r o d u c e d exclusively in the foreign country; and (3) oil, p r o d u c e d exclusively in O P E C . T w o g o o d s are p r o d u c e d in the future: a c o m m o n final g o o d p r o d u c e d in the h o m e and foreign countries, and oil in O P E C . The assumption of a c o m m o n final g o o d in the future greatly simplifies the analysis and is permissible given our focus on the current terms of trade between oil importers. 2 1Three-country world equilibrium models have previously been constructed by Sehmid (1980), Krugman (1983) and Sachs (1983), but they differ considerably from the one developed here. In Schmid's model there is no capital accumulation nor is there a role for the world interest rate. It is also assumed that both oil importers produce the same final goods, so relative price changes induced by oil price increases are ignored. Krugman considers the effect of oil price increases on the exchange rate between two industrial countries. His model combines interesting aspects of a goods-market and an assetmarket view of the exe"hangerate, and examines how OPEC's spending shares and asset-holding shares affect the exchange rate in the short and long run. However, his model relies on very simplitied behavioral assumptions, some of which are not quite consistent with maximizing behavior. Sachs' model of OPEC and two industrial oil importers is intertemporal in nature and gives an important role to capital accumulation and the world interest rate in the adjustment process. However, his model is too complicated to solve analytically, and is instead examined by simulation methods. 2Assuming a common final good in the future essentially means assuming that future home and final goods are perfect substitutes in either consumption or production, so that the future final-goods terms of trade are fixed. Changes in an endogenous relative price between future home and foreign goods seem to have no systematic effect on the present final-goods terms of trade.
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101
In the present period, the n o n - O P E C countries consume home and foreign goods. They can also use home and foreign goods for investment in order to increase their future capital stocks. In the future, both countries consume final goods. To capture the lag in O P E C consumption of its dramatically increased oil revenues and the corresponding high marginal propensity to save, we invoke the simplifying assumption that all O P E C consumption is confined to the future. None of our results would be changed by allowing O P E C to consume in the present as long as OPEC's marginal propensity to consume home and foreign goods is sufficiently smaller than that of the other two countries) Oil is used as an input in the production of home and foreign final goods. O P E C sets oil prices exogenously according to the Hotelling Rule and supplies whatever quantity is demanded at these prices. Equivalently, O P E C can be considered as controlling the total stock of exhaustible oil and letting it be priced competitively. All three countries can trade goods on the world market at each date. They also have access to a common world credit market, where home and foreign bonds are perfect substitutes. 4 In the present, no country has inherited debt from the past. The model is specified using prices expressed in present-value terms, s The home country's output is chosen as the numeraire in period 1, so its price Ph is set at unity. The price of foreign final goods in terms of home goods is P = Pf/Ph" This is the reciprocal of the home country's final-goods terms of trade. We shall refer to an increase (decrease) in p as a deterioration (improvement) in the home country's final-goods terms of trade. The price of the common final good is chosen as the numeraire in period 2, so p 2 = 1. The present value of future final goods in terms of currently-produced home goods is the discount factor 6, which is identical to the inverse of one plus the (home goods real) rate of interest (6 =(1 +r)-1). The present-value price of oil in terms of home goods is ql =q; its current-value price in period 2 is q2 =q(1 + r ) = q / 6 . Hence, oil prices follow the Hotelling Rule. Let us now examine the behavior of the home country, modeling first its production side. Let x t = f * ( k t, lt, z ~) denote its well-behaved concave production function at date t, where x t is output of home goods, k t the home 3Of course, if OPEC spending in the present was skewed strongly towards one importer, it could influence the terms of trade between oil importers. See Krugman (1983). Also, the assumption of a very high marginal propensity to save for OPEC, while certainly reasonable for the first oil price increase in 1973-1974, is much less reasonable for an analysis of the oil price decreases in the 1980s. 4The assumption that allows asset trade to be suppressed is not merely that all countries have access to a common world capital market, but also that there are no shocks to technology,no threats of repudiation and no dangers of exchange controls which create uncertainty and hence render the liabilities of the differentcountries imperfectsubstitutes. SFor a more extensivediscussion of these kind of intemporal models, see for instance Marion and Svensson (1984).
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country's capital stock, It its employment level, and z t its input (import)- or oil. Firms operate competitively. We can then represent the production side by means of the GDP functions, Yr(1,qt, kt, lt) defined as Yt(1,qt, kt, lt)= max { x ' - q'z':x t = f(k', ~, z')}. Using standard properties of G D P functions, we can express home goods supply and the home country's import of oil as x ' = Y~t and
z'= - Y~,
(2.1)
where Y] and ~ are the partial derivatives of the G D P function (Y~t denotes OYt/OPh). With respect to employment, we assume that labor is fixed in total supply within the home country. Flexible wages ensure a given full employment level,/t, at each date. In section 4 we shall consider rigid wages and variable employment as well. We next specify the home country's investment behavior. Since the home country can increase its future capital stock by investing today, we have k2= k t + i t, where i t is investment in the present and k t is the present capital stock, which is predetermined and exogenously given. Both home and foreign goods are used as investment goods. A simple way to model this is to assume that the capital stock consists of home and foreign goods in the fixed proportions ~, and l - y , respectively (0<~<1). Hence, the cost of a capital good is y +(1-y)p. The home country's investment demand, I I(p, 6, q, k 1,12), is given by the level of investment that maximizes the excess of the present value of future G D P over the cost of present investment. The investment function fulfills the in:st-order condition:
6 y2(1, q/6, k t + It(p, 6, q, k t, lZ), 12)= ), + (1 -),)p,
(2.2)
which says that firms invest up to the point where the present value of the future marginal product of capital (6 Y~) equals the cost of present investment goods. Let us next consider the home country's demand side. We assume that the home country can be represented by a well-behaved utility function U(Ch, Cf, C2), where Ch and cf are the home country's consumption of home and foreign goods in the present and c 2 is its consumption of final goods in the future. We define the corresponding present value expenditure function in terms of home goods as E(1, p, 6, u) = min {% + per + 6c 2: U(%, cf, c 2) > u}. The expenditure function gives the minimum present value of expenditure on consumption required to reach a given utility level at given prices. By standard properties of expenditure functions, the partial derivative of the expenditure function with respect to the price of a good is equal to the Hicksian compensated demand function for that good. That is,
103
N.P. Marion and L.E.O. Soensson, Terms of trade between oil importers Ch=E1,
cf=Ep
and
c2--Ea.
(2.3)
The home country's intertemporal budget constraint expressed in home goods can now be written as E(1, p, 6, u) + D' + (1 - y)p] I x(p, 6, q) = Y 1(1, q) + 6 y2(1, q/6,1 l(p, 6, q)), (2.4) where we have suppressed labor inputs and the present capital stock. The budget constraint states that the present value of expenditure on consumption and investment equals the present value of GDP. The budget constraint can alternatively be written as equating the present value of expenditure on consumption to the home country's wealth, W, defined as W = Y l - [ y + ( 1 - y ) p ] I I + 6 Y 2 , which is the sum of present GDP, net of investment, and the present value of future GDP. This completes our discussion of the home country. Let us now briefly examine the foreign country. Its variables and functions will be denoted by an asterisk. The foreign country produces foreign goods in the present period and final goods in the future using capital, labor and imported oil. Let Y*t(pt, qt, k*t,l*t) denote its G D P functions measured in home goods. 6 Its investment demand, l*~(p, 6, q, k *l, /,2), will fulfill: 6 Y~2(1, q/6, k *~ +I*t(p, 6, q, k *~, 1,2), 1,2) = y , +(1 - 7*)p,
(2.5)
where y*(0_<_y*=
(2.6)
where we have again suppressed labor inputs and the present capital stock. Finally, let us briefly examine OPEC, denoting its variables with an 'o' superscript. Since all O P E C consumption is confined to the future, we can write OPEC's intertemporal budget constraint as 6c °2 = qS, (2.7) 6Note that the foreign GDP function Y*~(p,ql,k*~,l*~) gives present GDP in terms of home goods while the function Y*2(l,q2,k*2,1.2) gives future foreign GDP in terms of future l'mal goods. Note also that the first argument in the GDP function Y*~ is the relative price of foreign goods.
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N.P. Marion and L.E.O. Svensson, Terms of trade between oil importers
where c°2 is OPEC's consumption of future goods and S is the total stock of oil produced in the two periods. In equilibrium, total oil use equals total production: S t a g 1 ,-[-Z.1 ..}-Z2 -[..Z.2.
(2.8)
Let us next look at a world equilibrium, where the oil market clears and the final-goods markets clear at each date. Due to Walras' Law, we can disregard one of the market equilibria, and we choose to disregard the future final-goods market. Consequently, a world equilibrium can be represented by the three countries' budget constraints, (2.4), (2.6) and (2.7), and by the following set of market equilibria: equilibrium in the oil market, (2.8), equilibrium in the market for currently-produced home final goods, E 1 +E* + y I I + y . i . t = x 1,
(2.9)
and equilibrium in the market for foreign goods. E2 + E~ + (1 - ~,)I~+ (1 - y,)i,1 = x,X,
(2.10)
where world spending on each importer's current output equals the supply. For the exogenous oil price q and given full employment levels in both countries, eqs. (2.4) and (2.6)--(2.10) determine welfare levels in each oil importer, u and u*, the discount factor, 6, the present terms of trade between foreign and home final goods, p, OPEC's future consumption, c02, and the amount of oil extracted, S. 3. The final-goods terms of trade
In this section we examine how an increase in today's oil price alters the competitive position of two oil importers vis-fi-vis each other. We proceed by totally differentiating the market-clearing equations for home and foreign final goods, eqs. (2.9) and (2.10). In the process, we take into account the welfare effects of an oil price increase which can be derived by differentiating eqs. (2.4) and (2.6). We get:
?h, < df~
dfpJ
dp
LSfJ
(3.1)
where on the left-hand side dha is the partial derivative of the world excess demand for home goods with respect to the discount factor, dhp is the partial with respect to the price of foreign goods, and dr~ and dfp denote the corresponding partials of the world excess demand for foreign goods. On the
N.P. Marion and L.E.O. Svensson, Terms of trade between oil importers
105
right-hand side, Sh is the change in the world excess supply of home goods following the oil price increase, given a constant discount factor and price of foreign goods, and sr is the corresponding change in the world excess supply of foreign goods. The partials in (3.1) are given by cumbersome but easily interpreted expressions which are found in the appendix. The solution to (3.1) is dc~= (dfps h -- dhpSf)/ A ~ 0
(3.2)
dp = (dhrSr-- drrsQ/A ~ O, + + -
(3.3)
and
where A is the determinant A =dh~ do,-dhp df,~. We assume gross substitutability, which is sufficient for stability and makes A <0. 7 An oil price increase generally has an ambiguous effect on the discount factor and the terms of trade between the two oil importers. Now consider the case where an oil price increase leads to an incipient excess supply of both home and foreign goods, implying excess world savings in the present. This outcome occurs if the contraction in home and foreign output is not severe enough to offset reduced world demand for these outputs. In this case, Sh and sr are positive. It follows that the discount factor increases; excess saving in the present period bids down the interest rate. a We shall take a fall in the rate of interest to be the 'normal' case in the discussion that follows. An increase in the oil price still has an ambiguous impact on the terms of trade, however. By rewriting (3.3) and assuming sh, sf > 0, we get: d p = ( Sf / Sh - -
df,~/dh~) dh6Sh/ A .
(3.4)
++-It follows that the sign of the foreign price change is given by sign dp = sign (du/dh, - sf/s~).
(3.5)
VThe assumption of gross substitutability implies that dhp>0 and dfp<0. That is, an increase in the relative price of foreign goods raises world excess demand for home goods and reduces world excessdemand for foreign goods. Similarly,it implies dh~, dr8> 0. SAn excesssupply of both home and foreign goods also leads to a rise in the foreign goods discount factor (~/p) and thus a fall in the foreign goods real rate of interest. Formally, let p'= I/p and 6'=6/p. Then d~5'=(dfp,Sh-d~p.sf)/A'>O if dfp,>0, dhp,<0 and A'=dhr, drp,--dhp,dfv>0 by gross substitutability, and Sh,sf>O by assumption. See Marion and Svensson (1984) for further discussion of the effecton world interest rates of oil price changes.
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This expression can be nicely interpreted. The ratio (dfddhn) gives the relative world excess demand for foreign goods from the change in the discount factor, at constant foreign goods prices. The ratio (Sf/Sh) gives the relative world excess supply of foreign goods from the oil price increase, at constant discount factor and foreign goods price. If the relative world excess demand for foreign goods exceeds the relative world excess supply, the price of foreign goods must rise.
4. Differences across oil importers and the relative price of foreign goods Clearly, if the home and foreign countries are alike in every respect, there will be no change in the relative price of foreign goods, and the two oil importers will have unaltered competitive positions vis-a-vis each other when OPEC raises today's oil price. In this section we look at how differences between the home and foreign oil importer influence the way the foreign goods price responds to an oil price increase. A number of asymmetries can be examined in order to assess their impact on the final-goods terms of trade when there is an oil price increase. We choose to focus on four: (1) the degree of oil dependence; (2) the degree of substitutability in production; (3) the pattern of trade in capital goods; and (4) the employment response. We shall examine the implications of each asymmetry in turn. Our method will be to assume that the home and foreign countries are identical except in one respect at a time. Let the initial situation be one where the relative price of foreign goods equals unity, p = 1.
(4.1)
Suppose that the home country is more oil dependent in each period than the foreign country, in the sense that z t > z *t, for t = 1, 2.
(4.2)
The two countries are alike in other relevant respects. That is, we assume that Exn=E* 6, Epr=E* 6, I6=I'~ 1, I~=I *z,
x q = x *t
and
bZ=b *z. (4.3)
In particular, we assume that in spite of the home country using more oil, the production substitution effects xq and x* are equal. (See also footnote 12 below.) Differences in substitution effects are treated separately below. In addition, we assume that both countries have the same marginal propensities
N.P. Marion and L,E.O. Svensson. Terms of trade between oil importers
107
to consume their own-produced good and the same propensities to consume the other country's final good, so that
,1 _ , * l
( hW -- ( fW
and
C~w =ch*lw.
(4.4)
Finally, we assume that both countries invest symmetrically in the sense that each uses the same fraction of own-produced output in its capital stock, so that ?,=(1-7*)-
(4.5)
It follows from (4.1)-(4.5) and the appendix that dh,~-- df,~= (c,1h w - C~w)(q/6) (z 2 - z* 2) and .X ,1 .1 Sh--Sf=((h),,--(.V)(-~ ---~_ ~ 1 + Z ""~ --Z*2).
(4.6)
If oil importers consume symmetrically across home and foreign final goods, i.e. if C~w=C~w, then dh,5=df~>0, s h = s f > 0 , and by (3.5) we have d p = 0 ; differences in oil dependence have no effect on the terms of trade between oil importers. The intuitive reason is straightforward. Even if an increase in today's oil price causes a greater welfare loss for the more oildependent home economy, that translates into an equal drop in demand for home and foreign goods if there are no consumption biases. Hence there will be no change in the relative price of final goods. This result is the same as the one in Sachs (1981). He analyzes a model with a single final good, which is equivalent to assuming that the final-goods terms of trade are given. In terms of our model, this would be the case where goods are perfect substitutes in each period and hence there are no biases in consumption. Now consider the case where each oil importer has a bias toward its ownproduced good, so that ~w'l_---*l'--,,t~fwl-~fw_---*l,,hw.This bias could be due to transport costs, for instance. If consumers have such a preference for their own-produced goods, then d h ~ - d f e > 0 , s h - s f > O and thus d p ~ 0 ; differences in oil dependence can affect the terms of trade between oil importers, but the direction of effect is uncertain. The source of the ambiguity arises from the fact that an increase in today's oil price does not necessarily cause a bigger welfare loss for the more oil dependent importer. To see this, we differentiate (2.4) and (2.6), which gives US
E, d u = - ( z l + z Z ) d q + [ b 2 +(q/<~)z2]d¢5-[E~,+(1-y)IX] dp
(4.7)
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and E~*du* = - (z* z + z.2) dq + ['b.2 + (q/6)z .2] d6 + [E,, + ( 1 - 7)I 1] dp, (4.8) where the expressions E,,du and E*du* are wealth-equivalent welfare changes. 9 Examining (4.7) and (4.8), we see that an increase in today's oil price causes a bigger deterioration in the oil terms of trade for the more oildependent importer since ] - ( z z + z 2) dql > l - ( z .1 + z .2) dq]. However, it also raises the discount factor. An increase in the discount factor for a given oil price will, via Hotellings Rule, decrease the future price of oil and hence most benefit the more oil-dependent importer, (q/6)z 2 d r > ( q / 6 ) z .2 dr. N o w if this latter benefit is relatively modest, 1° then on net an increase in today's oil price will cause a bigger welfare loss for the more oil-dependent country. Then, given the o w n - g o o d bias in consumption, there will be a bigger d r o p in c o n s u m p t i o n of h o m e goods relative to foreign goods and the relative price of foreign g o o d s will increase. The m o r e oil-dependent oil importer suffers a loss in competitiveness vis-/L-vis its industrial trading partner. This loss exacerbates the direct welfare cost already imposed by the oil price increase. In summary, differences in oil dependence can cause an oil price increase to alter the terms of trade between importers t h r o u g h differential welfare effects if c o n s u m e r preferences are biased. It can also be shown that certain other asymmetries between oil importers, such as differences in marginal propensities to save or in international debt positions, can also influence the terms of trade between them t h r o u g h the welfare channel if c o n s u m e r preferences are biased.Z z 9The expressions E, and E* in (4.7) and (4.8) are the partials of the expenditure functions with respect to welfare levels; they equal the inverse of the marginal utilities of wealth and are positive. 1°If the two oil importers have the same degree of oil dependence in the future (z2=z*2), this latter effect is eliminated. lZSee the discussion in Marion and Svensson (1983). For example, suppose that two importers are similar except that the home country has a larger (smaller) propensity to consume (save) than the foreign country. This assumption can be represented by Crw--~Chw,*l-J" " Chw--~Cfw,*I _ I . 0<~< 1. It follows that Sh--Sr=(ZZ+ZZ)(1--Ot)(C~w--C~w) and dha-dfa=[b2+(q/6)z"](l-~)(e~w-C~w) and dpX0. Again, the source of ambiguity in the terms-of-trade response is due to the fact that an increase in today's oil price has an uncertain impact on the welfare of the importers. It worsens their oil terms of trade but also lowers the rate of interest, which makes them better off by lowering the future oil price and lessening their debt burden. If on net welfare is reduced by today's oil price increase, then there will be a bigger drop in the consumption of home goods relative to foreign goods because of the home country's higher MPC, and the home country will face a deterioration in its final-goods terms of trade. Consider next the case where two oil importers are similar except for their net creditor/debtor positions. Let the home country have a larger net creditor or smaller net debtor position at present. This implies th~t bI >b .1 and b"
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N o w let us e x a m i n e a n a s y m m e t r y t h a t affects the terms of t r a d e t h r o u g h the p r o d u c t i o n side. S u p p o s e the two oil i m p o r t e r s are similar except for the degree of s u b s t i t u t a b i l i t y in p r o d u c t i o n between oil a n d d o m e s t i c factors. Let the h o m e c o u n t r y have less such s u b s t i t u t a b i l i t y at present. As a result, it will experience a s m a l l e r d r o p in the f u l l - e m p l o y m e n t level of c u r r e n t o u t p u t following an oil price increase: x2 x.I
(4.9)
It follows t h a t d f r = d u ~ > 0 a n d Sh--Se>0, SO t h a t b y (3.5) we have d p > 0 . T h e c o u n t r y with fewer s u b s t i t u t i o n possibilities - - in this case the h o m e c o u n t r y - - suffers a decline in its final-goods terms of trade. T h e r e a s o n is t h a t there is a smaller decline in p r o d u c t i o n of h o m e goods, a n d the relative excess d e m a n d for foreign g o o d s p u t s u p w a r d pressure on p. O u r results here agree with those of Obstfeld (1980). C o n s i d e r next a t h i r d a s y m m e t r y between oil i m p o r t e r s , n a m e l y their p a t t e r n of t r a d e in c a p i t a l goods. U p to this p o i n t we have a s s u m e d t h a t each c o u n t r y uses the s a m e fraction of o w n - p r o d u c e d g o o d s for investment, with y * = l - - y . S u p p o s e we relax this a s s u m p t i o n a n d allow the h o m e c o u n t r y to use a g r e a t e r fraction of o w n - p r o d u c e d g o o d s as capital goods. This implies t h a t y*>(1 -y).
(4.10)
(In the limit y = y * = 1 a n d o n l y h o m e g o o d s are used as c a p i t a l goods; the with the larger net creditor position faces a deterioration in its final-goods terms of trade. This is because the oil price increase lowers the rate of interest, generating a bigger welfare loss for the creditor country. Given biased preferences, there will be a larger fall in the consumption of home goods and hence upward pressure on the relative price of foreign goods. Of course, should there be no consumer biases, then an increase in today's oil price should not affect the terms of trade between two oil importers even if they differ in their marginal propensities to consume or in their international credit positions. 12Assume that date 1 production of home goods is separable between an aggregate of domestic capital and labor, o(k,l), and oil input, z. That is, the production function fulfills x=f(k,l,z)=g(o(k,l),z). Note that if g(.) and 0(.) are constant returns to scale, so is f(.). In particular, with this technology, frequently assumed in the literature, capital, labor and oil are all cooperative in the sense of having positive cross partials. With full employment of labor, only x and z vary. By standard results we have ~2=0~. and ~= - ~ , where ~ denotes the rate of change dx/x, etc., 0 is the cost share of oil in the value of output of home goods, and ~ (defined positive) is the elasticity of demand for oil with respect to the relative oil price. Furthermore, ~ equals or/(1-0), where ¢ is the elasticity of substitution between oil and the domestic aggregate factor o. Hence, we have x=-[0/(l-0)]~r~, and it follows that for a given oil price increase and a given output level, the absolute response in output is smaller the smaller the elasticity of substitution. Note that a difference in oil dependence (4.2) together with the similarity assumption (4.3) is equivalent to assuming that the elasticity of substitution in home-goods production is smaller than that in foreign-goods production.
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home country exports capital goods and the foreign country imports them.) It follows that dh~-- dfn > 0, s h - sf > 0 and that dp ~ 0. An increase in the oil price at constant discount factor will reduce investment demand if capital and oil are cooperative in future production, in the sense that the corresponding cross partial f~, of the production function is positive. At the same time, the induced increase in the discount factor (a drop in the real rate of interest) stimulates investment demand. If on net investment demand is depressed, there will be a bigger drop in demand for home goods relative to foreign goods since the home country is the larger supplier of capital goods. Consequently the relative price of foreign goods rises. The home country faces a deterioration in its final-goods terms of trade. On the other hand, should the home country produce capital goods which are considered to be non-cooperative with oil in future production (fg~ < 0), then investment demand will be stimulated by the oil price rise and the home country will experience an improvement in its final-goods terms of trade. So far we have assumed that both oil importers have flexible wages and full employment in the present and the future. Let us finally examine what happens when the countries differ in their wage behavior. Consider the case where the home country has rigid wages and variable employment in the present period. Suppose that the wage in the home country is presently fixed in terms of home goods, i.e. wages are indexed to the GDP deflator. The level of employment is then given by the condition that the demand price for labor, Y], equals the given wage w1. This condition determines the present employment function L~(w ~, q~, k~), which fulfills:
Y~( I, ql, k 1, L I(w 1, ql, kl)) = w1.
(4.11)
The change in the home country's present employment level in response to an oil price increase is dl I = L~ dq < O.
(4.12)
Employment falls if labor and oil are cooperative. 13'x4 Assuming that the 13We have Lqt = - YtJY~t
N.P. Marion and L.E.O. Svensson, Terms of trade between oil importers
111
two oil importers are alike in all relevant aspects except the employment response, we have dh~=drn>0 and Sh--Sf<0. ~5 By (3.4) we can then write dp = dh~ (s r - s h ) / A < O, (+) (+) (_)
(4.13)
which says that the foreign goods price falls. Since the oil price increase causes employment in the home country to fall, there is a greater drop in the production of home goods relative to the production of foreign goods. The relative excess supply of foreign goods puts downward pressure on foreign prices. Consequently with an oil price increase, the oil importer with rigid real wages experiences a welfare loss due to reduced employment but a final-goods terms of trade gain. Now consider a more c o m m o n form of wage indexation, where the wage in the home country is indexed to a consumer price index (CPI) rather than to the price of home goods. ~6 Let co1 denote this given real wage. Let the price index nl(l,p) denote the present C P I in terms of home goods. It is a function of the price of home goods (normalized to unity) and the price of foreign goods. Then the wage in terms of home goods will be a function, wX(1,p, m l ) , defined by wl(1, p, co1) = nl( 1, p)~o t.
(4.14)
It is an increasing function of the price of foreign goods and the C P I wage rate. In this case, the home country's present employment level will simply be given by L l ( w l ( 1 , p , t o l ) , q X , k l ) . It follows that the change in employment will be given by _ 1 1 1 dP - Lq dq + L w w p dp.
(-)
(-)(+)
(4.15)
At first glance, it appears that an oil price increase has an ambiguous impact on employment. While it directly reduces employment, it can also have a positive effect if it reduces the price of foreign goods and hence the wage in JsWith variable employment, the changes in excess supplies of home and foreign goods are modified from those given in the appendix to ,1 sh= [x,.1 Lq1 q_xol + chw( - wI Lq1 + z' + z2)+ c*~,(z*' + z*2) _ rl ~_ ~,.i.,] dq ~ 0 and s r = [.~:*~'+ ctw( - w tL~ + z t + zZ) + c~.,t.(z., + z*2)_ ( 1-),)I~ - ( 1- ~,*)I*'] dq ~ 0. t6Marston (1982) emphasizes the difference between indexing wages to the CPI and to the GDP deflator in a partial equilibrium analysis of a small open economy's adjustment to disturbances.
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terms of home goods. Indeed, it can be shown that the foreign goods price does fall. But the foreign goods price can only fall if the drop in output of home goods exceeds that of foreign goods. This outcome can occur only if home employment falls. Hence, (4.15) is actually negative. Thus whichever indexing scheme is used, the oil importer with rigid real wages experiences a drop in employment but an improvement in its final-goods terms of trade when the oil price increases.
5. Conclusion We have constructed an intertemporal model of O P E C and two largecountry oil importers in order to show that asymmetries between importers cause oil price increases to alter the terms of trade between them in systematic waysJ 7 A country's degree of oil dependence affects its final-goods terms of trade unless consumer preferences for home and foreign traded goods are identical across countries. A country's relative ability to substitute domestic factors for oil, its pattern of trade in capital goods, and its employment response will also influence its terms of trade with other oil importers when oil prices change. The model can also be used to show that other asymmetries between oil importers, such as differences in international debt positions or marginal propensities to save, can influence the terms of trade between them in predictable ways. The analysis therefore increases our understanding of why countries respond differently to the same external shock.
Appendix The partial derivatives of (3.1) are: dha = E16 + C~wEb2 + (q/6)z 2] + E*a + ~hWt"*lrh,2 + (q/6)z,2] +yl~ + y , i , 1 > 0 ,
17In Marion and Svensson (1983), the same sort of model is used to show that changes in the final-goods terms of trade play an important role in determining the relative trade balance response to oil price changes. The results there must be interpreted with caution, however, since the assumption of a single final good in the second period fixes the future final-goods terms of trade. Hence only the effects of temporary changes in the final-goods terms of trade on the relative trade balance are considered. As emphasized by Sachs (1981), Svensson and Razin (1983) and others, temporary and permanent terms of trade changes have very different effects on the trade balance. To be able to analyze both kinds of changes, two separate final goods have to be considered in the future. This transforms the model into a three-country model with six commodities (oil and two final goods in each period) and makes the model intractable.
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dfa = ep6 + clw[b 2 + (q/6)z 2] + E*6 + c~'#[b .2 + (qfiS)z .2] + ( 1 - ~,)I] + ( 1 - T * ) I ~ a > 0 , dhp = E Ip + clw[ -- Ep -- (I -- T)I I"]"F E*p + c* w [Ep + (I -- 9')II] 1
* .1~
+ t i p + ? Ip ¢~0, dtp=Epp+Cltw[_Ep_(1 _ ),)i 1] +E,p+C,w[Ep+( 1 _ ? ) i , ] +(1-
~,)lp~ + ( 1 - - ? * ) 1 . 1 - x .1 <>0, .1 . 1 +z*2)-Tl~--T*I*l]dq~O Chw(ZI +Z 2 )+Chw(Z
Sh = [Xql .if_ 1
and
sf = [x .1 + c~w(z 1 + z 2) + c~'~(z.1 + z .2) - (1 - ),)I~ - (1 -- ?*)1.1] dq ,~ 0. References Dixit, A., 1981, A model of trade in oil and capital, Woodrow Wilson School, Discussion paper no. 16, Princeton University. Dixit, A. and V. Norman, 1980, Theory of international trade (Cambridge University Press, London). Golub, S., 1983, Oil prices and exchange rates, Economic Journal 93, 576--593. Krugrnan, P.R., 1983, Oil and the dollar, in: J.S. Bhandari and B.H. Putman, eds., Economic interdependence under floating exchange rates (MIT Press, Cambridge) 179-190. Marion, N.P. and L.E.O. Svensson, 1983, Structural differences and macroeconomic adjustment to oil price changes: A three country approach, Institute for International Economic Studies, Seminar paper no. 248. Marion, N.P. and LE.O. Svensson, 1984, World equilibrium with oil price increases: An intertemporal analysis, Oxford Economic Papers 36, 86--102. Marston, R.C., 1982, Real wages and the terms of trade: Alternative indexing rules for an open economy, NBER Working paper no. 1046 Obsffeld, M., 1980, Intermediate imports, the terms of trade, and the dynamics of exchange rate and the current account, Journal of International Economics 10, 461-480. Sachs, J.D, 1981, The current account and macroeconomic adjustment in the 1970s, Brookings Papers on Economic Activity 1, 201-268. Sachs, J.D., 1983, Energy and growth under flexible exchange rates: A simulation study, in: J. Bhandari and B. Putnum, eds., Economic interdependence and flexible exchange rates (MIT Press, Cambridge) 191-220. Schrnid, M., 1980, International adjustment to an oil shock: The role of competitiveness, Board of Governors of the Fedral Reserve System, Mimeo. Svensson, L.E.O. and A. Razin, 1983, The terms of trade, spending and the current account: The Harberger-Laursen-Metzler effect, Journal of Political Economy 91, 97-125.