Dennis Novy University of Warwick, Department of Economics, Coventry CV4 7AL, United Kingdom

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1 Trade Coss and he Open Macroeconomy * Dennis Novy Universiy of Warwick, Deparmen of Economics, Covenry CV4 7AL, Unied Kingdom d.novy@warwick.ac.uk Absrac Trade coss are known o be a major obsacle o inernaional economic inegraion. Following he approach of New Open Economy Macroeconomics, his paper explores he effecs of inernaional rade coss in a micro-founded general equilibrium model ha allows for differen degrees of exchange rae pass-hrough. Trade coss are shown o creae an endogenous home bias in consumpion and he model performs well in maching empirical rade shares for OECD counries. In addiion, rade coss reduce cross-counry oupu and consumpion correlaions and hey magnify exchange rae volailiy. Trade coss urn a moneary expansion ino a beggar-hy-neighbor policy. Keywords: Trade Fricions; Pass-Through; Exchange Raes; Consumpion Correlaions; Inernaional Trade JEL classificaion: F2; F3; F4 I. Inroducion Trade coss have long been known as a major obsacle o inernaional economic inegraion. In a recen survey, James Anderson and Eric van Wincoop (2004) show ha empirical rade coss are large even when formal barriers o rade do no exis. They argue ha he ariff equivalen of represenaive inernaional rade coss is around 74 percen. This paper pus rade coss in he spoligh by inegraing hem ino a rigorous micro-founded general equilibrium model. Following he approach of New Open Economy Macroeconomics, I inroduce iceberg rade coss ino a wo-counry open economy model wih nominal price rigidiies. Alhough I allow for asymmeric counry sizes, due o logarihmic uiliy he complexiy of he model is kep a a manageable level so ha analyical soluions can be derived for he asymmeric equilibrium. The combinaion of rade coss and asymmeric counry sizes allows me o yield 0* I would like o hank Giancarlo Corsei, Pera Geraas, Neil Rankin and wo anonymous referees for useful commens. I graefully acknowledge research suppor from he Economic and Social Research Council, gran RES

2 rade shares ha mach empirically observed rade shares for OECD counries. The paper shows ha even moderae rade coss can subsanially inerfere wih inernaional linkages. For example, hey easily reduce he cross-counry correlaions of consumpion by more han half compared o a fricionless world. Those lower levels mach empirically observed consumpion correlaions. Inuiively, by raising he price of impored goods rade coss render domesic goods more aracive o consumers. As a consequence, spending is predominanly kep wihin he domesic counry and consumpion is iled owards domesic goods, creaing an endogenous home bias in consumpion. This conainmen effec of rade coss ends o isolae wo counries from each oher and makes hem behave more like closed economies. Shocks hiing one counry herefore have a reduced bearing on he oher, weakening curren accoun movemens and he inernaional correlaions of consumpion and oupu. However, as a resul of weaker inernaional linkages, nominal and real exchange raes respond more srongly o shocks. This helps o explain he high exchange rae volailiy observed in he daa. An addiional feaure of he model is o allow for varying degrees of exchange rae passhrough. This exension, adoped from Caroline Bes and Michael Devereux (2000), is paricularly suiable in he conex of rade coss. As Andrew Akeson and Ariel Bursein (2008) argue, lack of pass-hrough implies ha prices for he same good can differ across counries. Such deviaions from he law of one price require marke segmenaion. This can be jusified by rade coss. Bes and Devereux (2000) show ha in a world wih zero rade coss, lack of pass-hrough dramaically reduces cross-counry consumpion correlaions. In conras, I find ha in he presence of rade of coss, he behavior of key economic variables does no heavily depend on he degree of pass-hrough. For example, for plausible rade cos values cross-counry consumpion correlaions are raher similar in he wo opposie cases of local currency pricing (i.e. zero pass-hrough) and producer currency pricing (i.e. full pass-hrough). Likewise, if rade coss are presen he disincion beween local and producer currency pricing is no longer as sharp for welfare consideraions. Regardless of he degree of pass-hrough rade coss urn a moneary expansion ino a beggar-hy-neighbor policy. The model falls ino he New Open Economy Macroeconomics lieraure ha has evolved from Maurice Obsfeld and Kenneh Rogoff s (995) seminal conribuion. I represens a micro-founded wo-counry general equilibrium framework wih monopolisic compeiion and one-period price sickiness. The key conribuion of my paper is o combine his se-up wih iceberg rade coss as he cenral modelling device. As a consequence of rade coss, many conclusions from Obsfeld and Rogoff s (995) paper no longer hold. For example consumpion is no longer highly correlaed across counries and posiive moneary shocks no 2

3 longer lead o symmeric welfare gains in boh counries. In addiion, I exend he model o produciviy shocks. The resuls are qualiaively similar o moneary shocks in ha rade coss dampen inernaional linkages and increase exchange rae volailiy. Paul Krugman (980) is he firs auhor o inroduce iceberg rade coss ino a monopolisic compeiion framework bu my model is more closely relaed o he paper by Obsfeld and Rogoff (2000). They have given rade coss new impeus by poining ou heir poenial o elucidae major puzzles of inernaional macroeconomics like he consumpion correlaions puzzle. Bu Obsfeld and Rogoff (2000) only use a small open endowmen economy model, as do Paul Bergin and Reuven Glick (2006) who inroduce heerogeneous iceberg rade coss and endogenous radabiliy. Allan Brunner and Kanda Naknoi (2003) inegrae rade coss ino a more rigorous wo-counry general equilibrium model wih producion bu hey only allow for full pass-hrough and do no consider welfare implicaions. The inclusion of rade coss yields resuls ha are in many respecs similar o he ones obained by David Backus and Gregor Smih (993) and Harald Hau (2000) in heir models wih nonradable goods. Hau (2000) also finds ha consumpion becomes less correlaed across counries and ha boh nominal and real exchange raes are more volaile. I incorporae nonradable goods ino my model bu I find ha in conras o rade coss, nonradable goods would clearly overpredic he exen of inernaional rade. 2 In order o mach empirical rade shares, an implausibly large share of over 90 percen of goods would have o be nonradable. The reason is ha nonradabiliy simply reduces he range of goods available o consumers wihou changing relaive prices. Bu rade coss drive a wedge beween he prices of domesic and impored goods and, provided ha demand is elasic, generae nonlinear shifs in expendiure paerns owards domesic goods. Charles Engel (999) and V. V. Chari, Parick Kehoe and Ellen McGraan (2002) provide an addiional reason for choosing rade coss over nonradable goods. They show ha he relaive price of nonradable goods accouns for virually none of U.S. and European real exchange rae movemens. Insead, he real exchange rae appears o be driven almos exclusively by he relaive price of radable goods. 3 Francis Warnock (2003) shows ha he assumpion of a home bias in preferences can generae resuls ha are qualiaively similar o nonradable goods. However, empirical micro-evidence by Carolyn Evans (2007) shows ha naional preferences are negligible in Mos papers in his lieraure only consider nominal shocks, for example Svensson and van Wijnbergen (989), Hau (2000) and Warnock (2003). 2 This resul is no as apparen in Hau s (2000) paper because he assumes counries o be symmeric. 3 Naknoi (2008) presens a Ricardian rade model o explain he empirical observaion ha under fixed exchange rae regimes he nonraded real exchange rae is relaively more imporan. I absrac from fixed exchange raes. 3

4 explaining inernaional rade flows relaive o ransporaion coss and ariffs. Likewise, Helpman (999) argues ha here is no clear evidence of home bias in preferences. I herefore adop rade coss o generae an endogenous home bias in consumpion. John Fender and Chong Yip (2000) consider a unilaeral ariff bu no symmeric rade coss. Ravn and Mazzenga (2004) evaluae he effec of ransporaion coss in a real business cycle approach wih symmeric counries. In addiion, hey assume a home bias in preferences. Bu since ransporaion coss and home bias work in he same direcion, i is difficul o esablish he relaive conribuion of each assumpion in explaining empirical rade shares and cross-counry correlaions. Anoher difference is ha by consrucion, heir flexible-price environmen precludes he analysis of varying degrees of exchange rae pass-hrough. The paper is srucured as follows. Secion II inroduces rade coss ino a New Open Economy Macroeconomics model wih sicky prices. Secion III describes is flexible-price equilibrium, esablishing he endogenous home bias in consumpion and maching he model wih empirical rade shares. Secion IV discusses he effecs of moneary and produciviy shocks on exchange rae volailiy and inernaional oupu and consumpion correlaions. Secion V conducs a welfare analysis. Secion VI concludes. II.AModelwihTradeCoss The model follows he New Open Economy Macroeconomics lieraure and is based on he seing wih varying degrees of exchange rae pass-hrough in Bes and Devereux (2000). As a new ingredien here exis exogenous iceberg rade coss τ, whereτ represens he fracion of goods ha mels away during he rading process wih 0 τ<. Ifτ =0we have he special case of fricionless rade ha is cusomary in he lieraure. In he exreme case of τ, rade beween he wo counries breaks down and hey become closed economies. Households choose among a coninuum [0, ] of differeniaed, nondurable and radable goods which are produced by monopolisic firms. The sizes of he Home and Foreign counries are n and n wih 0 <n<. As in Bes and Devereux (2000), i is assumed ha s wih 0 s is he fracion of firms in each counry ha engage in local currency pricing (LCP). The remaining firmsengageinproducercurrency pricing (PCP). Households Households derive uiliy from consumpion C and also from real money balances M /P due o a ransacionary moive bu hey dislike work effor h. In Home counry noaion 4

5 uiliy is given by U = X β µln v C v + γ ln v= µ Mv P v + η ln ( h v ) () wih he composie consumpion index defined as µz C 0 ρ c ( ρ ρ ρ ) i d i (2) where ρ is he elasiciy of subsiuion wih ρ>. 4 c i is consumpion of good i a ime. β is he subjecive discoun facor wih 0 <β<. The parameers β, γ, η and ρ are posiive and idenical across counries. All above variables (C and h ec.) are Home percapia variables. Since all households wihin one counry are idenical by consrucion, he corresponding Home aggregae quaniies are nc and nh ec. Noe ha unlike in Warnock (2003) here is no home bias in preferences. The Home consumpion-based price index is defined as he minimum expendiure subjec o C =and can be derived as 5 " Z n P = p ρ i d i + 0 Z n+( n)s n µ ρ Z µ ρ ρ τ p i d i + n+( n)s τ e qi d i# (3) The Foreign price index is given by P = " Z ns 0 µ τ q i ρ d i + Z n ns µ ρ Z # ρ p i d i + qi ρ d i τ e n (4) where prices p represen goods prices denominaed in Home currency and prices q represen goods prices denominaed in Foreign currency. In general, aserisks indicae Foreign counry variables bu in he conex of goods prices an aserisk means ha a price is se by a Foreign firm. Thus, all p i are se by Foreign firms in Home currency and all qi are se by Foreign firms in Foreign currency. Thegoodsinherange[0,n] are produced by Home firmsandhegoodsinherange [n, ] are produced by Foreign firms. InheHomepriceindex(3),Foreignfirms price in local 4 As in Obsfeld and Rogoff (995) and Bes and Devereux (2000), real money balances in he uiliy ³ γ M funcion could alernaively be specified as v P v wih >0. Thisspecificaion would yield addiional feaures such as exchange rae overshooing bu hose feaures are no essenial o undersand he role of rade coss. Resuls are available from he auhor on reques. 5 The derivaions of his secion are oulined in Appendix A. 5

6 currency for he goods in he range [n, n +( n)s], i.e. hey se he corresponding prices p i in Home currency. The range [n +( n)s, ] represens he goods produced by Foreign firms ha se prices qi in producer (i.e. Foreign) currency. These are convered ino Home currency hrough muliplying by he nominal exchange rae e, which is defined as he Home price of Foreign currency. Noe ha he facor is included in he range [n, ] of Home price index (3) as well τ as in he range [0,n] of Foreign price index (4). The reason is ha all prices p i, p i, q i, qi aref.o.b. (freeonboard)unipriceshaare charged a he facory gae. If a Foreign good is shipped o he Home counry, only he fracion ( τ) arrives. The Home consumer mus herefore buy unis in he Foreign counry so ha one full uni arrives in he Home τ counry. Hence, from a Home consumer s perspecive τ p i is he c.i.f. (cos, insurance and freigh) uni price of a Foreign good priced in local currency, and e τ qi is he c.i.f. uni price of a Foreign good priced in producer currency. One can hink of his f.o.b./c.i.f. relaionship as firms charging an addiional markup for shipping he purchased goods over o he desinaion counry. 6 Asse markes are complee domesically such ha each household owns an equal share of an iniial sock of domesic currency and an equal share of all domesic firms. There is no bond denominaed in Foreign currency bu here is free and cosless rade in a Home currency nominal discoun bond. F represens he Home holdings of he bond mauring in period + and d is is price. The Home budge consrain a ime in per-capia erms is hus given by P C + M + d F = W h + π + M + Z + F (5) where W is he nominal wage rae and π are Home firms profis. If he Home governmen generaes revenue from prining money, i gives ou nominal lump-sum ransfers Z o is ciizens such ha Z = M M (6) The Home consumpion demand funcion can be derived as c i = µ ξi P ρ C (7) 6 However, he fracion τ of goods ges los in he rading process so ha firms do no receive he addiional markup. The model can be exended such ha rade coss are rebaed o consumers bu his does no change he qualiaive resuls. Deails are available from he auhor on reques. 6

7 where ξ i = analogous o he hree erms in price index (3). p i for 0 i n τ p i for n i n +( n)s τ qi for n +( n)s i (8) Firms Each firm faces he same linear producion echnology y = h (9) where y denoes Home per-capia oupu and h is Home per-capia labor inpu. The i subscrip is dropped as all firms face he same producion echnology. Home oupu can be divided ino oupu desined for he domesic counry, denoed by x, and oupu desined for he Foreign counry, denoed by z y = x + z (0) Labor markes in each counry are perfecly compeiive so ha he inernaionally immobile workers are wage-akers. The Home per-capia profi funcionforanys [0, ] is hen given by π = s(p x + e q z )+( s)(p x + p z ) W y () Noe ha () is expressed in f.o.b. erms and ha z isheamounofhomeoupuhais shipped o Foreign. Due o rade coss only he fracion ( τ) of z arrives and is consumed in Foreign. The firs erm on he righ-hand side of () reflecs he revenue of firms ha engage in local currency pricing, charging he Foreign currency price q o Foreign consumers. The second erm is he revenue from firms ha engage in producer currency pricing, charging he Home currency price p. The las erm of () consiues he coss of producion. Appendix A shows ha profi maximizaion leads o he sandard markups for Home firms p = e q = ρ ρ W (2) and for Foreign firms q = p /e = ρ ρ W (3) Equaions (2) and (3) imply ha in f.o.b. erms here is no price discriminaion across counries under flexible prices. Firms receive he same revenue per uni, no maer wheher 7

8 Consumpion C n= n= Trade coss Figure : Trade coss reduce consumpion in a nonlinear way. hey sell heir producs o Home or Foreign consumers. Noe ha equaions (2) and (3) only hold when firms are able o se heir prices freely, no when prices are sicky. III. The Flexible-Price Equilibrium The quesion of ineres in his secion is how rade coss affec he flexible-price equilibrium compared o a perfec, fricionless world. As usual in he New Open Economy Macroeconomics lieraure, i is assumed ha firmssepricesaferheexchangeraeandwagesare known and ha iniially here are no bond holdings and no lump-sum ransfers so ha F = F = Z = Z =0. The ime index is dropped o denoe iniial equilibrium values. An Endogenous Home Bias in Consumpion By comparing individual goods prices in (8) one can easily see ha rade coss drive up he price of impored goods and hus render domesic goods more aracive. As a resul, consumers spend a bigger fracion of heir income on domesic goods. This buffering feaure of rade coss will be referred o as he conainmen effec of rade coss, meaning ha spending ends o be reained wihin he domesic counry. Trade coss herefore lead o an endogenous home bias in consumpion in each counry. The home bias arises alhough he preference specificaion in (2) is symmeric such ha consumers equally desire all goods, regardless of where hey are produced. Of course, abandoning he symmery by inroducing an exogenous home bias in preferences, for example as in Warnock (2003), would be an alernaive way of explaining he home bias. However, 8

9 Carolyn Evans (2007) finds empirically ha he only significan reason for he endency of consumers o purchase domesic goods are locaional facors arising due o geographic disance and legal regulaions bu no consumer preferences. 7 Her findings are herefore consisen wih he preference specificaion in (2) and he model s iceberg rade coss bu no wih Warnock s (2003) assumpion of home bias in preferences. My approach is herefore o useradecossasawayoraionalize and endogenize home bias. As shown in Appendix B, equilibrium labor supply is no affeced by rade coss because of he logarihmic uiliy specificaion in (). However, rade coss reduce consumpion, real profis and real wages and hence, hey make individuals worse off. 8 Figure illusraes he reducion in consumpion wih a numerical example. 9 Two characerisic feaures of rade coss sand ou. Firs, rade coss operae in a nonlinear fashion. Moderae values, say, τ =0., already have a sizeable impac. Second, rade coss have a more derimenal impac on small counries, as can be seen in he case of n =0.25. Inuiively, since all he goods produced in he world are equally desired by consumers, smaller counries are more open economies and herefore more exposed o rade coss. Trade Shares In a fricionless world he model would predic ha a counry s expendiure share on domesic goods equals is share of world oupu. The remainder would be spen on impored goods. Empirically, however, counries end o spend a much larger fracion of heir incomes on domesic goods and he fracion spen on impored goods is smaller. Figure 2 shows ha he model performs reasonably well in predicing empirical rade shares for he OECD counries. 0 Counry size, measured as he share of world GDP, is ploed agains he share of GDP spen on impored goods. The daa are aken from he CIA World Facbook for he year 2007 (PPP-adjused). The graph also conains he European Union aggregae, which is he daa poin wih he highes GDP share (22 percen) and he lowes rade share (0 7 Evans (2007) compares prices and quaniies of impored goods produced by American firms for domesic sale wih hose of he same goods produced by foreign affiliaes of hese American firms for local sale. Her daa se encompasses seven indusries, ranging from ransporaion equipmen o food producs, across nine OECD counries over he period She finds ha he ad-valorem ariff equivalen of producing domesically and shipping abroad ranges beween 5 and 05 percen across indusries, which considerably reduces he araciveness of he foreign goods for local consumers. Esablishing and selling from a local affiliae, however, does no lead o any negaive effec on sales of hese foreign producs when compared o sales of local goods. For example, French consumers do no inrinsically prefer French o American beer, only if i is cheaper. 8 Formally, U/ τ < 0 and U / τ < 0. For given money supply rade coss also decrease equilibrium real money balances. 9 ρ = 0 The analyical expression for he rade share is given in Appendix C.2 afer equaion (??). The Foreign counry is reaed as he res of he world. 9

10 0 Trade share (share of GDP in logs) Counry size (share of world GDP in logs) Figure 2: Trade shares and counry sizes are inversely relaed. The solid line represens he model s predicion. Each daa poin refers o an OECD counry (daa for 2007). percen). The key parameers underlying Figure 2 are chosen as τ =0.37 and ρ =8. These values are based on he seminal paper by Eaon and Korum (2002). They run a graviy regression wih daa for he year 990 and, assuming an elasiciy of ρ =8hey esimae a range of percen for rade coss expressed as a ariff equivalen. Given ha rade coss are likely lower in 2007, I choose he lower end of ha range, corresponding o τ =0.37 when convered ino he iceberg form. Thechoiceofρ =8lies in he middle of he range ypically suggesed in he rade lieraure. In heir survey on rade coss, Anderson and van Wincoop (2004) conclude ha he elasiciy of subsiuion is usually esimaed beween 5 and 0. Figure 2 is robus o alernaive values. Anderson and van Wincoop (2004, Table 7) presen various combinaions of rade coss and subsiuion elasiciies ha prominen papers in he rade lieraure have found. Using U.S.-Canadian rade daa for he year 993, Anderson and van Wincoop (2003) esimae τ =0.47 under he assumpion of ρ =5and τ =0.26 under he assumpion of ρ =0. Boh combinaions yield roughly he same rade shares as ploed in Figure 2. All hese rade cos values are subsanial because hey capure a wide range of rade barriers such as ransporaion coss, ariffs, informaional coss, bureaucraic hurdles ec. Even in he European Union where ariffs wereabolishedinhe 960s, significan rade barriers remain in he form of echnical barriers o rade, for example packaging and labelling requiremens (see Chen and Novy, 2008). In conras, Ravn and The ariff equivalen of iceberg rade coss is given by 0.58 = / ( τ), implyingτ =

11 Mazzenga (2004) focus on ransporaion coss. They infer he magniude of ransporaion coss from c.i.f./f.o.b. raios, using a ariff equivalen value of 20 percen (τ =0.7). Tha number can be inerpreed as a lower bound. Nonradable Goods As Hau (2000) shows, he assumpion of nonradable goods also leads o a home bias in consumpion. To check wheher nonradable goods are a viable alernaive o rade coss for generaing realisic rade shares, I incorporae hem ino a version of he model wih zero rade coss. Like Hau (2000) I assume ha in each counry only an exogenous fracion ω of firms produces radable goods. 2 Appendix B. provides he deails. In conras o Hau (2000) and Warnock (2003) I solve for a seady sae in which he wo counries can have differen sizes. This allows me o calculae he fracion of radable goods ha corresponds o empirical rade shares and counry sizes. The general conclusion is ha nonradable goods fail o generae realisic rade shares. For example, he UK produces abou hree percen of world GDP (n =0.03) andhasarade share of around 29 percen of GDP. This rade share would correspond o ω =0.04, i.e. only four percen of all goods in he economy are radable. This share clearly seems oo low in he face of he UK s large engagemen in inernaional rade. Hau (2000) generaes much more favorable values, for example ω = 0.48 for he average of OECD counries beween , bu only because he consrains counries o be symmeric (n =0.5). Once rade shares are mached wih acual counry sizes he implied values of ω become implausibly low. Why do empirical rade shares correspond o reasonable values of rade coss (see Figure 2) bu no o reasonable values of ω? The inuiion is ha rade coss change relaive prices by driving a wedge beween domesic and foreign goods. Given ha demand is elasic (ρ >) even small amouns of rade coss can have a large impac on he allocaion of expendiure. However, nonradable goods do no change relaive prices. They merely resric he range ofgoodsavailableoconsumers. IV. Sicky Prices and Shocks This secion examines how key economic variables respond o shocks when prices are sicky for one period and when rade coss impede he inernaional exchange of goods. I is assumed ha all prices (p, p, q, q ) are prese every period and ha firms choose prices o be opimal in he absence of shocks. They herefore prese he prices of he iniial flexible- 2 I urns ou ha he parameer ω corresponds o ( τ) ρ in he model wih rade coss. This correspondence goes hrough for he log-linearized model in Secions IV and V.

12 price equilibrium. For a sufficienly small shock in period, firms have an incenive o mee he pos-shock marke demand since hey are monopolisic compeiors and sill make profis. As here is no capial in he model, prices and all oher variables reach heir new long-run equilibrium in +, one period afer he shock his he economy. Log-linear approximaions are aken around he pre-shock flexible-price equilibrium of Secion III. For any variable X le bx +k (X +k X)/X be he percenage deviaion from he iniial equilibrium a ime + k for k =0,. There are moneary shocks and produciviy shocks. 3 As in Obsfeld and Rogoff (995), produciviy shocks are modelled as shocks o he disuiliy of labor in uiliy funcion (). A fall in he parameer η can be inerpreed as a posiive produciviy shock in he sense ha less labor is required o produce a given amoun of oupu. The Foreign counry draws he produciviy shock bη which may be differen from bη. 4 Moneary shocks are modelled as shocks o M and M. I is assumed ha all shocks are permanen (bη = bη +, bη = bη +, cm = cm + and cm = cm +). 5 Tables a and b summarize heir effecs on key variables. The nex subsecion discusses he real exchange rae. The subsequen subsecion concenraes on he nominal exchange rae, consumpion, oupu and he curren accoun. Full analyical derivaions are given in Appendix C. The Real Exchange Rae Theshor-runresponsesofhepriceindicesoanexchangeraemovemeninperiod can be obained by log-linearizing (3) and (4). Under local currency pricing (s =) he price indices are no affeced by nominal exchange rae movemens since all prices are fixed irrespecive of rade coss ( P b = P b =0). A nominal exchange rae depreciaion herefore direcly ranslaes ino a real exchange rae depreciaion ( ψ b = be ). Bu when a leas some prices are sicky in producer currency (0 s<), a depreciaion of he Home currency increases he Home price level and decreases he Foreign price level. Trade coss weaken he effec ha exchange rae movemens have on price indices. 6 Inuiively, rade coss ac like buffers ha shif consumpion owards domesic goods hrough heir conainmen effec and hus decrease he weigh of impored goods in he price index. In he limi as he counries become closed economies (τ ), he price indices are 3 The model can be easily exended o governmen spending shocks as in Bes and Devereux (2000). Resuls are available from he auhor on reques. 4 For simpliciy η and η are he same in he iniial equilibrium. 5 As shor-run oupu is demand-deermined, purely emporary produciviy shocks a ime would be enirely absorbed by shor-run leisure so ha no oher variables would need o adjus, see Obsfeld and Rogoff (995, p. 653). 6 Formally, P b / be / τ < 0 and P b / be / τ < 0. 2

13 s= Real exchange rae movemen s=0 and posiive rade coss s=0 and zero rade coss Counry size n Figure 3: Trade coss increase he real exchange rae movemen under producer currency pricing (s =0). compleely insulaed from exchange rae movemens. This weakening effec of rade coss has consequences for he real exchange rae movemen which can be expressed as bψ = be + bp bp =(s + χ( s)) be (4) where χ is a funcion of rade coss and exogenous parameers only. χ has he propery ha χ =0for τ =0and ha i monoonically increases in τ such ha 0 <χ< for 0 <τ<. 7 Consider he case of producer currency pricing (s =0)andadepreciaion(be > 0). In he absence of rade coss (τ = χ =0) he price index movemens are exacly offse by he nominal exchange rae so ha he real exchange rae does no move a all ( ψ b =0). Bu in he presence of rade coss he price index movemens are weakened and he real exchange rae is no longer fixed ( ψ b > 0). The real exchange rae movemen is sronger for higher rade coss wih ψ b = be in he limi as τ. 8 Figure 3 illusraes his behavior wih he numerical example from Secion III. 9 In he 7 See Appendix C. for deails. 8 Formally, for 0 s<, ψ b / be / τ > 0 and lim ψ b / be τ =since lim χ =. This finding τ also implies ha for some degree of producer currency pricing and a given series of nominal exchange rae movemens, rade coss render he real exchange rae more volaile (see below for simulaion resuls). 9 τ =0.37 and ρ =8. Figure 3 and all subsequen figures are drawn for one-percen shocks. 3

14 presence of rade coss real exchange rae movemens approach he ones under local currency pricing. This effec is so srong ha even under full exchange rae pass-hrough, rade coss of a reasonable magniude come close o a siuaion as if all prices were fixedinlocalcurrency. The Nominal Exchange Rae, Consumpion, Oupu and he Curren Accoun One can express he nominal exchange rae movemen in period in erms of exogenous shocks and parameers as be = a (cm cm )+a 2 (bη bη ) a s + a 3 ( s) (5) where a = + σβ µ β χ + σβ > 0 ρ( β) (σ ) β a 2 = > 0 β a 3 = (ρ ) χ 2 + a > 0 σ ρ +ρη ρ +η > wih <σ<ρ. χ 0 depends on rade coss τ and counry size n (see Appendix C). Since a, a 2 and a 3 are all greaer han zero, a posiive Home moneary shock ( M c > 0) leads o a depreciaion of he Home currency (be > 0), whereas a posiive Home produciviy shock (bη < 0) leads o an appreciaion. Table a summarizes he responses of key variables o a posiive Home moneary shock. The resuls can be undersood wih he help of wo swiching effecs. Under local currency pricing (s =) relaive prices and hus relaive demand are fixed, bu measured in domesic currency Home firms generae higher revenue because of he exchange rae depreciaion. This will be referred o as he income-swiching effec. As a resul of he conainmen effec his addiional income is predominanly spen on domesic goods, leading o a higher increase in Home oupu and a lower increase in Foreign oupu ( b h > b h ). Buinheabsenceof rade coss he addiional income would be spen evenly across he wo counries ( b h = b h ). Apar from oupu rade coss do no affec he reacion of oher variables o he moneary shock. In paricular, as can be seen from (5) he nominal exchange rae does no behave differenly because he facor a cancels. More generally, i can be said ha rade coss dampen inernaional linkages. Take he case of producer currency pricing (s =0).Priceindicesarenolongerfixed and he familiar expendiure-swiching effec comesinoplay. Buasradecossreducehemovemenofprice 4

15 Table a A moneary shock and he impac of rade coss ( M>0) c LCP (s =) PCP (s =0) Direcion Impac of τ Direcion Impac of τ Shor run be + = + > bp 0 = + < bp 0 = < bc + = + > bc 0 = + < b h + > + < b h + < < Curren accoun d F 0 = + < Long run bc + 0 = + < bc + 0 = < b h+ 0 = < b h + 0 = + < + up, 0 unchanged, down, > reinforced, = neural, < aenuaed. Table b A produciviy shock and he impac of rade coss (bη <0) LCP (s =) PCP (s =0) Direcion Impac of τ Direcion Impac of τ Shor run be > > bp 0 = < bp 0 = + < bc 0 = + < bc 0 = < b h 0 = < b h 0 = + < Curren accoun d F < < Long run bc + + > + > bc + + < + < b h+ + < + < b h + < < + up, 0 unchanged, down, > reinforced, = neural, < aenuaed. 5

16 indices, he nominal exchange rae mus depreciae more srongly han i would wihou rade coss. 20 Trade coss dampen he increase in oupu of Home goods and hey dampen he decrease in oupu of Foreign goods. They obsruc he posiive spillover of he moneary simulus such ha Home consumpion increases more srongly han Foreign consumpion. The curren accoun response is herefore also dampened, oning down he long-run responses of consumpion and oupu. 2 Those reacions are qualiaively similar o he behavior of variables in he presence of nonradable goods (Hau, 2000) and home bias in preferences (Warnock, 2003). Trade coss also dampen inernaional linkages in he face of produciviy shocks. Table b illusraes ha he long-run response o a posiive Home produciviy shock is qualiaively he same for local and producer currency pricing. Due o he conainmen effec of rade coss he benefis of he Home produciviy improvemen are iled owards Home consumers in he sense ha Home long-run consumpion increases more srongly, whereas Foreign long-run consumpion increases less srongly. In he shor run, no variables adjus under local currency pricing apar from he nominal exchange rae because relaive prices do no change and he produciviy shock is enirely absorbed by leisure. 5 Under producer currency pricing he expendiure-swiching effec leads o an increase in Home consumpion and a decrease in Foreign consumpion bu boh hose movemens are oned down by rade coss. Finally, rade coss have he general feaure ha compared o a fricionless world hey lead o quaniaively more similar responses of variables under local and producer currency pricing. Pu differenly, one could say ha he quaniaive responses of variables under s =and s =0converge wih increasing rade coss. This is rue for boh moneary and produciviy shocks. 22 Take Figure 3 as an example. For mos counry sizes he real exchange rae responses under s =and s =0are quaniaively raher similar wih rade coss, whereas hey are markedly differen wihou rade coss. 23 This paern holds up for all variables in Tables a and b. Simulaion Resuls Two conclusions can be drawn from he resuls above. Firs, rade coss make boh nominal 20 Formally, (a /a 3 ) / τ > 0 is required. This is generally he case unless rade coss are very low (roughly below 2 percen) and one counry is overwhelmingly big (roughly over 98 percen of world size). 2 Devereux (2000) provides a deailed discussion of he impac on he curren accoun. 22 Formally, bx s= X b s=0 / τ < 0. This is generally he case unless rade coss are unreasonably low (roughly below 2 percen) and one counry is overwhelmingly big (roughly over 98 percen of world size). 23 Noe ha rade coss can a mos boos he real exchange movemen up o he value under zero exchange rae pass-hrough (s =) bu no furher. This is also rue for he nominal exchange rae movemen. 6

17 Var(e ) / Var(M -M* ) Var(ψ ) / Var(M -M* ) s s Figure 4: Trade coss render he nominal (lef) and real (righ) exchange raes more volaile (τ =0for solid lines, τ>0 for dashed lines). and real exchange raes more volaile. Second, rade coss dampen inernaional linkages and reduce cross-counry consumpion and oupu correlaions. These wo conclusions are illusraed by simulaion resuls in Figures 4 and 5. Each simulaed observaion is consruced from 00 replicaions over a draw of 00 periods for uncorrelaed shocks o M and M or bη and bη. As discussed in Secion III, rade coss and he elasiciy of subsiuion are chosen as τ =0.37 and ρ =8based on Eaon and Korum (2002). The counry size is se o n =0.05 which falls in he range of large OECD counries such as Japan, Germany or he UK. As in Bes and Devereux (2000) β is chosen o be 0.94, implying a real ineres rae of abou 6 percen, roughly he average long-run real reurn on socks. The seady-sae value of η is chosen as 0/ o mach a consumpion-consan elasiciy of labor supply near uniy. This value is low by he sandards of he real business cycle lieraure bu higher han mos microeconomic esimaes. 24 Figure 4 plos he volailiy of he nominal and real exchange raes agains he exen of local currency pricing s. Volailiy is measured as he relaive variance of exchange rae movemens and moneary shocks, Var(be )/V ar(cm cm ) and Var( ψ b )/V ar(cm cm ). Under producer currency pricing (s =0) rade coss increase he volailiy of he nominal exchange rae by 29 percen (from 0.65 o 0.84). The volailiy of he real exchange rae jumps up from zero o Thus, hedifferences in volailiy beween producer and local currency pricing end o diminish when rade coss are presen The elasiciy is given by (ρ ) / (ρη) = This resul holds up for produciviy shocks. For s =0he volailiy of he nominal exchange rae, measured as Var(be )/V ar(bη bη ), increasesby75 percen from 0.2 o 0.2. Real exchange rae volailiy, measured as Var( b ψ )/V ar(bη bη ), jumps up from zero o 0.4. These volailiies are hardly sensiive o 7

18 Given he difficulies measuring moneary and produciviy shocks, i is no easy o compare Figure 4 o empirically observed exchange rae volailiies. Insead, I follow Chari, Kehoe and McGraan (2002) in compuing he sandard deviaion of he exchange rae relaive o he sandard deviaion of oupu. For quarerly U.S. exchange rae daa wih respec o a number of European counries beween hey find raios of 4.67 for he nominal exchange rae and 4.36 for he real exchange rae. For s =and posiive rade coss my model yields a raio of.53 for boh he nominal and real exchange raes in response o moneary shocks. For zero rade coss he raio would be lower a Alhough rade coss move exchange rae volailiy in he righ direcion, he numbers clearly fall shor of he empirically observed volailiies. As Chari, Kehoe and McGraan (2002) explain, hey can only successfully mach he empirical raios by assuming a large degree of risk aversion equal o ϑ =5. They show ha he degree of risk aversion is almos one-for-one relaed o he raio of sandard deviaions. Bu since my model is based on logarihmic uiliy, implying a degree of risk aversion equal o ϑ =, i is by consrucion no well suied o mach he high empirical volailiy of exchange raes. Neverheless, rade coss increase exchange rae volailiy and herefore seem a promising ool for generaing higher volailiy for more moderae levels of risk aversion (i.e. ϑ<5). 27 Empirically, oupu is more srongly correlaed across counries han consumpion. For example, based on quarerly daa for 4 OECD counries from Ravn and Mazzenga (2004) repor cross-counry correlaions of 0.33 for oupu and 0.22 for consumpion. However, he lieraure on inernaional business cycles has sruggled o explain he low crosscorrelaion of consumpion known as he consumpion correlaions puzzle (for a discussion see Obsfeld and Rogoff, 2000). Figure 5 visualizes he cross-counry correlaions of consumpion growh and oupu growh, Corr( bc, bc ) and Corr( b h, b h ), as prediced by he model. The op panels depic correlaions in response o moneary shocks and he boom panels depic correlaions in response o produciviy shocks. As a general paern rade coss push consumpion and oupu correlaions owards zero. Trade coss mach he empirical consumpion correlaions raher well. For s =0he alernaive counry sizes, for insance n = For s =0he model yields significanly lower raios (0.37 for he nominal and 0.30 for he real exchange rae) bu hose numbers mach he fac ha nominal exchange raes are more volaile. The raios are similar in he case of produciviy shocks (0.3 and 0.26). A larger counry size, for insance n = 0.25, slighly increases hese raios bu hey are sill below. 27 Ravn and Mazzenga (2004, Table 5) predic a sandard deviaion of he real exchange rae below, compared o an empirical value of 4.03 in quarerly OECD daa from In conras o Chari, Kehoe and McGraan (2002), heir model is based on flexible prices and herefore canno capure he fac ha in he shor run real exchange raes are predominanly driven by nominal exchange rae movemens (see Rogoff, 996). 8

19 Moneary shocks Moneary shocks Co rr( C,C*) Co rr( h,h*) Corr( C,C*) s Produciviy shocks Co rr( h,h*) s Produciviy shocks Figure 5: Trade coss push inernaional consumpion and oupu correlaions owards zero (τ =0for solid lines, τ>0 for dashed lines, moneary shocks in he op panels, produciviy shocks in he boom panels). 9

20 correlaion is 0.9 for moneary shocks and 0.2 for produciviy shocks, compared o 0.97 and 0.4 in a fricionless world. Thus, rade coss subsanially reduce cross-counry correlaions, in paricular in he case of full pass-hrough. The correlaion of 0.2 for produciviy shocks can be mos readily compared o he value of 0.49 ha Ravn and Mazzenga (2004, Table 6) obain when hey assume ha echnology shocks are uncorrelaed and have no cross-counry spillovers. Their baseline specificaion wih more persisen echnology shocks yields an even higher correlaion of Backus, Kehoe and Kydland (992), who use he same persisen echnology shock process as Ravn and Mazzenga (2004), are no able o generae low cross-counry correlaions eiher even if hey inroduce ransporaion coss ino heir flexible price model. I herefore seems ha rade coss in combinaion wih sicky prices aremoreeffecive a reducing cross-counry consumpion correlaions. In conras, he model does no generae realisic oupu correlaions. Alhough rade coss move hem in he righ direcion, oupu correlaions end o be negaive and herefore do no mach he posiive correlaion observed empirically. Similarly, Ravn and Mazzenga (2004) repor oupu correlaions ha are close o zero and in some cases negaive. Bu as Chari, Kehoe and McGraan (2002) show, a business cycle model wih invesmen and capial is more successful in generaing realisic oupu correlaions when combined wih moneary shocks and sicky prices. V. Trade Coss and Welfare How do rade coss affec he welfare properies of he model? To address his issue, I adop Obsfeld and Rogoff s (995) mehodology and decompose he uiliy funcion () ino U = U R + U M where U R consiss of he consumpion and labor erms and U M of real money balances. As Obsfeld and Rogoff (995) argue, unless real money balances are assigned an implausibly large weigh γ in (), U R dominaes he overall welfare effec of a shock and U M can be negleced. Taking log-linear approximaions and noing ha bc + = C b ++k, b h + = b h ++k as well as bη + = bη ++k for k =, 2... yields d U R = bc µ ρ ρ b h + η ln ( h) bη + β bc + ( β) µ ρ b h+ + η ln ( h) bη + ThenoaionforheForeigncounryisanalogous.Table2summarizeshewelfareeffecs. The welfare effecofanincreaseinhomeproduciviy(bη <0) is paricularly easy o undersand. I unambiguously raises welfare in boh counries. Bu due o he conainmen 28 Moreover, symmeric counry sizes (n =0.5), as implicily assumed by Ravn and Mazzenga (2004), yield he lowes possible consumpion correlaion. For example, he correlaion of 0.2 wih n = 0.05 as menioned above compares o a correlaion of 0.05 inhecaseofcounrysymmery. ρ 20

21 Table2 Theimpacofradecossonwelfare LCP (s =) PCP (s =0) Direcion Impac of τ Direcion Impac of τ cm >0 d U R + < + > d U R < + becomes bη <0 d U R + > + > d U R + < + < +up, down, > reinforced, < aenuaed. effec rade coss reinforce he welfare gain for Home households and dampen he welfare gain for Foreign households. Given ha wih zero rade coss he Home welfare gain exceeds he Foreign gain (d U R > d U R ), his resul implies ha rade coss increase he welfare gap. The welfare effec of a Home moneary expansion (cm > 0) dependsonhedegreeof exchange rae pass-hrough. As Table a illusraes, under local currency pricing (s =) rade coss only affec he response of shor-run labor effor. They increase he labor effor of Home households, hus making hem worse off compared o a fricionless world. The opposie is rue for Foreign households. As depiced in he op panel of Figure 6 (drawn for n =0.05), rade coss herefore reduce he welfare gap beween Home and Foreign. In he limi when he wo counries become closed economies (τ ) Foreign households are no a all affeced. As he boom panel of Figure 6 illusraes, he welfare response under producer currency pricing (s =0) is hump-shaped wih he welfare gap peaking a inermediae rade cos values around τ =0.2. Table a shows ha rade coss affec boh he shor-run and he long-run responses of consumpion and labor effor. Trade coss reinforce he increase in shor-run consumpion C b and dampen he increase in shor-run labor effor b h so ha in he shor run, rade coss make Home households beer off compared o a fricionless world. This shor-run effec can be explained by he expendiure-swiching effechafavorshehome counry and ha is reinforced by rade coss. In conras, rade coss dampen he increase in long-run consumpion bc + as well as he fall in long-run labor effor b h + so ha in he long run, rade coss make Home households worse off. I urns ou ha he posiive shor-run effec dominaes he negaive long-run effec up o an inermediae value of roughly τ =0.2. Thus, rade coss iniially increase he welfare gap under producer currency pricing bu hey reduce i under local currency pricing. The middle panel of Figure 6 plos he welfare reacion for an inermediae degree of pass-hrough (s =0.5). Now he welfare gap is fairly 2

22 sable up o τ =0.2 and only shrinks for higher rade coss. In summary, he welfare resuls sand in sharp conras o Obsfeld and Rogoff s (995) finding ha moneary shocks enail posiive and symmeric inernaional welfare spillovers. Their finding refers o he special case of zero rade coss and full pass-hrough. Figure 6 shows ha his special case is no robus o rade coss and lower degrees of pass-hrough. VI. Conclusion The focus of his paper is o invesigae he implicaions of inernaional rade coss for key macroeconomic variables. This is achieved by inegraing iceberg rade coss ino a microfounded wo-counry general equilibrium model wih asymmeric counry sizes based on he New Open Economy Macroeconomics lieraure. The inclusion of rade coss is moivaed by Anderson and van Wincoop s (2004) recen survey showing ha empirical rade coss are widespread and large wih a ariff equivalen of represenaive inernaional rade coss of around 74 percen. Even moderae rade coss end o have a subsanial impac on he behavior of key economic variables. By increasing he price of foreign goods, rade coss il consumpion owards domesic goods and creae an endogenous home bias in consumpion. This feaure of rade coss is crucial in maching empirical rade shares for OECD counries. In conras, nonradable goods would overpredic rade shares. By impeding inernaional rade flows rade coss end o isolae counries from each oher and herefore weaken inernaional linkages, leading o smaller curren accoun movemens as well as lower inernaional oupu and consumpion correlaions. However, he weakened inernaional linkages force nominal and real exchange raes o move more srongly in response o shocks. Trade coss herefore increase exchange rae volailiy. Finally, he model is designed o allow for varying degrees of exchange rae pass-hrough. I urns ou ha rade coss render he disincion beween producer and local currency pricing less relevan. For example, simulaion resuls show ha cross-counry consumpion correlaions are raher similar under complee and incomplee pass-hrough. In he same way, rade coss urn a moneary expansion ino a beggar-hy-neighbor policy regardless of he degree of exchange rae pass-hrough. References Anderson, J., van Wincoop, E., Graviy wih Gravias: A Soluion o he Border Puzzle. American Economic Review 93, pp Anderson, J., van Wincoop, E., Trade Coss. Journal of Economic Lieraure 42, pp

23 Figure 6: Trade coss and welfare for varying degrees of exchange rae pass-hrough. 23

24 Akeson, A., Bursein, A., Pricing o Marke, Trade Coss, and Inernaional Relaive Prices. American Economic Review 98, pp Backus, D., Kehoe, P., Kydland, F., 992. Inernaional Real Business Cycles. Journal of Poliical Economy 00, pp Backus, D., Smih, G., 993. Consumpion and Real Exchange Raes in Dynamic Economies wih Non-Traded Goods. Journal of Inernaional Economics 35, pp Bergin, P., Glick, R., Endogenous Tradabiliy and Macroeconomic Implicaions. Mimeo, Universiy of California, Davis. Bes, C., Devereux, M., Exchange Rae Dynamics in a Model of Pricing o Marke. Journal of Inernaional Economics 50, pp Brunner, A., Naknoi, K., Trade Coss, Marke Inegraion, and Macroeconomic Volailiy. IMF Working Paper No. 54 (March). Chari, V., Kehoe, P., McGraan, E., Can Sicky Price Models Generae Volaile and Persisen Real Exchange Raes? Review of Economic Sudies 69, pp Chen, N., Novy, D., Inernaional Trade Inegraion: A Disaggregaed Approach. CEPR Discussion Paper 703. Devereux, M., How Does a Devaluaion Affec he Curren Accoun? Journal of Inernaional Money and Finance 9, pp Eaon, J., Korum, S., Technology, Geography and Trade. Economerica 70, pp Engel, C., 999. Accouning for U.S. Real Exchange Rae Changes. Journal of Poliical Economy 07, pp Evans, C., Naional Border Effecs: Locaion, No Naionaliy, Maers. Review of Inernaional Economics 5, pp Fender, J., Yip, C., Tariffs and Exchange Rae Dynamics Redux. Journal of Inernaional Money and Finance 9, pp Hau, H., Exchange Rae Deerminaion: The Role of Facor Price Rigidiies and Nonradeables. Journal of Inernaional Economics 50, pp Helpman, E., 999. The Srucure of Foreign Trade. Journal of Economic Perspecives 3, pp Krugman, P., 980. Scale Economies, Produc Differeniaion, and he Paern of Trade. American Economic Review 70, pp Naknoi, K., Real Exchange Rae Flucuaions, Endogenous Tradabiliy and Exchange Rae Regimes. Journal of Moneary Economics 55, pp Obsfeld, M., Rogoff, K., 995. Exchange Rae Dynamics Redux. Journal of Poliical Economy 03, pp

25 Obsfeld, M., Rogoff, K., The Six Major Puzzles in Inernaional Macroeconomics: Is There a Common Cause? In: NBER Macroeconomics Annual 5. Ravn, M., Mazzenga, E., Inernaional Business Cycles: The Quaniaive Role of Transporaion Coss. Journal of Inernaional Money and Finance 23, pp Rogoff, K., 996. The Purchasing Power Pariy Puzzle. Journal of Economic Lieraure 34, pp Svensson, L., van Wijnbergen, S., 989. Excess Capaciy, Monopolisic Compeiion, and Inernaional Transmission of Moneary Disurbances. Economic Journal 99, pp Warnock, F., Exchange Rae Dynamics and he Welfare Effecs of Moneary Policy in a Two-Counry Model wih Home-Produc Bias. Journal of Inernaional Money and Finance 22, pp Appendix A: Households and Firms Appendix A oulines he derivaions of he expressions in Secion II. Demand funcion (7) is derived by maximizing C in (2) subjec o he expendiure K given by Z n Z n+( n)s Z K = p i c i d i + 0 n τ p ic i d i + n+( n)s τ e qic i d i This also resuls in price index (3). Maximizing uiliy () subjec o he wo-period ineremporal budge consrain consruced from (5) P + C + + M + + d + F + = W + h + + π + + d d M + Z + + d [W h + π + M + Z + F P C ] yields he opimaliy condiion for labor supply η h = W P C (A) andhemoneydemandfuncion M = γc (A2) P d as well as he ineremporal consumpion sream d P + C + = βp C (A3) The corresponding equaions for he Foreign counry are analogous. 25