cyclical co-movements of output and trade in the world economy

Cyclical Co-Movements of Output and Trade in the World EconomyAuthor(s): Harris DellasSource: The Canadian Journal of Economics / Revue canadienne d'Economique, Vol. 20, No. 4(Nov., 1987), pp. 855-869Published by: Wiley on behalf of the Canadian Economics AssociationStable URL: http://www.jstor.org/stable/135420 .

Accessed: 18/06/2014 22:42

Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at .http://www.jstor.org/page/info/about/policies/terms.jsp

.JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range ofcontent in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new formsof scholarship. For more information about JSTOR, please contact [email protected].

.

Wiley and Canadian Economics Association are collaborating with JSTOR to digitize, preserve and extendaccess to The Canadian Journal of Economics / Revue canadienne d'Economique.

http://www.jstor.org

This content downloaded from 188.72.126.198 on Wed, 18 Jun 2014 22:42:14 PMAll use subject to JSTOR Terms and Conditions

http://www.jstor.org/action/showPublisher?publisherCode=black

http://www.jstor.org/action/showPublisher?publisherCode=cea

http://www.jstor.org/stable/135420?origin=JSTOR-pdf

http://www.jstor.org/page/info/about/policies/terms.jsp


Cyclical co-movements of output and trade in the world economy HARRIS DELLAS Vanderbilt University

Abstract. An intertemporal maximization general equilibrium model of an industrial block and an LDC resource-rich block is constructed and used to examine the cyclical behaviour of trade flows, investment and output in the world economy. It is demonstrated that supply disturbances originating in the raw materials market lead to positive across economic zones and persistent over time co-movements in trade, investment, and output if the world real interest rate moves counter cyclically. It is also shown that the sign of the response of the current account to a supply shock depends on the size of the distribution of gains from trade.

Les co-mouvements cycliques du niveau de production et du niveau de commerce dans l'eonomie mondiale. L'auteur utilise un modele de maximisation intertemporelle d'equilibre general d'un bloc de pays industriels et d'un bloc de pays moins developpes mais riches en ressources pour analyser le comportement cyclique des flux de commerce, de l'investissement et du niveau de production dans l'conomie mondiale. On montre que des chocs du c6te de l'offre en provenance du march6 des matieres premieres entrainent des co-mouvements positifs dans le commerce, l'investissement et la production d'une zone 'a l'autre (des co-mouvements qui persistent dans le temps) si le taux d'interet reel mondial evolue du maniere anticyclique. On montre aussi que le signe de la reponse du compte courant a un choc du c6te de l'offre d6pend de l'importance de la repartition des gains de l'echange suscites par la croissance.

INTRODUCTION

The issue of the origin and properties of world (international) business cycles' has received considerable attention, especially after the two oil shocks of the last decade. In Dellas (1985), we document the existence of several empirical regularities which characterize the behaviour of output, trade and the terms of trade both within and across countries, and economic zones. The findings

1 The term world (international) business cycles describes the existence of common elements in cyclical behaviour across countries.

Canadian Journal of Economics Revue canadienne d'Economique, xx, No. 4 November novembre 1987. Printed in Canada Imprime au Canada

0008-4085 / 87 / 855-869 $1.50 ( Canadian Economics Association



856 Harris Dellas

include: strong, positive contemporaneous correlation is present in trade economic activitf across countries and economic zones (and to a smaller degree, in aggregate economic activity); significant co-movements in trade and cNPs are also found over the business cycle (2.5 to four years); imports are procyclical and the trade balance is counter-cyclical; cyclical fluctuations persist over time; common disturbances seem to underlie the common economic developments across countries, with the trade balance being of secondary importance in the transmission of disturbances.

While no existing theoretical work has attempted an explicit incorporation of all these empirical features into a single model, there is a sizeable literature on specific aspects of international business cycle phenomena. Two issues are prominent in this literature. The first one is the source of economic shocks. Economic disturbances can be real or monetary and can originate either in the private sector (as supply or demand shocks) or in the public sector (as fiscal or monetary policy shocks); they can be country specific or they may represent common developments in the world economy (such as an oil shock). The second issue is the channel of the transmission of economic fluctuations across countries. Trade in goods and capital flows link economic activity in different countries.

In this paper we restrict attention to a particular subset of shocks and transmission mechanisms which seems quite promising in generating the above-described empirical regularities. We emphasize country specific real supply disturbances that get transmitted through the trade balance. While somewhat related models have been used to discuss the transmission of real disturbances, they have, with a few exceptions (Marion and Svensson, 1981) mostly analysed the effects of an exogenous oil pnrce increase on the economic activity of a small open economy (Sachs, 1981). However, business cycles are a dynamic phenomenon involving cross-country interactions and feedbacks; hence a large open economy set-up seems more appropriate. Moreover, as Lucas (1977) has argued, all business cycles are alike; that is, they are characterized by correlation patterns which are not country or time specific. Subsequently, despite the usefulness of analysing individual episodes, it is important to proceed in the direction of constructing models, which are general enough to account for most major economic fluctuations. What seems to be needed are theories that relate the recurrent (and stable) patterns of quantity and price correlations of the business cycle to a set of fundamental elements of market economies. In two recent papers, Long and Plosser (1983) and Kydland and Prescott (1982) demonstrated how the interaction of some standard characteristics of utility (like normality of all goods, current and future) and

2 By trade economnic activity I mean the real value of imports and exports. Cyclical movements in imports are positively correlated across countries and economic zones; the same holds true for exports. Imports are positively correlated with exports in both individual countries and economic zones. For more details see Dellas (1985).



Cyclical co-movements 857

production (like factor substitutability) in a utility maximization, market clearing set up, is sufficient to produce output dynanics that closely mimic business cycles.

In this paper we follow the spirit of this approach in the sense that we demonstrate how country-specific transitory supply disturbances can generate co-movements in certain macro variables consistent with an international business cycle and how the sign of these co-movements depends on certain elasticity and shares conditions. The disturbances that trigger world wide economic changes are assumed to occur in the raw materials market. A two-period, two-country model is developed and used to analyse the effects of supply disturbances on savings, investment, the real interest rate, the terms of trade, and output. This model is an extension of the one developed by Marion and Svensson3 (1981). One can argue that it represents the real world in the following sense. Group together all natural-resource-rich4 countries (primarily developing ones). These countries rely on exports of their natural resources to provide themselves with consumption goods and capital equipment. The imported physical capital is used with domestic labour to produce the intermediate good (the natural resource). Call this LDC group the foreign country. On the other side, group together all industrial countries that rely heavily on imported natural resources to produce both capital and consumption goods. Call this group the domestic country.

It is shown that the foreign current account may behave counter-cyclically when a foreign supply shock takes place, even in the absence of immiserization. What matters for this relationship is the size of country gains from trade. If, for instance, the domestic country uses in its productive activities a significant portion of the foreign product, it may gain relatively more than the foreign country when the foreign economy expands. Under the permanent income hypothesis this will produce a domestic current account surplus (a foreign current account deficit).

It is also shown that the empirical facts mentioned above obtain if the supply of industrial goods shifts more than the demand when growth in the production of the intermediate good (natural resource) takes place; in this case the world interest rate behaves counter-cyclically.

The real business cycle approach adopted in this paper can be interpreted in two ways. It can be taken to imply that a complete explanation of business cycle phenomena can be accomplished by ignoring money and nominal prices

3 Essentially, there are two important differences. The first and more crucial one is that we al- low for a non-trivial investment decision in both economic zones which enables us to discuss endogenous world business cycles. And second, we assume perfect competition so that the terms of trade are determined by demand and supply.

4 One can view this natural resource as a composite of inputs exported by the non-industrial countries, such as steel, copper, tin, agricultural products. With the collapse of OPEC one could also include oil in this composite commodity, since its price is now essentially determined by market forces.



858 Harris Dellas

and instead focusing exclusively on real variables5 (Prescott, 1986). In addition to its theoretical appeal, Kydland and Prescott's work - among others - offers strong empirical support to this interpretation. Or it can be interpreted as meaning that other considerations (such as monetary and fiscal policies) are important too, but one would like to hold them constant when discussing the effects of real economic factors. The very significant supply shocks of the last years and their transmission through real trade channels make real factors deserve special (if not exclusive) attention in the analysis of international business cycles (Dellas, 1985; Stockman, 1986).

The rest of the paper is organized as follows. The basic model is described in the second section. In the third section the world equilibrium is set out. In the fourth section the effects of a temporary current production shock are considered. In the fifth section we deal with an expected future output shock. We conclude by summarizing the results.

THE MODEL

The set-up of the model is as follows: the world consists of two countries, home and foreign, each one populated by an individual who lives for two periods. In each period two kinds of goods are produced: the home good, which can be either consumed or used to augment the existing capital stock in each country; and the foreign good, which can be used only as a completely perishable input in the production of the home good. In each period trade involves the exchange of the domestic commodity for the foreign intermediate good at endogenously determined terms of trade. Trade need not be balanced in either period; that is, the countries can lend or borrow in a world credit market. There is no inherited debt when the individuals start the first period, and all debt accumulated during the first period has to be paid back in the second period.

Let us look at the home country first. Capital letters represent domestic variables and small letters represent foreign variables. The domestic individual maximizes lifetime utility

V = U(CI) + 8U(C2), (1)

where Ci is domestic consumption of the home final good in period i, and /3 is the discount factor, subject to the constraint that the present value of his total consumption equals the present value of domestic output

(1 + r)[F'(K1, ZI) - PIZ- Cl - X] + F2(K2, Z2)

-P2Z2-C2 = O, (2)

5 One can introduce monetary complications into this type of real model to explain the behaviour of nominal variables (such as price procyclicality, etc.). This can be done by making the money supply respond to real variables but play no causal role in economic fluctuations (so monetary policy does not affect real economic activity). Whether this type of monetary theory can satisfy the real business cycle critics is another issue.




F' the ith period production function6 K1 the capital stock that has been inherited from the past Zi - imports of the foreign input in period i X = current investment (net of depreciation) Pi = the terms of trade in period i, that is, the relative price of

the foreign good in terms of the domestic good K2 - K1 + X, is the second period's capital stock r - the real interest rate that both countries face in the world

credit market (expressed in terms of the domestic good).

The utility and production functions are assumed to satisfy the standard conditions, and K, Z, X, and C are required to be non-negative.

The budget constraint tells the following story. At the beginning of the first period the domestic agent starts out with some fixed capital stock, K1. He imports Z1 quantity of the foreign good (which equals total foreign production) and combines K and Z with labour (which is fixed in supply) to produce the domestic good, F1 (K1, Z1). He consumes part of it, Cl, and he uses another part to replace and / or augment the existing capital stock. He exports the remaining to the foreign country in exchange for the already imported and completely used foreign output, as well as for claims to future foreign output. The value of the claims can be either negative or positive, since the domestic agent can be either a net debtor or a net creditor. The same procedure is repeated in the second and last period. The only difference is that there is no investment in the second period, since there is no future to take care of. Any debt created in the first period has to be paid back.

Substituting for C2 from (2) into (1) and performing the maximi-zation routine, one gets

Uj = ,B(1 + r)U2 (3a)

1+ r =- F2 (3b)

F = P1 (3c)

F2 = P (3d) F2 P2 The interpretation of (3) is straightforward.

(3a) says that if the individual does not consume a unit of the final good in the first period, he can lend it out and consume 1 + r units in the second period. Since only the home good is consumable, the consumption intertemporal price does not include the terms of trade.

(3b) says that the rate of the consumption trade-off has to equal the rate of the production trade-off.

6 While no substitution opportunities in production exist in the first period, such opportunities are available in the second period.



860 Harris Dellas

Z1 and Z2 are not investment goods. Hence the real interest rate does not enter directly the RHS of 3(c, d). The last two equations give the (inverse) factor demand functions.

By totally differentiating (3) we obtain the following demand equations:7

dCl = Cdr + CpldPl + Cp2dP2 + CKldKl

(-) (-) (+)

dX = Xrdr + Xp2dP2 (-) (-)

dZI = Zp11dPI + ZKIdKl

(-) (+)

dZ2 = Zp22dP2 + Zr2dr, (-) (-) (4)

where Cr - dC1 /ar, ZP22 = aZ2/"P2, and so on, dKI represents a change in initial conditions, and CA iS the current account, that is, the expression in the brackets in (2). A parenthesis ( ) refers to the sign of the partial derivative. The only ambiguous sign is that of C, when the home country runs a current account surplus in the first period. The reason is that in this case, the income and the substitution effect of a change in the world interest rate run counter to each other. If the home country is a net lender, the income effect is positive; this increases the demand for current consumption. The substitution effect is negative for current consumption, since future consumption becomes relatively cheaper when the interest rate increases.

Let us now look at the foreign country. Variables that refer to the foreign country will be represented by small letters. The foreign individual maximizes

V = U(CI) + /8U(C2) (5)

where ci is foreign consumption of the home good in period i, subject to the intertemporal budget constraint

(1 + r)[P1f(k1) - cl - x] + P2f2(k2) -C2 = 0 (6)

7 Total differentation of (3) gives (Al)

[Ul + (1 + r)2 8U5 ] dC = {/3 [ Ul + ( I + 1.)2 U' CA)1] dr

- I(l + I-)2 U?[ZIdPl - 72 dP2 + F,IdK1I }

F22 dZ1 = dP1 + F2 XdKl

)= (-F2 / R)dr - ( F22 / R)dP,

dX= (F,12/R)dr - (F212/R)dP2, (Al)

where R = F,F,I - F21F12 > 0. Solving out we get equation (4) in the text. Notice that F,, < 0, F,, < 0, F12 > (, F21 > (, U' < 0, U2' < 0.




As can be seen from (6), the foreign country relies exclusively on imports of the domestic good to satisfy its consumption and investment needs.

The first-order conditions are

ul -i(l + r)u1

1 + r P2f2

By totally differentiating the FOC we have

[u1j + (1 + r)2/8uf,]dc1 = f[u2 + u2'(1 + r)2ca]dr

+ /3(1 ? r)2u{2[Z1dPI + Z2dP2 +f1ldkI]

dr =f 2dx +f 2dP2

and solving out,

dCI cp1dPl + Cp2dP2 + crdr + Ckldkl (+) (+) (+)

dx x,.dr + xp2dP2. (-) (+) (7)

WORLD EQUILIBRIUM

In a world equilibrium both goods markets must clear in every period. There are four markets, but by Walras's Law, only three of them are linearly independent. Disregarding market equilibrium in the domestic final good in the second period we have

F(KI ,Z1)=C + X + cl + x (8a)

f(k1) = Zi (8b)

f(k2) = Z2 (8c)

(8a) defines equilibrium in the home good market in the first period. Total production equals total expenditure (consumption and investment). (8b) and (8c) define equilibrium in the intermediate good market. Totally differentiating (8) and using (4) and (7):

(CPI + P1 -F21Zp 1)dPI + (Cp2 + Cp2 + Xp2)dP2 +

(Cr + Cr + Xr + xr)dr (FlI - CKI)dKl - Ckldkl (9)

Zp tIdPI =fi dkl -f2IdKI

n f12x - )dP2 + (Zr2 _ f 2xr.)dr _ 0



862 Harris Dellas

or

E 1hldPI + E 2 hIdP2 + E,hldr = sdK, - Ckldkl

EpIfdPI -f Idk -f2IdKI (10)

E f2 dP2 + Ef2dr - O.

EpiF' is world excess demand for period i foreign good as Pi changes, and the other variables are defined similarly; s = fl - CKI1.

Notice that the Es can be written as explicit functions of demand and supply elasticities as well as consumption and production shares. For example,

Ehl dP, = (o ci + - cl o 'Z ZlP,

where 0c, = CI/F1, lCl - (aC /lPl)(P1/C1), P = aP/PI1 and so on. It is then obvious that any discussion of the sign and the magnitude of the

price partial derivatives would essentially involve the examination of shares and elasticities.

(10) is a three-equation system in three unknowns, so it can be explicitly solved to give dP1, dP2, dr as functions of the state variables dKI and dkl. Clearly in the case of a permanent shock (dal = da2) or an expected future shock (da, = 0, da2 > 0), the technological parameters, a, that are subject to change would enter the RHS of the reduced form.

In the next sections, I examine the effects of temporary current and expected future supply shocks.8 The purpose of the analysis is to reveal how different values of the structural parameters of the model lead to different business cycle dynamics. To be more specific, the analysis demonstrates how the sign of the various co-movement patterns depends on certain elasticity and shares conditions and identifies the values of these conditions which produce predictions consistent with the empirical findings of Dellas (1985) mentioned in the introduction. In addition, we try to explain how the relationship between the current account and supply shocks depends on these same structural parameters.

A TEMPORARY PRODUCTIVITY SHOCK

Before we proceed to the examination of a foreign temporary current production shock, it is useful to analyse the signs of the excess demand functions.

Ep fl is unambiguously negative. An increase in PI does not affect the production of Z1 (k1 is given) but decreases the domestic current demand for imports.

E,!hI is very likely to be negative. A sufficient condition is that the current

8 Of course other types of shocks such as monetary and fiscal may play an important role in world business cycles.




account surplus equals zero in the first period before the shock takes place, and hence there is no wealth redistribution effect stemming from the current account. Alternatively, one can assume that even if trade is imbalanced, the substitution effects in consumption prevail over the opposing wealth effects.

E 2hI can be of either sign. If domestic consumption and investment demands are more elastic (inelastic) than the foreign demands, and / or the share of domestic expenditure in the total expenditure on the domestic good is larger (smaller) than the foreign share, then this term will be negative (positive).

E,, 1: If consumption shares and elasticities with respect to P1 are of approximately the same (absolute) magnitude across countries, it will be positive, because the domestic production response to a change in P1 is negative. In other words, if the opposite wealth effects on consumption offset each other, the world demand curve remains at its initial position when P1 increases, while the world supply curve shifts upwards, bringing about excess demand. On the other hand, if domestic consumption of the home good constitutes a disproportionately high fraction of world consumption, and the production response is not particularly strong, excess supply may prevail in the home good market.

Epf2 is unambiguously negative (excess supply of Z2), since an increase in P2 reduces the domestic demand for imports and at the same time, by increasing the value of the marginal product of foreign capital, it encourages a higher production of Z2.

E/f2: If the direct negative effect of an increase in the world interest rate on foreign investment is stronger (weaker) than the indirect effect on the demand for Z2 (through the decrease in X), then supply decreases by more (less) than demand and the outcome is excess supply (demand); that is, Ef2 > 0 (< 0).

Let us now consider a temporary productivity shock that affects foreign output. To facilitate the analysis, we employ a few simplifying (arbitrary) assumptions with regard to the values of the various elasticities and shares. Clearly, one can relax these assumptions and still be able to trace out very precisely how our results will differ.

Suppose for the moment that C, = -c1, Cp2 - c&2 and Xp2 = Xp2* Then the coefficient of dP2 in (lOa) equals zero. Following the shock (dk, > 0), production of Z1 increases and the resulting excess supply of the foreign good will be eliminated by a decrease in the relative price of Z1. P1 goes down (equation (lOb) ).

If the foreign growth is not immiserizing (the domestic import curve is elastic), d(P, Z,) > 0, and consequently real income increases in both countries. Since we have assumed that C1 = -cl, the income redistribution that results from the improvement in the home terms of trade does not change aggregate consumption demand in the first period, and there is only the 'pure' foreign income effect (cklldkl) operating. This income effect is positive, leading to



864 Harris Dellas

S(P1,KI)

P2

S X ~~~~~~~~\D(P,*p2K k, )

Home good

FIGURE 1

excess demand for the home good. On the other hand, the lower price of the imported intermediate good leads to higher imports and hence higher production of the domestic good. This effect tends to generate excess supply. Now suppose that Ck I < -F21Zp22, that is, after P1 has adjusted to clear the foreign good market, we observe excess supply of the home good. As is clear from (lOa), the real interest rate has to decrease to encourage current expenditure (C1, cl, X, x). A lower r unambiguously increases both domestic and foreign investment (figure 1). The direction and magnitude of the change in the second period's terms of trade, P2, depends on relative output expansion in the second period. Continuing our story, the decrease in the interest rate increases domestic investment and consequently the demand for the other factor of production, Z2. But foreign investment responds positively to dr, increasing future availability of Z2. If the net result is excess demand (supply), P2 has to increase (decrease) to encourage more foreign investment and discourage domestic imports (figure 2). But in either case output in both countries will be higher in the second period.

Summarizing the results: an unexpected increase in foreign output in the first period results in an increase in foreign output in the next period and in an increase in domestic output in both periods. If the income effects in production dominate over the income effects in consumption so that the interest rate moves counter-cyclically, positive contemporaneous and over time correlation




\ \ /So

\D(r)

/

FIGURE 2

in the national output series obtains. Consumption, investment, imports, and exports all are higher in both countries, the real interest rate is lower, and the terms of trade are negatively (positively) correlated over time if excess demand (supply) prevails in the foreign good market in the second period.

What will the covariance pattern in prices and quantities be if one assumes that following the foreign productivity shock excess demand prevails in the home good market? In this case, the interest rate will have to increase to curtail desired current expenditure. Consequently, investment will decrease in both countries and future output, trade, and consumption all will be lower. Notice that in this case, a current increase in income leads to a lower future production (negative autocorrelation in economic activity), and that a supply shock in some large country results in higher world interest rates. The over time correlation in the terms of trade will depend, as before, on the relative demand versus supply responsiveness in the foreign good market in the second period.

In both cases examined above, one obtains a positive cross country correlation in national output movements.9 In fact, this is the only possible pattern, since investment in both countries responds to the same variable, the

9 For an example of negative correlation in economic activity across countries due to immiserizing growth, see Dellas (1985).



866 Harris Dellas

real interest rate.10 The change in the future terms of trade cannot reverse the effect of a change in the real interest rate on investment. For instance, assume that dr > 0, dP2 > 0. Apparently, domestic investment has to decrease. The question is whether the second term in the equation for foreign investment (equation (7) ) can outweigh the first term so that foreign investment increases. Clearly, this cannot happen, because in this case foreign output in the second period would have to be higher, and consequently dP2 would have to be negative, not positive as we have assumed.

The change in the current account can be determined by totally differentiating the CA equation.

dcA = -d(PZ1) - dCX - dX

The direction of the change is ambiguous. Before producing an example in which this relationship is positive - which means that the relationship between the foreign current account and a foreign positive innovation to output is negative - it may be useful to explain why no such ambiguity is found in the existing literature.

Suppose that we analyse the behaviour of a small open economy with a single good which can be either consumed, lent to (borrowed from) the rest of the world, or invested in some domestic production project. Clearly, if the domestic production is subject to decreasing returns to scale, a positive temporary supply shock will translate into an improvement in the current account because of the fixed return the small country receives on her loans. If the country is a large one, it can influence both rates of return (i.e., both the return on the domestic project and the world interest rate). Hence the effect on the current account is going to be smaller, yet positive if we rule out immiserizing growth.

In our model, a positive temporary technological shock may deteriorate the current account even in the absence of direct or indirect immiserizing growth. Suppose, for instance, that the elasticity of exports of the foreign country with respect to the terms of trade is unity, so that there is no immediate welfare improvement when the production of Z1 increases. Subsequently d(PZ,) -0

10 We have assumed perfect capital mobility, which may not be a very realistic assumption for developing countries. Allowing for capital controls, however, need not affect any of our results if the capital controls take the form of taxes. This is because our model requires a positive co-movement of domestic and foreign real interest rates only when a disturbance like the one analysed in section 3 occurs; equality of real interest rates is not necessary. A tax creates a wedge between real interest rates, but as long as tax policy is held constant, interest rates move in the same direction; hence the response of investment and output is qualita- tively the same and the same covariance pattems obtain. If capital controls take the form of quantity restrictions, it may not make much sense to discuss co-movements of investment across countries when the optimal investment response requires the violation of a rigidly binding constraint. I believe that (a) controls are effectively of the tax type (black markets and other widespread 'illegal' activities essentially convert quantity restrictions into implicit taxes, and (b) the public sector, which is not subject to the controls, is a major participant in international asset transactions in many developing countries.



Cyclicail co-movements 867

and the change in the foreign current account is dcA = - dx - dc1. We saw before that following an increase in Z1, we can have either excess supply or excess demand in the home good market. If excess supply prevails, the interest rate has to decrease to encourage current expenditure. Both x and cl respond inversely to interest rate changes, so the foreign current account, starting from a balanced position, goes into a deficit. Welfare is higher in both countries.

The crucial factor in the determination of the relationship between the current account and output expansion is not the comparison of the signs of welfare gains (as is the case with immiserizing growth) but rather the comparison of the size of country gains (that is, which country gains relatively more). For instance, consider the standard two-country / two-period / two-commodity trade model with incomplete specialization. If the domestic country experiences growth in a commodity which plays a more important role in the foreign consumption bundle than in the domestic, it is possible (under certain elasticity-shares conditions) for the foreign country to register a relatively larger welfare gain from higher output growth at home. In such a case, a deterioration in the home current account is to be expected as the foreigners try to smooth consumption over time.

In the next section we consider a future productivity shock.

A FUTURE PRODUCTIVITY SHOCK

Suppose that the foreign country expects a gain in future productivity. By writing second period's production function as a2f(k2), this gain means that for a given capital stock, second-period output is expected to increase by

f(k9da2. The first-order conditions for the maximization problem are

u' = /B(1 + r)u[

1 + r = P2a2fI2.

Then the analogue to (7) is

dc, = cp,dP, + cp2dP2 + c,dr, + ca2da2

dx = xrdr + xp2dP2 + xa2da2.

Ca2 is positive because people try to smooth consumption over time; Xa2 is positive because the expected technological shock increases the expected marginal productivity of capital.

Using the market clearing conditions, we have

Ep Ild hII + EP2hI dP2 ? Er.h I dr = (Ca2 + xa2)da2

E f'dP = 0

E 2dP + E'f2dr= (f2 + f2 p2 d2 r El' fX2)da2



868 Harris Dellas

or equivalently (since dPj = 0)1

Er2hl dP2 + Erh ' dr = (Dh l/ aa2)da2 (I la)

f 2dP2 + Ef2dr -(Sf2laa2*2, ( lb)

where the RHS in (1 la) is the increase in demand for consumption and investment by the foreigners in the face of expected productivity gains, and the RHS in (1lb) is the increase in second period's output (positive too). Again assume that Ep, h= 0. Then the interest rate has to increase (if Er"1 is negative) to clear first period's home good market. The reasons is that at the initial r excess demand prevails as the foreigners increase their desired expenditure. As r increases, domestic agents cut down on their spending hence making room for foreign expenditure to increase. Under the assumptions made earlier, a higher interest rate results in excess supply in the foreign good market in the second period (the supply of Z2 has gone up because both k2 and a2 are higher, while demand has gone down because of the reduction in X). Clearly P2 has to decrease to restore equilibrium.

Foreign output in the second period is definitely higher. The direction of change in domestic output is ambiguous. Recall that the production level depends on both X and Z2, and we know that X has decreased while Z2 has gone up. The net effect depends on relative production shares, as well as on the elasticities of Z2 and X with respect to r and P2.

The home current account improves because domestic expenditure is lower.

CONCLUDING COMMENTS

A two-country, two-period model has been used to examine the response of world trade and aggregate economic activity as well as the real interest rate and the terms of trade to various exogenous real disturbances. Despite the low time dimension of the model, we managed to obtain most of the empirical regularities that characterize world business cycles. Under the conditions described in the third section (that is, supply responds more to a change in the price of the intermediate good than demand does to a change in income), following a supply disturbance, output, investment, imports, and exports are higher in both economic zones, now and in the future, and the real interest rate is lower (positive and persistent co-movements in trade and GNPs). The sign of the relationship between the terms of trade and the current account is

11 A future technological change in the LDC leaves the present relative price of the raw material unchanged only because the raw material is perishable. Had the analysis taken the perspec- tive of changing future productivity in the industrial country, agents would have had an in- centive to store more or less of the home good in the first period, and PI would have been affected. Hence the analysis is not symmetric with respect to supply shocks originating at home versus abroad. The reason for choosing an asymmetric set-up is that in addition to capturing a feature of the nature of many LDC exportables, it greatly facilitates the analysis.




ambiguous, depending not only on the type of the exogenous disturbance but also on the structural parameters of the model. Similarly, the cyclical behaviour of the current account is ambiguous, depending on the size of the cross country distribution of gains from growth.12

REFERENCES

Branson, W. (1983) 'Economic structure and policy for external balance.' IMF Staff Papers 30

Choudri, E. and L. Cohen (1980) 'The exchange rate and the international transmission of business cycle disturbances: some evidence from the great depression.' Journal of Money, Credit and Banking 12, 565-74

Dellas, H. (1985) 'Cyclical co-movements in real economic activity and prices in the world economy.' PH D Dissertation, University of Rochester (1986) 'A real model of the world business cycle.' Journal of International Money and Finance 5, 381-94

Dornbusch, R. (1983) 'Real interest rates, home goods and optimal external borrow- ing.' Journal of Political Economy 91, 141-53

Kydland, F. and E. Prescott (1982) 'Time to build and aggregate fluctuations.' Eco- nometrica 50, 1345-70

Long, J. and C. Plosser (1983) 'Real business cycles.' Journal of Political Economy 91, 39-69

Lucas, R.E. (1977) 'Understanding business cycles.' In K. Brunner and A. Metzler, eds, Stablization of the domestic and international economy, Carnegie-Rochester series in public policy 5 (Amsterdam: North-Holland)

Marion, N. and L. Svensson (1981) 'World equilibrium with oil price increases: an intertemporal analysis.' IIES, University of Stockholm, no. 248

Prescott E. (1986) 'Theory ahead of business cycle measurement.' Federal Reserve Bank of Minneapolis Quarterly Review (Fall), 9-23

Sachs, J. (1981) 'The current account and macroeconomic adjustment in the 1970s.' Brookings Papers on Economic Activity 1, 20148

Stockman, A. (1982) 'International trade and business fluctuations.' Unpublished manuscript (1986) 'Sector disturbances, government policies, and industrial output in seven European countries.' Unpublished manuscript

12 The dependence of current account movements on parameters of the utility and production functions in a context of a small open economy with non-traded goods is also emphasized in Dornbusch (I 983).



cyclical co-movements of output and trade in the world economy

Documents