Nontradable Goods and the Real Exchange Rate

Transcription

1 Open Econ Rev DOI 1.17/s RESEARCH ARTICLE Nonradable Goods and he Real Exchange Rae Pau Rabanal Vicene Tuesa Springer Science+Business Media New York 212 Absrac How imporan are nonradable goods and disribuion coss o explain real exchange rae dynamics? We answer his quesion by esimaing a general equilibrium model wih inermediae and final radable and nonradable goods. We find ha he esimaed model can mach characerisics of he daa ha are relevan in inernaional macroeconomics, such as real exchange rae persisence and volailiy, and he correlaion beween he real exchange rae and oher variables. The disincion beween radable and nonradable goods is key o undersand real exchange rae flucuaions, bu he inroducion of disribuion coss is no. Nonradable secor echnology shocks explain abou one hird of real exchange rae volailiy. We also show ha, in order o explain he low correlaion beween he raio of relaive consumpion and he real exchange raes across counries, demand shocks are necessary. We wish o hank Pablo Guerrón and Carlos Monoro for helpful discussions, and an anonymous referee for very helpful commens. The opinions expressed in his paper are hose of he auhors and should no ne aribued o he IMF or IMF policy. Any errors and omissions are our own. Addiional maerial is available in an online appendix a P. Rabanal Inernaional Moneary Fund, 7 19h S., Washingon DC, NW 2431, USA prabanal@imf.org V. Tuesa B) CENTRUM Caólica, Ponificia Universidad Caólica del Perú, Lima, Peru viceneuesa@gmail.com

2 P. Rabanal, V. Tuesa Keywords Real exchange raes Nonradable goods Nominal rigidiies Bayesian esimaion JEL Classificaion F31 F32 F41 C11 1 Inroducion A main challenge in he empirical inernaional macroeconomics lieraure is he so called real exchange rae disconnec : models wih opimizing agens have difficuly in accouning for he behavior of he real exchange rae. A relaed problem is ha hese models are no able o explain key correlaions beween he real exchange rae and oher macroeconomic variables. In addiion, hese models canno capure he comovemen beween key macroeconomic variables across counries. In his paper, we focus on he role played by nonradable goods in explaining he behavior of he real exchange rae. There is empirical and quaniaive evidence supporing he role of nonradable goods for o undersand real exchange rae dynamics. On he empirical fron, Bes and Kehoe 26) provide evidence of he imporan role of nonradable goods in accouning for he variance of he real exchange rae of he mos imporan U.S. rade parners. They sugges ha he larger are rade flows beween wo counries, he lower is he imporance for deviaions from he law of one price i.e. radable goods prices) for real exchange rae behavior. Furhermore, in he U.S., consumpion of nonradable goods represens roughly 4 % of GDP and final goods also conain subsanial nonradable inpu componens beween 2 and 3 % of GDP). On he quaniaive fron, Sockman and Tesar 1995) show ha inroducing nonradable goods in macroeconomic models is crucial o explain inernaional business cycles. More recenly, Dosey and Duare 28), Benigno and Thoenissen 28)and Corsei e al. 28) highligh he role of nonradable goods in explaining real exchange rae behavior, and in paricular, is persisence and volailiy, and is correlaions wih oher inernaional relaive prices and real variables. In his paper, we find ha nonradable goods play an imporan role in explaining real exchange rae dynamics and several inernaional macroeconomics facs. Our saring poin is an esimaed wo-counry U.S.-euro area), wo-secor radable-nonradable goods) dynamic sochasic general equilibrium DSGE) model wih nominal rigidiies, of he class ha is now becoming mainsream in academic circles and policy insiuions for macroeconomic analysis. 1 Our analysis is empirical and model-based, and we esimae and 1 Empirical papers ha have esimaed fully specified general equilibrium inernaional macroeconomic models include Rabanal and Tuesa 21), Lubik and Schorfheide 25), Adolfson e al. 27), Jusiniano and Preson 21) and De Walque e al. 26). None of he above menioned sudies consider he role of nonradable goods.

3 Nonradable Goods and he Real Exchange Rae compare wo versions of his model: in he firs one, he wo secors radable and nonradable) produce final consumpion goods. In he second one, we inroduce a nonradable inermediae inpu ha is incorporaed in he producion of he final radable good. In his case, we aim a undersanding he role of disribuion coss in explaining feaures of inernaional macroeconomics, as suggesed by Dosey and Duare 28). Our mehodology consiss in esimaing each model using a Bayesian approach and eleven macroeconomic series, including boh he producer price index PPI) for finished indusrial goods and he consumer price index CPI) for he Unied Saes and he Euro Area. PPI inflaion for finished indusrial goods) allows us o capure inflaion in he radable goods secor of he economy, and unlike he goods componen of he CPI, should no include disribuion coss. Also, he PPI series is for finished indusrial goods, and hence i should exclude a larger proporion of nonradables han oher measures. 2 Our resuls can be summarized as follows. Firs, he parameer esimaes of he baseline model are quie similar o wha has been esimaed or calibraed in he vas exising lieraure. Therefore, our likelihood-based mehod does no rely on implausible parameer values for srucural coefficiens such as he degree of nominal rigidiy, he degree of backward looking behavior in inflaion or consumpion, he moneary policy rules in boh counries, and he size and persisence of economic shocks o explain he daa. Second, we find ha he version of he model wihou disribuion coss performs beer han he version wih disribuion coss. Since he model already includes several nominal and real rigidiies, he addiion of disribuion coss does no help in explaining he daa beer: in fac, model fi is worse in some dimensions, including real exchange rae persisence. Therefore, our esimaes suppor ha disribuion coss should no be reaed differenly han oher services in he producion of final goods. Third, our variance decomposiion exercise using he preferred model) shows ha he nonradable secor in he model does indeed help o explain real exchange rae flucuaions: nonradable secor echnology shocks explain as much as 3 % of he flucuaion of he bilaeral real exchange rae, while radable secor echnology shocks and moneary policy shocks ogeher explain less han 2 %. Ineresingly, demand shocks explain a grea amoun of real exchange rae flucuaions 45 %). Finally, our esimaed model allows us o draw imporan implicaions for he behavior of he real exchange rae, he erms of rade and he rade balance. The relaive price of domesic radables decreases under a radable secor echnology shock, which is consisen wih he radiional Balassa- Samuelson effec. Wih a produciviy improvemen in eiher he radable and nonradable secors, relaive oupu, consumpion and ne expors increase. Finally, following a produciviy shock in eiher radable or nonradable secors, domesic prices decrease and as a resul he real exchange rae depreciaes. 2 I is impossible o obain a pure measure of radable goods inflaion. Inpu-oupu able daa for he U.S. reveals ha services are an inermediae inpu for he producion of indusrial goods.

4 P. Rabanal, V. Tuesa The model feaures he usual ransmission mechanism wih erms of rade deerioraion following increases in produciviy. 3 In addiion, our esimaed model generaes, condiional on a radable secor produciviy shock, a real exchange rae depreciaion and an increase in he raio of relaive consumpions. Therefore, our resuls sugges ha demand shocks are he ones ha help o explain he negaive correlaion beween he real exchange rae and relaive consumpions observed in he daa. On his regard, our findings are in conras o hose of Corsei e al. 28), who find ha he radable secor produciviy shocks are able o explain he apparen lack of risk sharing across counries negaive correlaion beween relaive consumpions and he real exchange rae). In all he models we esimae, we do no include capial accumulaion. We argue ha his is unlikely o change our resuls. In esimaed DSGE models ha include invesmen in he model and in he se of observable variables, an invesmen-specific echnology shock is also included see Rabanal and Tuesa 21). This shock ypically explains mos of he volailiy of invesmen bu i also has counerfacual implicaions for consumpion. In paricular, his shock implies a negaive comovemen beween consumpion and invesmen. Hence, we suspec ha if we had inroduced invesmen and invesmen specific echnology shocks, hese shocks would no have conribued o explaining RER dynamics and he correlaion beween consumpion and he RER. Moreover, some recen papers have shown ha invesmen-specific echnology shocks are no volaile enough in he daa in order o solve cerain macroeconomic puzzles see Mandelman e al. 211 and Schmi-Grohe and Uribe 211). Finally, for mos counries i is no possible o obain daa on radable and nonradable invesmen. Given hese concerns and in order o keep he ransmission mechanism simple, we have chosen no o include invesmen. The res of he paper is organized as follows. In Secion 2, we presen he model ha we esimae. In Secion 3 we discuss he daa, and he prior and poserior disribuion of he model s parameers. In Secions 4 and 5 we discuss he implicaions of he esimaed model for real exchange rae behavior and he ransmission mechanism in open economies. In Secion 6 we discuss he esimaion of a model ha incorporaes disribuion services, while Secion 7 concludes. 2 The Model In his secion, we presen he model ha we use for analyzing real exchange rae dynamics and he inernaional ransmission of shocks. The model is a fairly sandard inernaional macro wo-counry, wo-secor radable and nonradable) economy, in he spiri of Sockman and Tesar 1995) and Dosey 3 On he conrary, Debaere and Lee 24), Corsei e al. 26) find evidence in suppor of erms of rade improvemen afer favorable produciviy shocks.

5 Nonradable Goods and he Real Exchange Rae and Duare 28). The model includes sicky prices in boh secors, and i assumes ha moneary policy is conduced wih an ineres rae rule of he Taylor ype. Based on he argumens by Benigno and Thoenissen 28) and on he empirical resuls of Rabanal and Tuesa 21), we only explore he possibiliy ha here are incomplee markes a he inernaional level. Finally, we assume ha he law of one price holds and inermediae firms se prices in heir own currency. 4 Since our conribuion is o esimae his model using Bayesian mehods and eleven observable variables, in his secion we briefly presen is main assumpions, parameers and funcional forms, and refer he reader o he online appendix for a full-blown version of he model. In he las secion of he paper, we sudy he effecs of inroducing a disribuion secor in he model. We follow Dosey and Duare 28) and assume ha he producion funcion of final radable goods includes a porion of nonradable inpus. Finally, o keep he exposiion of he model a is minimum, we only presen he equaions for households and firms in he home counry. The expressions for he foreign counry are analogous, and obaining hem is sraighforward, wih he appropriae change of noaion. 5 Households Represenaive households in he home counry are assumed o maximize he following uiliy funcion: { [ U = E β ψ log ]} ) L C b C 1+ϕ 1, 1) 1 + ϕ = subjec o he following budge consrain: B H P R + S B F ) P R S B F P Y B H 1 P + S B F 1 P + W P L C +. 2) E denoes he condiional expecaion on informaion available a dae =, β is he ineremporal discoun facor, wih <β<1. C denoes he level of consumpion in period, L denoes labor supply. The uiliy funcion displays exernal habi formaion wih respec o he habi sock, which is las period s aggregae consumpion of he economy C 1. b [, 1] denoes he imporance of he habi sock. ϕ> is inverse elasiciy of labor supply wih respec o he real wage. ψ is a preference shock ha follows a zero-mean AR1) process in logs: log ψ = ρ ψ log ψ 1 + ε ψ. 3) 4 Dosey and Duare 28) show ha alernaive assumpions regarding pricing decisions of firms, namely producer currency pricing PCP) and local currency pricing LCP), are no so differen for he real exchange rae dynamics. 5 The convenion will be o use an aserisk o denoe he counerpar in he foreign counry of a variable in he home counry i.e. if aggregae consumpion is C in he home counry, i will be C in he foreign counry and so on. The same applies o he model s parameers. When here is poenial for confusion we explicly clarify so.

6 P. Rabanal, V. Tuesa In he budge consrain, W is he nominal wage, P is he consumer price index, and are real profis for he home consumer. For modelling simpliciy, we choose o assume incomplee markes a he inernaional level wih wo risk-free one-period nominal bonds denominaed in domesic and foreign currency, and a cos of bond holdings is inroduced o achieve saionariy see Benigno 29). B H is he holding of he risk free domesic nominal bond and B F is he holding of he foreign risk-free nominal bond expressed in unis of foreign counry currency. S is he nominal exchange rae, expressed in unis of home counry currency per uni of foreign counry currency. R and R are he nominal ineres raes in he home and foreign counries. The funcion.) depends on he aggregae ne foreign asse posiion of he home counry, B F, in percen of home-counry GDP, and is aken as given by he domesic household..) is a convex funcion ha inroduces he cos of underaking posiions in he inernaional asse marke, and allows o have a well-defined seady-sae. In addiion, i is assumed ha ) = 1 and ha.) is a decreasing funcion. Also, while we do no make i explici in he budge consrain 2, we assume ha here are complee markes a he domesic level, such ha he consumpion/savings decision is he same among households in a counry, and he sochasic discoun facor o value fuure profis is also he same among households in a counry. The aggregae consumpion index C ) is a composie of final radable C T ) and final nonradable C N ) consumpion goods. We define he consumpion index as [ C γ 1/ε c C T ) ε 1 ε + 1 γ c ) 1/ε C N ) ε 1 ] ε ε 1 ε, 4) where ε is elasiciy of subsiuion beween he final radable C T ) and final nonradable C N ) goods, and γ c is he share of final radable goods in he consumpion baske a home. In his conex, he consumer price index ha corresponds o he previous specificaion is given by P [ γ c P T ) 1 ε + 1 γc ) P N ) 1 ε ] 1 1 ε, 5) where all prices are for goods sold in he home counry, in home currency and a he consumer level, for boh radable and nonradable goods. The demand funcions for he final radable and nonradable goods are given by: C T P T ) ε = γ P c C, and C N N ) ε = 1 γ c ) C, 6) P P while consumpion/savings decisions in home and foreign bonds are sandard: { } P λ = β E R λ +1, 7) P +1 ) S B F { } λ = β E R Q +1 λ +1, 8) P Y Q

7 Nonradable Goods and he Real Exchange Rae ψ where λ = is he marginal uiliy of consumpion, and Q C b C = S P 1 P real exchange rae. Labor supply is given by: is he λ W P = L ϕ. 9) Firms There are hree secors in each counry: i) a final goods producer secor, ha produces final radable and nonradable goods for consumpion by domesic households, ii) an inermediae radable goods secor, ha produces goods ha can be raded inernaionally o final radable goods producers eiher in he home or in he foreign counry, and iii) an inermediae nonradable goods secor, ha sells is producion o final nonradable goods producers. We assume ha he final goods producers operae under flexible prices and perfec compeiion, while inermediae goods producers operae under sicky prices à la Calvo wih parial indexaion, and monopolisic compeiion. Final Goods Producers The final radable good is consumed by domesic households. This good is produced by a coninuum of firms, each producing he same variey, labelled by Y T, using inermediae home ) ) X h and foreign goods wih he following echnology: X f Y T = { γx 1/θ ) θ 1 X h θ + 1 γ x ) 1/θ X f ) θ 1 } θ θ 1 θ, 1) where θ is he elasiciy of subsiuion beween home-produced and foreignproduced impored inermediae goods. X h and X f denoe he amoun of home and foreign inermediae radable inpus o produce he final radable good a home, are also Dixi-Sigliz aggregaors of all ypes of home and foreign inermediae goods, wih elasiciy of subsiuion σ.: X h [ 1 X h ] σ [ σ 1 1 σ 1 h) σ dh, and X f X f f ) σ 1 σ ] σ σ 1 df. Opimizing condiions by final radable goods producers deliver he following demand funcions: where P h P X h h ) σ h) = γ h) P h x P h X f f ) = 1 γ x ) [ 1 P f f ) P f P T ) θ Y T, and ) σ P f P T ) θ Y T, 11) ] 1 [ P h 1 σ 1 ] 1 h)1 σ dh, P f P f f ) 1 σ 1 σ df.

8 P. Rabanal, V. Tuesa Thus, he price index of radable goods is given by: P T = [ ) γ x P h 1 θ ) ] 1 1 θ + 1 γx ) P f 1 θ. 12) We assume ha he law of one price holds for inermediae inpus, such ha P h h) = Ph h)s,andp f f ) = P f f )S. The producion of he final nonradable good is given by: Y N [ 1 X N ] σ n) σ 1 σ 1 σ dn where we assume he same elasiciy σ>1 han in he case of final radable goods produced in he home counry. The price level for nonradables is P N [ 1 ] 1 p N n) 1 σ 1 σ dn Inermediae Goods Producers The srucure of inermediae goods producers in he wo secors is very similar. The main difference is ha he inermediae nonradable secor produces differeniaed goods ha are aggregaed by final nonradable good producing firms, and ulimaely used for final consumpion by domesic households only, while he inermediae radable secor produces differeniaed goods ha can be sold o home and foreign final radable good producers. The producion funcion in boh secors is linear in he labor inpu and has wo echnology shocks: Y N n) = A Z N L N n), for n [, 1], and Y h h) = A Z h Lh h), for h [, 1] 13) where A is a labor augmening aggregae world echnology shock which has a uni roo wih drif: log A = g + log A 1 + ε a 14) Hence, real variables in boh counries grow a a rae g. Z N and Z h are counry-specific, saionary produciviy shocks o he nonradable and he radable secor a ime, which evolve according o zero-mean, AR1) process in logs log Z N = ρ Z,N log Z N 1 + εz,n, and log Z h = ρ Z,h log Z h 1 + εz,h 15) Firms in boh secors face a Calvo loery wih parial indexaion when seing heir prices. In he nonradable secor, firms receive a sochasic signal ha allows hem o rese prices opimally in each period, wih probabiliy 1 α N. We assume ha here is parial indexaion wih a coefficien ϕ N o las period s

9 Nonradable Goods and he Real Exchange Rae secorial inflaion rae for hose firms ha do no ge o rese prices opimally. As a resul, firms maximize he following profis funcion: ) P Max P N n)e α k N N P N ϕn n) +k 1 P 1 N,+k MC+k N Y N,d +k P n) +k 16) k= subjec o Y N,d +k n) = [ ) P N n) P N +k 1 P N +k P N 1 ) ϕn ] σ Y N 17) where Y N,d n) is oal individual demand for a given ype of nonradable good n, andy N is aggregae demand for nonradable goods, as defined above, and,+k = β k λ +k λ is he sochasic discoun facor. MC N corresponds o he real marginal cos in he nonradable secor. From cos minimizaion: MC N W = P Z N 18) A The evoluion of he price level of nonradables is P N [ {α N P 1 N ) N ϕn ] 1 σ αn ) ˆp N ) 1 σ } 1 1 σ 19) where 1 N = PN 1. Similar expressions hold for he inermediae radable P 2 N secor, where he relevan parameers for price seing are α h and ϕ h,and wih he appropriae change of noaion in Eqs. 16, 17, 18, and19, and similar expressions hold for he foreign counry. Closing he Model The model includes a demand shock. One inerpreaion is ha his shock is a governmen spending shock ha is financed by lumpsum axaion. More generally, his demand shock is capuring movemens in GDP and in consumpion ha canno be explaining hrough ineres-rae changes. Hence, we will be using boh erms: demand shock and governmen spending shock, o refer o he shock in he marke clearaing condiion. We assume ha he demand shock is allocaed beween radable and nonradable goods in he same way ha privae consumpion is. Hence he marke clearing condiions for boh ypes of final goods, consising of privae consumpion and governmen spending, are: and Y T = C T + G T, 2) Y N = C N + G N, 21)

10 P. Rabanal, V. Tuesa where G N, G T follow AR1) processes in logs. The bond marke clearing condiions are: B H + B H =, 22) and B F + B F =. 23) For he nonradable inermediae goods, he marke clearing condiion is: Y N n) = X N n), for all n [, 1], while for he inermediae radable goods secor i is: Y h h) = X h h) + Xh h), for all h [, 1]. Moneary policy is conduced wih a Taylor rule ha arges CPI inflaion and oupu growh deviaion from seady-sae values: ) R = R 1 ρr) R ρ r P /P 1 ρr )γ π ) 1 Y /Y 1 ρr )γ y 1 1 expε r ). 24) 1 + g 3 Daa, Priors and Poserior Disribuions We use Bayesian mehods o esimae he parameers of he model of Secion 2. Bayesian esimaion of DSGE models has now become very popular, so we leave he echnical deails and a discussion of is benefis aside. 6 We use he following daa series for each counry: oupu real GDP) growh per capia, consumpion growh per capia, CPI inflaion, ineres raes on 3-monh T-Bills, and PPI inflaion for finished indusrial goods. CPI inflaion is used as a measure of overall inflaion, while PPI inflaion ries o measure he inflaion in he radable secor of he economy. Several auhors Engel 1999; Bes and Kehoe 26) have emphasized ha using he goods componen of he CPI migh no be a good proxy for radable goods, because i conains disribuion and reail services ha are nonradable. The home counry is he euro area, and he foreign counry is he U.S. The las series ha we use in he esimaion procedure is he bilaeral real exchange rae beween he euro and he US dollar. To consruc his series, we muliply he nominal exchange rae in euros per U.S. dollar) by he U.S. CPI, and divide i by he euro area CPI. An increase of he real exchange rae is an euro depreciaion. These eleven variables are our se of observable variables in he likelihood funcion. The sample period goes from 1985:2 o 24:4. We are consrained by he availabiliy of he PPI series for finished indusrial goods in he euro area, since all oher variables are available from earlier periods. 6 See An and Schorfheide 27), Lubik and Schorfheide 25) and Fernandez-Villaverde and Rubio-Ramírez 24) for deailed explanaions on how o implemen a Bayesian approach o esimaion of fully-specified dynamic sochasic general equilibrium models.

11 Nonradable Goods and he Real Exchange Rae Before we proceed o describe he prior and poserior disribuion of he model s parameers, we discuss wha parameers we calibrae firs. We follow Dosey and Duare 28) closely, and calibrae he wo economies wih he same parameers. We se he share of radable goods in he CPI o γ c =.44. We se he fracion of inermediae radable inpus in he producion of final radable goods o γ x =.6. Since we are no using labor marke daa we calibrae he value of ϕ = 1, which is in line wih parameer esimaes obained by Rabanal and Rubio-Ramírez 25, 28). We se he seady-sae growh rae of he economy, g, equal o.5 %, which implies ha he world growh rae of per capia variables is abou 2 % per year. In order o mach a real ineres rae in he seady sae of abou 4 % per year, we se he discoun facor o β =.99. For reasonable parameerizaions of hese wo variables he parameer esimaes do no change significanly. Finally, he parameer χ, ha measures he elasiciy of he risk premium wih respec o he ne foreign asse posiion, is se equal o.7 based on Rabanal and Tuesa 21). Wih he previous parameers fixed in advance, Table 1 presens he prior and poserior disribuions for he model s remaining parameers which are fairly sandard see Smes and Wouers 23; Lubik and Schorfheide 25 and Rabanal and Tuesa 21). In order o make he able more readable, we also include a brief descripion of each parameer. Since we are mosly ineresed in undersanding he implicaions of he model for real exchange rae dynamics and he inernaional ransmission of shocks, we briefly commen on he parameer esimaes. Overall, hey are quie similar o wha has been obained in he lieraure ha esimaes open economy dynamic macroeconomic models wih Bayesian mehods. 7 The esimaes for he degree of habi formaion are quie similar in boh counries, of.57 in he Unied Saes and of.58 in he euro area, respecively. The elasiciy of subsiuion beween home and foreign radable inpus, θ, is esimaed a.85, a value much smaller han he prior mean of 1.5, which was chosen according o Chari e al. 22). However, his value is higher han ha obained by Rabanal and Tuesa 21) and Lubik and Schorfheide 25) in a model wih radable goods only. As i will become clearer laer, he higher esimaed value for his elasiciy sems from endogenous volailiy ha nonradable goods adds o he model, hence making less necessary a small value of θ o accoun for real exchange volailiy. On he oher hand, he elasiciy of subsiuion beween radable and nonradable final consumpion goods, ε, is esimaed o be quie low, wih a poserior mean of.13, whichis much lower han he prior mean, of 1, and he value ypically used calibraed exercises in he lieraure of.44, following Sockman and Tesar 1995). The esimaed Phillips Curves sugges ha prices in he U.S. are rese opimally abou every 2 quarers in boh secors, wih a low degree of backward looking indexaion ϕ N,ϕ f ), beween.6 in he nonradable secor and.21 in he radable secor. The Phillips Curves in he euro area are more heerogeneous: 7 See Lubik and Schorfheide 25) and Rabanal and Tuesa 21).

12 P. Rabanal, V. Tuesa Table 1 Prior and poserior disribuions Prior Poserior Disribuion Mean S.Dev Mean Lower Upper Habi formaion b EMU Bea b USA Bea Elasiciies of subsiuion θ Home and foreign radable Normal in. goods ε Tradable and nonradable Gamma final goods Calvo parameers α h Tradable in. goods EMU Bea α f Tradable in. goods USA Bea α N Nonradable in. goods EMU Bea α N Nonradable in. goods USA Bea Indexaion parameers ϕ h Tradable in. goods EMU Bea ϕ f Tradable in. goods USA Bea ϕ N Nonradable in. goods EMU Bea ϕ N Nonradable in. goods USA Bea Taylor rule coefficiens ρ r Ineres rae smoohing EMU Uniform ρ r Ineres rae smoohing USA Uniform γ π Response o inflaion, EMU Normal γ π Response o inflaion, USA Normal γ y Response o growh, EMU Normal γ y Response o growh, USA Normal Prior and poserior disribuions of shock AR coefficiens Preference ρ ψ EMU Bea ρ ψ USA Bea Technology ρ Z,h Tradable in. secor EMU Bea ρ Z, f Tradable in. secor USA Bea ρ Z,N Nonradable in. secor EMU Bea ρ Z,N Nonradable in. secor USA Bea Governmen spending ρ G,T Tradable secor EMU Bea ρ G,T Tradable secor USA Bea ρ G,N Nonradable secor EMU Bea ρ G,N Nonradable secor USA Bea Sandard deviaions of shocks in percen) Preference ε ψ EMU Gamma ε ψ USA Gamma Technology ε Z,h Tradable in. secor EMU Gamma ε Z, f Tradable in. secor USA Gamma ε Z,N Nonradable in. secor EMU Gamma ε Z,N Nonradable in. secor USA Gamma ε a Permanen echnology shock. Gamma

13 Nonradable Goods and he Real Exchange Rae Table 1 coninued) Prior Poserior Disribuion Mean S.Dev Mean Lower Upper Governmen spending ε G,T Tradable secor EMU Gamma ε G,T Tradable secor USA Gamma ε G,N Nonradable secor EMU Gamma ε G,N Nonradable secor USA Gamma Moneary policy ε r EMU Gamma ε r USA Gamma he esimaed probabiliy of no reseing prices is.73 in he radable secor, while we obain a surprisingly low coefficien for he nonradable secor, where he poserior mean is.1, much lower han he prior mean of.5. Backward looking behavior is higher han in he case of he U.S., wih coefficiens of.3 in he radable secor and.4 in he nonradable secor. Finally, he coefficiens of he Taylor rule are quie similar o previous esimaes in he lieraure for he sample period ha we use, saring in 1985, wih coefficiens on he response of nominal ineres raes o inflaion of 2 in he Unied Saes Clarida e al. 2) and even higher in he euro area. Regarding he exogenous processes, all shocks are esimaed wih high, bu reasonable, persisence. The echnology shock in he inermediae nonradable secor has he highes persisence, wih a poserior mean of.97, while he persisence of all he oher shocks ranges beween ha value and.73 for he demand shock in he radable secor in he U.S. The high persisence in preference and echnology shocks in he nonradable secor in U.S. migh explain why he backward behavior in price seing is unimporan. Similar resuls have been found by Ireland 26) for an esimaed closed economy using U.S. daa. 4 Implicaions for Real Exchange Rae Dynamics: Second Momens and Variance Decomposiion Afer aking a linear approximaion of he equilibrium condiions around he seady sae, he equaions deermining he real exchange rae are as follows. Firs, combining he consumpion Euler equaions for boh households, we obain ha: [ ] [ 1 + g) E c +1 b c 1 + g) E c +1 E q +1 q ) = b c ] 1 + g b) 1 + g b ) + ) 1 ρ ψ ψ 1 ρψ) ψ + χb 25) where q is he real exchange rae, c and ) c are consumpion in he euro area S B and in he Unied Saes, b = F P Y 1 is he ne foreign asse posiion as percen of GDP, where χ ) Y, and ψ and ψ are he preference

14 P. Rabanal, V. Tuesa shocks all expressed in log deviaions from seady-sae values). 8 Therefore, in principle, if consumpion growh in boh areas is no relaed o he real exchange rae, he preference shocks should allow us o explain he daa in case of misspecificaion. In addiion, by aking he definiion of he real exchange rae as he raio of price levels expressed in common currency, and by using he definiion of he CPIs in boh counries and he definiions of he price level of radable goods, we obain he following expression: q = 2γ x 1) + 1 γ c )[ T N ) T N )] 26) where is he erms of rade, defined as he price of impors minus he price of expors, i = pi p, i = T, N is he relaive price beween radables and nonradables in he euro area CPI, and i = p i p, i = T, N is he relaive price beween radables and nonradables in he U.S. CPI. Therefore, he shocks ha drive he erms of rade, or ha move prices of radable and nonradable goods in boh counries in differen direcions, are also likely o affec he behavior of he real exchange rae. Indeed, he presence of nonradable goods helps in breaking he srong correlaion beween he real exchange rae and he erms of rade implied by a model wihou nonradable goods: In ha paricular case, γ c = 1, andq = 2γ x 1). Furhermore, as poined ou by Dosey and Duare 28), he presence of nonradable goods lowers he correlaion of real variables wih inernaional relaive prices, helping he model o beer explain he daa. In he nex sub-secion we analyze some second momens and evaluae how well he esimaed model works in he previous menioned dimensions. In he Bayesian approach, assessmens of he goodness of fi and model comparisons are performed using he marginal likelihood of he daa, which updaes he researcher s prior beliefs on which model is closer o he rue one afer observing he daa. Fernandez-Villaverde and Rubio-Ramírez 24) show ha, in he Bayesian framework, model comparison is consisen when models are misspecified, which is ypically he case. However, he marginal likelihood, which averages all possible likelihood values implied by he model across he parameer space, using he prior as a weigh, is a summary saisic of overall goodness of fi. In his secion, we focus insead on a subse of second momens ha are key in he inernaional macroeconomics lieraure. In Table 2 we presen some seleced poserior second momens of he raw daa, while in Table 3 we repor seleced poserior second momens of HP-filered real variables. The model overpredics he volailiy of consumpion and oupu growh, and of CPI and PPI inflaion in boh counries, while i underpredics he volailiy of nominal ineres raes and he real exchange rae Table 2). Ye, using a longer period ha includes he 197s makes he model fi he inflaion 8 The evoluion of ne foreign asses over GDP is: β b = 1+g 1 b ) 1 + X f Y x h x f where X f Y is he impors-gdp raio, x h is expors of inermediae radable goods, x f is impors, and is he erms of rade. Appendix B deails he full se of loglinearized condiions of he model.

15 Nonradable Goods and he Real Exchange Rae Table 2 Second momens in he model and in he daa Euro area Unied Saes Y C R CPI PPI Y C R CPI PPI Q Sandard Deviaion in %) Daa Model Variance decomposiion Preferences Tech. radable Tech. nonradable Demand shock Moneary policy Uni roo Shock Noe: Y is oupu, C is consumpion, R is nominal ineres rae. Q is he real exchange rae. Momens for R are based on he level of his variable, in all oher cases hey are based on heir quarerly growh rae daa beer as documened by Rabanal and Tuesa 21). To explain which shocks drive he behavior of macroeconomic variables, we perform a variance decomposiion exercise and hen add up shocks across counries. 9 Mos imporan for he purpose of his paper, we examine wha is he role of each shock in explaining real exchange rae flucuaions. In his case, demand shocks mosly in he radable secor, no shown) explain 43.5 % of he variance of he real exchange rae, while echnology shocks in he nonradable secor explain 31.8 %, and preference shocks explain 23.6 %. The oher shocks moneary policy, innovaions o he permanen echnology shock, and he radable secor echnology shock) explain abou he remaining 1 %. These resuls confirm he findings of Rabanal and Tuesa 21) wih a model wih radable goods only. Of course, in ha case we were no able o ell wha secor he shocks belonged o, bu we assigned an imporan conribuion abou 4 % each) o echnology and demand facors. In he presen esimaed model, nonradable echnology shocks, fiscal shocks and preference shocks are able o explain a large fracion of he volailiy of mos variables. Noe also ha he radable secor echnology shocks only explain an imporan fracion of radable PPI) inflaion in boh counries. Therefore, shocks arising in he nonradable secor are an imporan source of real exchange rae flucuaionsfinally, he moneary policy shock does explain a significan fracion of CPI inflaion in boh counries, abou 15 %. As suggesed by Table 3, he model does a good job in explaining he inernaional dimension of he daa, in paricular o he relaionship of oupu across counries and he correlaion beween relaive oupu and he real exchange rae. The model is also able o explain he so-called consumpion-real exchange 9 Tha is, he conribuion of he Preference shock adds up he conribuion of he euro area and he U.S. preference shock. The only excepion is he demand shock for which we have aggregaed across counries and secors.

16 P. Rabanal, V. Tuesa Table 3 Second momens in he model and in he daa Correlaion Y,Y* C,C* C-C*,Q Y-Y*,Q Q,Q 1 Daa Model Preferences Tech. radable Tech. nonradable Demand shocks Moneary policy Uni roo shock Noe: Y is oupu, C is consumpion, Q is he real exchange rae. All momens are compued by simulaing he model 1, imes wih 85 periods a he poserior mean and applying he HP filer rae anomaly. In he sample period ha we use, he correlaion beween he raio of relaive consumpions and he real exchange rae is basically zero. 1 The fac ha he model can mach a basically zero correlaion should no mask ha he ransmission mechanisms underlying his resul are very differen. While echnology shocks in boh secors, moneary policy and uni roo shocks deliver a high and posiive correlaion beween hese wo variables, preference and demand shocks deliver a highly negaive correlaion. Therefore, any model ha ries o be successful in explaining his correlaion mus have a combinaion of he wo, even when he model includes nonradable goods. The same resul applies when sudying he correlaion beween relaive oupus and he real exchange rae. Finally, we would like o remark ha he model is able o fi real exchange rae persisence, wih a firs auocorrelaion in he HPfilered real exchange rae in he model and in he daa of.78. Also, he hree shocks ha explain mos of real exchange rae volailiy are able o explain is persisence Implicaions for he Transmission Mechanism Having shown wha are he hree shocks ha explain he behavior of he real exchange rae in he previous secion, we now urn o discuss he impulse responses o a nonradable echnology shock, a radable secor demand shock, and a preference shock in he euro area. In Fig. 1 we depic he effecs of a 1 Adding he sevenies and mid-eighies sample, as in Rabanal and Tuesa 21), delivers a negaive correlaion of.17, ha a model wih incomplee markes and radable goods can mach. 11 We use HP-filered daa o be able o compare our resuls wih he inernaional real business cycle lieraure, including Corsei e al. 28). The empirical lieraure inerpreed real exchange rae persisence as he slow rae of mean reversion of he real exchange rae. Early examples of applicaions include Rogoff 1996) and he references herein. A ypical resul is he srong evidence of slow mean reversion, found by esimaing firs order auoregressive models for he level of he exchange rae insead of using HP filered daa. For a recen applicaion, see Seinsson 28).

17 Nonradable Goods and he Real Exchange Rae 8 x Pc. Dev. Seady Sae Y EMU Y USA RELATIVE Y Pc. Dev. Seady Sae C EMU C USA RELATIVE C Quarers Afer Shock Quarers Afer Shock Pc. Dev. Seady Sae RER TOT NX Pc. Dev. Seady Sae REL N EMU REL N USA Quarers Afer Shock Quarers Afer Shock Fig. 1 Impulse response o a nonradable echnology shock in he euro area posiive one sandard deviaion) nonradable secor echnology shock. As a resul, consumpion and oupu increase in he euro area. The real exchange rae and he erms of rade depreciae following he shock, and he relaive price of nonradables REL N = PN ) falls in he euro area where as i increases P T inheusa.fromeq.26, he RER dynamics can be decomposed in he ermsof-rade effec, 2γ x 1), and he movemens of relaive prices of radable o nonradable goods in boh counries. We can furher rearrange Eq. 26 o ge: where rel N = p N p T and rel N q = 2γ x 1) + 1 γ c )rel N rel N ) = p N p T. In his case, boh relaive-price effecs move he real exchange rae in he same direcion. The erms of rade depreciae because of he associaed nominal exchange rae depreciaion of he euro. This causes consumpion o fall in he U.S., and also he relaive price of radable goods o increase. Finally, here is a small improvemen of he rade balance bu of several orders of magniude smaller han all oher variables. Wih an esimaed θ close o one, he rade balance barely moves in all he exercises ha we show, because real quaniies offse he movemens in real prices. This shock implies a posiive correlaion beween boh he real exchange rae and he erms of rade wih boh relaive oupu and consumpion. The impulse response o a radable secor echnology shock no shown) displays similar behavior of he main variables, excep for he

18 P. Rabanal, V. Tuesa Pc. Dev. Seady Sae x Y EMU Y USA RELATIVE Y Pc. Dev. Seady Sae 2 x C EMU C USA RELATIVE C Quarers Afer Shock Quarers Afer Shock Pc. Dev. Seady Sae RER TOT NX Pc. Dev. Seady Sae REL N EMU REL N USA Quarers Afer Shock Quarers Afer Shock Fig. 2 Impulse response o a radable demand shock in he euro area relaive prices of nonradable o radable goods. 12 Our esimaed impulse responses are in line wih hose repored by Dosey and Duare 28) using a calibraed model for he U.S. and OECD counries. However, our empirical resuls challenge hose of Corsei e al. 26) which find exacly he opposie. Figure 2 displays he impulse response o a demand shock in he radable secor in he euro area. In his case, consumpion declines in he euro area and increases in he U.S., while he euro depreciaes in real erms. The erms of rade also depreciaes which booss consumpion in U.S. Why do boh he real exchange rae and he erms of rade depreciae? Since he model feaures, infiniely-lived Ricardian households, he posiive demand shock which works as a fiscal shock) induces a negaive wealh effec in euro area: agens work more and consume less oday. Hence, he labor supply increases, causing a reducion in real wages ha ranslaes ino a reducion in marginal coss in boh secors. Thus, domesic prices radable and nonradable) decrease, which riggers boh a real exchange rae and erms of rade depreciaion. The raio of relaive consumpions decreases wih he depreciaion, and implies a srong negaive correlaion beween he real exchange rae and relaive consumpions across counries. Negaive wealh effecs cause consumpion o 12 For robusness, we have also performed an esimaion using he erms of rade as an observable variable. Qualiaively, he impulse-responses do no change. Resuls are available upon reques.

19 Nonradable Goods and he Real Exchange Rae Pc. Dev. Seady Sae 2.5 x Quarers Afer Shock Y EMU Y USA RELATIVE Y Pc. Dev. Seady Sae 3.5 x C EMU C USA RELATIVE C Quarers Afer Shock Pc. Dev. Seady Sae RER TOT NX Pc. Dev. Seady Sae REL N EMU REL N USA Quarers Afer Shock Quarers Afer Shock Fig. 3 Impulse response o a preference shock in he euro area decrease in he euro area more han he reducion of consumpion in he U.S. Hence, as noed above, he presence of demand shocks are necessary o explain real exchange rae dynamics, hrough heir wealh effecs on consumpion, real wages and relaive prices. In our model, hese effecs are so srong ha hey imply a reducion of oupu as well. Finally, he rade balance deerioraes slighly being consisen wih he evidence repored in Monacelli and Peroi 26). Therefore, i is crucial o have demand shocks in he model, in order o be able o explain he real exchange rae-relaive consumpion anomaly. 13 Figure 3 shows he impulse response o a preference shock, which has very similar effecs o he demand shock regarding he implied comovemen beween he real exchange rae and relaive consumpion. However, unlike he demand shocks i induces a posiive wealh effec generaing insead a real exchange rae appreciaion. By increasing he marginal uiliy of consumpion, consumpion iself increases in he euro area, and he real exchange rae and erms of rade appreciae, which reduces consumpion bu increases oupu in 13 We also esimae our model assuming non-separable preferences in line wih Monacelli and Peroi 26). Under his specificaion we were able o reproduce impulse responses condiional o boh fiscal and radable echnology shocks ha are consisen wih he VAR evidence repored in Monacelli and Peroi 26) and Corsei e al. 26), respecively. Ye, he likelihood decreases subsanially and he overall fi of his specificaion underperforms our benchmark model. Resuls are available upon reques from he auhors.

20 P. Rabanal, V. Tuesa Change in he RER Change in he RER Q2 1987Q2 1989Q2 1991Q2 1993Q2 1995Q2 1997Q2 1999Q2 21Q2 23Q Q2 1987Q2 1989Q2 1991Q2 1993Q2 1995Q2 1997Q2 1999Q2 21Q2 23Q2 Change in he RER T. Demand Change in he RER NT Tech Change in he RER Change in he RER Q2 1987Q2 1989Q2 1991Q2 1993Q2 1995Q2 1997Q2 1999Q2 21Q2 23Q Q2 1987Q2 1989Q2 1991Q2 1993Q2 1995Q2 1997Q2 1999Q2 21Q2 23Q2 Change in he RER Preference Change in he RER Oher Fig. 4 Decomposiion of he real exchange rae he U.S. due o foreign demand. This also opens a small rade defici for he euro area. Why boh real exchange and he erms of rade appreciaes?. The preference shock induces a posiive wealh effec ha is refleced in higher consumpion. This increase of consumpion leads o an increase in wages, marginal cos increases and consequenly prices increase in boh secors. The price increase induces boh a real exchange rae and erms of rade appreciaion. Again, as noed above, we obain a negaive correlaion beween he real exchange rae and he raio of relaive consumpions, making his shock necessary o explain he daa. A he same ime, he relaive price of nonradables increases in he euro area, bu decreases in he U.S. To furher gauge he imporance of he previous shocks in accouning for he hisorical RER dynamics, Fig. 4 displays he observed value of he variaion in he real exchange rae bold line), ogeher wih he values wih only radable demand, nonradable echnology, preference, and he oher shocks, according o our esimaed model doed lines). 14 This exercise allows us o idenify he naure of he shocks ha have played a dominan role as a source of he real exchange rae dynamics. I is clear ha demand shocks explain a grea fracion of he real exchange rae flucuaions being posiive correlaed wih he real exchange rae, resuls ha are consisen wih he evidence illusraed above. Hence, he model 14 We use he Kalman filer o recover he sequence of shocks. We basically obain he cyclical componens of he change in he real exchange rae associaed wih each shock, according o our esimaed model a is poserior mean.

21 Nonradable Goods and he Real Exchange Rae wih demand shocks provides a very good approximaion o he daa. Bu, as we menioned before, a model wih only demand shocks would imply a oo negaive correlaion beween relaive consumpions and he real exchange rae, so his is why oher shocks in he model are needed. When he model is simulaed wih he nonradable componen only, we can see ha i is also able o capure some comovemen wih he acual series. On he oher hand, when he model is simulaed wih preference shocks only, or he res of shocks, he behavior of he change in he real exchange rae in he model and in he daa is quie differen. 6 The Role of he Disribuion Secor In recen papers, Corsei e al. 28) and Dosey and Duare 28) have emphasized he role of he disribuion secor in explaining real exchange rae dynamics. Here, we follow Dosey and Duare 28) and esimae wo differen versions of ha model. In he firs one, we assume ha he final radable consumpion good includes a nonradable inermediae inpu, and is produced under monopolisic compeiion here is produc differeniaion). In he second case, we furher assume ha he final radable good is also priced wih a Calvo-ype resricion. We modify he model along he following lines. The final radable good is consumed by domesic households. This good is produced by a coninuum of firms, each producing a differeniaed variey, labelled by Y T i), i [, 1]. Each firm combines a composie of home and foreign inermediae radable goods X T, wih a composie of inermediae nonradable goods X N wih he following producion funcion: Y T i) = { γ 1/ε [ Y y X T i) ] ε Y 1 ε Y + 1 γ y ) 1/ε [ Y X N i) ] } εy εy 1 ε Y 1 ε Y where ε y is he elasiciy of subsiuion beween radable and nonradable inermediae goods, and γ y is he share of radable inermediae goods in he producion funcion. The nonradable componen can be seen as disribuion services needed o bring he final consumpion good o consumers. This producion srucure somewha generalizes, bu does no nes, Corsei e al. 28), and implies a wedge beween he price of he CES aggregae of radable inpus and he price paid by he final consumer, due o disribuion coss. When γ y = 1, we go back o he model of Secion 2, bu wih produc differeniaion and monopolisic compeiion in he final radable goods secor. The local nonradable inermediae inpu is a Dixi-Sigliz aggregae of all nonradable varieies, wih he same elasiciy han he consumpion aggregae: [ 1 X N i) X N ] σ i, n) σ 1 σ 1 σ dn

22 P. Rabanal, V. Tuesa where X N i, n) is he amoun of inermediae nonradable inpu n by final good producer i. The price level P N is he same as he one defined in Secion 2. The composie of home and foreign inermediae radable goods is given by: X T i) = { γx 1/θ [ X h i) ] [ θ 1 ] θ + 1 γ x ) 1/θ X f θ 1 } θ θ 1 θ i) The definiion of he composie of home and foreign inermediae goods follows from Secion 2. Taking a linear approximaion o he firm s opimizing condiions, when prices of he final radable good are flexible, delivers he following inflaion rae for he final radable goods secor: [ ] p T = γ y γ x p h + 1 γ x ) p f + s ) + 1 γ y ) p N, 27) such ha he final radable goods secor includes a nonradable componen. Furher, if we assume ha here are sicky prices in he final radable good secor, inflaion dynamics in he final goods radable secor are given by: p T ϕ T p 1 T = β E p T +1 ϕ T p T ) + κt mc T T ), 28) ) ) where κ T = 1 α T )1 βα T ) /α T, mc T = γ y X + T + 1 γy N,and X =[γ x p h + 1 γ x ) p f + s )] p T. Raher han presening he full se of parameer esimaes which are available upon reques) we compare how he models wih a disribuion secor fi he daa, and in paricular some seleced momens of he daa. In Table 4 we presen he marginal likelihoods of he hree models baseline, Table 4 Model comparison Daa Baseline Disribuion Disribuion wih sicky prices Marginal likelihood Sandard DeviaionQ/Q 1 ) Percen variance explained by Preference shocks Nonradable ech. shocks Fiscal shocks Correlaion Q, Q 1 ) Correlaion C/C, Q) Noe: Sandard DeviaionQ/Q 1 ) is based on raw daa, Correlaion Q, Q 1 ) and Correlaion C/C, Q) is based on HP-filered daa