DISCUSSION PAPER SERIES. No DO TRADE COSTS IN GOODS MARKET LEAD TO HOME BIAS IN EQUITIES? Nicolas Coeurdacier INTERNATIONAL MACROECONOMICS ABCD

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1 DISCUSSION PAPER SERIES No DO TRADE COSTS IN GOODS MARKET LEAD TO HOME BIAS IN EQUITIES? Ncolas Coeurdacer INTERNATIONAL MACROECONOMICS ABCD Avalable onlne at:

2 ISSN DO TRADE COSTS IN GOODS MARKET LEAD TO HOME BIAS IN EQUITIES? Ncolas Coeurdacer, London Busness School (LBS) and CEPR Dscusson Paper No October 2008 Centre for Economc Polcy Research Goswell Rd, London EC1V 7RR, UK Tel: (44 20) , Fax: (44 20) Emal: Webste: Ths Dscusson Paper s ssued under the auspces of the Centre s research programme n INTERNATIONAL MACROECONOMICS. Any opnons expressed here are those of the author(s) and not those of the Centre for Economc Polcy Research. Research dssemnated by CEPR may nclude vews on polcy, but the Centre tself takes no nsttutonal polcy postons. The Centre for Economc Polcy Research was establshed n 1983 as an educatonal charty, to promote ndependent analyss and publc dscusson of open economes and the relatons among them. It s pluralst and nonpartsan, brngng economc research to bear on the analyss of medum- and long-run polcy questons. These Dscusson Papers often represent prelmnary or ncomplete work, crculated to encourage dscusson and comment. Ctaton and use of such a paper should take account of ts provsonal character. Copyrght: Ncolas Coeurdacer

3 CEPR Dscusson Paper No October 2008 ABSTRACT Do Trade Costs n Goods Market Lead to Home Bas n Equtes?* Two of the man puzzles n nternatonal economcs are the consumpton and the portfolo home bases. We solve for nternatonal equty portfolos n a twocountry/two-good stochastc equlbrum model wth trade costs n goods markets. We show that ntroducng trade costs, as suggested by Obstfeld and Rogoff (2000), s not suffcent to explan these two puzzles smultaneously. On the contrary, we fnd that trade costs create a foregn bas n portfolos for reasonable parameter values. Ths result s robust to the addton of nontradable goods for standard calbratons of the preferences. JEL Classfcaton: F30, F36 and F41 Keywords: home bas, portfolo choce and trade costs Ncolas Coeurdacer London Busness School Economcs Subject Area Regent s Park London NW1 4SA Emal: ncoeurdacer@london.edu For further Dscusson Papers by ths author see:

4 * I am especally grateful to Rchard Portes and Phlppe Martn for helpful dscussons. I thank Ncolas Govllot for excellent research assstance. I also thank Thomas Chaney, Wouter Denhaan, Perre-Olver Gournchas, Stephane Gubaud, Robert Kollmann, Phlp Lane, Francos Le Grand, Maury Obstfeld, Davd Thesmar, Ebrahm Rahbar, Xaver Ragot, Helene Rey, Davd Sraer and all the semnar partcpants at PSE, at HEC-Lausanne, CREI Pompeu Fabra, UCL, HEC-Pars, Carlos III Madrd, Pars 1, EUI, Ecares at the XXXth Spansh Economc Assocaton Meetng (Murca), at the Econometrc Socety Wnter Meetngs (Istanbul) and at the Socety for Economc Dynamcs Annual Meetng (Vancouver), at the EEA Meetng (Budapest) for ther valuable comments. Ths paper s part of my PhD dssertaton held at Pars School of Economcs (PSE) (November 2005). Submtted 25 September 2008

5 1 Introducton Ths paper s manly motvated by two broad stylzed facts: 1. People manly consume domestcally produced goods: the home bas n consumpton puzzle 2. People hold a dsproportonate share of domestc assets : the home bas n portfolos puzzle The frst fact s well known: lookng at consumpton baskets, countres are not very open to trade. The openness to trade rato n the US measured by the sum of exports and mports over GDP s only 25% n Gven that the US account for about a thrd of world producton, they should mport about two thrds of ther GDP n the absence of frctons n goods markets. Then, the openness rato should be hgher than 120%! Wthout beng so ambtous about market ntegraton, even the US and Canada are far from beng perfectly ntegrated (Mc Callum [1995] 1 ). The second fact s also well known: snce the semnal paper of French and Poterba [1991], the home bas n equtes s one of the most pervasve emprcal observatons n nternatonal economcs. Although home bas could be manly due to captal market segmentaton n the eghtes, ths explanaton mght be less vald nowadays. Indeed, developed countres opened up ther stock market to foregn nvestors n the eghtes, followed by many emergng economes n the early nnetes, leadng to a large ncrease n cross-border asset trade (Lane and Mles-Ferett [2003]). However, the home bas n equtes has not decreased szeably. In 2005, US nvestors stll hold 82% percent of domestc equtes and the home bas n equtes s observed n all developed countres (see Sercu and Vanpee [2007] for a recent survey). Moreover there s evdence that the two puzzles are related: countres whch are more open to trade are also more fnancally open. In other words, everythng else equal, countres wth hgher mport (or export) shares have larger stocks of foregn assets. Lane [2000], Azenman and Noy [2005], Heathcote and Perr [2007] show ths result usng panel data for a cross-secton of countres. Lookng at blateral data on trade n goods and asset holdngs, Portes and Rey [2005], Avat and Coeurdacer [2007] and Lane and Mles-Ferett [2004] show that country portfolos are strongly based towards tradng partners. There s now qute a consensus that nternatonal trade costs understood n a broad sense (.e transport costs, tarffs, border effect...) can explan the frst fact. As shown by Anderson and Van Wncoop [2004], nternatonal trade costs are very large, as large as producton costs for some products. Obstfeld and Rogoff [2000] argue that home bas n equtes mght also be due to frctons n nternatonal goods markets rather than frctons n fnancal markets. If ths s true, one can solve two mportant puzzles n nternatonal economcs wth only one smple frcton, namely trade costs. In ths paper, we ask whether the Obstfeld and Rogoff [2000] argument s vald,.e whether trade costs n goods markets alone can generate substantal home bas n portfolos. We do t n a standard statc two-country/two-good model wth symmetrc endowment economes (Home and Foregn). Each country produces one good but agents consume both goods, facng some trade costs when mportng foregn goods. 1 see also Anderson and Van Wncoop [2003] who correct Mc Callum estmates controllng for multlateral resstance. 2

6 Agents trade clams (equtes) of both countres n a frctonless fnancal market. Equtes are clams to the future endowment of the good (Lucas trees). In a set-up essentally smlar to ours, Obstfeld and Rogoff [2000] restrct ther attenton to the very specfc case where the effcent Arrow-Debreu consumpton allocaton can be perfectly replcated wth equtes only and do not solve for portfolos of tradable assets n the general case. We propose here to fll ths gap. Contrary to ther fndngs, we show that n general trade costs actually worsen the home bas n portfolos puzzle. Trade costs help to solve the Home bas n consumpton puzzle but at the expense of Foregn bas n equtes. The man ntuton for our result goes as follows: when Home output s hgh, so s Home consumpton due to the presence of trade costs. In these states of nature, Home nvestors want to make captal losses on ther portfolos to share output rsk effcently wth Foregners. Consequently, they bas ther portfolo towards Foregn equtes as Foregn equtes have a lower pay-off than Home equtes when Home output s hgher. Our result s closely related to the lterature that analyzes equty portfolos n presence of real exchange rate fluctuatons n partal equlbrum models (see Adler and Dumas [1983], Cooper and Kaplans [1994] and Warnock and van Wncoop [2007]). In these models, real exchange rate fluctuatons mght lead to portfolos that devate from the world market portfolo. Ths lterature shows that nvestors more rsk averse than log-nvestors bas ther portfolos towards assets that pay more when ther aggregate prce ndex s hgher,.e when the real exchange rate apprecates, n order to stablze ther purchasng power (and nversely, agents who are less rsk averse than logarthmc nvestors wll prefer assets that pay more when prces are low). Then, the key pont for portfolo allocaton s whether the Home equty returns (relatve to the Foregn ones) and the (Home) real exchange rate covary postvely or negatvely: a postve covarance meanng a Home bas n equtes when agents are more rsk averse than log-nvestors. The exact same mechansm s at work here but the model goes one step further snce the general equlbrum approach allows to analyze whether Home equty returns should be (or not) postvely correlated wth the (Home) real exchange rate n the presence of trade costs. We show that the sgn of ths correlaton s affected by the sze of trade costs. However, for trade costs consstent wth nternatonal consumpton patterns, the model predcts a negatve correlaton. When Home output s low, Home equty returns shrnk relatve to Foregn ones and the relatve prce of Home goods ncreases as they are scarcer: the (Home) real exchange rate apprecates. Low returns n the Home country are assocated wth hgher Home prces. Thus, consumers are better nsured aganst real exchange rate fluctuatons by holdng a larger share of foregn equtes. We nvestgate the robustness of our result n presence of non-tradable goods. Ths s a potental canddate to reconcle facts and theory as varatons of the real exchange rate reflects changes n the prce of tradable and non-tradable goods. Consequently, the hedgng of real exchange rate fluctuatons becomes more complex. We follow Obstfeld [2007] and extend our benchmark model by addng a non-tradable sector: each country s producng a tradable and a non-tradable good that are mperfect substtutes. We depart from Obstfeld [2007] and from exstng lterature by assumng that agents cannot trade separately 3

7 clams on the tradable and non-tradable sector. 2 We rather assume that agents trade Home and Foregn equtes that are clams over the aggregate output produced n the economy. Home bas n equtes can emerge although for reasonable calbratons t remans farly small and not very robust across specfcatons. Such equty home bas s drven by the presence of non-tradable goods together wth a low elastcty of substtuton between tradable and non-tradable goods. Lke n the model wth tradable goods only, a key feature of the model wth non-tradable goods s that there s equty home bas f and only f the Home real exchange rate and Home (relatve) equty returns co-vary postvely. Ths condton s rejected by the data, at least for the US (see van Wncoop and Warnock [2007]). Fnally and most mportantly, holdngs of local stocks are decreasng wth trade costs. In other words, n the presence of non-tradable goods, trade costs stll lead to Foregn equty bas and ths result s robust across the calbratons consdered. We also dscuss the man results of Obstfeld [2007] and Collard, Dellas, Dba and Stockmann [2007] when nvestors can buy separate clams on tradable and non-tradable output n each country. In these models, whle there mght be some home bas n equtes n the non-tradable sector, trade costs stll generate equty foregn bas n the tradable sector for reasonable calbratons of the preference parameters. Overall, we beleve that trade costs cannot account for the low level of nternatonal dversfcaton. Our paper s related to the lterature that solves for nternatonal equty portfolos n two-country general equlbrum models. Part of ths lterature has focused on the role of labor ncome as source of portfolo bases, generatng Home or Foregn bases dependng on the set-up (see Baxter and Jermann [1997], Engel and Matsumoto [2006], Heathcote and Perr [2007]). Abstractng from labor ncomes, we nvestgate a dfferent source of heterogenety among nvestors that could lead to portfolo bases, namely the presence of trade costs n goods markets. The closest paper to ours s Uppal [1993]: he develops a dynamc equlbrum of two endowment economes wth complete markets and trade costs. However, he restrcts hs attenton to the case of perfect substtutablty between Home and Foregn goods. We wll show that ths last assumpton plays a crucal role and relaxng t leads to a rcher and more complex portfolo allocaton. In ndependent work, Kollmann [2006a] solves for nternatonal portfolos n a twocountry/two-good dynamc equlbrum wth home bas n preferences but he focuses on the case of a low elastcty of substtuton between goods (smaller than 1) where trade costs are nconsstent wth consumpton and portfolo bases. Fnally, recent work by Devereux and Sutherland [2006a,b] and Tlle and Van Wncoop [2007] provdes new methods to solve for nternatonal equty portfolos n a large varety of context. We wll borrow ther technque and apply t to our set-up. In secton 2, we present our benchmark model wth tradable goods only and derve the exact condtons under whch trade costs lead to home bas n equtes. We show that these condtons are volated under standard preference parameters. In secton 3, we nvestgate the robustness of our result n the presence of non-tradable goods. Secton 4 dscusses the results and concludes. 2 see Dellas and Stockmann [1989], Baxter, Jermann and Kng [1998], Serrat [2001], Pesent and Van Wncoop [2002], Obstfeld [2007], Matsumoto [2007], Collard, Dellas, Dba and Stockmann [2007]. Besdes the fnancal asset structure, the model s dentcal to Obstfeld [2007]. 4

8 2 The benchmark model 2.1 Set-up of the model The model s a two perod (t = 0, 1) endowment economy wth two symmetrc countres, Home and Foregn. Home varables are denoted wth H, Foregn varables wth F. Each country produces one tradable good and the representatve agent n each country consumes both goods; goods can be shpped from one country to the other wth some trade costs. In perod t = 0, no output s produced and no consumpton takes place, but agents trade stocks (equtes) whch are clams on the future endowment of the country. 3 In perod t = 1, uncertanty s realzed and country receves an exogenous stochastc endowment y of good. We assume E 0 (y ) = y for both countres, where E 0 s the condtonal expectaton operator, gven date t = 0 nformaton Preferences The country household has the standard constant relatve rsk averson preferences, where γ denotes coeffcent of relatve rsk averson and C s the aggregate consumpton ndex n country : [ C 1 γ ] U = E 0 1 γ In both countres, the representatve household consumes a basket of Home and Foregn goods. The aggregate consumpton ndex of an agent n country s: C = [ c (φ 1)/φ ] φ/(φ 1) + c (φ 1)/φ j where c j s the total consumpton of goods from country j by a representatve agent n country. The parameter φ s the elastcty of substtuton between Home and Foregn goods. We wll assume that ths elastcty s strctly larger than one: 4 φ > Trade Costs, Terms-of-Trade and the Real Exchange Rate Exports from country j to country are subject to some exogenous trade costs τ of ceberg-type: for each good shpped, 1/(1 + τ) goods arrve at destnaton. If p denotes the prce of one unt of output n country n terms of the numerare, the prce faced by consumers n country over goods from country j s for j: p j = (1 + τ)p j Ths features frctons n nternatonal goods markets such as transport costs or other barrers to nternatonal trade (trade polces, border effect...). Trade costs wll be the only source of heterogenety among nvestors and consequently the only reason why they mght hold dfferent equty portfolos. The Home terms of trade q denotes the relatve prce of the Home tradable good n terms of the Foregn 3 A rsk-free bond could be added but due to the symmetry of countres, no bonds would be held n equlbrum. 4 Except n secton where we consder elastctes smaller than one. 5

9 tradable good: q = p H p F. The consumpton prce ndex (CPI) of agent = H, F s equal to (wth j ): ] 1/(1 φ) P = [(p ) 1 φ + [(1 + τ)p j ] 1 φ The (Home) real exchange rate (RER) s the rato of Home over Foregn CPI: RER = P H P F = { q1 φ + (1 + τ) 1 φ }1/(1 φ) 1 φ 1 + [(1 + τ)q] (1) An ncrease n RER s an apprecaton of the Home real exchange rate. The Home real exchange rate apprecates when the Home terms-of-trade q ncrease. Wthout trade costs, the real exchange rate s constant (purchasng-power-party holds and agents have dentcal preferences over the two goods) Fnancal markets There s trade n equtes n perod 0. In each country there s one stock (Lucas tree). Each stock represents a clam to the future endowment of the tree. The supply of each share s normalzed at unty. Each household fully owns the local stock, at brth, and has zero ntal foregn assets. The country household thus faces the followng budget constrant, at t = 0: p S µ + p S µ j = p S, wth j (2) where µ j s the number of shares of stock j held by country at the end of perod 0. p S s the share prce of stock that s dentcal for both stocks due to symmetry. 2.2 Goods and Asset markets equlbrum condtons Goods market equlbrum condtons In perod 1 (after the realzaton of the output shocks), a representatve consumer n country maxmzes C 1 γ 1 γ subject to a budget constrant (for j ): p c + (1 + τ)p j c j µ p y + µ j p j y j (λ,1 ) (3) P C µ p y + µ j p j y j (λ,1 ) (4) where λ,1 s the Lagrange-Multpler assocated to the budget constrant n perod 1 for household. The budget constrant equalzes consumpton expendtures to aggregate (fnancal) ncomes of the representatve agent n country, where fnancal ncomes depend on the portfolo {µ ; µ j }. At ths pont, we take portfolos chosen n perod 0 as gven. The frst-order condtons are: For consumpton: 1 = λ,1 P C γ (5) Intratemporal allocaton across goods (for j ): c = ( p ) φ ( ) φ (1 + τ)pj C c j = C (6) P P 6

10 Resource constrants for both goods are gven by: c HH + (1 + τ)c F H = y H (7) c F F + (1 + τ)c HF = y F. (8) Usng equatons (6) for both countres and market-clearng condtons for tradable goods (7) and (8) gves the relatve demand over Home and Foregn goods: [ q φ Ω ( P F ) C ] φ F = y H (9) P H C H y F where Ω(x) s a contnuous functon of x such that: Ω(x) = 1+x(1+τ)1 φ x+(1+τ) 1 φ Asset market equlbrum condtons Introducng (λ,0 ) the Lagrange-multpler of the perod 0 budget constrant (2) n country, we get the followng Euler equatons that equalzes the margnal cost of buyng an addtonal unt of stock n perod 0 to the expected margnal gan n perod 1. The Euler equatons determne the demand for stocks H and F n country : λ,0 p s = E 0 [λ,1 p H y H ] (10) λ,0 p s = E 0 [λ,1 p F y F ] (11) We can rewrte the Euler equatons n relatve terms usng (5) as follows: E 0 [ C γ ( p Hy H p F y F P p s )] = E 0 [ C γ (R H R F )] = 0 (12) P where R = p y p s denotes the return on stock. Takng the dfference of equaton (12) between the Home and Foregn household, we get: E 0 [( C γ H P H C γ F )(R H R F )] = 0 (13) P F Market clearng n asset markets for stocks requres: µ HH + µ F H = µ F F + µ HF = 1 (14) Countres symmetry mples that equlbrum portfolos are symmetrc: µ HH = µ F F. In what follows, country s holdngs of local stock are denoted by µ. (1 µ) wll be the nternatonally dversfed part of the equty portfolo. µ > 1 2 means that there s equty home bas. 2.3 Log-lnearzaton around the symmetrc equlbrum We use the world prce ndex as a numerare to preserve symmetry: P = P 1 2 H P 1 2 F = 1. We consder an approxmaton around the symmetrc equlbrum where both countres have the same endowment y (and the same goods prces: p H = p F = 1). We denote wth (ˆ) the devatons of the varables from the symmetrc equlbrum (n percents): x log( x x ) where x s the value at the symmetrc equlbrum. 7

11 To solve for portfolos, we follow Devereux and Sutherland [2006a] and Tlle and Van Wncoop [2007]. They show that a frst-order approxmaton of the non-portfolo equatons (equatons (4), (6) to (9)) and a second-order approxmaton of the Euler equatons are needed to express the zero-order component of equlbrum portfolos Frst-order approxmaton of non-portfolo equatons Due to symmetry, t s convenent to express all varables n relatve terms (Home over Foregn). Loglnearzng (9) around the symmetrc equlbrum gves: [ ŷ H = φ q + θ (φ 1) P H y F P F + P C ] (15) where P C = P H C H P ( ) 1 (1+τ) F C F denotes relatve consumpton expendtures and θ(τ) = 1 φ [0; 1]. 1+(1+τ) 1 φ θ s a monotonc transformaton of trade costs, ncreasng n τ. When θ s close to zero, trade costs are very low whereas θ converges to one when trade costs are nfnte. One can easly show that n equlbrum, (1 θ) s equal to the openness to trade rato defned as the sum of exports plus mports over GDP. From now on, θ wll be the relevant parameter to look at the mpact of trade costs. The log-lnearzaton of prce ndces gves n country = {H, F } (for j ): P = (1 + τ) p (1 + τ)1 φ 1 φ (1 + τ) p 1 φ j (16) We deduce the followng expresson for the Home real exchange rate around the symmetrc equlbrum: RER = P H P F = θ q (17) Due to trade costs, an ncrease n domestc prces apprecates the real exchange rate. θ measures the sze of trade barrers but t s also the elastcty of the real exchange rate wth respect to the terms-of trade. In presence of trade costs, an ncrease n the Home terms-of-trade s equvalent to a Home real exchange rate apprecaton. Ths s consstent wth a postve correlaton between the terms-of-trade and the real exchange rate n ndustralzed countres (see Obstfeld and Rogoff [2000b]). Usng (15) and (17), we get: ŷ H ŷ F = [ φ(1 θ 2 ) θ 2 ] q + θ P C (18) Then, the relatve demand over Home and Foregn goods s decreasng wth respect to the Home termsof-trade and ncreasng n Home (over Foregn) aggregate consumpton expendtures: when aggregate expendtures are hgher at Home, so s the demand for Home goods due to the presence of trade costs (θ > 0). Holdng constant (relatve) aggregate consumpton expendtures P C, Home terms-of-trade always decrease wth an ncrease the relatve supply of Home goods. Note that the response of the Home terms-of-trade to a (relatve) output shock wll be stronger when trade costs are hgh (hgher θ) snce the (relatve) demand for Home goods s more nelastc (for φ > 1). Then, Home excess returns (excess returns of the Home stock over the Foregn stock) R = R H R F can 8

12 be derved from (18): R = p H y H p F y F = (1 φ)(1 θ 2 ) q + θ P C (19) The last non-portfolo equaton that must be log-lnearzed s the perod 1 budget constrant (4). We express the perod 1 budget constrant n relatve terms whch gves (usng portfolo symmetry): P C = (2µ 1)( p H y H p F y F ) = (2µ 1) R (20) Wthout bas n the equty portfolo (µ = 1 ), relatve consumpton expendtures are equalzed snce 2 household have dentcal fnancal ncomes. Any portfolo bas drves a wedge between Home and Foregn consumpton expendtures Second-order approxmaton of (relatve) Euler equaton The second-order approxmaton of the portfolo equaton (13) s: cov( P C, R) = (1 1/γ)cov( RER, R) (21) where var( R) denotes the varance of excess returns of the Home stock over the Foregn stock and cov( x, R) denotes the covarance of varable x wth Home excess returns. (21) gves usng (20): (2µ 1)var( R) = (1 1/γ)cov( RER, R) (22) Wth a bt of rewrtng, we get: 5 µ = 1 2 [1 + (1 1 γ )cov( RER, R) var( R) ] (23) = 1 2 [1 + (1 1 γ cov( q, R) )θ ] (24) var( R) The expresson s smlar to the one obtaned by Van Wncoop and Warnock [2007]. Holdngs of domestc equty µ depend on two terms: - the market portfolo (whch s 1 ) due to dversfcaton motve (as n Lucas [1982]) 2 - the hedgng component due to real exchange rate fluctuatons, whch s 1 2 (1 1 cov( q, R) )θ γ var( R) We get a standard result: a logarthmc nvestor (γ = 1) s not affected by fluctuatons of the real exchange rate and the hedgng term dsappears n ths case. Of course, n absence of trade costs (θ = 0), the real exchange rate s constant and the hedgng term also cancels out. If γ > 1, ths term s postve when Home equty excess returns have a postve covarance wth the Home real exchange rate. Home nvestors prefer the stock that yelds hgher returns when the Home prce ndex s hgher. 5 Here we assume that var( R) = var( R H R F ) s non-zero. Ths mght happen for a pecular calbraton of the preferences and trade costs (see below). In that case the portfolo s undetermned snce Home and Foregn stocks are perfect substtutes. 9

13 2.4 Equlbrum Portfolos Analytcal expresson and Portfolo Bases To compute the equlbrum portfolo from the partal equlbrum expresson (24), we need to compute the equlbrum varance-covarance rato cov( q, R). Usng (19) and (20), we get the followng expresson: var( R) cov( q, R) 1 θ(2µ 1) var( R) = (1 φ)(1 θ 2 ) (25) Ths varance-covarance rato depends n turn on the equlbrum portfolo µ. As shown n Tlle and Van Wncoop (2007), we deduce the zero-order component of equty portfolo as soluton of a fxed-pont problem usng (24) and (25). Rearrangng terms, we get the equlbrum equty portfolo: µ = 1 2 [1 (1 1 γ ) θ (26) (φ 1)(1 θ 2 ) θ 2 (1 1 )] γ Real exchange rate fluctuatons generate a portfolo bas for nvestors wth non-logarthmc preferences. Assumng a coeffcent of relatve rsk averson larger than one, the drecton the bas depends on the sgn of the denomnator (φ 1)(1 θ 2 ) θ 2 (1 1 ). We have Foregn (resp. Home) bas n equtes f ths γ denomnator s postve (resp. negatve). We denote θ the unque θ (0; 1) such that ths denomnator s equal to zero: θ = ( ) 1 φ 1 2 (27) φ 1/γ In ths case, equty portfolos are undetermned as Home and Foregn equtes have perfectly correlated returns. We have Home bas n equtes f and only f θ > θ,.e trade costs are above a certan threshold. Below that threshold, the portfolo s based towards Foregn equtes Intuton for the result The key pont to understand portfolo bases s the equlbrum covarance between Home excess returns and the Home real exchange rate. When ths covarance s postve, Home nvestors prefer Home equtes as they provde hgher returns when the relatve prce of Home goods s hgher. Equty Foregn bas emerges when ths covarance s negatve. In standard cases, one should expect ths covarance to be negatve: ndeed, when output s hgh at Home, the Home terms-of-trade and the Home real exchange rate deprecate due to the scarcty of Foregn goods. But n the mean tme, Home equty returns are hgher snce Home producton s hgher. Home excess returns and the Home real exchange rate move n opposte drectons. Investors have a Foregn bas n equtes. We wll see n the calbraton of the model (see below) that ths case s the most lkely. However, whle ths reasonng holds for low level of trade costs (θ < θ ), ths s not always true. For (very) hgh level of trade costs (θ > θ ), a lower prce for Home goods (deprecated Home real exchange rate) s assocated wth lower equty returns n the Home country. When goods markets are very segmented, an ncrease n Home output leads to a larger fall n the Home terms-of-trade snce t s 10

14 harder to sell the addtonal output n the Foregn market. Potentally, the fall n Home terms-of-trade s so large that Home equty returns are lower than Foregn returns despte hgher Home producton. Ths s a case of mmserzng growth where a rse n Home output essentally benefts to Foregn stocks through the fall n the Home terms-of trade. The covarance between Home excess returns and the Home real exchange rate s postve and optmal portfolos are Home based. For a level of trade costs such that θ = θ, an ncrease n Home output s exactly offset by the response of the Home terms-of-trade (an extenson of Cole and Obstfeld [1991]): Home and Foregn equty returns are perfectly correlated and the equty portfolo s undetermned Calbraton Preferences Relatve rsk-averson γ = 2 Elastcty of substtuton φ = 5 Trade frctons Trade costs τ [0; 300%] Table 1: Parameter values of the benchmark model Calbraton of the parameters s presented n table 1. The coeffcent of relatve rsk averson s set at γ = 2 (lke n Backus, Kehoe and Kydland [1994]). The elastcty of substtuton between Home and Foregn goods s set to 5. Estmates of ths elastcty vary a lot across studes. Estmates from mcro (sectoral) trade data usually fnd much hgher elastctes, rangng from 4 to 15 (see Harrgan [1993], Hummels [2001] among others). Baer and Bergstrand [2001] reports an estmate of 6.4 usng aggregate trade flows between OECD countres. However, estmates from tme-seres macro data usually gve much lower elastctes, rangng from 1 to 3 (Backus, Kehoe and Kydland [1994]). Imbs and Mejean [2008] reconcle these two lteratures by pontng out an aggregaton bas and stands for elastctes of roughly 5 when they control for heterogenety. In lne wth Obstfeld and Rogoff [2000] and Imbs and Mejean [2008], we choose the lower bound of estmates from the trade lterature. However for values of ths elastcty larger than 1, qualtatve results reman unchanged. For the US, the openness to trade,.e the rato of (exports+mports) over GDP s 25% n 2005, whch corresponds to a steady-state mport share of 12.5%. 6 The model matches the observed steady-state mport share n the US wth an average trade cost of 63%. Anderson and Van Wncoop [2004] estmate nternatonal trade costs n the range of 40% to 70% so the calbraton used n the paper seems farly reasonable. Ths gves the equlbrum share of domestc equtes n the portfolo µ as a functon of τ shown n fgure 1. Portfolos exhbt a foregn bas for reasonable trade costs (trade costs smaller than 142%): at 6 In 2005, mports were hgher than exports but snce the model s approxmated around the symmetrc equlbrum where the trade balance s zero, we use Exp+Imp for the steady-state mport share. 2GDP 11

15 µ 1,5 1 0,5 0-0,5 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 1,1 1,2 1,3 1,4 1,5 1,6 1,7 1,8 1,9 2 2,1 2,2 2,3 2,4 2,5 2,6 2,7 2,8 2,9 3 τ Fgure 1: Holdngs of local stocks µ as a functon of trade costs τ. Benchmark Calbraton: γ = 2, φ = 5. the margn, an ncrease n trade costs τ reduces µ and ncreases the Foregn bas n portfolo. Ths s n sharp contradcton wth Obstfeld and Rogoff [2000]. Moreover, the effect s rather large: ncreasng trade costs from 50% to 100% (or equvalently decreasng the mport share by 10%) decreases the share of local equtes from 41.5% to 5.5%! For very hgh value of trade costs (trade costs hgher than 142%), the equty portfolo s based towards Home stocks. In ths case, though, the share of Home equtes s above unty and the model would actually delver too much Home bas. The reason s that for a level of trade costs such that θ s slghtly above θ, Home and Foregn stocks are almost perfect substtutes and the portfolo home bas s tremendously amplfed: the nvestor would short Foregn assets Robustness checks How realstc s the case θ > θ? For standard preferences (γ > 1 and φ > 1), 7 trade costs n goods markets wll lead to home bas n equtes f and only f θ > θ? (.e trade costs are suffcently hgh). Ths makes sense snce n the neghborhood of trade autarky, portfolos should be fully based towards local assets. We checked whether ths case can be emprcally realstc. Snce θ depends on the elastcty of substtuton between Home and Foregn goods and on the coeffcent of rsk-averson, we calculated θ for dfferent values of these parameters, the level of trade costs above whch nvestors would short foregn assets and the correspondng mport share (see table (4) n appendx 5.1). As shown n table (4), unless assumng a very hgh relatve rsk averson, a low elastcty of substtuton between Home and Foregn goods (and consequently ncredbly large trade costs), goods markets are not closed enough to generate some Home bas n equtes n ths model. And the bottom-lne s that the presence of trade costs n goods markets s certanly unable to delver realstc Home bas n equtes. 7 Hgher relatve rsk-averson γ than one seems farly uncontroversal. We wll dscuss the case of φ < 1. 12

16 The role of the elastcty of substtuton between home and foregn goods In the benchmark case, we consder an elastcty of substtuton between Home and Foregn goods φ larger than unty. Heathcote and Perr [2002] provdes short-run estmates of ths elastcty that are slghtly smaller than one. 8 One could thnk that such a hypothess would help us to generate Home bas n portfolos n ths model. When Home output ncreases, the fall n Home terms-of-trade s stronger snce consumers cannot substtute easly Home and Foregn goods and Home equty returns shrnk. In ths case, Home terms-of-trade and Home equty returns (relatve to Foregn) are postvely correlated. Agan, ths s a case of mmserzng growth: a good output shock s manly benefcal to the foregn country. In partcular, one can show that n the specfc case where φ = 1 γ < 1, the share of foregn assets s exactly equal to the mport share (case emphaszed by Kollmann [2006a]). However, even n ths case, at the margn, an ncrease n trade costs τ reduces the equty home bas and the consumpton home bas. Hgher trade costs rase mports n value snce the elastcty of demand wth respect to mports s very low and people wll hold more foregn stocks to stablze ther purchasng power on mports. Home consumers should tlt ther consumpton spendng towards Foregn goods and ther portfolo towards Foregn equtes n presence of trade costs! Then, gven that many emprcal works n nternatonal trade usually agree on larger elastctes of substtuton across goods and put forward trade costs as one of the man explanaton of the consumpton home bas, from now on, we stck on the more standard case where φ s above unty. 2.5 Related Lterature In Obstfeld and Rogoff [2000], portfolos are computed only when trade n equtes are able to reproduce the complete markets allocaton. Ths happens to be the case only f 9 γ = 1/φ. They assume φ > 1 n ther calbraton, whch mples γ < 1. In ths case, calculus smplfes tremendously and we get: µ = 1 (1 + θ) 2 When γ < 1, the substtuton effect domnates and nvestors prefer equtes that gve hgher returns when the prce of ther consumpton bundle s lower. The hedgng demand due to real exchange rate fluctuatons leads to Home bas n equtes and ths bas s ndeed ncreasng wth trade costs: µ τ = 1 θ 2 τ > 0 What we have shown s that the Home bas they replcate under ths specfc calbraton s far from beng general (especally, under more standard calbratons, one would expect γ > 1). For other parameter values, ther approxmate portfolos are actually far from the optmal ones computed n ths paper. 8 Corsett, Dedola and Leduc [2004] and Kollmann [2006a] also assume an elastcty smaller than 1. See also Tlle [2001] for some mplcatons of ths assumpton. 9 For other parameter values, two stocks are not enough to complete the market although, up to the frst-order, perod 1 Lagrange multplers are equalzed across countres. 13

17 Uppal [1994] descrbes equty portfolos n presence of trade costs n a one-good model. Ths corresponds to the case of φ close to nfnty (Home and Foregn goods are perfect substtutes). Snce the lmt of θ when φ approaches nfnty s 1, Home excess returns and the Home real exchange rate are negatvely related for any value of trade costs. Consequently, nvestors more rsk averse than log- have a foregn bas n equtes. More broadly, rasng the elastcty of substtuton ncreases the range of trade costs for whch the nvestor exhbts a foregn portfolo bas. Indeed for φ > 1 and γ > 1, we have: θ φ > 0 As goods become closer substtutes, a small decrease n Home prces ncreases a lot the demand for Home goods, whch dampens the response of Home terms-of-trade followng an ncrease n Home output. Ths ncreases the range of trade costs for whch Home terms-of-trade and Home excess returns move n opposte drecton. The benchmark model predcts a negatve covarance between Home equty excess returns and the Home real exchange rate when goods markets are not too closed. Ths, n turn, leads to Foregn bas n equtes. Van Wncoop and Warnock [2007] argue that ths covarance s very close to zero n the data for the US. Wth zero covarance, the hedgng term due to real exchange rate fluctuatons n the portfolo dsappears and nvestors should nether exhbt Foregn bas nor Home bas n equtes. However, n both cases (zero or negatve covarance), the man message of ths secton remans: one cannot explan the home bas n equtes wth trade costs alone. In the next secton, we look how our results are robust to the addton of non-tradable goods followng Obstfeld [2007]. Indeed, the addton of non-tradable goods can potentally change the response of the real exchange rate to output shocks as the real exchange rate depends both on the terms-of-trade and the relatve prce of non-tradable goods. 3 Addng non-tradable goods to the benchmark model Whle a large lterature focuses on the role of non-tradable goods to generate equty home bas (see Dellas and Stockmann [1989], Baxter Jermann and Kng [1998], Serrat [2001], 10 Obstfeld [2007], Matsumoto [2007], Collard, Dellas, Dba and Stockmann [2007]), most of ths lterature does not consder the nteracton between trade costs n the tradable sector and the presence of non-tradable goods (Obstfeld [2007] and Collard, Dellas, Dba and Stockmann [2007] are notable exceptons). Here, we want to nvestgate the robustness of our results to the addton of non-tradable goods. The framework s borrowed from Obstfeld [2007] but we depart from hs analyss (and from exstng lterature) by assumng a dfferent fnancal asset structure. We assume that agents trade shares n Home and Foregn mutual funds. Shares n Home (Foregn) mutual funds enttle nvestors to a share of aggregate Home (Foregn) output, but agents cannot trade separate clams on tradable and non tradable output n each country. Ths assump- 10 see also Kollmann [2006b] for a correcton of Serrat s results 14

18 ton can be justfed by the dffculty nvestors face when tryng to dstngush between the exposure of equty to traded and non-traded goods sectors. Ths dffculty s all the more relevant gven that, when allowng agents to trade separate clams on traded and non-traded output, optmal equty postons are very dfferent for the traded and the non-traded sector. 11 Ths dfferent structure of portfolos across traded and non-traded sectors seems nconsstent wth casual emprcsm as argued by Lews [1999] (see also Baxter, Jermann and Kng [1998] for a smlar crtcsm). 3.1 Set-up of the model wth non-tradable goods In a smlar two-perod (t = 0, 1) model wth two symmetrc economes, each country now produces two goods, a tradable (T ) and a non-tradable good (NT ). At date 0, agents trade Home and Foregn equtes, whch are clams to aggregate Home and Foregn output. Equty returns of country are a weghted share of returns n both sectors. At t = 1, country receves an exogenous endowment y T of the tradable good and an exogenous endowment y NT of the non-tradable good. We assume: E 0 (y T ) = y T and E 0 (y NT ) = y NT for = {H, F }. We wll assume that the stochastc propertes of the endowment shocks are symmetrc across countres. The country household has the same CRRA preferences over the aggregate consumpton ndex, but the aggregate consumpton ndex s now a bundle of tradable and non-tradable goods: C = [ η 1/ɛ ( c T ) (ɛ 1)/ɛ + (1 η) ( ) ] 1/ɛ c NT (ɛ 1)/ɛ ɛ/(ɛ 1) where c T s the consumpton of a composte tradable good usng Home and Foregn tradable goods and c NT s the consumpton of non-tradable goods. ɛ s the elastcty of substtuton between tradable and non-tradable goods. The tradable consumpton ndex for country = {H, F } s stll: c T = [ (c T (φ 1)/φ ) + ( ) ] c T (φ 1)/φ φ/(φ 1) j where c T j s country s consumpton of the tradable good from country j. The consumer prce ndex that corresponds to these preferences s (for = {H, F }): where P T [ P = η ( P T ) (1 ɛ) + (1 η) ( ) ] P NT 1 ɛ 1/(1 ɛ) s the prce ndex over tradable goods n country and P NT The tradable goods prce ndex s defned by (for = {H, F } and j ): P T = [ (p ) T 1 φ + ( ) ] (1 + τ)p T 1 φ 1/(1 φ) j s the prce of non-tradable goods. where p T s the prce of the tradable goods n country. Home terms-of-trade are denoted by q : q = p T H/p T F. 11 See e.g. Obstfeld (2007) and Collard, Dellas, Dba and Stockmann [2007]. See secton for a summary of ther results. 15

19 Resource constrants for tradable and non-tradable goods n country = {H; F } are gven by: c T + (1 + τ)c T j = y T (28) c NT = y NT (29) There s trade n stocks n perod 0. In each country, a stock gves nvestors a clam on the aggregate output of the country at market value (where aggregate output at market value of country s the sum of sales n the traded and non-traded sector, p T y T + P NT local stock and faces the followng budget constrant, at t = 0: y NT ). The country household fully owns the p s µ + p s µ j = p s, wth j where µ j s the number of shares of stock of country j held by country at the end of perod 0. p s s the share prce of the stock, dentcal across countres due to symmetry. Market clearng n asset markets for the two stocks requres (supply of stocks normalzed to unty) : µ HH + µ F H = µ F F + µ HF = 1 Symmetry of preferences and shock dstrbutons mples that equlbrum portfolos are symmetrc: µ HH = µ F F. As n the benchmark model, we denote a country s holdngs of local stock by µ (µ > 1 2 means that there s equty home bas). 3.2 Equlbrum condtons In perod 1, a representatve consumer n country maxmzes C1 γ 1 γ j ): P C = p T c T + (1 + τ)p T j c T j + P NT c NT µ (p T y T + P NT y NT subject to a budget constrant (for ) + µ j (p T j y T j + P NT j y NT j ) (λ,1 ) (30) wth λ,1 the Lagrange-Multpler of the perod 1 budget constrant. The frst-order condtons are: For aggregate consumpton: Intratemporal allocaton across goods: c T c T = ( ) p T φ c T P T c T j = 1 = λ,1 P C γ (31) ( ) P T ɛ = η C c NT = (1 η) P Usng budget constrant (30) and the symmetry of portfolos, we get: ( (1 + τ)p T ) φ j c T P T (32) ) ɛ C (33) ( P NT P P H C H P F C F = (2µ 1) (p T Hy T H + P NT H y NT H p T F y T F P NT F y NT F ) (34) whch mples that the dfference between countres consumpton spendng equals the dfference between ther fnancal ncomes. 16

20 As n the benchmark model, we can express the Euler equatons n relatve terms (Home relatve to Foregn) as follows: where R = pt yt NT +P y NT p s E 0 [( C γ H P H C γ F )(R H R F )] = 0 (35) P F denotes the return on stock = {H; F }. Note that snce nvestors cannot buy separate clams on the tradable and the non-tradable frms, equty returns n country depend on the aggregate dvdend of the country [p T y T + P NT y NT ]. 3.3 Soluton method and equlbrum portfolos As n the benchmark model, followng Tlle and Van Wncoop [2007] and Devereux and Sutherland [2007], one needs to solve for equlbrum equty portfolos µ usng the frst-order approxmaton of non-portfolo equatons and second-order approxmaton of the Euler equatons. We do not detal the resoluton and the approxmaton of the model (steps are smlar to the benchmark model) and just present some key equatons (see Obstfeld [2007] for smlar dervatons) Frst-order approxmaton of the non-portfolo equatons The log-lnearzaton of the Home country s real exchange rate RER P H P F gves: where P NT = P NT H /P NT F RER = P H = ηθ q + (1 η) P P NT. (36) F s the relatve prce of Home non-tradable goods over Foregn non-tradable goods and η s the steady-state share of spendng devoted to tradable goods. 12 tradable composte n both countres satsfes: P T H /P T F The relatve prce of the = θ q. Importantly, the real exchange rate now depends postvely on the Home terms-of-trade q as well as on the relatve prce of Home non-tradable goods P NT = P NT H /P NT F. Intratemporal allocaton across goods (32) and (33) together wth market-clearng condtons for tradable and non-tradable goods (28) and (29) mply the followng equlbrum condtons n both sectors (see Obstfeld [2007]): ŷ T = [(1 φ) (1 θ 2 ) + θ 2 (1 η)(1 ɛ) 1] q θ(1 η)(1 ɛ) P NT + θ P C (37) where P C = ŷ NT = (η(1 ɛ) 1) P NT θη(1 ɛ) q + P C (38) P H C H P F C F denotes relatve consumpton expendtures and ŷk = ŷk H ŷk F denotes relatve output n sector k = {T, NT }. We fnally log-lnearze equaton (34) and obtan: P C = P H C H P F C F = (2µ 1) R (39) 12 To smplfy notatons, we assume here that the share of spendng devoted to tradable goods s the same as the weght of tradable goods n the consumpton ndex. Ths s true only f n the steady state tradable and non tradable goods have the same prce: p T = p NT. Ths assumpton s however rrelevant for equty portfolos (see Obstfeld [2007]). 17

21 where R = R H R F denotes Home aggregate excess returns and s a weghted sum of relatve returns n the tradable and non-tradable sector: R = η( q + ŷ T ) + (1 η)( P NT + ŷnt ). It s convenent to rewrte the non-portfolo equatons (37) and (38) n matrx form as follows: where ŷ = ( ŷṱ y NT ), p = ( q P NT ŷ = M p + ( ) θ P C (40) 1 ) and M = (1 φ) (1 θ2 ) + θ 2 (1 η)(1 ɛ) 1 θ(1 η)(ɛ 1) θη(ɛ 1) η(1 ɛ) Second-order approxmaton of the Euler equatons As n the benchmark case, the second order approxmaton of (35) gves: cov( P C, R) = (1 1/γ)cov( RER, R) (41) A bt of rewrtng and usng (39) yelds: (2µ 1)var( R) = (1 1/γ)cov( RER, R) (42) As n the benchmark model, the Home nvestor wll demand a larger quantty of stocks that covary postvely wth the Home real exchange rate. The equty home bas then depends on the covarancevarance rato cov( RER, R)/var( R) (see also van Wncoop and Warnock [2007]) Analytcal expressons for equty portfolos One needs to solve for equlbrum equty portfolo µ usng the frst-order approxmaton of non portfolo equatons (equatons (37),(38),(39)) and the second-order approxmaton of the Euler equaton (equaton (41)). We have four endogenous varables (the two relatve prces q and P NT, relatve consumpton expendtures P C and the portfolo poston µ) and four equatons (3 non-portfolo equatons and 1 portfolo equaton). 13 As n Devereux and Sutherland [2007], t s convenent to rewrte Home excess returns and the Home real exchange rate n matrx form. Usng (39) and (40), we express aggregate Home excess returns R as a functon of the vector of fundamental shocks ŷ: R = ( η 1 η ) ( p + ŷ) R = R 1 ŷ + R 2 (2µ 1) R ( wth R 1 = η 1 η R = [1 R 2 (2µ 1)] 1 R 1 ŷ (43) ) ( ) ( ) I + M 1 and R 2 = η 1 η M 1( θ 1) (I denotes the 2 2 dentty matrx; note that R 1 s a 1 2 vector whle R 2 s a scalar) Note that equlbrum (relatve) equty returns are also unknown but solvng for relatve prces solve smultaneously for (relatve) equty returns snce endowments are exogenous. 14 Note that for the values of ɛ consdered n the calbratons (ɛ < 1), det(m) > 0 so the matrx M s nvertble. 18

22 Smlarly, one can rewrte the real exchange rate usng (36), (39), (40) and (43): ( wth P 1 = ηθ RER = ( ηθ 1 η ) p RER = P 1 ŷ + P 2 (2µ 1) R RER = [1 R 2 (2µ 1)] 1 [P 1 + (2µ 1) (P 2 R 1 P 1 R 2 )] ŷ (44) ) ( ) 1 η M 1 and P 2 = ηθ 1 η M 1( ) θ 1 From the expressons of Home excess returns (equaton (43)) and the Home real exchange rate (equaton (44)), one can deduce the followng portfolo equaton by substtutng var( R) and cov( RER, R) n the second order approxmaton of the Euler equaton (equaton (41)): (2µ 1) var (R 1 ŷ) = (1 1/γ) cov((p 1 + (2µ 1) (P 2 R 1 P 1 R 2 )) ŷ, R 1 ŷ) The (zero-order) equlbrum portfolo s a fxed-pont of the prevous equaton (Tlle and van Wncoop [2007]). As both sdes of the prevous equaton are lnear n µ, we get the followng analytcal expresson for the local equty holdngs as a functon of exogenous parameters: µ = 1 2 [ ] (1 1/γ) cov(p 1 ŷ, R 1 ŷ) 1 + var (R 1 ŷ) (1 (1 1/γ) P 2 ) + (1 1/γ) R 2 cov(p 1 ŷ, R 1 ŷ) (45) As n the benchmark model, the equlbrum portfolo s the sum of the market portfolo (1/2) held by the log-nvestor and a bas due to fluctuatons n the real exchange rate. Note that unlke Obstfeld [2007], the optmal portfolo s not ndependent of the stochastc propertes of the endowment shocks. In fact, nvestors cannot span perfectly the uncertanty (even up to a frst-order approxmaton) as the dmenson of the uncertanty s strctly hgher than the number of assets avalable (two endowment shocks n each country and only one stock). The key dfference wth our benchmark model s that the sgn of the covarance between the real exchange rate and Home equty excess returns depends on the response of the terms-of-trade and the relatve prce of non-tradable goods to endowment shocks n both sectors and as shown below ths covarance can be ether postve or negatve, dependng on parameter values. 3.4 Descrpton of equlbrum equty portfolos Calbraton Values for the parameters are shown n table 2. We keep the same elastcty of substtuton φ and the same rsk averson γ as n the benchmark model. Accordng to the Bureau of Economc Analyss (BEA), the average share of servces n total consumpton expendtures s 55% over the perod Assumng that most servces are non-tradable, we set the share of tradable goods n consumpton 15 to η = 45%. A key parameter s the elastcty of substtuton between tradable and non tradable goods ɛ. The exstng lterature focuses on low values for ɛ, rangng from 0 to 1 for ndustralzed countres (see 15 Stockman and Tesar [1995] provde slghtly hgher values for the share of tradable consumpton (from 45% to 55%). Note however that our results do not depend qualtatvely on η for a wde range of values. 19

23 Preferences Relatve rsk-averson γ = 2 Elastcty of substtuton between tradables φ = 5 Elastcty of substtuton between tradables and non-tradables ɛ = {0.25; 0.5; 0.75} Share of tradable goods n consumpton expendtures η = 0.45 Trade frctons Trade costs τ [0; 300%] Volatlty and correlaton of shocks Volatlty rato σ NT /σ T = {0.5; 1} Corr(ŷT, ŷnt ) ρ = 0.3 Table 2: Parameter values n the model wth non-tradable goods Van Wncoop [1999] and Matsumoto [2007] for a detaled dscusson). 16 Consequently, we provde some senstvty analyss of our results usng values for ɛ between 0 and 1. Whle the stochastc propertes of the shocks played no role for equlbrum portfolos n our benchmark model, they do matter n ths case. Usng US quarterly data from 1985 to 2005 from the BEA, we fnd that the volatlty of (annualzed) growth rates n the servce sector (our proxy for the non-tradable goods sector) s slghtly more than half of the volatlty of growth rates of fnal goods sales (our proxy for the tradable sector). 17 Stockman and Tesar [1995] provde estmates for G7 countres of the volatlty of output n both sectors: the rato between the volatlty of non-traded output and traded output s between 0.5 and 1 for all countres and the average s 0.6 (see also Van Wncoop [1999] and Serrat [2001] for smlar estmates). The key parameter for portfolos s the rato between the volatlty of relatve non-traded output ŷnt = ŷnt H ŷnt F and the volatlty of relatve traded output ŷt = ŷt H ŷt F. We denote ths rato by σ NT /σ T. Assumng that cross-country correlatons of traded and non-traded output are smlar n both sectors, we use 0.5 as a benchmark value for σ NT /σ T and provde some robustness checks when the volatlty s the same n both sectors: σ NT /σ T = The correlaton of output shocks wthn a country (correlaton between output shocks n the tradable and non-tradable sector) also affects the equlbrum portfolo. Usng the same BEA data, we fnd ths correlaton to be postve but qute low (equal to 0.3). We thus set the correlaton of shocks across sectors (wthn a country) equal to Some representatve estmates for ɛ used n the exstng lterature are: 0.19 (Pesent and Van Wncoop [2002]), 0.44 (Stockman and Tesar [1995]), 0.74 (Mendoza [1995] and Corsett, Dedola and Leduc (2004), from 0.6 to 0.8 (Serrat [2001]). Ostry and Renhart [1992] provdes estmates for developng countres n the range of 0.6 to Values for the two volatltes are 1.2% and 2.3%, respectvely. 18 Ths rato depends on the volatlty of shocks n each country but also on ther cross-country correlaton n each sector. Stockman and Tesar [1995] provde estmates of the cross-country correlaton of traded and non-traded output that are smlar n both sectors. If the cross-country correlaton s the same n both sectors, then σ NT /σ T s smply the rato of the volatlty of output shocks n a gven country and emprcal evdence shows that ths rato s between 0.5 and Stockman and Tesar [1995] estmates the correlaton between nnovatons n the non-tradable sector and nnovatons n the tradable sector to be equal to Our results are robust to a hgher correlaton. 20