Real Exchange Rate and Net Trade Dynamics: Financial and Trade Shocks

Board of Governors of the Federal Reserve System International Finance Discussion Papers ISSN 1073-2500 (Print) ISSN 2767-4509 (Online) Number 1419 August 2025 Real Exchange Rate and Net Trade Dynamics: Financial and Trade Shocks Marcos Mac Mullen, and Soo Kyung Woo Please cite this paper as: Mac Mullen, Marcos, and Soo Kyung Woo (2025). “Real Exchange Rate and Net Trade Dynamics: Financial and Trade Shocks,” International Finance Discussion Papers 1419. Washington: Board of Governors of the Federal Reserve System, https://doi.org/10.17016/IFDP.2025.1419. NOTE: International Finance Discussion Papers (IFDPs) are preliminary materials circulated to stimulate discussion and critical comment. The analysis and conclusions set forth are those of the authors and do not indicate concurrence by other members of the research staff or the Board of Governors. References in publications to the International Finance Discussion Papers Series (other than acknowledgement) should be cleared with the author(s) to protect the tentative character of these papers. Recent IFDPs are available on the Web at www.federalreserve.gov/pubs/ifdp/. This paper can be downloaded without charge from the Social Science Research Network electronic library at www.ssrn.com.

Real Exchange Rate and Net Trade Dynamics: ∗ Financial and Trade Shocks Marcos Mac Mullen† Soo Kyung Woo‡ This Draft: July 2025 Click here for the most recent version Abstract ThispaperstudiesthedriversoftheUSrealexchangerate(RER),withaparticular focusonitscomovementwithnettrade(NT)flows. Weconsidertheentirespectrum of frequencies, as the low-frequency variation accounts for 62 and 64 percent of the unconditionalvarianceoftheRERandNT,respectively. Wedevelopageneralization of the standard international business cycle model that successfully rationalizes the joint dynamics of the RER and NT while accounting for the major puzzles of the RER. We find that, while financial shocks are necessary to capture high frequency variationintheRER,tradeshocksareessentialforthelowerfrequencyfluctuations. JELClassifications: E30,E44,F30,F41,F44 Keywords: InternationalBusinessCycles,ExchangeRates,TradeBalance,TradeDynamics ∗Firstdraft:April2022.WearegreatlyindebtedtoGeorgeAlessandriaforhisguidanceandsupportthroughout thisproject. WewouldalsoliketothankMarkAguiar,YanBai,MarkBils,GastonChaumont,MarioCrucini,Mick Devereux, Fabrizio Perri, Rafael Guntin, Oleg Itskhoki, Narayana Kocherlakota, Roman Merga, Dmitry Mukhin, ThuyLanNguyen,JuanPabloNicolini,KimRuhl,KatherynRuss,MikeSposi,JosephSteinberg,WalterSteingress and Jón Steinsson for numerous comments and suggestions. Moreover, we would like to thank Felipe Saffie and KwangyongParkforinsightfuldiscussions. Finally,wethankseminarparticipantsatNBERIFMSummerInstitute 2023,SED2023,SEA2023,MidwestEconometricsFall2023,theRIDGEInternationalMacroSummerForum2023, KoreaUniversity,BankofKorea,SantaClaraUniversity,NationalTsingHuaUniversity,NationalTaiwanUniversity, UniversityofToronto,McGillUniversity,KDI,KIET,HongKongUniversityofScienceandTechnology,University of Hong Kong, University of Virginia, University of South Carolina, IMIM, Midwest Macro Fall 2022, EGSC in St. Louis2022andUniversityofRochester. Allauthorshavecontributedequally. Anyerrorsinthepaperareentirely thoseoftheauthors. †marcos.macmullen@frb.gov,FederalReserveBoard ‡sookyung.woo@sejong.ac.kr,DepartmentofEconomics,SejongUniversity

1 Introduction Recentyearshaveseenimportantadvancesintheliteratureontherealexchangerate(RER)dynamics,afoundationaltopicininternationaleconomics. Inparticular,agrowingbodyofworkhas shown that financial shocks can explain the exchange rate disconnect: the observation that exchange rates exhibit near-random-walk behavior and appear uncorrelated with macroeconomic fundamentals(DevereuxandEngel,2002;GabaixandMaggiori,2015;ItskhokiandMukhin,2021). Whilethesedevelopmentsrepresentsignificantprogress,wehighlighttwokeylimitationsinthe existingliterature. First, the literature has failed to account for the behavior of net trade (NT) flows.1 While the RER reflects the prices that clear the international goods and asset markets, the NT flows are thequantitiestradedinthosemarkets. Hence,acomprehensivetheoryofinternationalbusiness cycles should capture both the RER and NT dynamics, particularly in the context of general equilibrium. Figure1presentsthepathoftheRER(blue)andNT(red)fortheUS.Thefigureshows that while the RER and NT exhibit a weak correlation at high frequencies, their comovement strengthens at lower frequencies.2 In contrast, models developed in the recent literature tend to predict an almost perfect correlation at high and low frequencies. These models also generate excessvolatilityinNTrelativetotheRER.Second,theexistingliteraturehasfocusedonbusiness cycle-frequencyfluctuations,despitethefactthatmostofthevarianceoftheRERarisesatlower frequencies. From the figure, it is clear that the trend (solid red) of the RER drives a large share 1WemeasuretheNTflowsasthelogexport-importratio,log𝑋/𝑀,asopposedtothetradebalanceoverGDP, 𝑋−𝑀. Wedothisbecauseweleveragethestructureofourmodelwherewederiveanequationthatrelatesthelog 𝑌 export-importratiototheequilibriumintheinternationalgoodsmarkets,allowingforacleardecompositionofNT intorelativeprices,quantities,andwedges(Equation8).Furthermore,thetradeliteraturehighlightsthatchangesin 𝑋−𝑀 primarilyreflectvariationsinthescaleofgrosstrade(AlessandriaandChoi,2021;Alessandria,BaiandWoo, 𝑌 2024),whichismainlyduetothefallinglobaltradecosts. Incontrast,log𝑋/𝑀 measuresnettradecontrollingfor thescaleoftrade,asitapproximatesthetradebalanceasashareofgrosstrade, 𝑋−𝑀,whichisamoreconvenient 𝑋+𝑀 measuregivenouranalysisabstractsfromchangesinthescaleofgrosstrade. Nonetheless,bothmeasures,thelog export-importratioandthetradebalanceoverGDP,producesimilarmomentsinthedataandinthemodel,asshown inFigureH.4andTableH.3. 2WeshowinFigureH.1thatasimilarpatternisfoundinmanyothereconomies:theRERandNTshowadelayed comovement,andtheirdynamiccorrelationgrowsovertime. Thisisconsistentwiththeso-calledJ-curvefromthe tradeliteraturethathasbeenrobustlydocumentedfortheUSandmanyothercountries(BaldwinandKrugman,1989; RoseandYellen,1989;Backus,KehoeandKydland,1994;Fitzgerald,Yedid-LeviandHaller,2019;Hooper,Johnsonand Marquez,2000;Alessandriaetal.,2024).Hooper,JohnsonandMarquez(2000)documentthedelayedcomovement inG7countries.Alessandria,BaiandWoo(2024)showusingapanelof36countriesduringtheperiodof1970-2019 thatthecomovementissmallintheshortrunbutgrowslargerinthelongrun. 1

Figure1: RealExchangeRateandNetTradeFlows 0.2 0.1 0 -0.1 -0.2 -0.3 -0.4 RER NT -0.5 1980 1985 1990 1995 2000 2005 2010 2015 2020 Notes:RERisthelogofthequarterlyrealexchangeratesoftheUnitedStates.Normalizedwith1980q1=0. Effective exchange rate indices, Real, Narrow (BIS). NT is the log of Exports to Imports ratio for the UnitedStates. ExportsandImportsarefromQuarterlyNationalAccounts(OECD).Solidlinesplotthe trendcomponentofeachvariablefromtheHodrick–Prescottfilterwithasmoothingparameterof1600. ofitsfluctuation.3 Weshowthatincorporatinglow-frequencydynamicsoffersnewinsightsinto thefundamentaldriversoftheRER. In this paper, we provide a unified framework for studying the joint dynamics of the RER andNTflowsacrossallfrequencies. Wegeneralizethestandardtwo-countryinternationalbusinesscyclemodelofBackusetal.(1994)byincorporatingfinancialshocksfollowingItskhokiand Mukhin (2021), shocks to the cost of trading goods across countries, and dynamic trade as in AlessandriaandChoi(2021).4 OurmodelcapturesthedifferentialcomovementbetweentheRER andNTflowsatdifferentfrequencies,thefrequencydecompositionoftheRERandNTvariance observed in the data, and the RER disconnect, along with major business cycle moments. The omission of any feature–financial shocks, trade shocks, or dynamic trade–results in the inability to simultaneously account for these empirical patterns. Using this framework we find that, 3Ourspectrumanalysisshowsthat62percentofRERvariancearisesfromlower-frequencymovements,orcycles up to twenty years. This finding aligns with Rabanal and Rubio-Ramirez (2015), who find that 77 percent of the varianceintheUSRERisfromthelow-frequency. InTableH.1,weshowthesamepatternisfoundinaverylarge numberofeconomies.ThisispartlybecausetheRERisclosetoarandomwalk,forwhichitisawell-knownproperty that mostof thevariance isconcentrated atlow frequencies. We discussthe spectrumanalysis in Section5.3 and providefurtherdetailsinAppendixB. 4TheframeworkinBackusetal.(1994)issimilartothatinStockmanandTesar(1995),andhasbeenextendedto variousassetmarketstructuresbyHeathcoteandPerri(2002,2014). 2

consistent with the recent literature, financial shocks drive most of the variation of the RER at highfrequencies. However,tradeshocksarethedominantdriversatlowerfrequencies,precisely wheremostofthevarianceoftheRERarises. Wemodeltradeshocksasstochasticicebergtradecosts,providingatractablerepresentation ofchangesintradebarriers. Thesebarriershavebeenchangingdramaticallyinthelastdecades, leading to a global trade integration. However, these changes have occurred at different timings and paces across countries. The time series of gross trade flows not only display an overall upwardtrend,butalsopresentconsiderablefluctuationsanddifferencesinthegrowthratesamong countries.5 We focus on the differential component between outward and inward trade costs for the US and the rest of the world (ROW) and abstract from the average cost, as the latter would havenoeffectonrelativemeasuressuchastheRERandNT.6,7 Trade shocks capture many different sources of fluctuations in barriers to trading goods and servicesacrosscountries. Forinstance,numerousepisodesoftradeliberalization,includingthose of China, have been accompanied by substantial reduction in both tariff and non-tariff barriers like quotas and sanctions (Obstfeld and Rogoff, 2000; Delpeuch, Fize and Martin, 2021). There have also been asymmetric trade reforms, like GATT rules, and temporary policies, such as Reagan’s export restraints on Japanese automobiles. Expectations and uncertainty about future policy can also act as a barrier to trade by affecting firms’ investment and exporting decisions (Caldara, Iacoviello, Molligo, Prestipino and Raffo, 2020). Furthermore, technological advancements in shipping and transportation have considerably reduced the cost of international trade (Burstein, Neves and Rebelo, 2003; Corsetti and Dedola, 2005; Corsetti, 2016). More recently, geopolitical conflicts have led to the blockage of trade routes and fluctuations in oil prices. In a recent paper, Itskhoki and Mukhin (2022) find that changes in trade barriers are an important driver of the ruble exchange rate following Russia’s invasion of Ukraine in 2022. The COVID-19 pandemicandenvironmentalissuessuchasdroughtsaffectingthePanamaCanalhavealsocontributed to changes in trade costs. Given the abundance of these incidents, the relative size of 5SeeFigureH.2. 6Inourquantitativeexercise,theROWaggregateincludesCanada,Finland,Germany,Ireland,Italy,Japan,RepublicofKorea,Spain,SwedenandUnitedKingdom.Thissetofcountriesrepresents60percentoftotalUStradeon average.TheestimatedmomentsfromthedataarerobusttohavinganunbalancedpanelthatincludesChinasince 1990.Formoredetails,seeAppendixA. 7WealsoshowthatourquantitativeresultsarerobusttoincorporatingtheaveragetradecostsinSection7. 3

tradecostsacrosscountriesfluctuatessignificantlyatahighfrequency,emergingasanessential sourceofNTandRERvariation. Ourfirstcontributionistoshowthatincorporatingbothtradeandfinancialshocksenablesthe modeltocapturethejointdynamicsoftheRERandNTathighfrequenciesasmeasuredbytheir correlation and relative volatility. In the recent literature, the RER is predominantly driven by financial shocks. When such shocks raise the return on US bonds relative to the ROW, domestic savings in the US increase, and the resulting excess savings are exported abroad—leading to a rise in US NT. Simultaneously, due to the fall in aggregate demand in the US, the final good price falls–causing a depreciation of the US RER. Thus, models in which the RER is primarily driven by financial shocks predict a counterfactual near-perfect correlation between the RER and NT at high frequencies. Moreover, because the intertemporal budget constraint requires the initial depreciation to be reversed over time, financial shocks only induce a temporary RER depreciation.8 Asaresult,financialshockstendtogenerateexcessvolatilityinNTrelativetothe RER. We show that incorporating trade shocks mitigates these counterfactual dynamics, allowing the model to capture the observed high-frequency comovement and volatility patterns between the RER and NT. A trade shock that increases the relative cost of exporting for the US leads to a decline in its NT. With fewer intermediate goods exported and more imported, the domestic supplyoffinalgoodsrises,puttingdownwardpressureontheirpriceandresultinginadepreciation of the US RER. Thus, trade shocks induce a negative correlation between the RER and NT on impact. Importantly, trade shocks also shift volatility from NT to the RER. Unlike financial shocks,theinitialRERdepreciationdoesnotrequireafutureappreciationtosatisfytheintertemporalbudgetconstraint;instead,theNTmustriseovertime. Asaresult,tradeshocksproducea morepersistentequilibriumresponseoftheRERthanfinancialshocks. Takentogether,tradeand financialshocksgenerateopposingeffectsonthecomovementbetweentheRERandNT,aswell asontheirrelativevolatility,allowingthemodeltomatchtheobservedhigh-frequencydynamics oftheRERandNT. Oursecondcontributionistohighlighttheroleofdynamictradetoaccountforlow-frequency 8Giventheinitialincreaseinthetradebalance, thebudgetconstraintimpliesthatitmustturnnegativeinthe future.TheRERmustappreciateovertimetosupportthisre-balancing. 4

dynamics of the RER and NT. We incorporate dynamic trade following Alessandria and Choi (2007, 2021) by assuming that intermediate producers are heterogeneous in their idiosyncratic productivity and decide whether to participate in the export market or not, subject to a fixed costofexporting.9 Weassumethatthefixedcostislowerforincumbentsthanfornewexporters, whichmakestheexportingdecisionforward-looking. Consequently,thedistributionofexporters evolve slowly in response to shocks, and aggregate trade flows respond gradually over time. In other words, dynamic trade frictions make quantities in the short run more inelastic than in the long-run. Thishastwoimportantimplications. First,itweakensthecomovementbetweentheRERand NTathigherfrequenciesrelativetolowerfrequencieswherequantitiescanfullyadjustalongthe extensive margin. This allows the model to generate a differential short and long-run elasticity of NT to prices close to the data. Second, it increases the high frequency response of the RER to shocks, as quantities cannot fully adjust. This redistributes the variance of the RER from lower to higher frequencies, improving the model’s fit to the observed spectrum of the RER.10 Overall, incorporatingdynamictradefrictionsimprovesthemodel’sabilitytocaptureboththeshort-and long-rundynamicsoftheRERandNT. Weuseourquantitativemodel—whichcapturesthejointdynamicsoftheRERandNTacross all frequencies—to assess the relative importance of financial and trade shocks in driving RER fluctuations. We show that both shocks contribute to explaining the real disconnect—the high volatility and persistence of the RER, and the Backus-Smith-Kollmann correlation. In contrast, financial shocks are essential to account for the financial disconnect, or Forward Premium Puzzle—the low predictive power of interest rate differentials on the RER and the failure of the UIP condition. Finally, our central finding is that while financial shocks dominate RER fluctuations at short horizons,tradeshocksaretheprimarydriveroverlongerhorizons. Specifically,financialshocks explain 54 percent of the one-quarter-ahead forecast error variance of the RER, compared to 42 percent explained by trade shocks. However, at the 32-quarter horizon trade shocks account for 68 percent of the variance, while financial shocks explain only 23 percent. The more persistent 9AlessandriaandChoi(2007,2021)extendsthesunkcostmodelofexportingofDixit(1989),BaldwinandKrugman (1989)andDas,RobertsandTybout(2007)toageneralequilibriumframework. 10ThespectrumoftheRERmeasuresthedistributionofthevarianceacrossdifferentfrequencies. 5

equilibrium effect of trade shocks is not an artifact of a particular calibration resulting in identifying a higher persistence of trade shocks, but an implication of the general equilibrium effects from its propagation through the budget constraint. Since the majority of RER variance arises at low frequencies, we conclude that trade shocks are crucial for explaining the overall, broader dynamicsoftheRER. The remainder of the paper is structured as follows. Section 2 reviews the literature. Section 3 presents our benchmark model, while Section 4 discusses the calibration and identification strategy. Section 5 demonstrates the success of the benchmark model in capturing targeted and untargetedmomentsrelatedtotheRERandNTdynamicsatallfrequencies. Section6studiesthe roleofdifferentshocksinexplainingthevariationoftheRER.Section7discussestherobustness ofourresulttoalternativespecifications. Finally,Section8presentstheconcludingremarks. 2 Literature Review Ourpaperbridgesthegapbetweenthestudiesininternationalfinanceandinternationaltrade,by developingatheorythatisconsistentwithboththeRERandNTdynamics. Ononehand,thereis agrowingliteratureemphasizingtheroleoffinancialshocksforunderstandingthedynamicsof exchange rates, with a focus on the macro and financial disconnect (Devereux and Engel, 2002; Gabaix and Maggiori, 2015; Farhi and Gabaix, 2016; Itskhoki and Mukhin, 2021).11 On the other hand,aseriesofpapershaveexploredtheroleoftradebarriersinexplainingthevariationintrade andfinancialflowsacrosscountries(ObstfeldandRogoff,2000;Eaton,KortumandNeiman,2016; Reyes-Heroles, 2016; Alessandria and Choi, 2021; Sposi, 2021; Alessandria, Bai and Woo, 2024).12 Inourstudy,wegeneralizetheframeworkinBackusetal.(1994)byintegratingfinancialshocks, trade shocks, and dynamic trade.13 This unified approach not only enhances our understanding of the outcomes presented in both strands of the existing literature but also deepens our com- 11Whilethisliteraturediscussesthedynamicsofboththerealandnominalexchangerates,welimitourinterest torealvariables. 12Ayres,HeviaandNicolini(2020)exploretheroleofcommoditypricesindrivingthevariationoftheRERandthe Backus-Smith-Kollmanncorrelationindevelopedeconomies.Ourframeworkdoesnotincludeacommoditysector, butvariationoriginatedinthissectorismostlikelytobecapturedaschangesinthetradecostsinourmodel,asthey reflectchangesinthecostoftradingintermediategoodsacrosscountries. 13OurworkisalsorelatedtothatinHeathcoteandPerri(2014),whichprovidesacomprehensiveanalysisofthe Backusetal.(1994)frameworkunderdifferentparametrizationsandvariousassetstructures(StockmanandTesar, 1995;BaxterandCrucini,1995;HeathcoteandPerri,2002). 6

prehension of the economic dynamics at play. As emphasized in the financial literature, we find that financial shocks are important for high-frequency fluctuations of the RER and the financial disconnect. On the other hand, we highlight that dynamic trade and trade shocks are crucial for accountingforlow-frequencymovementsoftheRERanditscomovementwithNT. Second,onlyalimitednumberofpapersstudyingthedynamicsoftheRERingeneralequilibriumhavefocusedonthelow-frequencyvariation. RabanalandRubio-Ramirez(2015)showthata reducedformdynamictrademodelwithnon-stationarycointegratedproductivityshocksisable tocapturethespectrumoftheRER.14 Gornemann,Guerrón-QuintanaandSaffie(2020)proposea mechanism relying on endogenous spillovers that amplify stationary fluctuations. These papers highlighttheimportanceofatimevaryingtradeelasticityfortheabilityofthemodeltocapture the RER spectrum. We share with these papers the focus on the low frequency variation of the RERandtheimportance ofdynamictrade.15,16 Wedifferfromthem inthewaywemodelthedynamictradeelasticity. Whiletheyrelyonareduced-formspecification,weuseamicrofoundation basedonfirms’dynamicexportingdecisions. Moreover,weproposeaRERdeterminationmechanism based on shocks to trade costs, which contribute to explaining the real disconnect—that is, the excess volatility and persistence of the RER relative to macro aggregates and the Backus- Smith-Kollmanncorrelation. Furthermore,weshowthatthetransmissionoftradeshocksvaries significantly across horizons, with trade cost shocks accounting for the major share of the lowfrequencyRERvariation.17 Finally,ourpaperisrelatedtotheliteratureonthemeasurementoftradewedges. Levchenko, LewisandTesar(2010),Fitzgerald(2012)andAlessandria,KaboskiandMidrigan(2013a)measure trade wedges based on the Armington model to study the role of trade costs and asset market frictions for international risk sharing. Head and Mayer (2014) explore different methods of es- 14Drozd, Kolbin and Nosal (2021) show that dynamic trade is a key feature to improve the model’s ability to account for thetrade comovement puzzle, i.e. the significant relationshipin the data between countries’ business cyclessynchronizationandtradeflows. 15Corsetti,DedolaandViani(2012)alsostudytheRERdynamicsatthefrequencydomainthroughspectralanalysis,butfocusonthelowfrequencydisconnectbetweentheRERandrelativeconsumption(Backus-Smith-Kollmann Puzzle). Cao, EvansandLuo(2020)studythemediumtolongrundynamicsoftheUS-UKRERandhighlightthe roleofpersistentproductivityshocks,incompletefinancialmarketsandahighArmingtonelasticityinaccounting foritsdynamics. 16WealsosharewithGornemannetal.(2020)theimportanceofusingtradedatatodisciplinethemodelparameters. 17KekreandLenel(2024)alsostudiestheRERdynamicsinthepresenceoffinancialanddiscountfactorshocks. 7

timating the gravity equation. We contribute to this literature by considering a specification of trade costs that allows for a within-ROW component, and highlight its implications for the comovementoftheRERandmacroaggregates. 3 Model We build on the two-country international business cycle model of Backus et al. (1994) and Itskhoki and Mukhin (2021). The two countries are the ROW and the US, each producing a perfectlycompetitivenon-tradedfinalgood. Thenon-tradedfinalgoodismadeofamixoftradable intermediates, using a CES technology with home bias.18 The final good can be consumed or investedbythehousehold,andcapitalaccumulationissubjecttocapitaladjustmentcosts. Thereisaunitmassofintermediategoodproducersineachcountry,producingdifferentiated varieties. They are subject to aggregate productivity shocks and are heterogeneous in their idiosyncraticproductivity. Theymakedecisionsonentering,stayingorexitingtheexportmarket, subject to the fixed costs that depends on the experience in the export market as in Dixit (1989), Baldwin and Krugman (1989), Das et al. (2007), Alessandria and Choi (2007), and Alessandria and Choi (2021). Intermediate firms set destination specific prices, and use labor and capital as inputs of production. Optimal prices are set as a markup over the marginal cost. We introduce time-varying markups, capturing pricing to market frictions in a reduced form, which leads to persistent deviations from the law of one price. Intermediate firms also face stochastic iceberg tradecosts,depictedasonlyafractionofgoodsshippedarrivingatthedestination. On the asset side, there is an internationally traded bond, denominated in dollars. The ROW household is subject to a bond adjustment cost, which induces stationarity of the model and capturesportfoliore-balancingcostsinareducedform. TheROWhouseholdisalsosubjecttoa financial shock, capturing the shock to uncovered interest parity of Itskhoki and Mukhin (2021). WedescribebelowthemodelfromthepointofviewofROWagents. Households 18ItskhokiandMukhin(2021)emphasizestheimportanceofincompletepass-throughofthefinancialshockmechanism,whichtheymodelusingaKimballaggregator. EventhoughweuseaCESaggregator,wemodelincomplete pass-throughbyaddingfrictionsinthepricingtomarketbehavioroffirms. 8

TherepresentativehouseholdintheROWmaximizesthediscountedexpectedutility ∞ [𝐶𝜂(1−𝐿 )1−𝜂 ] 1−𝜎 𝔼 ∑𝛽𝑡 𝑡 𝑡 0 1−𝜎 𝑡=0 where𝐶 isconsumption,𝐿 islabor,𝜂istheweightonconsumption,𝛽 isthediscountfactor,and 𝑡 𝑡 1/𝜎 istheintertemporalelasticityofsubstitution. Theflowbudgetconstraintisgivenby  𝐵∗ 𝜒 𝑃 (𝐶 +𝐼 )+𝐵 + 𝑡 𝑡+1 + (𝐵∗ −𝐵̄ ) 2 ≤ 𝑊 𝐿 +𝑅𝑘𝐾 +𝐵 (1+𝑖 )+ 𝐵∗(1+𝑖∗ )+Π 𝑡 𝑡 𝑡 𝑡+1 𝑒𝜓 𝑡2 𝑡+1 𝑡 𝑡 𝑡 𝑡 𝑡 𝑡−1 𝑡 𝑡 𝑡−1 𝑡 𝑡 where 𝑃 is the price index, 𝐼 is investment, 𝐵 is the quantity of ROW bonds (zero net sup- 𝑡 𝑡 𝑡+1 ply), 𝐾 is capital, 𝑖 is the nominal interest rate on ROW bonds purchased at 𝑡 − 1, and Π is 𝑡 𝑡−1 𝑡 aggregateprofitsofintermediatefirms. Ontheinternationalassetside,𝐵∗ isthequantityofthe 𝑡+1 internationally traded bonds held by the ROW household, 𝑖∗ is the nominal interest rate on in- 𝑡−1 ternationalbondspurchasedat𝑡−1,and isthenominalexchangerate,measuredasthepriceof 𝑡 theROWcurrencyperunitofUScurrency. Theterm𝜓 isthefinancialshock,𝜒 istheadjustment 𝑡 costofinternationallytradedbonds,and𝐵̄ isthesteadystatelevelofnetforeignassets.19 Thestockofcapitalineachcountryfollowsthelawofmotion, 𝜅(Δ𝐾 )2 𝐾 = (1−𝛿)𝐾 + 𝐼 − 𝑡+1 , 𝑡+1 𝑡 [ 𝑡 2 𝐾 ] 𝑡 wheretheparameter𝜅 governstheadjustmentcostofcapital. The solution of the ROW household can be characterized by the labor supply condition and theEulerequationsforROWandinternationalbondsandcapital. Thestochasticdiscountfactor oftheROWhouseholdbetween𝑡 and𝑡 +1isgivenby 𝐶𝜂 (1−𝐿 )1−𝜂 1−𝜎 𝐶 Ω ≡ 𝛽 𝑡+1 𝑡+1 𝑡 . 𝑡,𝑡+1 ( 𝐶𝜂(1−𝐿 )1−𝜂 ) 𝐶 𝑡 𝑡 𝑡+1 From the log-linearized Euler equations of the ROW household for ROW and international 19Thefinancialshock𝜓 onlyaffectstheROWhousehold,hencegeneratingadifferentialreturnoninternationally 𝑡 tradedbondsforROWandUShouseholds. Ourresultisinvarianttowhethertheshock𝜓 affectstheadjustment 𝑡 costofdebtornot. Ourresultsarealsoinvarianttowhetherthenominalexchangerateispartoftheadjustment costtermornot. 9

bonds, we can derive an equation for the deviations from the uncovered interest parity (UIP) condition, 𝑖 −𝑖∗ −𝔼 [Δ𝑒 ] = 𝜓 −𝜒 ⋅(𝐵∗ −𝐵̄ ) (1) 𝑡 𝑡 𝑡 𝑡+1 𝑡 𝑡+1 where 𝔼 [Δ𝑒 ] ≡ 𝔼 [ln −ln ] is the expected change of the nominal exchange rate. The 𝑡 𝑡+1 𝑡 𝑡+1 𝑡 financialshock𝜓 propagatestotheeconomybyinducingdeviationstotheUIPcondition. While 𝑡 we model the financial shock as an exogenous shock, the derived UIP condition is isomorphic uptofirstordertomodelswithsegmentedfinancialmarkets,noisytradersorlimitstoarbitrage (Yakhin,2022).20 Finally,thesecondtermontherighthandsidecapturesthedeviationsfromUIP thatariseendogenouslythroughtheeffectsonthenetforeignassets.21 AggregationTechnology A competitive retail sector combines intermediate goods from the ROW and the US with a constantelasticityofsubstitution(CES)toproducethefinalgood,𝐷 ,whichcanbeconsumedor 𝑡 invested. TheCESaggregatorisgivenby 𝛾 𝛾−1 𝛾−1 𝛾−1 𝐷 𝑡 = [ 𝑌 𝑅𝑡 𝛾 +𝜔 𝛾 1𝑌 𝑈 𝛾 𝑡 ] where𝑌 isthequantityofdomesticgoodsconsumedintheROW,𝑌 isthequantityofimported 𝑅𝑡 𝑈𝑡 goods from the US consumed in the ROW, 𝜔 captures the home bias, and 𝛾 is the Armington elasticitybetweendomesticandimportedcompositegoods. Thetotalexpenditureintheretailsectorisgivenby 𝑃 𝐷 = 𝑃 𝑌 +𝑃 𝑌 𝑡 𝑡 𝑅𝑡 𝑅𝑡 𝑈𝑡 𝑈𝑡 where 𝑃 is the price of domestic goods in the ROW, and 𝑃 is the price of imported goods in 𝑅𝑡 𝑈𝑡 20DeviationstotheUIParisefromlimitstoarbitrageinGabaixandMaggiori(2015), andacombinationofsegmented markets and noisy traders in Itskhoki and Mukhin (2021). Financial shocks can also be microfounded by risk-premia(Verdelhan,2010;ColacitoandCroce,2013;FarhiandGabaix,2016)orheterogeneousbeliefsandexpectationalerrors(EvansandLyons,2002;GourinchasandTornell,2004;BacchettaandVanWincoop,2006). Under higherorderapproximations,thewedgesintheUIPmayshowupintheresourceconstraintleadingtoadditional effects(FanelliandStraub,2021;Amador,Bianchi,BocolaandPerri,2019). 21Whilewedisciplinewithdatathesizeoftheadjustmentcost𝜒 inSection4,wedonotfindthattheendogenous componentofthedeviationsfromUIPisquantitativelyimportant. 10

theROW. Theproblemoftheretailsectoristominimizeexpenditureonintermediategoodssubjectto the CES aggregator, by choosing quantities {𝑌 ,𝑌 }. The final good is used by households for 𝑅𝑡 𝑈𝑡 eitherconsumptionorinvestmentsothat𝐷 = 𝐶 +𝐼 . Solvingthismaximizationproblemyields 𝑡 𝑡 𝑡 thedemandfunctionsforROWandUScompositegoods,givenby 𝑃 −𝛾 𝑃 −𝛾 𝑌 = 𝜔 𝑈𝑡 (𝐶 +𝐼 ) and 𝑌 = 𝑅𝑡 (𝐶 +𝐼 ) 𝑈𝑡 ( 𝑃 ) 𝑡 𝑡 𝑅𝑡 ( 𝑃 ) 𝑡 𝑡 𝑡 𝑡 where𝑃 isgivenas 𝑡 𝑃 = [𝑃 1−𝛾 +𝜔𝑃1−𝛾 ] 1/(1−𝛾) . 𝑡 𝑅𝑡 𝑈𝑡 The domestic and imported goods, 𝑌 and 𝑌 , are the composite of varieties produced by 𝑅𝑡 𝑈𝑡 heterogeneousproducers. Theaggregatorsare 𝑌 𝑅𝑡 = ( ∫ 1 𝑦 𝑗 𝜃 ,𝑅 𝜃 −1 𝑡 𝑑𝑗 ) 𝜃 𝜃 −1 𝑌 𝑈𝑡 = ( ∫ 𝑦 𝑗 𝜃 , ̂ 𝑈 𝑡 𝜃̂ − 𝑡 𝑡 1 𝑑𝑗 ) 𝜃̂𝑡 𝜃̂ − 𝑡 1 (2) 0 𝑗∈∗ 𝑡 where 𝜃 and 𝜃 ̂ are the elasticity of substitution across varieties, and ∗ is the set of exporting 𝑡 𝑡 firmsintheUS.Thusthedemandfunctionforeachvarietyisgivenby 𝑝 −𝜃 𝑝 −𝜃̂ 𝑡 𝑦 = 𝑗,𝑅𝑡 𝑌 𝑦 = 𝑗,𝑈𝑡 𝑌 . (3) 𝑗,𝑅𝑡 ( 𝑃 ) 𝑅𝑡 𝑗,𝑈𝑡 ( 𝑃 ) 𝑈𝑡 𝑅𝑡 𝑈𝑡 Thepriceindexesforthecompositegoodsaregivenby 𝑃 𝑅𝑡 = ( ∫ 1 𝑝 𝑗,𝑅𝑡 1−𝜃 ) 1− 1 𝜃 𝑃 𝑈𝑡 = ( ∫ 𝑝 𝑗,𝑈𝑡 1−𝜃̂ 𝑡 ) 1− 1 𝜃̂𝑡 . 𝑗=0 𝑗∈∗ 𝑡 Note that firms set destination specific prices, subject to the demands that differ across destinations due to the time-varying elasticity for the imported varieties. We let the elasticity of substitutionacrossimportedvarietiestovarywiththeRER.Specifically,wedefinetheRERas  =  𝑃∗/𝑃 𝑡 𝑡 𝑡 𝑡 11

and set the elasticity for the imported varieties as 𝜃 ̂ = 𝜃𝜁, and symmetrically for the exported 𝑡 𝑡 varieties as 𝜃 ̂∗ = 𝜃−𝜁.22 This captures pricing-to-market behavior of firms in reduced form, 𝑡 𝑡 where an appreciation of the US RER increases the markups charged by ROW firms to exports to the US. This is consistent with the findings in Alessandria and Kaboski (2011) that shows that firms price to income, charging higher prices to higher income destinations.23 The pricing-tomarket allows the model to capture the incomplete pass-through of exchange rates to prices, which trigger persistent deviations from the law of one price, and to generate a volatility of the termsoftradethatissmallerthanthatoftheRER,asinthedata.24,25 TheproblemoftheUSretailersisgiveninasymmetricform max 𝑃∗(𝐶∗ +𝐼∗)−[𝑃∗ 𝑌∗ +𝑃∗ 𝑌∗ ] 𝑡 𝑡 𝑡 𝑈𝑡 𝑈𝑡 𝑅𝑡 𝑅𝑡 {𝑌∗ ,𝑌∗ } 𝑈𝑡 𝑅𝑡 subjecttotheCESaggregator,resultinginthedemandfunctionsof 𝑃∗ −𝛾 𝑃∗ −𝜌 𝑌∗ = 𝜔 𝑅𝑡 (𝐶∗ +𝐼∗) and 𝑌∗ = 𝑈𝑡 (𝐶∗ +𝐼∗). 𝑅𝑡 ( 𝑃∗ ) 𝑡 𝑡 𝑈𝑡 ( 𝑃∗ ) 𝑡 𝑡 𝑡 𝑡 IntermediateFirms Thereisacontinuumofheterogeneousfirmsindexedby𝑗 ∈ [0,1]ineachcountry,specializing intheproductionofadifferentiatedintermediategood. Thereismonopolisticcompetitionamong these firms. The firms are subject to aggregate and firm-specific shocks. The firm 𝑗’s production functionisgivenby 𝑦 = 𝑒𝑎 𝑡 +𝜇 𝑗𝑡𝑙𝛼𝑘1−𝛼, 𝑗𝑡 𝑗𝑡 𝑗𝑡 where𝛼 isthelaborshareofincome,𝑎 istheproductivityshock,and𝜇 isaidiosyncraticfirm- 𝑡 𝑗𝑡 specific shock, 𝜇 𝑖∼𝑖𝑑 𝑁(0,𝜎2). All firms sell their products in their own country, while some of 𝜇 22Anincreasein indicatesadepreciationofthehomeRER. 𝑡 23The pricing-to-market generates time-varying markups in a similar way as with a Kimball aggregator, as in ItskhokiandMukhin(2021),andcanbemicrofoundedwithsearchfrictions. SeeEdmond,MidriganandXu(2018) forastudyofheterogeneousfirmwiththeKimballaggregator.Ontheotherhand,AtkesonandBurstein(2008)and DrozdandNosal(2012)providealternativemodelsofpricingtomarket. 24SeeRaffo(2008)forananalysisonthecounterfactualdynamicsofthetermsoftradeinthestandardtwo-country internationalbusinesscyclemodel. 25Omittingthepricingtomarketfrictiondonotchangethemainresultsofthepaper. 12

themchoosetoexport. Theresourceconstraintofafirmisgivenby 𝑦 𝑗𝑡 = 𝑒𝜉 𝑅𝑡𝑦 𝑗,𝑅𝑡 +𝑚 𝑗𝑡 𝑒𝜉 𝑅 ∗ 𝑡 𝑦 𝑗 ∗ ,𝑅𝑡 (4) where 𝑦 is ROW variety used domestically, 𝑦∗ is ROW variety exported to the US, 𝜉 is the 𝑗,𝑅𝑡 𝑗,𝑅𝑡 𝑅𝑡 stochasticicebergcostfordomestictradewithintheROWcountries,𝜉∗ isthestochasticiceberg 𝑅𝑡 costforROWexportstotheUS,and𝑚 ∈ {0,1}isthecurrentexportstatusoffirm𝑗,with𝑚 = 1 𝑗𝑡 𝑗𝑡 being export and 𝑚 = 0 not export. Note that we are considering a case of iceberg costs that 𝑗𝑡 allowsfortheicebergtradecostwithintheROW,𝜉 ,tobenonzero. Thistakesintoaccountthat 𝑅𝑡 theROWisanaggregateofmultiplecountriesthattradewitheachother. Inordertocapturethe averagetradecostwithintheROWcountries,werelaxtheconstraintofastandardspecification withzerodomesticicebergcosts.26,27 In order to export, firms must pay a fixed cost, denominated in units of labor. The fixed cost for starting to export differs from the fixed cost to stay in the export market. To start exporting, afirmpaysacostof𝑊 𝑓0,whileanincumbentexporterpaysthecontinuationcostof𝑊 𝑓1,with 𝑡 𝑡 𝑓1 < 𝑓0. That is, there is a sunk cost associated with export participation, capturing exporter hysteresisandtheslowresponseofaggregateexportstoshocks. An intermediate good producer in the ROW is described by its idiosyncratic productivity and past export status, (𝜇 ,𝑚 ). The aggregate state which includes the aggregate produc- 𝑗𝑡 𝑗𝑡−1 tivity, trade and financial shock, and the endogenous assets and distribution of exporters and non-exporters is subsumed in the time subscript of the value function. The dynamic problem of afirmis,28 𝑉 (𝜇 ,𝑚 ) = max 𝑝 𝑦 +𝑚  𝑝∗ 𝑦∗ −𝑊 𝑙 −𝑅𝑘𝑘 −𝑚 𝑊 𝑓𝑚 𝑗𝑡−1 +𝔼 Ω 𝑉 (𝜇 ,𝑚 ) 𝑡 𝑗𝑡 𝑗𝑡−1 𝑗,𝑅𝑡 𝑗,𝑅𝑡 𝑗𝑡 𝑡 𝑗,𝑅𝑡 𝑗,𝑅𝑡 𝑡 𝑗𝑡 𝑡 𝑗𝑡 𝑗𝑡 𝑡 𝑡 𝑡,𝑡+1 𝑡+1 𝑗𝑡+1 𝑗𝑡 {𝑚 ,𝑝 ,𝑝∗ ,𝑙 ,𝑘 } 𝑗𝑡 𝑗,𝑅𝑡 𝑗,𝑅𝑡 𝑗𝑡 𝑗𝑡 subject tothe ROW retailer’sdemand forROW intermediates,𝑦 , theUS retailer’s demandfor 𝑗,𝑅𝑡 ROW intermediates, 𝑦∗ , and the resource constraint. The static optimality conditions of the 𝑗,𝑅𝑡 26Weexplaininmoredetailtheroleofthewithin-countrytradecostwhenwepresenttheshockprocesses. 27InAppendixE.6,usingathreecountrymodelweshowthatthisshockoperatesqualitativelyinthesameway asatradeshockbetweentwoROWcountries. 28Intermediatefirmsdiscountthefutureusingthehouseholdstochasticdiscountfactor. 13

firmaregivenbytheoptimaldemandforinputsandoptimalpricing, 𝑦 𝑦 𝑊 = (1−𝛼) 𝑗𝑡 and 𝑅𝑘 = 𝛼 𝑗𝑡 (5) 𝑡 𝑙 𝑡 𝑘 𝑗𝑡 𝑗𝑡 𝜃 𝜃−𝜁 𝑝 𝑗,𝑅𝑡 = 𝑒𝜉 𝑅𝑡 𝜃 −1 𝑀𝐶 𝑗𝑡 and  𝑡 𝑝 𝑗 ∗ ,𝑅𝑡 = 𝑒𝜉 𝑅 ∗ 𝑡 𝜃−𝜁 𝑡 −1 𝑀𝐶 𝑗𝑡 (6) 𝑡 where the 𝑀𝐶 = 1 (𝑅 𝑡 𝑘)𝛼 (𝑊 𝑡 )1−𝛼 is the marginal cost. Note that firms set different prices across 𝑗𝑡 𝑒𝑎𝑡+𝜇𝑗𝑡 𝛼𝛼(1−𝛼)1−𝛼 destinations, since they face different demands at home and foreign. Moreover, note that the pricingtomarketfriction,𝜁,generatesdeviationsfromthelawofonepricethatareproportional totheRER.29 Furthermore, the fixed cost 𝑓𝑚 𝑗𝑡−1 that a firm pays depends on its exporting status in the previousperiod𝑚 . Thus,wecan solveforthe thresholdproductivityto participateinthe export 𝑗𝑡−1 market depending on its previous status: 𝜇1 and 𝜇0 for those who were exporting and were not 𝑡 𝑡 inthepreviousperiod,respectively. Atthethreshold,afirmisindifferentbetweenexportingand notexporting. Hence,afirmwilldecidetoparticipateintheexportmarketonlyifitsproductivity isabovethethreshold. Thethresholdssatisfy 𝑊 𝑓𝑚 −𝜋∗(𝜇𝑚) = 𝔼 [Ω (𝑉 (𝜇 ,1)−𝑉 (𝜇 ,0))], 𝑚 ∈ {0,1} 𝑡 𝑡 𝑡 𝑡,𝑡+1 𝑡+1 𝑡+1 𝑡+1 𝑡+1 where𝜋∗(𝜇𝑚)isthestaticprofitfromexportingforafirmwithidiosyncraticproductivity𝜇 = 𝜇𝑚, 𝑡 𝑗𝑡 𝑡 givenas 𝜋∗(𝜇 ) =  𝑝∗ (𝜇 ) 𝑦∗ (𝑝∗ (𝜇 )) 𝑗𝑡 𝑡 𝑗,𝑅𝑡 𝑗𝑡 𝑗,𝑅𝑡 𝑗,𝑅𝑡 𝑗𝑡 with𝑝 and𝑦 fromEquations3and6asfunctionsoftheidiosyncraticproductivity𝜇 . Since 𝑗,𝑅𝑡 𝑗,𝑅𝑡 𝑗𝑡 the fixed cost is higher for a new exporter than for an incumbent exporter, 𝑓0 > 𝑓1, the productivitythresholdishigherfortheformerthanthelatter,𝜇0 > 𝜇1. 𝑡 𝑡 The presence of sunk costs of exporting generates a slow moving distribution of aggregate 29Inparticular,thedeviationsfromthelawofonepricearegivenby ln( 𝑡 𝑝 𝑗 ∗ ,𝑅𝑡 /𝑝 𝑗,𝑅𝑡 ) ∝ 𝜁 .Thisimpliesanexchange ln 𝜃−1 𝑡 ratepass-throughof (𝜃−1)−𝜁 ×100 percentatthesteadystate. [ (𝜃−1) ] 14

exporters,𝑁 . Thelawofmotionofaggregateexportersisgivenby 𝑡 𝑁 = 𝑁 ⋅𝑃 [𝜇 > 𝜇1 ]+(1−𝑁 )⋅𝑃 [𝜇 > 𝜇0 ]. 𝑡 𝑡−1 𝑗𝑡 𝑡 𝑡−1 𝑗𝑡 𝑡 Theaggregatelaborandcapitaldemandsfromintermediatefirmsaregivenby 1 𝐿 𝑡 = ∫ 𝑙 𝑗𝑡 +𝑓0 ⋅(1−𝑁 𝑡−1 )⋅𝑃 [𝜇 𝑗𝑡 > 𝜇 𝑡 0 ]+𝑓1 ⋅𝑁 𝑡−1 ⋅𝑃 [𝜇 𝑗𝑡 > 𝜇 𝑡 1 ] 𝑗=0 1 𝐾 = 𝑘 . 𝑡 ∫ 𝑗𝑡 𝑗=0 Notethattheaggregatelabordemandincludesthefixedcostofexportingofallfirmsbecausethe costsareintermsoflabor. ShockProcesses Productivityshocksfeatureacommonanddifferentialcomponent,30 ⎡ ⎤ ⎡ ⎤ 𝑎 𝑎 +𝑎 /2 ⎢ 𝑡 ⎥ ⎢ 𝑐𝑡 𝑑𝑡 ⎥ = ⎢ ⎥ ⎢ ⎥ 𝑎∗ 𝑎 −𝑎 /2 ⎣ 𝑡 ⎦ ⎣ 𝑐𝑡 𝑑𝑡 ⎦ where the common component, 𝑎 , and the differential component, 𝑎 , each follow an AR(1) 𝑐𝑡 𝑑𝑡 process, 𝑎 = 𝜌𝑐𝑎 +𝜀𝑐 𝜀𝑐 ∼ 𝑁(0,𝜎𝑐) 𝑐𝑡 𝑎 𝑐𝑡−1 𝑎𝑡 𝑎𝑡 𝑎 𝑎 = 𝜌𝑑𝑎 +𝜀𝑑 𝜀𝑑 ∼ 𝑁(0,𝜎𝑑). 𝑑𝑡 𝑎 𝑑𝑡−1 𝑎𝑡 𝑎𝑡 𝑎 WeassumethattherelativetradecostbetweenROWandUS,𝜉 ,followsanAR(1)process. This 𝑡 can be interpreted as decomposing country-specific trade shocks into common and differential components, as in Waugh (2011) and Alessandria and Choi (2021), and then abstracting from the common component. In our benchmark specification, we do not consider a common trade cost becauseitprimarilyaffectthelevelofgrosstrade,withoutfirstordereffectsonrelativevariables 30Alternativelycountry-specificshockscanbewrittenasacombinationoftheseorthogonalshocks. 15

suchastheRERandNT.31,32 Specifically,thetradecostshocksaregivenby 𝜉 𝜉 𝜉∗ = 𝑡 𝜉 = − 𝑡 𝑅𝑡 2 𝑈𝑡 2 𝜉 𝜉 = 𝜏 𝑡 𝜉∗ = 0 (7) 𝑅𝑡 2 𝑈𝑡 where𝜏 ∈ ℝand 𝜉 = 𝜌 𝜉 +𝜀 , 𝜀 ∼ 𝑁(0,𝜎 ). 𝑡 𝜉 𝑡−1 𝜉𝑡 𝜉𝑡 𝜉 Note that we are allowing for cost of trading ROW goods within the ROW to potentially be non-zeroandimposethegeneralassumption𝜏 ∈ ℝ.33 Thismodelneststhecaseofonlydifferential trade costs between countries under zero within-ROW cost, i.e. 𝜏 = 0.34,35 The parameter 𝜏 capturestheelasticity ofshippingcostswithintheROWtoexportcosttotheUS.Whenmapping themodeltothedata,𝜏 capturestheaveragetradecostsacrossROWcountries. Thisspecificationallowsthewithin-ROWtradecosttovaryovertimeandcapturetheevolution of trade integration among the countries that compose the ROW aggregate. In fact, during thetimeperiodweconsider,manycountriesimplementedtradereformsthatjointlyloweredthe exportingcosttotheUSandnon-USROWcountries,loweringboth𝜉∗ and𝜉 . Forexample,the 𝑅𝑡 𝑅𝑡 Asia-Pacific Economic Cooperation in the 1990s and the creation of the European Union generated significant changes in trade barriers among the countries in the ROW. Also, countries like China, Korea, and India focused on improving their export efficiency and entering the interna- 31InAppendixE.4weincludeacommontradecostcomponentandshowthatourmainresultsarerobusttothis specification. 32TheimportanceofasymmetriesintradecostshasalsobeenhighlightedbyDix-Carneiro,Pessoa,Reyes-Heroles andTraiberman(2023).Theyshowthatthissourceofvariationisanimportantdriverofmanufacturingproduction andtradeimbalancesintheUSduetotheemergenceofChinaininternationalgoodsmarkets. 33Weassumethatthewithin-countrycomponentisonlypresentintheROW.Thisistoaccountforthefactthe othercountriesintheROWwentthroughsignificantlylargerchangesintradebarrierscomparetotheregionswithin theUS.However,imposingtimevaryingcostforthewithin-UStradeinasymmetricwaydeliversthesameresults. 34Forvaluesof𝜏 closeenoughtothehomebiasparameter𝜔,itgeneratesaqualitativelysimilarmechanismasthe relativedemandshocks,orhomebiasshocks,inPavlovaandRigobon(2007). TheyuseaCESfunctionoftheform 𝛾 𝐶 𝑡 +𝐼 𝑡 = [ (1−𝜔)𝛾 1 (𝑒−𝜔𝜉 𝑡)𝛾 1 𝑌 𝑅 𝛾 𝑡 𝛾 −1 +𝜔𝛾 1 (𝑒(1−𝜔)𝜉 𝑡)𝛾 1 𝑌 𝑈 𝛾 𝛾 − 𝑡 1 ] 𝛾−1 .Thatis,theirrelativedemandshockscanbeinterpretedas capturingchangesintradeintegrationwithintheROWaggregate. 35Thewithintradecostmayalsocapturecorrelatedicebergtradeshocksandproductivityshocks. Forexample, when𝜏 =1atradecostshockaffectsthedomesticandforeignpricesinEquation6equally,similarlytohowaTFP shock affects both prices through the marginal cost. However, they are not entirely isomorphic as the trade cost showsupintheresourceconstraintinEquation4whiletheproductivityshockdoesnot,andtheoppositehappens withthedemandsforinputsinEquation5. 16

tional market. These events resulted in lower costs of exporting to the US, as well as to other countriesintheROWaggregate. Largerpositivevaluesof𝜏 leadtohigherwithincountrytradecostsfortheROW,conditional on a positive iceberg cost shock. Since this leaves fewer ROW intermediates to be aggregated to produce the final good, the trade shock induce a negative effect on output in the ROW. The strength of the negative effect on output is increasing in 𝜏, and so is the effect on domestic absorption. Therefore, the cross country correlation of domestic absorption will vary with 𝜏. In Section7wepresentadetailedanalysisontheroleof𝜏 intheresponseofaggregatevariablesto tradeshocksandshowthatthecrosscountrycorrelationofdomesticabsorptionidentifies𝜏. Finally,weassumethatthefinancialshockfollowsanAR(1)process, 𝜓 = 𝜌 𝜓 +𝜖 𝑡 𝜓 𝑡−1 𝜓𝑡 where𝜌 isthepersistenceand𝜖 ∼ 𝑁(0,𝜎 ). 𝜓 𝜓𝑡 𝜓 MarketClearingandCountryBudgetConstraint Goods market clearing for each firm 𝑗 requires that its production is split between supply to theROWandtheUSandsatisfiesthelocaldemandineachmarket: 𝑦 𝑗𝑡 = 𝑒𝜉 𝑅𝑡𝑦 𝑗,𝑅𝑡 +𝑒𝜉 𝑅 ∗ 𝑡 𝑦 𝑗 ∗ ,𝑅𝑡 . WiththeaggregationpresentedinEquation2,thisleadstotheaggregatemarketclearingconditionwherethetotalproductionoftheROWissplitbetweendemandforcompositegoodsinthe ROWandtheUS: 𝑌 𝑡 = 𝑒𝜉 𝑅𝑡𝑌 𝑅𝑡 +𝑒𝜉 𝑅 ∗ 𝑡 𝑌 𝑅 ∗ 𝑡 . Lastly,combiningthehouseholdbudgetconstraintwithaggregateintermediateprofitsaswell asthemarketclearingconditionsabove,weobtaintheROWcountrybudgetconstraint:  𝐵∗ 𝜒 𝑡 𝑡+1 − 𝐵∗(1+𝑖∗ ) = 𝑇𝐵 − (𝐵∗ −𝐵̄ ) 2 with 𝑇𝐵 =  𝑃∗ 𝑌∗ −𝑃 𝑌 𝑒𝜓 𝑡 𝑡 𝑡−1 𝑡 𝑡2 𝑡+1 𝑡 𝑡 𝑅𝑡 𝑅𝑡 𝑈𝑡 𝑈𝑡 𝑡 where𝑇𝐵 isthenominaltradebalance. ThelogofNTisthelogofrealexport-importratio,given 𝑡 17

by 1 1 𝑛𝑡 = 𝛾 (𝑡𝑜𝑡 +𝑞 )+(𝑑∗ −𝑑 )+((1−𝜃∗)𝜉∗ −(1−𝜃)𝜉 )+(1−𝛾) 𝑛∗ − 𝑛 (8) 𝑡 𝑡 𝑡 𝑡 𝑡 𝑅𝑡 𝑈𝑡 ( 1−𝜃 𝑡 1−𝜃∗ 𝑡) where𝑡𝑜𝑡 isthelogofthetermsoftrade,𝑞 = log𝑄 thelogoftheRER,𝑑 = log𝐷 and𝑑∗ = log𝐷∗ 𝑡 𝑡 𝑡 𝑡 𝑡 𝑡 𝑡 arethelogofdomesticabsorptionintheUSandtheROWrespectively,and𝑛 and𝑛∗ arethelog 𝑡 𝑡 ofthemassofUSandROWexportersrespectively. Foradetailedderivationof𝑛𝑡 seeAppendix 𝑡 F.Finally,thebudgetconstraintoftheUSissatisfiedbyWalrasLaw. FinalGoodsPriceNormalization Wefixthefinalgoodpricesinbothcountries,𝑃 and𝑃∗,toone. Implicitlyweareassumingthat 𝑡 𝑡 the monetary authority in each country perfectly stabilizes inflation as in Itskhoki and Mukhin (2021). Thus the RER,  , is same as the nominal exchange rate,  , which is the price of ROW 𝑡 𝑡 currencyperunitofUScurrency. DefinitionofCompetitiveEquilibrium A competitive equilibrium is defined by a sequence for 𝑡 = 0,1,…,∞ of aggregate prices {𝑊 ,𝑊∗,𝑅𝑘,𝑅𝑘∗, ,𝑃 ,𝑃∗ ,𝑃 ,𝑃∗ ,𝑖 ,𝑖∗},firm-levelprices{𝑝 ,𝑝∗ ,𝑝 ,𝑝∗ },aggregateallo- 𝑡 𝑡 𝑡 𝑡 𝑡 𝑅𝑡 𝑅𝑡 𝑈𝑡 𝑈𝑡 𝑡 𝑡 𝑗,𝑅𝑡 𝑗,𝑅𝑡 𝑗,𝑈𝑡 𝑗,𝑈𝑡 cations{𝐶 ,𝐶∗,𝐿 ,𝐿∗,𝐼 ,𝐼∗,𝐵∗ ,𝐵 ,𝑌 ,𝑌∗ ,𝑌 ,𝑌∗ ,},firm-levelallocations {𝑦 ,𝑦∗ ,𝑦 ,𝑦∗ }, 𝑡 𝑡 𝑡 𝑡 𝑡 𝑡 𝑡+1 𝑡+1 𝑅𝑡 𝑅𝑡 𝑈𝑡 𝑈𝑡 𝑗,𝑅𝑡 𝑗,𝑅𝑡 𝑗,𝑈𝑡 𝑗,𝑈𝑡 firm-levelinputchoicesandexportdecisions,andthemassofexporters{𝑁 ,𝑁∗},suchthat 𝑡 𝑡 1. Givenprices{𝑊 ,𝑊∗,𝑅𝑘,𝑅𝑘∗, ,𝑖 ,𝑖∗},{𝐶 ,𝐿 ,𝐼 ,𝐵 ,𝐵∗ }solvestheproblemoftheROW 𝑡 𝑡 𝑡 𝑡 𝑡 𝑡 𝑡 𝑡 𝑡 𝑡 𝑡+1 𝑡+1 households,and{𝐶∗,𝐿∗,𝐼∗,𝐵∗ }correspondinglyfortheUShouseholds. 𝑡 𝑡 𝑡 𝑡+1 2. Givenprices{𝑝 ,𝑝∗ ,𝑝 ,𝑝∗ },{𝑦 ,𝑦∗ ,𝑦 ,𝑦∗ }solvestheprobleminthefinalre- 𝑗,𝑅𝑡 𝑗,𝑅𝑡 𝑗,𝑈𝑡 𝑗,𝑈𝑡 𝑗,𝑅𝑡 𝑗,𝑅𝑡 𝑗,𝑈𝑡 𝑗,𝑈𝑡 tailsectorsintheROWandtheUS. 3. Firm-level input choices, prices, and export decisions solve the firm’s dynamic programmingproblems. 4. Themarketclearingconditionsforgoods,laborandbondsaresatisfied. 5. Rationalityholds,sothatthelawsofmotionsareconsistentwithagents’decisionrules. 18

4 Calibration We use data for the period 1980Q1-2019Q4 for the US and ROW to discipline our model.36 The detailsaboutthedataareinAppendixA. 4.1 BenchmarkModel We have three sets of calibrated parameters. First, we exogenously calibrate parameters that are standard in the literature. Second, we calibrate the parameters that are related to the export behavior of firms using firm level data. Third, we jointly calibrate the parameters related to the shocks processes, the pricing to market friction and adjustment costs to match a set of equal numberofmoments. StandardParameters ThestandardparametersthatareexogeneouslycalibratedaredisplayedinpanelAofTable1. Thetimeunitinthemodelisaquarter,andwechooseadiscountfactorof𝛽 = 0.99,whichimplies an annual interest rate of 4 percent. The depreciation rate is set to 𝛿 = 0.02. The risk aversion is 𝜎 = 2, a value frequently used in related business cycle studies. The labor share of 𝛼 = 0.64 is consistent with the share in the US. The preference weight on consumption is 𝜂 = 0.36, set to matchthesteadystatelaborof1/4. TheelasticityofsubstitutionbetweenROWandUSgoods,𝛾, issettobe1.5,followingtheestimatesinFeenstra,Luck,ObstfeldandRuss(2018). Theelasticity ofsubstitutionacrossvarieties𝜃 issetto4tomatchaproducermarkupof33percent. Thehome bias, governed by 𝜔, is set to match the average trade share of 14 percent in the US during our sampleperiod. WeassignthesevaluessymmetricallytotheUSandtheROW.Finally,wesetthe persistence of the common and differential productivity shocks, 𝜌 and 𝜌 , to be equal to 0.97, 𝑎 𝑎 𝑑 𝑐 followingItskhokiandMukhin(2021). ProducerTradeParameters One of the benefits of modeling the dynamic trade with the microfoundations of the sunk exporting cost is that we can directly use exporter data to pin down the producer parameters. 36TheROWaggregateincludesCanada,Finland,Germany,Ireland,Italy,Japan,RepublicofKorea,Spain,Sweden andUnitedKingdom.Thissetofcountriesrepresents60percentoftotalUStradeonaverage.Theestimatedmoments fromthedataarerobusttohavinganunbalancedpanelthatincludesChinasince1990. 19

Table1: CalibratedParameters Parameter Value TargetMoment A.StandardParameters Discountfactor 𝛽 0.99 Annualinterestrateof4% Riskaversion 𝜎 2 Intertemporalelasticityofsubstitutionof.5 Weightonconsumption 𝜂 0.36 Hoursworked(Frischelasticity) Laborshare 𝛼 0.64 Laborshareofincome Elasticityofsubstitutionacrossvarieties 𝜃 4 Producermarkupof33% ElasticityofsubstitutionbetweenHandF 𝛾 1.5 Long-runpriceelasticity Depreciationrate 𝛿 0.02 Homebias 𝜔 0.097 Trade-to-GDPratioof14% Commonproductivity,persistence 𝜌 0.97 GDPpersistence 𝑎𝑐 Differentialproductivity,persistence 𝜌 0.97 GDPpersistence 𝑎 𝑑 B.ProducerTradeParameters Fixedcostofnewexporters 𝑓0 0.14 Exportparticipationof20% Fixedcostofincumbentexporters 𝑓1 0.04 Exitrateof2.5% Volatilityofidiosyncraticproductivity 𝜎 0.15 Exporterpremiumof50% 𝜇 C.Shocks,AdjustmentCostsandPricingtoMarket Commonproductivity,volatility 𝜎 0.004 𝜎(Δ𝑦∗) 𝑎𝑐 Differentialproductivity,volatility 𝜎 0.006 𝑐𝑜𝑟(Δ𝑦,Δ𝑦∗) 𝑎 𝑑 Financialshock,volatility 𝜎 0.001 𝑐𝑜𝑟(Δ𝑐−Δ𝑐∗,Δ𝑞) 𝜓 Financialshock,persistence 𝜌 0.989 𝑎𝑢𝑡𝑜𝑐𝑜𝑟(𝑖−𝑖∗) 𝜓 Tradeshock,volatility 𝜎 0.049 𝜎(𝑛𝑡)/𝜎(𝑞) 𝜉 Tradeshock,persistence 𝜌 0.985 𝑐𝑜𝑟(Δ𝑛𝑡,Δ𝑞) 𝜉 Tradeshock,within-countryshare 𝜏 0.152 𝑐𝑜𝑟(Δ𝑑,Δ𝑑∗) Adjustmentcostofportfolios 𝜒 0.012 𝑎𝑢𝑡𝑜𝑐𝑜𝑟(𝑛𝑡) Adjustmentcostofcapital 𝜅 2.219 𝜎(𝑖𝑛𝑣∗)/𝜎(𝑦∗) Pricingtomarketparameter 𝜁 0.940 𝑐𝑜𝑟(Δ𝑡𝑜𝑡,Δ𝑞) Notes:Thetablepresentsthevaluesofcalibratedparametersofthebenchmarkmodel.Whenweconsideralternative models,someoftheparametersaresettoadifferentvaluewhiletheotherparametersareallrecalibrated.Inamodel withouttradeshocks,𝜎 =𝜌 =0. Inamodelwithouttradedynamics,𝑓0 =𝑓1 =𝜎 =0. InPanelC,thelowercases 𝜉 𝜉 𝜇 indicatethatvariablesareinlogs,forexample,𝑞 ≡ln()islogoftheRER. 20

We calibrate three parameters related to the export block: fixed costs of exporting for new and incumbentexporters,𝑓0 and𝑓1,andthevolatilityofidiosyncraticproductivityshocks,𝜎 . These 𝜂 parametersaredisplayedinpanelBofTable1. Thefixedcostsandthevolatilityaresettojointly matchfirmlevelmomentsonexporterdynamics. Inparticular,wetargetanexportparticipation of 20 percent, a quarterly exporter exit rate of 2.5 percent, and a size of exporters 50 percent largerthannon-exporters. TheseareconsistentwiththeUStradeandexportercharacteristicsin theearly1990s(BernardandBradfordJensen,1999;AlessandriaandChoi,2014). Shocks,AdjustmentCostsandPricingtoMarket The remaining parameters to calibrate are those related to trade, financial, and productivity shocks, the pricing to market friction, and the adjustment costs for capital and debt. There are tenparameterstobeestimated. Wejointlycalibratethemtomatchtenmoments. Wepresentthe parameters and moments used for the identification in Panel C of Table 1. We display the values ofthecalibratedparameters,togetherwiththemomentthatismostrelevantfortheidentification ofeachparameter. The volatility of the common productivity shock, identified mainly by the volatility of GDP growth, is found to be 0.004. The estimated volatility of the differential productivity shock, identified by the cross country correlation of the first difference of GDP, is 0.006. Given that both processes have a persistence of 0.97, this implies that the differential component of the productivityshocksslightlydominatesthecommonone. WefollowItskhokiandMukhin(2021)andidentifythevolatilityofthefinancialshockusing the Backus-Smith-Kollmann correlation. We find a value of 0.001 for the volatility of financial shocks. Hence,thevolatilityofproductivityshocksisestimatedtobebetween4to6timeslarger thanthatoffinancialshocks. ThisishigherthanthevaluesfoundinItskhokiandMukhin(2021), between 2.5 and 3.3.37 The persistence of financial shocks is identified by the autocorrelation of theinterestratedifferential. Weestimateapersistenceof0.989,closetowhathasbeenestimated intheliterature. WeidentifythevolatilityoftradeshocksusingthevolatilityofNTrelativetothevolatilityof the RER, similar to Itskhoki and Mukhin (2017) for the case of foreign demand shocks. The persistenceofthetradeshockisidentifiedbythecontemporaneouscorrelationbetweenthegrowth 37NotethatthemodelinItskhokiandMukhin(2021)doesnothavetradeshocksanddynamictrade. 21

ratesofNTandtheRER.Wefindthatthevolatilityandpersistenceoftradeshocksare0.049and 0.985, respectively. Hence, trade shocks are found to be more volatile but slightly less persistent than financial shocks. However, the propagation effects of trade shocks depends on the value of the home bias parameter (𝜔). The ratio 𝜔𝜎 /𝜎 is around 4.75, higher than the values identified 𝜉 𝜓 in Itskhoki and Mukhin (2017) for the ratio of the volatility of the foreign demand shock to the financialshock,between2.4and2.7. The within-country elasticity of domestic to foreign trade costs, 𝜏, is identified using the cross-country correlation of the growth rates of domestic absorption. Since 𝜏 imposes a wedge in the aggregation of intermediate goods, it affects the response of the supply of final goods to trade shocks, ultimately impacting domestic absorption. We present a detailed analysis on the roleof𝜏 inSection7. The adjustment cost of capital directly affects the volatility of investment relative to that of GDP, while the adjustment cost of debt directly affects the autocorrelation of NT. We find an adjustmentcostofcapitalof2.219andandadjustmentcostofdebtof0.012. Finally,wediscipline thepricingtomarketfrictionusingthecorrelationbetweenthegrowthratesofthetermsoftrade and the RER, since this friction induces a wedge between them. We find a value of 𝜁 = 0.940, which implies an exchange rate pass-through of 69 percent, in line with the estimated values in theliterature(GopinathandItskhoki,2010). 4.2 AlternativeModels We consider three alternative specifications to our benchmark model to understand the role of each feature in our model: trade shocks, financial shocks, and dynamic trade. We recalibrate modelswhenoneofthesefeaturesisabsent. Thecalibratedvaluesofthesemodelsareshownin TableH.2. For the model without trade shocks, we set to zero the volatility and persistence of trade shocksandthewithin-ROWtradecost,andrecalibratetheremainingparameters. Wetargetthe samemomentsconsideredbefore,exceptforthevolatilityofNT,itscontemporaneouscorrelation withtheRER,andthecross-countrycorrelationofthegrowthrateofdomesticabsorption.38,39 38Weexcludethecross-countrycorrelationofdomesticabsorptionfromthetargetsincethewithin-ROWtrade costisabsentinthismodel. 39WealsoshowinSection7thatamodelwithouttradeshocksbutwithamoresophisticatedfinancialshock,in 22

Inthemodelwithoutfinancialshocks,wesettozerothevolatilityandpersistenceoffinancial shocks. WedropastargetsthecontemporaneouscorrelationbetweenthegrowthrateoftheRER andNT,andtheirrelativevolatility.40 For the model without dynamic trade, we set to zero the fixed costs of exporting for new andincumbentexportersandthevolatilityofidiosyncraticshocks. Giventhesevalues,theother parametersrelatedtoshocksandadjustmentcostsareestimatedinthesamewayasinthebenchmarkmodel. Wefindahighervolatilityandalowerpersistenceofbothfinancialandtradeshocks in the model with no dynamic trade, since the presence of dynamic trade endogenously raises thepersistenceinducedbyshocksontheRERandNT. 5 Results In this section, we present the results of our model. We first show that our benchmark model successfully replicates the targeted moments, including the RER and NT moments at the high frequency. WethenshowthatthemodelisabletocapturetheRERandNTdynamicsatthewhole spectrum of frequencies, in terms of their comovement and the frequency decomposition of the variances. Finally,weshowthatthemodelaccountsfortheRERdisconnectpuzzlesandstandard internationalbusinesscyclemoments. Throughoutthissection,weemphasizetheimportanceof includingallthreefeatures—financialshocks,tradeshocks,andtradedynamics—inthemodelto effectivelycapturethesepatterns. 5.1 TheRERandNTattheHighFrequency TheresultsofthebenchmarkmodelforthetargetedmomentsarepresentedinPanelAofTable 2 (column 2). The model closely matches all of the targeted moments, such as the volatility and cross-country correlation of output. It also successfully generates the imperfect correlation particularamixoftwoAR(1)processeswithdifferentpersistence’s,isstillunabletocapturetheNTmomentsatthe highfrequency. 40Alternatively,inthemodelwithoutfinancialshockswecoulddroptheBackus-Smith-Kollmanncorrelationand keepthecontemporaneouscorrelationbetweenthegrowthrateoftheRERandNT.However,sincetradeshocksare abletomatch theBackus-Smith-Kollmanncorrelation, duetotherole ofthewithin-ROWtradecost, wechose to keeptheBackus-Smith-Kollmanncorrelationanddropthecontemporaneouscorrelationbetweenthegrowthrateof theRERandNTtoshowthatthismodelalsofailstocapturethelattercorrelation.Hence,conditionalonmatching theBackus-Smith-Kollmanncorrelation, inordertomatchthehighfrequencycomovementbetweentheRERand NTweneedbothfinancialandtradeshocks. 23

betweentermsoftradeandtheRER. More importantly, the benchmark model accurately reproduces the comovement of the RER and NT. First, our model exactly matches the contemporaneous correlation of the RER with NT, 𝑐𝑜𝑟 (Δ𝑛𝑡,Δ𝑞). In data, the RER and NT exhibits a relatively weak connection at high frequencies, with a correlation of 0.3. Our model successfully accounts for this weak correlation. Both financial and trade shocks are necessary to capture this pattern. To see this, consider two alternative models: the model without trade shocks (column 3 of Table 2) and the model without financialshocks(column4ofTable2). Whenthemodelisrecalibratedwithouttradeshocks,the correlation between two variables is too high (0.89) compared to data. On the other hand, when financial shocks are absent, the correlation is too low (-0.94). This is because financial shocks generateapositivecorrelationbetweentheRERandNTuponimpact,whereastradeshockslead toanegativecorrelation.41 Second,ourmodelsuccessfullyreplicatestherelativevolatilityofNTtotheRER,𝜎(𝑛𝑡)/𝜎(𝑞). Inthedata,NTandtheRERexhibitroughlyequalvolatility,withNTbeing1.21timesmorevolatile than the RER. Our model effectively captures this pattern. Again, it requires incorporating both trade and financial shocks: in a model without trade shocks, the volatility of NT relative to the RER becomes too high (1.75), while without financial shocks, this ratio decreases significantly (0.74). Thatis,financialshocksgeneratetoolargevolatilityinNTrelativetotheRER.Thisexcess volatilityinducedbyfinancialshockshasalsobeennotedbyMiyamoto,NguyenandOh(2022). Hence,havingbothshocksisnecessaryforcapturingthehighfrequencymomentsrelatedto theRERandNT.42 5.2 ComovementbetweentheRERandNT WeshowthatthemodelcapturesthecomovementbetweentheRERandNTatlowerfrequencies withoutdirectlytargetingthem. WefocusonthecorrelationbetweenthegrowthratesoftheRER and NT at different horizons. To complement this analysis, we also estimate the elasticity of NT 41WhenfinancialshocksgenerateanexcessreturnonbondsfortheUSrelativetotheROW,theexcesssavingsis exportedtotheROW(USNTincreases),USaggregatedemandfalls,andtheUSRERdepreciates.Ontheotherhand, tradeshocksthatraisetherelativecostofexportingfortheUSleadstoadeclineinitsNT,andthesupplyoffinal goodsintheUSincreases,causingitspricetofall(theUSRERdepreciates).SeeSection6.2foradetaileddiscussion onthepropagationmechanismofthetwoshocks. 42Fukui,NakamuraandSteinsson(2023)alsohighlightthatfinancialshockalonecannotcapturethejointdynamicsofRERsandmacroaggregates,althoughtheyfocusonthematchingofconditionalmoments. 24

Table2: ModelResults (1) (2) (3) (4) (5) Moments Data Benchmark NoTradeShock NoFinancialShock NoDynamics A.TargetedMoments 𝑐𝑜𝑟(Δ𝑛𝑡,Δ𝑞) 0.30 0.30 0.89† -0.94† 0.30 𝜎(𝑛𝑡)/𝜎(𝑞) 1.21 1.21 1.75† 0.74† 1.21 𝜎(Δ𝑦∗) 0.007 0.007 0.007 0.007 0.007 𝑐𝑜𝑟(Δ𝑦,Δ𝑦∗) 0.40 0.43 0.39 0.39 0.41 𝑐𝑜𝑟(Δ𝑐−Δ𝑐∗,Δ𝑞) -0.10 -0.10 -0.10 -0.10 -0.10 𝑎𝑢𝑡𝑜𝑐𝑜𝑟(𝑖−𝑖∗) 0.87 0.87 0.88 0.96 0.88 𝑎𝑢𝑡𝑜𝑐𝑜𝑟(𝑛𝑡) 0.98 0.97 0.96 0.97 0.94 𝜎(𝑖𝑛𝑣∗)/(𝑦∗) 2.21 2.16 2.21 2.15 2.19 𝑐𝑜𝑟(Δ𝑑,Δ𝑑∗) 0.34 0.32 0.26† 0.35 0.33 𝑐𝑜𝑟(Δ𝑡𝑜𝑡,Δ𝑞) 0.49 0.49 0.49 0.49 0.49 B1. FrequencyDecompositionofRER Highfrequency 0.07 0.07 0.10 0.05 0.07 Businesscyclefrequency 0.31 0.21 0.29 0.18 0.19 Lowfrequency 0.62 0.72 0.60 0.77 0.74 B2. FrequencyDecompositionofNT Highfrequency 0.06 0.07 0.08 0.07 0.09 Businesscyclefrequency 0.30 0.24 0.32 0.19 0.23 Lowfrequency 0.64 0.69 0.60 0.74 0.68 C.DisconnectPuzzles 𝜎(𝑞)/𝜎(𝑦∗) 2.23 2.53 1.41 2.14 2.77 𝜎(Δ𝑞)/𝜎(Δ𝑦∗) 3.90 3.02 2.89 1.59 3.76 𝑎𝑢𝑡𝑜𝑐𝑜𝑟(𝑞) 0.97 0.97 0.93 0.99 0.97 𝛽 -1.34 0.42 0.23 0.90 -4.19 𝑓𝑎𝑚𝑎 𝑅2 0.04 0.01 0.00 0.81 0.16 𝑓𝑎𝑚𝑎 𝑐𝑜𝑟(𝑞,𝑖−𝑖∗) -0.50 -0.36 -0.41 -0.27 -0.27 𝑎𝑢𝑡𝑜𝑐𝑜𝑟(𝑖) 0.93 0.93 0.93 0.95 0.93 𝜎(𝑖−𝑖∗)/𝜎(Δ𝑞) 0.15 0.04 0.06 0.08 0.04 Notes: ‘NoTradeShock’presentstheresultofre-calibratedmodelonlywithproductivityandfinancialshocks. ‘No FinancialShock’presentstheresultofre-calibratedmodelonlywithproductivityandtradeshocks.‘NoDynamics’ is for the model without fixed exporting costs and producer heterogeneity. Superscript † in Panel A denotes that the moment is not targeted during the calibration procedure. The empirical moments for the level of GDP and investmentwerecalculatedusingthecyclicalcomponentfromalinearde-trend. 25

Figure2: DynamicCorrelationbetweenRERandNTFlows 1 0.8 0.6 0.4 0.2 Data 0 Benchmark No Dynamics No Dynamics & No Trade Shocks -0.2 1 2 3 4 5 6 7 8 Quarters Notes: Wecalculatethedynamiccorrelationsas𝑐𝑜𝑟(Δ ℎ 𝑞 𝑡 ,Δ ℎ 𝑛𝑡 𝑡 ),where𝑞 𝑡 and𝑛𝑡 𝑡 arelogof theRERandtheexport-importratio,respectively,andΔ denotesℎ−quarterdifference. ‘No ℎ Dynamics&NoTradeShocks’correspondstothemodelwithoutfixedexportingcosts,firm heterogeneity,andtradeshocks. topricesintheshortandlongrunusinganerrorcorrectionmodel,whichwereportinAppendix D.Ourmainfindingisthat,conditionalonhavingbothfinancialandtradeshocks,dynamictrade isnecessarytocapturethedifferentialcomovementbetweentheRERandNT. To capture the differential comovement between the RER and NT, consider the correlation between the growth rates of the RER and NT at different horizons. In Figure 2, we plot the correlationbetweentheℎ−quartergrowthratesoftheRERandNTinthedata(solidblackline). Whilethecontemporaneouscorrelationatℎ = 1is0.30,thecorrelationgraduallyincreasesover the horizon, reaching a value of 0.48 at the 8-quarter growth rate. The growth rates of RER and NTpresentastrongercomovementinthelongerthanintheshorterrun. The benchmark model successfully captures the dynamic correlation between the RER and NT, without being targeted except for the contemporaneous correlation (blue line with circles). The contemporaneous correlation in the model is 0.30, while for the 8-period growth rate it is 0.48 as in the data.43 The green dotted line shows the results for the model without trade 43Wealsoconsiderusingthetrade-expenditureratioasameasureofNT,definedas𝑇𝐸 𝑡 = log 𝑀 𝑋 𝑡 −log𝐷 𝐷 𝑡 ∗. Using thetrade-expenditureratioallowsustoisolatethesubstitutioneffectthatchangesintheRERgene𝑡rateonN𝑡 Tfrom theeffectonrelativeexpenditure. AsshownininFigureH.5, theRERandNTpresentastrongercomovementin thelongrunthantheshortrunevenaftercontrollingforrelativeexpenditure.Ourmodelsuccessfullycapturesthis pattern. 26

dynamics where we also shut down the trade shock, so that financial shocks are the dominant driversoftheRERandthemodelhasstatictrade,asintherecentliterature(ItskhokiandMukhin, 2021). Aswearguedbefore,thesetypesofmodelsimplyanalmostperfectcorrelationatthehigh frequency, shown by a contemporaneous correlation close to one. However, these models also missthedynamiccomovementastheyimplyanalmostconstantpatternforthecorrelationaswe increasethehorizon. Hence,modelsdrivenbyfinancialshocksdevelopedintherecentliterature missthedynamiccomovementbetweentheRERandNTacrosshigherandlowerfrequencies. The violet line with crosses shows the result for the model with trade and financial shocks butnotradedynamics(Column5inTable2). Thisversionalsomissesthedynamiccomovement between the RER and NT. When comparing to the benchmark model (blue line with circles) it becomesapparentthatthepresenceofdynamictradeallowsthemodeltogenerateacomovement betweentheRERandNTthatisweakerathigherfrequenciesandstrongeratlowerfrequencies. Hence, dynamic trade plays a crucial role in the ability of the benchmark model to account for thesemoments. We also consider the cases in the absence of shocks but in the presence of dynamic trade (Columns3and4inTable2). InFigureH.6,weplotthedynamiccorrelationforthemodelswith nofinancialandnotradeshocks. Absenteitherfinancial(dashedredline)ortradeshocks(dashdotted green line), the model fails to capture the differential co-movement, even under dynamic trade. Asbefore,weobservethatfinancialshocksinduceanalmostperfectcorrelationacrossthe eight quarter horizon between these variables, while trade shocks induce a strong negative one, althoughthecorrelationisincreasinginthiscaseasitisinthedata. Thisreinforcesourresultthat both shocks are needed for capturing the comovement. Therefore, conditional on having both financial and trade shocks, dynamic trade is necessary to capture the differential co-movement observedinthedata. Finally,wefindsimilarresultsifweestimatetheshortandlongrunelasticityofNTtoprices throughanerrorcorrectionmodel,whichwereportinAppendixD. 5.3 SpectrumAnalysis WenowturntostudytheabilityofthemodeltocapturethespectrumoftheRERandNTflows, which are not targets in our calibration. We consider the spectrum to study the dynamics rep- 27

resentedatthefrequencydomaininsteadofthetimedomain(Hamilton,2020). Itisusefulsince it allows to decompose the variance of these variables into different frequencies. That is, the sumofthespectrumforallfrequenciesequalsitsunconditionalvariance. Weestimatethespectrumnon-parametricallyusingthemodifiedBartlettkernel. Forthedetailsonthisapproach,see AppendixB. Figure3showsthespectrumoftheRERinthedata(blacksolidline). Wefindthatthespectrum is the highest at the zero frequency, and decreasing as the frequency increases. The standard businesscyclefrequency,cyclesbetween8to32quarters,isrepresentedbytheshadedgreyarea. Theareaunderthespectrumforthefrequencylowerthanthebusinesscycleismuchlargerthan that for the frequency of business cycles. In particular, it takes about 62 percent of its variance, aspresentedinPanelB1ofTable2(column1). We now turn to estimate the spectrum of the RER using model simulated data.44 The benchmark model (blue line with circles) captures well the size and shape of the spectrum of the RER, eventhoughitisnotatargetinourcalibration. Theshapeofthespectrumcanbemappedtothe share of the variance of the RER arising at different frequencies, which is displayed in Panel B1 ofTable2. Inthemodel,thelargestshare(72percent)oftheRERvariationisassignedtothelow frequency,followedbythebusinesscyclefrequency(21percent),andthenthehighfrequency(7 percent). Dynamic trade contributes to matching the RER spectrum. To see this, consider the recalibrated model without dynamic trade (violet line with crosses). It is evident that the overall size and the shape of the RER spectrum in this model is worse than in our benchmark case. The unconditional volatility of the RER relative to GDP in the model is higher than in the data, 2.77 and 2.21 respectively (Panel C in Table 2). Moreover, a larger share of the RER variance is attributedtothelowfrequency(74percent)thaninthebenchmarkmodel(72percent). Thisresult is consistent with the “Excess Persistence Puzzle” documented by Rabanal and Rubio-Ramirez (2015). The intuition for this result is the following. When trade is static, quantities in the short runaremoreelasticthanunderdynamictrade. Therefore,pricesintheshortrunhaveaweaker response absent trade dynamics, so a higher share of the RER variance is assigned to low fre- 44Wesimulatethemodelfor10,000periodsandburnthefirsthalf.WeshowinSections7andE.2thattheresult isrobusttousingmultiplesamplesofshorterperiods. 28

Figure3: SpectrumoftheRER 0.03 Data Benchmark Model 0.025 No Trade Dynamics 0.02 0.015 0.01 0.005 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Frequency Notes:Thegraphisenlargedforthefrequencyof[0,1],asthespectrumon[1,𝜋]isnearzero. ThefullgraphispresentedinFigureB.1. Grayareashowstherangeofthefrequenciesfor thebusinesscycle.Thebluelinewithcirclesshowstheresultinthebenchmarkmodel,while thevioletlinewithcrossesshowstheresultofthemodelrecalibratedwithnosunkcostof exporting. quency fluctuations. Once we incorporate dynamic trade, quantities in the short-run are more inelastic and prices need to adjust more to clear the market. This leads to a redistribution from the lower to the higher frequencies. However, since the deterioration on the shape of the spectrum of the RER is only modest absent dynamic trade, this moment may not be well suited for distinguishing between alternative models. Especially the model without trade shocks (Table 2 column3)generatesaspectrumdecompositionasinthedata.45 5.4 DisconnectwithMacroFundamentals ThereareseveralmomentsrelatedtheRERandmacrofundamentals,socalledpuzzles,thathave been hard to explain in existing models. First, empirically, the RER follows a near random-walk processandisthreetosixtimesmorevolatilethanoutput,whilestandardBKK-typemodelsgeneratelowRERvolatilityandpersistence(Meese-RogoffPuzzle).46 Second,thecorrelationbetween thegrowthratesofrelativeconsumptionandtheRERisnegativeinthedata,contradictingmod- 45Thisdoesnotimplythatproductivityshocksinthealternativemodelgeneratethelow-frequencymovements intheRERinthesamewaythattradeshocksdo.SeeSection6.2foradetaileddiscussion. 46BKKstandsforBackusetal.(1994). 29

els’ strong positive correlation implied by the risk-sharing condition (Backus-Smith-Kollmann Puzzle). Third,thereisafinancialdisconnectsummarizedbytheFama(1984)regression, 𝔼 [Δ𝑞 ] = 𝛼 +𝛽 (𝑖 −𝑖∗)+𝑢 . (9) 𝑡 𝑡+1 𝐹𝑎𝑚𝑎 𝑡 𝑡 𝑡+1 wherestandardmodelspredict𝛽 = 1,indicatinghigherinterestratesleadtoRERdepreciation. 𝐹𝑎𝑚𝑎 However, empirical estimates yield 𝛽 < 1, often negative, and weak predictive power (𝑅2 ≈ 𝐹𝑎𝑚𝑎 0).47 Our benchmark model is able to generate these patterns of disconnect.48 The results are presentedinPanelCofTable2. While the role of financial shocks in driving the disconnect has been studied (Itskhoki and Mukhin, 2021, 2025a), and hence the ability of the benchmark model to generate these moments isnotsurprising,theimportanceoftradeshocksinexplainingthedisconnectremainsrelatively underexplored. In this section, we show that trade shocks alone can generate dynamics of the RERconsistentwiththerealdisconnectbutnotthefinancialdisconnect. First, trade shocks generate a RER that is more volatile than GDP. Although absent financial shocks the volatility of the RER relative to GDP falls, both in first difference and levels, the ratio isstillgreaterthanone. Furthermore,inthemodelwithoutfinancialshockstherelativevolatility ofthelevelsis2.14,veryclosetothevalueinthedataof2.23. Thereasonwhytradeshocksaffects more the level of the volatility of the RER is because of its effect on the autocorrelation of the RER, which increases from 0.97 in the benchmark model to 0.99 in the model without financial shocks. AswillbeexplainedinSection6.2thisarisesfromamorepersistentgeneralequilibrium effect of trade shocks due to its effect on the budget constraint. This means that trade shocks generate a near-random walk behavior in the RER. Finally, absent financial shocks the model generatesalowBackus-Smith-Kollmanncorrelation,whichisevennegative(BackusandSmith, 1993;Kollmann,1995). Hence,tradeshockscontributetoaccountingfortherealdisconnect. ItisimportanttonoticethatthenegativevalueoftheBackus-Smith-Kollmanncorrelationis 47Strictlyspeaking,theFamaregressionisusedtoshowthedisconnectfornominalvariables(ForwardPremium Puzzle). In this paper we consider a real version of the puzzle. In Table H.5 in Appendix H we present the Fama coefficientwefindusingbothrealandnominaldata,whichisverysimilartoeachother. Thisarisesfromthehigh correlationbetweentheRERandtheNER. 48Engel,Kazakova,WangandXiang(2022)emphasizesthatthelow𝑅2 oftheFamaregressionisamorerobust statisticforthefinancialdisconnectthanthenegativecoefficient.Inourbenchmarkmodel,wehaveasmall𝑅2,and thuswearguethatthemodeldoesafairlygoodjobaccountingforthefinancialdisconnect. 30

duetothepresenceofthewithintradecostintheROW.When𝜏 > 0,atradeshockthatreduces the export cost for the ROW, and reduces the import cost from the US, also reduces the cost of delivering goods within the ROW. While the first effect appreciates the RER, the second boosts ROWconsumption,creatinganegativeBackus-Smith-Kollmanncorrelation.49 On the other hand, the model without financial shocks fails to account for the financial disconnect, or Forward Premium puzzle (Fama, 1984). Absent the financial shock (column 4), the Fama coefficient and the 𝑅2 increases significantly, showing the importance of financial shocks for capturing the financial disconnect, consistent with the results in Itskhoki and Mukhin (2021, 2023).50 Finally, recent work by Kekre and Lenel (2024) emphasizes that models in which the RER is mainly driven by financial shocks lead to a counterfactual correlation between the interest rate differentialandtheRER,andproposeaddingdiscountfactorshockstofixthisissue. However,the presenceofdynamictraderesolvestheissueevenwithoutadditionalshocks,ascanbeseenfrom column (3) ‘No Trade Shock’ in Table 2.51 The presence of trade frictions dampens the effect of financial shocks on consumption growth, making it negative in the early periods which triggers a fall in the interest rate differential in response to the shock, while the RER depreciates.52 This results in a negative correlation between the interest rate differential and the RER, 𝑐𝑜𝑟(𝑞,𝑖 −𝑖∗), asinthedata. Furthermore,absentdynamictrade,themodelreproducesthenegativecorrelation due to the presence of trade shocks (column (5) ‘No Dynamics’ in Table 2).53 Therefore, both dynamic trade and trade shocks offer alternative resolutions to the counterfactual correlation betweentheinterestratedifferentialandtheRERinstandardfinancialshockmodels. 49When 𝜏 > 0 the trade shock mechanism operates similarly to the home bias or domestic demand shocks in PavlovaandRigobon(2007). 50Potentially,tradeshocks(andproductivityshocks)couldaccountforthefinancialdisconnect,sincetheygenerate changes in net foreign assets that induce UIP deviations through the adjustment cost of debt (Equation 1). However,wefindthatthisindirecteffectisquantitativelysmall. 51As shown in the variance decomposition of Table H.6, financial shocks drive the RER variation in this model acrossallhorizons. 52SeeFigureH.9foracomparisonoftheIRFstofinancialshocksinstaticanddynamictrademodels. 53SeeFigureH.10fortheIRFstotradeshocks. 31

5.5 InternationalBusinessCycleMoments Ourbenchmarkmodelisalsoconsistentwiththestandardinternationalbusinesscyclemoments. We report the results in Table 3. The model is able to capture a volatility of consumption that is lowerthanoutput. Itgeneratesacrosscountrycorrelationofconsumptionandinvestmentvery close to the data. Overall, we find that our benchmark model accounts for the dynamics of the RERandNTatthewholespectrumoffrequencies,withoutcompromisingtheabilitytoaccount fortherealandfinancialpuzzles,andotherinternationalbusinesscyclemoments. Table3: InternationalBusinessCycleMoments (1) (2) (3) (4) (5) Data Benchmark NoTradeShock NoFinancialShock NoDynamics 𝜎(Δ𝑐∗)/𝜎(Δ𝑦∗) 0.83 0.57 0.55 0.50 0.66 𝑐𝑜𝑟(Δ𝑦∗,Δ𝑐∗) 0.65 0.96 0.97 0.99 0.98 𝑐𝑜𝑟(Δ𝑦∗,Δ𝑖𝑛𝑣∗) 0.78 0.98 0.96 0.99 0.91 𝑐𝑜𝑟(Δ𝑐,Δ𝑐∗) 0.31 0.24 0.34 0.46 0.46 𝑐𝑜𝑟(Δ𝑖𝑛𝑣,Δ𝑖𝑛𝑣∗) 0.31 0.24 0.19 0.25 0.18 𝑎𝑢𝑡𝑜𝑐𝑜𝑟𝑟(𝑦∗) 0.99 0.98 0.98 0.98 0.98 𝑎𝑢𝑡𝑜𝑐𝑜𝑟𝑟(𝑐∗) 0.99 0.99 0.99 0.99 0.99 𝑎𝑢𝑡𝑜𝑐𝑜𝑟𝑟(𝑖𝑛𝑣∗) 0.98 0.96 0.96 0.95 0.95 𝜎(Δ𝑡𝑜𝑡)/𝜎(Δ𝑞) 0.46 0.03 0.02 0.13 0.10 𝑐𝑜𝑟(Δ𝑡𝑜𝑡,Δ𝑞) 0.49 0.49 0.49 0.49 0.49 𝑐𝑜𝑟(Δ𝑛𝑡,Δ𝑡𝑜𝑡 +Δ𝑞) 0.32 0.32 0.90 -0.92 0.22 𝑐𝑜𝑟(𝑛𝑡,𝑡𝑜𝑡 +𝑞) 0.39 0.41 0.83 -0.07 -0.03 𝑐𝑜𝑟(𝑖−𝑖∗,𝑡𝑜𝑡 +𝑞) -0.46 -0.36 -0.39 -0.30 -0.30 Notes: ‘NoTradeShock’presentstheresultofre-calibratedmodelonlywithproductivityandfinancialshocks. ‘No FinancialShock’presentstheresultofre-calibratedmodelonlywithproductivityandtradeshocks.‘NoDynamics’ isforthemodelwithoutfixedexportingcostsandproducerheterogeneity. Theempiricalmomentsforthelevelof GDP,investmentandconsumptionwerecalculatedusingthecyclicalcomponentfromalinearde-trend. 32

6 Quantifying the Effect of Financial and Trade Shocks Using our benchmark model, which provides a unified framework to study the dynamics of the RERatallfrequencies,weevaluatetheroleoftradeandfinancialshocksinshapingthedynamics of the RER. First, we compute the contribution of each shock for the error forecast variance of theRERatdifferenthorizons. Second,wepresenttheimpulseresponsefunctionsofvariablesof interesttotradeandfinancialshocks. 6.1 ConditionalVarianceDecomposition We inspect the relevance of each shock for driving the variation in the RER by computing the contributionofeachshocktotheℎ−quarteraheaderrorforecastvarianceoftheRER.Theresults for the benchmark model are presented in Panel A of Table 4. The main result is that the trade shockexplainsmostoftheerrorforecastvarianceoftheRERinthelong-run(i.e. lowfrequency), whilethefinancialshockisimportantfortheshort-run(i.e. highfrequency)fluctuations. In particular, the financial shock explains 54 percent of the one-quarter ahead error forecast variance, with the trade shock explaining around 42 percent. Hence, at the high frequency, financialshocksmattermorethantradeshocksforexplainingthevariationoftheRER.However, when focusing at the 32 quarters ahead error forecast variance of the RER, the trade shock explains around 68 percent, while the financial shock explains 23 percent. More so, at 80 quarters ahead trade shocks explain around 71 percent and financial shocks around 20 percent. Hence, tradeshocksmattermorethanfinancialshocksforthevariationintheRERatlowerfrequencies. Since, 62 percent of the overall variance of the RER is at frequencies lower than business cycles, wefindthattradeshocksarecrucialforcapturingtheoverallvariationintheRER. We find consistent results using the analysis at the frequency domain. In particular, we conductaspectralanalysisoftheRERinthemodelforthecounterfactualcaseswhereonlythetrade or the financial shock is present under the identified parameters of the benchmark model. We presentthisinFigureH.7andTableH.4. Wefindthatinthecaseofonlytradeshocksthevolatility is only slightly smaller than in the benchmark as discussed before, which can be seen in the Figurebythetotalareabelowthespectrum. Furthermore,theshapeofthespectrumfollowsvery closely that of the benchmark model. However, having only financial shocks largely misses the 33

sizeofthespectrum. Table4: ConditionalVarianceDecomposition(%) quarters=1 8 32 80 Financialshock 54.4 43.1 22.8 20.4 Tradeshock 41.7 51.1 67.9 70.8 Productivityshock 3.9 5.8 9.3 8.8 6.2 InspectingtheFinancialandTradeShockMechanism We now turn to study the propagation mechanism triggered by financial and trade shocks in more detail. For this purpose, we present the impulse response functions of relative domestic absorption,NTandtheRERtothetwoshocksinFigure4. First,considertheeffectofafinancialshockthatincreasesthereturnonbondsfortheROW (redlinewithdots). SincehouseholdsintheROWfaceahigherreturnonbonds,theyoptimally decide to increase their savings. Hence, domestic absorption in the ROW falls relative to the US. Due to the presence of home bias in expenditure, the fall in demand of ROW households translatesintoastrongershortageindemandforintermediategoodsintheROWthanintheUS. For markets to clear, the price of ROW intermediate goods must fall, so that the US increases its expenditure in ROW intermediates. As a consequence, NT for the ROW increase, while at the sametimetheRERdepreciates. Inparticular,aonestandarddeviationfinancialshockgenerates a1.5percentdepreciationoftheRERonimpactanda2.11percentincreaseinNT. Due to dynamic trade, domestic absorption and trade flows take time to respond, leading to hump shaped responses, peaking two quarters after the shock. On the other hand, prices adjust without any delay. This contributes to a lagged response of NT relative to the RER. Eventually, households in the ROW consume their initial savings, so that NT becomes negative, around 8 years after the shock. Higher domestic absorption in the ROW induce an upward pressure on ROWprices,whichtranslatesintoanappreciationofitsRERrelativetothepre-shockvalue. Next,westudytheeffectofatradecostshockthatincreasesthecostofexportingfortheROW relativetotheimportingcost(greenlinewith𝑜). AhigherexportingcostintheROWgenerates 34

Figure4: SelectedIRFstoTradeandFinancialShocks(%) d-d* NT RER 0.2 3 1.5 Trade Shocks 0.1 Financial Shocks 2 1 0 1 -0.1 0.5 -0.2 0 -0.3 0 -1 -0.4 -0.5 -2 -0.5 0 20 40 60 80 100 0 20 40 60 80 100 0 20 40 60 80 100 Quarters Quarters Quarters a fall in NT. Larger inflows of foreign intermediates, together with smaller outflow of domestic intermediates, increases the supply of final goods in the ROW. These effects evolve gradually over time due to the dynamic nature of trade. For markets to clear, the ROW final good price must fall. Consequently, domestic absorption in the ROW increases and the RER depreciates. In particular, a one standard deviation trade shock generates a 1.3 percent depreciation of the RER on impact and a 1.2 percent decrease in NT on impact. Note that both magnitudes are smaller (inabsoluteterms)thanunderfinancialshocks,allowingthemodeltogenerateanunconditional correlationbetweenthegrowthratesofNTandtheRERthatisslightlypositive(0.30). Thisalso explainswhyfinancialshocksdrivemostofthevariationoftheRERathigherfrequencies. Over time, domestic absorption in the ROW falls to repay the debt used to finance negative NT flows intheshortrun,triggeringanincreasingpathofNTflows. Moreover, as can be seen from the last panel, trade shocks induce a more persistent effect on the RER than financial shocks. It is worth noticing that it is the effect of trade shocks that is more persistent and not the process itself. In fact, the calibrated persistence of the financial and trade shocks are very similar (𝜌 = 0.989 for financial shocks; 𝜌 = 0.985 for trade shocks). 𝜓 𝜉 Giventhatfinancialshocksinduceanincreaseonimpactinthetradebalance,theintertemporal budgetconstraintimpliesthatthetradebalancemustturnnegativeinthefuture. TheRERmust appreciate over time to support this re-balancing, so financial shocks only induce a temporary RER depreciation. On the other hand, under trade shocks the initial RER depreciation does not requireafutureappreciationtosatisfytheintertemporalbudgetconstraint;instead,theNTmust 35

rise over time. Consequently, trade shocks produce a more persistent equilibrium response of the RER than financial shocks, due to the effect on the intertemporal budget constraint.54 Taken together, trade and financial shocks generate opposing effects on the comovement between the RER and NT, as well as on their relative volatility, allowing the model to match the observed dynamicsoftheRERandNT. It is important to note that the finding that financial shocks do not dominate RER variation in the long run relies critically on the presence of trade shocks. Panel A in Table H.6 reports the conditionalvariancedecompositionfromthemodelwithouttradeshocks(Column3inTable2). Although financial shocks induce only a temporary depreciation in the RER, while productivity andtradeshocksaffecttheeconomythroughthebudgetconstraintandcangeneratemorepersistentRERmovements,themodelwithouttradeshocksattributesmostoftheRERvariationacross all frequencies to financial shocks. Consistent with the underlying mechanism, the contribution offinancialshocksdeclineswiththeforecasthorizon,buttheyremainthedominantdriverinthe absenceoftradeshocks. PanelBofTableH.6alsoreportsresultsfromaspecificationinwhichthestandarddeviation of the productivity shock is calibrated to generate the same impact effect on the RER as the financial shock. In that case, productivity shocks become the main source of RER variation at lower frequencies. This illustrates that the dominance of trade shocks at low frequencies in the baselinemodelisnotmechanicalorguaranteed. Finally, in the introduction, we mentioned that trade cost shocks capture in reduced form different sources of fluctuations in barriers to trading goods and services across countries. In FigureH.8,weshowthattariffandhomebiasshocksinducesimilardynamicstotheRERandNT flowsasthetradecostshockshowninFigure4. 7 Sensitivity and Robustness In this section, we explore the sensitivity and robustness of our quantitative results. First, we provide a detailed analysis of the role of the elasticity of domestic to foreign trade costs, 𝜏, and further consider a model when the elasticity is zero. Next, we consider alternative estimation 54InAppendixGwepresentananalyticalsolutiontoasimplifiedmodeltofurtherillustratetheroleofthebudget constraintchanneloftradeshocks. 36

methods, namely Bayesian estimation and using short sample simulations. We show that we obtainsimilarestimatesofparameterscomparedtothoseundertheBenchmarkmodelinSection 4.1. We also examine the robustness of our results to different model specifications, including modeling of dynamic trade, a three-country model, common shocks to trade costs, investment adjustment costs, a case where we target the short and long run trade elasticity, and a model withouttradeshocksbutwithamoresophisticatedfinancialshock. Overall, our findings are robust across these models, while the benchmark model tends to bettercapturethedynamicsofkeyvariablescomparedtothealternativespecifications. Moreover, we find that trade shocks drive most of the variation in the RER at low frequencies in all of the alternativemodels. MoredetaileddescriptionsareprovidedinAppendixE. Within-ROWTradeCosts WefirstanalyzeindetailthenonzerotradecostwithinROWcountriesanddevelopintuition ontheroleoftheelasticity𝜏. Figure5displaystheIRFsofrelativedomesticabsorption,NT,and the RER to a shock that increases the shipping cost from the ROW to the US (an increase in 𝜉) fordifferentvaluesof𝜏,whilekeepingconstanttheothercalibratedparameters. When 𝜏 = 0 (the dashed line), a positive trade shock, which increases the cost of the ROW exportsanddecreasesitsimportcosts,triggersafallinNTfortheROW.Theincreaseinimports fortheROWraisesthesupplyoffinalgoodsintheROW.Thiseffectisreinforcedbyanincreasein theuseofROWintermediatesfortheproductionoffinalgoods,duetotheincreaseinexporting costs. For markets to clear, the final good price in the ROW must fall for domestic absorption to increase,inducingadepreciationoftheRER.Now,considerthecaseofapositivebutsmallvalue of𝜏 = 0.152(linewithcircles). Withapositive𝜏,whenthecostofexportingfromtheROWtothe US increases, there is also a small increase in the marginal trade cost within the ROW, between its intermediate and final good producers. This makes exporting for the ROW relatively more attractivethanunderzero𝜏,sothatthefallofnetexportsissmaller. Thisimpliesthatthefallin thefinalgoodpriceneededtoclearthemarketsisweaker,sothatinequilibriumthereisasmaller depreciation of the RER and a weaker increase in domestic absorption.55 If 𝜏 is sufficiently high, NTfortheROWcanbepositivewithdomesticabsorptionintheROWdecreasingrelativetothe 55AsmallerresponseofrelativeconsumptionintheROWrelativetotheUSalsocontributestogeneratingasmall valueoftheBackus-Smith-Kollmannstatistic. 37

US (dash-dotted line with 𝜏 = 0.50). This explains why the model without financial shocks can generate a negative Backus-Smith-Kollmann correlation. It is due to the calibrated value of the within-ROW trade cost elasticity that is higher than in the benchmark model (0.256, shown in TableH.2.) Figure5: IRFstoTradeShockforDifferentValuesof𝜏 (%) d-d* NT RER 2 2 2 1 1 1 0 0 0 -1 -1 -1 -2 -2 -2 =0 =0.151 =0.50 -3 -3 -3 0 20 40 60 80 100 0 20 40 60 80 100 0 20 40 60 80 100 Quarters Quarters Quarters Notes: TherestoftheparametersaresetasinTable1. It is clear that the cross-country correlation of the first difference of domestic absorption is sensitive to the choice of 𝜏. Figure 6 shows this by displaying the cross country-correlation of thefirstdifferenceofdomesticabsorptionacrossdifferentvaluesof𝜏. Weusethiscorrelationto identifythesizeof𝜏,aswasbrieflymentionedinSection4. Inourcalibration,wefindavalueof𝜏 of 0.152. Moreover, in Appendix C, we provide external evidence supporting a positive elasticity usingbilateraldataontradeflows. To see role role of 𝜏 in a full model, we look at the results of the nested model with zero domestictradecosts. ThedetailsofthisexercisearedisplayedinAppendixE.5. Weexogenously set 𝜏 = 0 and do not target the cross country correlation of domestic absorption. The calibrated parameters and resulting moments are reported in Tables E.5 and E.6 under ‘𝜏 = 0.’ This model generatesaslightlyworsefitfortheBackus-Smith-Kollmanncorrelation(−0.01)andsignificantly worsecrosscountrycorrelationofdomesticabsorption(0.13). Thus,𝜏 mattersforaccountingfor the Backus-Smith-Kollmann puzzle and the cross country correlation of domestic absorption. Finally,thecontributionoffinancialandtradeshockstothevariationintheRERacrossdifferent frequenciesissimilartothebenchmarkmodel(seeTableE.7). 38

Figure6: Identificationof𝜏 0.5 0 -0.5 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 )*d ,d ( Notes: CorrelationofthecrosscountrygrowthratesofdomesticabsorptionbetweentheUSandROWgivendifferentvaluesof𝜏.Theotherparametersareset asinTable1. Basedonmodelsimulationof10,000periods. Blackdashedlineis thecorrelationinthedata. BayesianEstimation We estimate the model using Bayesian methods along with four data series: US GDP, ROW GDP,NTandtheRER.DetailsabouttheBayesianestimationareprovidedinAppendixE.1. Overall,wefindthattheestimatedparametersareverysimilartothoseobtainedfromourbenchmark model in Section 4.1. We present the estimated parameters in Table E.1. Moreover, we find that the dynamic trade model is preferred to the static trade model. That is, the model with dynamic trade has a better fit, as shown by the log data density higher in the dynamic trade model than thestatictrademodel. ThisisconsistentwithourresultsfromSection5.3andSection5.2,where weargueinfavorofthedynamictrademodel. TostudytheroleofeachshockinshapingthevariationoftheRER,weconsiderthecounterfactualpathoftheRER,whenitisdrivenbyonlyoneoftheestimatedshocks. Thecounterfactual RERunderonlytradeshockstrackscloselytheactualpathoftheRERacrossthewholetimeperiod. With only financial shocks, the RER follows a similar path up to the early 2000s, but not after that. Productivity shocks do not seem to generate a path for the RER closely related to the data. Overall, trade shocks generate a path of the RER that most closely tracks the actual data.56 56InTableE.2,weshowthatthecorrelationbetweentheactualRERandthecounterfactualunderonlytradeshocks is0.83. Underonlyfinancialshocks,thecorrelationisslightlylower,0.73. Thecorrelationunderonlyproductivity 39

Finally,wecomputethevariancedecompositionoftheRERusingtheestimatedparameters,and find similar results as in our benchmark model (see Table E.3). Thus, we find that trade shocks arecrucialtocapturethedynamicsoftheRER.57 ShortSampleSimulations AsopposedtoourBenchmarkcasewherethesimulationisbasedononelong-periodsample, weestimatethemodelusingmultiplesamplesconsistingofshorterperiods. Specifically,werun simulations of 160 periods, to be consistent with our quarterly data during 1980Q1-2019Q4, and take average over the moments calculated from each simulation. More details are presented in AppendixE.2. The parameters and their calibrated values are presented in Table E.5 under ‘Short.’ The estimated parameters are almost the same as the Benchmark case. This is because the moments calculated from multiple short-samples are very similar to those from one long-sample. If anything,theestimatesfortheautocorrelationsareslightlysmallerinshortsamples,duetothewell knownfactthatleastsquareestimatesofAR(n)modelsarebiased,althoughconsistent(Marriott andPope,1954;Kendall,1954). Howeverthedifferencesarenegligible,andthemodelresultagain showsthattradeshocksplayacrucialroleforlowfequencydynamicsoftherealexchangerate. SpecificationofDynamicTrade While our benchmark specification of dynamic trade follows that in Alessandria and Choi (2021), there are other mechanisms that generate similar aggregate dynamics. These include adjustment costs in the use of imported to domestic intermediates (Erceg, Guerrieri and Gust, 2006), trade in capital goods (Engel, 2011), customer base effects (Arkolakis, 2010; Drozd and Nosal, 2012; Fitzgerald, Haller and Yedid-Levi, 2024), infrequent substitution (Auclert, Rognlie, Souchier and Straub, 2024), and sticky prices (Auer, Burstein and Lein, 2021). To explore the robustness of our specification of dynamic trade, we consider an alternative way of modeling it following Erceg et al. (2006). We introduce adjustment costs in the use of imported inputs in shocksis-0.20. 57ThisisconsistentwiththemessageinRios-Rull,Santaeulalia-Llopis,Schorfheide,Fuentes-AlberoandKhrysko (2012) that argues that it is not the choice of quantitative methodology that is responsible for empirical findings, butratherthedataemployedintheidentification.DataonNTiskeytotheidentificationofparametersrelevantto capturethedynamicsoftheRERatthewholespectrumoffrequencies. 40

thefinalgoodaggregatorasareducedformwayofgeneratingadifferentialshort-andlong-run trade elasticity. We identify the adjustment cost using the estimated speed of adjustment of NT to prices in the error correction model estimated in the data.58 The parameters and calibrated valuesarepresentedinTableE.5under‘InputAdj.’ The alternative model generates similar targeted and untargeted moments as in the benchmark model (see Table E.6). We also find that financial shocks dominate the RER variation at high frequencies and trade shocks at low frequencies, but those effects are stronger than in the benchmarkmodel(TableE.7). ThreeCountryModel We verify the claim that the within-ROW trade cost elasticity captures the cost of trade between countries that compose the ROW. We consider the world consisting of three countries, where one of them is the US and the remaining two countries are aggregated as a ROW. The detailsarepresentedinAppendixE.6. We show that changing the elasticity of trade cost between the two ROW countries to trade costs against the US generates similar results as varying the domestic trade cost elasticity in the two country model. That is, a higher elasticity of trade costs between the ROW countries in responsetohigherexportcoststotheUSdampensboththeeffectoftradecostshocksonrelative domesticabsorptionandtheRER. CommonTradeCosts ItiswellknownthatthescaleoftradeasashareofGDPformostcountrieshasbeenincreasing significantly since the fall of the Bretton Woods system in 1973. A large part of this increase can be attributed to the reductions in intratemporal trade frictions across countries, induced by technological progress and policies promoting free trade (Alessandria, Bai and Woo, 2024). The frequentandsignificantchangesinthetradecostsofmostcountries,infact,arethemainreasons forthefluctuationsinrelativetradecostsacrosscountries. Whilewecapturedthedifferencesin these costs in our benchmark model, we study the robustness of our specification to include a commoncomponentbetweentheROWandtheUS. 58Thespeedofadjustmentiscapturedwiththeparameter𝛼 intheerrorcorrectionmodelequation15,whichis estimatedtobe0.03. 41

Specifically, we consider a shock to common trade cost, which affects the US and ROW in tandem,inadditiontotheshockstodifferentialtradecosts. Thesumofcommonanddifferential componentswillbetheprocessofthecountry-specifictradecosts. Thedetailsofthisrobustness checkarepresentedinAppendixE.4. Wefindthattheresultsaresimilartothebenchmarkmodel, althoughthecommontradecostshockincreasesthevolatilityofmacroaggregatesrelativetothe benchmarkcase,consistentwiththefindingsinAlessandria,KaboskiandMidrigan(2013b)inthe absenceofinventories. InvestmentAdjustmentCosts We consider investment, as opposed to capital, adjustment costs since the two types of costs generatedifferentresponsestoshocks(e.g. hump-shapeinvestmentresponsesunderinvestment adjustment costs) which potentially matters for the co-movement of variables of interest. The details are presented in Appendix E.7. We consider the specification in Christiano, Eichenbaum andEvans(2005)andcalibratetheparametersinthesamewayasinthebenchmarkmodel. The results are presented in Tables E.5 and E.6, under ‘Inv Adj’. Overall, the calibrated parameters andtheresultsofthismodelareverysimilartothebenchmarkmodel,includingthevolatilityof investment. We find that this model generates a slightly higher share of the variance of the RER for the low frequency than in the benchmark model. Finally, we also find that financial shocks dominatetheRERvariationathighfrequenciesandtradeshocksatlowfrequencies,butwefind amoreimportantroleforproductivityshocksthaninthebenchmarkmodel(seeTableE.7). SunkExportingCostandTradeElasticity In our benchmark model, the trade elasticity is larger in the long run than in the short run, correctly displaying the J-curve feature. However, because we are restricting the elasticity of substitution to be 𝛾 = 1.5 as in Itskhoki and Mukhin (2025a) and fixed costs of exporting to be consistent with firm level data, there are slight disparities from the values of the short and long runtradeelasticityinthedata. Weshowthatbyvaryingthesethreeparameters,wecanimprove the fit of these long- and short-run trade elasticities. To do so, we jointly estimate the elasticity of substitution and fixed exporting costs along with other parameters and target the estimates from the error correction model. The details are in Appendix E.8. As shown in Table E.6 under ‘TE,’ we get the elasticities much closer to data. This is driven by higher sunk costs and a larger 42

elasticityofsubstitution,aspresentedinTableE.5. Finally,wefindthatfinancialshocksincrease their importance in driving variation in the RER across all horizons relative to the benchmark model(seeTableE.7),butwestillfindthattradeshocksarethedominantshockinthelongrun. AMoreSophisticatedFinancialProcess We show that our result that trade shocks are needed to match the RER and NT moments at the high frequency is robust to considering a more sophisticated financial process. In particular, we present a model without trade shocks but where we allow the financial shock to be the mix of two AR(1) processes, each of them with a different persistence. The details are in Section E.9. ThismodelfailstocapturetheRERandNTmomentsatthehighfrequencybecausebothfinancial shock processes trigger a positive comovement between the RER and NT on impact, as shown in Figure E.6. As a consequence, the model cannot match the weak high frequency correlation. Moreover, conditional on matching the other target moments, the model generates an excess volatility of NT at the high frequency. Hence, our claim that we need to have both financial and tradeshockstocapturetheRERandNTdynamicsisfurthersupportedbythismodel. 8 Concluding remarks In this paper, we present a comprehensive analysis of the joint dynamics of the RER and NT flows by integrating financial shocks, trade shocks, and dynamic trade into a standard internationalbusinesscyclemodel. Ouranalysisshowsthenecessityof incorporatingallofthesethree features to capture the joint dynamics of the RER and NT across the frequency domain, while stillaccountingforthemajorRERpuzzlesandbusinesscyclemoments. Inlinewithexistingliterature,wefindthatfinancialshocksareimportantforexplainingthe RER variation at higher frequencies, especially for the financial disconnect. However, our novel contributionliesindemonstratingthecriticalimportanceoftradeshocksincapturingmovements of the RER and NT flows. Given that 62 percent of the RER unconditional variance is attributed tothelow-frequencymovements,tradeshocksareessentialtoaccountforitsoveralldynamics. While this study represents substantial advances understanding the factors shaping the RER and NT dynamics across various frequencies, it also highlights avenues for future research that 43

warrant exploration. Specifically, further investigation is necessary to shed light on the sources of variation of financial and trade shocks. Our analysis suggests that extending the work that focusesonthedynamicsoftradeshockswouldbeveryvaluable.59 Finally,recentdevelopmentsintheglobalpoliticalandeconomiclandscapehaveunderscored the growing importance of understanding the dynamics of net trade flows. As emphasized in the introduction, we need models that capture both the dynamics of international prices and quantities. The framework developed in this paper provides such a foundation. Extending this framework to incorporate various macroeconomic policy instruments could prove valuable for analyzing the effects of recent policy shifts—such as the increase in U.S. tariffs—and for complementingongoingresearchinthefield(BianchiandCoulibaly,2025;Monacelli,2025;Itskhokiand Mukhin, 2025b; Costinot and Werning, 2025; Aguiar, Amador and Fitzgerald, 2025; Alessandria, Ding,KhanandMix,2025). 59Furthermore,whilewehavetreatedfinancialandtradeshocksasindependent,itisalsoconceivablethatthey share common underlying causes. For example, Costinot, Lorenzoni and Werning (2014) show that intertemporal policy,suchascapitalcontrols,havesimilarimplicationsasintratemporaltradepolicyintermsofpolicyoutcomes. 44

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Appendix A Data Description In this section, we describe the data sources and how we construct the variables for our calibration. • Period: 1980Q1-2019Q4,quarterly • ROW:Trade-weightedaverageof10Countries – Countries: Canada, Finland, Germany, Ireland, Italy, Japan, Republic of Korea, Spain, Sweden,UnitedKingdom. Thesecountriesaccountfor60percentoftotalUStrade. – Weights: Country-specific averageof thesampleperiod (FederalReserve). Whilethe weights are updated every year, we use the constant weights using country-specific average during our sample period. For countries in Euro Area after 1999, we allocate theweightsforthetotalofEuroAreaintothesecountriesusingtheaveragedistributionwithinEuroAreaduring1980-1999. – We check the robustness of the empirical moments across using other weights than mean trade (output and time-varying trade). Moreover, we consider adding China intothesample,althoughdataforChinaisavailableonlyafter1990. TableA.1shows thatthemomentsweconsideraresimilaracrossthesevariations. • US interest rate: Effective federal funds rate (IMF), deflated with consumer price index (OECD) • ROWinterestrate: Moneymarketrates,deflatedwithconsumerpriceindex(OECD) – For most countries, money market rates (IMF). In a few cases where the data is not available from the IMF for the whole sample period, we consider different sources as below. – China,Germany,UK:Immediatecallmoney/interbankrate(OECD) – Canada: Shortterminterestrate(OECD) – Japan: Overnightcallrate(BankofJapan) – Figure H.3 shows that the interest rate data from different sources we use align very wellwiththemoneymarketratefromtheIMF. • QuarterlyNationalAccounts(OECD) – USdollars,volumeestimates,fixedPPPs,seasonallyadjusted – Y:Grossdomesticproduct-expenditureapproach – C:Privatefinalconsumptionexpenditure 51

– I:Grossfixedcapitalformation – X:Exportsofgoodsandservices – M:Importsgoodsandservices • Realexchangerate: Effectiveexchangerate,Real,Narrowindices,2010=100(BIS) • Termsoftrade: Termsoftradeindex(BEA,retrievedfromFRED) • USexportercharacteristics(AlessandriaandChoi2021) TableA.1: EmpiricalMomentswithDifferentWeights Meantrade Output Trade WithChina 𝜎(Δ𝑦∗) 0.007 0.008 0.011 0.006 𝑐𝑜𝑟(Δ𝑦,Δ𝑦∗) 0.40 0.26 0.03 0.32 𝑐𝑜𝑟(Δ𝑐 −Δ𝑐∗,Δ𝑞) -0.10 -0.07 -0.02 -0.09 𝑎𝑢𝑡𝑜𝑐𝑜𝑟(𝑖 −𝑖∗) 0.87 0.86 0.85 0.86 𝑎𝑢𝑡𝑜𝑐𝑜𝑟(𝑛𝑡) 0.98 0.98 0.98 0.98 𝜎(𝑖𝑛𝑣∗)/(𝑦∗) 2.21 2.21 2.21 2.21 𝑐𝑜𝑟(Δ𝑑,Δ𝑑∗) 0.34 0.24 -0.08 0.11 𝑐𝑜𝑟(Δ𝑛𝑡,Δ𝑞) 0.30 0.30 0.30 0.30 𝜎(𝑛𝑡)/𝜎(𝑞) 1.21 1.21 1.21 1.21 𝑐𝑜𝑟(Δ𝑡𝑜𝑡,Δ𝑞) 0.49 0.49 0.49 0.49 B Spectrum Analysis In this section, we describe our spectrum analysis. For more detailed and rigorous steps, see Hamilton(2020). To study the RER represented at the spectrum domain, we convert its time-domain representationusingtheFouriertransform. Givenacovariance-stationaryprocess𝑞 ,thespectrumis 𝑡 definedastheFouriertransformofitsautocovariancefunction𝐶(𝜏): 1 ∞ 𝑆(𝜔) = ∑ 𝑒−𝑖𝜔𝜏 𝐶(𝜏) (10) 2𝜋 𝜏=−∞ where 𝐶(𝜏) = 𝔼(𝑞 −𝜇 )(𝑞 −𝜇 ). 𝑡 𝑞 𝑡−𝜏 𝑞 Note that 𝜔 is a (angular) frequency measure of radians per period.60 Given that upper and lower bounds for business cycle frequency are 8 and 32 quarters, the range of frequency that 60Foranordinaryfrequency𝜉 =𝜔/2𝜋 (Hz),thespectrumisdefinedas ∞ 𝑆(𝜉)= 𝐶(𝜏)𝑒−2𝜋𝑖𝜉𝜏𝑑𝜏. ∫ −∞ 52

correspondstothebusinesscycleis 2𝜋 2𝜋 𝜔 ∈ , = [0.196,0.785]. [32quarters 8quarters] ThisisconsistentwiththerangeusedbyRabanalandRubio-Ramirez(2015). UsingtheinverseofEquation(10),wecanwritetheautocovariancefunctionas 𝜋 𝐶(𝜏) = 𝑒𝑖𝜔𝜏 𝑆(𝜔) 𝑑𝜔 ∫ −𝜋 Then with 𝜏 = 0, the variance 𝐶(0) = ∫ 𝜋 𝑆(𝜔)𝑑𝜔 is the sum of spectrum. In this sense, the −𝜋 spectrumdecomposesthevarianceintodifferentfrequencies. Also,wecanshowthatspectrumissymmetricaroundzero,periodicwithaperiodof2𝜋,and canbewrittenas 1 2 ∞ 𝑆(𝜔) = 𝐶(0)+ ∑𝑐𝑜𝑠(𝜔𝜏) 𝐶(𝜏). (11) 2𝜋 2𝜋 𝜏=1 In order to estimate the population spectrum given the data sample of 𝑇 observations, we couldusethesampleautocovariance 1 𝑇 𝐶̂(𝑗) = ∑(𝑞 −𝑞̄)(𝑞 −𝑞̄), 𝑇 𝑡 𝑡−𝑗 𝑡=𝑗+1 where 𝑞̄ is a sample mean. This yields an estimate of Equation (11), known as the sample periodogram: 1 2 𝑇−1 𝑆̂𝑠𝑝(𝜔) = 𝐶̂(0)+ ∑𝑐𝑜𝑠(𝜔𝑗) 𝐶̂(𝑗). (12) 2𝜋 2𝜋 𝑗=1 However,suchestimateissubjecttoafewlimitations. Thusweuseanonparametricestimationinstead. Thatis,weestimatethespectrumby ℎ 𝑆̂(𝜔 ) = ∑ 𝑘(𝜔 ,𝜔 ) 𝑆̂𝑠𝑝(𝜔 ) (13) 𝑗 𝑗+𝑚 𝑗 𝑗+𝑚 𝑚=−ℎ where 𝑘(𝜔 ,𝜔 ) is a kernel with a bandwidth ℎ. The idea is to take a weighted average of the 𝑗+𝑚 𝑗 sample periodograms 𝑆̂𝑠𝑝(𝜔̃) for the values 𝜔̃ around 𝜔, where the distance between 𝜔 and 𝜔̃ determinesthekernel,i.e. theweight. AftersubstitutingEquation(12)intoEquation(13)andsomecalculations,itcanbeshownthat Equation(13)isequivalentto 1 2 𝑇−1 𝑆̂(𝜔) = 𝐶̂(0)+ ∑ 𝑘∗ 𝑐𝑜𝑠(𝜔𝑗) 𝐶̂(𝑗). 2𝜋 2𝜋 𝑗 𝑗=1 where{𝑘∗}𝑇−1isaweightingsequencecorrespondingtoakernelfunction𝑘(𝜔 ,𝜔 ). Theweight 𝑗 𝑗=1 𝑗+𝑚 𝑗 53

forthemodifiedBartlettkernelisgivenas { 1− 𝑗 for𝑗 = 1,2,⋯,𝐽 𝑘∗ = 𝐽+1 𝑗 0 for𝑗 > 𝐽 where 𝐽 is the length of a window for the weight that is related to the kernel bandwidth. This yieldsthespectrumestimateof 1 2 𝐽 𝑗 𝑆̂(𝜔) = 𝐶̂(0)+ ∑ 1− 𝑐𝑜𝑠(𝜔𝑗) 𝐶̂(𝑗). 2𝜋 2𝜋 [ 𝐽 +1] 𝑗=1 On the other hand, there is no fixed rule for the choice of the bandwidth ℎ (or window 𝐽). Hamilton (2020) suggests trying different values and “relying on subjective judgement for the most plausible estimate." For the benchmark exercise we use the window of 𝐽 = 16, and check thatothervaluesyieldasimilarresultthatiswithintherangeoffindingsoftheliterature. Figure B.1showstheestimatedspectrumoftheRERforthefullrangein[0,𝜋]. FigureB.1: SpectrumoftheRER 0.03 Data Benchmark Model 0.025 No Trade Dynamics 0.02 0.015 0.01 0.005 0 0 0.5 1 1.5 2 2.5 3 3.5 Frequency C Empirical Evidence of Trade Costs Inthissection,weprovideanexternalvalidationforourspecificationoftradecosts. First,weuse data on bilateral trade to measure these costs for different pairs of countries. Next, we estimate theelasticityofwithin-countrytradecostsandshowitisconsistentwiththespecificationinour benchmarkmodel. WemeasuretradecostsfromdataasawedgeintheCESdemand,commoninanyArmington 54

FigureC.1: EmpiricalRelationshipofTradeCosts .4 y = 0.199 x + 0.163 (R2= 0.34) .3 .2 .1 0 Rξ tsoc citsemoD .4 y = 0.328 x + 0.144 (R2= 0.42) .3 .2 .1 0 −.6 −.4 −.2 0 .2 Differential cost ξ*R−ξU Rξ tsoc citsemoD −.4 −.2 0 .2 .4 Export cost ξ*R Notes: Each point represents trade costs of each year. The plots corresponds to the first and second columnsofTableC.1. trademodel. Thedemandforcountry𝑖 goodsincountry𝑗 isgivenby: −𝛾 𝑒𝜉𝑖𝑗𝑝𝑖𝑗 𝑋𝑖𝑗 = 𝑡 𝑡 𝐷 𝑡 ( 𝑃 ) 𝑗𝑡 𝑗𝑡 where𝑋𝑖𝑗 isbilateraltradeflowsfromcountry𝑖 to𝑗,𝑝𝑖𝑗 isthepricelevelofexportsfromcountry 𝑡 𝑡 𝑖 to 𝑗, 𝑃 is the price level of domestic absorption in country 𝑗, 𝐷 is the domestic absorption 𝑗𝑡 𝑗𝑡 of country 𝑗, and 𝛾 is the elasticity of substitution. Our model assumes the same type of CES structureforthedemandfordifferentiatedgoods. Moreover,itisthebasictradeblockforalmost allstudiesintradeliterature. Note that all of the terms in the demand function except for 𝜉𝑖𝑗 are observables. Thus, we 𝑡 can recover trade costs 𝜉𝑖𝑗 as a gap between actual and predicted trade flows given prices and 𝑡 aggregate demand. In particular, we estimate the above demand function using the following regression log𝑋𝑖𝑗 = 𝛽log(𝑃𝑖𝑗/𝑃 )+log𝐷 +𝜀𝑖𝑗. (14) 𝑡 𝑡 𝑗𝑡 𝑗𝑡 𝑡 andconsidertheresiduals𝜀𝑖𝑗 astradecosts. Byestimatingthedemandfunction,wedonotrestrict 𝑡 ourselves to a particular value of elasticity. In fact, there is a broad range of values used for the elasticity in the literature, and the estimated elasticity varies greatly depending on the sample and the length of period considered. Also, the estimation by construction minimizes the size of tradecostsandletsustakeaconservativestanceontheroleoftradecosts. WeestimatethedemandfunctionusingdatafortheUSandtenothercountriesfortheROW, asisdoneinourbenchmarkquantification. Fordataonbilateraltradeflows,weuseannualdata from UN Comtrade, converted into real terms using the price levels of the US dollars from Penn World Table 10.0. Domestic absorption and price levels of different countries in our sample also comefromPennWorldTable10.0. Oursampleperiodcoverstheperiodof1994-2019,mostlydue todataavailabilityoftradeflows.61 61Wealsochecktherobustnesswithquarterlydataduringtheperiodof2008Q1-2019Q4.Wefindthatthepathof tradecostsissimilartousingannualdata. 55

For the trade cost between the US and the ROW, 𝜉∗ and 𝜉 , we aggregate the data on the 𝑅𝑡 𝑈𝑡 ten countries and use it as the variables for the ROW. Then we run the regression (14) for the US-ROWpair. Ontheotherhand,forthetradecostwithintheROW,𝜉 ,weusebilateraldataon 𝑅𝑡 each pair of countries in the ROW, and take average of the recovered residuals across countries toconstructtimeseries. TableC.1: EmpiricalEstimatesof𝜏 (1) (2) (3) (4) (5) (6) (7) (8) Dependentvariable: 𝜉𝑅 (𝜉∗ −𝜉 ) 0.199∗∗ 0.546∗ 0.493∗∗∗ 0.443 𝑅 𝑈 (0.0581) (0.223) (0.100) (0.304) 𝜉∗ 0.328∗∗∗ 0.843∗∗∗ 0.583∗∗∗ 0.972∗∗ 𝑅 (0.0798) (0.166) (0.0627) (0.293) CountryFE Y Y Y Y SpendingConstraints Y Y Y Y Observations 25 25 25 25 25 25 25 25 R-squared 0.338 0.423 0.207 0.530 0.513 0.790 0.0847 0.324 Notes: Standarderrorsinparentheses. *𝑝 < 0.05, **𝑝 < 0.01, ***𝑝 < 0.001. ‘CountryFE’denotesthefixedeffect fororiginanddestinationcountrieswhenestimatingthedemandfunctionforthepairofROWcountries.‘Spending Constraints’arearestrictiononthecoefficientofdomesticabsorptiontobe1,aspredictedinthemodelwithCES demand. Given the path of trade costs, we check the relationship of 𝜉 with 𝜉∗ or 𝜉∗ − 𝜉 . We use 𝑅𝑡 𝑅𝑡 𝑅𝑡 𝑈𝑡 these estimates to compare with the model analogue. As shown in Equation 16, in our model we allow trade costs within the ROW aggregate, 𝜉 , to be nonzero. We further assume it to be 𝑅𝑡 𝜉 = 𝜏𝜉 𝑡,where𝜏 measurestheelasticityofthewithincomponentrespecttotheROW-UStrade 𝑅𝑡 2 cost. Inthecalibrationofthebenchmarkmodel,displayedinSection4.1,wefindthat𝜏 isasmall positive number (0.16). Thus 𝜉 is positively correlated with trade costs from ROW to the US, 𝑅𝑡 𝜉∗ = 𝜉 𝑡,andalsowiththedifferencebetweenexportingandimportingcosts,𝜉∗ −𝜉 = 𝜉 . 𝑅𝑡 2 𝑅𝑡 𝑈𝑡 𝑡 Figure C.1 shows that we do find a consistent pattern in the data. It plots the relationship of 𝜉 (leftpanel)with𝜉∗−𝜉 and𝜉∗ (rightpanel). Theestimatedelasticityisbetween0.199and0.32. 𝑅 𝑅 𝑈 𝑅 Finally, table C.1 displays the result with additional controls. Although the size of estimated 𝜏 differs slightly, we have the robust result that the estimated 𝜏 is positive as in our benchmark model presented in Section 4.1. Moreover, the coefficient of 𝜉∗ is always larger than 𝜉∗ − 𝜉 , as 𝑅 𝑅 𝑈 specifiedinourbenchmarkmodel. D Dynamic Trade Elasticity In Section 5.2, we show that our model captures the comovement between the RER and NT at lower frequencies by showing their dynamic correlation. In this section, we complement this analysisbyestimatingtheelasticityofNTtopricesintheshortandlongrun. 56

TableD.1: TradeElasticity (1) (2) (3) (4) (5) Data Benchmark NoTradeShock NoFinancialShock NoDynamics Shortrun 0.18 0.44 1.17 -1.10 0.16 (0.002) Longrun 2.01 0.82 1.71 0.83 0.36 (1.025) Adjustment 0.03 0.03 0.35 0.03 0.05 (0.000) Todoso,weleveragetherelationshipbetweenpricesandNTbasedontheArmingtontrade model. The Armington model, which is also nested within our benchmark model, serves as the basic trade block for almost all multi-good international macro models. From the demand structure of the Armington model, NT can be expressed as a function of the RER, the terms of trade anddomesticabsorption.62 Weestimateanerrorcorrectionmodelofthisrelationship: Δ𝑛𝑡 = 𝛽+𝛾 Δ(𝑡𝑜𝑡 +𝑞 )+Δ(𝑑∗ −𝑑 ) 𝑆𝑅 𝑡 𝑡 𝑡 𝑡 −𝛼[𝑛𝑡 −𝛾 (𝑡𝑜𝑡 +𝑞 )−(𝑑∗ −𝑑 )]+𝜀 (15) 𝑡−1 𝐿𝑅 𝑡−1 𝑡−1 𝑡−1 𝑡−1 𝑡 where 𝑛𝑡 = ln(𝑋/𝑀) is log of NT, 𝑡𝑜𝑡 = ln(𝑝𝑀/𝑝𝑋) is the log of the terms of trade, 𝑞 is the log 𝑡 𝑡 𝑡 𝑡 𝑡 of the RER, and 𝑑 = ln(𝐶 + 𝐼 ) and 𝑑∗ = ln(𝐶∗ + 𝐼∗) are the log of domestic absorption in the 𝑡 𝑡 𝑡 𝑡 𝑡 𝑡 domestic and foreign country. Here, 𝛾 is the short-run elasticity, 𝛾 is the long-run elasticity, 𝑆𝑅 𝐿𝑅 and 𝛼 captures the speed of adjustment. The term in square brackets captures the cointegration relationshipimpliedbytheArmingtonmodel, 𝑛𝑡 = 𝛾 (𝑡𝑜𝑡 +𝑞 )+(𝑑∗ −𝑑 ). 𝑡 𝑡 𝑡 𝑡 𝑡 This type of regression has been widely used in studies of trade dynamics (Hooper et al., 2000; Marquez,2002;AlessandriaandChoi,2021;Alessandriaetal.,2024). Using the data described in Appendix A, we estimate Equation 15, and present the results in TableD.1. Theshort-runelasticityisestimatedtobearound0.18,whilethelong-runelasticityis larger,around2.01. TheestimatedvaluesaresimilartotheestimatesfromAlessandriaandChoi (2021) that covers a similar time period for the US, and are also consistent with Alessandria, Bai and Woo (2024) which uses panel data of a broader set of countries, although their size of the long-runelasticityisslightlylargercomparedtoourestimates. Usingthemodelsimulateddata,weconductthesameexerciseinourbenchmarkmodel(column 2). Note that all of the shocks simultaneously affect prices, quantities, and the error term, which implies that the regression estimates do not have a structural interpretation. We estimate alongrunelasticitythatislarger(𝛾 =0.82)thantheshortrun(𝛾 =0.44),capturingthedynamic 𝐿𝑅 𝑆𝑅 adjustment of NT to prices.63 Trade dynamics are crucial for capturing the difference between 62SeeAppendixFforthederivationofNTequationinthebenchmarkmodelanditscomparisonwiththeArmingtonmodel. 63InSection7wepresentaspecificationinwhichwetargettheseelasticities. Thisalternativespecificationgeneratessimilarresultsasinourbenchmarkcase. 57

short and long run elasticity. In column 5, we present the results for the model without trade dynamics. The short run elasticity is estimated to be 0.16, and the long run elasticity is 0.36. Althoughthereisasmallgapbetweentwoelasticitiesduetotheeffectoftradeshocks,thedifferencebetweenthemissmallerthaninthebenchmarkmodel. Weconcludethatdynamictrade,by generating a slow moving distribution of exporters in response to shocks, bring the model close tothedataintermsoftheshortandlongrunelasticityofnettradetoprices.64 Moreover, similar to our analysis of the correlation of the growth rates of the RER and NT at different horizons, we find that both trade and financial shocks are necessary to capture the differential elasticity. While the long-run elasticity improves absent the trade shock, the short run elasticity becomes too large. On the other hand, absent the financial shock both elasticities aretoolow. E Robustness Inthissection,weconsideralternativespecificationstochecktherobustnessoftheresultsofthe benchmarkmodel. First,weexploreanalternativeestimationstrategytoidentifytheparameters andshocksdrivingtheRER:Bayesianmethods. WeshowthatweobtainsimilarestimatesofparametersthanunderourBenchmarkmodelinSection4.1. Next,weshowthatexplorealternative specifications to our benchmark model, in particular an estimation based on short sample simulations,areducedformspecificationofdynamictrade,amodelwithcommontradecosts,amodel with no within-ROW trade costs (i.e. 𝜏 = 0), a three-country model, and an alternative model with investment adjustment costs. Overall, we find that our benchmark model better captures thedynamicofkeyvariablesinourmodelrelativetothealternativespecifications. Moreover,we find that the result that financial shocks matter more for the short run and trade shocks for the longrunisrobustacrossthealternativespecifications. E.1 BayesianEstimation We explore an alternative estimation strategy to identify the shocks driving the RER: Bayesian methods. First, we show that we obtain similar estimated of parameters than under our benchmark model in Section 4.1. Second, we show that the model with dynamic trade is preferred to that of static trade. Finally, we show that trade shocks are crucial for generating the dynamics of the RER. That is, the counterfactual RER under trade shocks is closer to the RER in the data than under the financial shock. We also present the estimated path of the different shocks and computetheconditionalvariancedecompositionoftheRER. 64Wedonotconsideramodelwithouttradedynamicsandtradeshocks,sinceinthatcasetheshortandlong-run tradeelasticitieswillbethesame,andequaltotheArmingtonelasticityof1.5,ascanbeinferredfromequation8.For thesamereason,themodelinSection7wherewedropthetradeshockbutallowforamoresophisticatedfinancial shockdoesnotcapturethedifferentialtradeelasticity. 58

TableE.1: EstimatedParameters DynamicTrade StaticTrade PriorDistribution PostMean 90%Interval PostMean 90%Interval 𝜌 Uniform[0.8,0.999] 0.9703 (0.9469,0.9950) 0.9816 (0.9664,0.9971) 𝜓 𝜌 Uniform[0.8,0.999] 0.9930 (0.9862,0.9990) 0.9877 (0.9818,0.9945) 𝜉 𝑑 𝜎 Inversegamma(0.081,0.01) 0.0050 (0.0045,0.0056) 0.0047 (0.0041,0.0052) 𝑐 𝜎 Inversegamma(0.081,0.01) 0.0060 (0.0054,0.0068) 0.0061 (0.0053,0.0068) 𝑑 𝜎 Inversegamma(0.081,0.01) 0.0019 (0.0010,0.0026) 0.0008 (0.0005,0.0010) 𝜓 𝜎 Inversegamma(0.081,0.01) 0.0526 (0.0431,0.0614) 0.0980 (0.0867,0.1074) 𝜉 𝑑 𝜏 Uniform[-0.5,0.5] 0.1911 (0.1610,0.2226) 0.1123 (0.0977,0.1288) 𝜒 Uniform[0.00001,0.25] 0.0269 (0.0019,0.0521) 0.0154 (0.0041,0.0281) 𝜅 Uniform[0,20] 8.3042 (1.9080,15.6279) 3.5289 (0.0021,6.9175) 𝜁 Uniform[0.85,1.20] 1.0995 (1.0128,1.1988) 1.1364 (1.0561,1.1997) Logdatadensity 1843.59 1839.95 EstimatedParameters Weestimatethesameparametersasweinternallycalibrateinthebenchmarkcase. Inparticular, we estimate the productivity shock volatility, 𝜎 and 𝜎 , financial shock parameters, 𝜌 and 𝑐 𝑑 𝜙 𝜎 , trade shock parameters, 𝜌 , 𝜎 and 𝜏, as well as the adjustment costs parameters 𝜒 and 𝜅. 𝜙 𝜉𝑑 𝜉𝑑 We impose loose priors, mostly uniform distribution and inverse gamma for volatility parameters. Forobservables,weusefourdataseries: GDPgrowthoftheUSandtheROW,theNTflows andtheRER,withthesamesampleperiodasinthebenchmarkcase(1980Q1-2019Q4). TheleftpanelofTableE.1reportsthepriorsandposteriordistributions. Theestimatedresults aresimilartothebenchmarkcase. Thesizeofthefinancialshockvolatilityisthesmallest,while the size of trade shock is largest. The within-country trade cost parameter 𝜏 = 0.191 is also very closetothebenchmarkcase(0.152). DynamicvsStaticTrade To show that dynamic trade model better captures the data on trade and the RER compared tothestaticmode,weestimatethestaticmodelwithnofixedcostofexporting. Weusethesame priorsasbefore. TheresultofthestaticcaseispresentedintherightpanelofTableE.1. We find that the log data density (Laplace Approximation) in the dynamic trade model is 1843.59 while in the static model it is 1839.95, so that the dynamic trade model is preferred over the static trade model by a Bayes factor of 𝑒𝑥𝑝(3.640).65 This is consistent with our results from Section5.3andSection5.2,whereweargueinfavorofthedynamictrademodel. EstimatedShocks Figure E.1 shows the estimated path of productivity shocks of the ROW, trade shocks, and financialshocks. Thetradeshocksweremostvolatileduringthe1980s,whentheseriesofdifferent trade policy were implemented in many countries. For example, Uruguay Round launched 65TheBayesfactorissimilartoalikelihood-ratiotest. 59

multilateral trade negotiations. Also, countries like India and Mexico introduced trade reforms and lowered their trade barriers. In recent years trade shocks became more stable, while 2009 markstheperiodofthehighesttradecost. CounterfactualRER In Figure E.3, we show the path of the RER in the data, as well as the counterfactual where the RER is driven by only one of the shocks. We present the correlation between the data and counterfactual cases in Table E.2. It is clear that the RER under trade shocks closely tracks the actual RER during the whole sample period. The path generated only with the Trade shocks, shown in green dashed line, very closely follow the data path. The correlation with the data is 0.85. On the other hand, with only financial shocks, the RER follows a similar path up to the early 2000s, but rather departs from data in the later periods. The correlation is 0.65 and lower thanthecasewithonlytradeshocks. Productivityshocksdonotseemtogenerateapathforthe RER that closely related to the data. The correlation in this case is slightly negative. Overall, we conclude that trade shocks generate a dynamics of the RER that more closely tracked the actual data. We turn to look at the spectrum of the counterfactual cases when muting each shock. The result is presented in Figure E.3. The spectrum is disrupted the most when we shut down the tradeshocks. Hence,tradeshocksarecrucialtocapturethespectrumoftheRER. Finally, in Table E.3 we provide the conditional variance decomposition obtained from the Bayesian estimation of the dynamic trade model. In particular, we compute the share of the ℎ−quarter ahead error forecast variance of the RER explained by each shock. It is clear that the trade shock explains most of the forecast error variance of the RER in the long run (i.e. low frequency),whilethefinancialshockisimportantfortheshortrun(i.e. highfrequency)fluctuations. Thisisconsistentwiththeresultsofourbenchmarkmodel. E.2 SimulationwithShortSamples In this section, we take a different approach to estimate the parameters that are jointly pinned down to match the targeted moments. Instead of taking moments from one long-sample simulation, we simulate each samplefor 400 periods, to be consistent with our quarterlydata during 1980Q1-2019Q4,andtaketheaverageofthelast160observationsfrommultipleruns. Theresults arepresentedinTablesE.5andE.6under‘Short.’ FigureE.1: EstimatedShocks Productivity Shocks Financial Shocks Trade Shocks 4 4 4 2 2 2 0 0 0 -2 -2 -2 -4 -6 -4 -4 1980 1990 2000 2010 2020 1980 1990 2000 2010 2020 1980 1990 2000 2010 2020 60

FigureE.2: RERDynamicsunderDifferentShocks 0.2 0.1 0 -0.1 -0.2 Data -0.3 Only Trade Only Financial Only Productivity -0.4 1980 1985 1990 1995 2000 2005 2010 2015 2020 Notes: This figure shows the counterfactual path of RER with only one type of shocks. The productivity shocks includeboththedifferentialandcommoncomponent. Theestimatedparameters,andthusthevaluesoftargetedmoments,areverysimilartothose of the benchmark. However, notice that the moments of persistence tend to be slightly smaller than those from longer samples. To analyze the effect of using different sample periods further, we consider keeping the same parameters as in the benchmark case and use different periods to comparethecalculatedmoments. The result of these exercises is presented in Table E.4. First, we consider the effect of the distancefromtheinitialpoint(orsteadystate). Toseethis,weusesamplesofsamelengthstarting at different periods, which are presented in the first three columns. We find that given the same samplelengths,distancefromtheinitialpointseemstohavenoimpactontheestimates. Second, weconsiderusingsamplesofincreasinglengths. Fromthelastfivecolumns,wefindthatvolatility momentsaresimilaracrosssamplelength,butautocorrelationsareincreasinginsamplelengths. Thisisacasenotonlyfortheendogenousvariables,liketheRER,butalsofortheshockprocess such as 𝜓 and 𝜉 . This is because least square estimates of AR(n) models are downward biased 𝑑 (Marriott and Pope, 1954; Kendall, 1954). The bias is decreasing in the sample length, and the estimateisconsistent. Howeverevenwithverysmallsizesthedifferenceisnegligibleleadingto a very similar result as using longer samples as in our benchmark case. Finally, Table E.7 shows TableE.2: CorrelationbetweenDataandCounterfactuals Onlyproductivity Onlytrade Onlyfinancial 𝑐𝑜𝑟(data,model) -0.02 0.85 0.65 61

FigureE.3: RERSpectrumUnderDifferentShocks 0.025 Data No productivity No trade 0.02 No financial 0.015 0.01 0.005 0 0 0.5 1 1.5 2 2.5 3 Frequency Notes: ThisfigureshowsthecounterfactualspectrumofRERwithonlyonetypeofshocks. Theproductivityshocksincludeboththedifferentialandcommoncomponents. the results in terms of the conditional variance decomposition. We find that trade shocks are moreimportantundertheshortsampleidentification. E.3 DynamicTradeSpecification Inthissection,weconsiderthefinalgoodaggregatorwithadjustmentcostsintheuseofimported inputs, as in Erceg et al. (2006), Rabanal and Rubio-Ramirez (2015) and Gornemann et al. (2020). TheCESaggregatoroftheretailsectorineachcountryisnowgivenby 𝛾 𝛾 𝐷 𝑡 = [ 𝑌 𝑅 𝛾 𝑡 𝛾 −1 +𝜔 𝛾 1 (𝜑 𝑡 𝑌 𝑈𝑡 ) 𝛾 𝛾 −1 ] 𝛾−1 𝐷 𝑡 ∗ = [ 𝑌 𝑈 ∗𝛾 𝑡 𝛾 −1 +𝜔 𝛾 1 (𝜑 𝑡 ∗𝑌 𝑅 ∗ 𝑡 ) 𝛾 𝛾 −1 ] 𝛾−1 where 𝜑 and 𝜑∗ is the weight on the use of imported inputs in the production of the final good. 𝑡 𝑡 Theirfunctionalformsaregivenby 𝜄 𝑌 /𝑌 2 𝜄 𝑌∗ /𝑌∗ 2 𝜑 = 1− 𝑈𝑡 𝑅𝑡 −1 𝜑∗ = 1− 𝑅𝑡 𝑈𝑡 −1 . 𝑡 [ 2 (𝑌 /𝑌 ) ] 𝑡 [ 2 (𝑌∗ /𝑌∗ ) ] 𝑈𝑡−1 𝑅𝑡−1 𝑅𝑡−1 𝑈𝑡−1 whereparameter𝜄 determinesthesizeoftheadjustmentcostintheuseofimportedinputs. We identify the adjustment cost 𝜄 using the speed of adjustment of NT to prices, i.e. the estimated parameter 𝛼 in the error correction model equation 15, which has a value of 0.03 in data. That is, on top of the other targeted moments, we add the speed-of-adjustment parameter tojointlyestimatetheparameters,includingthenewparameter𝜄(11parametersand11moments). Sincewecomparethismodelwithourbenchmark,weshutdowntradedynamicsthatarisesfrom thefixedcostsofexporting. The parameters and their calibrated values are presented in Table E.5 under ‘Input Adj.’ The 62

TableE.3: ConditionalVarianceDecomposition(%) quarters=1 8 32 80 BayesianEstimation Financialshock 51.0 35.9 16.6 12.7 Tradeshock 44.4 57.8 75.7 81.0 Productivityshock 4.6 6.3 7.7 6.3 BenchmarkModel Financialshock 54.4 43.1 22.8 20.4 Tradeshock 41.7 51.1 67.9 70.8 Productivityshock 3.9 5.8 9.3 8.8 calibrated value of the input adjustment cost parameter 𝜄 is 36.84. This implies that when the share of home to foreign inputs, 𝑌 𝑈𝑡 /𝑌 𝑅𝑡 , deviates 1 percent from the steady state, then, given 𝑌 /𝑌 𝑈𝑡−1 𝑅𝑡−1 𝜄 = 36.84and𝜔 = 0.097,thehome-countryoutputwillbe0.017percentsmallerthanwithoutthe presenceofthiscost. In Table E.6, we label the column for the result of this alternative dynamic specification as ‘Input Adj.’ The model is generates a speed of adjustment of NT to prices of 0.08, a bit higher thanthedata(0.03). Wefindthatthisalternativemodelisabletogenerateadifferentialshortand long run trade elasticity to prices. However, it does not generate a differential elasticity as close tothedataasinthebenchmarkmodel. Furthermore, we plot in Figure E.4 the spectrum of the RER in the data (solid black line), the benchmark model (dashed blue line) and the alternative input adjustment model (green line with x). The alternative dynamic trade model does not capture the size of the spectrum as well as the benchmark model. Hence, the benchmark model, where we exploit information from the microdata on firm dynamics, captures the shape of the spectrum of the RER better than the alternativedynamictrademodel. Finally, Table E.7 present the variance decomposition of this alternative model, under ‘Input Adj.’ We find a stronger role of financial shocks as drivers of the RER in the short run, relative to our benchmark model. The contribution of financial shocks to the one-quarter ahead error forecast variance of the RER is around 94 percent in the alternative model, as opposed to 54 percentinourbenchmark. However,inthelongrunwefindsimilarresultsasinourbenchmark model for the contribution of financial and trade shocks in explaining the variation of the RER. We find that trade shocks explains around 72 percent of the 80-quarters ahead error forecast variance in this alternative model, close to the 71 percent in the benchmark model. On the other hand, financial shocks explain around 35 percent in the alternative model, higher than the 20 percent found in our benchmark model. Hence, our main result holds: trade shocks are crucial to explain the low frequency variation in the RER, thus being crucial for capturing its overall variation. 63

TableE.4: MomentswithDifferentSampleLengths Length 100 100 100 300 900 2900 6900 Startperiod 501 1801 7801 7701 7401 6401 3401 Endperiod 600 1900 7900 8000 8300 9300 10300 𝜎(Δ𝑦) 0.007 0.007 0.007 0.007 0.007 0.007 0.007 (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) 𝑐𝑜𝑟(Δ𝑦,Δ𝑦∗) 0.442 0.450 0.439 0.452 0.452 0.454 0.454 (0.006) (0.006) (0.006) (0.003) (0.002) (0.001) (0.001) 𝑐𝑜𝑟 (Δ𝑐 −Δ𝑐∗,Δ𝑞) -0.076 -0.077 -0.076 -0.081 -0.081 -0.081 -0.082 (0.007) (0.007) (0.007) (0.004) (0.002) (0.001) (0.001) 𝑎𝑢𝑡𝑜𝑐𝑜𝑟(𝑖 −𝑖∗) 0.786 0.790 0.778 0.857 0.886 0.892 0.893 (0.006) (0.007) (0.006) (0.003) (0.002) (0.001) (0.001) 𝑎𝑢𝑡𝑜𝑐𝑜𝑟(𝑛𝑡) 0.947 0.945 0.949 0.966 0.972 0.974 0.975 (0.002) (0.002) (0.002) (0.001) (0.000) (0.000) (0.000) 𝜎(𝑖𝑛𝑣∗)/𝜎(𝑦∗) 2.947 2.882 3.028 2.477 2.296 2.230 2.202 (0.049) (0.046) (0.048) (0.026) (0.016) (0.009) (0.006) 𝑐𝑜𝑟(Δ𝑑,Δ𝑑∗) 0.335 0.343 0.330 0.344 0.342 0.345 0.345 (0.006) (0.007) (0.006) (0.004) (0.002) (0.001) (0.001) 𝑐𝑜𝑟(Δ𝑛𝑡,Δ𝑞) 0.282 0.288 0.291 0.287 0.282 0.281 0.283 (0.006) (0.006) (0.006) (0.004) (0.002) (0.001) (0.001) 𝜎(𝑛𝑡)/𝜎(𝑞) 1.564 1.544 1.548 1.322 1.226 1.149 1.128 (0.048) (0.040) (0.042) (0.026) (0.016) (0.009) (0.006) 𝑐𝑜𝑟(Δ𝑡𝑜𝑡,Δ𝑞) 0.464 0.470 0.473 0.464 0.461 0.460 0.463 (0.005) (0.005) (0.005) (0.003) (0.002) (0.001) (0.001) 𝜎(Δ𝑞)/𝜎(Δ𝑦) 2.902 2.936 2.953 2.917 2.913 2.906 2.909 (0.020) (0.019) (0.019) (0.012) (0.006) (0.004) (0.002) 𝑎𝑢𝑡𝑜𝑐𝑜𝑟(𝑞) 0.925 0.924 0.928 0.963 0.973 0.978 0.979 (0.004) (0.004) (0.003) (0.001) (0.001) (0.000) (0.000) 𝑎𝑢𝑡𝑜𝑐𝑜𝑟(𝜓) 0.937 0.943 0.945 0.974 0.985 0.988 0.989 (0.003) (0.003) (0.003) (0.001) (0.000) (0.000) (0.000) 𝑎𝑢𝑡𝑜𝑐𝑜𝑟(𝜉 ) 0.937 0.932 0.934 0.969 0.980 0.984 0.985 𝑑 (0.003) (0.003) (0.003) (0.001) (0.001) (0.000) (0.000) 64

TableE.5: Robustness–CalibratedParameters Parameters Benchmark Short InputAdj Common 𝜏 =0 InvAdj TE Sophisticated𝜓 Commonproductivity,volatility𝜎 0.004 0.004 0.004 0.003 0.004 0.004 0.004 0.004 𝑎𝑐 Differentialproductivity,volatility𝜎 0.006 0.007 0.004 0.006 0.003 0.006 0.006 0.005 𝑎𝑑 Financialshock,volatility 𝜎 0.001 0.002 0.009 0.001 0.001 0.001 0.001 0‡ 𝜓 Financialshock,persistence 𝜌 0.989 0.976 0.816 0.988 0.990 0.988 0.987 0‡ 𝜓 Tradeshock,volatility 𝜎 0.049 0.076 0.084 0.041 0.057 0.032 0.022 0‡ 𝜉 Tradeshock,persistence 𝜌 0.985 0.975 0.990 0.988 0.990 0.990 0.999 0‡ 𝜉 Tradeshock,within-countryshare𝜏 0.152 0.202 0.030 0.197 0.00‡ 0.278 0.357 0‡ Adjustmentcostofportfolios 𝜒 0.012 0.030 0.001 0.008 0.008 0.008 0.010 0.0001 Adjustmentcostofcapital 𝜅 2.219 10.600 0.097 2.298 0.000 1.35∗ 3.846 1.470 Pricingtomarketparameter 𝜁 0.940 0.987 1.489 0.964 0.790 0.973 0.923 1.028 Importadjustmentcost𝜄 0‡ 0‡ 36.84 0‡ 0‡ 0‡ 0‡ 0‡ Fixedcostofnewexporters 𝑓0 0.14 0.14 0‡ 0.14 0.14 0.14 0.33 0.14 Fixedcostofincumbentexporters 𝑓1 0.04 0.04 0‡ 0.04 0.04 0.04 0.08 0.04 Volatilityofidiosyncraticproductivity𝜎 0.15 0.15 0‡ 0.15 0.15 0.15 0.15 0.15 𝜇 CommonTradeshock,volatility𝜎 0‡ 0‡ 0‡ 0.038 0‡ 0‡ 0‡ 0‡ 𝜉𝑐 CommonTradeshock,persistence 𝜌 0‡ 0‡ 0‡ 0.937 0‡ 0‡ 0‡ 0‡ 𝜉𝑐 ElasticityofSubstitution𝛾 1.5‡ 1.5‡ 1.5‡ 1.5‡ 1.5‡ 1.5‡ 1.9 1.5‡ HighPersistenceFinshock,volatility 𝜎ℎ 0‡ 0‡ 0‡ 0‡ 0‡ 0‡ 0‡ 0.002 𝜓 HighPersistenceFinshock,persistence 𝜌ℎ 0‡ 0‡ 0‡ 0‡ 0‡ 0‡ 0‡ 0.911 𝜓 LowPersistenceFinshock,volatility 𝜎𝑙 0‡ 0‡ 0‡ 0‡ 0‡ 0‡ 0‡ 0.015 𝜓 LowPersistenceFinshock,persistence 𝜌𝑙 0‡ 0‡ 0‡ 0‡ 0‡ 0‡ 0‡ 0.007 𝜓 Correlationinnovations𝜖ℎand𝜖𝑙 0‡ 0‡ 0‡ 0‡ 0‡ 0‡ 0‡ 0.21 𝜓 𝜓 Notes: Superscript‡denotesthattheparameterisexogeneouslysetwhilesuperscript∗specifiesthatthecalibrated adjustmentcostisforinvestmentnotcapital. ‘Benchmark’showsthesameresultspresentedinSection5. ‘Short’ shows the result of the estimation using short period samples (Section E.2). ‘Input Adj’ shows the result of the modelwithreduced-formtradedynamics(SectionE.3). ‘Common’isforthemodelwithcommonshockstotrade costs (Section E.4). ‘𝜏 = 0’ is the case with no within-ROW trade cost shocks (Section E.5). ‘Inv Adj’ is the case withinvestmentadjustmentcost(SectionE.7). ‘TE’iswhenwetargetshort-andlong-runelasiticies(SectionE.8). ’Sophisticated𝜓’isthecaseofamixoftwoAR(1)processesforthefinancialshock(SectionE.9). 65

TableE.6: Robustness–ModelResults Moments Data Benchmark Short InputAdj Common 𝜏 =0 InvAdj TE Sophisticated𝜓 A.TargetedMoments 𝑐𝑜𝑟(Δ𝑛𝑡,Δ𝑞) 0.30 0.30 0.30 0.31 0.30 0.37 0.30 0.24 0.94 𝜎(𝑛𝑡)/𝜎(𝑞) 1.21 1.21 1.21 1.21 1.21 1.32 1.21 1.28 1.76 𝜎(Δ𝑦) 0.007 0.007 0.007 0.007 0.007 0.007 0.007 0.007 0.007 𝑐𝑜𝑟(Δ𝑦,Δ𝑦∗) 0.40 0.43 0.40 0.40 0.41 0.42 0.40 0.39 0.43 𝑐𝑜𝑟(Δ𝑐−Δ𝑐∗,Δ𝑞) -0.10 -0.10 -0.10 -0.10 -0.10 -0.01 -0.10 -0.15 -0.11 𝑎𝑢𝑡𝑜𝑐𝑜𝑟(𝑖−𝑖∗) 0.87 0.87 0.66 0.96 0.89 0.99 0.87 0.77 0.88 𝑎𝑢𝑡𝑜𝑐𝑜𝑟(𝑛𝑡) 0.98 0.97 0.94 0.90 0.98 0.98 0.98 0.99 0.96 𝜎(𝑖𝑛𝑣∗)/𝜎(𝑦∗) 2.21 2.16 2.21 2.18 2.18 2.45 2.21 2.01 2.19 𝑐𝑜𝑟(Δ𝑑,Δ𝑑∗) 0.34 0.32 0.33 0.34 0.33 0.13† 0.34 0.31 0.31 𝑐𝑜𝑟(Δ𝑡𝑜𝑡,Δ𝑞) 0.49 0.49 0.49 0.49 0.49 0.47 0.49 0.48 0.49 𝑎𝑢𝑡𝑜𝑐𝑜𝑟(𝑥+𝑚) 0.98 0.98† 0.95† 0.93† 0.95 0.99† 0.98† 0.99† 0.98† 𝑦 𝑐𝑜𝑟(Δ𝑥+𝑚,Δ𝑦) 0.35 -0.56† -0.66† 0.32† 0.35 -0.39† -0.56† -0.54† -0.49† 𝑦 B1.FrequencyDecompositionofRER Highfrequency 0.07 0.07 0.11 0.09 0.06 0.06 0.06 0.07 0.12 Businesscyclefrequency 0.31 0.21 0.30 0.23 0.20 0.19 0.20 0.20 0.23 Lowfrequency 0.62 0.72 0.59 0.69 0.73 0.74 0.73 0.73 0.65 B2.FrequencyDecompositionofNTFlows Highfrequency 0.06 0.07 0.10 0.12 0.06 0.06 0.06 0.05 0.08 Businesscyclefrequency 0.30 0.24 0.35 0.32 0.23 0.23 0.23 0.22 0.23 Lowfrequency 0.64 0.69 0.55 0.56 0.71 0.71 0.71 0.72 0.69 C.DisconnectPuzzles 𝜎(𝑞)/𝜎(𝑦∗) 2.23 2.53 3.78 3.68 2.39 3.83 1.51 2.92 1.77 𝜎(Δ𝑞)/𝜎(Δ𝑦∗) 3.90 3.02 4.37 6.59 2.46 3.93 1.69 3.41 4.22 𝑎𝑢𝑡𝑜𝑐𝑜𝑟(𝑞) 0.97 0.97 0.93 0.95 0.98 0.98 0.98 0.98 0.90 𝛽 -1.34 0.42 0.80 2.89 0.52 -0.68 0.71 1.18 -2.90 𝑓𝑎𝑚𝑎 𝑅2 0.04 0.01 0.09 0.04 0.02 0.03 0.08 0.13 0.02 𝑓𝑎𝑚𝑎 𝑐𝑜𝑟(𝑞,𝑖−𝑖∗) -0.50 -0.36 -0.39 -0.18 -0.37 -0.18 -0.28 -0.39 -0.25 𝑎𝑢𝑡𝑜𝑐𝑜𝑟(𝑖) 0.93 0.93 0.67 0.96 0.94 0.97 0.88 0.83 0.93 𝜎(𝑖−𝑖∗)/𝜎(Δ𝑞) 0.15 0.04 0.06 0.02 0.05 0.04 0.07 0.06 0.02 D.TradeElasticity SRelasticity 0.18 0.44† 0.28† -0.07† 0.36† 0.83† 0.27† 0.25 1.05† (0.002) LRelasticity 2.01 0.82† 1.16† 0.36† 0.99† 0.54† 1.00† 1.90 1.81† (1.025) Adjustment 0.03 0.03† 0.09† 0.08† 0.02† 0.02† 0.02† 0.02 0.22† (0.000) Notes: Superscript†denotesthatthemomentisnottargetedduringthecalibrationprocedure. ‘Benchmark’shows thesameresultspresentedinSection5.‘Short’showstheresultoftheestimationusingshortperiodsamples(Section E.2).‘InputAdj’showstheresultofthemodelwithreduced-formtradedynamics(SectionE.3).‘Common’isforthe modelwithcommonshockstotradecosts(SectionE.4). ‘𝜏 = 0’isthecasewithnowithin-ROWtradecostshocks (SectionE.5). ‘InvAdj’isthecasewithinvestmentadjustmentcost(SectionE.7). ‘TE’iswhenwetargetshort-and long-run elasticities (Section E.8). ’Sophisticated 𝜓’ is the case of a mix of two AR(1) processes for the financial shock(SectionE.9). TheempiricalmomentsforthelevelofGDPandinvestmentwerecalculatedusingthecyclical componentfromalinearde-trend. 66

FigureE.4: RERSpectrumRobustness 0.06 Data Benchmark Model 0.05 Reduced Form Dynamic Trade 0.04 0.03 0.02 0.01 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Frequency TableE.7: Robustness–VarianceDecomposition Benchmark ShortSample CommonTradeCost 𝜏 = 0 Quarters P F T P F T P F T P F T 1 3.9 54.4 41.7 4.3 54.2 41.5 6.3 54.1 39.5 0.5 53.4 46.1 8 5.8 43.1 51.1 5.8 39.5 54.7 9.3 43.9 46.8 0.9 41.9 57.2 32 9.3 22.8 67.9 8.1 21.6 70.3 14.8 23.9 61.2 1.5 20.1 78.4 80 8.8 20.4 70.8 8.6 21.8 69.6 13.7 20.4 65.9 1.3 15.5 83.2 Benchmark InvAdj InputAdj TE Quarters P F T P F T P F T P F T 1 3.9 54.4 41.7 12.0 52.5 35.4 0.3 94.3 5.4 5.7 67.3 27.0 8 5.8 43.1 51.1 16.9 43.0 40.2 1.1 82.9 16.1 8.5 57.6 34.0 32 9.3 22.8 67.9 30.8 22.6 46.6 2.9 47.8 49.3 14.0 34.9 51.1 80 8.8 20.4 70.8 29.9 20.2 49.9 2.4 25.5 72.1 12.0 27.2 60.8 Notes:‘P,’‘F’and‘T’refertoshareaccountedbyproductivityshocks,financialshocks,andtradeshocks,respectively. ‘Benchmark’showsthesameresultspresentedinSection5.‘InputAdj’showstheresultofthemodelwithreducedformtradedynamics(SectionE.3). ‘𝜏 = 0’isthecasewithnowithin-ROWtradecostshocks,with𝜏 = 0(Section E.5). ‘Short Sample’ shows the result of the estimation using short period samples (Section E.2). ‘Common’ is for themodelwithcommonshockstotradecosts(SectionE.4). ‘TE’iswhenwetargetshort-andlong-runelasciticies (SectionE.8). 67

E.4 CommonTradeCosts Weextendthetradeshockprocesstoincludeacommontradecost. Specifically,tradecostshocks aregivenby 𝜉 𝜉 𝜉∗ = 𝑡 +𝜉𝑐 𝜉 = − 𝑡 +𝜉𝑐 𝑅𝑡 2 𝑡 𝑈𝑡 2 𝑡 𝜉 𝜉 = 𝜏 𝑡 𝜉∗ = 0 (16) 𝑅𝑡 2 𝑈𝑡 where𝜏 ∈ ℝ, 𝜉 = 𝜌 𝜉 +𝜀 , 𝜀 ∼ 𝑁(0,𝜎 ) 𝑡 𝜉 𝑡−1 𝜉𝑡 𝜉𝑡 𝜉 and 𝜉 = 𝜌 𝜉 +𝜀 , 𝜀 ∼ 𝑁(0,𝜎 ). 𝑐,𝑡 𝜉 𝑐,𝑡−1 𝜉𝑐𝑡 𝜉𝑐𝑡 𝜉 𝑐 𝑐 This means we need to discipline two extra parameters: the persistence 𝜌 and volatility 𝜎 𝜉 𝜉 𝑐 𝑐 of the common trade cost shock. We target the autocorrelation of the share of trade over GDP, (𝑥 +𝑚)/𝑦, and the correlation between the growth rates of the trade share and GDP to identify theseparameters,sincethecommontradeprocesshasadirecteffectonthescaleoftrade. TableE.5presentthecalibratedparameters. Theparametersincommonwiththebenchmark model are similar, although we find a slightly higher persistence of the differential trade shock process and a higher domestic trade cost elasticity. We find that the persistence of the common tradeshockprocessishigh,around0.937. ThemomentmatchingofthecommontradecostmodelispresentedinTableE.6. Ingeneral, we find that the model performs similarly as the benchmark model. Finally, Table E.7 shows the results in terms of the conditional variance decomposition of the RER, which is consistent with ourbenchmarkmodel: financialshocksdominateinthehighfrequencyandtradeshocksinlower frequencies. E.5 Within-ROWTradeCosts In this section, we evaluate the role of the within-ROW trade cost 𝜏. We set up an alternative model where the elasticity of domestic trade costs to international costs is 𝜏 = 0. Then, we calibratethemodelbytargetingthesamemomentsasinthebenchmarkmodel,exceptthecross countrycorrelationofdomesticabsorption. The calibrated parameters and resulting moments are reported in Tables E.5 and E.6 under ‘𝜏 = 0.’ This model generates a worse fit for the Backus-Smith-Kollmann correlation, which is -0.01 in the model as opposed to -0.10 in the data, although it lies within the estimated range in theliterature. Themodelmissesthecrosscountrycorrelationofdomesticabsorption,being0.13 inthemodeland0.34inthedata. Thus,𝜏 mattersforaccountingfortheBackus-Smith-Kollmann puzzleandthecrosscountrycorrelationofdomesticabsorption. Overall,thismodelhasaworse fitintomatchingthetargetmomentsrelativetoourbenchmarkmodel. In Table E.7 we present the results related to the variance decomposition of the RER, under ‘𝜏 = 0.’ Ourmainresultsholdsunderthisspecification: financialshocksexplainahigherportion ofthevariationintheRERintheshortrun,whiletradeshocksexplainsmostofthevariationin thelongrun. 68

E.6 ThreeCountryModel We extend the static trade model to include and extra country. One of the countries is the US, which has measure 0.5, whereas each of the two extra countries are ROW countries with size 0.5. The aggregate of the ROW is an average of the two ROW countries, and we use the same momentsasinthetwocountrymodel. Tradecostshocksaregivenby 𝜉 = 𝜉 /2 𝜉 = 𝜉 /2 𝑅1,𝑈 𝑑 𝑅2,𝑈 𝑑 𝜉 = −𝜉 /2 𝜉 = −𝜉 /2 𝑈,𝑅1 𝑑 𝑈,𝑅2 𝑑 𝜉 = 𝜏 ⋅𝜉 /2 𝜉 = 𝜏 ⋅𝜉 /2 𝑅1,𝑅2 𝑑 𝑅2,𝑅1 𝑑 whereR1andR2denotetwocountriesconsistingtheROW,USdenotestheUS,and𝜉 followsan 𝑑 AR(1) processes as in the benchmark model. To calibrate the model we set the value of 𝜏 to the benchmarkcase(0.152),anddisciplinetheremainingparametersusingthesamemomentsasthe benchmarkcase. TableE.8showthematchingofthemoments.66 Figure E.5 shows the Impulse Response Functions of selected variables to a differential trade cost shock, for different values of 𝜏. As it is the case with the domestic trade cost elasticity in the two country model (Figure 5), a higher elasticity dampens the effect on relative domestic absorptionandtheRER. TableE.8: TargetedMomentsfromThreeCountryModel Moments Data Benchmark Three-CountryModel 𝑐𝑜𝑟 (Δ𝑛𝑡,Δ𝑞) 0.30 0.30 0.49 𝜎(𝑛𝑡)/𝜎(𝑞) 1.21 1.21 1.45 𝜎(Δ𝑦) 0.007 0.007 0.006 𝑐𝑜𝑟 (Δ𝑐 −Δ𝑐∗,Δ𝑞) -0.10 -0.10 0.12 𝑎𝑢𝑡𝑜𝑐𝑜𝑟 (𝑖 −𝑖∗) 0.87 0.87 0.81 𝑐𝑜𝑟(Δ𝑦,Δ𝑦∗) 0.40 0.43 0.71 𝑐𝑜𝑟(Δ𝑑,Δ𝑑∗) 0.34 0.32 0.26 𝑎𝑢𝑡𝑜𝑐𝑜𝑟(𝑛𝑡) 0.98 0.97 0.97 E.7 InvestmentAdjustmentCosts In this section, we consider an adjustment cost in investment as in Christiano et al. (2005). That is,thelawofmotionforcapitalisnowgivenby 𝐼 𝐾 = (1−𝛿)𝐾 + 1−𝑆 𝑡 𝐼 𝑡+1 𝑡 [ (𝐼 )] 𝑡 𝑡−1 66WefindthatmatchingtheaggregateUSandROWmomentsinthethreecountrymodelisharderthaninthetwo countrycase. However,themodeldoesareasonablejobinmatchingthem. Moreover,thepurposeofthisexercise is to show that the elasticity of domestic to foreign trade cost in the two country model operates as a trade cost betweenROWcountries,whichweshowitdoesqualitatively. 69

FigureE.5: IRFstoTradeShockinThree-CountryModel d-d* RER 0.4 0.7 0.35 0.6 0.3 0.5 0.25 0.4 0.2 0.3 0.15 0.2 0.1 0.1 0.05 =0 =0.151 =0.50 0 0 0 20 40 60 80 100 0 20 40 60 80 100 Quarters Quarters where𝑆(1) = 𝑆′(1) = 0and𝑆′′(1) > 0. Here,weconsiderthefunctionalformof𝑆 as 𝐼 𝜅̃ 𝐼 2 𝑆 𝑡 = 𝑡 −1 . (𝐼 ) 2 (𝐼 ) 𝑡−1 𝑡−1 Toestimatetheadjustmentcostparameter𝜅̃,weagainusethevolatilityofinvestment. That is, the targeted moments remain unchanged. The result of the estimated model with the new investmentadjustmentcostispresentedinTablesE.5andE.6,under‘InvAdj.’ The estimated parameter for the adjustment cost is smaller than in the benchmark model, sincenowtheadjustmentcostisoveraflowratherthanastock. Thisversionofthemodelrequires higher standard deviations of trade shocks relative to our benchmark, where the variance of the common and differential productivity shocks are almost the same. We find that the adjustment cost of debt is smaller under investment adjustment costs. Finally, we find a similar pricing to marketcoefficientasinthebenchmark,withanimpliedpass-throughofexchangeratetoprices of68percent. The model is able to match the target moments, and performs well in terms of untargeted moments. TheshortandlongrunelasticityofNTtopricesisalsoverysimilartothebenchmark model. However,thevarianceoftheRERisworsethaninthebenchmarkmodel. Finally, in Table E.7 we present the contribution of each shock to the error forecast variance oftheRER.Consistentwithourbenchmarkmodel,wefindthatfinancialshocksexplainsmostof thevariationintheshortrun,whiletradeshocksexplainmostofitinthelongrun. However,we find that the importance of productivity shocks is higher in this version of the model, although asmentionedabovethevarianceoftheRERinthismodelisworse. E.8 SunkExportingCostandTradeElasticity In this section, we improve the performance of the model in generating short- and long-run trade elasticities. To do so, we allow the Armington elasticity and the exporter fixed costs to be 70

estimatedjointlyalongwithotherinternally-calibratedparameters. The Armington elasticity is a crucial parameter that determines the relationship between relativepricesandNTflows. Yettheestimatesfortheelasticitytendtovary,andalargerangeof valuesareusedinthetradeliterature. Inourbenchmarkmodel,wesettheArmingtonelasticity exogenouslywith𝛾 = 1.5asinItskhokiandMukhin(2021). However,thelong-runtradeelasticity islowerinourbenchmarkmodelthaninthedata(0.82inthebenchmarkmodeland2.01indata, seeTableD.1),suggestingtheneedforalargerArmingtonelasticity. Moreover,sincethebehavior ofindividualfirmsaffectsaggregatetradeflows,re-calibratingthefixedcostsofexportingwould allowthemodeltogenerateashortandlongruntradeelasticityclosertodata. To estimate these three additional parameters, we add to our targeted moments three estimates from the error correction model, namely, short- and long-run trade elasticities and the speedofadjustment. TheresultofthisexerciseispresentedinTablesE.5andE.6,underthecolumn ‘TE.’ Consistent with our conjecture, the estimated Armington elasticity 𝛾 = 1.9 is slightly largerthanthebenchmarkcase. Withtheestimatedfixedcosts𝑓0 = 0.33,𝑓1 = 0.08,wegetlarger sunk costs, contributing to generating a larger gap between short- and long-run elasticities so thattheyareclosertodata. Overall, we find similar results as in the benchmark model. However, the persistence of NT and, as a consequence, the low frequency share of variation are higher than in the benchmark model which arises from estimating a higher persistence of trade shocks and higher sunk costs. Finally, as shown in Table E.7, financial shocks explain a higher portion of the variation of the RERatallhorizonsrelativetothebenchmarkmodel,althoughtradeshocksarestilldominantin thelongrun. E.9 AMoreSophisticatedFinancialProcess We show that our result that trade shocks are needed to match the RER and NT moments at the high frequency is robust to considering a more sophisticated financial process. In particular, we allow the financial shock to be the mix of two AR(1) processes, each of them with a different persistence. Assumethattherearetwpfinancialprocessesgivenby, 𝜓ℎ = 𝜌ℎ𝜓ℎ +𝜖ℎ and 𝜓𝑙 = 𝜌𝑙 𝜓𝑙 +𝜖𝑙 𝑡 𝜓 𝑡−1 𝜓𝑡 𝑡 𝜓 𝑡−1 𝜓𝑡 where 𝜌ℎ ≥ 𝜌𝑙 are the persistence of the processes, 𝜖ℎ ∼ 𝑁(0,𝜎ℎ) and 𝜖𝑙 ∼ 𝑁(0,𝜎𝑙). We 𝜓 𝜓 𝜓𝑡 𝜓 𝜓𝑡 𝜓 also allow the innovations 𝜖ℎ and 𝜖𝑙 to be correlated. We target the same moments as in the 𝜓𝑡 𝜓𝑡 benchmarkmodel (wehavethe samenumberofmoments thanparameterssince weincludethe correlationbetweenthetwofinancialinnovations). Whenweestimatethemodelweimposethe followingconstraints: 0.5 ≤ 𝜌ℎ < 1and0 ≤ 𝜌𝑙 ≤ 0.5.67 𝜓 𝜓 The estimated parameters are displayed in Table E.5 and the moments in Table E.6, under ’Sophisticated 𝜓’. This model fails to capture the RER and NT moments at the high frequency because both processes trigger a positive comovement between the RER and NT on impact, as shown in Figure E.6. As a consequence, the model cannot match the weak high frequency correlation. Moreover, conditional on matching the other target moments, the model generates an excess volatility of NT at the high frequency. Hence, the main results of the paper hold under thismoresophisticatedfinancialprocess. 67Increasingtheupperboundof𝜌𝑙 intheestimationdidnotchangetheresults. 𝜓 71

FigureE.6: ImpulseResponseFunctions: TwoAR(1)FinancialProcesses RER NT 2 2.5 Low Persistence ( l) High Persistence ( h) 2 1.5 1.5 1 1 0.5 0.5 0 0 -0.5 -0.5 0 20 40 60 80 100 0 20 40 60 80 100 Quarters Quarters F Theoretical Decomposition of NT Inthissection,weprovidethederivationofNTinourbenchmarkmodel. Forsimplicity,weomit thetimesubscript𝑡. ThedemandfunctionforaggregateexportsofROWisgivenby 𝑃∗ −𝛾 𝑌∗ = 𝜔 𝑅 𝐷∗ 𝑅 (𝑃∗) where𝑃∗ = 1. Thedemandfacedbyaproducerofeachvariety𝑗 is 𝑝∗ −𝜃 𝑝∗ −𝜃 𝑃∗ −𝛾 𝑦∗ = 𝑅𝑗 𝑌∗ = 𝜔 𝑅𝑗 𝑅 𝐷∗ 𝑅𝑗 (𝑃∗ ) 𝑅 (𝑃∗ ) ( 𝑃 ) 𝑅 𝑅 wherethesecondequalityusestheaggregatedemandfunction. Usingthattotalsalesisasumof salesofallvarieties, 𝑃∗ 𝑌∗ = 𝑝∗ 𝑦∗ 𝑑𝑗 = 𝜔𝑝∗1−𝜃𝑃∗𝜃−𝛾𝐷∗ 𝑑𝑗 𝑅 𝑅 ∫ 𝑅𝑗 𝑅𝑗 ∫ 𝑅𝑗 𝑅 = 𝜔 𝑃∗1−𝛾 𝐷∗. 𝑅 Aggregateexportsandimportsinnominaltermsaregivenby 𝑋𝑁 =  𝑝∗ 𝑦∗ 𝑑𝑗 = 𝑃∗𝑌∗ = 𝜔  𝑃∗(1−𝛾)𝐷∗ ∫ 𝑅𝑗 𝑅𝑗 𝑅 𝑅 𝑅 𝑗∈ 𝑀𝑁 = 𝑝 𝑦 𝑑𝑗 = 𝜔 𝑃(1−𝛾)𝐷 ∫ 𝑈𝑗 𝑈𝑗 𝑈 𝑗∈∗ 72

andtheexportandimportpricesare 1 1 𝑝∗ 1−𝜃∗ 1−𝜃∗ 𝑃𝑥 =  ∫ 𝑅𝑗 𝑑𝑗 =  𝑃∗ 𝑒𝜉 𝑅 ∗(𝜃∗−1) 𝑁 1− − 𝜃 1 ∗ (𝑁 (𝑒𝜉∗ ) ) 𝑅 𝑗∈ 𝑅 1 1 𝑝 1−𝜃 1−𝜃 𝑃𝑚 = (𝑁∗ ∫ ( 𝑒𝜉 𝑈𝑗 ) 𝑑𝑗 ) = 𝑃 𝑈 𝑒𝜉 𝑈 (𝜃−1) 𝑁∗ 1 − − 1 𝜃 𝑗∈∗ 𝑈 where𝑁 denotesthemassofexporters. Inlogs, 𝑥𝑁 = log𝜔 +(1−𝛾)𝑝∗ +𝑑∗ +𝑞 𝑅 𝑚𝑁 = log𝜔 +(1−𝛾)𝑝 +𝑑 1 𝑝𝑥 = 𝑞 +𝑝∗ + 𝑛−(1−𝜃∗)𝜉∗ 𝑅 1−𝜃∗ 𝑅 1 𝑝𝑚 = 𝑝 + 𝑛∗ −(1−𝜃)𝜉 𝑈 1−𝜃 𝑈 wherelowercaselettersdenotevariablesinlogs. Using that in real terms real exports and real imports are 𝑋 = 𝑋𝑁/𝑃𝑥,𝑀 = 𝑀𝑁/𝑃𝑚, respectively,logofrealexportsandimportsaregivenby 1 𝑥 = 𝑥𝑁 −𝑝𝑥 = log𝜔 −𝛾𝑝∗ +𝑑∗ − 𝑛 𝑅 1−𝜃∗ 1 𝑚 = 𝑚𝑁 −𝑝𝑚 = log𝜔−𝛾𝑝 +𝑑 − 𝑛∗. 𝑈 1−𝜃 Therefore,NT,measuredbylogofExport-Importratio,is 𝑛𝑡 = 𝑥 −𝑚 1 1 = 𝛾(𝑝 −𝑝∗)+(𝑑∗ −𝑑)+ 𝑛∗ − 𝑛 𝑈 𝑅 ( 1−𝜃 1−𝜃∗ ) 1 1 = 𝛾 (𝑡𝑜𝑡 +𝑞)+(𝑑∗ −𝑑)+((1−𝜃∗)𝜉∗ −(1−𝜃)𝜉 )+(1−𝛾) 𝑛∗ − 𝑛 . (17) 𝑅 𝑈 ( 1−𝜃 1−𝜃∗ ) where𝑡𝑜𝑡 = 𝑝𝑚−𝑝𝑥 isthetermsoftrade. 𝑡 On the other hand, in the Armington trade model, demand for exports and foreign goods follows a standard CES structure. Taking the ratio of demand functions for exports and imports impliedintheArmingtonmodel,wehave 𝑛𝑡 = 𝛾 (𝑡𝑜𝑡 +𝑞 )+(𝑑∗ −𝑑 ). (18) 𝑡 𝑡 𝑡 𝑡 𝑡 Comparingthisequation,Equation17forthebenchmarkmodelhasadditionalterms((1−𝜃∗)𝜉∗ − 𝑅 (1−𝜃)𝜉 )and(1−𝛾)( 1 𝑛∗ − 1 𝑛).Thesereflectthatinourmodelwehavetwofeatures,trade 𝑈 1−𝜃 1−𝜃∗ shocksandtradedynamics. 73

G Analytical Solution and Impact of Shocks on the RER Persistence Inthissection,wederivetheanalyticalsolutionfortheRERtostudytheimpactoffinancialand tradeshocksontheRERpersistence. Westartwiththelog-linearizedresourceconstraintwithtradeshock𝜉 : 𝑡 𝑦 = (1−𝜔)𝑦 +𝜔(𝑦∗ +𝜉 ) 𝑡 𝐻𝑡 𝐻𝑡 𝑡 wherethesmallcasedenoteslog-linearizedvariables. Usinglog-linearized𝑁𝑋 andsubstituting 𝑡 thesolutionforpricesandquantities,weget ̃ 𝑛𝑥 = 𝜔(𝑦 −𝑦 −𝑠 ) = 𝜔(𝜆 𝑞 −𝜆 𝜉 ) 𝑡 𝐻𝑡 𝐹𝑡 𝑡 𝑞 𝑡 𝜉 𝑡 forsomecoefficients𝜆 ,𝜆 and𝜉 ̃ = 𝜉 −𝜉∗. Noticethatwehaveanadditionalshockintheresource 𝑞 𝜉 𝑡 𝑡 𝑡 constraintwhiletheequationsforotherquantitiesandpricesaresameasinItskhokiandMukhin (2021). Also,wearesettingproductivityshocks𝑎 = 𝑎 = 0tofocusontwoothershocks. 𝑐𝑡 𝑑𝑡 FollowingsimilarstepsasdescribedinItskhokiandMukhin(2021),weendupinasystemof twoequations,whichcanbeexpressedinamatrixformas 1 −𝜒̂ 𝑞 1 0 𝑞 −𝜒̂ 𝑘(1−𝜌) 𝜓 𝐸 2 𝑡+1 = 𝑡 − 1 𝑡 𝑡( 0 1 )( 𝑏 ̂∗ ) ( 1 1 )( 𝑏 ̂∗ ) ( 0 1 )( 𝜉 ̂ ) 𝑡+1 𝛽 𝑡 𝑡 ̂ ̃ where𝑘isacoefficientsubstitutedforsimplicity,and𝜉 isanormalizationof𝜉 . WeuseBlanchard- 𝑡 𝑡 Khanmethodstoderivetheclosed-formsolutionfortheRER.Thatis,wediagonalizethedynamic systemof 𝐸 𝑧 = 𝐵𝑧 −𝐶(𝜓 𝜉 ̂ )′ 𝑡 𝑡+1 𝑡 𝑡 𝑡 𝑞 1+𝜒̂ 𝜒̂ 2 where 𝑧 = 𝑡 , 𝐵 = 2 𝛽 , and 𝐶 is a coefficient matrix to the vector of shocks. 𝑡 ( 𝑏∗ ) ( 1 1 ) 𝑡 𝛽 Eigenvalues𝜇 ,𝜇 ofthematrix𝐵 aresolutionsto 1 2 1 𝜒̂ (1+𝜒̂ −𝜇) −𝜇 − 2 = 0. 2 (𝛽 ) 𝛽 The left eigenvector for an eigenvalue 𝜇 > 1 is 𝑣 = (1,1/𝛽 − 𝜇 ). We pre-multiply the dynamic 2 1 systemby𝑣 andgettheequilibriumcointegrationrelationship: 1 𝑣𝑧 = 𝑞 + −𝜇 𝑏 𝑡 𝑡 (𝛽 1) 𝑡 𝛽𝜇 𝜒̂ 1−𝛽𝜇 +𝛽(1−𝜌)𝑘𝜇 = 1 1 𝜓 + 1 1 𝜉 ̂ . (19) 1−𝛽𝜌𝜇 𝑡 ( 1−𝛽𝜌𝜇 ) 𝑡 1 1 74

Combiningthiswiththeseconddynamicequationfor𝑏 ̂∗ ,weget 𝑡+1 1 𝑏 ̂∗ −𝜇 𝑏 ̂∗ = 𝑞 + −𝜇 𝑏 ̂∗ −𝜉 ̂ 𝑡+1 1 𝑡 𝑡 (𝛽 1) 𝑡 𝑡 ̂ = 𝑣𝑧 −𝜉 𝑡 𝑡 𝛽𝜇 𝜒̂ 𝛽(1−𝜌)(𝑘 −1)𝜇 = 1 1 𝜓 + 1𝜉 ̂ . 1−𝛽𝜌𝜇 𝑡 1−𝛽𝜌𝜇 𝑡 1 1 Nowapplylagoperator(1−𝜇 𝐿)toEquation(19)tofinallyget 1 ⎡ ⎤ ⎢ ⎥ 1 ⎢ 𝛽𝜇 𝜒̂ 𝛽(1−𝜌)𝑘𝜇 ⎥ 1−𝛽𝜇 (1−𝜇 𝐿)𝑞 = 1− 𝐿 ⎢ 1 1 𝜓 + 1 𝜉 ̂ ⎥+ 1 (1−𝜌𝜇 𝐿)𝜉 ̂ . 1 𝑡 ( 𝛽 ) 1−𝛽𝜌𝜇 𝑡 1−𝛽𝜌𝜇 𝑡 1−𝛽𝜌𝜇 1 𝑡 ⎢ 1 1 ⎥ 1 ⏟⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏟⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏟ ⏟⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏟⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏟ ⎢ ⎥ ⎣ (∗) ⎦ (∗∗) ThisequationshowsthattheequilibriumRERfollowsastationaryARMA(2,1)process. Notethat the term (∗) captures the trade shock effect through the UIP deviation, and (∗∗) is for the effects viathebudgetconstraint. As can be seen from this equation, the main reason that effect of trade shock has a different impactthanthefinancialshockisduetothesecondterm,(∗∗),themechanismthroughthebudget constraint. Absentofthisterm,financialandtradeshocksdifferonlyintheircoefficientsbutshare the same lag operator. Then the impacts of financial and trade shocks become proportional to eachotherthatonlydifferintheirsizesbutnotpersistences. Forexample,ashock𝜀 willaffect 𝜓𝑡−1 the left-hand-side, (1−𝜇 𝐿)𝑞 = 𝑞 −𝜇 𝑞 , in a proportional way as a shock 𝜀 . Therefore, the 1 𝑡 𝑡 1 𝑡−1 𝜉𝑡−1 autocorrelation of two IRFs are going to be equal. However, due to the existence of the second them, the trade shock has another layer of affecting the left-hand-side. In specific, a shock 𝜀 𝜉𝑡−1 has a lag operator (1−𝜌𝜇 𝐿) and its effect on the left-hand-side is not proportional to the others 1 anymore. This can be seen by plotting IRFs using the derived equation. Using the parameter values of the benchmark case, and also checking robustness with other values, we plot the IRFs of two shocks in Figure G.1. The result is similar to the one from our quantitative exercise, presented in Figure 4. The calculated autocorrelations of each IRF is 0.96 (trade shock) and 0.86 (financial shock). Now consider a case when we shut off the effects through the budget constraint. If we force (∗∗) = 0, the IRF of trade shock becomes much less persistence, and the autocorrelation reduces to0.86(reddottedlineinFigureG.1). On the other hand, shutting of (∗) term has a negligible effect. That is, its IRF coincides with the original case (red solid line in Figure G.1). This result is consistent with our quantitative exercisethateffectoftradeshockthroughgeneratingtheUIPdeviationissmall. 75

FigureG.1: IRFsfromAnalyticalSolution q q 0.12 0.12 Financial Shock Trade Shock 0.1 0.1 Trade Shock, (**)=0 Trade Shock, (*)=0 0.08 0.08 0.06 0.06 0.04 0.04 0.02 0.02 0 0 -0.02 -0.02 0 20 40 60 80 100 0 20 40 60 80 100 76

H Additional Figures and Tables FigureH.1: RERandNT–OtherEconomies Australia Austria 0.7 0.1 0.3 0.2 0.6 0.2 0 0 0.5 0.1 RER -0.2 NT Dynamic correlation 0.4 -0.1 0 1980 1990 2000 2010 2020 2 4 6 8 1980 1990 2000 2010 2020 2 4 6 8 Belgium Canada 0.1 0.6 0.2 0.5 0 0.4 0 0.4 -0.1 0.2 -0.2 0 -0.2 0.3 1980 1990 2000 2010 2020 2 4 6 8 1980 1990 2000 2010 2020 2 4 6 8 Denmark Finland 0.2 0.2 0.6 0.2 0 0.1 0 0.4 -0.2 0.2 -0.2 0 1980 1990 2000 2010 2020 2 4 6 8 1980 1990 2000 2010 2020 2 4 6 8 France Germany 0.1 0.1 0.4 0.3 0.05 0.25 0 0.2 0 0.2 -0.05 0.15 -0.1 0.1 -0.1 0 1980 1990 2000 2010 2020 2 4 6 8 1980 1990 2000 2010 2020 2 4 6 8 Greece Italy 0.3 0.2 0.6 0.2 0 0.2 0 0.4 -0.2 0.1 -0.2 0.2 1980 1990 2000 2010 2020 2 4 6 8 1980 1990 2000 2010 2020 2 4 6 8 Korea Portugal 0.5 0.4 0.3 0.66 0.2 0 0.2 0.64 0 -0.5 0.62 -0.2 0.1 1980 1990 2000 2010 2020 2 4 6 8 1980 1990 2000 2010 2020 2 4 6 8 Spain Sweden 0.4 0.6 0.2 0.5 0.2 0.5 0.4 0.4 0 0 0.3 0.3 -0.2 0.2 -0.2 0.2 1980 1990 2000 2010 2020 2 4 6 8 1980 1990 2000 2010 2020 2 4 6 8 Notes: The left panel shows the linearly detrended RER and NT for each economy. The right panel is a dynamic correlationbetweenthetwovariables,𝑐𝑜𝑟(Δ 𝑞 ,Δ 𝑛𝑡 ),withthex-axisrepresentingquarters. ℎ 𝑡 ℎ 𝑡 77

FigureH.2: GrossTradetoGDPRatio 1 US Canada Finland Germany Italy Japan Korea Spain Sweden UK .8 .6 .4 .2 0 1/1/1980 1/1/1990 1/1/2000 1/1/2010 1/1/2020 Notes:Thefigureshowstheshareofgrosstradeasashareoftotaloutput,measuredbytheratioofvolumeestimates ofexportsplusimportstoGDPforeachcountry. FigureH.3: DataSourceComparison Canada Germany 20 IMF 15 IMF OECD OECD 15 10 10 5 5 0 0 1980q1 1990q1 2000q1 2010q1 2020q1 1980q1 1990q1 2000q1 2010q1 2020q1 Japan UK 15 IMF 20 IMF BOJ OECD 15 10 10 5 5 0 0 1980q1 1990q1 2000q1 2010q1 2020q1 1980q1 1990q1 2000q1 2010q1 2020q1 78

FigureH.4: MeasuresofNetTrade .05 0 −.05 −.1 −.15 −.2 )M/X(gol 5.0 ,)M+X(/)M−X( .02 0 −.02 −.04 −.06 Y/)M−X( (X−M)/Y (X−M)/(X+M) 0.5 log(X/M) 1980q1 1990q1 2000q1 2010q1 2020q1 Notes: Thefigureshowstradebalanceasashareofoutput(leftaxis),tradebalanceasashareofgrosstrade(right axis),andahalfoflogexport-importratio(rightaxis)fortheUS. FigureH.5: DynamicCorrelationbetweenRERandTrade-ExpenditureRatio 0.6 0.5 0.4 0.3 0.2 0.1 0 -0.1 Data -0.2 Benchmark No Dynamics -0.3 1 2 3 4 5 6 7 8 Quarters Notes: Thefigurepresentsdynamiccorrelationsas𝜌(Δ ℎ 𝑞 𝑡 ,Δ ℎ 𝑇𝐸 𝑡 ),where𝑞 𝑡 and𝑇𝐸 𝑡 arelog oftheRERandthetrade-expenditureratio,respectively.andΔ denotesℎ−perioddifference. ℎ 79

FigureH.6: DynamicCorrelationbetweenRERandNT 1 0.5 0 -0.5 -1 Data No Dynamic Trade No Trade Shock Benchmark No Financial Shock -1.5 1 2 3 4 5 6 7 8 Quarters Notes: We calculate the dynamic correlations as 𝜌(Δ ℎ 𝑞 𝑡 ,Δ ℎ 𝑛𝑡 𝑡 ), where 𝑞 𝑡 and 𝑛𝑡 𝑡 are log of the RER and the export-import ratio, respectively. and Δ denotes ℎ−period difference. It ℎ presenttheresultsforthebenchmarkmodelandalternativemodels: nofinancialshock,no tradeshock,andnotradedynamics. FigureH.7: CounterfactualSpectrum 0.025 Data Benchmark Model Only Trade Shocks 0.02 Only Financial Shocks 0.015 0.01 0.005 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Frequency Notes: Spectralanalysisofcounterfactualmodelswithoutre-calibrating,asourgoalistouse theidentifiedparametersfromthebenchmarkmodeltoperformexercisesinformativeabout theroleofeachshockatdifferentfrequencies. Thegraphisenlargedfortherange[0,1]to showbetterthelowandbusinesscyclefrequencies. 80

FigureH.8: IRFstodifferentialTradeCost,ImportTariff&HomeBiasShocks(%) d-d* NT RER 1.8 1 0.9 Trade Cost 1.6 0.8 Domestic Import Tariff 0 Home Bias 1.4 0.7 1.2 -1 0.6 1 0.5 0.8 -2 0.4 0.6 -3 0.3 0.4 0.2 0.2 -4 0 0.1 -0.2 -5 0 0 20 40 60 80 100 0 20 40 60 80 100 0 20 40 60 80 100 Quarters Quarters Quarters Notes: alltheshocksfollowanAR(1)process.Wesetthepersistenceofallshockstobe0.90, andtheirstandarddeviationsarechosentogeneratethesameimpacteffectontheRER. FigureH.9: IRFstoFinancialShocksinDynamicandStaticTradeModels(%) C i 0.05 0.02 0 0.01 -0.05 0 -0.1 -0.01 Dynamic Trade Static Trade -0.15 -0.02 0 20 40 60 80 100 0 20 40 60 80 100 Quarters Quarters i-i* RER 0.04 2 1.5 0.02 1 0 0.5 -0.02 0 -0.04 -0.5 0 20 40 60 80 100 0 20 40 60 80 100 Quarters Quarters 81

FigureH.10: IRFstoTradeShocks(%) C 10-3 i 0 5 Trade Shock -0.05 0 -0.1 -5 -0.15 -10 -0.2 -0.25 -15 0 20 40 60 80 100 0 20 40 60 80 100 Quarters Quarters i-i* RER 1.5 0 -0.005 1 -0.01 0.5 -0.015 -0.02 0 0 20 40 60 80 100 0 20 40 60 80 100 Quarters Quarters 82

TableH.1: FrequencyDecompositionofRER–OtherEconomies Country Low Businesscycle High Australia 0.60 0.32 0.08 Austria 0.63 0.29 0.07 Belgium 0.54 0.38 0.08 Canada 0.61 0.31 0.08 ChineseTaipei 0.65 0.26 0.09 Denmark 0.64 0.29 0.07 Finland 0.60 0.33 0.07 France 0.47 0.42 0.11 Germany 0.63 0.30 0.07 Greece 0.63 0.28 0.09 HongKongSAR 0.61 0.30 0.09 Ireland 0.39 0.43 0.18 Italy 0.64 0.27 0.09 Japan 0.62 0.30 0.08 Korea 0.67 0.25 0.08 Netherlands 0.62 0.31 0.07 NewZealand 0.52 0.36 0.12 Norway 0.58 0.32 0.10 Portugal 0.58 0.34 0.08 Singapore 0.62 0.30 0.07 Spain 0.59 0.31 0.10 Sweden 0.60 0.31 0.09 Switzerland 0.68 0.25 0.07 UnitedKingdom 0.58 0.33 0.09 UnitedStates 0.61 0.32 0.08 Euroarea 0.41 0.45 0.14 Average(excl. EuroArea) 0.60 0.32 0.09 Notes: ThetablepresentstheshareoftheRERvarianceexplainedby different frequencies for other economics. We use the effective exchangerate,real,narrowindices,fromBIS. 83

TableH.2: CalibratedParameters–AlternativeModels Parameter Benchmark NoTradeShock NoFinancialShock NoDynamics B.ProducerTradeParameters Fixedcostofnewexporters 𝑓0 0.14 0.14 0.14 0‡ Fixedcostofincumbentexporters 𝑓1 0.04 0.04 0.04 0‡ Volatilityofidiosyncraticproductivity 𝜎 0.15 0.15 0.15 0‡ 𝜇 C.Shocks,AdjustmentCostsandPricingtoMarket Commonproductivity,volatility 𝜎 0.004 0.004 0.004 0.003 𝑎𝑐 Differentialproductivity,volatility 𝜎 0.006 0.006 0.006 0.007 𝑎𝑑 Financialshock,volatility 𝜎 0.001 0.002 0‡ 0.008 𝜓 Financialshock,persistence 𝜌 0.989 0.950 0‡ 0.596 𝜓 Tradeshock,volatility 𝜎 0.049 0‡ 0.048 0.108 𝜉 Tradeshock,persistence 𝜌 0.985 0‡ 0.990 0.972 𝜉 Tradeshock,within-countryshare 𝜏 0.152 0‡ 0.265 0.199 Adjustmentcostofportfolios 𝜒 0.012 0.013 0.001 0.001 Adjustmentcostofcapital 𝜅 2.219 2.051 0.0004 2.081 Pricingtomarketparameter 𝜁 0.940 0.973 1.085 1.636 Notes: Thetablepresentsthevaluesofcalibratedparametersofthebenchmarkandalternativemodels. Whenwe consideranalternativemodels,someoftheparametersaresettoadifferentvaluewhiletheotherparametersareall recalibrated.PanelAissameasthebaselinecasepresentedinTable1forallmodels. TableH.3: MeasuresofNetTrade: Moments Data BenchmarkModel Export-ImportRatio 𝑎𝑢𝑡𝑜𝑐𝑜𝑟(𝑛𝑡) 0.98 0.97 𝑐𝑜𝑟(Δ𝑛𝑡,Δ𝑞) 0.30 0.30 𝜎(𝑛𝑡)/𝜎(𝑞) 1.21 1.21 Tradebalance-OutputRatio 𝑎𝑢𝑡𝑜𝑐𝑜𝑟((𝑋 −𝑀)/𝑌) 0.99 0.97 𝑐𝑜𝑟 (Δ(𝑋 −𝑀)/𝑌,Δ𝑞) 0.31 0.30 𝜎((𝑋 −𝑀)/𝑌)/𝜎(𝑞) 0.14 0.08 DetrendedTradebalance-OutputRatio 𝑎𝑢𝑡𝑜𝑐𝑜𝑟((𝑋 −𝑀)/𝑌) 0.98 0.97 𝑐𝑜𝑟 (Δ(𝑋 −𝑀)/𝑌,Δ𝑞) 0.31 0.30 𝜎((𝑋 −𝑀)/𝑌)/𝜎(𝑞) 0.10 0.08 Notes:Thetablepresentsthemomentsrelatedtonettrade,measuredaslogofexport-import ratio,log𝑋/𝑀ortradebalance-outputratio,(𝑋−𝑀)/𝑌.Inthelastpanel,tradebalance-output ratioislinearlydetrended. 84

TableH.4: ShareinCounterfactualSpectrum Data Benchmark TradeShockOnly FinancialShockOnly ProdShockOnly Lowfrequency 0.62 0.72 0.75 0.67 0.75 BCfrequency 0.31 0.21 0.19 0.25 0.19 Highfrequency 0.07 0.07 0.06 0.08 0.06 TableH.5: FamaEstimatesinData Moments Nominal Real 𝛽 -1.15 -1.34 𝑓𝑎𝑚𝑎 (0.59) (0.52) 𝑅2 0.02 0.04 𝑓𝑎𝑚𝑎 Notes: ‘Nominal’ denotes the results of using nominal data for the Famaregression, Δ𝑒 = 𝛼 +𝛽 (𝑖𝑛 −𝑖𝑛∗)+𝑢 , where𝑒 isnominal 𝑡+1 𝐹𝑎𝑚𝑎 𝑡 𝑡 𝑡 exchangerate,and𝑖𝑛 isthenominalinterestrate. ‘Real’denotesthe resultofusingrealdatafortheregression(9). 85

TableH.6: ConditionalVarianceDecompositionoftheRER(%)–ModelWithoutTradeShocks quarters=1 8 32 80 A.NoTradeShock Financialshock 95.3 89.4 71.6 69.3 Productivityshock 4.7 10.6 28.4 30.7 B.HigherVarianceofDifferentialProductivityShock Financialshock 50.0 29.2 11.0 9.9 Productivityshock 50.0 70.8 89.0 90.1 Notes:PanelAcorrespondstothemodelinTableH.2.PanelBpresents results from a version of the no trade shock model in which we adjustthevarianceoftheproductivityprocesstogeneratethesameonimpact effect as the financial shock on the RER. Specifically, we set 𝜎̂ =𝜎 ×𝑓,where𝑓 isafactorequalto4.52,whileholdingallother 𝑎 𝑎 𝑑 𝑑 parametersfixedattheirvaluesinthe‘NoTradeShock’specification. 86