Net Foreign Assets and Imperfect Pass-through: The Consumption Real Exchange Rate Anomaly

Board of Governors of the Federal Reserve System International Finance Discussion Papers Number 764 May 2003 Net Foreign Assets and Imperfect Pass-through: The Consumption Real Exchange Rate Anomaly Jorge D. Selaive and Vicente Tuesta NOTE: International Finance Discussion Papers are preliminary materials circulated to stimulate discussion and critical comment. References in publications to International Finance Discussion Papers (other than an acknowledgment that the writer has had access to unpublished material) should be cleared with the author or authors. Recent IFDPs are available on the Web at www.federalreserve.gov/pubs/ifdp/.

Net Foreign Assets and Imperfect Pass-through: The Consumption Real Exchange Rate Anomaly* ✝ & Jorge D. Selaive Vicente Tuesta New York University New York University May 2003 (First draft: January 2002) Abstract: An unresolved issue in international macroeconomics is the apparent lack of risk-sharing across countries, which contradicts the prediction of models based on the assumption of complete markets. We assess the importance of financial frictions in this issue by constructing an incomplete market model with stationary net foreign assets (NFA) and imperfect pass-through (IPT). In this paper, there is a cost of bond holdings that allows us to incorporate the dynamics of NFA into the risk-sharing condition. On theoretical grounds, our results suggest that the dynamics of NFA may account for the lack of risk-sharing across countries. In addition, the IPT mechanism, by closing the current account channel, does not help to explain this feature of the data. On empirical grounds, we test the risk-sharing condition derived in the paper, and we find that growth factors of consumption and real exchange rates behave in a manner that may be consistent with a significant role for the net foreign asset position. Keywords: Net Foreign Assets, Imperfect Pass-through, Incomplete Markets, Uncovered Interest Rate Parity JEL Classification Numbers: F31, F32, F41 * We are especially grateful to Pierpaolo Benigno for his guidance. We would also like to thank David Backus, Giancarlo Corsetti, Jon Faust, Joseph Gagnon, Mark Gertler, Dale Henderson, Fabrizio Perri, John H. Rogers, Jonathan Wright and seminar participants at NYU and the Federal Reserve Board for their comments and useful suggestions. The views in this paper are solely the responsibility of the authors and should not be interpreted as reflecting the views of the Board of Governors of the Federal Reserve System or of any other person associated with the Federal Reserve System. ✝ Correspondence to Jorge D. Selaive, e-mail: js899@nyu.edu. & Correspondence to Vicente Tuesta, e-mail: vt246@nyu.edu.

1 Introduction Chari, Kehoe and McGrattan (2001), hereafter CKM, find that the main discrepancy between complete markets sticky price models and the data is that models predict a high cross-correlation between the real exchangerateandrelativeconsumptionsacrosscountries. However,inthedatathereisnotaclearpattern. They refer to this discrepancy as the consumption-real exchange rate anomaly.1 In order to break the tight link between the real exchange and relative consumptions, CKM restricted the set of assets that can be traded across the countries. In their setup, uncontingent nominal bonds denominated in home currency are traded, so asset markets are incomplete. Although this channel was theoretically promising in addressing the anomaly, it failed to explain it.2 One of the limitations of their approach is that the uncovered interest parity (UIP) holds. The UIP relation postulates that the interest rate differential between two countries should equal the expected exchange rate change. However, there is vast empirical evidence suggesting that UIP does not hold (see Chinn and Meredith (2002) for a recent reference). Moreover, recent evidence presented by Lane and Milesi-Ferretti (2001b) assigns a significant role to the net foreign asset position (hereafter, NFA) in determiningtherealinterestratedifferential3. Finally,theassetsmarketstructurewhereasinglerisk-free uncontingent nominal bond is traded has been tested and partially rejected by Obstfeld (1989), Ravn (2001) and Head, Mattina and Smith (2002). During the last few years, New Open EconomyMacroeconomics models (NOEM) havegained appeal among designers of business cyclemodels and policymakers. One of themain advantages ofthese models is that they allow the analysis of positive implications and normative policy prescriptions under the rigor of an explicit microfunded model (Lane (2001) provides a survey of this literature). In general, these modelshaveassumedcompleteassetsmarket4. However,modelsunderthisassetmarketstructurecannot explain the consumption-real exchange rate anomaly since the real exchange rate evolves according to the ratioofmarginalutilitiesofconsumption, andalargepositivecross-correlationbetweentherealexchange rate and relative consumption is predicted5. Another feature of these models is that they have considered the implications of two polar cases of pricing assumptions under nominal rigidities6: Producer Currency Pricing, where there is perfect passthrough(PPT),andPrice-to-Market wherethepass-throughiszerointheshort-run. ProducerCurrency Pricingbringsaboutastrongexpenditure-switchingeffect thatredirectsworlddemandinfavorofdomestic 1BackusandSmith(1993)hadreportedthisanomalyinaIRBCmodelwithnon-tradedgoods. 2ObstfeldandRogoff(2000)listthis“disconnect”amongthecentralunresolvedpuzzlesininternationalmacroeconomics. 3MonetaryshocksmayalsoaccountforlargedeviationsintheUIP. SeeKimandRoubini(2000)andFaustandRogers (2003). 4Corsetti and Pesenti (2002), in a stochastic environment, introduce incomplete markets, although they shut down the currentaccountchannelbyassumingunitaryintratemporalelasticityofsubstitutionbetweenhomeandforeigngoods. 5Thisconclusionis limitedtothe case wherethere arenopreferenceshocks. Wedonot relyontheseshocks toexplain theanomaly. 6EmpiricalevidenceassembledbyEngelandRogers(1996),Engel(1993)andGoldbergandKnetter(1997),amongothers, showsthattherearelargedeviationsfromthelawofonepricefortradedgoods. Ontheotherhand,departuresfromPPP are also an empirical regularity already documented by many other authors. It is important to clarify that the law of one pricemayholdevenwhenPPPdoesnot. 1

tradable goods after a nominal depreciation of the exchange rate which ends up splitting outputs and commoving consumptions. On the other hand, under Price-to-Market, prices are set in the currency of the final consumer, and the expenditure-switching effect is eliminated. The previous two extreme pricesetting assumptions have been rejected at the empirical level7, and it seems to be appealing to consider intermediate degrees of pass-through. The aim of this paper is to evaluate how a stochastic new open macro model with incomplete and imperfectfinancialmarkets,alongwithimperfectpass-through,helpstosolvetheconsumption-real exchange rate anomaly. We also check the robustness of our results by testing econometrically the risk-sharing condition derived in the paper. To set up our model we follow previous contributions by Kollmann (2002), P. Benigno (2001) and Schmitt-Grohe and Uribe (2001). Two risk-free one period nominal uncontingent bonds are traded, and a cost of undertaking positions in the international financial markets allows us to characterize imperfect financialmarkets. Underourassetmarketstructure,theNFAbreaksthetightlinkbetweenrealexchange rate and marginal utilities that characterizes models with complete markets. This result arises because in our model the uncovered interest parity does not hold, and importantly, it is affected by the net foreign asset position due to the presence of a cost of bond holdings. We also need to choose the channel of real exchange rate fluctuations. There are two approaches: deviationsfromthelawofonepricefortradedgoodsacrosscountries,orfluctuationsintherelativeprices ofnon-tradedtotradedgoods. Inourpaper,wecombinebothbyintroducingnon-tradablegoodsintothe economy, and distribution costs in order to generate deviations from the law of one price in the tradable sector8. Non-traded goods areappealing in anincompletemarket setup becausetheyallowan assessment of the impact on transfers from their relative prices. Recently, Lane and Milesi-Ferretti (2001a) argue that a model with only tradable goods may neglect the potential impact on transfers from the relative price of non-traded goods. Hence, the wealth effect stemming from the level of net foreign assets on the labor supply of non-tradable goods may be better captured in a heterogenous sector model. On the other hand, we follow Bunstein, Neves and Rebelo (2000) and Corsetti and Dedola (2002) in order to get deviations from the law of one price so we allow for partial degrees of pass-through in a dynamic sticky prices environment.9 In the model, the UIP does not hold because of the presence of a cost of undertaking positions in the international asset market that interacts with theincompleteasset market structure. Deviations from the UIP will allow us to give an explicit role to the NFA in the risk-sharing condition, breaking the monotonic positive relation between the real exchange rate and relative consumptions. 7See Campa and Goldberg (2002) for an extensive analysis of the determinants of the pass-through across the OECD countries. 8Betts and Kehoe (2001) investigate the relationshipbetweena measure of relative price of non-traded goodsto traded goods across countries and the real exchange rate in a sample of 52 countries. They find that 1/3 of the real exchange varianceisexplainedbyfluctuationsintherelativepriceofnontradedgoods. StockmanandTesar(1995)presentmodelsin whichtherealexchangerateisexactlytherelativepriceofnontradedtotradedgoodsacrosscountries. BackusandSmith (1993)alsoconcludethatnon-tradedgoodsmayaccountformanyfeaturesofinternationalmacroeconomicsdata. 9Thelatterauthorsdevelopatwo-periodmodelwheredistributioncostsincurredinthedeliveryoftradablegoodsgenerate agapbetweentheconsumerandtheproducerpriceofimportgoods. 2

Ourresultssuggest that incompleteassetmarkets, inwhichthenetforeignasset positionentersinthe risk-sharing condition, help to address the consumption-real exchange rate anomaly. The model predicts a zero or even negative cross-correlation between the real exchange rate and relative consumptions as it is observed in the data. When a country accumulates assets, there is a wealth effect that reduces the labor supply in the non-tradable sector, which affects the relative price of non-traded goods, and disconnects the real exchange rate and relative consumptions. After considering intermediate degrees of pass-through the anomaly turns out to be more severe since the current account channel is dampened, and therefore, the wealth effects are diminished. The sensitivity analysis shows that the larger the intratemporal elasticity of substitution between foreign and home traded goods the better the model does in explaining the anomaly. The previous result stems from the fact that the NFA position becomes more responsive to changes in the terms of trade as this elasticity gets higher. Another interesting result is that the larger the international financial friction the stronger is the wealth effect associated with the incomplete market structure. Thus, the NFA becomes more important in explaining the anomaly. We also investigate two variations of the benchmark model, and doing so we check the robustness of our results. The first variation introduces perfect mobility of labor across sector. The second variation is a flexible-price version of the model. Our previous results hold under these two extensions. In our model, a negative comovement between the real exchange rate and relative consumptions is predicted after a productivity shock in the tradable sector. Following the shock, there is a worsening of the terms of trade that generates an increase in domestic output above domestic consumption. The assetaccumulationtriggersarealexchangerateappreciationwhichisconsistentwiththeHarrod-Balassa- Samuelsoneffect(HBS).Thewealtheffectgeneratesadecreaseinthelaborsupplyinthenontradedsector thatincreasestherelativepricesofnontradedgoods,andconsequently,appreciatestherealexchangerate. When we introduce IPT, the NFA accumulation is smaller due to the dampening of the expenditureswitching effect. Motivated by the results of the calibrated model, we use the generalized method of moments (GMM) to test the risk-sharing condition derived in the paper. Our estimations suggest that growth factors of consumption and real exchange rates may behave in a manner which is consistent with a significant role for the NFA. Therefore, it seems reasonable to consider a theory where the NFA position affects the risk-sharing across countries. Our paper is organized as follows. In Section 2 we introduce the model and illustrate briefly the equations in log-linear form. In Section 3 we analyze the quantitative properties of the model and we also performasensitivityanalysis.In Section4wetest empiricallytherisk-sharingconditionderived insection 2. Finally, section 5 concludes. 3

2 The Model In this section, we introduce a dynamic two-country new open macro model. We extend the model to allowfor tradableand non-tradable goods, incomplete financial integration andimperfect pass-through in a stochastic environment. 2.1 Preferences Population in the home country belongs to the interval [0,n], while in the foreign economy it is in the segment (n,1]. Similarly, tradable and non-tradable firms at home produce goods on the interval [0,n] andareindexedbyh. Foreignfirmsdosoontheinterval(n,1]andareindexedbyf. Ch denotesthelevel t of consumption in period t for individual h, M t h his real balances holdings and Nh Nh denotes agent Pt T,t NT,t hs labor supply in the tradable and non-tradable sector, respectively. The preferences of a household h 0 in the country H are assumed to be10 Uh =E ∞ βs t U(Ch )+L M t h +s V Nh ,Nh , (1) t t ( s=t − · t+s µ P t+s ¶ − T,t+s NT,t+s ¸) X ¡ ¢ Labor is the only input in this economy, and V(.) is increasing, convex and separable in both labors11 (Nh,Nh ). L(.) is increasing and concave in real balances. T, NT We define the consumption index as ε ε 1 ε 1 ε 1 Ch γ1/ε Ch −ε +(1 γ)1/ε Ch −ε − , (2) t ≡ T,t − NT,t · ¸ ¡ ¢ ¡ ¢ whereεiselasticityofsubstitutionbetweentradableandnon-tradablegoods,andγ istheshareoftradable goods in the consumption basket. C is the sub-index of consumption for traded goods defined as T θ C T h ,t ≡ nθ 1 C H h ,t θ −θ 1 +(1 − n)θ 1 C F h ,t θ −θ 1 θ − 1 , (3) · ¸ ¡ ¢ ¡ ¢ where θ is elasticity of substitution between home and foreign tradable goods. Cj and Cj are indexes of H F consumption across the continuum of differentiated goods produced in country H and F, and are given by σ σ C H h ,t ≡"µ n 1 ¶ σ 1 Z0 n ch t (h) σ −σ 1 dh # σ − 1 ,C F h ,t ≡"µ 1 − 1 n ¶ σ 1 Zn 1 ch t (f) σ −σ 1 df # σ − 1 , (4) where σ > 1 is the elasticity of substitution across goods produced within a country. Similarly, the consumption of non-traded goods in the home country is given by σ C N h T,t ≡ n 1 σ 1 n ch NT,t (h) σ −σ 1 dh σ − 1 , (5) "µ ¶ Z0 # 10Note that utility is separable in consumption, real money holdings and labour effort. β is the intertemporal discount factor(0<β<1). 11Thisassumptionimpliesinmobilityoflaborsacrosssectors. Inoursensitivityanalysiswerelaxthisassumptionallowing forperfectlabormobilityacrosssectors. 4

In this context, the general price index that corresponds to the previous specification is given by 1 P t γ(P T,t )1 − ε+(1 γ)(P NT,t )1 − ε 1 − ε , (6) ≡ − h i where the price index for tradable goods has the following form 1 P T,t n(P H,t )1 − θ+(1 n)(P F,t )1 − θ 1 − θ , (7) ≡ − h i with prices of home and foreign tradable goods, and non-tradable goods defined, respectively as P 1 n p (h)1 σdh 1 − 1 σ , P 1 1 p (f)1 σdf 1 − 1 σ , (8) H,t ≡ n t − F,t ≡ 1 n t − ·µ ¶Z0 ¸ ·µ − ¶Zn ¸ 1 n 1 1 σ P p (h)1 σdh − , (9) NT,t ≡ n NT,t − ·µ ¶Z0 ¸ where p (i) and p (i) are prices of good i sold in the home country, in home currency and at consumer t NT,t level, for both tradable and nontradable goods, respectively. Afeatureofourspecificationisthepresenceofdistributioncostswhichimplyawedgebetweenproducer and consumer prices. This follows closely Burnstein, Neves and Rebelo (2000) and Corsetti and Dedola (2002). With competitive firms in the distribution sector, the consumer price of good h will be given by p (h)=p (h)+κP (10) t t NT,t wherep (h)denotethepriceofhomegoodsatproducerlevelandκaretheunitsofabasketofdifferentiated t non-tradedgoodsnecessarytobringoneunitoftradedgoodstotheconsumers12. Fortherestofthepaper, upper bar represents prices at producer level. 2.2 Asset Market Structure In this section, we first introduce the complete asset market structure that has been the workhorse of most NOEM literature after Obstfeld and Rogoff (1995). Then, we briefly present the incomplete asset marketsstructurethatCKMtreatedintheirwork-alsoknownasbond economy. Finally,wecharacterize an incomplete and imperfect financial assets market structure where the net foreign assets position plays adifferentroleinthedynamicoftherealexchangerate, andentersexplicitlyintherisk-sharingequation. 2.2.1 Complete Markets Wedefinetherealexchangerateasq t ≡ St P P t t∗. Underbothdomesticandinternationalcompletemarkets13, it follows that the ratio of marginal utilities of the two countries equalizes the real exchange rate at every σ 12Here,κ= 0 1κ(h) σ −σ 1 dh σ − 1 isaDixit-Stiglitzindexthatalsoappliestotheconsumptionofdifferentiatednon-traded goods. Forsimhp R licity,weareaissumingthattherearenodistributioncostsinthedeliveryofnon-tradablegoods. 13Theconsumersinbotheconomiescantradecontingentone-periodnominalbondsdenominatedinhomecurrency. 5

state of the nature (see CKM for details). U (C ) q =k c t (11) t oU (C ) c t∗ where k is a function of predetermined variables. o From (11), we can see that the relative consumption across countries is proportional to real exchange rate14. In our model, the presence of non-traded goods precludes full risk-sharing across countries, even if the law of one price holds. This equilibrium condition predicts a positive and high cross-correlation between the real exchange rate and the relative consumptions. We will build our model under the realistic assumption of imperfect degree of pass-through from exchange rate to import prices. The introduction of IPT in a complete asset market structure allows to capture a key aspect of the transmission mechanism of shocks across countries. However, it fails to break the link between real exchange rate and relative consumption which tends to be very low in the data (see Table A.2.). Therefore, in order to factor the relevance of IPT, we need to incorporate an incomplete asset market structure. 2.2.2 Incomplete Markets The standard approach: Bond Economy. An alternative incomplete assets market structure may be based on the possibility of househols to trade an uncontingent nominal bond denominated in units of home currency. Under this structure the risk-sharing condition reads as follows (see CKM for further details). U (C ) P U (C ) S P E c t+1 t =E c t∗+1 t t∗ (12) t U (C ) P t U (C ) S P µ c t t+1¶ µ c t∗ t+1 t∗+1¶ Fromtheaboveexpressiontherelationbetweentherealexchangerateandmarginalutilitiesonlyholds inexpectedfirstdifferences15. Astationarityproblemcouldariseunderthismarketstructure,whichwould prevent a proper analysis of small deviations around a deterministic steady state. In particular, without further modification, such incomplete markets structrure implies a non-stationary distribution of wealth across countries. Lucas and Stokey (1984) propose an endogenous discount factor that increases the marginal“impatience”astheeconomyaccumulatesnetforeignassetssothedistributionofwealthevolves along a stationary path16. On the other hand, Cavallo and Ghironi (2002) and Ghironi (2000) achieve stationary by an overlapping generation model that ensures an endogenously well-defined steady-state17. 14UnderPPP,thisconditionimpliesperfectrisk-sharingofconsumptionacrosscountries. Thisisnotthecasewhenthere areshockstopreferences. SeeP.Benigno(2001). 15Inlog-linearform,thisexpressionreadsas Et(qt+1 − qt)=Et Uc(C t∗+1 ) − Uc(Ct+1) − Uc(C t∗) − Uc(Ct) h³ ´ ³ ´i 16Theoretically, Mendoza (19b91) devbelops an sm b all open eco b nomy model, i b ncomplete b market economy and a endogenous discountfactor. Head,MattinaandSmith(2002)evaluateempiricallythismarketstructure,andrejectitsincekeyparameters oftheutilityfunctionareinsignificantandinconsistentwiththetheory. 17Under a different approach, Corsetti and Pesenti (2001) shut down the current account transmission mechanism by assumingaunitaryintratemporalelasticityofsubstitutionbetweenhomeandforeigngoods. 6

As equation (12) illustrates, incomplete asset markets-bond economy- allows us to break the link between real exchange rate and relative consumptions. However, as CKM pointed out, this asset market structure does not help to resolve the anomaly. They find that the wealth effects in their model are extremely small.18 One of the limitations of this approach is that the uncovered interest parity holds, a result that has been extensively rejected in empirical studies (see Chinn and Meredith (2002) for a recent reference). In particular, there is no role for the net asset position in determining real interest rate differentials. Lane and Milesi-Ferretti (2001b) reveal the importance of this channel. Furthermore,Ravn(2001)andHead,MattinaandSmith(2002)haveshownthatthismarketstructure is not supported by the empirical evidence under many different assumptions on preferences. They show that, under exogenous incomplete asset markets, the real exchange rate does not play a significant role in explaining the risk sharing across countries. Therefore, a bond economy seems to fail on both empirical and theoretical grounds. Incomplete and Imperfect Asset Markets. In order to break the monotonic relationship between the real exchange rate and relative consumptions we generate deviations from the UIP. We assume that thesedeviationsstemfromacostofholdingforeignbondsthatallowsustointroducethenetforeignasset position dynamics into the UIP. In this context, we have chosen to model incomplete markets following P. Benigno (2001) where two risk-free one-period nominal bonds are traded, and a cost of bond holdings is introduced to achieve stationarity19. One bond is denominated in domestic currency and the other one in foreign currency. Then, the real budget constraint of the domestic household h will be given by B H h ,t + S t B F h ,t B H h ,t − 1 +S t B F h ,t − 1 +M t h − 1 M t h P t (1+i t ) P (1+i )φ StBF,t ≤ P t − P t t ∗t Pt ³ ´ WhNh+Wh Nh TRh Πh + T T NT NT Ch+ t + t (13) P − t P P t t t where Wh and Wh are the nominal wages in the tradable and nontradable sectors, respectively. Πh are T NT t nominalprofitsforhomeconsumer. Weassumethateachconsumerholdsonefirmineachsector(domestic firms are located in theinterval [0,n] and thesizeof the home population is normalized to n) and thereis no trade in firms’ shares. TRh is a nominal transfer that individual j receives from the government. B t H,t is household h’s holding of the risk free nominal bond, in Home currency. B is household h’s holding F,t of the risk-free nominal bond in Foreign currency. The function φ(.) depends on the real holdings of the foreign assets in the entire economy, and therefore is taken as given by the domestic household20. φ(.) 18Corsetti et. al (2002) consider a different incomplete asset market structure where an endogenous discount factor is neededtopindownawelldefinedsteadystate. 19Schmitt-Grohe and Uribe (2001) and Kollmann (2002) develop small open-economy models introducing the same cost toachievestationarity. HeathcoteandPerri(2001)alsomakeasimilarassumptioninatwo-countryRBCmodel. 20As Benigno, P.(2001) points it out, some restrictions on φ(.) are necessary: φ(0) = 1; assumes the value 1 only if BF,t=0;differentiable;anddecreasingintheneighborhoodofzero. 7

will allow us to obtain a well-defined steady state, and to capture the costs of undertaking positions in the international asset market21. The government has a budget given by n n n Mhdh Mh dh+ TRhdh=0 Z0 t − Z0 t − 1 Z0 t Thefirstorderconditionswithrespecttothelaborsupplyfortradableandnontradablesectorsimply22 Wh V Nh = U (C ) T,t (14) N T,t c t P t ¡ ¢ Wh V Nh = U (C ) NT,t (15) N NT,t c t P t ¡ ¢ The first order condition with respect to real money holdings implies Mh i L t =U (C ) t (16) P c t 1+i µ t ¶ t Inthismodelwedescribethemonetarypolicythroughaninterestratefeedbackrule,therefore,equation (16) determines the optimal holdings of real money balances. We further assume that the initial level of wealth is the same across all households belonging to the same country. This assumption combined with the fact that all households within a country work for all firms sharing the profits in equal proportion, implies that within a country all the households face the same budget constraint. In their consumption decisions, they will choose the same path of consumption. We can then drop the index h and consider a representative household for each country. The conditions characterizing the allocations of domestic and foreign consumption, and holding of nominal bonds are: P U (C ) = (1+i )βE U (C ) t (17) c t t t c t+1 P ½ t+1¾ P U (C ) = (1+i )βE U (C ) t∗ (18) c t∗ ∗t t c t∗+1 P ½ t∗+1¾ B S P S U (C ) = (1+i )φ F,t t βE U (C ) t t+1 (19) c t ∗t P t c t+1 P S µ t ¶ ½ t+1 t¾ P (1+ S i t ) B φ F,t BF,tSt = S t B P F t ,t − 1 + P H, P t C t H,t + S t P H∗ P ,t t C H∗,t + P NT, P t Y t NT,t − C t (20) t ∗t Pt ³ ´ Equations (17) and (18) correspond to the euler equations of the home and foreign countries, respectively. Equation (19) represents household H’s Euler equation derived by maximizing the holdings of the nominal bond denominated in foreign currency. Finally, equation (20) corresponds to the resource constraintofcountryH,whichisobtainedbyaggregatingtheequilibriumbudgetconstraintofthehouseholds 21Another way to describe this cost is to assume the existence of intermediaries in the foreign asset market (which are owned by the foreign households) who can borrow and lend to households of country F at a rate (1+i ), but can borrow ∗ fromandlendtohouseholdsofcountryH atarate(1+i )φ(.). ∗ 22We are assuming that sectorial labors enter separately in the utility function which we may associate to the following analyticalexpression: V (NT,NNT)= N T 1+η+N N 1+ T η /(1+η). ³ ´ 8

withthatofthegovernment. Fromtheseconditionsweareabletoderiveboththenewuncoveredinterest parity and the risk-sharingequilibriumcondition whereboth areaffected bythenet foreign asset position of the domestic economy. 2.3 Price Setting under IPT In order to get a tractable model, we assume that prices are sticky in the non-tradable sector and flexible inthetradableone. Wealsoconsiderdistributioncostsinordertogetdeviationsfromthelawofoneprice and consequently intermediate degrees of pass-through. This follows previous contributions by Burnstein, Neves and Rebelo (2000) and Corsetti and Dedola (2002) where they assume that to deliver traded goods to consumers requires a component of differentiated non-traded goods. 2.3.1 Non-Tradable Sector The firms’ price setting decision behavior is modelled through a Calvo-type mechanism. We assume that prices are subject to changes at random intervals. In each period a seller faces a fixed probability (1 α) − of adjusting the price, irrespective on how long it has been since the last change had occurred. In this model suppliers behave as monopolists in selling their products. The objective of a home firm selling non-traded goods is to maximize the expected discounted value of profits23. ∞ Max E αkζ p (h)yd (h) Wh Nh (21) pNT,t(h) t t,t+k{ NT,t+k NT t,t+k − NT,t+k NT,t+k} k=0 X e subject to e e yd (h)= p NT,t (h) − σ Cd +ηd , (22) NT,t P NT,t t µ NT,t ¶ e £ ¤ where e Cd = n(1 γ) P NT,t − ε C , (23) NT,t − P t µ t ¶ ηd = knγ P H,t − θ P T,t − ε + P F,t − θ P T,t − ε C , (24) t P P P P t "µ T,t¶ µ t ¶ µ T,t¶ µ t ¶ # where yd (h) is the total individual demand for nontraded goods which is composed by the demand of NT,t nontraded goods for consumption, Cd , and the demand for distribution services by the tradable firms NT,t ηd. e t The supplier maximizes (21) with respect to p (h) given the demand function and taking as given NT,t the sequences of prices Pi ,Pi ,Pi ,Pi ,Pi,Ci for i = H,F. Each firm produces according to a H,t F,t T,t NT,t t t e linear technology © ª y (h)=Z Nh (25) NT,t NT,t NT,t 23ζ = βsUC (Ct+s ) Pt is the pricing Kernel associated to the first order condition for the recursive competitive t+s Pt+s UC(Ct) equilibrium. 9

where Z is the country-specific productivity shock to the non-tradable sector at time t. NT,t The optimal choice of p (h) is: NT,t p e (h)= σ E t ∞k=0 αkζ t,t+k W ZN N h T T ,t t + + k ky N d T t,t+k (h) (26) NT,t (σ − 1) P E t ∞k=0 αkζ t+k y N d T t,t+k (h) e Finally, Calvo-price seetting implies the followingPstate equation for P e NT,t P N 1 −T σ ,t =αP N 1 −T σ ,t − 1 +(1 − α)p NT,t (h)1 − σ (27) Analogousexpressioncanbederivedfortheoptimalnon-teradablepricesettingintheforeigneconomy. 2.3.2 Tradable Sector Inthismodelweassumethatthetradablesectoriscompletelyflexible. Thepresenceofdistributionservices intensiveinlocalnon-tradedgoodswillimplydifferentdemandelasticitiesacrossmarkets,therefore,firms will charge different prices in each market. Then, firms face the following maximization problem: W Max p(h),p ∗ (h) [P H C t d(h)+S t P∗ H C t∗ d(h)] − Z T,t[C t d(h)+C t∗ d(h)] (28) T,t subject to Cd(h) = nγ p t (h)+κP NT,t − σ P H,t − θ P T,t − ε C , (29) t P P P t µ H,t ¶ µ T,t¶ µ t ¶ Cd (h) = (1 n)γ p ∗t (h)+κP N∗T,t − σ P H∗,t − θ P T∗,t − ε C , (30) t∗ − Ã P H∗,t ! Ã P T∗,t! µ P t∗ ¶ t∗ The optimal prices at producer level, p (h) and p (h) are t ∗t σ W k p (h)=P = T,t + P , (31) t H,t (σ 1) Z (σ 1) NT,t T,t − − σ W k p ∗t (h)=P∗ H,t = (σ 1)S Z T,t + (σ 1) P N∗T,t , (32) t T,t − − The marginal cost for tradable goods varies as a function of the prices of non-traded goods. In this sense, the pricesetting oftradablegoods at homewill depend implicitlyontheproductivityshocks inthe non-tradable sector. Under the presence of distribution costs the elasticity of demand for domestic goods is not the same at home and abroad, and firms will charge different prices in each market. Optimal price setting implies deviations from the law of one price P H,t 6 =S t P∗ H,t unless the degree of distribution margin, k, is equal to zero. ³ ´ 10

2.4 Monetary Policy For the specification of monetary policy we consider a rule that embeds different types of rules. The general form of the interest rate rule is 1+i t =Ψ(F,ξm) (33) 1+i t where F is the set of target variables for the home country, and ξm is a pure monetary shock reflecting t interest rate movements that do not correspond to the endogenous reaction of the monetary authority to instrumental variables. Monetary shocks can be motivated by assuming that the central bank sometimes deviates from its own rule, that it makes mistakes in doing the monetary policy, or by assuming that the demand for money is itself stochastic. In the latter case, the shock rather than being policy shock would correspond to shocks to the parameters of the model. 2.5 The Log-linear Model Inthissection,wepresentafulllog-linearversionofthemodelwhichissummarizedintable1. Appendices A,B,CandDprovidedetailsonthederivation. Inwhatfollows,avariableX representsthelog-deviation t of X with respect to its steady state, X , and X represents the log-deviation of the flexible price level of t t b X with respect to its steady. t e From the first order condition (17) we obtain the standard Euler equation, IS, for the representative domestic consumer. This equation holds under both complete and incomplete markets. The uncovered interest rate parity is derived by taking the difference between the log-linear approximation of equations (17) and (19), and is given by the following expression: i i =E ∆S δb (34) t − ∗t t t+1 − t Notice that the above equation incobrporbates a cost of borrowing in foreign currency and may be consistent with the empirical failure of the UIP24. In our case, there is a time varying risk-premium that dependsonboththenetforeignassetpositionofthecountry(b )andacostofbondholdings(δ). Thisriskt premiumcouldbepositiveornegativedependingontheHomecountrybeingaborroweroralenderinthe internationalassetsmarket. Thisequationimpliesanegativerelationbetweentheinterestratedifferential and the NFA position of the economy. A country that accumulates assets faces a smaller implicit cost of bond holding (δb ), and consequently, the interest rate differential is smaller. The parameter δ measures t the elasticity of the interest rate differential to changes in the NFA position. The higher this elasticity, the larger the effect of the current account channel on the interest rate differential. Notice that the UIP does not hold even if the law of one price does. 24WhentheUIP relationholdsaregressionofexchangeratereturnsontheinterestratedifferentialshouldgiveanintercept ofzeroandaslopecoefficientofunity. However,thishypothesishasbeenconsistentlyrejectedinthedata. 11

Table 1 The sticky-price version of the model ρE C C =i E π IS t t+1 t t t t+1 − − ³ ´ E ∆S =i i +δb UIP t tb+1 tb − ∗t b t ρE C C C C =E (q q ) δb Risk-Sharing t t+1b − tb∗+1 − t − t∗ t t+1 − t − t ³³ ´ ³ ´´ π NT,t =bκNT ab0 T t +(ρ+bη)Cbt +a 1 R t − ( b 1+η)Z bNT,t +βE t π NT,t+1 AS H h i π ∗NT,t =κNT∗ − ba ∗0 T t∗ +(ρ+bη)C t∗ +ba ∗1 R t∗ − (1+η)Z NT∗,t +βE t π ∗NT,t+1 AS F h i βb t =b t − 1 +b 1 T t +bb 2 R t +b 3 R t∗b − b 4 C tb − C t∗ − q t NFA ³ ´ − R(1 − n)T t =b − c 0 R tb − (1+ηb)Z T,t +ρbC t +bηY Hb P H R(1 n)T = c R (1+η)Z +ρC +ηY q P − − bt∗ − 0bt∗ − T,t b t bH − t H ∗ RnT = c R (1+η)Z +ρC +ηY +q P t − b0 t − b T∗,t t∗ bF tb b F nRT = c R (1+η)Z +ρC +ηY P − b t∗ −b0 t∗ − T∗,t b t∗ b F b F ∗ q t =q bt − 1 +∆S bt + γ+(1 γ γ)Rε − 1 π ∗T,t−b π T,tb + γR1 − (1 ε− + γ (1 ) γ) π ∗NT,t− π NT,t RER − − b b π t ≡ γ+(1 γ γ)Rε − 1 π T,t + γR ¡ 1 − (1 ε− + γ (1 ) γ) π N ¢ T,t ; π ∗t ≡ γ+(1 ¡γ γ)Rε − 1 π ∗T,t + γ ¢ R1 − (1 ε− + γ (1 ) γ) π ∗NT,t CPI H ;CPI F − − − − π T,t ≡ R R − 1π NT,t + (1 − R n)∆S t ; π ∗T,t ≡ R R − 1π ∗NT,t− R n∆S t TI H ;TI F h i h i Parameters: a 0 ≡ 1 2 − n θηυ;a ∗0 ≡ 1 2 − n θηυ ∗ ;a 1 ≡ γR 1 − ε / γR 1 − ε +(1 − γ) +ηµ; a ∗1 ≡ ¡γR 1 − ε /¢ γR 1 − ε +¡(1 − γ)¢ +ηµ ∗ ; ³ ´ ³ ´ b 1 ≡ n λ(1 − n)³(θ − 1)+(1 − λ/n´)υθ 1 2 − n ; 1 ε 1 ε b 2 λ(1 γ)(1 ε) (1 λ/n)γR ¡ − ) ¢ / γR − +(1 γ) +(1 λ/n)µ; ≡ − − − − − − b 3 h[λ(1 n)(1 γ)/n(1 ε)]/ γR 1 − εi+(³1 γ) ;b 4 λ(1´ n)/n; ≡ − − − − ≡ − where λ nγR 1 − ε / γR 1 − ε + γ ³ +(1 γ)R ε − 1 1 − 1´ ε (1 γ)R ε +2nkγ /R ε ; ≡ − − κNT (1 αβ)(1 · α)/α(1+³ση);κNT∗ (1 ´α ∗ β³)(1 α ∗ )/α ∗ (1+´ση); ¸ ≡ − − ≡ − − µ ε (1 − υ)γR1 − ε − υ(1 − γ) ;µ ε (1 − υ∗)γR1 − ε − υ∗(1 − γ) ≡ ³ γR1 − ε+(1 γ) ´ ∗ ≡ ³ γR1 − ε+(1 γ) ´ υ =2nκ/ 2nκ+ − (1 −γ γ)R ε ;υ ∗ =2(1 − n)κ/ − 2(1 − n)κ+ (1 −γ γ)R ε ; c 0 = R(1³ − γ)+γ R − 1´R 1 − ε / γR 1 − ε +³(1 − γ) and R=1+´ σ kσ 1 . − δ ≡− ³φ 0 (0)C, b t =(¡B F,t /P¢ t∗ )C − ´1, T³ t ≡ P P H F, , t t , T t∗ ≡ P P ´H F ∗ ∗, , t t, R t ≡ P P N T T ,t ,t , and R t∗ ≡ P P N∗ T∗ T ,t ,t . Y ,Y are defined in appendix C. H F b b 12

The risk-sharing condition under incomplete markets is obtained by combining the UIP equation and the corresponding Euler equations for each country, and reads as:25 ρE C C C C =E (q q ) δb (35) t t+1 − t∗+1 − t − t∗ t t+1 − t − t ³³ ´ ³ ´´ Equation (35) illustrates the mbechanisbm throughbwhicbh the NFAbpositiobn affects the risk-sharing. The characterizationofthisincompleteassetmarketstructuremaintainsthegapbetweenrelativeconsumptions thatemergesintheincompleteassetstructurespecifiedinequation(12),butnow,inaddition,thedynamic ofthenetforeignassetsplaysanexplicitrole. Aslongasthereiseitherassetaccumulationordecumulation, therealexchangeratewillbeaffectedbythenetforeignassetposition,andtherefore,thelinkbetweenthe real exchange rate and relative consumptions that characterizes complete markets models will be broken down. Ceteris paribus, there is a negative relation between the real exchange rate and the NFA, i.e., an asset accumulation implies a real exchange rate appreciation. The larger the asset accumulation the greaterwillbetheeffectoftheNFApositionontherealexchangeratedynamics. Similarly,thelargerthe costofundertakingpositionsintheinternationalfinancialmarket,δ,thegreatertheeffectoftheNFAon the risk-sharing condition. Finally, if either δ 0 or b =0 at every period, the risk-sharing boils down t → to the one that characterizes a bond economy. The aggregate supply, AS , comes from thelog-linearization of equation (26) and (27). The aggregate H supplyblockwillnot differ under adifferent specification ofthemarket structure, butitisaffected bythe degree of pass-through in the economy. The dynamics for the net foreign asset position is obtained after log-linearizing equation (20). The terms of trade enter in the NFA and its effect is influenced by the presence of distribution costs. As expected, the relative price of non-traded goods along with the real exchange rate affect the current account dynamics. It is also possible to establish a relation between the market rate,T t ≡ P P H F, and the terms of trade at producer level ToT t ≡ P F,t /S t P∗ H,t . Combining equation (10) and the previous definition of the terms of trade, we obtain that R ToT = T Ψp, (36) t t R k − t − R k 1 d Ψp t = Ψ bp t − 1− R − b − k π NT,t − π ∗NT,t− ∆S t (37) − ¡ ¢ where Ψp t ≡ S t P∗ H,t /P H,t . b b Notice that Ψp accounts for the deviations from the law of one price at producer level. Hence, we can t 25Toassesstheempiricalrelevanceofthenetforeignassetpositioninthe”disconnectness”ofrelativeconsumptionsand therealexchangerate,testingthisrisk-sharingconditionisanaturalnextstep. Gagnon(1996),focusingonannualdatafor 20industrialcountriesfrom1973-1995,findsthat,inthelongrun,thereisasignificantandrobustrelationshipbetweenthe realexchangerateandNFA. Conversely,Kollmann(1995),Ravn(2001)andHeadet. al. (2002)testdifferentrisk-sharing conditions derivedunder perfectlyintegrated financial markets. They findlittle connectionbetweentherealexchange rate andrelativeconsumptions. InSelaiveandTuesta(2003),wefurtherexplorethisissueremarkingtheimportanceoffinancial frictionsandthekeyroleoftheNFAinexplainigtheapparentlackofinternationalrisk-sharing. 13

derive a relationship between deviations from the law of one price at consumer and at producer level R k k∆S Ψc Ψc = − Ψp Ψp + t (38) t − t − 1 R t − t − 1 R ³ ´ where Ψc S P /P . b b b b t ≡ t H∗,t H,t Whenk =0,thereisperfectpass-throughandthelawofonepriceholds,T =ToT andΨp =Ψc =0.26 t t t t Finally, to completely characterize the equilibrium dynamics of the model, we specify the monetary b d b b policy through interest rate feedback rules. The instruments the authority targets are CPI expected inflation (π ) and Output Gap (y ).27 t t i = γ E π +γ y +ξm (39) t π t t+1 y t t i = γ E π +γ y +ξ m (40) b ∗t ∗π t ∗t+1 ∗y t∗ ∗t where γ and γ are the weights givebn to instrumental targets. π y By the previous endogenous feedback rules, we are able to consider the systematic component of monetary policy. This is in line with recent normative literature in monetary policy28. FromidentitiesCPI andTI ,weobservethatchangesinnominalexchangerateisanindirecttarget H H for the monetary authority, and in particular, it is affected by the degree of pass-through. Lower degrees of pass-through tend to close that channel and to equalize non-tradable and CPI inflations. 3 Simulation of the Model 3.1 Parametrization Theparametersutilizedinourmodelarereportedintable2. Ourparametrizationintendstocharacterize thequalitativepropertiesofthemodelandtohighlightthemainmechanismintroducedbytheincomplete and imperct asset market structure, rather than match the data. We set a quarterly discount factor, β, equal to 0.99, which implies an annualized rate of interest of 4%. We calibrate our model assuming that country H is U.S. and country F is Europe, with a symmetric country size, n, equal to 0.5. For the coefficient of risk aversion parameter, ρ, we choose a value of 5 as in CKM. Regarding this parameter, Eichenbaum et. al. (1988) find a range between 0.5 and 3. On the other hand, Hall (1988) suggests a value greater than 5. The inverse of the elasticity of labor supply, η, is calibrated according to Rotemberg and Woodford (1998) and is set equal to 0.47. For parameter δ we assume two possible values, 10 3 and 10 2 which imply a 10 and 100-basis point − − spreads of the domestic rate (in the foreign currency market) over the foreign rate, respectively. In order 26Observe that Ψc could be associated to an analogous variable in Monacelli (2002) that measures the law of one price t gap. Thisauthorincorporatesanimperfectpass-throughmechanismbydomesticimportersfacingapricingdecisionsimilar tothedomesticprboducer,settingpricesdirectlyinlocalcurrency. 27We define output gap asthe deviations of output with respect to the flexible price allocationunder complete markets. SeeappendixC. 28SeeGali,GertlerandLopez-Salido(2001)amongothersforempiricalevidence. 14

to highlight the importance of NFA positions in the transmission mechanism of shock, we assume a very low value for δ in our benchmark parametrization. We choose a degree of monopolistic competition, σ, equal to 7.66 following Rotemberg and Woodford (1998). This implies an average mark-up of 15 percent. The value of the elasticity of substitution between traded and non-traded goods, ε, is set following Kravis and Lipsey (1987) equal to 0.77. The value of the elasticity of substitution between traded goods, θ, is set equal to 2, in the line of values reported by Backus, Kehoe and Kydland (1992), even though, we make sensitivity analyses for values in the interval [1,6]29. The weight associated with traded versus non traded goods, γ, is set equal to 0.6 following Gatsios, Kollinzas and Levasseur (2002). We set the distribution cost parameter, κ, equal to 0.8 which implies a margin of 47 percent of the retailpriceofconsumergoodsduetodistributioncosts30. InordertoevaluatetheeffectofIPT, wemake also a sensitivity analysis varying this parameter in the interval [0,1]. Consistent with the RBC literature, wechoosealow-persistentscenarioforproductivityshocksinthe tradablesector, andwesetautocorrelationsequalto0.95.WeassumetheirvariancesfollowingKehoeand Perri (2002) and Baxter and Crucini (1995) where var(ε ) = var(ε ) = (0.007)2. Baxter and Crucini T T ∗ (1995) and Kollmann (1996) find little evidence of spillover effects in technology shocks, and we rely on their result in our paper. For the non-tradable sector productivity shocks, we assume in both countries an autocorrelation equal to 0.93, and var(ε ) = var(ε ) = (0.002)2 following Corsetti et. al.(2002). NT NT ∗ We do not impose any further structure on the shocks. Following recent literature related with forward-looking monetary policy rules, in particular, Clarida GaliandGertler(2000),weassumethatαandα are0.66and0.75,respectively,whichimpliesaduration ∗ of price stickiness of 3 and 4 quarters in U.S. and Europe, respectively. With respect to the monetary policy, we set the coefficient on output gap, φ = 0.5, and the coefficient on inflation, γ = 1.5. In our π simulations we do not incorporate monetary shocks. 3.2 Responses to Productivity Shocks We can get some intuition of our quantitative results by analyzing the IRFs to domestic shocks. Any linkage between real exchange rate and relative consumptions across countries depends on two aspects: the asset market structure and the nature of the shock. We focus on two economies: imperfect financial integration with both PPT (dotted line) and IPT (thick line). Traded sector productivity shock: InFigure3wedepicttheresponsestoa1percentproductivity shock in the tradable sector of the domestic economy which decays with an autoregressive coefficient of 0.95. Under PPT, a productivity shock in the tradable sector delivers a negative comovement between real exchangerateandrelativeconsumptions. Followingthisshock,andstemmingfromtheworseningofterms 29ObstfeldandRogoff(2000)presentsasurveyregardingtheempiricalestimatesofθ. Ingeneral,theysuggesthighvalues forthiselasticity. 30Burnstein, Neves and Rebelo (2002) show that distribution costs are large and account for about 40-60 percent of the retailpriceinU.S. 15

of trade, domestic output increases and foreign output decreases. In addition, consumption increases but less than proportional than real income, and therefore, an asset accumulation occurs. The NFA accumulation generates a real exchange rateappreciation. The wealth effect decreases thelabor supply in the non-traded sector, and consequently, an increase in the relative price of nontraded goods triggers an appreciation of the real exchange rate. The domestic economy continues accumulating assets within the first20quartersbeforerevertingonthedownwardpathtothesteadystate. Notably,thenetforeignasset dynamics shows the similar high persistence as in the data. With IPT the expenditure-switching effect is dampened, and the NFA accumulation is smaller.31 It is important to note that in our benchmark calibration, θ was set larger than 1 which implies that worsening of the terms of trade bring about current account surpluses in the domestic economy. In a nutshell, conditional to a traded productivity shock, a net foreign asset accumulation contributes toarealappreciationduetowealtheffectsthataretransferedtothenontradedsector. Ontheotherhand, the worsenings in the terms of trade increases the relative consumptions and decreases relative outputs. The IPT mechanism amplifies the real exchange rate appreciation and dampens the increase in both relative consumptions and relative outputs. Non-tradedsectorproductivityshock: Responsestoa1percentdomesticnon-tradedproductivity shock are shown in Figure 4. The autorregresive coefficient is equal to 0.93. When the economy is hit by a productivity shock in the non-tradable sector, the comovement between real exchange rate and relative consumptionsispositiveunderbothPPT andIPT. Thiscomovementisdrivenmainlybythetraditional HBS. According to the HBS effect, an increase in the relative price of traded/non-traded goods in the home country with respect to the foreign country leads to a real exchange rate depreciation. When the price of non-traded goods falls, the real exchange rate depreciates because the domestic consumption bundle becomes less expensive than the foreign consumption bundle. Non-traded consumption increases athomeandsodoesrelativeconsumptions. Whenthepass-throughisimperfecttheexpenditure-switching effect is dampened, and the NFA reacts by less. 3.3 Quantitative Properties of the Model Theresultsofoursimulations aresummarized inTable3. Both relativetradableandnon-tradableshocks areincluded. Weevaluatetheunconditionalcorrelationbetweenrealexchangerateandrelativeconsumptions as well as some other statistics. The first column of the table reports H-P filtered statistics for the data from quarterly time series. United States is considered as the home country and an aggregate of Europe as the foreign country. A good starting point is the complete market-PPT model. We perform our simulations under a standard Taylor Rule where the monetary authority reacts to expected CPI inflation and output gap. The expenditure-switching effect, which is complete for tradable goods, triggers a very positive correlation betweenconsumptions(0.88). Thisbenchmarkmodeldeliversaperfectcross-correlationoftherealexchange 31TheresponsesareverysimilartotheonesobtainedbyCavalloandGhironi(2002)wheretheyfindanassetaccumulation afteratradableproductivityshock. 16

rate and relative consumptions while it is well known that in the data this correlation is negative (-.17). Our results are in the line of Kehoe and Perri (2002) and Heathcote and Perri (2001), among others. Asawaytoreconcilethepreviousfindingswiththedata, weintroduceIPT (seethirdcolumnintable 3). We dampen the link of consumptions and this is basically the main aspect in which the PPT and IPT models look different32. The next step is to analize the bond economy. In terms of the anomaly the results are virtually identical to the ones under complete markets, and the cross-correlation is still equal to one. This result is in the line of CKM (2001) where they point out that that the wealth effects that arise from this market incompleteness are too small, and therefore, the link between the real exchange rate and relative consumptions is not affected. Considering the discrepancy between the data and the simulated model under both complete markets and the bond economy structures, we study an incomplete and imperfect markets. First, we consider a conservativefrictionintheinternationalfinancialmarkets,andsetδ equalto10 3 whichimplies10-basis- − point spread of the domestic rate over the foreign rate. Intermsoftheconsumption-real exchange rate anomaly,theincompleteassetsmarketstructureunder PPT delivers a cross-correlation closer to the data (0.17 vs -0.17), and clearly lower than the value we obtain under the bond economy. Furthermore, if weincreasetthecost ofbond holdings by settingδ equal to 10 2, we can get values even closer to the ones observed in the data (-0.13 vs -0.17). − WeperformasimilarexerciseunderIPT. Thecross-correlationbetweenrealexchangerateandrelative consumptions increases with respect to the PPT model, and the anomaly gets more severe. Therefore, IPT does not help in solving the consumption-real exchange rate anomaly. In fact, the IPT model worse the fit under the benchmark parametrization. The bottom line is that incomplete and imperefect asset markets along with imperfect markets can help resolve the anomaly in a PPT environment. The interaction of the incomplete markets structure and financial frictions arecrucial. On the other hand, the IPT mechanism does not help in this direction. Basically, as we decrease the degree of pass-through, the effect of the net foreign asset position on the risk-sharing condition is dampened, and we get closer to a bond economy. 3.4 Sensitivity Analysis The Elasticity of substitution between home and foreign traded goods, θ : Here, we examine ourfindingsconsideringscenarioswithdifferentvaluesfortheelasticityofsubstitutionbetweenhomeand foreign traded goods. We have already showed that the asset market structure we have introduced breaks down the cross-correlation between the real exchange rate and relative consumption through the current account channel. Furthermore, the effect of the terms of trade on the NFA is shaped by the elasticity of substitutionbetweenhomeand foreign tradedgoods. In table4weperforma sensitivityanalyses toshow 32Thereareimportantgainsinvolatilityoftherealexchangerate,buttheseresultsarebeyondthescopeofthispaper. 17

the importance of the elasticity of substitution in explaining the anomaly33. Clearly, θ isacrucialparameter, andasit becomes largerit exacerbates thenetforeignassets position channel breaking the link between the real exchange rate and relative consumptions that characterizes a bondeconomy. Whenθ=1,underPPT,thetermsoftradedonotenterinthecurrentaccountdynamics34 (see equation NFA in table 1). Hence, the cross-correlation turns out to be perfect. Conversely, under IPT,thecross-correlationisnotperfectsincewealtheffectsarenowsolelytransmittedthroughtherelative prices of non-traded goods. CostofBondHoldings:Notforcharacterizingtheincompleteassetmarketstructure,butforgetting a well defined steady state, we need to introduce a cost of undertaking positions in the international financial markets. This cost is captured by the parameter δ. As we have already pointed out, in our model there is a tight link between the UIP and the risksharingcondition. Thepresenceofacost ofbondholdings generatedeviationsfromUIP whichaffectthe risk-sharing across countries. In this context, δ is at the heart of this incomplete asset market structure and turns out to be important in explaining the anomaly. In figure 3, weplot different values ofthecross-correlation between thereal exchangerateand relative consumptions by varying the cost of bond holdings parameter. Clearly, the larger the cost, the lower the cross-correlation. Thus,thelargerarethefinancialfrictionsintheinternationalmarketsthemorerelevant is the NFA in explaining the lack of risk sharing that characterizes complete markets models. Degrees of Pass-Through: To show how the degree of pass-through affects the cross-correlation betweentherealexchangerateandrelativeconsumptions,wevarytheparameterkwhichiscloselyrelated to the degree of pass-through (see figure 4). As we increase the distribution margin, the cross-correlation increases. The IPT mechanism undermines the NFA dynamics by dampening the expenditure-switching effect.35 Perfect Labor Mobility: Thus far, the analysis has been focused on a specification where the labor supply across sectors is separable. In this context, there is no labor mobility across tradable and nontradable sector. Our logic for relaxing this assumption is to allowfor somedegree oflabor mobilityacross sectors36. WefollowStockmanandTesar(1995)wheretheyassumethatlaborisperfectlymobilebetween traded and nontraded sectors. To this end, we consider a disutility of working of the following form: 1 V Nh +Nh = [N +N ]1+η (41) T,t NT,t 1+η T NT ¡ ¢ 33ObstfeldandRogoff(2000)outlinetheimportanceoftheintratemporalelasticityofsubstitution. BenignoP.(2001)find thatthelargertheintratemporalelasticityofsubstitutionthehigherthecostofimperfectrisksharing. 34Whenθ=1,underPPT,thecurrentaccountchannelisinhibitedwhicheliminatestheeffectofNFAontherisk-sharing condition. 35This constrast with Corsetti, Dedola and Leduc (2002), where the incomplete asset market structure is not enough to breakthetightlinkbetweentherealexchangerateandrelativeconsumptions. 36It is also the case, as Corsetti, Dedola and Leduc (2002) and Burnstein, Eichenbaum and Rebelo (2001) point it out, thattheIPT mechanismbydistributioncostsseemstoworkmainlythroughalargeflowoflaborbetweenthetradableand nontradablesectors. 18

Underthisspecificationthemarginalrateofsubstitutionbetweenconsumptionandworkingisequalized acrosssectors,andtherefore,realwagesarethesame. Thus,onceweaddperfectmobility,themarginalcost dynamics changes and so does the Phillips curve. In particular, the Phillips curve under this specification will also depend on the foreign consumption and the relative price between traded and non-traded goods abroad. Wecalculated the statistics under thebenchmarkparametrization. The results, reported in table 5, confirm our previous findings. Flexible Prices: The results of a flexible price version of our model are reported in table 5. The statistics behave quite similarly to the ones obtained under sticky-prices. However, with flexible prices we get smaller cross-correlations between the real exchange rate and relative consumptions under both PPT and IPT. The previous result is driven mainly by the particular Taylor rule used in the benchmark calibration since the response to output gap tends to offset the real exchange rate appreciation that is triggered by the effect of the foreign assets on the relative price of non-traded goods. It is also the case that IPT does not help in explaining the anomaly with respect to the PPT model, unlesstheelasticityofsubstitutionbetweenhomeandforeigntradedgoodsisequaltoone. Withaunitary elasticity and perfect pass-though, tradable shocks do not enter in the reduced form coefficient matrix, and the real exchange rate reacts only to non-tradable shocks37. 4 Empirical Testing Inthissectionweaimtotestempiricallytherisk-sharingconditionwehavederivedinourpaper,equation (35). First pointed out by Obstfeld (1989), under complete markets the link between real exchange rate and relative consumptions holds even if there are frictions in goods markets, including non-traded goods, pricing to market, local currency pricing, or transportation costs. Previous results have shown that the complete market model cannot match the observed consumption and real exchange rate growth rates. It is also the case that empirical evidence has cast strong doubts on the incomplete market assumption in which only one risk-free bond can be used for international financial transactions (e.g. Kollmann (1995)). Weusethegeneralizedmethodofmoments(GMM),inthelineof previouscontributionsbyKollmann (1995) and Head et. al. (2002), to test the risk-sharing condition derived in the paper for Australia. The data for all the estimations are obtained from the Quarterly National Accounts (QNA) of the OECD, the IMF’s International Financial Statistics (IFS), and the net foreign asset position database of Lane and Milesi-Ferretti(2001a). WecompletethedatafortheNFApositionfortheperiod1998to2000usingthe quarterly cumulative current account. First, we estimate the risk-sharing condition between Australia and the Rest of the World (RoW) considering in our definition of RoW the Euro Area, Japan and US.38 Consumption series include private 37Stickiness in the non-traded sector has been introduced to deliver a very tractable model. Thus, by considering a perfectly flexible tradable sector, the real exchange rate evolves following closely the relative prices of non-tradable goods across countries. In this context, neither the degree of pass-through nor the the stickiness in the non-traded sector affects thepersistenceofthisvariable. 38ThiscontrastswithKollmann(1995),Headet. al. (2002)whopresentresultsoncountry-pairsbasis,withtheUSacting asthereferencecountry. Ravn(2001)analyzesthecaseofcountry-RoW;however,hisincompleteassetmarketstructureis 19

consumption plus services. The real effective exchange rate is taken from the IFS for the period 1980:1- 2000:4. TheNFApositionwasdisaggregatedtogetquarterlyseriesbythemethodologyofChowandLin (1971) considering the current account as the related series. By way of contrast, our first estimation closely follows Kollmann (1995). In the moment condition we allowfordifferent coefficientsofriskaversionforAustraliaand RoW. For theperiod1970:1to2000:4, the risk-sharing condition estimated by Kollmann gives us the following E 0.333∆C 0.603∆C ∆q =0, (42) t −(1.196) t+1 −(1.517) t∗+1− t+1 · ¸ Standard errors are shown in parenthbeses. We havebused twoblags of each variable as instruments. The associated p value of the J statistic is 0.92. All standard errors were modified using a Newey-West − correction. From equation (42) we see that the risk aversion parameter has the correct sign but is not significant for the domestic economy while the coefficient that corresponds to the rest of the world is negative. It is also useful to test the bond economy restricting the risk aversion coefficient to be the same across countries. Below we show the results E 0.197 ∆C ∆C ∆q =0, (43) t −(1.246) t+1 − t∗+1 − t+1 · ³ ´ ¸ The associated p value of the J statistibc is 0.80.bThe instrbuments in this case are two lags of each − variable. Again,therisk-aversionparameterisnegativeandnotsignificant,whichconfirmsthelackoflink betweentherealexchangerateandrelativeconsumptionsthatcharacterizesabondeconomy, anditisalso consistent with previous findings by Kollmann (1995) and Ravn (2001). These results may be due to the choice of the functional form and/or to the risk-sharing condition failure39. Even so, we argue that this risk-sharinghypothesiscouldbefailingbecauseoftheomissionoftheNFApositionofthecountry. Thus, weperformanempirical testingoftherisk-sharingunderimperfect financialintegration. As abenchmark we will use the results obtained in the estimation of equation (43). In our model, the incomplete and imperfect asset market structure described in section 2 implies that thelinkbetweentherealexchangerateandrelativeconsumptionsisaffectedbythepresenceofnetforeign assets. Therisk-sharingconditionimpliesthatanincreaseinthenetforeignassetpositiontodaygenerates a expected real depreciation. By the same token, as consumers expect the relative price of home goods to be cheaper, home consumption increases relative to foreign consumption. Under rational expectations, we define the following new set of orthogonality conditions associated with the asset market structure proposed in the paper: E ρ ∆C ∆C ∆q +δb Z =0 (44) t t+1 − t∗+1 − t+1 t t n ³ ´ o where Z t corresponds to the vector obf instrumbents, and b ∆ stands as the first difference operator so ∆C ∆C is the growth rate of relative consumptions. Similarly, ∆q is the growth rate of t+1 − t∗+1 t+1 ³ ´ indepbendentofbtheNFApositiondynamics. b 39Ravn(2001)includesnon-separabilityintheutilityfunction,moneybalances,leisure,governmentexpenditureandhabit persistence. Hisresultsalsorejectthisrisk-sharinghypothesis. 20

the real exchange rate, and b corresponds to the ratio of NFA position in current dollars to GDP in t current dollars. We use instruments dated t or earlier. For the estimation, our vector of instruments includes lagged growth of relative consumptions, lagged change in real exchange rate and lags of the net foreign asset position. WehavechosenareducedsetofinstrumentsotherthanNFAinordertominimizethepotential bias that might arise from the excess of overidentifying restrictions in small samples.40 Theoretically, the NFA position has to return to a long-run stationary equilibrium. We performsome tests to check for non-stationarity in the NFA position for Australia, and we can not reject the null of unit root for this variable.41 Equation (45) shows the estimation of the new risk-sharing condition between Australia and the RoW for the period 1980:1 to 2000:4. E 2.503 ∆C ∆C ∆q + 0.006b =0 (45) t (0.620) t+1 − t∗+1 − t+1 (0.002) t · ³ ´ ¸ The striking result is that estimate obf the riskb-aversion pbarameter turns out to be positive and significant42. It seems that the inclusion of the NFA position allows us to capture some aspects of the smooth consumptionpossibilities, makingtherisk-aversionestimatepositiveandsignificant. Furthermore,theestimate of the cost of bond holdings is also positive and significant43. This finding confirms the prediction of our theory that a NFA accumulation will generate an expected real exchange depreciation. To check the robustness of our findings, we perform a bilateral estimation between Australia and US. In this case, we extend the sample period to run from 1975:1 until 2000:4. The results are shown in the next equation44 E 1.583 ∆C ∆C ∆q +0.0044b =0 (46) t (0.465) t+1 − t∗+1 − t+1 (0.0022) t · ³ ´ ¸ The result are quite similar to the Abustralia vbs RoW estbimation. Again the coefficient of risk aversion is positive, bigger than one and significant. On the other hand, the cost of bond holding parameter has the right sign. Our previous findings bring some evidence in favor of a theory in which the net foreign asset position plays an explicit role in risk-sharing across countries. The influence of the net foreign asset position may be better capturing both the associated time varying risk-premium and smooth consumption possibilities for Australia. 40TheNFApositionforAustraliaisverypersistent. Inthiscontext,itisadvisabletoconsideralargenumberoflagsas instrumentstocapturethisfact. 41AugmentedDicker-FullerandPhillipsPerrontestscannotrejectthenullhypothesisofunitroot. Itisalsothecasethat the power of unit root test is limited in small samples and can lead to misleading interpretations under highly persistent series. 42Recent empirical evidence presented by Yogo (2002) locates the value of the elasticity of intertemporal substitution -inverseoftheriskaversionparameter-belowone. 43Apropercorrectionofstandarderrosrmaybeappealingwhentheseriesareverypersistent. 44ThebilateralestimationAustralia-USAofthebondeconomy performsquitesimilartoitsmultilateralversionshownin thetext. 21

Sinceweakidentificationproblemsmayinvalidatehypothesistesting45,weusetheproceduresuggested by Stock and Wright (2000) to test if our instruments are weak.46 We construct the conventional 90% confidence ellipse with the 90% S-set, and the tests for our models are reported in figure 5.47 Under the reasonable assumption that the risk-aversion parameter is not “too large” as previous empirical evidence has suggested (see Yogo (2002)), our estimations may not be driven by important weak identification problems. Inanutshell, itseemsreasonabletoconsideratheorywheretheNFApositionaffectstherisk-sharing across countries.48 It appears that growth factors of consumption and real exchange rates behave in a manner which may be consistent with the assumptions implicit in our incomplete and imperfect market structure. Although our findings are in favor of our theory, for some other larger economies the NFA position may not be capturing a time varying risk-premium. To assess more precisely the importance of NFA in the risk sharing across countries, a more extensive analysis covering a larger number of countries is a natural next step. 5 Conclusions An important issue in international macroeconomics is the lack of risk-sharing across countries. Standard complete market models predict a high and positive cross-correlation between the real exchange rate and relative consumptions while in the data we observe the opposite. In this paper we have taken a step toward solving this anomaly stressing the importance of internationalfinancialfrictionsinthisissue. Wehaveenrichedpreviousmodelswithaparticularincompleteasset marketstructureinwhichthenetforeignassetpositionaffectstherealexchangeratedynamicsbyentering in the risk-sharing condition. Our results suggest that the interaction of incomplete markets and imperfect financial integration may deliver very low cross-correlations between real exchange rate and relative consumptions. In our model, financial frictions generate deviations from UIP, which allow us to affect the risk-sharing condition through the NFA position. In this context, there is an explicit link between the UIP puzzle and the consumption real exchange rate anomaly. Finally, the imperfect pass-through mechanism, by closing the current account channel, does not help to explain the lack of risk-sharing. We conclude our work by testing empirically the risk-sharing condition derived in the paper. We find some support for the incomplete asset market structure since growth factors of consumption and real 45Consumptiongrowthisveryunpredictable,andthechangeintherealexchangerateexhibitsaverylowpersistencewith respecttotheoriginalseries. Therefore,ourinstrumentscouldbeweaklycorrelatedwiththeendogenousregressorsandthe possibilityofweakidentificationcouldarise. 46Stock, Wright and Yogo (2002) also present a survey about the procedures available for detecting and handling weak instrumentsinGMM estimations. 47TheS-set consistsofparametervaluesatwhichonefailstorejectthejoinhypothesisthattheparametersarethetrue values and that the overidentifying conditions are valid. It contains all parameters that pass the 90% χ2 test, where k is k thedegreeoffreedom,andtherefore,containsthetopologyoftheobjectivefunction. Asarule-of-thumb,iftheS-sets are unreasonablylarge,thentheparametersarepoorlyidentified. SeeStockandWright(2000)formoredetails. 48Gagnon(1996),focusingonannualdatafor20industrialcountriesfrom1973-1995,findsthatthereisasignificantand robustrelationshipbetweentherealexchangerateandNFA. AnincreaseintheNFApositiondeliversarealexchangerate appreciation. 22

exchange rates behave in a manner which is consistent with a significant role for the net foreign asset position. Throughoutthepaperwehaveemphasizedtheimportanceofnetforeignassetsexplainingthelowcrosscorrelation between real exchange rate and relative consumptions. Our results are based on simplifying assumptionsthatfacilitatetheanalysis. Extendingthemodelallowingforhomebias,capitalaccumulation, different Taylorrulesandstickinessinthetradablesectormaychangethedynamicsofrealexchangerate, and therefore, the comovement between the real exchange rate and relative consumptions. 23

Appendices A. Steady State We define the symmetric steady state around which we will approximate the economy. The inflation and depreciation rates are zero, and there are no productivity shocks (Z =1) for all i=T,NT,T ,NT . i ∗ ∗ From equations (17) and (18) we get 1 1 β = = (A1) 1+i t 1+i∗ t which along with equation (19) implies SBF =0 in steady state. P From equation (20) we obtain W W C = TN + NTN (A2) P T P NT and from the resource constraint of the foreign country W∗ W∗ C = TN + NTN (A3) ∗ P T∗ P N∗T ∗ ∗ In equilibrium,(14) and (15) together with the corresponding foreign conditions imply W V N =U C T (A4) N T c P ¡ ¢ ¡ ¢ W V N =U C NT (A5) N NT c P ¡ ¢ ¡ ¢ W V N N∗ T =U c C∗ ∗T (A6) P∗ ³ ´ ³ ´ W V N N∗ NT =U c C∗ ∗NT (A7) P∗ ³ ´ ³ ´ Welog-linearizearoundasteadystatewhereN =N andN =N ,andcombining(A4),(A5),(A6) T T∗ NT N∗T and (A7) we get C =C∗ In steady state the consumer prices in domestic and foreign markets are P = ΦW (A8) NT NT P∗ = ΦW∗ (A9) NT NT 24

kσ P =ΦW + P (A10) H T (σ 1) NT − W kσ P∗ =Φ T + P∗ (A11) H S (σ 1) NT − kσ P F =ΦW∗ T S+ (σ 1) P NT (A12) − kσ P∗ =ΦW∗ + P∗ (A13) F T (σ 1) NT − or equivalently (n+(1 n)T 1 − θ )θ − 1 1(γ+(1 γ)R ε − 1 )ε − 1 1 = Φ V N Y H + kσ (1 γ+γR 1 − ε )ε − 1 1 − − U (C) (σ 1) − c¡ ¢ − (n+(1 n)T∗θ − 1 )1 − 1 θ(γ+(1 γ)R∗ε − 1 )ε − 1 1 = Φ V N Y H + kσ (1 γ+γR∗1 − ε )ε − 1 1 − − U c¡ (C∗) ¢ (σ − 1) − (1 n+nT θ − 1 )θ − 1 1(γ+(1 γ)R ε − 1 )ε − 1 1 = Φ V N Y F + kσ (1 γ+γR 1 − ε )ε − 1 1 − − U (C) (σ 1) − c¡ ¢ − (1 n+nT∗1 − θ )θ − 1 1(γ+(1 γ)R∗ε − 1 )ε − 1 1 = Φ V N Y F + kσ (1 γ+γR∗1 − ε )ε − 1 1 − − U c ( ¡ C∗) ¢ (σ − 1) − where Φ= σ (σ 1) − Similarly, the domestic prices for the non-tradables goods are given by (γR 1 − ε +(1 γ))ε − 1 1 = Φ V N Y NT − U (C) ¡c ¢ (γR∗ 1 − ε +(1 γ))ε − 1 1 = Φ V N Y NT ∗ − U ¡c (C∗) ¢ where Y H = C H +C H∗ Y F = C F +C∗ F Y NT = (1 γ)((1 γ)+γR 1 − ε )1 − ε εC+k C H +C F Y∗ NT = (1 − − γ)((1 − − γ)+γR∗1 − ε )1 − ε εC∗+ £ k C H∗+C ¤∗ F and h i C H =nγ(n+(1 n)T 1 − θ )1 − θ θ(γ+(1 γ)R ε − 1 )1 − ε εC − − C H∗ =(1 n)γ((n+(1 n)T∗θ − 1 )1 − θ θ(γ+(1 γ)R∗ε − 1 )1 − ε εC∗ − − − C F =nγ((1 n)+nT θ − 1 )1 − θ θ(γ+(1 γ)R ε − 1 )1 − ε εC − − C∗ F =(1 − n)γ((1 − n)+nT∗1 − θ )1 − θ θ(γ+(1 − γ)R∗ε − 1 )1 − ε εC∗ η(n)=k C +C H F Since Y H£ =Y F and ¤ Y NT =Y∗ NT . We can pin down T, T∗, R and R∗. It is easy to show that T = T∗ =1, and R=R∗ = 1+ kσ is a solution. Then we get (σ 1) − η Y (n N ) =2nκ/ 2nκ+ (1 −γ γ)R ε =v, and Y CN N ≡ 1 − v³which will´be used in the next appendix. ³ ´ 25

B. Phillips Curve In this section we log-linearize the price setting for non tradable goods, equation (26), around the steady state defined in appendix A. We can write equation (26) as: E ∞ (αβ)k U C (C t+k )P NT,t+k p NT,t (h) σ W N h T,t+k yd (h)=0 (B1) t P {P − σ 1P Z } NT t,t+k t+k NT,t+k NT,t+k NT,t+k k=0 − X e which can be re-written as e E ∞ (αβ)k U C (C t+k )P NT,t+k p NT,t (h) σ W N h T,t+k P t+k yd (h)=0 (B2) t P {P − σ 1P Z P } NT t,t+k t+k NT,t+k t+k NT,t+k NT,t+k k=0 − X e Aftertakingalog-linearapproximationofthepreviousexpression,anddefiningpe (h)=ln(p (h)/P ), NT t,t+k NT,t NT,t+k we obtain b e E ∞ (αβ)k p (h) W N h T,t+k P t+k =0, (B3) t " NT t,t+k − P t+k Z NT,t+k P NT,t+k# k X =0 c b where b Wh Wh NT,t+k = NT,t+k Z (B4) P Z P − NT,t+k t+k NT,t+k t+k c c From the first order condition respect to the labor supply inb the non-traded sector, equation (15) we get Wh NT,t+k =ηNh +ρC , (B5) P NT,t+k t+k t+k c where η NVNN (N) and ρ CUCC (C) . From log b -linearizing b the production of non tradable goods we ≡ VN (N) ≡ − UC (C) obtain N (h)=y (h) Z (B6) NT,t+k NT,t+k NT,t+k − Recall that R t = P P N T T ,t ,t ,R t∗ = P P N b ∗ T∗ T ,t ,t ,T t = P P H F, , t t , b T t∗ = P P H F ∗ ∗, , t t. Thben, from the price index definitions P P t ≡ [γR t 1 − ε+(1 − γ)]1 − 1 ε, (B7) NT which in log-linear form can be expressed as 1 ε P t γR − R t, (B8) P NT ≡ X 1 b b 26

1 ε where X 1 γR − +(1 γ). ≡ − Now we are able to get the total demand for home non-traded goods, equation (22),that in log-linear form can be expressed: 1 ε y (h) = C N σp (h)+ γεR − R t +C + NT,t+k NT t,t+k t Y N Ã− X 1 ! b b η(n) bσp NT t,t+k (h)+ CH θ(1b n)T t (1 − γ)εR t +C t + − CH+CF − − X1 (B9) Y N  CF θnT³ t (1 − γ)εR t +C t ´  b CH+CF − − X1 b b b  ³ ´  b b b 1 y (h)= σp (h)+υθ n T +µR +C (B9 A) NT,t+k − NT t,t+k 2 − t t t µ ¶ ε (1 υ)γRb1 − ε υ(1 γ) b b b b where µ − − − . ≡ ³ γR1 − ε+(1 γ) ´ Toobtain theaboveexpr−essionwehaveusedthelog-linearformsofthedemandsforhomeandforeign goods domestically, equations (29) and (30). Note that k p (h)=p (h) π (B10) NT t,t+k NT t,t NT,t+j − j=1 X and from log-linearizing (27) b b α p (h)= π (B11) NT t,t 1 α NT,t − Then, combining expressions (B4),(B6),(B5)and (B8) we get b W N j T,t+k P t+k = ηy (h)+ρC (1+η)Z + γR 1 − ε R t (B12) P t+k Z NT,t+k P NT,t+k ( NT,t+k t+k − NT,t+k X ) c b b Plugging (B9) into (B12) and usingbthis result toge b ther with (B1 b 1) and (B3) we get the aggregate supply equation : π =κmc +βE π (B13) NT,t t t NT,t+1 wheremc a T +(ρ+η)C +a R (1+η)ZNT .Thiscorrespondstotheaggregatesupplyexprest ≡ 0 t t 1 t − ct sion AS H in Thable 1. i c b b b The coefficients are: a 0 ≡ 1 2 − n θηυ; a 1 ≡ γR 1 − ε / γR 1 − ε +(1 − γ) +ηµ, κNT ≡ (1 − αβ)(1 − α)/α(1+ση), κNT∗¡ ≡ (1 − ¢α ∗ β)(1 − α ∗ )/α ∗ (³1+ση), where υ´ ≡ 2nκ/ 2nκ+ (1 − γ γ)R ε and R ≡ 1+ σ kσ 1 >1 − When we assume perfect mobility across sectors, the home³aggregate suppl´y will read as π =κNT a T +(ρ+η Ω)C +ΩC +a R +a R (1+(1 ω)η)Z ωηZ +βE π ; NT,t 0 t − t t∗ 1 t 2 t∗ − − NT,t − T,t t NT,t+1 h i b b b b b b b where ω =1/ 1+2nκ+ (1 −γ γ)R ε and Ω=ωη(1 − n). ³ ´ 27

C. Flexible Price Allocation and Output Gap In this appendix we derive the flexible priceallocation needed to determine theoutput gap. We define XR =X X and XW =nX+(1 n)X . First, the flexible price allocation under complete markets is ∗ ∗ − − given by (1+η) T = ZR t R+ηθ T,t (1+η)ρ R eR = e ZR t (ρ+η)c +ρa NT,t µ 0 1¶ 1+η ReW = ZW eZW t c +a NT,t− T,t µ 1 1¶h i c (1+η) eCR = 0 e ZeR t (ρ+η)c +ρa NT,t µ 0 1¶ (1+η) CeW = ec ZW +a ZW t (ρ+η)(c +a ) 1 NT,t 1 T,t µ 1 1 ¶h i e 1 ε 1 ε e e 1 ε wherec 0 = R(1 γ)+γ R 1 R − / γR − +(1 γ) andc 1 =c 0 +ηε(1 γ)/ γR − +(1 γ) . − − − − − Then, w³e can determin ¡ e the o ¢ utput´gap³as ´ ³ ´ y = ωY +(1 ω)Y ωY +(1 ω)Y , t H,t NT,t H,t NT,t − − − ³ ´ y = ωY +(1 ω)Y ωY +(1 ω)Y t∗ bF,t − bN∗T,t− eF,t − eN∗T,t ³ ´ b bwhere e e W R Y = Y +(1 n)Y , H,t t t − W R Y = Y nY , eF,t et − t e Y = YW +(1 n)YR , NeT,t eNT,t e − NT,t Y = YW nYR , eN∗T,t eNT,t− NT,t e e e and e 28

ε(1 γ) Y H = θ(1 − n)T t − γR 1 − ε + − (1 γ) nR t +(1 − n)R t∗ +nC t +(1 − n)C t∗ − ³ ´ b b ε(1 γ) b b b b Y F = − θnT t − γR 1 − ε + − (1 γ) nR t +(1 − n)R t∗ +nC t +(1 − n)C t∗ − ³ ´ b b1 b b b b Y = υθ n T +µR +C NT t t t 2 − µ ¶ R bY = θT b b b t t W (1 γ) Y = ε − RW +CW et −eγR1 ε+(1 γ) t t − − Y Ne R T,t = µR t R+C t R e e 1 YeN W T,t = υθe 2 − en T t +µR t W +C t W µ ¶ e e e e 29

D. Current Account Dynamics under IPT Here, we will log-linearize the current account equation (20). First, some steady state definitions are needed: R ≡ 1+ σ k − σ 1 ; η Y (n N ) =υ =2nκ/ 2nκ+ (1 − γ γ)R ε . Remember that T t = − T t∗ . ³ ´ b b 1 Y = υθ n T +µR +C NT t t t 2 − µ ¶ ε(1 γ) Cb = θnT b − b bR +C F,t − t − γR 1 − ε +(1 γ) t t − b b ε(1 γ)b b C = θ(1 n)T − R +C H,t − t − γR 1 − ε +(1 γ) t t − b b ε(1 γ) b b C H∗,t = θ(1 − n)T t − γR 1 − ε + − (1 γ) R t∗ +C t∗ − b εγRb1 − ε b b C = R +C N,t 1 ε t t γR − +(1 γ) − b b b ε (1 υ)γR1 − ε υ(1 γ) where µ − − − ≡ ³ γR1 − ε+(1 γ) ´ The current account can−be rewritten (20)as: P t (1+ S i ∗t t ) B φ F,t BF P ,t t St − S t B P F t ,t − 1 = P P T t ,t P P H T, , t tC H,t +q t P P T∗ t∗ ,t P P H T ∗ ∗, , t tC H∗,t + P N P T t ,tC NTt − C t (E1) ³ ´ We will log-linearize the following component of the right hand side of (E1) Y P T,t P H,tC +q P T∗,t P H∗,tC + P NT,tC (E2) t ≡ P P H,t t P P H∗,t P NTt t T,t t∗ T∗,t t we need the following steady state definitions: 1 ε P P T P P H T C H = nγ[γ+(1 − γ)R 1 − ε ] − 1 = γR 1 − n ε γ + R ( − 1 γ) − 1 1 ε ε Y = γR − +(1 γ)+2nκγR− γR 1 − ε +(1 γ) − − h i P P T P P H T C H = λ nγR 1 − ε / γR 1 − ε +(1 γ)+2nkγR− ε Y ≡ − h i q t P P ∗ T ∗ P P H T ∗ ∗ C H∗ = λ (1 − n) Y n P P NC N = 1 λ λ (1 − n) =1 λ Y − − n − n 30

Log-linearizing Y we get t (1 γ) (1 n) (1 γ) Y t = λ "γR 1 − ε + − (1 γ) R t − (1 − n)T t +C H,t # +λ − n " q t + γR 1 − ε + − (1 γ) R t∗ − (1 − n)T t +C H ( ∗ E ,t 3 # ) − − b λ γbR 1 − ε b b b b b b + 1 R +Y µ − n ¶" −γR 1 − ε +(1 γ) t N,t # − b b combining the above equation with the demands C and C we get H,t H∗,t b b βb =b +v T +v R +v R +v q +C +v Y +v C (E4) t t 1 1 t 2 t 3 t∗ 4 t t∗ 5 NT 6 t − ³ ´ v 1 ≡ n λ(1 − n)(θ − 1); b b b b b b b 1 ε 1 ε v 2 λ((1 γ) ε(1 γ)) (1 λ/n)γR − ) / γR − +(1 γ) ; ≡ − − − − − − v 3 h[λ(1 n)/n((1 γ) ε(1 γ))]/ γR 1 − εi+(³1 γ) ´ ≡ − − − − − v 4 λ(1 n)/n;v 5 (1 λ/n);v 6 λ³ 1 ´ ≡ − ≡ − ≡ − Plugging Y NT b 1 βb =b +v T +v R +v R +v q +C +v υθ n T +µR +C +v C (E5) t t − 1 1 t 2 t 3 t∗ 4 t t∗ 5 2 − t t t 6 t ³ ´ µ µ ¶ ¶ Replacing the parbameterbs in ordber to getbequabtion NFA in table 1: b b b b βb =b + v +v υθ 1 n T +(v +v µ)R +v R +v q +C +(v +v )C t t − 1 1 5 2 − t 2 5 t 3 t∗ 4 t t∗ 5 6 t βb t =b t − 1 +¡ n λ(1 − n)(θ¡ − 1)+¢¢(1 b− λ/n) 1 υθ ε 1 2 −b n 1 T ε t b ³ b b ´ b + λ((1 γ ¡ ) ε(1 γ)) (1 λ/n)γR − ) ¡ / γR ¢¢− +(1 γ) +(1 λ/n)µ R t − − − − − b − − +³[λh(1 − n)/n((1 − γ) − ε(1 − γ))]/ γR 1 − ε +i(1³ − γ) R t∗ +λ(1 − ´n)/n q t +C t∗ ´+ b λn −n 1C t we get the dynamics of the current a³ccount shown in t´able 1: ³ ´ b b b b βb =b +b T +b R +b R b C C q (E6) t t − 1 1 t 2 t 3 t∗ − 4 t − t∗ − t ³ ´ where b b b b b b b λ(1 n)(θ 1)+(1 λ/n)υθ 1 n ; 1 ≡ n − − − 2 − 1 ε 1 ε b 2 λ((1 γ) ε(1 γ)) (1 λ ¡ /n)γR ¢− ) / γR − +(1 γ) +(1 λ/n)µ; ≡ − − − − − − − b 3 h[λ(1 n)/n((1 γ) ε(1 γ))]/ γR 1 − εi+(³1 γ) ; ´ ≡ − − − − − b 4 λ(1 n)/n; ³ ´ ≡ − b =(B /P )C 1. t F,t t∗ − 31

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Table 2 Benchmark Parametrization Baseline Preferences β =0.99; σ =7.88; η =0.47; ρ=5; θ =2; ε=0.77;γ =0.6;n=0.5 Technology shocks ρ =ρ =0.95;var(ε )=var(ε )=(0.007)2. T ∗T T ∗T ρ =ρ =0.93;var(ε )=var(ε )=(0.002)2. NT ∗NT NT ∗NT Distributions costs No distribution costs. κ=0; Distribution costs. κ=0.8 Taylor Rule γ =1.5; γ =0.5 π y Incomplete Markets δ =0.001 (10 basis points) − Sticky prices α=0.75;α =0.66 ∗ 36

Table 3 Statistic Data Complete Markets Bond Economy Incomplete and Imperfect Asset Market Model PPT, delta PPT, delta IPT, IPT, PPT IPT PPT IPT =0.001 =0.01 delta=0.001 delta=0.01 Autocorrelations Real Exchange Rate 0.814 0.70 0.71 0.72 0.77 0.71 0.70 0.71 0.72 Net Foreign Asset Position ** 0.95 -.- -.- 0.94 0.95 0.95 0.95 0.96 0.96 Cross-Correlations RER-Relative Consumption -0.17 1.00 1.00 1.00 1.00 0.17 -0.13 0.61 0.10 RER-Net Foreign Assets 0.02 -.- -.- -.- -.- -0.11 -0.12 -0.15 -0.26 Domestic Consumption-Foreign Consumption 0.16 0.88 0.32 0.89 0.35 0.63 0.10 0.49 0.27 - Based on H-P filtered quaterly data from US time series (1973-2000) and an aggregate of European countries. The data was obtained from Chari et al (2002) and Heathcote and Perri (2002) webpages. Some statistics are authors' calculations - The imperfect pass-through was simulated under k=0.8 which implies a 47% margin of distribution costs * The benchmark economy considers a standard Taylor Rule targeting CPI inflation and Output Gap. ** Lane and Milesi-Ferretti (2001). Quarterly series were constructed by disaggregating annual data by Chow and Lin (1971)'s methodology 37

Table 4 Cross-Correlation Real Exchange Rate and Relative consumptions (δ =0.001) θ =1 θ=2 θ=3 θ =4 θ =5 θ =6 PPT 1.00 0.17 0.01 -0.04 -0.05 -0.05 IPT 0.75 0.61 0.43 0.31 0.24 0.19 -Exercises are over thebenchmark parametrization(ε=0.77,η =0.47,γ =0.6,ρ=5) 38

Table 5 Statistic Data Non-Separability of labor * Flexible Prices PPT, delta IPT, PPT, delta PPT, delta IPT, IPT, =0.001 delta=0.001 =0.001 =0.01 delta=0.001 delta=0.01 Autocorrelations Real Exchange Rate 0.814 0.71 0.71 0.71 0.72 0.71 0.72 Net Foreign Asset Position ** 0.95 0.96 0.96 0.96 0.96 0.96 0.96 Cross-Correlations RER-Relative Consumption -0.17 0.37 0.51 0.10 -0.42 0.72 0.31 RER-Net Foreign Assets 0.02 -0.04 -0.14 -0.19 -0.34 -0.17 -0.28 Domestic Consumption-Foreign Consumption 0.16 0.65 0.51 0.86 0.71 0.61 0.47 - Based on H-P filtered quaterly data from US time series (1973-2000) and an aggregate of European countries. The data was obtained from Chari et al (2002) and Heathcote and Perri (2002) webpages. Some statistics are authors' calculations - The imperfect pass-through was simulated under k=0.8 which implies a 47% margin of distribution costs * With a standard Taylor Rule targeting CPI inflation and Output Gap. ** Lane and Milesi-Ferretti (2001). Quarterly series were constructed by disaggregating annual data by Chow and Lin (1971)'s methodology 39

Figure 1: Incomplete Markets: Productivity Shock in the Domestic Tradable Sector Real Exchange Rate 0 -0.1 -0.2 -0.3 -0.4 0 20 40 60 80 100 etats ydaets morf noitaived % Relative Consumption 0.06 0.04 0.02 0 0 20 40 60 80 100 etats ydaets morf noitaived % Terms of Trade 1 0.5 0 -0.5 0 20 40 60 80 100 etats ydaets morf noitaived % NFA 3 2 1 0 0 20 40 60 80 100 etats ydaets morf noitaived % Relative Output 1 0.5 0 -0.5 0 20 40 60 80 100 Quarters etats ydaets morf noitaived % Home Tradable Shock 1 0.5 0 0 20 40 60 80 100 Quarters etats ydaets morf noitaived % PPT IPT 40

Figure 2: Incomplete Markets:Productivity Shock in the Domestic Non-Tradable Sector Real Exchange Rate 1 0.5 0 -0.5 0 20 40 60 80 100 etats ydaets morf noitaived % Relative Consumption 0.3 0.2 0.1 0 -0.1 0 20 40 60 80 100 etats ydaets morf noitaived % Terms of Trade 0.1 0 -0.1 -0.2 -0.3 0 20 40 60 80 100 etats ydaets morf noitaived % NFA 1 0.5 0 -0.5 0 20 40 60 80 100 etats ydaets morf noitaived % Relative Output 0.3 0.2 0.1 0 -0.1 0 20 40 60 80 100 Quarters etats ydaets morf noitaived % Home Nontradable Shock 1 0.5 0 0 20 40 60 80 100 Quarters etats ydaets morf noitaived % PPT IPT 41

Figure 3. Effect of the Cost of Bondholding Parameter (δ) 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 10 20 30 40 50 60 70 80 90 100 -0.1 -0.2 Basis Points *C/C,RER(roC Perfect Pass-Through Imperfect Pass-Through Notes: Graphunder thebenchmark parametrization(ε=0.77,θ=2;η =0.47,γ =0.6,k =0.8,ρ=5) Figure 4. Effect of Distribution Costs (k) 0.75 0.65 0.55 0.45 0.35 0.25 0.15 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 k *C/C,RER(roC Notes: Graph under the benchmark parametrization(ε=0.77,θ=2;η =0.47,γ =0.6,δ =0.001,ρ=5) 42

Figure 5: Join S-sets (a) (b) Note: Join S-set (shaded) and 90% confidence ellipse. 43