Macroeconomic interdependence with trade and multinational activities

Macroeconomic Interdependence with Trade andMultinational Activities

Lilia Cavallari*

AbstractThis paper examines how differences in the integration strategies followed by firms active in foreign marketsaffect the way productivity and policy shocks spread their effects worldwide.The analysis incorporates costlytrade and local sales by multinational firms in a general-equilibrium open economy macroeconomic model.The mode of foreign market access is found to play a major role in the international business cycle, affectingthe dimension of consumption and output spillovers worldwide.We show that despite financial markets beingeffectively complete, consumption risks may not be fully insured in the world economy as long as multi-national firms discriminate prices across markets. Furthermore, cross-country differences in firms’ integrationstrategies can account for extensive asymmetries in the way country-specific and global shocks are transmit-ted in the world economy.We argue that this may have relevant consequences for the welfare implications ofmonetary and trade policies.

1. Introduction

This paper incorporates costly exports and local sales by multinational enterprises in anew open economy model with the aim of investigating the macroeconomic implica-tions of cross-country differences in the mode of serving foreign markets.

The mode of foreign market access has attracted growing attention in the tradeliterature, with a number of recent contributions focusing on the determinants of entrybehavior by multinational corporations.1 Much less attention has been typicallydevoted to the issue in international macroeconomics, at least until a novel generationof general-equilibrium open economy models has emerged where foreign marketaccess is at the forefront. One line of research investigates the determinants of firms’entry and exit decisions in an environment characterized by nominal rigidity and/ortrade costs, with only a very limited number of papers in this area allowing for multi-national activities.2 A second approach stresses the macroeconomic implications offrictions in international goods markets arising from trade costs, as in Obstfeld andRogoff (2000), and from multinational sales as in Devereux and Engel (2001) andCavallari (2004). The present paper contributes to the latter line of research by pro-viding a unified framework that conveniently nests earlier models with trade costs andmodels with internationalized production. Specifically, our study investigates whetherthe way firms access foreign markets, through trade or with sales by local affiliates ofmultinational corporations, matters for the international transmission of changes inproductivity, monetary policy and trade liberalization policies.

The paper considers a two-country world economy in the tradition of the “new openeconomy” literature where markets are characterized by monopoly distortions and

* Cavallari: University of Rome III, DIPES, Via Chiabrera, 199, 00146 Rome, Italy. Tel: 39-065 733 5327; Fax:39-065 733 5282; E-mail: [email protected]. I wish to thank two anonymous referees, AlessandroCalza, Bartosz Markowiak, and participants in the 9th ICMAIF conference, the ECB workshop on “Glo-balisation and Regionalism” and the CFSifo–Delphi conference on “Global Economic Imbalances: Prospectsand Remedies” for many useful comments. The usual disclaimer applies.

Review of International Economics, 16(3), 537–558, 2008DOI:10.1111/j.1467-9396.2008.00744.x

© 2008 The AuthorJournal compilation © 2008 Blackwell Publishing Ltd, 9600 Garsington Road, Oxford, OX4 2DQ, UK and 350 Main St, Malden, MA, 02148, USA

mailto:[email protected]

prices are sticky. We depart from most contributions in this area by considering twoalternative ways of serving foreign customers. In our set-up, firms can either exporttheir products abroad, incurring trade costs, or they can produce in the sales market bymeans of production facilities located overseas. The model rests on the basic assump-tion that imported goods and goods produced by local affiliates of multinationalcorporations are imperfect substitutes. The assumption captures the fact that multi-nationals may have a comparative advantage relative to exporters in customizing theirproducts across different locations. They can, for instance, include local nontradedcomponents in the process of production or distribution of their products. The mainadvantage of our specification is that it encompasses a variety of integration strategiesworldwide, depending on whether countries mostly trade between each other orengage in multinational activities, yet keeping the model analytically tractable.

Our results reveal that the mode of foreign market access plays a remarkable role inthe international transmission of productivity and policy shocks, such as changes intransport costs and the global monetary stance. Moreover, accounting for multinationalsales along with trade helps explain a number of “puzzling facts” in internationalbusiness cycle data.

First, we show that despite financial markets being effectively complete, segmenta-tion in international goods markets may give rise to large fluctuations in the level ofconsumption across countries. Moreover, local sales by multinational enterprises canexacerbate consumption asymmetry in the world economy and reduce the possibilitiesof risk-sharing worldwide. For an intuitive account of the result, consider a decline indomestic productivity.The productivity slowdown raises the marginal costs faced by allfirms located on home soil, thereby leading to a permanent increase in the price ofdomestic products. Yet, the fall in home productivity has only a negligible effect onforeign consumers as long as home firms mainly serve foreign markets through theiraffiliates abroad. The fall in home demand, however, will reduce the profits of foreignmultinationals in the home market, thereby leading dividend incomes to co-moveacross countries. The combination of tiny consumption spillovers and substantialincome co-movements is consistent with a well-documented fact in internationalmacroeconomics, showing that the cross-country correlation of consumption acrossindustrialized economies is much smaller than what is predicted by standard theoreticalmodels and well below that of output.

Secondly, we establish that differences in the integration strategies across countrieslead to asymmetries in the way country-specific and global shocks spread their effectsworldwide. This in turn may have relevant consequences for the welfare implicationsof monetary and trade policies. We stress that a policy which is beneficial for acountry that engages in large multinational activities might turn counterproductive incountries that mostly trade with the rest of the world. Consider for instance a policyof trade liberalization, as represented by a symmetric worldwide decrease in tradecosts. The drop in trade costs, by reducing the price of traded goods relative to theprice of goods produced in the sales market, will deteriorate the terms of trade ofcountries, like emerging economies, which mainly export their goods rather thanoperating through multinational corporations. Consequently, agents in less-developedeconomies will need to supply more labor effort in order to buy a given unit of theforeign good. We similarly argue that cross-country asymmetries in the mode offoreign market access may also affect the distribution of the gains from a worldmonetary expansion.

Thirdly, we show that including multinational activities along with trade providesexcess volatility in nominal exchange rates. Multiple temporary equilibria and

538 Lilia Cavallari

© 2008 The AuthorJournal compilation © Blackwell Publishing Ltd 2008

exchange rate overshooting may materialize in our set-up as a consequence of cross-border profit flows by multinational firms.

The paper is structured as follows. Section 2 models the world economy. Section 3derives the equilibrium allocation when prices are flexible and discusses the long-runimplications of the model. Section 4 examines the world equilibrium and the inter-national monetary transmission when prices are sticky. Section 5 concludes.

2. The Model

We consider a two-country world economy in the tradition of the new open economymacroeconomics where goods markets are characterized by monopoly distortions andprice are predetermined. Each country is specialized in the production of one type ofgood, as in Corsetti and Pesenti (2002), and each type of good appears in an infinitevariety of imperfectly substitutable brands.All varieties of home and foreign goods areconsumed in the world economy. We depart from most contributions in this area byconsidering two alternative ways of serving foreign markets: firms can either exporttheir products abroad, incurring trade costs, or they can produce in the sales market bymeans of affiliates overseas.

Consumers’ Preferences and Intratemporal Choices

Each country is inhabited by a continuum of agents of unit mass. Expected lifetimeutility of a typical home agent i is defined as:

Ωit tt

iti

ii

t

U CMP

L= ⎛⎝⎜

⎞⎠⎟

−

=

∞

∑E βτ

τ, , , (1)

where flow utility is a positive function of real consumption, C, and real money bal-ances, M/P, a negative function of labor effort, L, and b is the discount factor.3 In orderto keep algebraic complexity at a bare minimum, we adopt the additively-separablespecification:

U CMP

Lit itit

tt it= + −ln ln ,χ κ (2)

where c is a measure of liquidity and k is a real disturbance which can be interpretedas a shock to the natural rate of output.

The consumption basket C comprises home, CH, and foreign goods, CF, with aconstant elasticity of substitution equal to one:

CC CH F=

−( )

−

−

γ γ

γ γγ γ

1

11. (3)

Foreign goods consumed in the home market can be either imported from abroad orproduced in the home country by local subsidiaries of foreign firms. We assume thattraded goods and goods produced in the sales market are imperfect substitutes:

C C CF FF FH= −1 Ψ Ψ* *, (4)

where CFF is consumption of the foreign imported good, CFH is consumption of theforeign good produced in the home country, and the parameter Y* captures the degreeof internationalization of foreign production. As will be discussed below, a value of Y*

MACROECONOMIC INTERDEPENDENCE 539


close to one implies that almost all foreign firms are multinational enterprises thatserve the home market through their affiliates in the home country.

The consumption index (4) states that traded goods and goods produced in thesales market are differentiated, leaving in the background the reasons why this mightbe so. One possible line of argument draws on the presence of different nontradablecomponents in the process of production and distribution faced by exporters andmultinationals. In this vein, one might say that goods produced in the sales marketcan be better tailored to the preferences of local consumers, for example, by incor-porating some nontradable input or passing through noncompetitive local retailingnetworks. Alternatively, one could claim that firms are inherently heterogeneous invarious dimensions that are potentially relevant for consumers and that only certaintypes of firm choose to become multinational.4 For instance, multinational firmsmight be characterized by higher levels of productivity or they can have access tomore advanced technologies or they can invest more in advertising their products. Inall these cases, consumers perceive the products of multinationals as varieties ofhigher quality.

Domestic and foreign goods appear in an infinite variety of imperfectly substitutabletypes, indexed by h ∈[0, 1] in the home country and f ∈[0, 1] in the foreign country, asshown below:

C C h dh

C C f df

H H

FH FH

= ( )⎡⎣⎢

⎤⎦⎥

= ( ) ( )

− −( )

−

∫φφ

φφ

φ φφ

1

0

1 1

11

0

1Ψ

Ψ

** *

**

∫∫

∫

⎡

⎣⎢⎢

⎤

⎦⎥⎥

=−( ) ( )

⎡

⎣⎢⎢

⎤

⎦⎥⎥

−( )

−

φφ

φ φφ

**

* **

* *

1

111 1

1C C f dfFF FFΨΨ

φφφ

**−( )1

,

(5)

where varieties of the foreign good in the interval (0, Y*) are produced in the homemarket by local affiliates of foreign multinational firms and the remaining varieties aretraded. All varieties of home goods in the unit interval are produced in the domesticmarket. In the above indices, f > 1 and f* > 1 capture the elasticity of substitutionamong the different brands of, respectively, home and foreign goods.

As usual with Cobb–Douglas preferences, demand for home and foreign consump-tion goods is a constant share of total consumption expenditure:

P C PC

P C PCH H

F F

== −( )γ

γ1 ,(6)

where P is the utility-based consumer price index, and PH and PF the price of, respec-tively, home and foreign goods. Similarly, the demand for foreign traded goods and forthe products of foreign multinationals is:

P C P C

P C P CFH FH F F

FF FF F F

== −( )Ψ

Ψ*

*1 ,(7)

where PFH is the price for the products of foreign multinationals and PFF the price offoreign traded goods.

540 Lilia Cavallari


Finally, CES preferences imply that the demand for each variety of home and foreigngoods is negatively associated with its relative price:

C hP h

PC

C fP f

PC

HH

HH

FF

FF

( ) = ( )⎛⎝

⎞⎠

( ) = ( )⎛⎝

⎞⎠

−

−

φ

φ*

,

(8)

where PH(h) is the price of variety h of the home good and PF( f ) the price of varietyf. The price indices that correspond to the above specification of preferences are:5

P P PH F= −γ γ1 (9)

P P PF FH FF= −Ψ Ψ* *1 (10)

P P h dh

P P f df

H H

FH FH

= ( )⎡⎣ ⎤⎦

= ( )⎡⎣⎢

⎤⎦⎥

− −

− −

∫

∫

1

0

11

1

1

0

111

φ φ

φ φ

ΨΨ

*** *

PP P f dfFF FF=−

( )⎡⎣⎢

⎤⎦⎥

− −∫

11

111

1

Ψ Ψ**

*

*φ φ.

(11)

Individual Budget Constraint and Intertemporal Choices

We assume that markets are incomplete. Each Home resident holds home currency,two international bonds, BH

i and BFi* , respectively denominated in home and foreign

currency and an equal share in the profits of home firms. In our set-up with multi-national firms, the domestic equity market comprises all home firms, independently ofwhere their production units are located while excluding some firms, as the homesubsidiaries of foreign multinationals, that produce on the home soil.

Home agents receive labor income at the nominal wage rate W from domestic andforeign firms active at home, a share si in the profits of home national and multinationalfirms, P, where Sisi = 1, and pay nondistortionary net taxes, T, to the government. Theflow budget constraint of agent i is therefore:

B B M B i B i MW

Hti

t Fti

ti

Hti

t t Fi

t ti

t

+ + + + ++ + ≤ +( ) + + ++

1 1 1 1 11 1ε ε* * *( )LL L s P C Tht

ifti

i t ti

ti

ti+( ) + − −Π , (12)

where i and i* are, respectively, home and foreign nominal interest rates and e is thenominal exchange rate defined as units of home currency for one unit of foreigncurrency.

Home agents choose consumption, labor effort, money, and bond holdings in eachperiod so as to maximize utility (2) over their whole life horizon subject to the budgetconstraint (12). By aggregating the first-order conditions across symmetric agents, wecan easily derive money demand as a function of nominal spending and the nominalinterest rate:

MP

Ci

it

tt

t

t

= + +

+χ 1 1

1

, (13)



the risk-adjusted uncovered interest rate parity:

E E*

tt

t tt

t

t t

t

tP C P Cii

ε ε+ +

+

+ +

+

+

⎛⎝

⎞⎠ =

⎛⎝

⎞⎠

++1 1

1

1 1

1

1

11

, (14)

which links domestic and foreign interest rates to the expected movements in thenominal exchange rate and, finally, labor supply:

WP

Ct

tt t=κ . (15)

Firms

Without loss of generality, we associate each firm to a single variety, so that the homefirm h is the sole producer of the corresponding variety of the home good and similarlyfor the foreign firm f.6 We assume that a share Y of domestic firms serve foreigncustomers through subsidiaries located abroad while the remaining share 1 - Y oper-ates via exports. In the foreign country, the shares of multinationals and exporters are,respectively, Y* and 1 - Y*. As is common in proximity–concentration models afterBrainard (1993), we also posit that exports entail iceberg-type transport costs, so thatfor one unit of the final good to arrive at a foreign destination t > 1 units must be sent.These shipping costs capture a variety of (variable) costs associated with internationaltrade.7 The presence of trade frictions typically provides a motive for multinationalactivities, as firms invest in sales facilities abroad whenever the gains in avoidingshipping costs outweigh the sunk costs of maintaining capacity in multiple locations(the proximity–concentration tradeoff).

We are now ready for discussing how our assumptions on the structure of trade andmultinational activities relate to similar approaches in the literature. We begin bystressing that our specification conveniently nests earlier models with trade costs, asObstfeld and Rogoff (2000) and Obstfeld (2001), and models with internationalizedproduction as Devereux and Engel (2001) and Cavallari (2004).8 The first line ofresearch focuses on the role of trade costs in explaining major empirical puzzles ininternational macroeconomics. Trade costs alone, however, do not allow to tackleproperly the pricing puzzles related to the dynamics of exchange rates and the terms oftrade. For this purpose, as Obstfeld and Rogoff put it, “it is necessary to build-in adistinction between retail and wholesale pricing,” therefore introducing some form ofdistribution activity both within and across the boundaries of the firm. The second lineof research stresses the role of multinationals in segmenting international goodsmarkets, thereby contributing to the disconnect between consumers’ and producers’prices that we observe in terms of trade and exchange rate data. Devereux and Engelfocus on the currency of denomination of multinational products and its implicationsfor the choice of the exchange rate regime. In Cavallari, segmented markets arise fromintra-firm trade in intermediate goods. Both papers make the extreme assumption thatall trade takes place through foreign affiliates of multinational corporations, implicitlyassuming prohibitive trade costs.

We further emphasize that the structure of foreign market access in the abovecontributions as well as in the current paper is consistent with a variety of alternativemodels of endogenous trade and foreign direct investments.A number of contributionsstress the role of various dimensions of firms’ heterogeneity in explaining the structureof international trade, from differences in productivity, as in Mélitz (2003), to variability

542 Lilia Cavallari


of trade costs at the firm level, as in Bergin and Glick (2007).9 Other studies emphasizecross-country cyclical asymmetry as a possible determinant of entry in foreign mar-kets.10 In this vein, it is argued that countries characterized by higher levels ofproductivity will attract new investors and have a larger market size (the well-knownhome market effect) and the more so the lower the legal and economic barriers tofirms’ entry.

Production Technology is linear in labor and symmetric across countries.A home firmthat produces variety h for sales to domestic residents and exports faces the followingproduction function:

Y h LH hi( ) = ,

where YH(h) is output of variety h of the home good produced in the home country andLh

i is the corresponding labor input. A home multinational that produces variety h inthe foreign country for sales to foreign residents has the following technology:

Y h LF hi( ) = *,

where YF (h) is output of variety h produced in the foreign country and Lhi* is the foreign

labor input. Similarly, for foreign firms we have:

Y f L Y f LF fi

H fi* **( ) = ( ) = .

The structure of technology captures the fact that multinational firms incur someproduction costs abroad and are therefore directly affected by foreign productivityshocks as well as by a change in the nominal exchange rate.

Pricing strategy Firms act as monopolistic competitors and are therefore price-makerin the goods market. With flexible prices, each firm sets the price for its own variety soas to maximize current profits given market demand (8). All firms face similar pricingproblems and, therefore, set identical prices in a symmetric equilibrium. Aggregatingthe first-order conditions for profit maximization across firms, we obtain the usualmarkup rule:

� � �

� � �

P W PW

P W

P W P W P

Ht t HHtt

tHFt t

Ft t FHt t FFt

= = =

= =

Φ Φ Φ

Φ Φ

* * *

* * * *

τε

== Φ* *τεt tW ,

(16)

where F ≡ f/(f - 1) and F* ≡ f*/(f* - 1) are indices of monopoly distortions in, respec-tively, the home and foreign market. For future reference, note that a tilde over avariable indicates that it is calculated with flexible prices.

When prices are predetermined, firms maximize the expected value of profits in eachperiod conditional on market demand. Home and foreign firms that operate on domes-tic markets will therefore set the prices for their products as follows:

PW PC

PCP

W P C

P CHt

t t t t

t t tFt

t t t t

t t

=( )( )

=−

−

−

−

Φ ΦEE

* *E * * *

E *1

1

1

1

( )

( tt*), (17)

where a bar over a variable indicates that it is calculated in the regime with stickyprices. It is worth stressing that preset prices incorporate a risk premium over expected



nominal marginal costs, Et-1(Wt), arising from the covariance of profits with the mar-ginal utility of consumption. As long as profits increase, in fact, the marginal value ofeach additional unit of profits in terms of consumption will decrease.

Firms active in foreign markets face an additional source of uncertainty related tounexpected movements in the nominal exchange rate. A depreciation of the homecurrency, for instance, might reduce the profits of foreign firms as long as it leads to arise in the home-currency price of their products and a consequent drop in marketdemand. The risk premium in foreign markets will clearly depend on the extent towhich fluctuations in the nominal exchange rate are transmitted into final prices. In theabove example, foreign firms would have no reason to expect a decline in their profitswhen the home-currency price of their product does not respond to the depreciation,i.e. when the degree of exchange rate passthrough in the home market is zero.

Foreign-currency prices can be set in the currency of consumers, in that of theproducers or according to any combination of these two pricing strategies, implyingdifferent degrees of exchange rate passthrough. Empirical evidence on traded goodprices, as documented by, among others, Engel and Rogers (1996, 1998), Goldberg andKnetter (1997), Parsley and Wei (2001), and, more recently, Campa and Goldberg(2005) points to a degree of exchange rate passthrough into import prices which ishigher than zero on average, although far below unity.11 As regards the pricing strate-gies of multinational firms, Lipsey (1999) documents that US multinationals do engagein substantial pricing to market activities through their sales facilities overseas, imply-ing that exchange rate passthrough in multinational sales is far from complete.

Following Corsetti and Pesenti (2005), we allow for any degree of exchange ratepassthrough by assuming that firms optimally choose the predetermined price for theirproducts in foreign currency and recognize that the final price for consumers will varywith the exchange rate at a constant elasticity equal to h in the home market and h* inthe foreign market:

P h P h P f P f i H FHi Hi Fi Fi( ) = ( ) ( ) = ( ) =−ˆ ˆ , , ,* *ε εη η (18)

where P̂ hHi*( ) is the predetermined foreign-currency price for variety h of the homegood produced in country i and P̂Fi( f ) the predetermined price in home currency forvariety f of the foreign good produced in country i. In this setting, firms take the degreeof exchange rate passthrough as given when fixing their prices. A value of h* = h = 0corresponds to local currency pricing, namely a situation where prices are set in theconsumers’ currency and do not respond to movements in the exchange rate. The caseh = h* = 1 corresponds to producers’ currency pricing: producers set prices in their owncurrency and let the foreign-currency price of their product vary with the nominalexchange rate.

Optimal price setting in foreign markets yields:

PW P C

P CP

WHHt

t t t t t

t t t t t

HFtt t* E * *

E * ** E*

*= =−

−

−Φ Φτ εε ε

η

η1

1

1( )

( )

( ** * *

E * *

* E *

*

*

P C

P C

PW PC

t t t

t t t t t

FFtt t t t t

t

εε ε

τ εε

η

η

η

)

( )

( )

−

−−

=

1

1Φ−−

−−

−−

−−

−=η

η

η ηεε

ε εE*

EEt t t t

FHtt t t t t

t t t t tPCP

W PCPC1

11

1( )( )

( )Φ ..

(19)

In the expressions above, firms active in foreign markets consider both movements innominal marginal costs and the exchange rate in the future when setting their prices.Anexpected appreciation of the domestic currency, i.e. a fall in e, for instance, will reducesales revenue in foreign currency, leading home firms to hedge against the risk of a

544 Lilia Cavallari


future decline in profits by incorporating a premium in the foreign-currency price oftheir products.

Optimal prices (19) and (17) are valid for any distribution of the underlying shocks,provided the participation constraints are not violated:

P W

P W

P W

P W

P W

P W

H

F

H

F

HF

FH

≥

≥

≥

≥

≥

≥* * * *

* *ˆ

ˆ

ˆ

ˆ .

τ

τ(20)

In what follows, the domain of real and nominal shocks is restricted so that the aboveconstraints are always satisfied.

Government’s Budget Constraint

The domestic government simply rebates all seigniorage revenue in lump-sum transfersto households:

M M di T diit it it− + =−∫ ∫10

1

0

10. (21)

Governments affect the stock of domestic monetary assets by controlling the short-term interest rate. Following Corsetti and Pesenti (2005), we define an index ofmonetary stance m in the home country such that:

11

11

1μβ

μtt

t

i≡ +( ) ⎡⎣⎢

⎤⎦⎥

++

E . (22)

In equilibrium, it is immediate to derive m as the inverse of the marginal utility ofconsumers’ wealth, PC.12 Expression (22) links a given time path of m to a correspond-ing sequence of home nominal interest rates: a monetary expansion is associated witha higher m and a lower i.

Aggregate Resource Constraints

Asset markets’ equilibrium implies that international bonds are in zero net supply inthe world economy:

B di B di B di B diHti

Hti

Fti

Fti

0

1

0

1

0

1

0

10 0∫ ∫ ∫ ∫+ = + =* * . (23)

Goods markets are cleared when the world supplies of home and foreign goods equalthe corresponding world demands:

Y h dh Y h dh C di C C di

Y f

H F Hi

Hfi

HHi

F

( ) + ( ) ≥ + +

(

∫ ∫ ∫ ∫0

1

0 0

1

0

1Ψ[ ]* * *

*

* *τ

)) + ( ) ≥ + +[ ]∫ ∫ ∫ ∫df Y f df C di C C diH Fi

FHi

FFi

0

1

0 0

1

0

1* * *

* *Ψτ .

(24)

Finally, labor market equilibrium requires that the total amount of labor used indomestic production must equal aggregate labor supply in the home and foreigncountry, L and L*, respectively:

L Ldi Y h dh Y f df

L L di Y f df Y

iH H

iF

≡ ≥ ( ) + ( )

≡ ≥ ( ) +

∫ ∫ ∫∫ ∫

0

1

0

1

0

0

1

0

1

*

* * *

*Ψ

FF h dh( )∫0Ψ

.(25)



Aggregating the budget constraint (12) across home agents and using the govern-ment (21) and resource constraints (24) and (25), yields the aggregate accountingequation for the home economy:

PC P C P C WC W CH H H H FH HF= + + −ε ε* * * * , (26)

where use has been made of the assumption of initial financial autarky in each country,i.e. B BH F0 0 0= =* . The equality above simply states that nominal spending, on theleft-hand side, must equal nominal incomes as given by dividend and labor incomes. Inour set-up with multinational firms, nominal incomes coincide with the revenues fromsales at home and abroad (the first two terms on the right-hand side) net of laborcosts—wherever they are incurred—and plus the labor income of home residents,which gives the last two terms on the right-hand side.The current account equation (26)can be reformulated as follows:

ε εP C P CP W

PP C

P WP

PHH HH FF FFHF

HF

H HFH

FH

* ** *

** *− + −⎛

⎝⎜⎞⎠⎟

− ∗ −⎛⎝

⎞⎠Ψ Ψ FF FC = 0, (27)

where the first two terms represent the value of home exports minus the value of homeimports, i.e. the trade balance, and the last two terms are net factor payments, namelydividends of home multinationals abroad less dividends of foreign multinationals athome.

It is worth stressing that in the class of models that use log utility, net assets are zeroat any point in time provided initial nonmonetary wealth is zero as well.13 This well-known property of our specification will be used in deriving the nominal exchange rate.

3. The Flexible Price Benchmark

In this section, we express the equilibrium levels of the endogenous variables asfunctions of monetary and real shocks in the regime where prices are flexible. Theequilibrium in the world economy is characterized as follows. Given the stochasticprocesses driving monetary policies, m and m*, and shocks to productivity, k and k*, andgiven the initial holdings of bonds, money, and shares, the flex-price equilibrium is a setof processes for the nominal exchange rate �ε , the home allocations and prices (L̃, C̃H,C̃FH, C̃FF, P̃H, P̃FH, P̃FF, and W̃) and their foreign counterparts (L̃*, �CF*, �CHH* , �CHF* , �PF*, �PHH* ,PHF* , and W̃*) such that (a) consumers’ optimality conditions are satisfied, (b) firms’profits are maximized, (c) the market-clearing conditions are met for each asset, eachgood, and for labor, and (d) the resource constraints are satisfied.

Our solution strategy begins by recognizing that the nominal exchange rate is impli-citly defined in the aggregate accounting equation. Since in equilibrium m = PC andm* = P*C*, labor supply (15) implies that nominal wages are equal to km in the homecountry and k*m* in the foreign economy. Using the above fact together with demands(6) and (7) and optimal prices (16) into (27), we call rewrite the current accountequality as follows:

� �ε γ μ γ μ ε γμ γ μ1 1 1 1 0−( ) − −( ) −( ) + − −( ) =Ψ Ψ ΨΦ

ΨΦt t t t* * *

*,

i.e.

�ε γγ

μμ

= − −[ ]( )− [ ]( )

1 11*

* *Ψ ΦΨ Φ

. (28)

546 Lilia Cavallari


Expression (28) states that the nominal exchange rate in the equilibrium with flexibleprices is determined by the relative monetary stance in the world economy.A domesticmonetary expansion, an increase in m, leads to an exchange rate depreciation, anincrease in �ε , while an appreciation of the home currency is associated with an easingof the foreign monetary stance.

It is straightforward to verify that the following prices satisfy the markup rule (16):

�

��

�

�

�

P

P

P

P

P

P

H

HF

FH

HH

FF

F

=

==

=

=

=

Φ

ΦΦ

Φ

Φ

Φ

κμ

κ μκμ

τκμετεκ μ* * *

*

*

* * *

* *κκ μ* *.

(29)

Next, we obtain the equilibrium levels of consumption in the world economy fromm = PC and m = P*C*, where P and P* are calculated using (29) into the CPI definition(9):

�

�

C a

C a

= ( ) ( )= ( ) ( )

+ −( ) −( ) −( )

−( ) − +

1 1

1 1

1 1 1

1 1

κ κ

κ κ

γ γ γ

γ γ

Ψ Ψ

Ψ

* *

*

* **

γγΨ

,

(30)

where the constants are inversely related with world monopolistic distortions:

a

a

≡ ( ) −( ) − [ ]( )− [ ]( )

⎛⎝⎜

⎞⎠⎟

≡

− −−( ) −( )

Φ Φ Ψ ΦΨ Φ

Φ

Ψγ γ

γγτγ

** *

*

*1

1 11 11

−− −−( )

( ) −( ) − [ ]( )− [ ]( )

⎛⎝⎜

⎞⎠⎟

γ γγγ

τγΦ Ψ Φ

Ψ Φ

Ψ

** *1

11 11

.

Equations (30) say that consumption in the world economy is a function of globalproductivity shocks. A fall in world productivity, i.e. an increase in k or k*, is associatedwith a lower level of consumption at home and abroad. The extent to which country-specific shocks spread their effects worldwide depends on countries’ size, as captured bythe parameter g ,as well as on the degree of internationalization in production,Y and Y*.A decline in, say, home productivity will increase home marginal costs and therefore theprice of goods produced at home, thereby reducing consumption both at home andabroad. International spillovers are large as long as foreign agents consume a largeamount of goods produced in the home country, i.e. when g is high and Y is low.Movements in the terms of trade ensure that the benefits and costs from country-specificproductivity shocks spread around the world, changing the composition of world spend-ing. In the example above, the fall in home productivity will improve the home terms oftrade, thereby shifting world spending towards foreign goods. As a consequence, con-sumption will decrease in both countries. The decline in home productivity, on thecontrary, has no effect for foreign consumption whenever foreign customers are mainlyserved through local subsidiaries of home multinational firms (Y = 1).14

Finally, we derive the equilibrium level of employment at home and abroad from thelabor market-clearing equation (25), yielding:

� �Lb

Lb= =

κ κ*

**

, (31)



where

b

b

≡ + −( ) −( ) − [ ]( )− [ ]( )

+ −( )

≡ − + −

γ γτ

γ

γ γΦ

Ψ Ψ ΦΦ Ψ Φ

ΨΦ

ΦΨ

1 1 11

1

1 1

* * **

**

*** *

( ) − [ ]( )− [ ]( )

+11

Ψ ΦΦ Ψ Φ

ΨΦτγ

.

Equations (31) indicate that output is exclusively determined by country-specificproductivity shocks independently on the way firms serve foreign markets.A decline inhome productivity leads to a fall in home employment as a result of the choice on thepart of home agents to optimally smooth labor effort along time.

International Prices

In order to see more clearly how the mode of foreign market access affects the wayshocks are transmitted in the world economy, we consider the relative price of homegoods in international markets, � � �Q P PH F= ε * :15

�Q = −[ ]( ) −( )− [ ]( )

⎛⎝⎜

⎞⎠⎟

−− +

τ γ κγκ

Ψ ΨΨ ΨΦ

ΦΨ Φ

Ψ Φ*

*

** * *1 1

1

1

. (32)

We first observe that Q̃ reacts to a policy of trade liberalization, as represented by asymmetric, worldwide decrease in iceberg-type transport costs, t, whenever countrieshave asymmetric integration strategies, i.e. when Y* � Y. A drop in transportationcosts, in fact, reduces the price of traded goods and has no consequences for multi-national sales. The relative price of home goods in international markets will thereforefall as long as home firms mainly export their products abroad while foreign firmsmainly operate through local affiliates of multinational firms, namely when Y* > Y.Thedeterioration of home prices in turn implies that more labor effort on the part of homeagents is needed in order to buy a given unit of the foreign good. This is not to say,however, that trade liberalization is necessarily counterproductive for countries, likedeveloping economies, where production is less or not at all internationalized. Theloss from deteriorating terms of trade, in fact, might be more than compensatedin welfare terms if the rise in labor effort is accompanied by a large enough increase inconsumption.

Secondly, we emphasize that country-specific shocks to productivity might be asso-ciated with rising or falling prices in international markets, depending on the mode offoreign market access that prevails in the world economy. In less integrated andsymmetric economies, namely when Y* = Y � 0, a decline in domestic productivityleads to an improvement in the home terms of trade. The rise in ε � �P PHH FF* , on the otherhand, allows to shift part of the costs of the productivity slowdown abroad.16 Amonghighly integrated and similar economies, i.e. when Y* = Y � 1, high marginal costs athome raise the price for goods produced on the home soil, hence ε � �P PHF FH* willdecrease. Multinational firms, by producing directly in the sales market, reduce theextent to which the price of their products reacts to external cyclical conditions, therebyisolating final consumers from cyclical conditions abroad.

Finally, equation (32) reveals that international prices hardly react to country-specific disturbances in economies characterized by asymmetric integration strategies.Consider, as a way of example, the case where home firms mainly export their productsabroad while foreign firms operate through subsidiaries overseas (Y* � 1; Y � 0).

548 Lilia Cavallari


A fall in productivity, wherever it is originated, has no permanent consequences forrelative prices in international markets (32).A slowdown in, say, home productivity willin fact raise the price that home consumers face for foreign goods as much as theforeign-currency price of home goods, implying that home exports and foreign multi-national sales will fall in the same proportion. The finding is consistent with a broadevidence showing that, despite lower trend productivity, less-developed countries neednot experience a secular deterioration in their terms of trade relative to the developedworld.17

The Consumption–Output Anomaly

One notable feature of our equilibrium outcome is that multinational activities leadincomes to co-move across countries much more than consumption and spending, as istrue in the data for most industrialized countries. Several studies document that thecross-country correlation of consumption is remarkably lower than what is predictedby theoretical models, a fact known as the consumption–correlation puzzle. Moreover,the correlation of output across developed economies is much higher than that ofconsumption, raising the so-called consumption–output anomaly. The paradoxes ariseas one would expect that, despite large fluctuations in output, consumption can bestabilized in the world economy through trade in financial assets. In a world withcomplete asset markets, in fact, idiosyncratic risks are eliminated, implying that con-sumption differentials should be perfectly correlated across countries as predicted bystandard real business cycle models (Backus et al., 1992).

In order to see the point, we focus on the case where there is no trade, and foreignmarkets are exclusively served through subsidiaries of multinational enterprises,Y = Y* = 1. It is easy to verify that the income ratio is constant in the two countries:

PLP L* * * *

=−

−( )−( )

γγ

φ φφ φ1

11

,

while consumption and spending vary with country-specific shocks:

CC

PCP C*

** * *

= =κκ

μμ

.

In our framework, less than perfect risk-sharing in consumption is the result ofsegmentation in international goods markets. Despite incomes being equalized acrosscountries, consumption diverges in real terms as agents consume a basket that com-prises different proportions of goods produced at home and abroad. The products ofmultinationals, as other nontraded goods, imply a wedge between home and foreignconsumption. Multinational activities, on the other hand, increase the degree of incomeinterdependence in the world economy by exposing the profits of firms with productionfacilities in multiple countries to global cyclical conditions. Consequently, the dividendincomes of multinationals will tend to co-move across countries.

The Failure of the PPP

We finally consider the real exchange rate R ≡ eP*/P as defined using the consumption-based price indices in the two economies. These price indices change over time asa result of movements in transportation costs as well as changes in world cyclical



conditions. Making use of (29) and (28) and recalling the definition of the CPI in thetwo countries yields the long-run real exchange rate:

�R = − −[ ]( )− [ ]( ) ( )− − −( )

−( ) − −( ) −1 11

11 1 1γ

γκκ

τγ γ

γ γΨ ΦΨ Φ

Ψ ΨΨ Ψ* *

*

** (( ). (33)

Despite price flexibility, purchasing power parity may not hold, R � 1. Many studiesdocument that real exchange rate movements are highly persistent, so much that thehypothesis of unit roots in real exchange rate data can hardly be rejected for mostindustrialized and developing countries, thereby violating the parity condition.18 Theconvergence to parity remains very slow even when structural changes in long-horizontime series are accounted for: it takes more than five years on average for the exchangerate to return to its long-run mean or trend (Lothian and Taylor, 1996; Murray andPapell, 2002).

Deviations from purchasing power parity arise from transport costs and multi-national sales in our model. In a less integrated world (Y = Y* � 0), failures of the lawof one price are mainly due to trade costs.19 We stress that a rise in trade frictionsappreciates the real exchange rate in large and relatively closed economies, namelywhen g > 1/2. A high degree of global production, (Y = Y* � 1), on the other hand,implies that violations of the parity are positively associated with cross-country differ-ences in size, cyclical conditions, and monopoly distortions, i.e. R̃ = (1 - g)fk*/gf*k.

4. The Short-run Equilibrium

In this section, we characterize the world equilibrium when prices are set at thebeginning of each period, before shocks occur, and remain fixed for the whole period.Our solution strategy follows the same steps as in the preceding section. All optimalityand market-clearing conditions hold as before with the exception of optimal pricesetting, which is now given by (19) and (17).

The markup rule under nominal rigidity implies that prices may vary within theperiod only as a result of movements in the nominal exchange rate:

P

P

Ht t t t

t t

HHt t t t t

t t

=( )( )

=

−

−

−

−

Φ

Φ

EE

* E *

E

*

*

1

1

1

1

κ μ μμ

τ κ μ μ εε μ

η

η

( )

( tt t

FFt t t t

t t t t

Ft

P

P

*

* E * *

E

* *E

ε

τ μ κ μ εε μ ε

κ

η

η

)

( )

(

= ( )

=

−−

−−

−

−

Φ

Φ

1

11

1 ** * *

E *

* E * * *

E *

*

*

μ μμ

κ μ μ εε μ ε

η

η

t t

t t

HFt t t t

t t t t

P

P

)

( )

( )

( )

−

−

−

=

1

1

1

Φ

FFHt t t t t

t t t t

= ( )( )

−−

−−

−Φ*E

E1

11

κ μ μ εε μ ε

η

η .

(34)

As will be apparent soon, the nominal exchange rate may deviate from its long-runequilibrium value as long as prices are preset. Rearranging the aggregate accountingequation and making use of preset prices (34), we obtain:

ε γ μ κ μ ε μ εκ μ μ ε

η

ηt tt t t t t t

t t t t

** * E *

E * * *

*

*1 11

1

−⎛⎝⎜

⎞⎠⎟= −−

−

ΨΦ

( )

( )γγ μ κ μ ε μ ε

κ μ μ ε

η

η( ) − ( )( )

⎛⎝⎜

⎞⎠⎟

−−

−

−−t

t t t t t t

t t t t t

1 11

1

ΨΦ* E

*E. (35)

The equality above, which implicitly defines the short-run exchange rate, comprisesnonlinear terms in ε . In general, the value of ε that solves (35) may not coincide with

550 Lilia Cavallari


the equilibrium value under flexible prices �ε .20 In the Appendix, we provide an examplewhere the current account equation has either one solution, coinciding with the long-run exchange rate (28), or two more solutions, one higher and one lower than (28). Thefinding that nominal exchange rates may display excess volatility is well-known ininternational macroeconomics. It is consistent with a broad evidence showing thatmovements in fundamentals have a minor role, if any, in explaining short-termexchange rate fluctuations. Moreover, the possibility of multiple temporary equilibriaimplies that the fundamental forces that drive exchange rate movements on a longhorizon, as monetary policy in our model, may give rise to different patterns ofexchange rate fluctuations when prices are sticky. Therefore, exchange rates may tem-porarily over-react to a change in fundamentals, as originally stressed by Dornbusch(1976), or they can move despite fundamentals not changing, as emphasized in modelsof currency crises.

In order to illustrate the short-run dynamics of the exchange rate in more detail, wesolve equation (35) with h = h* = 0, yielding:

ε γγ

μμ

κ μ μκ μ μ

κ μt

t

t

t t t t

t t t t

t t

= −− ( )

( )⎛⎝⎜

⎞⎠⎟

−

−

−11

1

1

1

*

* E*E

* *E

ΨΦΨ tt t

t t t t

−

−

⎛⎝⎜

⎞⎠⎟

1

1

( )

( )

.μ

κ μ μ*

E * * *Φ

We first emphasize that the short-run nominal exchange rate may react to othercyclical conditions than monetary policy. Consider, for example, an increase in homeproductivity, a fall in k. The exchange rate will temporarily depreciate as follows:

∂∂ε εκ κ

κ μ μκ μ μ

κ μ μ= −

( )( )

−

−

−

−

−

ΨΦΨΦ

* E*E

* *E *

E

t t t t

t t t t

t t t t

t

1

1

11( )

11( )κ μ μt t t* * *

⎛⎝⎜

⎞⎠⎟

and return to its long-run equilibrium level (28), once prices adjust. The reason whythe exchange rate needs to move more when prices are sticky is that goods demandsdo not vary as much as they would with flexible prices (in our example, they do notvary at all). Consequently, the main economic effect of the productivity rise will be anunexpected increase in firms’ profits. As the home affiliates of foreign multinationalsrepatriate their unexpectedly high profits, dividends flow out of the home countryand the home currency needs to depreciate in order to maintain a balanced currentaccount.

It is worth noticing that the exchange rate moves in the opposite direction followinga change in expected productivity. The expectation of lower marginal costs, in fact,induces the firms active in the home market to charge lower prices.This in turn will shiftworld expenditure in favor of goods produced at home, thereby appreciating the homecurrency.

Finally, we stress that excess volatility may materialize also following a change in theglobal monetary stance. To see the point, consider a 1 percent world monetary expan-sion. With flexible prices, there will be a 1 percent depreciation or appreciation of thehome currency depending on whether the expansion originates at home or abroad.Under sticky prices, instead, the response of the exchange rate might be more or lessthan 1 percent, precisely as follows:



∂∂ε εμ μ

κ μ μκ μ μ

κ μ μt t

t t t t

t t t t

t t t t= −

( )( )

− ( )

−

−

−1

1

1

1

1

ΨΦΨΦ

* E*E

* E*Ett t t t

t t

t t t t

t t t

−

−

−

( )⎛⎝⎜

⎞⎠⎟

= +

1

1

11

κ μ μ

ε εμ μ

κ μ μκ μ∂

∂ * *

* *E *

E *

ΨΦ

( )

( ** *

* *E *

E * * *

μκ μ μ

κ μ μ

t

t t t t

t t t t

)

( )

( )

.

1 1

1

−⎛⎝⎜

⎞⎠⎟

−

−

ΨΦ

Interpreting the expressions above, the exchange rate needs to deviate from its long-run equilibrium value so as to compensate for the lack of adjustment in prices. When ahome monetary easing is in place, the firms located at home face higher nominalmarginal costs.They are, however, committed to supply the amount of goods demandedin the economy at the preset price. The ex-post profits of home firms and local affiliatesof foreign multinationals will consequently shrink, thereby reducing the dividend out-flows towards the foreign country. This dampens the movements in the nominalexchange rate. By the same token, the home currency will overshoot its long-run valuewhen the monetary expansion originates abroad.

The International Monetary Transmission

We obtain the short-run equilibrium levels of consumption and employment in theworld economy in a similar way as in the flexible price equilibrium:

LP P P

LP P

t

H

t

HH FH

t

F

t

= + −( )+ −( )

= −( )+ −( )

γ μ γμ γ μ

γ μ γμ

1 1

1 1

Ψ Ψ

Ψ

*

*

*

**

*

*

FFF

t

HFP+ γ μΨ *

*

(36)

C c C ct t t= =− −( )μ ε μ εγ η γη1 * * * *, (37)

where

c t t t t t

t t t

≡ ( ) ( )( )

⎛⎝⎜

⎞⎠⎟

− − −−

−−

− − −( )

Φ ΦΨ

γ γη γ γκ μ μ ε

μ ετ

*E

EE

*1 1

11

1tt t t t t

t t t

c

−−

−−

− −( ) −( )

−

( )⎛⎝⎜

⎞⎠⎟

≡ ( )

1

11

1 1( )μ κ μ ε

μ ε

η γ

γ

* *

E

* *

*Ψ

Φ Φ γγη γ γ

κ μ μ ε

μ ετ κ μ− −

−

− + −

−( )⎛

⎝⎜⎜

⎞

⎠⎟⎟

1 1

1

1

1E * * *

E *

E*

t t t t t

t t t

t t

( )

(Ψ

tt t t

t t t

μ εμ ε

η γ*

E *

*)

( ).

−

− −( )⎛⎝⎜

⎞⎠⎟1

1 Ψ

In the above expressions, world consumption and employment are determined byglobal monetary conditions. Monetary policy controls nominal spending while outputaccommodates any change in aggregate demand at the ongoing prices. Productivityshocks, on the contrary, appear to have a minor role. They can influence consumptionand output only indirectly through their effect on the short-run nominal exchangerate.21 Since agents are committed to meet market demand at the given price, they mustbe ready to supply more effort in the event of a decline in productivity. Therefore, the

552 Lilia Cavallari


major effect of a productivity slowdown will be a temporary increase in labor effort.This clearly prevents agents from optimally smoothing effort over time.

Monetary policy is transmitted in the world economy through changes in worlddemand and the terms of trade. An easing of the global monetary stance, wherever itis originated, boosts world demand and output. In a high passthrough environment,i.e. when h = h* � 1, a domestic monetary expansion raises consumption both athome and abroad, as it appears in (37). The depreciation of the home currency, bydeteriorating the home terms of trade, switches world expenditure in favor of homegoods. Since domestic prices are fixed, home consumer prices will rise less thannominal spending (precisely, as much as the home-currency price of home imports).Foreign consumer prices, on the other hand, will fall with the depreciation of thehome currency. As a consequence, consumption will rise in real terms in bothcountries.

Worldwide output needs to increase as well in the wake of a home monetary expan-sion so as to provide a larger amount of goods for consumption. International outputspillovers may, however, be negligible.As apparent in (36), a rise in m affects L* throughits impact on the volume of home imports from abroad (the second addend on theright-hand side) as well as on the volume of home multinational sales in the foreigncountry (the third addend). Both these effects will be small when consumption expen-diture switches in favor of home goods. To illustrate this point, consider the case wherefirms mainly serve foreign markets through exports, Y = Y* � 0. A rise in m increasesspending on the part of home agents and hence their import demands.The depreciationof the home currency, however, makes foreign goods more expensive, thereby reducingthe demand for home imports. With linear demand functions and complete exchangerate passthrough the two effects exactly cancel out.

In a setting where prices are invariant to exchange rate movements, as is the casewhen prices are mainly set in the consumers’ currency (h = h* � 0), an easing of thehome monetary stance boosts domestic consumption only. Despite fixed local prices,however, output spillovers may be non-negligible. As evidenced in (36), foreignemployment needs to increase after the home monetary expansion so as to satisfy theboost in the external demand for foreign products.

The finding that international spillovers depend on firms’ integration and pricingstrategies has relevant consequences for welfare. In a high passthrough setting, adomestic monetary expansion certainly benefits the residents in partner economies.Foreign agents can in fact consume more for a given level of work effort by substitutingdomestic products with cheaper imports. By the same token, the monetary easing mayturn potentially harmful for domestic consumers.22

Moreover, cross-country asymmetries in the mode of foreign market access may alsoaffect the distribution of the gains from a world monetary expansion. Consider, forexample, the case where home firms mainly export their products abroad, while foreignfirms operate through subsidiaries located on home soil, Y � 0, Y* � 1. It is immediateto verify from (36) that home employment varies with a change in the global monetarystance while foreign employment depends on foreign monetary policy only. Consump-tion spillovers, on the other hand, are non-negative. A home monetary expansion istherefore “thy neighbor enrich” for any positive degree of exchange rate passthrough.An easing of the foreign monetary stance, on the contrary, may turn “beggar thyneighbor” as long as it leads to an excessive increase in home employment. Homeagents, in fact, will have to work more so as to satisfy the temporary boost in theexternal demand for their products as well as in the domestic demand for the productsof foreign multinationals.



5. Conclusions

This contribution has incorporated multinational sales along with costly trade in ageneral-equilibrium model in the tradition of the new open economy macroeconomicsso as to investigate how firms’ integration strategies affect the way monetary policy,trade liberalization policies, and productivity shocks spread their effects worldwide.

Our results reveal that the mode of foreign market access, whether through exportsor through sales by overseas branches of multinational corporations, plays a remark-able role in the international business cycle, affecting the dimension of consumptionand output spillovers worldwide. We have emphasized that the welfare implications ofa policy of trade liberalization as well as of a world monetary expansion may vary in asubstantial way depending on the integration strategies that prevail in the worldeconomy.

Moreover, our set-up with trade and multinational sales allows to shed some light ona number of puzzling facts in international macroeconomics. First, we stress that tradefrictions, as represented by trade costs and multinational sales, can help explain whyconsumption is so poorly correlated across industrialized countries despite a highdegree of financial integration and why it is less correlated than output (the well-knownconsumption–output puzzle).

Secondly, the response of international prices to country-specific and global distur-bances depends crucially on the integration strategies followed by firms active inforeign markets. In particular, we find that the terms of trade are almost invariant tocountry-specific productivity shocks whenever there are substantial differences in theintegration strategies across countries, as between industrialized and emerging econo-mies. Despite lower productivity, countries like developing economies that mainly hostforeign multinationals need not experience a deterioration in the relative price of theirproducts, as is true in long-horizon terms-of-trade data between the two groups ofcountries.

Finally, our model provides a degree of excess volatility in nominal exchange ratesthat is comparable with the one found in short-horizon exchange rate data.

Appendix

In this appendix we show that our economy may have multiple temporary equilibria.Consider a deterministic steady state in which the current account is zero and allexogenous variables are set equal to constant values. The steady-state exchange rate isgiven by equation (28).

Proposition 1. If

μγ

μγ

κ κ=−( ) −( )

=−( )

= =ΦΦ Ψ

ΦΦ Ψ

** *

* *1

1, ,and

there always exists an equilibrium in which the nominal exchange rate �ε is equalto 1. Moreover, there will be two more temporary equilibria when prices arepreset in which the nominal exchange rate is equal to el and eh, where 0 < el < 1and eh > 1.

Proof. It is straightforward to verify that the steady-state value of the nominalexchange rate is equal to 1 by evaluating equation (28) with

554 Lilia Cavallari


μγ

μγ

=−( ) −( )

=−( )

ΦΦ Ψ

ΦΦ Ψ

** *

and *1

.

This establishes the first part of the proposition.The current account equality is identically equal to zero in every period included in

the initial steady state. In the equilibrium with preset prices, the current accountequality is given by equation (35) in the text that we report below:

ε γ μ κ μ ε μ εκ μ μ ε

η

ηt tt t t t t t

t t t t

** * E *

E * * *

*

*1 11

1

−⎛⎝⎜

⎞⎠⎟= −−

−

ΨΦ

( )

( )γγ μ κ μ ε μ ε

κ μ μ ε

η

η( ) − ( )( )

⎛⎝⎜

⎞⎠⎟

−−

−

−−t

t t t t t t

t t t t t

1 11

1

ΨΦ* E

*E.

In order to prove the second part of the proposition, we note that both the left- andright-hand sides of the expression above are nonlinear functions of et. For et = 0, theterm on the left-hand side is equal to zero, but the term on the right-hand side ispositive and equal to (1 - g)mt. For et → •, the left-hand side diverges while the rightside converges to (1 - g)mt. The functions described by the two sides of the expressionabove cross at et = 1 where the temporary equilibrium coincides with the steady state.If the function on the right side crosses the function on the left side from below, i.e. ifthe derivative of the right-hand-side term with respect to et evaluated for et = 1 is lessthan the derivative of the left term always evaluated with et = 1, then equilibrium issatisfied by two more values of the nominal exchange rate, el and eh, such that 0 < el < 1and eh > 1. This proves the second part of the proposition.

We finally calculate the derivatives of the two functions in the current accountequality, yielding:

η γ μ κ μ ε μ εκ μ μ ε

η

η11

11

1

−( ) ( )( )− −

−−

−−t

t t t t t t

t t t t t

ΨΦ* E

*E

for the right-hand-side term and

γ μ η κ μ ε μ εφ κ μ μ ε

η

ηtt t t t t t

t t t t

* ** * E *

E * * *

*

*1 1 1

1

− +( )⎛⎝⎜

⎞⎠

−

−

Ψ ( )

( ) ⎟⎟

for the term on the left-hand side. Evaluating the expressions above in a steady-stateequilibrium with et = 1, the condition for the existence of multiple equilibria simplifiesas follows:

η ηΨΦ Ψ

Φ ΨΦ Ψ

** *

*−

≤ − +( )−

1.

For instance, in a symmetric world economy with Y* = Y = 0.5 and f = f* = 10, thecondition is satisfied for a value of h = h* = 11/18. �

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Notes

1. See Helpman (2006) for a comprehensive survey.2. A non-exhaustive list of papers in this area includes: Corsetti et al. (2005), Ghironi and Mélitz(2005), Bergin and Glick (2007), and Bilbiie et al. (2007).Among these, only Cavallari (2007) andRuss (2007) incorporate endogenous entry by multinational firms.3. Unless otherwise stated, foreign variables denoted by an asterisk, coincide with the corre-sponding domestic variables and will not be explicitly indicated.4. Mélitz (2003) has initiated a burgeoning literature on firms’ heterogeneity. Later in the paperwe will clarify how our model relates to this line of research.5. Each price index P, PH, PF, PFH, and PFF is defined as the minimum expenditure required tobuy one unit of the corresponding composite consumption good, C, CH, CF, CFH, and CFF.6. One could alternatively think of each variety as one of several production lines within a singlefirm.7. Tariff barriers range on average between 4 and 5 percent of the price of traded goods. Tradecosts—including tariff and nontariff barriers, shipping and distribution costs—vary greatly acrossclasses of goods.8. It is easy to verify that our model is isomorphic to the one in Obstfeld and Rogoff (2000) whenY = Y* = 0. With Y = Y* = 1, it mimics the production side in Devereux and Engel (2001).9. A common finding is that only the most productive firms access foreign markets and only themost productive among those operating in foreign markets engage in multinational activities.See, for instance, Helpman et al. (2004).10. See, for instance, Corsetti et al. (2005) and Cavallari (2007).11. On average, a 1 percent increase in the nominal exchange rate determines a 0.6 percentincrease in the final price of traded goods.12. We have recursively used the index of monetary stance in the Euler equation (14).13. As pointed by Corsetti and Pesenti (2002), a balanced current account is the result of threehypotheses: (i) a Cobb–Douglas consumption index, (ii) logarithmic utility in consumption, and(iii) zero initial net assets.14. It is straightforward to verify that consumption spillovers are positive as long as countriestrade between each other.15. The international relative price Q̃ is calculated as a weighted average of the terms oftrade, ε � �P PHH FF* , and the relative price of multinationals’ products, ε � �P PHF FH* , where the weightsare, respectively, the share of exporters and multinationals in each country.16. With Y = Y* = 0, consumption is fully stabilized in the world economy:

CC*

= − −1 2 1γγ

τ γ .

More open economies obtain a larger share of world consumption and the more so the smallertransport costs.17. The long-lasting debate on the secular deterioration of the terms of trade of developingcountries was initiated by Singer (1950). It is currently widely accepted that the terms of tradeacross developed and less-developed countries move to a much lesser extent than previouslythought and may not have a secular trend, once transport costs, product quality, and cross-country specialization patterns are accounted for (Salvatore, 2001).18. Early stationarity tests for real exchange rate data are surveyed in Rogoff (1996). See Frootand Rogoff (1996) for a very long-run perspective on PPP.19. Equation (33) blurs to R̃ = t 2g -1 in this case.20. Comparing (35) and (28), it is easy to verify that the short-run and the long-run ex-change rates coincide when Y = Y* = 0. In the absence of multinational activities, the trade



balance is identically equal to zero. Therefore, the value of exports must equal the value ofimports:

εP C P CHH HH FF FF* * − = 0,

i.e.

εγ μ γ μt t* − −( ) =1 0

independently on whether prices are fixed or flexible.21. The minor role of supply shocks in driving aggregate consumption and output is consistentwith the so-called New Keynesian view of the business cycle, as synthesized by Clarida et al.(1999).22. The monetary expansion is “beggar myself” whenever the welfare loss from increasing laboreffort outweighs the welfare gain from higher consumption.

558 Lilia Cavallari


Macroeconomic interdependence with trade and multinational activities

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