Can World Real Interest Rates Explain Business Cycles in a Small Open Economy? *

Transcription

1 Can Wold Real Inees Raes Explain Business Cycles in a Small Open Economy? * William Blankenau a M. Ayhan Kose b Kei-Mu Yi c July 999 Revised: Novembe 999 Absac: While he wold eal inees ae is poenially an impoan mechanism fo ansmiing inenaional shocks o small open economies much of he ecen quaniaive eseach ha sudies his mechanism concludes ha i has lile effec on oupu invesmen and ne expos. We e-examine he impoance of wold eal inees ae shocks using an appoach ha eveses he sandad eal business cycle mehodology. We begin wih a small open economy business cycle model. Bu ahe han specifying he sochasic pocesses fo he shocks and hen solving and simulaing he model o evaluae how well hese shocks explain business cycles we use he model o back ou he shocks ha ae consisen wih he model s obsevable endogenous vaiables. Then we use vaiance decomposiions o examine he impoance of each shock. We apply his mehodology o Canada and find ha wold eal inees ae shocks can play an impoan ole in explaining he cyclical vaiaion in a small open economy. In paicula hey can explain up o one-hid of he flucuaions in oupu and moe han half of he flucuaions in ne expos and ne foeign asses. JEL Classificaion: F4 E32 D58. Key Wods: wold inees aes business cycles dynamic sochasic geneal equilibium models small open economy. * We hank Naayana Kochelakoa Simon Poe and wo anonymous efeees fo helpful commens. We also benefied fom he suggesions of semina paicipans a Clak Univesiy he 999 Souheas Inenaional Economics Confeence and he 999 Compuing in Economics and Finance Confeence. The views expessed in his pape ae hose of he auhos and ae no necessaily eflecive of views a he Fedeal Reseve Bank of New Yok o he Fedeal Reseve Sysem. a Depamen of Economics Univesiy of Wisconsin-Whiewae 800 Wes Main See Whiewae WI [email protected]. b Gaduae School of Inenaional Economics and Finance Bandeis Univesiy Walham MA [email protected]. c Coesponding Auho: Inenaional Reseach Fedeal Reseve Bank of New Yok 33 Libey S. New Yok NY [email protected]

2 . Inoducion In heoy he wold eal inees ae is an impoan mechanism by which foeign shocks ae ansmied o small open economies. Changes in he wold eal inees ae can affec behavio along many magins: hey affec households by geneaing ineempoal subsiuion wealh and pofolio allocaion effecs and hey affec fims by aleing incenives fo domesic invesmen. I is supising hen ha much of he ecen quaniaive eseach on he effecs of wold eal inees aes find ha hey ae no impoan in explaining he dynamics of small open economies. This lieaue (see fo example Mendoza 99 Coeia Neves and Rebelo and Schmi-Gohe 998 finds ha wold eal inees ae shocks have small effecs on oupu consumpion and labo hous and in some cases even on invesmen ne expos and ne foeign asses. In obaining hese findings he auhos menioned above follow he sandad inenaional eal business cycle appoach. They build a dynamic sochasic model of a small open economy. Then hey paameeize he model including he pocesses fo he sochasic shocks one of which is he wold eal inees ae. Finally hey solve he model and/o conduc impulse esponses o quaniaively evaluae he ole of inees ae shocks. Thee ae howeve hee difficulies wih his sandad appoach. Fis hee is no consensus on a good poxy fo he ex ane wold eal inees ae which is of couse unobsevable. A wide vaiey of nominal inees aes pice indices and inflaion expecaions have been used o consuc measues of wold eal inees aes. Fo example he 3-monh U.S. T-Bill ae he ae of eun on he S&P 500 he LIBOR ae as well as a weighed aveage of seveal counies T-Bill aes have been employed as nominal inees aes fo example. 2 These diffeen measues ae no necessaily highly coelaed wih each ohe as Table shows fo fou ex ane eal inees aes consuced fom he same pice index and inflaion Obsfeld and Rogoff (995 p. 78 in discussing ess of ineempoal cuen accoun models noe ha a fis difficuly is ha i is no obvious wha eal inees ae o use o discoun expeced fuue oupu flows. Indeed sudying inees aes in a eal business cycle conex is a elaively ecen phenomenon. King Plosse and Rebelo (988 p. 226 do no sudy inees aes because of he well-known difficulies of obaining measues of expeced eal inees aes. Beaudy and Guay (996 and van Wincoop (993 ae among he fis o focus explicily on compaing inees aes implied by eal business cycle models o inees aes consuced fom he daa. 2 Mendoza (99 Schmi-Gohe (998 van Wincoop (993 Beaudy and Guay (996 and Bao and Sala-i- Main (990 use he U.S. and ohe counies 3-monh T-bill ae. Schmi-Gohe (998 and Coeia Neves and Rebelo ( use he S&P 500 index. Gagnon and Unfeh (996 use he Euo-make inees aes on ceificaes of deposi. Kose (998 and Senhadji (998 use he LIBOR ae. Wih espec o pices van Wincoop (993 and Bao and Sala-i-Main (BSM (990 use he CPI Beaudy and Guay (996 use he GNP deflao and Schmi-Gohe (998 uses he GDP deflao. Fo modeling inflaion expecaions he Livingson Suvey as well as many ARMA specificaions have been employed.

3 expecaions bu wih diffeen nominal inees aes. Half of he coelaions ae less han Second as discussed exensively in Ingam Kochelakoa and Savin (IKS (994a 994b 997 models in which he numbe of unobsevable exogenous shocks is less han he numbe of obsevable endogenous vaiables imply ha some of he obsevable vaiables ae elaed deeminisically. This feaue exiss in many small open economy models and is fundamenally inconsisen wih he daa. The models ae singula which implies ha i is no possible o back ou a unique ealizaion of unobsevable exogenous shocks. In such models hee ae an infiniy of ways in which he impoance of shocks even ohogonal shocks in diving business cycles can be calculaed. Finally in any model wih muliple shocks i is possible o deemine he impac of any single shock only by imposing ofen-abiay idenificaion esicions. Fo example one ofen-imposed esicion in models of small open economies is ha domesic shocks ae uncoelaed wih he wold inees ae. Baxe and Cucini (993 p. 432 find ha his assumpion is empiically indefensible. A bes hen only a ange of esimaes coesponding o diffeen idenificaion odeings of he shocks can be obained on he impoance of wold inees ae shocks. The pupose of his pape is o pusue an alenaive quaniaive mehodology o assessing he impoance of wold eal inees aes on small open economies. We coninue o employ a sandad dynamic sochasic small open economy model (augmened o include pefeence and depeciaion shocks. Howeve ahe han paameeizing a shock pocess and using he model o solve fo he endogenous vaiables we le he model and he endogenous vaiables ell us he exogenous shocks including he wold eal inees ae ha ae consisen wih he model. Specifically we use he model s Eule equaions daa on he model s endogenous vaiables as well as esimaed decision ules fo he capial sock and ne foeign asses o ecove he exogenous shocks implied by he model and he daa. 3 Then o compue he impoance of hese backed-ou shocks in diving business cycles we pefom vaiance 3 Ou mehodology daws fom wok by Ingam Kochelakoa and Savin (994a 994b Hall (986 Pakin (988 and Lee (996 among ohes. Ingam Kochelakoa and Savin (IKS (994a back ou exogenous shocks of a nonsingula closed economy eal business cycle model o examine he impoance of he poduciviy shocks. To sudy he cyclical behavio of home poducion IKS (997 geneae ealizaions of make and non-make hous. Using a simila mehodology Baxe and King (998 back ou he ealizaions of poduciviy and pefeence shocks and Amble and Pague (994 back ou he ime seies of depeciaion shocks. Smih and Zin (997 esimae he policy funcions in a closed economy eal business cycle model o geneae ealizaions of oupu consumpion and employmen. Thee ae ohe appoaches o esolving he singulaiy poblem. In ode o ensue ha he numbe of unobsevable exogenous shocks equals he numbe of obsevable endogenous vaiables measuemen eo can be added. See fo example McGaan (994. 2

4 decomposiions. By aleing he odeing of he shocks we geneae a ange of esimaes on he impoance of each of he shocks. To a lage exen hen ou mehodology eveses he sandad appoach. Moeove ou appoach deals wih all hee difficulies highlighed above. Fis we avoid he poblems associaed wih calculaing he appopiae wold eal inees ae; ou backed-ou inees ae measues ae consisen wih he model and he daa. Second because ou model is nonsingula we can evaluae he impoance of he wold eal inees ae in businesses cycles wihou violaing any elaionships implied by he model. Thid by using shocks ha ae consisen wih he model and by examining all possible odeings of shocks we do no need o ake a paicula sand on he elaionship beween hem no on hei ohogonaliy. We apply ou mehodology o quaely Canadian daa fom 96: o 996:4. Ou backed-ou wold eal inees ae measue is quie diffeen fom poxies consuced fom he daa. Ou vaiance decomposiions indicae ha wold eal inees ae shocks can play a significan ole in explaining Canadian business cycle flucuaions. If wold inees aes shocks ae odeed fis hey explain 33% of Canada s oupu vaiaion. They can also accoun fo a significan facion of vaiaion in Canada s exenal balances: up o 62% (57% of he vaiaion in ne expos (ne foeign asses is explained by hese shocks. These quaniaive findings conas shaply wih he esuls of Mendoza (99 and Schmi-Gohe (998. Howeve hei esuls ae qualiaively simila o ou findings and hey ae quaniaively simila o he vaiance decomposiion esuls we obain when eal inees aes ae odeed las. The es of his pape is oganized as follows: in secion 2 we pesen ou dynamic sochasic small open economy model. In secion 3 we calibae he model o Canada and pesen ou mehodology on ecoveing he exogenous shocks. Ou esuls ae pesened in secion 4 and secion 5 concludes. 2. The Model Ou model is based on he sandad small open economy eal business cycle model. 4 epesenaive household maximizes expeced lifeime uiliy given by: The 4 Mendoza (99 was he fis small open economy eal business cycle model. See also Coeia Neves and Rebelo ( Schmi-Gohe (998 Lee (996 Sadka and Yi (996 Kose (998 and Senhadji (998 fo he use of dynamic small open economy models in evaluaing he oles of diffeen shocks. Simila models have been used exensively in he lieaue on he ineempoal appoach o cuen accoun behavio. See Baxe (995 fo a suvey of dynamic geneal equilibium business cycle models of open economies and hei use in sudying he souces and ansmission of inenaional business cycles. 3

5 f KT T [ c l ] E E J 0 0 J ( whee c is consumpion in peiod l is leisue K is a ime-vaying pefeence shock T is he consumpion shae paamee E is he discoun faco and J is he household s coefficien of elaive isk avesion. 5 The economy poduces an inenaionally adable good y accoding o: y z k D n D 0 D (2 whee k is he domesic capial sock a he beginning of he peiod n = -l is labo hous D govens he shae of income accuing o capial and z is he echnology shock. Following Baxe and Cucini (993 we specify he following law of moion fo capial: k ( G k I( k i k (3 whee i is invesmen G is an exogenous depeciaion shock and I (. epesens he sandad adjusmen cos funcion wih I (.! 0 I (. c! 0 and I (. cc 0. The epesenaive household has access o wold capial makes o boow and lend foeign financial asses. Ne foeign asses A evolve accoding o: A nx ( A (4 whee nx is ne expos measued in unis of he domesic consumpion good and is he exogenously deemined sochasic isk-fee eal inees ae fom peiod - o. To peven he epesenaive household fom playing a Ponzi game we impose he condiion: lim E0 ( A of ( 0 (5 Finally he aggegae esouce consain is: c i nx d y. (6 5 Noe ha we use a consan discoun faco ahe han he endogenous discoun faco in Mendoza (99 and Schmi-Gohe (998. Endogenous discoun facos ae used o ensue ha models of small open economies have a saionay sochasic seady sae. Howeve ou appoach does no equie us o solve fo he model s seady-sae o fo he dynamics aound he seady-sae. Moeove because Coeia Neves and Rebelo ( use a consan discoun faco he esul ha inees aes ae no impoan is appaenly obus o he ype of discoun 4

6 In ou model hee ae fou exogenous shocks he wold eal inees ae and a echnology shock which ae he shocks in Mendoza s model as well as a pefeence shock and a depeciaion shock. 6 Because ou model has fou obsevable endogenous vaiables (consumpion invesmen labo hous and ne expos we need fou exogenous shocks o insue ha he model is non-singula. Singula models ha is models wih fewe exogenous unobsevable vaiables han endogenous obsevable vaiables imply deeminisic elaionships beween he obsevable vaiables. These elaionships ae clealy violaed in he daa (wheneve he vaiance-covaiance maix of he daa is non-singula. 7 We subsiue (2 ino (6 and subsiue he esuling expession fo ne expos ino (4. The epesenaive household hen maximizes: max E f [ c l ] E J 0 0 subjec o KT T J c i A ( A d z k D n D (O k ( G k I( k i k (O2 whee O and O2 ae he LaGange muliplies. The fis ode condiions ae: K ( ( ( T J T J c : KTc ( n O 0 (7 n : c K T( J ( T ( n (T( J O z k D ( D n D 0 (8 i : wi O O 2 wi 0 (9 faco. This lae infeence is consisen wih Kim and Kose (999 who show ha a model wih a fixed discoun faco geneaes simila business cycle implicaions o one wih an endogenous discoun faco. 6 Ou shocks ae he same as hose in Lee (996. Sockman and Tesa (995 employ pefeence shocks in a wocouny business cycle model. Amble and Pague (994 employ depeciaion shocks in a closed economy eal business cycle model. Geenwood Hecowiz and Huffman (988 sudy a model whee he maginal efficiency of invesmen is a sochasic shock ha is simila o he depeciaion shocks we conside hee. 7 IKS sae ha using a singula model when he vaiance-covaiance maix of he daa is nonsingula is equivalen o solving a se of inconsisen linea equaions; hee is no soluion. (IKS 994a p. 46 5

7 ª y i i wi k : O 2 EE «O D O 2 { I( ( G } k k k wk º» ¼ 0 (0 A : O EE > O 0 ( Equaions (7 and (8 yield: ( D y n c ( T ( n KT (2 and equaions (9 and (0 yield: M O y i i I } ª w EE «O D M O { I( ( G k k k wk º» ¼ (3 wi whee M. wi ¹ Equaion ( govens he dynamics of ne foeign asses. Equaion (2 equaes he maginal ae of subsiuion beween consumpion and leisue o he maginal poduc of labo. Equaion (3 is he ineempoal efficiency condiion peaining o he domesic capial sock. 3. Recoveing he Exogenous Shocks 3.. Paamee Calibaion We calibae ou sucual paamees o coespond o he exising eal business cycle lieaue. Following Backus Kehoe and Kydland (992 he consumpion shae paamee T is se o 0.34 which is consisen wih allocaing on aveage 30 pecen of he endowmen of non-sleeping ime o labo make aciviies. The isk avesion paamee J is se o.5; his is an inemediae value beween he commonly used values of 2 and (logaihmic uiliy. Following Mendoza (99 and Schmi-Gohe (998 he shae of capial income in he poducion D is se o The discoun faco and he iniial value of he depeciaion shock ae se o and especively; boh values ae widely employed in eal business cycle models calibaed o quaely daa. (See fo example King Plosse and Rebelo 988. We specify he following funcional fom fo he adjusmen cos funcion: i i I( Z( Z2 k k Z 3 6

8 The adjusmen cos paamees Z Z 2 and Z 3 ae chosen so ha he iniial equilibium of he model is he same as ha wihou adjusmen coss. This implies ha I ( i / k i / k and I ( i / k c. In addiion I ( i / k cc is se so ha he elasiciy of he maginal adjusmen cos funcion [ ( / (i / k is equal o 5. This is he benchmak value used by Baxe and Ic Icc Cucini (993. Togehe hese hee condiions deemine he values of Z Z 2 and Z 3. We examine he sensiiviy of ou esuls o diffeen paameeizaions in secion Solving fo he Shocks The sandad eal business cycle appoach involves calibaing he model s paamees specifying focing pocesses of he exogenous shocks and hen solving he model. The model s soluion would hen be used o deive he fis and second momens of inees calculae impulse esponses o compue vaiance decomposiions. Ou appoach eveses his mehodology: ahe han poduce simulaed ime seies fo endogenous vaiables we use he obsevable endogenous vaiables and he ohogonaliy condiions implied by he Eule equaions o ecove he exogenous shocks ^ z K G ` consisen wih he endogenous vaiables. We ea consumpion invesmen labo hous and ne expos as obsevable; howeve we ea he wo endogenous sae vaiables k and A as unobsevable. 8 To solve fo hese wo vaiables we esimae he policy funcions fo capial and ne foeign asses. We specify he * * following appoximae policy funcions k k ( \ and A A ( \ 2 s s : ln(k + = \ + \ 2 ln(c + \ 3 ln(k + \ 4 ln(z + \ 5 ln (k + \ 6 G - A + = \ 2 ln(c + \ \ 23 ln(z + \ 24 ln (K + \ 25 G + \ 26 ln (i As in Lee (996 we choose appoximae policy funcions ha ae compuaionally convenien and include mos of he elevan sae vaiables. 9 The effec of addiional lagged vaiables is accouned fo by he inclusion of c. The exclusion of he wold eal inees ae in he policy 8 While daa on hese wo vaiables exis we believe hese daa because hey ae calculaed as accumulaed flows ae poo counepas o he conceps of capial and ne foeign asses. In he case of capial invesmen flows ae ypically accumulaed using depeciaion aes ha ae assumed consan acoss diffeen ypes of capial and ove ime. Also no valuaion adjusmens ae ypically made. In he case of ne foeign asses valuaion adjusmens ae made bu diffeen adjusmens poduce diffeen numbes. Accoding o he Bueau of Economic Analysis depending on whehe cuen cos valuaion o make valuaion is used he U.S. ne foeign asse (invesmen posiion a yeaend 998 was -$.2 illion o -$.5 illion. Moeove he ne invesmen income fom he U.S. posiion was only abou -$7 billion which implies eihe ha he $4.9 illion in U.S. asses aboad wee eaning a consideably highe ae of eun han he $6.2 illion foeign asses in he U.S. o ha he asse socks wee pooly measued. 9 We expeimened wih seveal policy funcions o assess he sensiiviy of ou esuls o changes in funcional foms. These changes have lile effec on ou main findings. 7

9 8 funcion fo capial allows us o decease he dimensionaliy of he poblem; we ae able o esimae \ and \ 2 sequenially ahe han simulaneously. Replacing k + and A + wih ou appoximae policy funcions we esimae he sample analogs of (3 and ( given below: ¹» ¼ º «ª w w T i Z k k i k i k y T 2 2 } ( ( { G I I O D O O E (4 ( 2» ¼ º «ª T i Z A nx A T O O E (5 whee D T O J T J K T ( ( ( ( ( y n n c and 2 ¹ w w i I O O Z and Z 2 ae (p x and (p 2 x vecos of insumens. We employ a genealized mehod of momens esimao (GMM o esimae he paamees \ fom equaion (4 and \ 2 fom equaion (5. 0 Ou insumen vecos ae: nx h h z z c c Z 2 G G K K H H h h z z c c c Z G G K K H H whee ĉ is he gowh ae of c in peiod and whee H- and H2 - ae he lagged eo ems fom he esimaion. Fom he esimaed policy funcions ou model s equaions and iniial values k 0 A 0 G- and 0 we can ecove he shocks ^ z K G`. Equaion (2 above idenifies he seies of pefeence shocks (K. To obain he ohe shocks as well as ou esimaes fo k + and A + we employ equaions (2 (3 and (4 and ou esimaed policy funcions (s k * \ and (s A 2 * \. Fo example fom equaion (2 and he iniial k 0 we obain z 0. We can hen back ou k fom he esimaed policy funcion and we use k o obain z and so foh Daa 0 In addiion o Lee (996 Smih and Zin (997 and Beauchemin (996 specify appoximae policy funcions and hen esimae hem by GMM. K 0 is se by assuming he seady-sae vesion of (3 and using daa on invesmen. 0 equals /E - and G- is se o A 0 is se by assuming he seady-sae vesion of (4 holds fo 96:. We uncae he fis 8 daa poins fom he ecoveed shocks so ha he emaining pa of he seies is less sensiive o ou choice of saing values.

10 Seasonally adjused quaely values of consumpion invesmen and ne expos fo Canada fom 96: o 996:4 ae dawn fom he IMF s Inenaional Financial Saisics (IFS naional accoun seies. Consumpion is household consumpion expendiues; invesmen is he sum of goss capial fomaion and invenoy adjusmens; ne expos is he diffeence beween expos and impos of goods and sevices. Oupu y is he sum of c i and nx. 2 We conve hese daa o eal pe capia values by using he GDP deflao (990 pices fom he IFS and populaion daa dawn fom he Bank of Inenaional Selemens daabase. Seasonally adjused quaely labo hous and civilian employmen daa ae dawn fom he OECD. 3 Following King Plosse and Rebelo (988 oal hous woked n is defined as he poduc of hous woked pe week in he manufacuing seco and he employmen ae nomalized by he weekly ime endowmen. 4. Resuls In his secion we fis examine he popeies of ou backed ou shocks. In so doing we povide some economic inuiion on how ou model woks. We also compae ou backed ou inees ae seies wih measues consuced fom he daa. Finally we examine he elaive impoance of ou fou exogenous shocks in inducing business cycles in Canada. 4.. Popeies of he Exogenous Shocks The coefficiens fom esimaing equaions (4 and (5 and hei associaed sandad eos ae given in Table 2. Because he numbe of insumens exceeds he numbe of esimaed paamees we ae able o conduc a es of he ove-idenifying esicions. Fo each equaion he null hypohesis ha he ove-idenifying esicions ae saisfied is no ejeced a he 0% significance level. Figue plos he fou backed-ou exogenous shocks and Table 3 pesens volailiy and co-movemen popeies of hese shocks. 4 They show ha he wold eal inees ae is he mos volaile of he fou shocks wih a sandad deviaion.5 imes lage han ha of he 2 In ou model hee is no ole fo govenmen expendiues. Hence following Wason (99 King Plosse Sock and Wason (99 and Beaudy and Guay (996 we exclude govenmen expendiues fom ou measue of aggegae oupu. 3 The labo hous daa is manufacuing hous woked pe week and is dawn fom he OECD s Main Economic Indicaos. The civilian employmen daa is dawn fom he OECD Saisical Compendium on CD-ROM. This daa is seasonally adjused fom 965: o 996:4. We impue he seasonally adjused daa fo 964:4 by muliplying he ecipocal of he 4-quae gowh ae fom 964:4 o 965:4 of he non-seasonally adjused employmen level by he 965:4 seasonally adjused employmen level and similaly fo 964:3 964:2 96:. 4 Following he sandad pacice in he eal business cycle lieaue we deend he seies using Hodick and Pesco (HP (997 file. 9

11 depeciaion shock and abou 8 imes lage han ha of he pefeence and echnology shocks. 5 Table 3 also shows ha he coelaion coefficien of he wold eal inees ae shock wih he echnology shock and he depeciaion shock is 0.38 and 0.32 especively. These coelaions ae consisen wih he findings in Baxe and Cucini (993. In hei wo-couny model calibaed o epesen a lage economy and a small economy hey find ha flucuaions in he wold eal inees ae ae coelaed wih domesic shocks. Coelaions beween ou shocks and macoeconomic vaiables ae pesened in Table 4. We focus on he coelaions involving he wold eal inees ae. The coelaion beween oupu and he wold eal inees ae is We noed ealie ha he echnology shock and he wold eal inees ae shock ae posiively coelaed. This helps explain why a posiive coelaion beween oupu and he wold eal inees ae shock can be geneaed. Thee is also a posiive coelaion (0.52 beween he wold eal inees ae shock and ne expos. All else equal highe eal inees aes imply moe savings and less invesmen leading o geae ne expos. The echnology shocks ae no pesisen; hence he posiive coelaion beween he wold inees ae and echnology shocks is pobably no song enough o induce changes in savings and invesmen o compleely offse he diec effec of he highe inees ae. Finally he coelaion beween he eal inees ae and consumpion is posiive lagely because wold inees ae shocks ae posiively coelaed wih domesic poduciviy shocks. We examine he sensiiviy of ou esuls wih espec o changes in he paamees of he model. In paicula we sudy whehe he esuls in Tables 3 and 4 ae obus o changes in he isk avesion coefficien he discoun faco he elasiciy of he maginal adjusmen cos and he shae of capial income in oal oupu. In geneal we find ou esuls o be quie obus. Fo example changes in he paamees do no affec he signs of he coelaions beween he wold eal inees ae and oupu: inees aes ae always weakly pocyclical. While changes in he paamees affec he volailiy of he shocks hei effecs on he co-movemen popeies of he shocks ae quie small. I is woh compaing some of he popeies of ou inees ae measues wih he popeies of alenaive measues. Table 5 pesens compaisons involving he fou ex ane 5 Fom Figue.2 we see ha he depeciaion shocks ae highly vaiable and occasionally negaive. See Amble and Paque (994 and Ingam Kochelakoa and Savin (994a fo a discussion of occasionally negaive depeciaion and highly vaiable depeciaion aes. They ague ha a composie capial seies epesens many highly subsiuable capial goods whose maginal poducivies need no move ogehe. Thus hee is subsiuion acoss capial ypes wih fixed bu diffeing depeciaion aes and he composie depeciaion ae can be highly vaiable. 0

12 inees aes pesened in Table. While he volailiy of ou inees ae measue is simila o he ohe measues hee is vey lile coelaion beween he ohe measues and ou measue. 6 Also he alenaive inees ae measues end o be negaively coelaed wih oupu bu ou model-geneaed inees ae is posiively coelaed wih oupu. This finding is he same as in Beaudy and Guay s (996 closed economy famewok. Howeve he coelaions wih ne expos and invesmen end o be boadly simila acoss he diffeen inees ae measues. Summaizing ou inees ae shock diffes fom he alenaive measues on wo impoan dimensions bu he co-movemen popeies coespond o basic economic inuiion Impoance of Shocks in Business Cycle Flucuaions In a muli-shock model measuing he conibuion of any single shock o business cycle flucuaions is difficul because he shocks ae coelaed wih each ohe as we have shown fo Canada. The sandad appoach in he RBC lieaue which examines each shock in isolaion fom he ohe shocks can hen yield misleading infeences. Ou appoach is o apply a vaiance decomposiion mehod analogous o wha is employed in he veco auoegession (VAR lieaue. 7 Following he usual VAR seing we pefom vaiance decomposiions in ou famewok by imposing a ecusive odeing scheme ha geneaes ohogonal shocks fom he coelaed shocks. 8 Because he ode of pecedence of he shocks is cucial o deemining he shocks elaive impoance in explaining he vaiance of a paicula macoeconomic vaiable and because we have lile pio infomaion on which odeing o employ we compue he conibuion of each shock fo all possible odeings (24. To illusae le G K ] = T denoe he veco of ime seies of ou fou shocks. [ z The odeing G K ] indicaes ha he eal inees ae is fis in pecedence any [ z conempoaneous coelaion beween and he ohe shocks is assigned o and he 6 This finding is simila o findings in Beaudy and Guay (996 and van Wincoop ( See Ingam Kochelakoa and Savin (994a 994b Cochane (994 and King (995 fo exensive discussions of he sandad appoach and is shocomings. IKS (994a fo example focefully ague ha hee is no way o ge a definiive answe o he quesion of how much vaiaion in oupu can be aibued o echnology shocks. Ou vaiance decomposiion mehod is closely elaed o hose employed in Ingam Kochelakoa and Savin (994a McGaan (994 Koupaisas (997 and Kose ( Ou appoach employs he familia Choleski decomposiion. I is possible of couse o pefom ohe decomposiions such as hose employed in Claida and Gali (994 and ohe papes. Howeve he idenificaion esicions in hese papes ypically involve linkages beween nominal and eal vaiables i.e. money shocks have no effec on oupu. Ou seing involves only eal shocks and i is difficul o hink of inuiive esicions ha would involve a shock having zeo effec on one of ou vaiables. Hence we focus on he moe adiional iangula decomposiions. Pesaan and Shin (998 and ohes have developed genealized vaiance decomposiions in which ohogonalized shocks ae no equied. Howeve one dawback of his appoach is ha he vaiance decomposiions do no add up o.

13 pefeence shock is las only ha pa of K uncoelaed wih he ohe shocks is assigned o K. We obain he vaiance decomposiion of oupu ino he fou exogenous shocks by unning he following egession y L l 0 b L L L z G K l l bez le l beg le l bek le l H l 0 l 0 l 0 which we can ewie as: y { y y z y G y K H whee L is he numbe of lags and e z l G e l and K l e ae he esiduals fom he egessions of on he veco [... L ] of G l on [... L... z z z L ] and of K l on z l [ L z z z L G G G L vaiance of H... ] especively. As L becomes vey lage he va( H goes o zeo because cuen and lagged values of he fou shocks accoun fo all of he vaiaion in oupu flucuaions. Fo each egession we se he lag lengh a he smalles numbe fo which va( H <0.0va(y. The facion of he vaiance of oupu explained by each shock is hen given by: q z va( y va( y z q va( y va( y q G G va( y va( y q K va( y va( y K Hence he sum of he conibuions of he shocks is one. We follow his pocedue fo all weny-fou odeings and hen epea i fo five ohe macoeconomic vaiables. The esuls of ou vaiance decomposiions ae pesened in Table 6. The able gives he maximum median and minimum pecenage of vaiaion in each vaiable ha is explained by each shock. Noe ha fo each vaiable and each shock he ange of vaiances is lage indicaing a good deal of sensiiviy o he odeing assumpions. Fo example echnology shocks explain as much as 78% of oupu vaiaion which occus when i is odeed fis and as lile as 9.5% of oupu vaiaion which occus when i is odeed las. The hid column of he able suggess ha inees ae shocks exe hei lages effec on ne expos and ne foeign asses and can accoun fo ove 50% of he flucuaions in hese vaiables. The median vaiance aibuable o inees aes was abou 35% fo hese wo vaiables. The medians also indicae ha inees ae shocks accouned fo moe vaiaion in ne 2

14 foeign asses han he ohe shocks and hey accouned fo moe vaiaion in ne expos han all bu he pefeence shock. Even when inees aes ae odeed las hey sill explain ove 2% of he vaiaion in ne expos and ne foeign asses. The able also shows ha inees ae shocks can accoun fo up o 22%-33% of he flucuaions in oupu invesmen consumpion and labo hous. The median vaiance aibuable o inees aes is abou 4%-23% fo hese fou vaiables. Examining he impac of he ohe shocks we see ha ou esuls sugges ha echnology shocks end o explain he lion s shae of oupu and invesmen vaiaion and pefeence shocks end o explain moe consumpion vaiaion han do he ohe shocks. Depeciaion shocks have hei geaes impac on invesmen and labo hous. Ou findings on he impoance of depeciaion and pefeence shocks mio esuls in Amble and Pague (994 and Sockman and Tesa (995 who find ha inoducing depeciaion (pefeence shocks ino a one-couny (wo-couny eal business cycle model especively impoves he fi of he model o he daa. Ou main esuls ae no oo sensiive o depaues fom he benchmak paameeizaion. Fo example as he isk avesion coefficien inceases fom.5 o 5 he pecenage of oupu vaiance explained by he wold eal inees ae shock deceases. The dop occus because he volailiy of he backed-ou inees ae shock declines. Changes in he elasiciy of he adjusmen cos and of he shae of capial income in oal income also do no have any majo impac in he esuls. The conibuion of he eal inees ae o explaining ne expos and ne foeign asses exhibis simila anges as hose lised in Table 6. A his poin i is insucive o compae ou esuls o hose of Mendoza (99 Schmi- Gohe (998 and Coeia Neves and Rebelo (CNR 995 especially he wo fome sudies because hey wee also based on Canadian daa. We find ha he wold eal inees ae shock can accoun fo up o 33% 57% and 62% of oupu ne foeign asse and ade balance vaiaion in Canada. By conas Mendoza (99 p.809 finds ha inees ae shocks have only minimal effecs on model vaiables. Schmi-Gohe (998 uses impulse esponses o assess he impoance of inees ae shocks (diven by changes in U.S. oupu o Canada. She finds ha he inees ae ansmission mechanism alone canno geneae sufficienly song oupu and employmen esponses elaive o he daa. In addiion CNR conclude ha inees ae shocks exe small effecs on oupu consumpion and hous woked. Hence ou esuls clealy sugges a much songe ole han pevious sudies fo inees ae shocks in geneaing macoeconomic flucuaions in small open economies. 3

15 Because ou mehodology is consideably diffeen fom hei mehodologies hee could be many easons why ou esuls could diffe fom heis. Ou esimaed inees ae measue is quie diffeen fom he poxies ha hei shock pocesses ae chaaceized fom. We allow fo moe shocks han jus inees ae and echnology shocks. In addiion we do no ake a sand on he elaion beween he shocks o on he ohogonaliy of he shocks. Neveheless we implemen one sensiiviy analysis o assess whehe he way we geneae ou inees ae shocks o he way we calculae he conibuion of hese shocks o macoeconomic volailiy is moe impoan in diving ou esuls. We engage in he same vaiance decomposiion execises bu we eplace ou inees ae measue wih alenaive inees ae measues including he U.S. T- Bill ae he S&P 500 eun and a weighed aveage of seveal developed counies inees aes. We use he same backed ou pefeence depeciaion and poduciviy shocks as in he oiginal execises. We find ha ha he conibuion of inees aes o explaining macoeconomic volailiy deceases. Fo example he median conibuion of inees aes o he volailiy of ne expos and of foeign asses is abou 5% compaed o abou 35% in he oiginal decomposiions. Howeve he median conibuion of inees aes o oupu and consumpion volailiy deceases only slighly o 2% fom 4% (oupu and o 6% fom 7% (consumpion. If he conibuion of inees aes had fallen o zeo hen ha would have suggesed ha he way we geneae he inees ae shocks is impoan and ha he esuls ae no diven by ou muliple-odeing vaiance decomposiions. If he conibuion of inees aes had emained unchanged hen ha would have suggesed ha ou vaiance decomposiions ae impoan and ha he esuls ae no diven by he way we geneaed he shocks. Ou findings ae beween hese wo exemes suggesing ha ou main esuls ae due o boh feaues of ou mehodology he backed-ou shocks and he muliple-odeing vaiance decomposiions. Despie he diffeences in mehodology howeve hee ae seveal similaiies in he esuls. The benchmak model in Mendoza (99 involves only echnology shocks. When inees ae shocks ae added he conibuion o macoeconomic flucuaions is quie small. Fo example he sandad deviaion of oupu ises fom 2.8% o 2.84%. This is consisen wih ou esuls when inees ae shocks ae odeed las. We find ha hey accoun fo only 0.2% of oupu flucuaions and less han 7% of he flucuaions in consumpion hous and invesmen. Fom impulse esponses CNR find ha compaed o echnology shocks inees ae shocks exe a elaively lage effec on ne expos and a elaively smalle effec on oupu. Fom ou vaiance decomposiions we obain his finding as well. Ou esuls sugges ha while he 4

16 median conibuion of inees ae shocks o he volailiy of oupu is abou 5% is median conibuion o he volailiy of ne expos is abou 35%. Finally Mendoza (99 finds ha as he sandad deviaion of inees ae shocks inceases o abou five imes he sandad deviaion of echnology shocks flucuaions in oupu and invesmen also incease. The sandad deviaion of ou inees ae shock is an even lage muliple of he sandad deviaion of ou echnology shock. We sumise his helps incease he facion of oupu and invesmen flucuaions aibuable o inees aes. 9 Summaizing we find ha inees ae shocks can be impoan in explaining flucuaions paiculaly flucuaions in ne expos and ne foeign asses in a small open economy. This is in conas o he esuls of seveal ecen quaniaive sudies on his opic. Howeve ou esuls ae qualiaively simila o hese esuls indicaing he pesence of simila economic mechanisms a wok. Also ou esuls become quaniaively simila o hei esuls when inees ae shocks ae odeed las in ou vaiance decomposiions. 5. Conclusion Mos models of small open economies posi seveal channels by which wold shocks ae ansmied o he small economy. Of hese channels he inees ae channel is ofen given special pominence. Hence i is supising ha seveal ecen quaniaive analyses applying he sandad eal business cycle appoach have found ha flucuaions in wold inees aes have lile effec on domesic invesmen oupu ne expos and ne foeign asses. In his pape we employ an alenaive appoach o quaniaively addess he impoance of inees ae shocks in a small open economy. The key poin of depaue is ha we use he model and daa on he endogenous vaiables o back ou he exogenous shocks ha ae consisen wih he model while he sandad appoach posis saisical pocesses fo he exogenous shocks (based on poxies of hese shocks and feeds hese pocesses hough he model o geneae he endogenous vaiables ha ae consisen wih he model. We view ou appoach as addessing difficulies in he sandad appoach aising fom he quesion of he appopiae poxy fo wold eal inees aes and fom he singulaiy of he models ypically employed. A second feaue of ou famewok 9 Thee is one addiional similaiy beween Mendoza (99 and ou esuls. Mendoza s Table 5 shows ha even when he coelaion beween echnology shocks and inees ae shocks is 0.9 he momen popeies of key vaiables ae basically unchanged. We noe ha when he shocks ae his highly coelaed vaiance decomposiions ha ode inees aes fis (second will end o aibue much (lile of he vaiaion in oupu and ohe vaiables o inees aes. 5

17 is ha we deal wih he fac ha he exogenous shocks ae coelaed by pefoming vaiance decomposiions fo all possible odeings of he shocks. We apply ou appoach o Canada a couny ha has been sudied quie hooughly via he sandad appoach. Ou findings indicae ha wold inees ae shocks can have lage effecs paiculaly on ne expos and ne foeign asses bu also on oupu. Ou sensiiviy analysis indicaes ha boh feaues of ou mehodology he backed-ou shocks and he muliple-odeing vaiance decomposiions ae diving ou findings. We conclude ha he wold eal inees ae can be an impoan ansmission mechanism of wold business cycles o small open economies. Neveheless he esuls of he ohe ecen eseach ae qualiaively simila o ou esuls and quaniaively simila o he lowe bound of ou vaiance decomposiions occuing when he wold eal inees ae is odeed las. In ou model we do no include fiscal and moneay policy shocks which ae impoan in undesanding business cycle dynamics in open economies. I would be useful o apply his mehodology o examine he ole of hese shocks in a moe complex small open economy model. 6

18 REFERENCES Amble S. and A. Paque 994 Sochasic depeciaion and he business cycle Inenaional Economic Review vol. 35 no Backus D. K. P. J. Kehoe and F. E. Kydland 992 Real business cycles Jounal of Poliical Economy Bao R. and X. Sala-i-Main 990 Wold eal inees aes NBER Macoeconomics Annual 5-6. Baxe M. 995 Inenaional ade and business cycles in: Handbook of Inenaional Economics Gene Gossman and Kenneh Rogoff (eds Amsedam: Noh Holland. Baxe M. and M. Cucini 993 Explaining saving-invesmen coelaions Ameican Economic Review Baxe M. and R. King 998 Poducive exenaliies and business cycles fohcoming Euopean Economic Review. Beauchemin K. R. 996 Whihe he sock of public capial? woking pape Univesiy of Coloado a Boulde. Beaudy P. and A. Guay 996 Wha do inees aes eveal abou he funcioning of eal business cycle models? Jounal of Economic Dynamics and Conol Claida R. and J. Gali 994 Souces of eal exchange ae flucuaions: How impoan ae nominal shocks? Canegie-Rochese Confeence Seies on Public Policy Cochane J. H. 994 Shocks Canegie Rochese Confeence Seies on Public Policy Coeia I. J. C. Neves and S.Rebelo 992 Business cycles in Pougal: Theoy and evidence in J. Amaal D. Lucena and A. Mello (eds. The Pouguese Economy Towads 992. Kluwe -64. Coeia I. J. C. Neves and S.Rebelo 995 Business cycles in a small open economy Euopean Economic Review Gagnon J.E. and M.D. Unfeh 995 Is hee a wold eal inees ae? Jounal of Inenaional Money and Finance Geenwood J. Z. Hecowiz and G. Huffman 988 Invesmen capaciy uilizaion and he eal business cycle Ameican Economic Review Hall R. E. 986 The ole of consumpion in economic flucuaions in R J. Godon ed. The Ameican business cycle: coninuiy and change Univesiy of Chicago Pess

19 Hansen L. 982 Lage sample popeies of genealized mehod of momen esimaion Economeica Hecowiz Z. 986 The eal inees ae and aggegae supply Jounal of Moneay Economics Hodick R. J. and E. C. Pesco 997 Poswa U. S. business cycles: an empiical invesigaion Jounal of Money Cedi and Banking Ingam B. 995 Recen advances in solving and esimaing dynamic sochasic macoeconomic models in ed. K. Hoove Macoeconomeic Developmens Tensions and Pospecs Kluwe Academic Publishes Ingam B. N. Kochelakoa and N. E. Savin 994a Explaining business cycles: A muliple shock appoach Jounal of Moneay Economics Ingam B. N. Kochelakoa and N. E. Savin 994b Raional expecaions shock esimaion mimeo Univesiy of Iowa. Ingam B. N. Kochelakoa and N. E. Savin 997 Using heoy fo measuemen: An analysis of he cyclical behavio of home poducion Jounal of Moneay Economics Kim S.H. and M.A. Kose 999 Dynamics of open economy business cycle models: undesanding he ole of he discoun faco manuscip Bandeis Univesiy. King R.G. C. I. Plosse and S. Rebelo 988 Poducion gowh and business cycles I: The basic neoclassical model Jounal of Moneay Economics King R. G. C. I. Plosse J. H. Sock and M. W. Wason 99 Sochasic ends and economic flucuaions Ameican Economic Review King R. G. 995 Quaniaive heoy and economeics Fedeal Reseve Bank of Richmond Economic Quaely Kose M. A. 998 Explaining business cycles in small open economies woking pape Bandeis Univesiy. Koupaisas M. 997 Noh-Souh business cycles woking pape Fedeal Reseve Bank of Chicago. Lee J. S. 996 Change of cyclical paen in developing counies: evidence fom Koea woking pape The Bank of Koea. McGaan E.R. 994 The macoeconomic effecs of disoionay axaion Jounal of Moneay Economics

20 Mendoza E. G. 99 Real business cycles in a small open economy Ameican Economic Review Obsfeld M. and K. Rogoff 995 The ineempoal appoach o he cuen accoun in: Handbook of Inenaional Economics Gene Gossman and Kenneh Rogoff (eds Amsedam: Noh Holland. Pakin M. 988 A mehod fo deemining whehe paamees in aggegaive models ae sucual Canegie-Rochese Confeence Seies on Public Policy Pesaan M.H. and Y. Shin 998 Genealized impulse esponse analysis in linea mulivaiae models Economics Lees Pesco E. C. 986 Theoy ahead of business cycle measuemen Fedeal Reseve Bank of Minneapolis Quaely Review Sadka J. C. and K. Yi 996 Consume duables pemanen ems of ade shocks and he ecen U.S. ade deficis Jounal of Inenaional Money and Finance Ocobe Schmi-Gohé S. 998 The inenaional ansmission of economic flucuaions Jounal Inenaional Economics Senhadji A. 998 Dynamics of he ade balance and he ems-of-ade in LDCs: The S- cuve Jounal of Inenaional Economics Smih G. W. and S. E. Zin 997 Real business cycle ealizaions Canegie-Rochese Seies on Public Policy Sockman A. and L. Tesa 995 Tases and Technology in a Two-Couny Model of he Business Cycle: Explaining Inenaional Comovemens Ameican Economic Review van Wincoop E. 993 Real inees aes in a global bond economy Woking pape no. 52 Innocenzo Gaspaini Insiue fo Economic Reseach. Wason M. W. 99 Measues of fi calibaed models Jounal of Poliical Economy

21 Table Popeies of he Real Inees Rae Measues (Conempoaneous Coelaions In. ae USA W SP L USA W.85 SP.2.23 L y : y=usa U.S.A. T-Bill ae; y=w weighed ae of developed economies; y=sp S&P 500 eun; y=l Libo ae. T-Bill ae weighed ae and Libo ae daa ae consuced using he IFS. The S&P 500 eun index is aken fom he Ibboson Associaes Daabase. In consucing ou ex ane eal inees aes we assume ha inflaion follows a andom walk. We use changes in he CPI as ou measue of inflaion. The daa is quaely fom 963: o 994:4. 20

22 Capial Sock Table 2 Policy Funcion Coefficiens Asse Holdings Paamee Esimae Paamee Esimae \ \ (0.445 (0.7 \ (0.498 \ (0.4 \ (0.508 \ (0.7 \ (0.057 \ (0.067 \ (.729 \ (.27 \ (.29 \ (0.089 J-Saisic=.766 [3.366] J-Saisic= [3.366] Numbes in paenheses ae sandad eos associaed wih he paamees. The J-Saisic is he chi-squae es value fo he numbe of ove-idenifying esicions (8 in each case. The numbes in backes ae he ciical values o ejec he null hypohesis ha he ove-idenifying esicions hold a he 0% level of significance. The policy funcions ae esimaed fom quaely daa fom 963: o 996:4. 2

23 Table 3 Popeies of he Esimaed Shocks (Volailiy and Coelaions Vaiable Volailiy Coelaion wih G G K z K z The echnology (z and pefeence (K shocks ae logged and hen deended by he Hodick and Pesco (HP (00 file. The wold inees ae ( and depeciaion (G shocks ae in levels. Volailiy is measued as he sandad deviaion of he (deended seies. Table 4 Coelaion wih Macoeconomic Vaiables Coelaion w/ G K z Oupu Consumpion Invesmen Ne Expos Labo Hous The echnology (z and pefeence (K shocks ae logged and hen deended by he Hodick and Pesco (HP (00 file. The wold inees ae ( and depeciaion (G shocks ae in levels. All macoeconomic vaiables excep ne expos ae logged and hen HP(00 fileed. Ne expos is nomalized by oupu hen HP(00 fileed. The daa ange fom 963: o 996:4. 22

24 Table 5 Compaison of Real Inees Rae Shock wih Alenaive Inees Rae Measues Model USA W SP L Volailiy Coelaion wih Real Inees Rae Shock Coelaion wih Macoeconomic Vaiables Oupu Consumpion Invesmen Ne Expos Labo Hous y : y=usa U.S.A. T-Bill ae; y=w weighed ae of developed economies; y=sp S&P 500 eun; y=l Libo ae. T-Bill ae weighed ae and Libo ae daa ae consuced using he IFS and he S&P 500 eun index is aken fom he Ibboson Associaes Daabase. Consumpion invesmen and ne expos ae dawn fom he IFS; fo he consucion of he labo hous seies see fn.. All macoeconomic vaiables excep ne expos and he inees ae measues ae logged and hen HP(00 fileed. Ne expos is nomalized by oupu hen HP(00 fileed. The inees ae measues ae in levels. The daa ange fom 963: o 996:4. 23

25 Table 6 Vaiance Decomposiions z G K Saisic Oupu [max min] [ ] [ ] [ ] [39.78.] median Consumpion [max min] [ ] [ ] [ ] [ ] median Invesmen [max min] [ ] [ ] [ ] [ ] median Labo Hous [max min] [ ] [ ] [ ] [ ] median Ne Expos [max min] [ ] [ ] [ ] [ ] median Ne Fo. Asses [max min] [ ] [ ] [ ] [ ] median In each cell he shae of he vaiable s vaiance explained by a paicula shock is epoed. max min and median efe o he uppe bound lowe bound and median of he vaiance decomposiions acoss all odeings. The echnology (z and pefeence (K shocks ae fis logged and hen deended by he Hodick and Pesco (HP (00 file. The wold inees ae ( and depeciaion (G shocks ae in levels. Consumpion invesmen and ne expos seies ae dawn fom he IFS daa labo hous seies is aken fom he OECD Main Economic Indicaos. All macoeconomic vaiables excep ne expos and ne foeign asses ae logged and hen HP(00 fileed. Ne expos and ne foeign asses ae nomalized by oupu hen HP (00 fileed. Daa ange fom 963: o 996:4. 24

26 : 67: 7: 75: 79: 83: 87: 9: 95: Figue.. Technology Shocks and Oupu. Quaely echnology shocks implied by he model (dashed line and measued oupu (solid line fo each peiod fom 963: o 996:4. Each seies is nomalized by is 963: value : 67: 7: 75: 79: 83: 87: 9: 95: Figue.2. Depeciaion Shocks. Quaely depeciaion shocks implied by he model fom 963: o 996:4. 25

27 : 67: 7: 75: 79: 83: 87: 9: 95: Figue.3. Pefeence Shock and Hous. Quaely pefeence pefeence shocks implied by he model (solid line and measued hous (dashed line fo each peiod fom 963: o 996:4. Each seies is nomalized by is 963: value : 67: 7: 75: 79: 83: 87: 9: 95: Figue.4. Real Inees Rae Shocks. Annualized quaely eal inees aes implied by he model fom 963: o 996:4. 26