Monetary Policy Spillovers through Invoicing Currencies

Transcription

1 Moetary Policy Spillovers through Ivoicig Currecies Toy Zhag Jauary 17, 2018 Click here for the most updated versio. Abstract Uited States moetary policy affects macro-fiacial outcomes globally. I itroduce heterogeeity i ivoicig currecies ito a ope ecoomy New Keyesia model that also allows for differeces i coutry size ad household prefereces. Withi the model, crosssectioal variatio i U.S. moetary policy spillover effects is fully captured by heterogeeity i coutries shares of dollar ivoiced trade. Moreover, cetral baks of coutries i which a larger share of exports are ivoiced i dollars face a worse output-iflatio trade-off, i.e., a steeper Phillips Curve. Usig high frequecy measures of moetary policy shocks, I fid support for the model s predictios. Coutries shares of dollar ivoiced trade explai cross-sectioal heterogeeity i spillovers from U.S. moetary policy shocks oto foreig exchage rates, iterest rates ad idustrial productio. Costructig a ew data set of moetary policy shocks emaatig from the Europea Cetral Bak, the Bak of Japa ad the Bak of Eglad, I show currecy ivoicig explais variatio i moetary policy spillovers from these other cetral baks as well. After cotrollig for currecy ivoicig i trade, the magitude of U.S. moetary policy spillovers are ot sigificatly differet from those of other cetral baks. Uiversity of Chicago; Postal Address: 5807 S Woodlaw Aveue, Chicago IL 60637, USA; wzhag6@chicagobooth.edu. I thak my advisers Tarek Hassa, Bret Neima, Lars Peter Hase ad Pietro Veroesi for their support ad may helpful coversatios. I also thak Simcha Barkai, Adam Jorrig, Paymo Khorrami, Willem va Vliet, Michael Weber, Ursula Wiriadiata ad semiar participats at the Uiversity of Chicago for their commets ad feedback.

2 1 Itroductio The actios of the Federal Reserve Bak of the Uited States are of fudametal cocer for cetral bakers aroud the world. A growig literature fids moetary policy actios of the Uited States sigificatly impact macroecoomic coditios (Rey, 2013; Mirada-Agrippio ad Rey, 2015) ad asset prices (Brusa et al., 2015) globally. What features of the global ecoomy allow the Federal Reserve to ifluece global macroecoomic coditios, ad to what extet do moetary policy actios from other cetral baks also ifluece outcomes abroad? Recet evidece from Gopiath (2015) shows that over 80 percet of traded goods are ivoiced i dollars ad euros. This paper studies how patters i currecy ivoicig geerate iteratioal moetary policy spillovers, ad its implicatios for moetary policy. Buildig o Egel (2011), I develop a ope ecoomy New Keyesia model i which prices of traded goods are sticky i their currecy of ivoicig. Firms i each coutry ivoice their exports i domestic currecy or i a global trade currecy issued by a ceter coutry. 1 show cetral baks of coutries i which firms ivoice more of their exports i the global trade currecy should face a worse output-iflatio trade-off (i.e. a steeper Phillips curve), ad I characterize iteratioal moetary policy trasmissio oto key elemets of the New Keyesia framework: exchage rates, iterest rates, ad the level of output. Usig high-frequecy measures of moetary policy shocks, I test the model s predictios for omial exchage rates, omial iterest rates ad output, ad I fid support for each oe. Coutries i which a larger share of imports ad exports are ivoiced i dollars are more exposed to U.S. moetary policy shocks. Furthermore, I provide evidece that moetary policy spillover effects emaate from other cetral baks i the world, ad the large magitude of U.S. moetary policy spillover effects ca be explaied by the dollar s domiace as a global trade currecy. I begi with the theoretical aalysis, ad characterize the effect of currecy ivoicig o moetary policy trasmissio across coutries i a model where asset markets are complete. I allow coutries to differ i size, households to differ i their prefereces for varieties of traded goods ad firms to differ i their ivoicig currecy of exports. Cotractioary moetary policy 1 Ivoicig i domestic currecy is typically labeled producer currecy pricig. Withi the model, I take the firm s ivoicig currecy as give. A cocer is that uderlyig factors expose a coutry to moetary policy shocks from the ceter coutry ad also cause the coutry to ivoice exports i the global trade currecy. The iteratioal trade literature has idetified some characteristics that ifluece the firm s ivoicig currecy choice (Devereux et al., 2004; Goldberg ad Tille, 2008; Gopiath et al., 2010). Examples iclude the liquidity of the currecy, idustry structure ad desired exchage rate pass-through. However, there is o cosesus for why we observe the heterogeeity i ivoicig currecy use at the coutry level. I the empirical sectio of the paper, I cotrol for alterative hypotheses for explaiig heterogeeity i moetary policy spillovers beyod the role of currecy ivoicig itself. I 1

3 from the ceter coutry icreases the value of the global trade currecy relative to all other currecies i the world. Hece, the relative price of traded goods ivoiced i the global trade currecy icreases. Households cosume a aggregate budle of traded ad o-traded goods. As the relative price of traded goods icreases, foreig households decrease their traded good cosumptio as well as their aggregate cosumptio. Withi the model, variatio i moetary policy spillover effects from the ceter coutry oto foreig cosumptio is fully captured by the share of each coutry s cosumptio ivoiced i the global trade currecy. I each coutry, the share of cosumptio ivoiced i the global trade currecy is a fuctio of uderlyig household prefereces ad the fractio of traded goods ivoiced i the global trade currecy. Whe the ceter coutry egages i cotractioary moetary policy, coutries with a larger share of cosumptio ivoiced i the global trade currecy suffer a larger icrease to their cost of cosumptio, because the currecy appreciatio affects a larger fractio their aggregate cosumptio budle. As a result, these coutries observe a larger decrease i their aggregate cosumptio i respose to the ceter coutry s cotractioary moetary policy. The model shows cetral baks of coutries i which a larger fractio of firms ivoice their exports i the global trade currecy face a worse output-iflatio trade-off. A cetral bak s moetary policy affects the demad for all goods ivoiced i its currecy domestically ad abroad. Whe domestic firms ivoice their exports i the global trade currecy, the cetral bak loses cotrol over foreig demad for these traded goods. A icrease i the fractio of domestic firms ivoicig i the global trade currecy should dimiish the effect of domestic moetary policy o domestic output. Hece, the cetral bak faces a steeper Phillips curve. I this sese, variatio i the ivoicig currecies of exports is importat for characterizig the effectiveess of moetary policy across coutries. After establishig this result, I derive additioal predictios characterizig how heterogeeity i currecy ivoicig iflueces the trasmissio of moetary policy oto other compoets of the New Keyesia framework. Withi the model, heterogeeity i spillover effects to cosumptio drives the two mai asset pricig predictios. I respose to cotractioary moetary policy shock from the ceter coutry, foreig coutries with a larger share of cosumptio ivoiced i the global trade currecy appreciate, ad their iterest rates icrease relative to coutries with a smaller share of cosumptio ivoiced i the global trade currecy. I respose to cotractioary moetary policy from the ceter coutry, coutries with a larger share of cosumptio ivoiced i the global trade currecy observe their margial utility of cosumptio icrease more. This icrease i the margial utility of cosumptio directly traslates ito a real exchage rate appreciatio ad a icrease i real 2

4 iterest rates. Chages i omial exchage rates ad omial iterest rates mirror the chages i real exchage rates ad real iterest rates. Moetary policy spillover effects are ot uique to ay coutry, ad heterogeeity i currecy ivoicig explais cross-sectioal variatio i moetary policy spillover effects from each coutry. Withi the model, the magitude of moetary policy spillover effects oto exchage rates ad iterest rates are the same for all coutries after cotrollig for shares of cosumptio ivoiced i each currecy. I other words, the model suggests that the Federal Reserve strogly iflueces global macro-fiacial coditios because of the dollar s preemiet positio as a ivoicig currecy. After showig the mai isights of the paper i the complete asset markets model, I show the theoretical predictios of the model cotiue to hold i a icomplete markets extesio. Although the complete asset markets model is a importat bechmark, a well kow empirical short-comig of the model is that it predicts a perfectly egative correlatio betwee aggregate cosumptio ad real exchage rates (Backus ad Smith, 1993). The icomplete markets extesio serves two purposes. First, it shows that the forces idetified i the model carry over to a broader class of models with more elaborate frictios. Secod, the additio of icomplete markets breaks the tight lik betwee exchage rates, iterest rates ad aggregate cosumptio. As a result, the empirical sectio of the paper focuses o testig the predictios for exchages rates, iterest rates ad productio rather tha aggregate cosumptio. The predictios of the model are most effectively summarized by the result that coutries i which firms ivoice more of their exports i foreig currecies should face a steeper Phillips curve. However, empirical estimates of Phillips curves are strogly subject to specificatio error, ad ofte give rise to coflictig results (Mavroeidis et al., 2014). Hece, I focus o testig the followig predictios i which I ca use high frequecy measures of moetary policy shocks to idetify the effects of moetary policy. I respose to a cotractioary U.S. moetary policy shock, coutries with a larger share of dollar ivoiced imports should observe (1) their omial exchage rates depreciate less ad (2) their omial iterest rates icrease more. (3) Moetary policy spillover effects from the Uited States are o larger tha the magitude of moetary policy spillover effects from other cetral baks, after cotrollig for heterogeeity i currecy ivoicig. Fially, (4) coutries that ivoice a larger share of their exports i dollars observe their productio decrease more i respose to U.S. cotractioary moetary policy. I the empirical sectio of the paper, I use currecy ivoicig data from Gopiath (2015) to costruct coutries shares of cosumptio ivoiced i dollars, euros, ye ad pouds. Usig high 3

5 frequecy moetary policy shock data from Nakamura ad Steisso (2015), I show variatio i dollar ivoicig explais moetary policy spillovers from the Federal Reserve. Afterwards, I measure moetary policy shocks cosistetly for the Federal Reserve Bak, the Europea Cetral Bak, the Bak of Japa ad the Bak of Eglad, ad test whether spillovers from the Federal Reserve stad out. Figure 1 summarizes my mai empirical results. I start by measurig resposes i omial exchage rates ad omial iterest rates i a oe-day widow aroud U.S. moetary policy aoucemets. Usig the sample of U.S. moetary policy shocks from Nakamura ad Steisso (2015), I estimate a pael regressio of chages i each coutry s omial exchage rates ad omial iterest rates o coutry fixed effects, date fixed effects ad a iteractio term betwee coutry fixed effects ad Federal Reserve moetary policy shocks. The coefficiet o the iteractio term captures each coutry s respose to U.S. moetary policy shocks relative to the average coutry s respose. Figure 1 plots the coefficiets o the iteractio term, agaist each coutry s share of dollar ivoiced cosumptio. The left-had plot i Figure 1 provides evidece that coutries with a higher share of dollar ivoiced cosumptio depreciate less i respose to a cotractioary U.S. moetary policy shock. The right-had plot i Figure 1 provides evidece that omial iterest rates i coutries with a higher share of dollar ivoiced cosumptio icrease more i respose to cotractioary U.S. moetary policy shocks. I the paper, I show if a coutry experieces a oe stadard deviatio icrease i its share of dollar ivoiced cosumptio, a 100 basis poit cotractioary moetary policy shock causes its omial exchage rate to depreciate by 130 fewer basis poits ad causes its omial iterest rate to icrease by a additioal 53 basis poits. Moreover, I provide evidece that currecy ivoicig explais moetary policy spillover effects from other cetral baks. Importatly, I fail to reject the ull hypothesis that the magitude of moetary policy spillover effects from the Federal Reserve are the same as those from other cetral baks after cotrollig for currecy ivoicig. Fially, I costruct mothly moetary policy shocks for the U.S., ad provide evidece that idustrial productio i coutries with a larger share of dollar ivoiced exports is more resposive to U.S. moetary policy. Cosistet with the literature, I fid the strogest effects occur with a two to three year lag. The rest of the paper is orgaized as follows. Sectio 2 reviews the related literature. Sectio 3 presets the model, ad sectio 4 characterizes the equilibrium ad derives the theoretical predictios of the model. Sectio 5 presets the data ad empirical methodology. Sectio 6 4

6 presets empirical results ad sectio 7 cocludes. 2 Related Literature This paper cotributes to a large literature o the trasmissio of moetary policy shocks by characterizig how ivoicig imports ad exports i a global trade currecy effects moetary policy trasmissio withi ad across borders. The existig literature has largely focused o models i which coutries are symmetric (Clarida et al., 2002; Bacchetta ad va Wicoop, 2005; Flode ad Wilader, 2006; Egel, 2011) or i which all coutries are of measure zero ad each coutry s moetary policy has o exteralities o other coutries (Gali ad Moacelli, 2005, 2008; Farhi ad Werig, 2013). This paper aalyzes the macroecoomic cosequeces of itroducig a asymmetry i currecy ivoicig across coutries. Furthermore, the literature typically studies models where coutries ivoice traded goods i domestic currecy (producer currecy pricig) or the currecy of the coutry importig the traded goods (local currecy pricig). A otable exceptio is Casas et al. (2017) who allow for domiat currecy ivoicig (ivoicig i oe particular coutry s currecy) i a small ope ecoomy settig. This paper also relates to a literature o exchage rate pass through by idetifyig ad aalyzig higher frequecy effects of exchage rate movemets. I geeral, this literature focuses o measurig log ru cosequeces of exchage rate movemets i macroecoomic variables (Gopiath ad Rigobo, 2008; Burstei ad Gopiath, 2014; Gopiath, 2015). By focusig o high-frequecy moetary policy shocks, I idetify causal relatioships betwee moetary policy, exchage rate movemets ad chages i iterest rates. Withi this literature, my paper is most similar to Boz et al. (2017). Boz et al. (2017) also use currecy ivoicig data from Gopiath (2015) to uderstad heterogeeity i exchage rate pass through i the medium- to log-ru. My results for omial exchage rates complemet lower frequecy empirical evidece from Boz et al. (2017). Moreover, I cotribute to this literature by aalyzig the theoretical implicatios of the patters i ivoicig currecies for moetary policy, as well as by providig ew empirical results showig spillover effects to asset prices ad from multiple cetral baks. This paper cotributes to a growig literature measurig the cosequeces of moetary policy usig high frequecy measures of moetary policy shocks (Kutter, 2001; Gurkayak et al., 2005; Gertler ad Karadi, 2015; Gorodicheko ad Weber, 2016; Leombroi et al., 2017; Ozdagli ad Weber, 2017; Wiriadiata, 2017). The methodology i my paper is most similar to that of Nakamura ad Steisso (2015) i the sese that I also focus o measurig resposes i high 5

7 frequecy outcomes. The literature focuses o measurig the effects of U.S. moetary policy shocks ad estimatig the reactio of U.S. macroecoomic ad fiacial variables. A otable exceptio is Rey (2014), who exteds the methodology i Gertler ad Karadi (2015) to measure the effect of U.S. moetary policy shocks o macroecoomic variables i a sample of four foreig coutries. Complemetary work by Wiriadiata (2017) studies the effect of U.S. moetary policy shocks o exchage rates i credit costraied coutries ad shows that coutries with larger amouts of dollar deomiated debt are more exposed to U.S. moetary policy shocks. This paper focuses o a sample of advaced ecoomies, which are ulikely to credit costraied. I exted the methodology used i this literature to aalyze moetary policy spillovers across coutries. Furthermore, I show moetary policy spillovers emaate from o-u.s. cetral baks as well. Fially, Shah (2017) uses high frequecy asset pricig data to argue for a icomplete asset markets explaatio of joit movemets i exchage rates ad log-term bod yields. 2 Fially, this paper is related to a growig literature i iteratioal fiace that studies the effects of heterogeeity across coutries o exchage rates, currecy returs ad capital accumulatio (Marti, 2012; Hassa, 2013; Maggiori, 2013; Richmod, 2015; Farhi ad Gabaix, 2015; Hassa et al., 2016, 2017). This paper studies a differet form of heterogeeity that iflueces how shocks trasmit across coutries, ad drives variatio i the properties of asset prices across coutries. 3 The Model I develop a static ope ecoomy New Keyesia model to capture key features of the distributio i currecy ivoicig. The model builds o caoical ope ecoomy New Keyesia models (Flode ad Wilader, 2006; Egel, 2011) by allowig for heterogeeity i currecy ivoicig across coutries. I each coutry, a fractio of firms ivoice their exports i domestic currecy, whereas the remaider of firms ivoice their exports i a global trade currecy. I also allow for heterogeeity i coutry sizes ad heterogeeity i household prefereces for varieties of traded goods. These additioal forms of heterogeeity have bee show to be importat for explaiig cross-sectioal patters i iteratioal trade ad i asset prices (Marti, 2012; Hassa, 2013). I will later show that the impact of these additioal forms of heterogeeity o the moetary policy trasmissio mechaism is fully captured by heterogeeity i currecy 2 A separate literature looks at returs o asset prices o moetary policy aoucemet days (Savor ad Wilso, 2013; Lucca ad Moech, 2015; Brusa et al., 2015; Mueller et al., 2017). 6

8 ivoicig. Hece, it is eough to oly look at variatio i currecy ivoicig of imports ad exports to uderstad cross-sectioal variatio i moetary policy spillovers. To develop ituitio for the role of currecy ivoicig i trasmittig moetary policy shocks, I first aalyze a model i which fiacial markets are complete. However, the complete markets model has well kow empirical short-comigs. Hece, I later exted the complete markets model to allow for segmeted markets where oly a subset of households withi each coutry have access to complete asset markets. The remaiig households i each coutry ca oly hold omial bods deomiated i domestic currecy. I show that the empirical predictios of the complete markets model cotiue to hold i a icomplete markets eviromet. 3.1 Households Two time periods exist: t = 1, 2. A uit mass of households is partitioed ito three coutries. For expositioal purposes, I label these coutries the Uited States (US), Japa (JP) ad Europe (EU). Let µ deote the mass of households residig i coutry. Households i each coutry gai utility from cosumptio ad disutility from providig labor services. I coutry, a mass µ of firms also exists, ad each firm produces a uique itermediate traded good. Households supply labor to all firms withi their ow coutry i the productio of itermediate traded goods, ad share i the profits of all sales of itermediate traded goods. I this maer, all households withi a coutry are idetical. Households i coutry behave accordig to the followig utility fuctio, U = E t=1,2 { } β t 1 (Ct ) 1 γ 1 γ (N t ) 2. (1) 2 N t is the amout of labor supplied by each household i coutry i period t, ad C t is the period t aggregate cosumptio budle cosumed by a household i coutry. This aggregate cosumptio budle is comprised of traded ad o-traded goods, C t = ( C T,t) τ ( C N,t ) 1 τ. τ govers the share of the coutry household s aggregate cosumptio that is comprised of traded goods. CN,t represets the household s cosumptio of its coutry specific o-traded good, ad CT,t represets coutry household s cosumptio of a aggregate traded good com- 7

9 prised of traded goods from each coutry: C T,t = ( C T,US,t) α US ( C T,JP,t ) α JP ( C T,EU,t ) α EU. C T,m,t represets a cosumptio budle of itermediate traded goods produced by firms i coutry m ad cosumed i coutry for m {US, JP, EU}. The parameters α m determie what fractio of coutry s traded cosumptio is comprised of itermediate traded goods produced i coutry m. These parameters ca be thought of as capturig differeces i trade costs or prefereces across coutries. I assume α US + α EU + α JP = 1. Each cosumptio budle of itermediate traded goods is a CES aggregate of differetiated itermediate traded goods from withi each coutry: [ µ m ] ( ) 1 CT,m,t ε = C ε T,m,j,t dj. (2) 0 j idexes firms i coutry m, ad ε < 1 determies the elasticity of substitutio betwee the differet varieties of coutry m s itermediate traded goods. At the start of each period, each household i coutry is edowed with Y N,t o-traded good, where YN,t is log-ormally distributed: log [ ( ] YN,t N 1 ) 2 σ, σ. uits of the 3.2 Firms Itermediate traded goods are produced by employig labor. I coutry m, firm j s output of its variety of itermediate traded good is Y T,m,j,t = A m t µ m N m,j,t, where N m,j,t is the quatity of labor firm j demads i coutry m from each household, ad A m t is the aggregate productivity shock to the itermediate traded sector of coutry m: log [A m t ] N ( 1 ) 2 σm T, σt m. I assume the itermediate traded goods firms either ivoice their exports (sales to foreig households) i domestic currecy or i U.S. dollars. Withi each coutry, firms oly differ i their choice of ivoicig currecy. I coutry m, a fractio X$ m of firms ivoice their exports 8

10 i dollars. The remaiig fractio 1 X m $ of firms ivoice their exports i domestic currecy. Domestic sales of itermediate traded goods are ivoiced i domestic currecy. Nomial prices i the first period are set prior to the realizatio of productivity shocks, edowmets of o-traded goods ad moetary policy actios. Nomial prices of itermediate traded goods are fixed i their currecy of ivoicig i the first period, ad I assume the law of oe price holds for traded goods. Hece, the omial price of ay itermediate traded good i ye is equal to the omial price of the traded good i dollars multiplied by the ye - dollar exchage rate: P T,m,j,t JP = ẼJP,US t P T,m,j,t. US (3) P T,m,j,t is the omial price of itermediate traded good j i uits of coutry currecy. ẼJP,US is the ye - dollar omial exchage rate give as uits of ye per dollar. Throughout this paper, tildes preset omial prices. These pricig assumptios capture key features of the iteratioal price system described i Gopiath (2015). The followig example provides ituitio for the cosequeces of these pricig assumptios. Cosider a firm located i the Uited States that ivoices its exports i dollars. Suppose this firm sets the omial price of its exports as P dollars. Because omial prices of itermediate traded goods are fixed i their currecy of ivoicig, the regardless of ay chages i the omial exchage rate betwee the dollar ad the ye, households i Japa pay a price i ye equivalet to P dollars for the itermediate traded good. If the dollar depreciates relative to the ye, this good becomes relatively cheaper for Japaese households to cosume. I assume omial prices adjust freely i the secod period. Thus, moetary policy shocks i the model oly affect real allocatios i the short ru, ad they are iterpreted as temporary shocks. 3.3 Moetary Policy Prices of itermediate traded goods are fixed i the first period, cetral baks ca use moetary policy to affect first-period allocatios. I assume the moetary policy actio of the cetral bak i each coutry is to choose the domestic aggregate omial price level. Because the fial cosumptio budle is a Cobb-Douglas aggregate of traded ad o-traded goods, Appedix A.1 9

11 shows the aggregate omial price level, P t, i coutry ca be writte as P t = ( ) τ ( ) 1 τ P T,t P N,t (τ) τ (1 τ) 1 τ. P T,t is the omial price idex for the cosumptio of itermediate traded goods for households i coutry. I assume the cetral bak of coutry chooses P t. The omial prices of traded goods, P T,t, ad o-traded goods, P N,t adjust oce the cetral bak chooses the aggregate price level i the coutry. This form of moetary policy provides a coveiet shorthad for modelig some other forms of moetary policy. For example, it is equivalet to explicitly itroducig moey ito the model, forcig households to purchase goods usig cash holdigs ad allowig the cetral bak to cotrol the moey supply. Withi models with moey explicitly itroduced, the cetral bak determies the aggregate omial price level, P, by chagig the moey supply. Ituitively, oe ca also thik of a icrease i the aggregate omial price level as a currecy devaluatio. Whe the cetral bak icreases P t, more uits of coutry currecy are required to purchase a uit of fial cosumptio i coutry. Hece, each uit of coutry currecy purchases fewer real cosumptio goods. As the real value of the currecy decreases, the relative cost of traded goods whose prices are fixed i that currecy decreases as well, which stimulates productio. 3.4 Fiacial Markets Households trade a complete set of state-cotiget claims deomiated i U.S. dollars. Because I do ot itroduce ay frictios ito fiacial markets, which currecy is used to deomiate the state-cotiget claims is irrelevat. The state of world at date t is determied by the edowmet of o-traded goods, Y N,t, the productivity shocks to traded productio, A t, ad moetary policy actios, P t. I this sese, households ca use state-cotiget claims to isure agaist o-traded edowmet shocks, productivity shocks ad moetary policy actios. However, frictios exist i goods markets such that cosumptio risk is ot perfectly shared across coutries. First, a fractio of each household s cosumptio caot be traded across borders. Secod, I assume households must use domestic currecy to purchase domestic cosumptio. Hece, households caot fully isure agaist o-traded edowmet shocks ad moetary policy actios. 10

12 Households receive wages for supplyig labor i the productio of itermediate traded goods ad ow a equal share of all itermediate traded goods firms located withi their coutry. The coutry household faces the followig budget costrait: E t=1,2 { E t=1,2 Q t Ẽ US, t Q t Ẽ,US t P N,t C N,t + i {US,JP,EU} ( 1 ( P N,tY N,t + W t N t + Γ t ) } + κ. 0 P T,i,j,tCT,i,j,tdj) = (4) W t is coutry s omial wage. Γ t is the household s share of omial profits eared from owig coutry itermediate traded goods firms. P N,t ad P T,i,j,t are the omial prices of the o-traded good ad the jth variety of the itermediate traded good produced i coutry i. The superscript above the prices deote these prices are deomiated i coutry currecy. Q t is the price of a state-cotiget claim. I multiply Q t by the omial exchage rate ẼUS, t to traslate the domestic currecy value of household wealth ito dollars. κ is a trasfer across households, which equalizes the margial utility of iitial wealth across households i differet coutries. This is the trasfer required to decetralize a Social Plaer s problem with uit Pareto weights, ad it allows me to abstract from wealth effects that result from itroducig heterogeeity across coutries. 3.5 Solvig the Model This sectio describes first order coditios for the households problem. All households withi a coutry face the same optimizatio problem. I relegate the itermediate firm s pricig decisio to the Appedix. 3 Households maximize utility (1) subject to their budget costraits (4). The first order coditio for households i coutry with respect to their itermediate traded cosumptio of good j produced i coutry m is, α mτ ( C T,m,t C t CT,m,t CT,m,j,t ) 1 ε = P T,m,j,t P t. (5) The first order coditio with respect to o-traded cosumptio determies the price of the 3 See Appedix A.2 for additioal details ad the derivatio of the first order coditios. 11

13 o-traded good (1 τ) C t C N,t Household labor supply is pied dow by the first order coditio with respect to N t, = P N,t P t (6) C γ t N t = W t. (7) P t These first order coditios describe the demad side of the ecoomy ad hold i each period regardless of the omial rigidity i the supply side of the ecoomy. The market clearig coditio for itermediate traded good j produced i coutry m is, Y T,m,j,t = A m t µ m N m,j,t = µ CT,m,j,t (8) {US,JP,EU} Recall that N m,j,t deotes the quatity of labor each firm j demads i coutry m from each household. Hece, µ m N m,j,t is the total quatity of labor firm j i coutry m demads. Households cosume their edowmet of o-traded goods: Y N,t = C N,t. (9) Fially, the labor market clearig coditio for households i coutry m is, µ Nt m = N m,j,t dj. (10) 0 All firms withi a coutry ad ivoicig i dollars face the same optimizatio problem ad demad the same quatity of labor. The same is true for firms ivoicig i domestic currecy withi a coutry. Let N m,$,t represet labor demad by firms i coutry m that ivoice i dollars, ad let N m,h,t represet labor demad by firms that ivoice i domestic (home) currecy, I ca rewrite equatio (10) as Nt m = µ m X$ m N m,$,t + µ m (1 X$ m )N m,h,t. For all pairs of coutries ad m, the omial exchage rate ca be derived by takig the ratio of households first order coditios with respect to aggregate cosumptio. Naturally, the omial exchage rate betwee two coutries is the ratio of the coutries margial utilities of aggregate cosumptio divided by the omial price level: (C t ) γ P t = (Cm t ) γ. (11) Ẽ,m t P m t 12

14 The omial exchage rate Ẽ,m is defied as uits of coutry currecy per uit of coutry m currecy. A equilibrium i this ecoomy is a set of cosumptio ad labor supply allocatios for each household { CT,m,j,t, C N,t, N } t, a set of itermediate output, labor demad ad omial prices { for each itermediate firm YT,m,j,t, N m,j,t, P } T,m,j,t, a set of traded good prices ad o-traded { good prices P T,t, P } N,t, a set of omial wages for each coutry ad a omial exchage rate { } W t, Ẽ,m t, such that households maximize utility subject to their budget costraits, ad the resource costraits are satisfied. 4 Theoretical Results The model characterizes how heterogeeity i currecy ivoicig iflueces the moetary policy trasmissio across coutries. I use the model to provide ituitio ad to derive empirical predictios. To study the model i closed form, I log-liearize the model aroud the determiistic solutio. 4 Lowercase variables deote logs. I focus o the first period because omial rigidites oly affect allocatios i the short-ru. Hece, I drop the time t subscript wheever possible. All variables represet first-period prices ad allocatios uless otherwise oted. Moetary policy shocks from the Uited States affect the demad for all dollar ivoiced itermediate traded goods. Suppose the Uited States egages i cotractioary moetary policy ad decreases the log U.S. omial price level, p US. Mechaically, this actio icreases the omial value of the dollar relative to all other currecies. Fewer dollars are eeded to purchase a uit of the fial cosumptio budle i the Uited States. Hece, each dollar is more valuable. Whe the dollar appreciates with respect to foreig currecy, the cost of dollar ivoiced itermediate traded goods icreases i terms of foreig currecy. This icreases the cost of the foreig household s traded cosumptio budle. I respose, foreig households decrease their cosumptio of traded ad fial cosumptio. The respose of Japaese household cosumptio to U.S. cotractioary policy is cjp p US = γτ 2 (1 + (γ 1)τ) 4 See Appedix A.3 for additioal details. (( 1 α EU EU ) ( 1 α JP JP ν ) ( 1 X JP $ (1 τ)(1 + (γ 1)τ) ν ) ( ) ) 1 X EU $ α EU JP αjp EU τ ( ) αus JP + X$ EU αeu JP }{{} M$ JP (12) 13

15 ν is a positive costat, which I discuss below. M JP $ is the equilibrium share of Japa s aggregate cosumptio budle that is ivoiced i dollars. It is comprised of the share α JP US Japaese households import from the Uited States ad the share X EU $ α JP EU of goods of dollar ivoiced goods Japaese households import from Europe multiplied by the share of traded goods i aggregate cosumptio, τ. The effect of cotractioary U.S. moetary policy o cosumptio i Europe is aalogously defied where M$ EU = τ ( αus EU + ) XJP $ αjp EU. The first lie of equatio (12) is a term that is commo to the effect of U.S. moetary policy o Japaese ad Europea cosumptio. It shows that, o average, cotractioary U.S. moetary policy should decrease foreig cosumptio, ad foreig cosumptio should decrease more whe a larger share of global trade is ivoiced i dollars. The coefficiet i frot of the α EU JP αjp EU term captures how dollar ivoicig icreases the average effect of U.S. moetary policy o foreig cosumptio. If all firms ivoiced their exports i domestic currecy ( X JP $ = X EU $ = 0 ), U.S. moetary policy would oly affect relative prices of traded goods whe tradig with the Uited States. The relative prices of trade goods betwee Europe ad Japa would be uaffected. Dollar ivoicig by Japaese ad Europea firms allows U.S. moetary policy to distort the relative prices of traded goods betwee Japa ad Europe. The secod lie o the right-had side shows coutries with a larger share of dollar ivoiced cosumptio see their cosumptio decrease more. Moreover, heterogeeity i the moetary policy spillover effect to cosumptio is fully captured by M $, eve though α m ad X $ differ across coutries. Households that cosume more dollar ivoiced itermediate traded goods observe a price icrease over a larger share of their traded cosumptio budle. Hece, their cosumptio of traded goods falls more. ν is a positive costat that captures the degree of risk-sharig across coutries. The expressio for ν is relegated to Appedix A.4. Appedix A.4 also derives two properties of ν. Lemma 1. ν is positive ad icreasig i α m for all m. A positive ν allows me to sig aalytic expressios. The fact that ν icreases with α m for m meas icreased risk sharig across coutries dampes moetary policy spillover effects. α m determies the share of coutry household s traded cosumptio that is comprised of imports from coutry m. If α m = 0 for all m, coutries oly cosume traded goods produced domestically. No coutry trades with ay other. Positive α m allow coutries to share risk by shippig traded goods to households with high margial utilities of cosumptio. 14

16 4.1 Moetary Policy A cetral compoet for the implemetatio of moetary policy i the New Keyesia literature is the short-ru trade-off betwee output ad iflatio. The previous sectio showed that patters of currecy ivoicig impact how domestic moetary policy affects foreig demad. As a result, the share of firms that ivoice their exports i dollars matters for determiig the domestic cetral bak s trade-off betwee output ad iflatio. Propositio 1. Holdig foreig moetary policy costat, the respose of domestic traded productio to domestic moetary policy is decreasig i the share of the coutry s dollar ivoiced exports ( ) X$. Hece, cetral baks of coutries where a larger share of firms ivoice their exports i foreig currecy face a steeper Phillips Curve. Proof. See Appedix A.7 I a ope ecoomy, the cetral bak policy affects demad from domestic households as well as foreig households. Suppose the cetral bak of Japa egages i cotractioary moetary policy to decrease domestic productio. Part of the cotractioary effect comes from households decreasig cosumptio of Japaese goods i the rest of the world, because cotractioary moetary policy icreases the relative cost of ye ivoiced traded goods. The stregth of the effect of Japaese moetary policy o foreig cosumptio of Japaese goods depeds o the share of Japaese firms that ivoice their exports i ye. I the limitig case, if o firms i Japa ivoiced their exports i ye, the chages to relative value of the ye have o impact o the relative price of Japaese traded goods abroad. I this case, Japaese moetary policy oly affects domestic demad. Foreig demad for Japaese produced goods would be tied to the relative value of the U.S. dollar. Hece, the effect of Japaese moetary policy o foreig demad decreases with the share of firms that ivoice exports i dollars. I the real world, data from Gopiath (2015) show that a sigificat umber of coutries ivoice the majority of their exports i foreig currecies, e.g., the U.S. dollar. Propositio 1 suggests the cetral baks of these coutries icur a greater cost of iflatio for each chage i domestic output. I this sese, cetral baks i coutries where a large fractio of firms ivoice their exports i foreig currecy should be less effective at implemetig moetary policy. Prior literature has show that empirical estimates of Phillips curves are strogly subject to specificatio ad samplig ucertaity. As a result, empirical studies of the New Keyesia Phillips curve ofte give rise to coflictig results (Mavroeidis et al., 2014). However, the model yields a umber of other predictios for key variables i the New Keyesia framework that 15

17 are easier to measure. I the followig sectios, I characterize how heterogeeity i currecy ivoicig affects moetary policy trasmissio ito these compoets of the ope ecoomy New Keyesia framework: the real iterest rate, the omial iterest rate, the real exchage rate, the omial exchage rate ad the level of output. 4.2 Exchage Rates ad Iterest Rates A coutry s omial dollar exchage rate is comprised of its real dollar exchage rate ad the differeces i omial price levels betwee coutries, ẽ,us = γ ( c c US) ( p p US). }{{} real exchage rate U.S. moetary policy affects three compoets of this equatio: the omial price level i the Uited States, the cosumptio i the Uited States ad the cosumptio i coutry. However, heterogeeity i the trasmissio of U.S. moetary policy shocks oly comes from the heterogeeous impact of U.S. moetary policy o cosumptio i coutry withi the real exchage rate. Predictio 1. Holdig foreig moetary policy costat, U.S. cotractioary moetary policy should cause foreig currecies to depreciate agaist the U.S. dollar. Coutries with higher M $ depreciate less tha coutries with lower M $. Equatio (13) shows cotractioary U.S. moetary policy causes all other currecies to depreciate agaist the dollar: ẽ,us (1 τ)(1 + (γ 1)τ)(1 + = p US ( ( γ 2 α JP JP ) EU) αeu 1 τ) ν γ(1 τ)(1 + (γ 1) τ) M$. ν (13) The first lie of equatio (13) describes the commo compoet of U.S. moetary policy spillover oto foreig omial exchage rates. Because the omial exchage rate is give as uits of foreig currecy per dollar, this equatio shows that more uits of foreig currecy are eeded to purchase a dollar. Hece, foreig currecies depreciate agaist the dollar. This average effect has two compoets. As metioed above, oe compoet is mechaical: cotractioary moetary policy decreases the umber of dollars used to purchase a uit of fial 16

18 cosumptio i the U.S, which icreases the value of each dollar. The secod compoet to this effect trasmits itself through the real exchage rate. Cotractioary U.S. moetary policy decreases household cosumptio i the Uited States, which icreases the U.S. household s margial utility of cosumptio. A uit of the U.S. fial cosumptio budle becomes more valuable i real terms, which also icreases the real value of the dollar. The secod lie o the right-had side is coutry specific ad shows heterogeeity i import currecy ivoicig fully captures the variatio i moetary policy spillovers. Coutries with higher shares of dollar ivoiced cosumptio depreciate less with respect to coutries with lower shares of dollar ivoiced cosumptio. Equatio (12) shows cotractioary U.S. moetary policy decreases aggregate cosumptio more i foreig coutries with a larger share of dollar ivoiced imports. Hece, their margial utility of cosumptio icreases relative to coutries with a smaller share of dollar ivoiced cosumptio. Because the real exchage rate betwee two coutries is the ratio of their margial utilities of cosumptio, coutries with larger shares of dollar ivoiced cosumptio appreciate, i real terms, relative to coutries with smaller shares of dollar ivoiced cosumptio. Predictio 2. Holdig foreig moetary policy costat, cotractioary moetary policy from the Uited States should icrease foreig omial iterest rates. Coutries with higher M $ observe larger icreases i omial iterest rates tha coutries with lower M $. The omial iterest rate, R, i coutry is pied dow by the followig cosumptio Euler equatio: [ (C ) ] γ 1 R = βe 2 P 1. (14) C1 P 2 Holdig foreig moetary policy fixed, the U.S. moetary policy actio affects foreig real iterest rates by chagig the foreig household s margial utility of cosumptio i the first period, C1. Foreig cosumptio i the log-ru, C2, is uaffected because omial prices are flexible i the secod period. Cotractioary policy from the Uited States icreases the foreig margial utility of cosumptio today. Hece, both the real ad omial iterest rate i the foreig coutry icrease. Nomial iterest rates i coutries with a higher share of dollar ivoiced cosumptio icrease more, because their cosumptio decreases more. 17

19 4.3 Policy Spillovers from Other Cetral Baks Although I have focused o discussig moetary policy spillovers from the Uited States i the model, moetary policy spillovers should clearly emaate from all coutries. Predictio 3. Cotrollig for the share of cosumptio that is ivoiced i each coutry s currecy, the magitude of spillover effects from Japaese moetary policy ad the Europea moetary policy are the same as the magitude of the spillover effects from U.S moetary policy. The magitude of moetary policy spillover effects oly differs accordig to the share of iteratioal trade that is ivoiced i each currecy. Equatio (15) shows the effect of a Japaese cotractioary moetary policy shock o ye exchage rates: ( ( e,jp (1 τ)(1 + (γ 1)τ)(1 + γ 2 α US US = αeu XJP $ αjp US ) XEU $ αeu) US 1 τ) p JP ν γ(1 τ)(1 + (γ 1) τ) M ν, (15) where M = τα JP ( ) 1 X JP $ is the share of coutry s total cosumptio that is ivoiced i ye. It is the product of the share of coutry imports produced i Japa (αjp ), the share of Japaese traded goods ivoiced i ye (1 X JP $ ), ad the share of traded goods i aggregate cosumptio (τ). Comparig the secod lies from equatios (13) ad (15) shows the heterogeeity i moetary policy spillovers from the Uited States ad Japa are exactly the same after cotrollig for currecy ivoicig. Moetary policy spillovers from Japa aturally icrease i magitude with the share of a coutry s ye ivoiced cosumptio. Symmetry i moetary policy spillover effects i exchage rates exists for cosumptio ad iterest rates as well. I formally derive these results i Appedix A Productio I this sectio, I characterize the role of currecy ivoicig i determiig moetary policy spillovers to traded productio. Aggregate output i the traded sector of coutry m is the weighted sum of its productio ivoiced i dollars ad its productio ivoiced i domestic currecy, yt m = µ m X$ m y T,m,$ + µ m (1 X$ m ) y T,m,h. 18

20 y T,m,h represets the productio i a firm that ivoices its exports i domestic currecy. As we have show earlier, cotractioary U.S. moetary policy decreases the productio of traded goods. As the dollar appreciates, households traded cosumptio becomes more expesive, ad households demad fewer traded goods. The magitude of the effect of cotractioary U.S. policy o productio i coutry m is a weighted average of the effect of U.S. moetary policy o the cosumptio of coutry m itermediate traded goods i each coutry: y T,m p = US {US,JP,EU} µ αm µ US α U S m + µ JP αm JP + µ EU αm EU ( c ) T,m. p US The weights are a fuctio of the size of each coutry (µ ), ad how much each coutry prefers differet varieties of traded goods, (α m). The demad fuctio for coutry m itermediate traded goods, c T,m, further depeds heavily o the preferece parameters (α m), ad the elasticity of substitutio betwee differet varieties of traded goods (ε). Hece, aalytic expressios of the demad fuctio ca be difficult to aalyze i closed form. To characterize this spillover effect, I simplify the model ad cosider a world i which coutries are more symmetric. Let µ = 1/3, α = α for all coutries ad α m = (1 α)/2 for m. Hece, all coutries are the same size, ad the share of domestically produced traded goods i each household s fial cosumptio budle is the same across all coutries. The parameter α determies household demad for foreig traded goods. Higher α forces households to cosume fewer foreig traded goods. However, each household cosumes a equal share of traded goods from each foreig coutry. These assumptios force the demad fuctios of all firms to become symmetric alog all dimesios except currecy ivoicig. I this special case, the behavior of U.S. moetary policy spillover effects oto foreig traded productio mirrors Predictios 1 through 3. Predictio 4. Suppose coutries are symmetric. Holdig foreig moetary policy costat, cotractioary moetary policy shock from the U.S. should decrease foreig traded productio. Coutries with higher X$ s should observe larger decreases i traded productio more tha coutries with smaller X $ s. The effect of a cotractioary U.S. policy shock o aggregate productio i the traded sector of foreig coutry is y T p US = δ y (1 α)(1 τ)(1 + (γ 1)τ) (1 + (3/4) (γ(1 α) 1 α) τ) X$, (16) ν 19

21 where δ y is a costat relegated to Appedix A.6. Equatio (16) shows the impact of U.S. moetary policy o foreig traded productio icreases i proportio to the coutry s share of dollar ivoiced exports. Each firm that ivoices its exports i dollars observes a greater drop i demad for its itermediate traded good compared to firms that ivoice their exports i local currecy. Hece, the aggregate effect depeds o the total mass of firms i each coutry that ivoice i dollars. As households demad more foreig produced traded goods (α decreases), the magitude of these spillover effects icrease. 4.5 Icomplete Asset Markets Although the complete asset markets model is a importat bechmark, it has some well kow empirical shortcomigs. Oe key shortcomig is that it predicts a perfect egative correlatio betwee appreciatios i the real exchage rate ad aggregate cosumptio (Backus ad Smith, 1993). Hece, it predicts chages i asset prices across coutries are also perfectly egatively correlated with chages i cosumptio. As a result, may authors have argued for a icomplete asset market model i which the effect of moetary shocks o equilibrium exchage rates improves the fit of the model to the data (Alvarez et al., 2002). I exted the model i sectio 3 ad characterize the effect of currecy ivoicig o moetary policy spillovers whe markets are segmeted. 5 Withi each coutry, oly a fractio φ of households (labeled active ) trade a complete set of state-cotiget securities. The remaiig 1 φ of households (labeled iactive ) are excluded from tradig i fiacial markets. Istead, iactive households cede the claims to their firm profits ad their edowmets of o-traded goods to active households. I retur, iactive households receive a omial bod that makes a fixed omial paymet B t i each period. Exchage rates ad iterest rates are determied by the margial utility of cosumptio of active households oly. Equatios (34), (35) ad (36) provide the icomplete markets couterparts to equatios (13), (12) ad (16). These equatios show that i the icomplete markets model, U.S. moetary policy shocks still trasmit more to coutries with a larger share of dollar ivoiced cosumptio. I particular, a cotractioary U.S. moetary policy shock decreases the cosumptio of active households more i coutries with a higher share of dollar ivoiced cosumptio relative to coutries with a lower share of dollar ivoiced cosumptio. Propositio 1 ad Predictios 1 through 4 hold i the icomplete markets model. 6 5 See Appedix A.8 for the formal setup. 6 See Appedix A.8 for a formal proof. Hece, 20

22 The itroductio of icomplete asset markets does however break the tight lik betwee chages i aggregate cosumptio ad movemets i asset prices across coutries. Whe the Uited States egages i cotractioary moetary policy, a cosequece of the decrease i demad for itermediate traded goods is that labor demad ad wages decrease for iactive households i Japa ad Europe. However, labor icome decreases more for iactive households i Japa, which is the coutry with fewer dollar ivoiced imports. Hece, the relative chage i iactive household cosumptio is exactly opposite of the relative chage i active household cosumptio. Cotractioary moetary policy from the U.S. decreases iactive household cosumptio more i coutries with fewer dollar ivoiced imports as a share of per capita cosumptio. Equatio (38) i Appedix A.8 shows that eve though the cosumptio of active households i Europe decrease relative to the cosumptio of active households i Japa, aggregate cosumptio i Europe ca icrease relative to aggregate cosumptio i Japa uder certai parameter combiatios. 7 Thus, the icomplete markets model extesio to the model i sectio 3 achieves two goals. First, the icomplete markets model reiforces the isights from the model with complete fiacial markets. Secod, icomplete markets ca improve the quatitative implicatios of the model by breakig the perfectly egative correlatios betwee exchage rates ad aggregate cosumptio across coutries. 5 Empirical Aalysis ad Data The model i sectio 3 predicts moetary policy from ay coutry affects exchage rates, iterest rates ad productio, globally, whe omial prices are sticky ad traded goods are ivoiced i that coutry s currecy. Heterogeeity i currecy ivoicig of imports ad exports characterizes the stregth of these moetary policy spillover effects. Rather tha test the implicatios of the model for New Keyesia Phillips curves or aggregate cosumptio directly, I ivestigate Predictios 1 through 4. To re-iterate, empirical estimates of New Keyesia Phillips curves are subject to a umber of cocers, which ofte lead to coflictig results. Furthermore, the previous sectio showed that oly the cosumptio of the margial ivestor is relevat for explaiig chages i iterest rates ad exchages rates. However, it is ofte hard to idetify the cosumptio of the margial ivestor, ad chages i the cosumptio of the margial ivestor are ot equivalet to chages i aggregate cosumptio. 7 For example, φ [1/2, 2/3] ad γ > φ ετ(1 (3/2)φ. 21