Inernaional Journal of Economics and Finance; Vol. 7, No. 2; 205 ISSN 96-97X E-ISSN 96-9728 Published by Canadian Cener of Science and Educaion Non-Traded Goods and Real Exchange Rae Volailiy in a Two-Counry DSGE Model Nesor Azcona Economics Division, Babson College, Wellesley, MA, USA Correspondence: Nesor Azcona, Economics Division, Babson College, Babson Park, MA, 02457, USA. Tel: -78-239-4533. E-mail: nazcona@babson.edu Received: November 9, 204 Acceped: December 5, 204 Online Published: January 25, 205 doi:0.5539/ijef.v7n2p36 URL: hp://dx.doi.org/0.5539/ijef.v7n2p36 Absrac This paper uses a wo-counry dynamic sochasic general equilibrium model (DSGE o sudy how differen characerisics of an economy, such as openness or price sickiness, affec he conribuion of he relaive price of non-raded goods o real exchange rae flucuaions. The model shows ha changes in he relaive price beween raded and non-raded goods are he main channel hrough which produciviy shocks are ransmied o he real exchange rae. Produciviy and moneary shocks also affec he real exchange rae hrough changes in he inernaional relaive price of raded goods. The economy s characerisics have a significan effec on he ransmission mechanism and he overall volailiy of he real exchange rae in response o boh ypes of shocks. Keywords: non-raded goods, purchasing power pariy, real exchange rae. Inroducion The real exchange rae measures he cos of goods and services in one counry relaive o he cos of goods and services in anoher. I is one of he mos imporan facors deermining a counry s inernaional compeiiveness and rade balance, and is a key macroeconomic variable in he inernaional ransmission of business cycles. Real exchange rae flucuaions are known o be highly volaile and a he same ime quie persisen, a phenomenon known as he purchasing power pariy puzzle (Rogoff, 996. Tradiionally, macroeconomic research has followed wo alernaive approaches o modeling real exchange rae movemens. In some macroeconomic models purchasing power pariy (PPP holds for raded goods prices and real exchange rae flucuaions are he resul of changes in he prices of non-raded goods relaive o he prices of raded goods (e.g. Backus and Smih, 993. (Noe In pracice, for a variey of reasons, purchasing power pariy for raded goods prices does no hold a all imes. However his PPP-based approach should offer a good descripion of real exchange rae movemens if PPP deviaions are small or shor-lived. In oher macroeconomic models all goods are radable bu domesic and foreign goods are no perfec subsiues and can have differen prices (e.g. Chari e al., 2002. In ha case real exchange rae movemens are caused by changes in he relaive price beween raded goods sold a home and abroad, which creae deviaions from purchasing power pariy for raded goods prices. This approach is appropriae if hose PPP deviaions are large relaive o changes in he relaive price beween raded and non-raded goods. Wha ype of model offers a beer descripion of real exchange rae movemens? Engel (999 offered an answer by calculaing which fracion of real exchange rae changes can be aribued o changes in he inernaional relaive price of raded goods and which fracion can be aribued o changes in each counry s domesic relaive price beween raded and non-raded goods. His mehodology consised in decomposing he real exchange rae (RER ino wo componens, as in equaion (, where S sands for he nominal exchange rae, P and P * sand for he overall consumer price level a home and abroad, respecively, and P T and P T* sand for he price of raded goods sold a home and abroad, respecively. RER T is he relaive price beween raded goods sold a home and hose sold abroad. I equals one when purchasing power pariy holds for raded goods prices. RER N is a funcion of he domesic relaive price beween raded and non-raded goods in each counry (Noe 2. S P S P P P RER = = RER RER ( * T* * T* T N T T P P P P By aking logarihms and differences in equaion ( we obain equaion (2. The variance of he changes in he 36
www.ccsene.org/ijef Inernaional Journal of Economics and Finance Vol. 7, No. 2; 205 real exchange rae depends on he variances of he wo componens and a covariance erm (equaion (3. If we allocae he covariance erm proporionally o he variance of each componen, he fracion of real exchange rae movemens caused by changes in he inernaional relaive price of raded goods, VD( rer T, is given by equaion (4, and he fracion caused by changes in he domesic relaive prices beween raded and non-raded goods, VD( rer N, is given by equaion (5. Δ rer =Δ rer +Δ rer (2 T N T N T N var( Δ rer = var( Δ rer + var( Δ rer + 2cov( Δrer, Δ rer (3 T T var( Δrer VD( Δ rer = T N var( Δ rer + var( Δrer (4 N N var( Δrer VD( Δ rer = T N (5 var( Δ rer + var( Δrer Engel (999 found ha, for he counries and periods he sudied, almos all of he changes in he real exchange rae are caused by changes in he inernaional relaive price of raded goods. (Noe 3 The fac ha in he shor run he nominal exchange rae is more volaile han prices could explain his resuls for shor-erm real exchange rae movemens. Bu he found ha his findings were also rue for long-erm changes of he real exchange rae. (Noe 4 Similar real exchange rae variance decomposiion sudies followed and confirmed ha changes in he inernaional relaive price of raded goods are he main driver of real exchange rae flucuaions (e.g. Chari e al., 2002. However some of hese sudies poined ou ha he choice of he price indices used o measure raded goods prices has a significan effec on he resuls (Bes and Kehoe, 2006; Bursein e al., 2006 and showed ha he domesic relaive price beween raded and non-raded goods also maers for real exchange rae movemens. While some auhors have used he consumer price index (CPI for goods or he producer price index (PPI as a proxy for raded goods prices, Bursein e al. (2006 sugges using impor and expor price indexes insead. Their argumen is ha he CPI for goods includes he cos of non-raded disribuion and reail services, while impor and expor price indexes measure prices a he dock. Moreover, hey measure he prices of goods acually raded raher han assuming ha all goods are radable and all services are non-radable. They find ha his approach increases he conribuion of he relaive price beween raded and non-raded goods o more han fify percen of he oal variance of real exchange rae movemens for some counries. Mendoza (2000; 2005 also provides evidence ha he relaive price beween raded and non-raded goods may be more imporan han wha Engel s resuls suggesed, a leas under cerain circumsances. He sudies he U.S. Mexico real exchange rae and finds ha he relaive price beween raded and non-raded goods is subsanially more imporan during he managed exchange rae period han during he floaing period. His findings suppor he view ha changes in he inernaional relaive price of raded goods are more imporan han changes in he relaive price of non-raded goods due o sicky prices and a very volaile nominal exchange rae. However sicky prices canno explain why Engel s resuls don change a long horizons, when prices become fully flexible. The objecive of his paper is o beer undersand he role of he relaive price beween raded and non-raded goods in real exchange rae flucuaions. The empirical sudies discussed above indicae ha, if measured properly, changes in ha relaive price may be an imporan driver of real exchange rae movemens. However hose sudies have lile o say abou how he characerisics of an economy affec heir relaive imporance vis-à-vis changes in he inernaional relaive price of raded goods. To ha end I develop a wo-counry dynamic sochasic general equilibrium (DSGE model and compare he overall real exchange rae volailiy and variance decomposiion under differen assumpions abou he economy. The DSGE model shows ha he ype of shock hiing he economy has a large influence on he relaive imporance of he wo real exchange rae componens. Moneary shocks are ransmied o he real exchange rae almos exclusively hrough changes in he inernaional relaive price of raded goods, while produciviy shocks are ransmied o he real exchange rae hrough boh channels. The effec of he characerisics of he economy on he level of real exchange rae volailiy and on he conribuion of he relaive price of non-raded goods also depends on he ype of shock. Therefore I conduc he analysis for each ype shock separaely. I firs sudy how real exchange rae dynamics are affeced by he level of inernaional inegraion, deermined in he model by he relaive weigh of he non-raded goods secor and he degree of preference for domesic raded goods. Since price sickiness is a common explanaion for he imporance of he inernaional relaive price of raded goods in he shor run, I also compare he properies of he real exchange rae under differen degrees of price sickiness. In addiion I sudy he effec of he degree of risk aversion on he overall level of real exchange rae volailiy and is variance 37
www.ccsene.org/ijef Inernaional Journal of Economics and Finance Vol. 7, No. 2; 205 decomposiion. Undersanding he role of he relaive price beween raded and non-raded goods in real exchange rae flucuaions is an imporan ask in macroeconomics. In fac, many sudies have inroduced non-raded goods ino heir models o beer undersand some empirical facs inconsisen wih one-good open economy models. For example, Backus and Smih (993 incorporae non-raded goods in a wo-counry model o sudy he small correlaion of consumpion across counries and he exisence of large ineres-rae differenials. Sockman and Tesar (995 sudy he role of non-raded goods in explaining he behavior of consumpion, invesmen, and he rade balance. Benigno and Thoenissen (2008 develop a model wih non-raded goods and incomplee markes o explain he lack of correlaion beween he real exchange rae and relaive consumpion across counries. Corsei e al. (2005 sudy Rogoff s PPP puzzle using a model in which produciviy shocks in he raded and non-raded secors are imperfecly correlaed. They show ha such a model is capable of maching he daa if he economy is characerized by eiher a very high degree of risk aversion or a very low elasiciy of subsiuion beween domesic and foreign raded goods. The paper proceeds as follows. Secion 2 presens he heoreical model. In Secion 3 he model is simulaed o sudy he behavior of he real exchange rae under differen assumpions. Secion 4 concludes. 2. Two-Counry DSGE Model This secion presens a small-scale wo-counry dynamic sochasic general equilibrium (DSGE model ha will be used o analyze he effecs of differen key feaures of an economy on he level of real exchange rae volailiy and he fracion of his volailiy explained by changes in he relaive price beween raded and non-raded goods. In he model each counry produces wo ypes of goods: raded and non-raded. Goods produced in he Home economy are denoed by H if hey are radable and by N if hey are non-radable. Tradable goods produced in he Foreign counry are denoed by F. Prices wih an aserisk are denominaed in Foreign currency. Quaniies wih an aserisk are consumed by he Foreign counry. For example, C F* denoes consumpion of Foreign good F by Foreign consumers, and P H* denoes he foreign-currency price a which Home good H is sold in he Foreign marke. Since he Foreign counry is a mirror image of he Home counry, only he laer is described in his secion. 2. Households There is a group of idenical households of mass one. They receive wages (W from perfecly compeiive wholesale firms and profis (PR from monopolisically compeiive reail firms. Each household supplies labor (L o boh secors (raded and non-raded. They have access o a complee se of inernaionally-raded coningen securiies ha pay one uni of domesic currency if a paricular sae z is realized in period. Their budge consrain given a hisory of saes z = (z 0,z,,z is described by (6, where C denoes consumpion, P is he price index for he consumpion baske, Q (z + z denoes he price in sae z of a securiy ha pays off if sae z + is realized, and D (z + z denoes he quaniy of such securiies held a he end of period. Households preferences over consumpion and labor are described by he uiliy funcion (7, where β is he subjecive discoun facor and prob(z is he probabiliy of hisory z. H H N N H N P( z C( z + { Q( z+ z D( z+ } = D ( z + W ( z L ( z + W ( z L ( z + PR ( z + PR ( z (6 0 z+ (7 U = β prob( z ( C ( z ( + ω L ( z ( + ω L ( z = 0 H + ω N + ω z Households maximize he uiliy funcion (7 subjec o he budge consrain (6. The firs order condiions wih respec o labor in each secor are given by equaions (8 and (9. ( ( H H ω W ( z P( z C ( z = L ( z (8 N N ω W ( z P( z C ( z = L ( z (9 The firs order condiions wih respec o consumpion and asse holdings imply equaion (0, where prob(z + z is he probabiliy of sae z + condiional on hisory z. Summing up across saes we can obain he convenional sochasic Euler equaion (. The gross reurn of a risk-less one-period nominal bond is deermined by (2. + + ( ( β prob( z z C ( z C ( z P ( z P ( z = Q ( z z (0 + + + + 38
www.ccsene.org/ijef Inernaional Journal of Economics and Finance Vol. 7, No. 2; 205 + + ( ( β ( + R( z prob( z z C ( z C( z P( z P ( z z + + + + = ( + R( z = Q( z+ z (2 z+ The foreign counerpars of equaions (0 and ( are equaions (3 and (4, where S is he nominal exchange rae. We can use (0 and (3 o obain he ypical risk-sharing condiion (5 ha links he real exchange rae o he relaive consumpion levels and a consan ξ ha depends upon iniial condiions. In addiion we can combine he Home and Foreign Euler equaions ( and (4 o obain he ineres pariy condiion linking he domesic and foreign ineres raes. ( * + * ( * * + ( + + + + ( + (( ( + + + * ( ( (( ( * ( ( / σ C z ξc z S z P z P z β prob( z z C ( z C ( z P ( z P ( z S ( z S ( z = Q ( z z (3 + + + + + * * * * * β ( + R ( z prob( z z C ( z C ( z P ( z S( z P ( z S ( z = z+ (4 = (5 2.2 Consumpion Baskes The consumpion baske in he Home counry includes non-raded goods (N and domesic (H and foreign (F raded goods. Consumers buy differen varieies of each good, which are sold by monopolisically compeiive reailers and indexed by i [0,]. Preferences over he varieies of good j=h,f,n are described by he consan-elasiciy-of-subsiuion (CES aggregaor (6, where ε is he elasiciy of subsiuion beween varieies. j j ( ε / ε C C di i ε/( ε = ( (6 0 Preferences beween baskes of Foreign and Home raded goods are described by equaion (7, where ς denoes he elasiciy of subsiuion beween Foreign and Home raded goods and κ measures he degree of preference bias owards domesic raded goods. Similarly, preferences beween baskes of non-raded and raded goods are described by equaion (8, where η denoes he elasiciy of subsiuion beween raded and non-raded goods and γ measures he degree of preference bias owards non-raded goods. C = κ( C + ( κ( C T H ( ς / ς F ( ς / ς ς/( ς ( η / η T ( η / η η/( η N C = γ( C + ( γ( C Price indexes for hese baskes of goods can be derived by calculaing heir uni cos. They are given by equaions (9, (20 and (2. j j ε P P di i /( ε (7 (8 = ( (9 0 T H ς F ς /( ς P = κ( P + ( κ( P (20 η T η /( η N P = γ( P + ( γ( P These preferences imply he following domesic demand funcions for each variey: ( ( ε i ( ς κ γ ( η ( κ( γ ( i ( ( N N N N Ci ( Pi P ε η γ ( P P C C = P P P P P P C (22 H H H H T T i F F F ε F T ς T η i C = P P P P P P C (23 (2 = (24 2.3 Producion Wholesale oupu for each good is produced by compeiive firms using labor as he only inpu. In he seady sae a fracion γ of household labor is he dedicaed o he producion of non-raded goods and he res o he producion of raded goods. The producion funcion in secor j is given by (25, where A denoes labor 39
www.ccsene.org/ijef Inernaional Journal of Economics and Finance Vol. 7, No. 2; 205 produciviy. j j j Y ( z = A ( z L( z (25 Monopolisically compeiive reail firms purchase oupu from wholesale firms, differeniae i, and sell i wih a mark-up. Reail prices are sicky as in Calvo (983. In any given period he probabiliy of a firm being able o adjus is price is -θ. Each period Home firms in he non-raded secor ha are able o adjus heir price will N choose P, ( z o maximize heir expeced discouned profis (26 subjec o he demand funcion (27. i ( ( ( ( + + N + + P ( z C ( z N W ( z + + + N + βθ prob z P i, z C N i, z + + = 0 + z P( z C( z A+ ( z (26 ε ( ( N + N N + N + + η + i, + γ i, + + + + C ( z = P ( z P ( z P ( z P ( z C ( z (27 N The opimal price Pi, ( z mus saisfy equaion (28. Since all firms in he same secor face a similar problem, N N i mus be ha Pi, ( z = P ( z for all i. The presence of many firms implies ha every period only a fracion -θ of firms will be able o adjus heir prices. This implies ha he evoluion of he price index for non-raded goods is given by (29. + + N + P ( z C ( z ε W ( z P( z C ( z ( ε A ( z + + + N + N + ( βθ prob( z Pi, ( z Ci, ( z 0 N + + = (28 = 0 + z + ε ( θ ( /( N N N ε ε ( = θ ( + ( ( P z P z P z The log-linearizaion of (28 and (29 implies a New Keynesian Phillips curve for non-raded goods. The pricing problem for firms producing a raded good is similar, bu in his case each firm chooses wo prices, one for he Home marke and one for he Foreign marke. Each price is se in he local currency of he marke where he good is sold. Home firms will separaely choose P and H i, H * i, (29 P o maximize (30 and (3, respecively. Following similar seps we can derive he New Keynesian Phillips curves for domesic raded goods a home and abroad. ( ( ( ( + + H + + P ( z C ( z H W ( z + + + H + βθ prob z P i, z C H i, z + + = 0 + z P( z C( z A+ ( z (30 ( ( ( ( ( + + H + + P ( z C ( z H* + W ( z + + + H* + βθ prob z P i, z S+ z C H i, z + + = 0 + z P( z C( z A+ ( z (3 Since prices are sicky in he currency of he counry where hey are sold, he law of one price may no hold for raded goods sold in boh counries. Local prices can immediaely fully adjus o changes in he nominal exchange rae. Tha incomplee exchange-rae pass-hrough implies ha exogenous shocks can creae deviaions from PPP for he baskes of raded goods sold in each counry. Deviaions from PPP can also arise even when he law of one price holds for individual goods if he baskes of raded goods a home and abroad are no idenical. 2.4 Moneary Policy The cenral bank chooses is policy insrumen, he one-period nominal ineres rae, based on he pas ineres rae, expeced fuure inflaion and he curren oupu gap. The cenral bank s policy rule is described by (32, where R is he seady-sae nominal ineres rae (equal o he naural real ineres rae plus he arge inflaion rae Π, and δ deermines he degree of ineres-rae ineria. Exogenous i.i.d. moneary shocks (v are inroduced as deviaions of he ineres rae from he cenral bank s arge rae. + R( z = δr ( z + ( δ R+ δπ prob( z z ( ( z δyy( z v( z z + Π + Π + + + (32 3. Model Simulaion 3. The Log-Linearized Model In order o simulae he model I firs log-linearize i around is seady sae. Percenage deviaions from he 40
www.ccsene.org/ijef Inernaional Journal of Economics and Finance Vol. 7, No. 2; 205 seady sae are denoed by lower-case leers. The Euler equaion, ineres-pariy and risk-sharing condiions are given by equaions (33, (34 and (35, respecively. ( π c = r E + Ec (33 + + EΔ rer = r Eπ ( r Eπ (34 * * + + + * c c σ rer = (35 The aggregae supply equaions for goods sold in he Home counry are given by equaions (36, (37 and (38, where he lambdas depend on he model s parameers, rpn is he relaive price beween non-raded and raded goods, and rer F is he raio beween he foreign price and he domesic price of he foreign raded good. N ( βθ( θ ( ( ( ( N N π = σ + ω c + ω γ rpn + ω a + β Eπ + θ (36 π = λ c + λ c + λ o λ o + λ rpn + λ rpn λ a + β E π + (37 H * * * H H A B C D E F G π = λ c + λ c + λ o λ o + λ rpn + λ rpn λ a + λ rer + β Eπ + (38 F * * * F F F A B C D E F G H The produciviy levels in each secor follow he auoregressive process (39, where χ j are secorial produciviy shocks ha may be correlaed across secors. a = ρ a + χ (39 j j j j Finally, he ineres-rae rule is given by equaion (40. r = δr + ( δ( δ Eπ + δ y + v (40 π + y 3.2 Parameerizaion The baseline parameer values used in he model are presened in Table. The share of non-raded goods in he overall consumpion baske is se o mach he sum of he shares of personal consumpion expendiures on services (43%, consrucion (9% and governmen spending (5% in he U.S. final domesic demand during he period 980-202. The share of home goods in he raded goods baske is chosen so ha he model s impors/gdp raio in he seady sae maches he share of foreign value added in he U.S. final domesic demand (2%, which is obained from he OECD s Trade in Value Added daabase. The res of parameers are sandard or wihin he usual range used in he inernaional macroeconomics lieraure. The parameers ha depend on frequency are chosen o mach quarerly frequency. The subjecive discoun facor is se a he convenional value of 0.99. The coefficien of relaive risk aversion is se o 2, which is wihin he rage found in he macroeconomics lieraure. The parameer ω is se o 2, which implies an elasiciy of labor supply equal o /2. As in Sockman and Tesar (995, he elasiciy of subsiuion beween raded and non-raded goods is 0.44. The elasiciy of subsiuion beween domesic and foreign raded goods is.5, as suggesed by Backus e al. (994. The probabiliy ha a firm is no able o adjus is price in a given quarer is 0.75, which implies ha, on average, firms change heir prices every four quarers. The moneary policy rule parameers are also wihin he range of commonly used values: 0.75 for he lagged ineres rae,.5 for deviaions of inflaion from is arge and 0.25 for he oupu gap. Table. Model parameers β Subjecive discoun facor 0.99 σ Coefficien of relaive risk aversion 2 ω Inverse of he elasiciy of labor supply 2 γ Share of non-raded goods in consumpion 0.67 κ Share of home goods in raded goods spending 0.64 η Elasiciy of subsiuion beween raded and non-raded goods 0.44 ς Elasiciy of subsiuion beween home and foreign raded goods.5 θ Calvo probabiliy of no price adjusmen 0.75 δ Ineres-rae smoohing 0.75 δ π Inflaion arge coefficien.5 δ y Oupu gap coefficien 0.25 4
www.ccsene.org/ijef Inernaional Journal of Economics and Finance Vol. 7, No. 2; 205 Esimaes of he variances, covariances and auocorrelaions of he secorial produciviy shocks are obained from Sockman and Tesar (995. They esimae hese parameers using daa from he Unied Saes and four oher OECD counries. The auocorrelaion coefficiens of he produciviy disurbances in he raded and non-raded goods secors are 0.54 and 0.632, respecively. Their esimaed correlaion is 46%. The variance-covariance marix for he produciviy shocks is given by (4. H χ 3.62.23.2 0.5 N.23.99 0.5 0.27 var χ = F χ.2 0.5 3.62.23 M χ 0.5 0.27.23.99 The moneary shocks are assumed o be uncorrelaed. Their sandard deviaion is se a % so ha he benchmark model s raio of real exchange rae volailiy o oupu volailiy equals hree, as in U.S. quarerly daa during he period 985-203. (Noe 5 The persisence of he moneary shocks is deermined by he persisence of he moneary policy rules. 3.3 Simulaion Resuls Table 2 shows some saisics for he benchmark model, which includes boh produciviy and moneary shocks, and for models in which only one ype of shock is included. While he benchmark model maches he volailiy of he real exchange rae relaive o oupu found in U.S. quarerly daa (2.98 vs. 3.06, he model exhibis less real exchange rae persisence (0.62 vs. 0.79. If only produciviy shocks were presen he level of real exchange rae volailiy (relaive o oupu would be lower han in he benchmark model, bu he real exchange rae would be much more persisen. By conras, moneary shocks alone would generae more real exchange rae volailiy, bu wih less persisence. In all models, despie he exisence of complee financial markes allowing risk-sharing across counries, domesic consumpion is highly correlaed wih domesic oupu. Tha is consisen wih he oupu-consumpion correlaions calculaed by Sockman and Tesar (995 for several OECD economies, which range from 0.82 o 0.95. Foreign and domesic consumpion are correlaed (alhough no much in he model wih only produciviy shocks. However hey are uncorrelaed when moneary shocks are included. Tha is a odds wih he daa. Sockman and Tesar find cross-counry consumpion correlaions ranging from 0.35 o 0.7. This discrepancy may be caused by he fac ha he only demand shock in he model is a moneary shock, which is assumed o be independen across counries. (4 Table 2. Model saisics Benchmark Model Produciviy Shocks Moneary Shocks Sd. Dev. (rer / Sd. Dev. (y 2.98.9 3.40 Auocorrelaion (rer 0.62 0.9 0.57 Correlaion (y,c 95% 9% 98% Correlaion (c,c* % 29% -6% RER Variance Decomposiion, VD(Δrer T VD(Δrer N 90%-0% 3%-69% 00%-0% RER Variance Decomposiion, VD(rer T VD(rer N 67%-33% 23%-77% 98%-2% The second o las row of Table 2 indicaes he fracion of real exchange rae quarerly movemens explained by changes in he inernaional relaive price of raded goods and he fracion explained by changes in he domesic relaive prices beween raded and non-raded goods in each counry. These are he saisics described earlier in equaions (4 and (5, and correspond o he ypical real exchange rae variance decomposiion calculaed in empirical sudies. Chari e al. (2002 find ha changes in he inernaional relaive price of raded goods explain 98% of U.S. real exchange rae quarerly movemens. Engel (999 finds similar resuls for monhly daa. Bursein a al. (2006 use a differen mehodology and reduce ha esimae o 39%. In he benchmark model changes in he inernaional relaive price of raded goods explain 90% of real exchange rae quarerly movemens (Noe 6. The las row provides he fracion of real exchange rae deviaions from is seady sae explained by deviaions from purchasing power pariy for raded goods prices (which holds in he model s seady sae and he fracion explained by deviaions of he domesic relaive prices beween raded and non-raded goods from heir respecive seady-sae values. Alhough relaed, here is an imporan difference beween he wo real exchange 42
www.ccsene.org/ijef Inernaional Journal of Economics and Finance Vol. 7, No. 2; 205 rae variance decomposiion measures repored in Table 2. The firs one describes he reasons behind real exchange rae movemens, while he second one indicaes he reasons for is persisence away from is seady-sae value. In he benchmark model here is a significan difference beween he wo measures: while movemens in he inernaional relaive price of raded goods cause 90% of he quarerly changes of he real exchange rae, many of hese movemens offse each oher, so ha deviaions from purchasing power pariy for raded goods prices explain only wo hirds of he deviaions of he real exchange rae from is long-run rend. The variance decomposiion of he real exchange rae (boh for quarerly changes and for seady-sae deviaions significanly depends on he ype of shocks affecing he economy. In he case of moneary shocks pracically all real exchange rae movemens are he resul of changes in he inernaional relaive prices of raded goods. In he case of produciviy shocks mos of he real exchange rae changes are explained by changes in he relaive price beween raded and non-raded goods, bu changes in he inernaional relaive price of raded goods are also imporan. Those differences beween shocks are also eviden in he impulse-response funcions in Figure. They show he responses of he real exchange rae (solid line, rer N (shor dash and rer T (long dash o one-sandard-deviaion-sized shocks over he following welve quarers. (Noe 7 Figure (d shows ha a moneary shock (defined as an exogenous increase in he domesic ineres rae appreciaes he real exchange rae. (Noe 8 Since he ineres-rae differenial causes a sharp appreciaion of he nominal exchange rae, he real appreciaion is almos exclusively explained by domesic raded goods becoming more expensive han foreign raded goods. The impac on he relaive price beween raded and non-raded goods is relaively small. As a resul, changes in rer T explain abou 00% of changes in he real exchange rae caused by moneary shocks, as shown in Table 2. 0.4% 0.03% 0.3% 0.2% 0.% 0.02% 0.0% 0.00% -0.0% 0.0% -0.% -0.2% -0.02% -0.03% -0.04% -0.05% -0.3% 2 4 6 8 0 2-0.06% 2 4 6 8 0 2 (a Non-Traded Secor Produciviy Shock (b Traded Secor Produciviy Shock 0.3% 2% 0.2% 0% 0.% -2% 0.0% -4% -0.% -6% -0.2% -8% -0.3% 2 4 6 8 0 2-0% 2 4 6 8 0 2 (c Economy-wide Produciviy Shock (d Moneary Shock Figure. Impulse-response funcions of he real exchange rae and is componens 43
www.ccsene.org/ijef Inernaional Journal of Economics and Finance Vol. 7, No. 2; 205 Secor-specific produciviy shocks reduce he price of he good produced by ha secor. They also creae an ineres-rae differenial, bu in his case i is caused by he response of he cenral banks o economic condiions. Figures (a and (b show ha a produciviy shock s impac on he real exchange rae and is componens varies dramaically by secor. A produciviy shock in he non-raded secor reduces he absolue and relaive price of non-raded goods, which depreciaes rer N. The nominal appreciaion makes domesic raded goods more expensive relaive o foreign raded goods. Since mos raded goods sold a home are domesic, ha causes a shor-erm deviaion from purchasing power pariy for raded goods prices (rer T appreciaes. Even hough raded goods become more expensive a home han abroad, he fall in he price of non-raded goods causes he real exchange rae o depreciae. By conras, a produciviy shock in he raded goods secor causes a real appreciaion, alhough relaively small. This may be surprising, since he produciviy shock makes domesic raded goods cheaper. However he increase in oupu makes he cenral bank increase he domesic ineres rae. The resuling nominal appreciaion more han offses he effec of lower prices for domesic raded goods on he overall price level. I s imporan o noice ha in he previous case here is also a nominal appreciaion. In ha case he real exchange rae depreciaes because non-raded goods prices have a larger weigh on he overall price index. Produciviy shocks in he raded goods secor also cause diverging responses of he wo real exchange rae componens, bu in he opposie direcion. Due o home bias (κ > 0.5, he fall in domesic raded goods prices has a bigger impac on he domesic raded goods baske han on he foreign raded goods baske. As a resul rer T depreciaes. Since domesic raded goods prices fall and he nominal appreciaion makes impors cheaper, non-raded goods become relaively more expensive han raded goods and rer N appreciaes. Figure (c shows ha, when produciviy shocks affec boh secors equally, he responses of he real exchange rae and is componens are more similar o hose corresponding o shocks o he non-raded goods secor han o hose corresponding o shocks o he raded goods secor. The reason is ha non-raded goods represen a larger fracion of GDP han raded goods (γ = 0.67. To beer undersand he role of non-raded goods in real exchange rae flucuaions, I simulae he model under differen assumpions abou he characerisics of he economy. In each case I calculae he volailiy of he real exchange rae (relaive o oupu and is variance decomposiion. Since Table 2 indicaes ha he role of non-raded goods depends on he ype of shock, hese simulaions are made separaely for produciviy shocks (Figure 2 and for moneary shocks (Figure 3. The solid line corresponds o real exchange rae volailiy (righ scale, and he oher wo lines correspond o he fracion of real exchange rae movemens explained by changes in he relaive price beween raded and non-raded goods, boh for percenage deviaions from is seady sae (VD(rer N, shor dash, lef scale and is quarerly changes (VD( rer N, long dash, lef scale. 3.4 Real Exchange Volailiy and he Role of Non-Traded Goods in he Case of Produciviy Shocks The fracion of non-raded goods in he consumpion baske (γ affecs he degree of openness in an economy (expors and impors over GDP and he correlaion beween is domesic oupu and is domesic consumpion. Figure 2(a shows ha, as he fracion of non-raded goods increases, he real exchange rae becomes more volaile. Oher hings equal, produciviy shocks generae four imes more real exchange rae volailiy in an economy where 90% of is consumpion is made of non-raded goods han in one in which non-raded goods represen only 0%. As discussed in he previous secion, produciviy shocks in he non-raded secor cause more real exchange rae volailiy han shocks in he raded secor. Therefore an increase in he weigh of he non-raded goods secor will cause an increase in he volailiy of he real exchange rae. This increase in overall real exchange rae volailiy can be aribued o a significan increase in he volailiy of rer N. The volailiy of rer T also increases, bu no as much. As a resul, he fracion of real exchange rae movemens caused by changes in he relaive price of non-raded goods increases dramaically, from as lile as 6% o as much as 72%. The large effec of γ on rer N can be explained by equaion (42, which links he variance of he relaive price of non-raded goods o ha of he real exchange rae. A higher fracion of non-raded goods does no significanly increase he volailiy of he relaive price of non-raded goods. However, i significanly increases he effec ha changes in he relaive price of non-raded goods have on he real exchange rae. For example, holding he price of raded goods consan, a % increase in he price of domesic non-raded goods will increase he relaive price of non-raded goods by % regardless of he weigh on non-raded goods in he economy. Bu as ha weigh increases he effec on he overall domesic price level will be larger, causing a larger difference beween he domesic and foreign price levels. 2 var( rer N = γ var( p N p T (42 The weigh of domesic goods in he baske of raded goods (κ is anoher facor deermining he degree of 44
www.ccsene.org/ijef Inernaional Journal of Economics and Finance Vol. 7, No. 2; 205 openness in he economy. A value of κ above 0.5 represens a preference bias oward he counry s own goods. (Noe 9 Figure 2(b shows ha an increase he degree of home bias has a non-monoonic, U-shaped effec on he volailiy of he real exchange rae, bu i has a sricly increasing effec for he more relevan range in which he economy consumes more domesic raded goods han foreign raded goods (κ > 0.5. This implies ha produciviy shocks generae more real exchange rae volailiy in economies ha don rade a lo wih each oher and have very differen consumpion baskes of radable goods han in more inerdependen economies. This resul canno be aribued o eiher componen of he real exchange rae. A closer look reveals ha he volailiy of boh componens acually falls as home bias rises, bu he overall variance of he real exchange rae increases because heir covariance becomes less negaive. We know from Figure (b ha in response o a posiive produciviy shock in he domesic raded goods secor he nominal exchange rae appreciaes and creaes a deviaion from PPP for raded goods prices. Tha PPP deviaion is parially offse by he fall in he price of he raded goods baske a home (P T. As home bias increases, a change in he price of domesic raded goods (P H has a larger impac on he price of raded goods a home (P T, and ha diminishes he response of rer T o hose produciviy shocks. Produciviy shocks in boh secors are posiively correlaed. When boh P N and P H rise, he effec on P N /P T is smaller if κ is larger and P H has a larger impac on P T. Tha conribues o reducing he volailiy of rer N. Figure 2(b shows ha, in general, as κ increases he variance of rer T falls faser han he variance of rer N. This implies ha in less open economies a larger fracion of real exchange rae movemens are caused by changes in he relaive price of non-raded goods. 2.50 80% 2.3 RER Variance Decomposiion 70% 2.25 2.00 60%.75 50%.50 40%.25 30%.00 0.75 20% 0.50 0. 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 RER Volailiy RER Variance Decomposiion 76% 2.2 72% 2. 68% 2.0 64%.9 60%.8 0. 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 RER Volailiy (a Seady-Sae Fracion of Non-Traded Goods (b Home Bias for Traded Goods RER Variance Decomposiion 75% 70% 65% 60% 55%.95.90.85.80.75.70.65 0.3 0.4 0.5 0.6 0.7 0.8 0.9 RER Volailiy RER Variance Decomposiion 80% 3.2 2.8 76% 2.4 72% 2.0 68%.6.2 64% 0.8 2 3 4 5 RER Volailiy (c Price Sickiness (d Coefficien of Relaive Risk Aversion 2.3 RER Variance Decomposiion 2.2 76% 2. 74% 2.0 72%.9.8 70%.7.6 0.0 0. 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 RER Volailiy (e Correlaion Bew een Traded and Non-Traded Secor Shocks Figure 2. Real exchange rae volailiy and variance decomposiion (produciviy shocks 45
www.ccsene.org/ijef Inernaional Journal of Economics and Finance Vol. 7, No. 2; 205 Price sickiness (measured by θ refers o he frequency wih which firms change heir prices o adjus o curren and expeced economic condiions. As firms keep prices unchanged for longer periods he effec of produciviy shocks on prices becomes smaller. Tha reduces he response of he relaive price beween raded and non-raded goods bu also ha of he relaive price beween domesic and foreign raded goods. A low levels of price sickiness he volailiy of rer T falls faser and rer N gains imporance, bu he opposie happens a high levels of price sickiness, creaing he invered U-shaped variance decomposiions in Figure 2(c. Price sickiness also reduces he overall volailiy of he real exchange rae. Bu since price sickiness reduces he effec of supply shocks on oupu, he volailiy of he real exchange rae relaive o oupu does no decrease monoonically. I remains more or less unchanged for low degrees of price sickiness and i falls very rapidly when prices adjus very infrequenly. I is well-known ha he coefficien of relaive risk-aversion (σ has a significan effec on he overall volailiy of he real exchange rae (Chari e al., 2002; Corsei e al., 2005. The coefficien of relaive risk aversion is equal o he inverse of he elasiciy of iner-emporal subsiuion, and i links he volailiy of he real exchange rae o ha of he domesic-foreign consumpion raio. This is clear by aking he sandard deviaion on boh sides of equaion (35, which resuls in equaion (43. In he case of produciviy shocks, when he coefficien of relaive risk-aversion rises from one o five he volailiy of he real exchange rae relaive o oupu rises from.2 o 3.2. Boh he volailiy of rer T and rer N increase, bu he effec on rer N is sronger. * sd( c c = σ sdrer ( (43 The las parameer examined is he correlaion beween produciviy shocks in he raded goods secor and produciviy shocks in he non-raded goods secor. In he benchmark model his correlaion is 46%, as esimaed by Sockman and Tesar (995. When produciviy shocks are secor-specific and no perfecly correlaed, hey change he cos of non-raded goods relaive o domesically-produced raded goods, adding an addiional source of movemens in he relaive price beween raded and non-raded goods. Figure 2(e shows ha when he cross-secor correlaion decreases from 90% o 0%, he volailiy of he real exchange rae relaive o oupu rises from.7 o 2.3. However, he relaive imporance of changes in he relaive price beween raded and non-raded goods only increases by 2%, from 68% o 70%, since he volailiy of movemens in he inernaional relaive price of raded goods also rises. 3.5 Real Exchange Volailiy and he Role of Non-Traded Goods in he Case of Moneary Shocks 3.5% 5.2 2.0% 4.0 RER Variance Decomposiion 3.0% 2.5% 2.0%.5%.0% 0.5% 4.8 4.4 4.0 3.6 3.2 2.8 RER Volailiy RER Variance Decomposiion.6%.2% 0.8% 0.4% 3.8 3.6 3.4 3.2 RER Volailiy 0.0% 2.4 0. 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.0% 3.0 0. 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 (a Seady-Sae Fracion of Non-Traded Goods (b Home Bias for Traded Goods 8% 3.500 8% 9 RER Variance Decomposiion 7% 6% 5% 4% 3% 2% % 3.475 3.450 3.425 3.400 3.375 3.350 3.325 RER Volailiy RER Variance Decomposiion 7% 6% 5% 4% 3% 2% % 8 7 6 5 4 3 2 RER Volailiy 0% 3.300 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0% 2 3 4 5 (c Price Sickiness (d Coefficien of Relalive Risk Aversion Figure 3. Real exchange rae volailiy and variance decomposiion (moneary shocks 46
www.ccsene.org/ijef Inernaional Journal of Economics and Finance Vol. 7, No. 2; 205 Figure 3 shows he effec of cerain model parameers on he level of real exchange rae volailiy relaive o oupu and on he wo ypes of real exchange rae variance decomposiions when he model is exclusively driven by moneary shocks. In his case, since moneary shocks do no have a direc impac on he relaive price of non-raded goods, movemens in ha relaive price only explain a very small fracion of overall real exchange rae movemens. Thus he effec of he model parameers on overall real exchange volailiy mainly depends on he effec ha hose parameers have on he inernaional relaive price of raded goods. Unlike in he case of produciviy shocks, moneary shocks have a smaller impac on real exchange rae flucuaions when he non-raded secor represens a larger fracion of he economy (Figure 3(a. When he weigh of non-raded goods rises from 0% o 90% of he economy, he volailiy of he real exchange rae caused by moneary shocks falls from 4.4 o 3 imes he volailiy of oupu. An exogenous ineres rae increase appreciaes he nominal exchange rae and creaes deviaions from PPP for raded goods prices. The ineres rae increase also curbs domesic consumpion and reduces prices of goods consumed a home, which parially offses he nominal appreciaion. If non-raded goods represen a larger fracion of he consumpion baske hen he fall in he home price level is larger, and deviaions from PPP are more moderae. Tha also conribues o increase he relaive imporance of movemens in he relaive price of non-raded goods, alhough moderaely. When he economy becomes less open due o an increase in home bias (κ, he volailiy of he real exchange rae also falls, for similar reasons. As he weigh of domesically-produced raded goods rises from 0% o 90% of he raded goods baske, he volailiy of he real exchange rae falls from 3.9 o 3 imes he volailiy of oupu. However, unlike wih changes in γ, he variance decomposiions exhibi an invered-u shape cenered a κ = 0.5 because home bias has a non-monoonic effec on he volailiy of rer N. An increase in price sickiness (θ reduces he effec of moneary shocks on he volailiy of he real exchange rae. This may appear o be a odds wih Dornbusch s (976 overshooing effec, in which sicky prices magnify he response of he nominal and real exchange raes o moneary shocks. The difference is due o he alernaive (bu equivalen ways of inroducing moneary shocks in he model. In Dornbusch s model moneary shocks consis of changes in he money supply. If prices are sicky, changes in he money supply ranslae ino changes in he ineres rae. The sickier prices are, he higher is he response of he ineres rae and he nominal exchange rae. However in his model moneary shocks are direcly inroduced as exogenous changes in he ineres rae. A higher degree of price sickiness does no affec he size of he exogenous ineres rae change. Bu he addiional price sickiness reduces he response of prices o moneary shocks. The increase in price sickiness reduces he volailiy of rer N (which depends only on prices faser han ha of rer T (which depends on prices bu also on he more flexible nominal exchange rae. Therefore as prices become sickier he relaive imporance of rer N falls. As in he case of produciviy shocks, a higher degree of risk aversion increases he volailiy of he real exchange rae. In his case, when he coefficien of relaive risk-aversion rises from one o five he volailiy of he real exchange rae relaive o oupu rises from.7 o 8.4. However in his case he increase in real exchange rae volailiy is primarily due o an increase in he volailiy of rer T. 4. Summary and Conclusions This paper uses a wo-counry DSGE model o sudy how differen characerisics of he economy affec he volailiy of real exchange rae flucuaions and he fracion of hose flucuaions ha are caused by movemens in he relaive price of non-raded goods. The model shows ha produciviy shocks, wheher secor-specific or economy-wide, cause real exchange rae movemens mainly by changing he relaive price beween raded and non-raded goods. They also creae significan deviaions from purchasing power pariy for raded goods prices. By conras, moneary shocks are ransmied o he real exchange rae almos exclusively hrough changes in he inernaional relaive price of raded goods. This has imporan implicaions for economic modeling. A model mean o sudy he effecs of produciviy shocks on he real exchange rae canno assume ha all goods are radable, since ha would ignore a major channel hrough which produciviy shocks affec he real exchange rae. On he oher hand, he omission of non-raded goods in a model driven by moneary shocks may be less significan. The model s impulse-response funcions show ha he response of he real exchange rae o produciviy shocks depends on how he shock affecs he relaive price of non-raded goods. A posiive produciviy shock in he non-raded goods secor reduces he relaive price of non-raded goods and causes a real depreciaion, while a shock in he raded good secor raises he relaive price of non-raded goods and causes a real appreciaion. Produciviy shocks also cause deviaions from PPP for raded goods prices, bu hey can only parially offse he effec of he relaive price of non-raded goods on he real exchange rae. In he case of moneary shocks he 47
www.ccsene.org/ijef Inernaional Journal of Economics and Finance Vol. 7, No. 2; 205 change in he real exchange rae depends on wheher raded goods become more or less expensive a home han abroad. The change in he relaive price of non-raded goods is quaniaively much less imporan. The resuls from he model s simulaion under differen assumpions indicae ha wheher openness and global inerdependence conribue o increase or decrease he volailiy of he real exchange rae depends on he ype of shock. In more open economies he real exchange rae exhibis smaller swings in response o produciviy shocks bu larger movemens in response o moneary shocks. The reason is ha, in general, as wo economies become more inegraed, he relaive price of non-raded goods loses relaive imporance as he driver of real exchange rae flucuaions. Since moneary shocks are ransmied almos exclusively hrough PPP deviaions for raded goods prices, hey generae more volailiy as ha componen gains relaive imporance. A higher degree of price sickiness moderaes he response of he real exchange rae o boh ypes of shocks, as prices of raded and non-raded goods change more slowly. In he case of moneary shocks i also reduces he relaive imporance of he relaive price of non-raded goods. In he case of produciviy shocks he effec on he variance decomposiions is no monoonic. The real exchange rae is more volaile when counries exhibi a high degree of risk aversion. In he case of produciviy shocks ha increase in volailiy is mosly aribued o movemens in he relaive price of non-raded goods. Bu in he case of moneary shocks i s aribued o deviaions from PPP for raded goods prices. Produciviy shocks generae changes in he relaive price beween raded and non-raded goods even when hey are no secor-specific. Bu a higher degree of correlaion beween secorial shocks reduces hose movemens and causes a reducion in he volailiy of he real exchange rae. One ineresing observaion is ha, since he wo componens of he real exchange rae are negaively correlaed, i s possible ha a facor ha reduces he volailiy of one or boh componens of he real exchange rae may acually conribue o increase he overall volailiy of he real exchange rae. Tha s he case wih an increase home bias: produciviy shocks generae fewer movemens in he relaive price of non-raded goods and fewer PPP deviaions for raded goods prices, ye he real exchange rae becomes more volaile because changes in he laer now offse fewer movemens of he former. Overall he sudy shows ha real exchange rae variance decomposiions are highly sensiive o he ype of shock hiing he economy. Tha is imporan because empirical sudies in which PPP deviaions for raded goods prices seem o dominae real exchange rae movemens may be inerpreed as implying ha changes in he relaive price of non-raded goods are no imporan, even if hey are very imporan for he ransmission of produciviy shocks. The level of real exchange rae volailiy and is variance decomposiion also depend on he characerisics of he economy. Bu wheher hose facors increase or reduce ha volailiy and he conribuion of changes in he relaive price of non-raded goods ofen depends on wha ype of shock is more prevalen. References Backus, D., Kehoe, P., & Kydland, F. (994. Dynamics of he Trade Balance and he Terms of Trade: The J-Curve? American Economic Review, 84(, 84 03. Backus, D., & Smih, G. (993. Consumpion and Real Exchange Raes in Dynamic Economies wih Non-Traded Goods. Journal of Inernaional Economics, 35(3 4, 297 36. hp://dx.doi.org/0.06/0022-996(939002-o Balassa, B. (964. The Purchasing Power Pariy Docrine: A Reappraisal. Journal of Poliical Economy, 72(6, 584 596. hp://dx.doi.org/0.086/258965 Benigno, G., & Thoenissen, C. (2008, Consumpion and Real Exchange Raes wih Incomplee Markes and Non-raded Goods. Journal of Inernaional Money and Finance, 27(6, 926 948. hp://dx.doi.org/0.06/j.jimonfin.2008.04.008 Bes, C., & Kehoe, T. (2006. U.S. Real Exchange Rae Flucuaions and Relaive Price Flucuaions. Journal of Moneary Economics, 53(7, 297 326. hp://dx.doi.org/0.06/j.jmoneco.2005.05.0 Bursein, A., Eichenbaum, M., & Rebelo, S. (2006. The Imporance of Nonradeable Goods Prices in Cyclical Real Exchange Rae Flucuaions. Japan and he World Economy, 8(3, 247 253. hp://dx.doi.org/0.06/j.japwor.2006.02.003 Calvo, G. (983. Saggered Prices in a Uiliy Maximizing Framework. Journal of Moneary Economics, 2(3, 383 398. hp://dx.doi.org/0.06/0304-3932(8390060-0 48
www.ccsene.org/ijef Inernaional Journal of Economics and Finance Vol. 7, No. 2; 205 Chari, V., Kehoe, P., & McGraan, E. (2002. Can Sicky Price Models Generae Volaile and Persisen Real Exchange Raes? Review of Economic Sudies, 69(3, 533 563. hp://dx.doi.org/0./467-937x.0026 Corsei, G., Dedola, L., & Leduc, S. (2005. DGSE Models of High Exchange-Rae Volailiy and Low Pass-Through. FRB Inernaional Finance Discussion Papers, 845. Dornbusch, R. (976. Expecaions and Exchange Rae Dynamics. Journal of Poliical Economy, 84(6, 6 76. hp://dx.doi.org/0.086/260506 Engel, C. (999. Accouning for U.S. Real Exchange Rae Changes. Journal of Poliical Economy, 07(3, 507 538. hp://dx.doi.org/0.086/250070 Mendoza, E. (2000. On he Insabiliy of Variance Decomposiions of he Real Exchange Rae across Exchange Rae Regimes: Evidence from Mexico and he Unied Saes. NBER Working Paper 7768. hp://dx.doi.org/0.3386/w7768 Mendoza, E. (2005. Real Exchange Rae Volailiy and he Price of Nonradeable Goods in Economies Prone o Sudden Sops. Economia, 6(, 03 48. hp://dx.doi.org/0.353/eco.2006.0008 Rogoff, K. (996. The Purchasing Power Pariy Puzzle. Journal of Economic Lieraure, 34(2, 647 668. Samuelson, P. (664. Theoreical Noes on Trade Problems. Review of Economics and Saisics, 46(2, 45 54. hp://dx.doi.org/0.2307/92878 Sockman, A., & Tesar, L. (995. Tases and Technology in a Two-Counry Model of he Business Cycle: Explaining Inernaional Comovemens. American Economic Review, 85(, 68 85. Noes Noe. This approach is used o explain he well-known relaionship beween produciviy and real exchange rae raes known as he Balassa-Samuelson effec (Balassa (964, Samuelson (964. Noe 2. For example, assuming ha he overall price index is a geomeric average of he price indices for boh ypes of goods, P = (P T (-γ (P N γ, hen P/P T = (P N /P T γ, where P N /P T is he domesic relaive price beween raded and non-raded goods and γ is he weigh of non-raded goods in he overall price index. Noe 3. Engel (999 used he mean square error raher han he variance o ake ino accoun he rend. Noe 4. Among he counries ha he sudied he only excepion was he U.S.-Canada exchange rae, for which he relaive price of non-raded goods gained imporance a longer horizons. Noe 5. The daa used o calculae ha raio is in logarihms and derended wih he Hodrick-Presco filer. The measure of real exchange rae used corresponds o he broad real effecive real exchange rae provided by he Federal Reserve. Noe 6. The variance decomposiion resuls from obained from a log-linearized DSGE model are more direcly comparable o resuls obained using derended daa, bu he empirical sudies menioned in he ex do no derend he real exchange rae. One excepion is Bes and Kehoe (2006, bu hey only use derended daa o compue he variance decomposiion in he case of annual deviaions, no quarerly changes. Noe 7. The hree models discussed earlier in his secion do no include economy-wide, unbiased produciviy shocks. The properies of he economy-wide produciviy shock used in he impulse-response funcions are consruced using weighed averages of he properies of he secor-specific produciviy shocks. Noe 8. Recall ha he real exchange rae is defined as he cos of foreign goods in erms of domesic goods. Therefore a rise in he real exchange rae represens a depreciaion and a fall represens an appreciaion. Noe 9. Home bias creaes an addiional source of deviaions from purchasing power pariy for raded goods prices. Even if he law of one price is saisfied, meaning ha goods produced in a counry cos he same a home and abroad (P H = S P H* and P F = S P F*, under home bias differences beween he prices of goods produced a home and abroad (P H P F cause differences in he prices of he baskes of raded goods consumed in he Home and Foreign economies (P T P T*. However his addiional source of volailiy is no quaniaively significan in his case. 49