Business Cycles in Small Developed Economies: The Role of Terms of Trade and Foreign Interest Rate Shocks

WP/8/86 Business Cycles in Small Developed Economies: The Role of Terms of Trade and Foreign Ineres Rae Shocks Jaime Guajardo

28 Inernaional Moneary Fund WP/8/86 IMF Working Paper IMF Insiue Business Cycles in Small Developed Economies: The Role of Terms of Trade and Foreign Ineres Rae Shocks Prepared by Jaime Guajardo 1 Auhorized for disribuion by Enrica Deragiache April 28 Absrac This Working Paper should no be repored as represening he views of he IMF. The views expressed in his Working Paper are hose of he auhor(s) and do no necessarily represen hose of he IMF or IMF policy. Working Papers describe research in progress by he auhor(s) and are published o elici commens and o furher debae. Empirical evidence for small developed economies finds ha consumpion is procyclical and as volaile as oupu, and real ne expors are counercyclical. Earlier sudies have no been able o reproduce hese regulariies in a DSGE small open economy model when produciviy shocks drive he business cycles and households have a normal ineremporal elasiciy of subsiuion. Insead, hese sudies have reduced his elasiciy o make consumpion more procyclical and volaile and real ne expors counercyclical. This paper shows ha a sandard model can reproduce hese regulariies, wihou lowering he ineremporal subsiuion, if he erms of rade and foreign ineres rae are added as source of business cycle flucuaions. These shocks, compared o produciviy shocks, make consumpion and invesmen more volaile and procyclical relaive o oupu, and make real ne expors counercyclical. JEL Classificaion Numbers: E21, E32, F32, F41 and N12 Keywords: Small Open Economy Model, Terms of Trade, Foreign Ineres Rae, Consumpion, Ne Expors, and Ineremporal Elasiciy of Subsiuion Auhor s E-Mail Address: jguajardo@imf.org 1 I am graeful for useful commens received from Harold L. Cole from he Deparmen of Economics in UCLA and from he paricipans a he IMF Insiue inernal seminar in November 25.

2 Conens Page I. Inroducion...3 II. Empirical Regulariies...4 III. Lieraure Review...4 IV. The Model...6 A. Households...7 B. Firms...8 C. Definiion of a Compeiive Equilibrium...9 V. Seady Sae and Calibraion...9 A. Shock Processes...1 VI. Simulaions and Impulse Responses...1 A. Impulse - Responses...11 B. Simulaions...12 VII. Conclusions...14 References...15 Tables 1. Business Cycles Indicaors for Developed Economies, Annual Daa, 198 23...16 2. Business Cycles Indicaors for Developed Economies, Quarerly Daa, 198 23...17 3. Calibraed Parameers and Macroeconomic Raios...18 4. Shocks Processes...19 5. Daa Momens, Sandard and Benchmark Model Simulaions...2 6. Model Simulaions, Differen Measures of R*...21 7. Model Simulaions, Differen Ineremporal Elasiciies of Subsiuion...22 Figure 1. Impulse - Response Funcions...23

3 I. INTRODUCTION Since Backus and ohers (1992), several aricles have sudied he business cycles regulariies in small developed economies (SDEs) in he poswar period. They find ha oupu volailiy is he same as in he large developed economies; privae consumpion is procyclical and as volaile as oupu; invesmen is procyclical and abou hree imes as volaile as oupu; and real ne expors are counercyclical. These regulariies conras wih he resuls from a dynamic sochasic general equilibrium (DSGE) small open economy model, when produciviy shocks drive he business cycles and households have a normal ineremporal elasiciy of subsiuion (IES). In hese models consumpion is less volaile han oupu and real ne expors are procyclical. Previous sudies, Mendoza (1991, 1995), Correia and ohers (1995) and Raffo (26), use a low IES or GHH preferences (Greenwood and ohers, 1988), in which he ineremporal subsiuion of leisure is zero. Wih GHH preferences, labor supply depends only on wages and no on consumpion. Thus, produciviy shocks creae more volaile and procyclical hours of work and consumpion, and counercyclical real nex expors. This paper shows ha a DSGE small open economy model, wih a normal IES, can replicae he regulariies menioned above if he erms of rade and he foreign ineres rae shocks are added as source of business cycle flucuaions. Compared o produiviy shocks, hese wo shocks increase he volailiy of consumpion and invesmen relaive o oupu, and produce counercyclical real ne expors. Furhermore, hey reinforce each oher as heir innovaions are negaively cross-correlaed in he daa. The erms of rade shocks produce smaller changes in oupu han similar produciviy shocks, bu larger procyclical flucuaions in consumpion and invesmen, and counercyclical, insead of procyclical, changes in real ne expors. The foreign ineres rae shocks also produce small changes in oupu, bu affec he ineremporal price of consumpion and invesmen, making boh more volaile and procyclical, and making real ne expors counercyclical. This sudy uses a wo secor model, he expor one and he nonradable one. Domesic firms produce boh goods using labor and capial inpus. Households have sandard preferences, consume he nonradable good, buy he imporable good for consumpion and invesmen, and supply labor and capial o he firms. There are four shocks: Produciviy in he expor and nonradable secors, he erms of rade and he foreign ineres rae. The model is calibraed for Canada, which is also he case sudy in Mendoza (1991) and Raffo (26). The simulaions show ha when all four shocks are considered, he model is able o replicae he regulariies of Canada's business cycles for values of he IES beween ½ and ¼, in he normal range defined by Mehra and Presco (1985). I capures he volailiies and correlaions wih oupu of consumpion, invesmen, real ne expors, and hours of work. Bu when business cycles are driven only by produciviy shocks, he model predics an excessive consumpion smoohing and procyclical real ne expors for he same preferences and IES.

4 The paper is organized as follows: Secion 2 documens he SDEs business cycle regulariies. Secion 3 discusses he relaed lieraure. Secion 4 presens he model. Secion 5 presens he calibraion and shocks' processes. Secion 6 shows he impulse responses and simulaions comparing he momens from he model wih hose of he daa. Secion 6 concludes. II. EMPIRICAL REGULARITIES The firs sudy of he SDEs business cycles regulariies in he poswar period is Backus and ohers (1992). For annual daa beween 195 and 1985, hey find ha oupu is as volaile as in he large developed economies; privae consumpion is procyclical and as volaile as oupu; fixed invesmen is procyclical and beween wo and four imes as volaile as oupu; and real ne expors are counercyclical. The excepion is public consumpion, which is counercyclical almos as ofen as procyclical. Aferwards, oher sudies have found similar regulariies for differen samples of counries and daa frequency. Table 1 reproduces he exercise in Backus and ohers (1992) for 15 SDEs and he G-7 excluding Canada, for annual daa beween 198 and 23. I shows he same regulariies idenified in he original aricle: SDEs oupu is as volaile as in he big developed counries; consumpion and invesmen are procyclical, he former as volaile as oupu, and he laer abou 3 imes as volaile as oupu. Real ne expors are counercyclical in boh groups, excep for Ausria and Swizerland, for which hey are procyclical and acyclical, respecively. Finally, public consumpion does no have a common volailiy or cyclical paern across counries. Table 2 presens he regulariies documened by Aguiar and Gopinah (27) for a sample of 13 SDEs for quarerly daa beween 198 and 23. They find ha he main regulariies in Backus and ohers (1992) are also valid a quarerly frequency. Aggregae consumpion is procyclical and as volaile as oupu, invesmen is procyclical and abou 3.5 imes as volaile as oupu, and real ne expors are counercyclical, alhough less han for annual daa. III. LITERATURE REVIEW Earlier sudies have ried o replicae hese regulariies using a small open economy model or a wo counry model. Mendoza (1991) used a small open economy model o sudy he Canada s business cycles regulariies. Alhough, he model reproduced hem for a moderae adjusmen cos of capial and a low persisence in produciviy shocks, i relied on using GHH preferences. While his sudy did no presen simulaions for sandard preferences, Correia and ohers (1995), using a similar seup o sudy Porugal s business cycles, considered wo differen specificaions for he momenary uiliy funcion: A Cobb-Douglas one and he GHH one. They find ha, for business cycles driven by produciviy shocks, he seup wih Cobb-Douglas preferences yielded a consumpion less volaile and procyclical han in daa, and procyclical real ne expors. Only wih GHH preferences hey could reproduce he regulariies in he daa. Aguiar and Gopinah (27) used a small open economy model wih wo ypes of produciviy shocks, a ransiory shock around a rend and a permanen shock o he rend growh rae, o

5 replicae Canada s empirical regulariies. Their model wih sandard preferences replicaed he procyclical and volaile pah of consumpion, bu no he counercyclical ne expors. Sill, heir resuls relied largely on he specificaion of shocks o he rend growh of produciviy, which by heir persisence creae larger flucuaions in consumpion and invesmen relaive o he ones produced by he sandard shocks o produciviy around a rend. Among he sudies using a wo counry model, lile aenion has been paid o he implicaions for a small open economy. The pioneer work by Backus and ohers (1992) ried o replicae he regulariies of wo big open economies, he US and Europe. They find ha wih complee asse markes and moderae foreign ransacion coss, he model replicaed he volailiy of invesmen and ne expors, and he procyclicaliy of invesmen, bu no he volaile and procyclical pah of consumpion nor he counercyclical pah of ne expors. Sockman and Tesar (1995) added non radable goods o he model, finding ha i could replicae he procyclical and volaile pah of consumpion, and he counercyclicaliy of ne expors, alhough i under prediced is volailiy. They also find a high correlaion of consumpion of radable goods across counries, which hey solved by inroducing shocks o preferences, which makes he rade balance acyclical. Baxer and Crucini (1995) added incomplee asse markes o he model, finding i no imporan when produciviy shocks are rend saionary wih spillovers. Resricions on asse rade are imporan when shocks are persisen and he inernaional spillovers of shocks are smaller. Only very persisen shocks, combined wih incomplee asse markes, were able o replicae he cyclical co-movemen and volailiy of he main macroeconomic aggregaes in he daa. Backus and ohers (1994) endogeneize he erms of rade by allowing each counry o produce a single differeniaed good. Consumpion, invesmen and governmen purchases are composies of foreign and domesic goods, and business cycles are driven by shocks o produciviy and governmen purchases. This seup predics a procyclical consumpion and counercyclical ne expors, bu as noed by Raffo (27), he laer is due o changes in relaive prices (erms of rade) insead of quaniies, while he opposie is observed in he daa. Raffo (27) uses a wo counry model o reproduce he regulariies of he US and Canada. He finds ha he model s abiliy o creae counercyclical ne expors relies on he erms of rade flucuaions, as i delivers procyclical real ne expors. This is worse for a small open economy, in which even nominal ne expors are procyclical due o he lack of erms of rade effecs. He solves he problem by using GHH preferences, finding ha his is enough o reproduce he regulariies in he daa no only for a small open economy, bu also for large economies. None of he small open economy models discussed above used he erms of rade or foreign ineres rae shocks as source of business cycles, and he wo counry models could no generae he erms of rade volailiy observed in he daa (Backus and ohers, 1994). The nex secions show ha adding hese shocks as sources of business cycles allows a small open economy model, wih sandard preferences, o reproduce he regulariies in he daa.

6 IV. THE MODEL Consider a small open economy perfecly inegraed o he world in goods, bu faces he following aggregae upward sloping supply of exernal funds: where R is he domesic rae of reurn, ( ) R = R + η b b (1) * * R is he foreign rae of reurn, b is he ne exernal asses posiion, b is he level of ne exernal asses a which he risk premium is zero, and η is he elasiciy of such premium o he level of ne foreign asses. where * R is is uncondiional mean and R R ( ε ) * * * R is sochasic according o: = exp R (2) R ε is firs-order auo regressive shock: R R 2 wih E( v + 1) = and V ( v 1) σ R ε = ρ ε + v (3) R R R R + 1 + 1 + =. This model is no a fricionless seup, in which R = R, because when a fricionless model is log-linearized around he seady sae, i yields a uni roo for ne foreign asses (see Correia and ohers, 1995). A unique seady sae requires o anchor exernal deb in equilibrium. This can be done by seing an upward-sloping supply of exernal funds, a cos funcion of adjusing he exernal asse porfolio, or an endogenous discoun facor. Schmi-Grohe and Uribe (23) show ha all of hese hree forms yield he same firs and second momens. I chose he firs, and I kep η small o make he model a good approximaion of he fricionless seup. There are hree goods in he economy, an exporable good ( X ), an imporable good ( ) nonradable good ( N ). The wo producion facors are labor ( h ) and capial ( k ). Firms * M and a produce he X and N goods, using h and k inpus. Capial is secor specific and labor is freely mobile across secors. The law of one price holds for boh radable goods. The exernal price of M is normalized o one, and he exernal price of he exporable is sochasic, according o: X X P X* P = exp( ε ) P (4) where X * P is is uncondiional mean and P X ε is firs-order auoregressive shock: X X X X P P P P + 1 v+ 1 ε = ρ ε + (5)

X X P P 2 wih E( v + 1 ) = and V ( v 1 ) σ P 7 + = X. There are wo ypes of domesic agens: households and firms. Households own he firms, consume he M and N goods, supply h and k o he firms, and have access o he foreign capial marke. There are wo firms, he nonradable and he expor ones; boh use h and k o produce heir oupu. The economy follows a balanced growh pah a he rae ( γ 1), and populaion is consan. In he following, he model is se in saionary form. A. Households Households maximize heir lifeime uiliy given by equaion 6: U = E α { ( ) 1 α c 1 } 1 h σ * β = 1 σ (6) ( ) * α 1 σ where β = βγ, β is he discoun facor, h is he normalized hours of work and c is a M N CES aggregaion of consumpion of imporable ( c ) and nonradable ( ) ( ( ) ) 1 M N ϖ 1 ϖ ρ ρ ρ c goods: c = c + c (7) The ineremporal elasiciy of subsiuion is 1 σ. The households flow budge consrain is: wh + q k + q k + Rb = c + P c + i + i + b (8) X X N N M N N X N γ + 1 where w is he wage rae, N P he relaive price of N o M, and j k, j i and j q are capial, invesmen, and he renal rae of capial in secor j, respecively. Invesmen covers he capial adjusmen coss, replaces depreciaed capial, and accumulaes new capial, according o: j j j θ j γk = ( ) ( ) 2 1 1 δ k + i + i 2 (9) For j = X, N, where δ is he depreciaion rae and θ a coefficien in he quadraic adjusmen cos. Households choose he sequence { M, N,, X, N, X 1, N c c h i i k+ k+ 1, b+ 1} o maximize equaion = 6, subjec o equaions 8 and 9. Their firs-order condiions are as follows: α Mρ Nρ ( ( ) ) ( 1 σ ) 1 ( ) ( 1 α )( 1 σ ) M ( ρ 1 ) c 1 c ρ 1 h c αϖ ϖ + ϖ = λ (1) ρ ρ ( ) ( 1 σ ) 1 ( ) ( 1 α )( 1 σ ) ρ N ( ρ 1 ) ( ) ( ) α M N N α 1 ϖ ϖc + 1 ϖ c 1 h c = P λ (11)

8 ρ Nρ ( ) ( 1 ) ( ) ( 1 ) ρ M ( ) ( ) α σ ασ σ 1 α ϖc + 1 ϖ c 1 h = λw (12) φ = λ + φ θi (13) X X X φ = λ + φ θi (14) N N N ( ) γφ X X X 1 = βe λ+ 1q+ 1+ φ+ 1 δ (15) ( ) γφ N N N 1 = βe λ+ 1q+ 1+ φ+ 1 δ (16) [ R ] γλ = β E λ + 1 + 1 (17) ( 1 1 1) X N E lim βλ k+ + k+ + b + = (18) where λ, X φ N and φ are he Lagrange mulipliers on equaions 8 and 9, respecively. B. Firms Boh firms have Cobb-Douglas consan-reurn-o-scale echnologies and choose { fj fj h, k } = maximize profis, wih j = X, N. The firs-order condiions for he nonradable firm are: o N N fn α N fn ( 1 α ) exp( ε )( ) ( ) N = N (19) w P k h ( )( ) ( 1 α ) ( ) ( 1) N αn ε N N N fn fn q = α P exp h k (2) N while he firs-order condiions for he expor firm are X X fx α X fx ( 1 α ) exp( ε )( ) ( ) α X = X (21) w P k h ( )( ) ( 1 α ) ( ) ( 1) X αx ε X X X fx fx q = α P exp h k (22) X j Where ε is he produciviy shock in each secor j = X, N, respecively. These shocks follow a firs-order auoregressive process: j j 2 wih E( v + 1) = and V ( v 1) σ j + =. ε j j j j + 1 + 1 α = ρ ε + v (23)

9 X Given b, k and C. Definiion of a Compeiive Equilibrium X N R P X N k, and shocks' processes ( ε, ε, ε, ε ) =, a compeiive equilibrium corresponds o sequences of households allocaions { c M, N,, X, N, X 1, N c h i i k+ k+ 1, b+ 1} allocaions { h fx, fn, fx, fn h k k }, and prices = { P X, N, X, N P q q, w, R} =, such ha: =, firms X Given prices, b, k, he households' problem. N k, and shocks' processes, { M, N,, X, N, X 1, N c c h i i k+ k+ 1, b+ 1} = solve Given prices and shocks' processes, { fx fx h, k } = Given prices and shocks processes, { fn fn h, k } = solve firm X's problem. solve firm N's problem. Markes clear: c N = y, N k X = k, fx k N = k, and fn h = h + h fx fn γ + X X M X N The resource consrain is saisfied: Rb+ P y = c + i + i + b 1 V. STEADY STATE AND CALIBRATION The parameers are calibraed o mach Canada's average macroeconomic raios beween 1979 and 24. Table 3 presens he resuls and he macroeconomic raios in he daa and in he model s seady sae. The risk premium elasiciy, η, is.1 as in Schmi-Grohe and Uribe (23), ne foreign deb is 1 percen of GDP as in Aguiar and Gopinah (27), and * b is 6.6 percen of GDP, o yield a spread R R of 25 basis poins in seady sae. The value of γ is 1.7, or one plus he average quarerly growh rae of GDP. Secoral oupu is buil by allocaing GDP from naional accouns as expor or nonradable as in Sockman and Tesar (1995). The expor secor consiss of agriculure, manufacuring and mining, equal o 24 percen of GDP, and he nonradable secor consiss of consrucion, services and uiliies, equal o 76 percen of GDP. The same aggregaion is used for hours of work, obaining a 22 and 78 percen in he expor and nonradable secors, respecively. Wih he secoral allocaions of work hours and oupu in seady sae, and as labor is freely mobile across secors, he capial shares are obained by equaing he marginal produciviy of labor across secors, making he average share equal o.36 as in Raffo (26). The respecive capial shares in he expor and nonradable secors are.41 and.34. The capial sock is build using equaion (9), wih δ equal o.25 as in Raffo (26), while he iniial capial and θ are se o equae he average growh rae of capial o he one of GDP, and o

1 mach he volailiy of invesmen in he benchmark simulaions. The seady sae allocaions of capial are 27.4 and 72.6 percen in he expor and nonradable secors, respecively. On preferences, β is.98 o saisfy equaion (17), and ρ is -.34 as in Mendoza (1995). σ is se a 2.6 o replicae he correlaion of ne expors o GDP in he daa, wih an ineremporal elasiciy of subsiuion of.38, in he normal range of Mehra and Presco (1985), and only slighly lower han in Backus and ohers (1994), Baxer and Crucini (1995), Sockman and Tesar (1995), and Aguiar and Gopinah (27). Nonradable consumpion is equal o nonradable oupu, and imporable consumpion is equal o he res of oal consumpion. The values of ϖ, λ, X φ N, and φ were se o saisfy he households' firs order condiions. Noe ha he curren accoun balance is equal o zero in seady sae, whereas i is in surplus in he daa, so I increased he raios o GDP of imporable consumpion and invesmen o calibrae a consisen seady sae. Table 3 shows ha he calibraion is consisen wih he macroeconomic raios in he daa, excep for he adjusmens made o achieve a zero curren accoun balance in seady sae. A. Shock Processes The erms of rade is he raio of prices of expors o impors of goods and services, and he foreign real ineres rae is he US Fed Funds rae minus inflaion. Toal facor produciviy in he expor and nonradable secors is he Solow residual. The secoral series of work hours and capial are buil by equaing he marginal produciviy of labor and capial across secors. This is an equilibrium condiion for he freely mobile labor, bu no for he secor specifc capial. Households, however, can freely allocae invesmen o eiher secor, hus equaing he marginal produciviy of capial across secors is a firs bes allocaion, bu is consrained as invesmen can no be negaive. Secoral invesmen was obained for his allocaion using equaions (2) and (22), finding ha invesmen in boh secors is always posiive. Table 3 presens he auocorrelaions and sandard deviaions of all shocks, and heir innovaions cross-correlaions. All shocks are highly auocorrelaed, wih coefficiens beween.6 and.9. The erms of rade are he mos volaile, beween four and five as volaile as he oher shocks. The innovaions o he foreign ineres rae shocks are negaively cross-correlaed wih he ones of all oher shocks, while he innovaions o boh produciviy shocks are highly cross-correlaed beween hem, bu barely correlaed o he erms of rade. VI. SIMULATIONS AND IMPULSE RESPONSES The model is log-linearized around he seady sae, so he simulaions and impulse-response funcions are percenage deviaions of he variables from heir seady sae values. Two scenarios are simulaed: The benchmark one, when business cycles are driven by all four shocks, and he sandard one, when business cycles are driven by shocks o produciviy. In he benchmark case, hree parameers are se o make he model replicae some specific

11 feaures of he daa. The sandard deviaions of all four shocks are scaled by he same facor o mach he volailiy of GDP, while θ and σ are se o replicae he volailiy of invesmen and correlaion beween real ne expors and GDP, respecively 2. In he sandard case, only he shocks sandard deviaions and θ are modified for he simulaions o mach he volailiy of GDP and invesmen, respecively. The IES is kep as in he benchmark case. A. Impulse - Responses Figure 1 presens four differen impulse-response funcions derived from he benchmark scenario. Each line represens he endogenous reacion of he respecive variable o a posiive shock of 1 percen o produciviy or erms of rade, or o a fall of 5 basis poins in he foreign real ineres rae. These impulse-response funcions reflec he shocks auocorrelaions and cross-correlaions presened in able 4. Figure 1 shows ha a posiive produciviy shock o any secor produces large increases in oupu of exporable and nonradable, as hey are highly cross-correlaed. Consumpion and invesmen also increase, bu less han oupu, which added o he increase in expors, creae procyclical real and nominal ne expors. Toal work hours also increase less han oupu, raising in he expor secor and falling in he nonradable one. A posiive erms of rade shock, however, produces a lower increase in oupu han a similar produciviy shock, bu generaes larger changes in consumpion and invesmen han he one of oupu, and reduces exporable oupu. This resuls in lower real and nominal ne expors, as he fall in he real ne expors more han offses he increase in he erms of rade. Also, aggregae hours of work increase more han wih a similar produciviy shock, raising in he nonradable secor and falling in he expor one. A reducion in he foreign real ineres rae produces a small increase in oupu, bu a larger increase in consumpion and invesmen han he one of oupu. I also reduces oupu of exporables and worsen real and nominal ne expors, as he erms of rade do no change significanly. Aggregae work hours decrease, resuling in lower hours of work in he exporable secor and in higher hours in he non radable one. The inuiion is as follows: A posiive produciviy shock increases oupu in boh secors direcly hrough he producion funcion, while a posiive erms of rade shock only increases he foreign value of he expor good. Boh shocks, however, increase he households wealh and demand for imporable and nonradable goods, and reduce heir supply of work hours. The imporable good is brough from abroad, bu raising consumpion of nonradable requires increasing is domesic producion. For produciviy shocks, nonradable oupu increases wihou exra work hours or invesmen, bu for erms of rade shocks, work hours 2 As discussed above, he resuling IES is inside he range considered normal by Mehra and Presco (1985).

12 and invesmen have o increase, generaing a reallocaion of work hours from he expor secor o he nonradable one. Finally, aggregae consumpion increases less, and oal work hours increase more, wih erms of rade shocks han wih produciviy shocks. Figure 1 shows ha when produciviy increases by one percen, invesmen increases by half as much and hours of work by a 1/3 as much, as for a similar erms of rade shock. However, oupu raises more due o he gains in produciviy. Thus, erms of rade shocks produce smaller increases in exporable oupu han similar produciviy shocks, bu larger increases in consumpion of imporable and invesmen, generaing lower real and nominal ne expors. A fall in he foreign real ineres rae lowers he cos of invesmen and he price of fuure consumpion relaive o presen consumpion. Consumpion and invesmen increase, and work hours fall. As nonradable goods are produced domesically, labor is shifed o his secor from he expor one. Nonradable oupu increases and expor oupu falls, and as a resul real and nominal ne expors decrease as he erms of rade remain relaively consan. Thus, produciviy shocks generae a low volailiy of consumpion and invesmen relaive o oupu, and procyclical ne expors, while he erms of rade and foreign real ineres rae produce more procyclical and volaile consumpion and invesmen, and counercyclical ne expors. Thus, adding hese las wo shocks o a sandard DSGE small open economy model can make i able o generae he regulariies observed in he daa. B. Simulaions This secion sudies he model s abiliy o replicae seleced firs and second momens of Canada's business cycles for he wo scenarios previously defined. Table 5 presens he sandard deviaions, firs order auocorrelaions and correlaions wih curren and lagged oupu, of he main series in he daa and in he simulaions for boh scenarios. Sandard scenario: Only produciviy shocks The sandard deviaions of boh produciviy shocks are scaled up by 5 percen wih respec o Table 4, and θ is reduced from.5 o.1, o make he model mach he volailiy of GDP and invesmen in he daa, respecively. The shocks' auocorrelaions and crosscorrelaions are kep as in Table 4, while he IES remains as in Table 3. Table 5 shows ha when business cycles are driven only by produciviy shocks, he model produces conradicing resuls wih he daa. Firs, alhough consumpion is procyclical, is volailiy is small, specially for imporable goods. Second, real ne expors are procyclical and oo volaile. Third, invesmen is oo procyclical, specially in non radable capial. Las, alhough oal hours of work are procyclical, he model under predics heir volailiy. Inuiively, produciviy shocks increase nonradable oupu wihou exra work hours or invesmen in his secor, and households use he exernal capial marke, a a roughly

13 consan ineres rae, o smooh imporable consumpion over ime. As a resul, domesic demand is less volaile han oupu, and real ne expors are procyclical and volaile. Benchmark scenario: All four shocks The sandard deviaions of all four shocks are increased by 15 percen relaive o Table 4 o make he model mach he volailiy of GDP in he daa, while heir auocorrelaions and cross correlaions remain as in Table 4. Also, θ and he IES are se o replicae he observed volailiy of invesmen and correlaion beween real ne expors and GDP, respecively. Table 5 shows ha he erms of rade and foreign ineres rae shocks improve he model s abiliy o replicae he momens of consumpion, invesmen and real ne expors relaive o he previous case. Consumpion is as volaile as in he daa, alhough more procyclical, and invesmen is less procyclical, alhough sill more han in he daa. Adding hese shocks also brings he volailiy of work hours closer o he daa, making hem more procyclical and volaile in he nonradable secor, and less procyclical bu more volaile, in he expor one. In summary, domesic demand is more procyclical and volaile han oupu, and real ne expors are counercyclical and less volaile han in he sandard scenario. However, nominal ne expors are sill procyclical, while hey are weakly counercyclical in he daa. This raises he quesion of wheher he Fed Funds rae is a good measure of he foreign ineres rae shock, and wheher a lower IES could improve he abiliy of he model o replicae he regulariies in he daa. The nex wo subsecions explore hese quesions in more deail. Differen Foreign Ineres Raes Table 6 presens he simulaions for hree alernaive measures of he foreign ineres rae: he 3 monhs and 1 years US reasury bill raes, and he 3 monhs LIBOR rae in US dollars. In each case he sandard deviaions of all four shocks are scaled by he same facor o mach he volailiy of GDP, θ is chosen o mach he volailiy of invesmen, and he IES is se o make he model replicae he observed correlaion beween real ne expors and GDP. This exercise shows ha all hree measures of he foreign ineres rae yield abou he same momens of consumpion, invesmen, work hours and ne expors. Nominal ne expors are as procyclical as in he benchmark case, showing ha his avenue is no adequae o replicae he momens of nominal ne expors while keeping he oher momens close o he daa. Differen ineremporal elasiciies of subsiuion Table 7 shows simulaions for hree values of σ : σ = 2, σ = 3 and σ = 4, and in each case he sandard deviaions of all shocks are scaled by he same facor, and θ is se, o mach he volailiy of GDP and invesmen in he daa, respecively. The shocks' auocorrelaions and cross-correlaions are kep as in Table 4. Noe ha hese simulaions are no bound o replicae he observed correlaion beween real ne expors and GDP.

14 The simulaions are sensiive o he choice of he IES. Raising i o.5 makes consumpion and aggregae work hours less procyclical and volaile han in he daa, makes invesmen acyclical and exporable oupu more procyclical and volaile, resuling in more procyclical and volaile real and nominal ne expors han in he daa. Reducing he IES o.25 makes consumpion, invesmen and work hours are more procyclical and volaile han in he daa, and makes nominal ne expors acyclical by making real ne expors more counercyclical han in he daa. Thus, reducing he IES does no seem adequae o reduce he procyclicaliy of nominal expors eiher, as i worsens oher momens. VII. CONCLUSIONS A DSGE small open economy model wih sandard preferences and a normal ineremporal elasiciy of subsiuion, can replicae he SDEs business cycles regulariies if he erms of rade and foreign ineres rae shocks are added o he produciviy shocks as source of business cycles flucuaions. Produciviy shocks produce large procyclical flucuaions in exporable oupu, and a lower volailiy of consumpion and invesmen han he one of oupu. Thus, when business cycles driven only by produciviy shocks, he model generaes excessive consumpion smoohing, and procyclical and volaile real and nominal ne expors. The erms of rade, however, produce smaller changes in oupu han produciviy shocks, bu generae more procyclical and volaile variaions in consumpion and invesmen relaive o oupu, and counercyclical flucuaions in real and nominal ne expors, as changes in quaniies more han offse changes in prices. The foreign ineres rae shocks also produce small variaions in oupu, bu large procyclical flucuaions in consumpion and invesmen relaive o oupu, and counercyclical changes in real and nominal ne expors. Furhermore, boh shocks reinforce each oher as heir innovaions are negaively correlaed in he daa. The failure in previous sudies using DSGE small open economy models has been o exclude he erms of rade and foreign ineres rae shocks as source of business cycles, while he wo counry models have failed replicaing he volailiy of hese shocks in he daa. However, alhough he model in his paper replicaes he momens of mos variables, i over esimaes he correlaion beween nominal ne expors and GDP. Changing he measure of he foreign ineres rae or he ineremporal elasiciy of subsiuion does no solve he issue, as hey reduce he abiliy of he model o replicae oher momens.

15 References Aguiar, Mark and Gia Gopinah, 27, Emerging Marke Business Cycles: The Cycle is he Trend, Journal of Poliical Economy, Vol. 115, No. 1, pp. 69-12. Backus, David and Parick Kehoe, 1992, Inernaional Evidence on he Hisorical Properies of Business Cycles, The American Economic Review, Vol. 82, No. 4, pp. 864 88. Backus, David, Parick Kehoe, and Finn Kydland, 1992, Inernaional Real Business Cycles, The Journal of Poliical Economy, Vol. 1, No. 4, pp. 745 75., 1994, Dynamics of he Trade Balance and he Terms of Trade: The J-Curve? The American Economic Review, Vol. 84, No. 1, pp. 84 13. Baxer, Marianne, and Mario Crucini, 1995, Business Cycles and he Asse Srucure of Foreign Trade, Inernaional Economic Review, Vol. 36, No. 4, pp. 821 54. Correia, Isabel, Joao Neves, and Sergio Rebelo, 1995, Business Cycles in a Small Open Economy, European Economic Review, Vol. 39, pp. 189 113. Greenwood, Jeremy, Zvi Hercowiz, and Gregory Hoffman, 1988. "Invesmen, Capaciy Uilizaion and he Real Business Cycle," The American Economic Review, Vol. 78, No. 3, pp. 42-417. Mehra, Rajnish, and Edward Presco, 1985, The Equiy Premium Puzzle, Journal of Moneary Economics, Vol. 15, pp.141 83. Mendoza, Enrique, 1991, Real Business Cycles in A Small Open Economy, American Economic Review, Vol. 81, No. 4, pp. 797 818., 1995, The Terms of Trade, The Real Exchange Rae and Economic Flucuaions, Inernaional Economic Review, Vol. 36, No. 1, pp. 11 37. Neumeyer, Pablo, and Fabrizio Perri, 25, Business Cycles in Developing Economies: The Role of Ineres Raes, Journal of Moneary Economics, Vol. 52, No. 2, pp. 345 8. Raffo, Andrea, 26, Ne Expors, Consumpion Volailiy and Inernaional Business Cycle Models, Research Working Paper 6-1, The Federal Reserve Bank of Kansas Ciy. Schmi-Grohe, Sephanie, and Marin Uribe, 23, Closing Small Open Economies, Journal of Inernaional Economics, Vol. 61, pp. 163 85. Sockman, Alan, and Linda Tesar, 1995, Tases and Technology in a Two-Counry Model of he Business Cycle: Explaining Inernaional Comovemens, The American Economic Review, Vol. 85, No. 1, pp. 168 85.

16 Table 1. Business Cycles Indicaors for Developed Economies, Annual Daa, 198 23 A. Cross-Correlaions wih Oupu: ρ(y,y -1 ) ρ(cpriv,y) ρ(cpub,y) ρ(c,y) ρ(i,y) ρ(nx/y,y) G 7 exc. Canada.7.91.14.85.91 -.54 Ausralia.51.5.42.58.86 -.35 Ausria.63.87.18.8.7.18 Belgium.67.87 -.2.8.91 -.57 Canada.64.91 -.2.78.83 -.28 Denmark.7.78 -.26.69.91 -.78 Finland.78.94.62.92.96 -.63 Greece.53.58.3.62.71 -.4 Iceland.67.87.49.87.79 -.53 Ireland.66.68.18.72.87 -.56 Neherlands.69.87.15.88.87 -.43 New Zealand.58.86.43.81.82 -.48 Norway.72.83 -.28.8.7 -.49 Porugal.77.93.83.93.85 -.75 Spain.83.94.68.91.96 -.92 Sweden.72.8 -.28.71.94 -.53 Swizerland.63.86.35.85.77. Mean Small Economies.67.82.22.79.84 -.45 B. Sandard Deviaions Relaive o Oupu: σ(y) σ(cpriv)/σ(y) σ(cpub)/σ(y) σ(c)/σ(y) σ(i)/σ(y) σ(nx/y) G 7 exc. Canada 2.11 1.11.92.92 2.82.91 Ausralia 1.66.7.93.62 3.51 1.1 Ausria 1.44.9 1.3.79 2.96.76 Belgium 1.63.92.6.69 4.54 1.13 Canada 2.38.95.97.76 2.73 1.27 Denmark 1.89 1.12 1.19 1.85 5.4 1.42 Finland 3.9 1..58.83 3.12 1.53 Greece 1.99 1.1 1.14.78 2.7 1.3 Iceland 3.37 1.59.54 1.27 3.38 3.14 Ireland 2.65 1.17 1.18.92 3.5 1.9 Neherlands 1.89 1.16.94.83 2.59.74 New Zealand 2.31.92 1.86.98 3.53 1.16 Norway 2.15 1.24.85.79 3.9 1.56 Porugal 3.23 1.16.92 1.9 2.84 1.82 Spain 2.33 1.24 1.11 1.18 3.51 1.75 Sweden 2.26 1.39.66.9 4.3 1.2 Swizerland 1.85.64 1.8.61 2.46.88 Mean Small Economies 2.31 1.7.99.93 3.4 1.35 Source: World Economic Oulook, IMF. Noe: GDP (Y), privae consumpion (Cpriv), public consumpion (Cpub), oal consumpion (C) and invesmen (I) are Hodrick-Presco filered logarihms; ne expors (NX) is he Hodrick-Presco filered raio o oupu. For he firs and las variables, he repored saisic in par B is he sandard deviaion of he variable muliplied by 1, while for he ohers is he raio of sandard deviaion of he variable o he one of GDP.

17 Table 2. Business Cycles Indicaors for Developed Economies, Quarerly Daa, 198 23 A. Cross-Correlaions wih Oupu: ρ(y,y -1 ) ρ(c,y) ρ(i,y) ρ(nx/y,y) Ausralia.84 (.4).48 (.13).8 (.14) -.43 (.16) Ausria.9 (.8).74 (.2).75 (.11).1 (.13) Belgium.79 (.5).67 (.14).62 (.14) -.4 (.1) Canada.91 (.4).88 (.8).77 (.13) -.2 (.21) Denmark.49 (.14).36 (.2).51 (.11) -.8 (.18) Finland.85 (.9).84 (.9).88 (.1) -.45 (.17) Neherlands.77 (.7).72 (.11).7 (.11) -.19 (.9) New Zealand.77 (.1).76 (.11).82 (.13) -.26 (.15) Norway.48 (.11).63 (.12). (.11).11 (.11) Porugal.72 (.11).75 (.12).7 (.14) -.11 (.15) Spain.82 (.3).83 (.9).83 (.12) -.6 (.12) Sweden.53 (.21).35 (.17).68 (.13).1 (.12) Swizerland.92 (.5).58 (.14).69 (.17) -.3 (.17) Mean.75.66.67 -.17 B. Sandard Deviaions Relaive o Oupu: σ(y) σ(c)/σ(y) σ(i)/σ(y) σ(nx/y) Ausralia 1.39 (.21).69 (.) 3.69 (.3) 1.8 (.12) Ausria.89 (.9).87 (.14) 2.75 (.4).65 (.4) Belgium 1.2 (.9).81 (.13) 3.72 (.4).91 (.7) Canada 1.64 (.21).77 (.9) 2.63 (.3).91 (.8) Denmark 1.2 (.16) 1.19 (.1) 3.9 (.2).88 (.14) Finland 2.18 (.39).94 (.7) 3.26 (.2) 1.11 (.1) Neherlands 1.2 (.13) 1.7 (.9) 2.92 (.3).71 (.9) New Zealand 1.56 (.2).9 (.1) 4.38 (.2) 1.37 (.18) Norway 1.4 (.1) 1.32 (.12) 4.33 (.3) 1.73 (.19) Porugal 1.34 (.14) 1.2 (.11) 2.88 (.5) 1.16 (.12) Spain 1.11 (.12) 1.11 (.7) 3.7 (.3).86 (.7) Sweden 1.52 (.2).97 (.14) 3.66 (.4).94 (.9) Swizerland 1.11 (.13).51 (.31) 2.56 (.5).96 (.9) Mean 1.34.94 3.41 1.2 Source: Aguiar, M. and G. Gopinah, "Emerging Marke Business Cycles: The Cycle is he Trend". Federal Reserve Bank of Boson.

18 Table 3. Calibraed Parameers and Macroeconomic Raios Macroeconomic Raios Parameer Value Variable Daa Model Preferences Aggregae Demand β.98 c/y.844.85 ρ -.34 c N /y 76. 76.?.51 c M /y 8.4 8.6 σ 2.58 i/y 13.7 15.3 α.669 b/y.21. b/y n.a. -.1 Technology Producion α X.413 α N.343 y N /y 76. 76. θ.53 y X /y 24. 24. δ.25 Inpus Supply of Exernal Funds k/y n.a. 3.5 b -6.63 k N /k n.a..73 η.1 k X /k n.a..27 h.27.27 Long Term Growh h N /h.77.78 γ 1.7 Source: CANSIM - Canadian Economic Indicaors. h X /h.23.22

19 Table 4. Shocks Processes Sandard Cross correlaion of innovaions wih Shocks Saisic ρ Deviaion P X r* z X z N Terms of Trade P X.883 3.7 1. -.21.55.49 Foreign Ineres Rae r*.783.68 -.21 1. -.1 -.11 Produciviy Exporable z X.721.91.55 -.1 1..995 Produciviy Non Tradable z N.646.84.49 -.11.995 1.

2 Table 5. Daa Momens, Sandard and Benchmark Model Simulaions Daa Only produciviy shocks Adding TOT and R* Variable x ρ(x,y ) ρ(x,y -1 ) σ(y) σ(x)/σ(y) ρ(x,y ) ρ(x,y -1 ) σ(y) σ(x)/σ(y) ρ(x,y ) ρ(x,y -1 ) σ(y) σ(x)/σ(y) Aggregae oupu y 1..9 1.57 1. 1..52 1.57 1. 1..6 1.57 1. Oupu exporables y x.91.79 3.26 2.7.99.55 3.6 1.95.7.42 3.6 1.95 Oupu non radables y n.93.87 1.23.78.99.49 1.12.71.9.53 1.55.99 Aggregae consumpion c.81.7 1.55.98.99.48.93.59.87.53 1.66 1.6 Consumpion imporables c m -.5 -.15 4.47 2.84.4 -.19.22.14.64.43 3.12 1.99 Consumpion non radables c n.93.87 1.23.78.99.49 1.12.71.9.53 1.55.99 Invesmen i.49.55 5.57 3.54.89.47 5.57 3.55.66.46 5.57 3.55 Invesmen exporable i x -- -- -- -- -.22 -.18 4.64 2.96.61.44 14.62 9.31 Invesmen non radable i n -- -- -- --.97.52 7.47 4.76.7.46 3.9 1.97 Real ne expors nx -.17 -.17 --.88.8.48 -- 3.28 -.17 -.15 -- 1.3 Nominal ne expors nnx -.5 -.1 --.97.8.48 -- 3.29.54.36 -- 1.15 Hours of work h.88.88 1.65 1.5.97.55.22.14.71.49 1.52.97 Hours of work exporable h x.89.81 3.23 2.6.96.57 2.61 1.66.44.31 4.39 2.8 Hours of work non radable h n.75.8 1.42.9 -.93 -.56.47.3.46.32 1.81 1.15 Capial exporable k x.72.62 1.71 1.8 -.65 -.52.17.11.31.11 1.28.82 Capial non radable k n -.6 -.45.97.62.25 -.1.46.29.13 -.7.18.11

21 Table 6. Model Simulaions, Differen Measures of R* Tresury Bill 3 Monhs Libor 3 Monhs Tresury Bill 1 Years Variable x ρ(x,y ) ρ(x,y -1 ) σ(y) σ(x)/σ(y) ρ(x,y ) ρ(x,y -1 ) σ(y) σ(x)/σ(y) ρ(x,y ) ρ(x,y -1 ) σ(y) σ(x)/σ(y) Aggregae oupu y 1..59 1.57 1. 1..6 1.57 1. 1..59 1.57 1. Oupu exporables y x.8.49 2.82 1.8.68.4 3.1 1.97.69.41 3.4 1.94 Oupu non radables y n.93.54 1.45.92.89.53 1.58 1.1.9.54 1.56.99 Aggregae consumpion c.91.54 1.56.99.87.53 1.69 1.8.87.53 1.68 1.7 Consumpion imporables c m.65.43 3.7 1.96.64.43 3.17 2.2.63.43 3.26 2.8 Consumpion non radables c n.93.54 1.45.92.89.53 1.58 1.1.9.54 1.56.99 Invesmen i.68.46 5.57 3.55.65.46 5.57 3.55.65.45 5.57 3.55 Invesmen exporable i x.63.46 13.94 8.88.61.44 14.84 9.45.6.44 14.98 9.54 Invesmen non radable i n.71.46 3.26 2.8.7.46 3.4 1.94.69.46 3.1 1.92 Real ne expors nx -.17 -.15 -- 1.15 -.17 -.16 -- 1.34 -.17 -.16 -- 1.33 Nominal ne expors nnx.64.43 -- 1..52.34 -- 1.17.55.36 -- 1.13 Hours of work h.7.49 1.5.96.71.49 1.52.97.7.49 1.5.96 Hours of work exporable h x.56.4 3.81 2.43.41.29 4.49 2.86.42.29 4.31 2.75 Hours of work non radable h n.45.31 1.63 1.4.46.32 1.86 1.18.45.32 1.83 1.17 Capial exporable k x.3.1 1.24.79.31.11 1.29.82.31.11 1.3.83 Capial non radable k n.12 -.9.2.13.13 -.7.18.11.13 -.7.17.11

22 Table 7. Model Simulaions, Differen Ineremporal Elasiciies of Subsiuion σ = 2 σ = 3 σ = 4 Variable x ρ(x,y ) ρ(x,y -1 ) σ(y) σ(x)/σ(y) ρ(x,y ) ρ(x,y -1 ) σ(y) σ(x)/σ(y) ρ(x,y ) ρ(x,y -1 ) σ(y) σ(x)/σ(y) Aggregae oupu y 1..51 1.57 1. 1..64 1.57 1. 1..67 1.57 1. Oupu exporables y x.88.47 4.4 2.57.59.37 2.47 1.57.43.29 1.78 1.13 Oupu non radables y n.84.41 1.11.71.93.6 1.72 1.1.96.65 1.9 1.21 Aggregae consumpion c.77.36 1.18.75.92.6 1.71 1.9.96.65 1.69 1.8 Consumpion imporables c m.12.1 5.29 3.37.74.53 1.87 1.19.9.16.42.27 Consumpion non radables c n.84.41 1.11.71.93.6 1.72 1.1.96.65 1.9 1.21 Invesmen i.8.2 5.57 3.55.8.57 5.57 3.55.9.66 5.57 3.55 Invesmen exporable i x.4.1 15.42 9.82.75.56 13.5 8.6.85.64 12.16 7.75 Invesmen non radable i n.14.3 3.1 1.92.84.58 3.32 2.11.93.66 3.61 2.3 Real ne expors nx.46.27 -- 1.6 -.39 -.31 -- 1.1 -.61 -.46 --.86 Nominal ne expors nnx.63.34 -- 1.6.38.27 --.9.8.7 --.61 Hours of work h.33.22 1.1.64.83.59 1.81 1.15.92.66 2.7 1.32 Hours of work exporable h x.62.36 5.79 3.69.35.27 3.54 2.25.19.18 2.56 1.63 Hours of work non radable h n -.99 -.52.6.38.7.49 2.25 1.43.87.61 2.66 1.69 Capial exporable k x -.6 -.7 1.33.85.43.19 1.18.75.54.27 1.7.68 Capial non radable k n -.9 -.14.15.1.21 -.3.22.14.3.4.27.17

23 Figure 1. Impulse - Response Funcions.1.8 A: Terms of Trade -.1 B: Foreign Ineres Rae.6 -.4 -.3 -.4 -.5.1 C: Produciviy Exporables.1 D: Produciviy Non Tradables.8.8.6.6.4.4.12.1 E: Aggregae GDP.9.8.7 F: Aggregae Consumpion.8.6.6.5.4.4.3.1 -.1.16 G: Aggregae Invesmen 2. H: Real Ne Expors (% GDP).14.12 1..1.8.6. -1..4 - -2. -3. -4.

24 Figure 1. Impulse - Response Funcions (Coninued) 2. 1.. -1. I: Nominal Ne Expors (% GDP) -.1 - J: Domesic Ineres Rae -2. -.3-3. -.4-4. -.5.3 K: Aggregae Hours of Work.14 L: Wage Rae.12.1.8.1.6.4 -.1 -.15 M: GDP Exporables.1 N: GDP and Consumpion Non Tradables.1.8.5.6 -.5.4 -.1 -.15 -.7 O: Consumpion Imporables.15 P: Price Non radables.6.5.1.4.3.5.1 -.1 -.5

25 Figure 1. Impulse - Response Funcions (Concluded).1 Q: Work Hours Exporables.5 R: Work Hours Non Tradables.5.4 -.5 -.1 -.15.3.1 -.1 -.2 -.4 S: Invesmen Exporables.8.7 T: Invesmen Non Tradables.3.6.5.2.4.1.3. -.1.1 -.1.4 U: Capial Sock Exporables 9 V: Capial Sock Exporables 8.3 7 6 5 4.1 3 2 1.15 W: Renal Rae Exporable.18.16 X: Renal Rae Non Tradable.1.14.12.1.5.8.6 -.5.4 -