International Business Cycles and Exchange Rates

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1 Revew of Intenatonal Economcs, 7(4), , 999 Intenatonal Busness Cycles and Exchange Rates Chstan Zmmemann* Abstact Models of ntenatonal eal busness cycles ae not able to account fo the hgh volatlty of expots, mpots, the tade balance, and the tems of tade. By ntoducng exogenous exchange ate movements n addton to standad technologcal shocks, the model pesented hee comes much close to eplcatng the elatvely hgh volatlty obseved n the data whle also mpovng othe moments.. Intoducton Models of ntenatonal eal busness cycles wth stochastc technologcal nnovatons ae geneally unable to account smultaneously fo the hgh volatlty of expots, of mpots, of the tade balance, o of the tems of tade. It can be suspected that the lack of exchange ate vaablty mght be the eason fo the dscepancy wth the data. Ths pape ncludes exchange ate consdeatons n a thee-county eal busness cycle model. Some authos (e.g., Baxte and Stockman, 989; Gelach, 988) have obseved that some economc aggegates, especally the tade aggegates mentoned above, ae moe volatle unde flexble exchange ates than unde fxed ones. Whle othe vaables mght play a ole, one can ndeed pesume that exchange ates ae elevant. Table shows the volatlty of vaous aggegates fo sx countes dung fxed and flexble exchange ate egmes. Many economc aggegates ae moe volatle n the second peod fo the countes pesented, and the statstcs fo the wold busness cycle clealy show that the economes ndeed became moe volatle. Consdeng that exchange ates have been moe volatle, too, a lnk between them and the busness cycle seems natual. Theefoe, I want to ncopoate some monetay effect nto the standad eal busness cycle model. Schlagenhauf and Wase (992, 995) consdeed a dynamc stochastc geneal equlbum model wth fnancal ntemedaes wth a cash-n-advance constant, theeby focng households and fms to hold foegn cuences befoe they puchase mpoted goods. Even wth vaous assumptons about the nfomaton stuctue of the model, they wee not able, by fa, to match volatlty and pesstence of eal and nomnal exchange ates. Wth cash-n-advance constants and wth exchange ates detemned on asset makets, Camchael (994) was able to eplcate the coelaton of eal and nomnal exchange ates as well as the volatlty faly well, but wthout the obseved pesstence of exchange ates. Fnn (996) matched the mentoned coelaton and pesstence, but not the volatlty, wth a cash-n-advance model ncludng shocks to the magnal effcency of nvestment. Many othes have attempted to eplcate the moments of exchange ates wth less stuctual models, also wthout success. * Cente fo Reseach on Economc Fluctuatons and Employment (CREFE), Unvesté du Québec à Montéal, PO Box 8888, Downtown Staton, Montéal Canada H3C 3P8. E-mal: zmmemann.chstan@uqam.ca. Ths s a evsed veson of the thd chapte of my dssetaton at Canege Mellon Unvesty. Steve Amble, Fnn Kydland, José-Vícto Ríos-Rull, Kjetl Stoesletten, Susanne Weum, and semna patcpants at the Austan Natonal Bank have povded nsghtful comments, but ae not esponsble fo any eos. I acknowledge the suppot of the Wllam Lame Mellon Foundaton. Blackwell Publshes Ltd 999, 08 Cowley Road, Oxfod OX4 JF, UK and 350 Man Steet, Malden, MA 0248, USA

2 INTERNATIONAL BUSINESS CYCLES 683 Table. Standad Devatons of Vaous Aggegates unde Fxed Exchange Rates (960.I 972.IV) and (n talcs) unde Flexble Exchange Rates (973.I 99.II) Tade Tems of Output Consumpton Investment Expots Impots balance tade Austala.60 a a Canada.29 a a Fnland.83 a a Gemany.83 b b Japan.47 b b South Afca.63 a a UK.8 a a US.30 b b Euope c Noth Ameca d Wold e a GDP. b GNP. c Aggegaton of Fnland, Gemany, and the UK. d Aggegaton of Canada and the US. e Aggegaton of the economes above. Data ae HP-flteed, as n all subsequent tables. The queston I am askng hee s: Can the ncluson of exchange ate shocks n an ntenatonal eal busness cycle model explan the hgh volatlty of mpots, expots, and the tade balance? To answe ths, we need the moments of the exchange ates to be as close as possble to the data. As shown above, exstng stuctual models of the exchange ate cannot lve up to that task. In contast to Schlagenhauf and Wase (992, 995), I choose theefoe to take the exchange ate movements as exogenous, theeby guaanteeng that the behavo matches the data. In ths othewse eal model, the nonneutalty of the exchange ates ases fom the tmng of mpot decsons. Impots take some tme to be delveed, and the exchange ate elevant fo the bllng n foegn cuency s detemned at delvey. The quantty decson s based on antcpatons of futue exchange ates that cannot be hedged. I consde a model economy to eplcate thee economc aeas tadng wth each othe: Euope, Noth Ameca, and Japan. Secton 2 descbes some facts about the busness cycle n these aeas. Secton 3 pesents the model and the equlbum condtons. Secton 4 goes though the paametezaton. Secton 5 dscusses the esults of the smulated economes. Secton 6 concludes. Blackwell Publshes Ltd 999

3 684 Chstan Zmmemann 2. Busness Cycle Popetes of the Data The developed countes account fo a vast majoty of wold tade, and they tade mostly wth each othe. In the followng, I wll theefoe examne the busness cycle popetes of the OECD countes gouped n thee economc aeas: Euope, Noth Ameca, and Japan. The Appendx shows the souces of the data as well as the aggegaton pocedue. The fst lnes of Tables 2 4 gve the majo busness cycle statstcs of these thee economc aeas. The man featues of the data ae: Consumpton s less volatle than output. Ths s not the case fo Japan, clealy a Table 2. Volatlty Statstcs fo Thee Economc Aeas Tade Tems of Output Consumpton Investment Expots Impots balance tade Data Euope N. Ameca Japan Benchmak economy Euope (0.2) (0.06) (0.43) (0.39) (0.27) (0.03) (0.85) N. Ameca (0.6) (0.07) (0.52) (0.49) (0.30) (0.04) (0.89) Japan (0.9) (0.0) (0.85) (0.48) (0.32) (0.08) (0.77) No exchange ate movements Euope N. Ameca Japan Constant technology Euope N. Ameca Japan Elastcty of substtuton of 0.50 Euope N. Ameca Japan Elastcty of substtuton of 4.00 Euope N. Ameca Japan Expot bllng (p = 0) Euope N. Ameca Japan Impot bllng (p = ) Euope N. Ameca Japan Blackwell Publshes Ltd 999

4 Table 3. Coelaton Statstcs fo Thee Economc Aeas INTERNATIONAL BUSINESS CYCLES 685 Tade Tems of Consumpton Investment Expots Impots balance tade Data Euope N. Ameca Japan Benchmak economy Euope N. Ameca Japan No exchange ate movements Euope N. Ameca Japan Constant technology Euope N. Ameca Japan Elastcty of substtuton of 0.50 Euope N. Ameca Japan Elastcty of substtuton of 4.00 Euope N. Ameca Japan Expot bllng (p = 0) Euope N. Ameca Japan Impot bllng (p = ) Euope N. Ameca Japan specal case f we look at Table. Investment s much moe volatle than output. Expots and mpots have oughly the same volatlty as nvestment, but ae moe volatle n Japan. The standad devaton of the tade balance pesented hee excludes ntenal tade (tade among membes of the same economc aea). Agan, the volatlty s hghe n the smalle county, Japan. The standad devaton of the tems of tade ae agan n the ode of that of nvestment, hghe fo Japan. Blackwell Publshes Ltd 999

5 686 Chstan Zmmemann Table 4. Coss-Coelatons of Output and Consumpton n Thee Economc Aeas Output Consumpton Euope Noth Ameca Japan Euope Noth Ameca Japan Data Euope N. Ameca Benchmak economy Euope (0.8) (0.8) (0.5) (0.) N. Ameca (-0.02) (0.4) No exchange ate movements Euope N. Ameca Constant technology Euope N. Ameca Elastcty of substtuton of 0.50 Euope N. Ameca Elastcty of substtuton of 4.00 Euope N. Ameca Expot bllng (p = 0) Euope N. Ameca Impot bllng (p = ) Euope N. Ameca Investment s moe coelated to output than consumpton. Impots ae moe coelated to output than ae expots. The tade balance s countecyclcal. The tems of tade ae negatvely, although not stongly, coelated wth output. The coss-coelatons of output ae geneally hghe than those of consumpton. Pevous models of ntenatonal eal busness cycles have been able to eplcate seveal of the featues descbed above; see, among othes, Backus et al. (992, 994), Stockman and Tesa (995), and Zmmemann (997). They have, howeve, faled so fa to epoduce the hgh volatltes of the tade vaables (mpots, expots, tade balance as well as tems of tade), a falue that could at least patly be coected by the ncluson of exchange ates. Also, they do not qute gve a coelaton of output wth nvestment that s hghe than wth consumpton.also, they fal to eplcate the countecyclcalty of the tems of tade. Anothe weak pont s that they geneate vey low coss-coelatons of output, a featue shaed by the cuent model. Blackwell Publshes Ltd 999

6 3. The Model Economy Thee countes ae populated by dentcal agents wth fms shang the same technology wthn the county. In each, a epesentatve agent maxmzes hs utlty ove an nfnte hozon. The labo foce and bult captal ae mmoble acoss countes, whle consumpton and nvestment goods ae taded acoss countes wthout estctons. The sze of an economy s defned by the numbe of ts agents. Fo expostonal puposes, all vaables ae scaled to own-county pe capta unts. I use a model wth thee countes to pevent symmetc tade balance movements occung systematcally: wth a two-county model, wheneve a county has a tade balance suplus the othe one must have a defct, but such systematc behavo s not obseved n the data. The expected utlty of the epesentatve agent n each county s epesented by the functonal fom whee c t s the consumpton of an agent n county at tme t, n t s the shae of tme devoted to maket actvtes n at t, and 0 < b <, 0 < m <, g <. Each county specalzes n the poducton of one good, y t, usng captal k t and labo n t. The poducton functon F( ) s Cobb Douglas, wth a stochastc technology paamete z t : whee È t E0 Â b U( ct, - nt ), Î t= 0 m -m Uc ( t, - nt )= ct ( -nt ) g, g y = z F( k, n ), t t t t q -q Fk (, n) = kn, 0< q <. t t t t [ ] INTERNATIONAL BUSINESS CYCLES 687 The poducton s used fo domestc consumpton and nvestment as well as fo expot. Let y jt be the amount of goods pe nhabtant of county j used n j and poduced n county at tme t. Defne futhemoe a as the numbe of agents of county. We have then that, fo any county, total poducton equals the total consumpton and nvestment of ths poducton at home and aboad: a y t = a y t + a j y jt + a k y kt, π j π k. Impots and domestc poducton ae used fo consumpton c t and nvestment x t. In ode to take nto account the fnte elastcty of substtuton between goods of dffeent ogns, an Amngton (969) aggegato G( ) s used. Ths functon allows fo coss-haulng (smultaneous mpots and expots), by attachng a label of ogn to the goods, and ntoduces nonpefect substtuton between the labeled goods. A county then specalzes n the poducton of the home good, but uses thee dffeent goods fo consumpton and nvestment. The Amngton aggegato s used wdely n the ntenatonal economcs lteatue, although t eles on elastctes that ae dffcult to assess; but no othe aggegato s convncng enough and homogeneous of degee one. I add the featue that the delvey of mpoted goods takes one quate ( tme-to-shp ), and that the pces ae set at delvey tme. Ths mples that Blackwell Publshes Ltd 999

7 688 Chstan Zmmemann mpot decsons have to be taken wthout knowng the exchange ate at the tme of delvey: c + x = G( y, y, y ), t t t j, t - k, t - whee ( ) Gy (, y, y )= w y + w y + w y, t j, t - k, t - t j j, t- k k, t- - w, w j, w k 0, -. The captal stock depecates at a ate d and s eplenshed by nvestment that takes J quates to be effectve: whee s t, the nvestment on the poject that s ntated n t + J -, becomng effectve n t +. Ths nvestment has the law of moton: s j,t+ = s j+,t, j =, J -. Ths tme-to-buld technology fo captal accumulaton was ntoduced by Kydland and Pescott (982) nto the busness cycle lteatue. All esouces dedcated to buldng captal at tme t ae then aggegated nto total nvestment, assumng that nvestment nto pojects s made evenly ove tme: The technology paamete z t shows hgh pesstence n the data. I captue ths fact by modelng ts law of moton though a VAR() stuctue allowng fo splloves acoss countes as well as seally ndependent, contempoaneously coelated nnovatons e t+ : whee k + = ( -d) k + s x, t t t, t = J J Â j= s jt z = z+ A ( L) z + B ( L) e,, t+ z t z z t+ Èzt Èe z, t+ zt = z t zt = 2, e, + e z2, t+, Î z3t Î e z3, t+ Èa a a Az ( L)= a a a Î a a a. z z2 z3 z2 z22 z23 z3 z32 z33 ÈÈ0 Èu z u z2 u z3 e z,t+ 0, u z 2 u z 22 u z 23. Î Î 0 Î u z3 u z 32 u z33 Èbz bz2 bz3, Bz ( L)= bz bz b 2 22 z23, Î bz3 bz32 bz33 Fo a thee-county famewok, thee ae sx exchange ates. By the law of one pce, fou of them ae endogenously detemned by two exchange ates. If we defne e jk as the exchange ate of the cuency n naton j wth espect to that of naton k, then e jk = /e kj. Moeove, e k = e jk /e j. Say e 2 and e 3 ae the two elevant, exogenous exchange Blackwell Publshes Ltd 999

8 INTERNATIONAL BUSINESS CYCLES 689 ates.as n the case of the technology levels, they move accodng to a VAR() pocess wth coelated nnovatons: whee e = e + A ( L) e + B ( L) e,, e t+ e t e e t+ t e t e t = È et Î 2 e = È e Î 2, +, e, +, ee3, t+ 3t ae ae be be Ae ( L) = È Be L Î 2 ( ) = a a È Î 2,, b b ÈÈ e e,t+ 0 Î È Î 0, Î u e 2 u e 22. The exchange ate entes nto the budget constant of the household. A shae p of the mpots s blled at a pce p j n foegn cuency wth the exchange ate e j and theefoe subject to exchange ate shocks. Also, a shae ( - p ) of the expots s sold n foegn cuency. The maxmzaton poblem of the epesentatve household n each county has fve constants. The fst s the lfetme tade balance equlbum, the second s the lfetme equvalence of ncome and expendtue, the thd s the Amngton aggegato, the fouth s the law of moton of captal, and the ffth s the law of moton of the nvestment pojects: È t m -m max E0 Â ct ( - nt ), t, Jt, b g t, g Î Ï c s n Ô Ô Ìyt, yjt, ykt Ô Ó "> t 0 Ô e2 e22 t= 0 u e u e2 [ ] e2 e22 s.t. s.t. s.t., "t s.t., "t È Ê a ( p p + ( -p ) p e ) y + a ( p p + ( -p ) p e ) y E0 ÂÁ t Î t= 0 Ë ( + t ) È Ê ( p p e + ( -p ) p ) y + ( p p e + ( -p ) p ) y = a E0 ÂÁ t Î t = 0 Ë ( + ) E c È wn t t + ( t + d ) kt È ct + ( / J)Â J j= sjt 0 Â E t = 0 Â t Î t= 0 ( + t ) Î t= 0 ( + t ) J t + Â sjt = ( w yt + wj yj, t- + wk yk, t-), J j= k + = ( -d ) k + s j j t j jt jt jt k k t k kt kt kt, t t t, jt jt t jt kt kt t kt t, ˆ ˆ, s.t., "t, "j < J s j,t+ = s j+,t. Notce that the aguments n the fst constant have multplcatve factos elated to the sze of the countes, as unts of y j ae defned as a shae of output n county j. Dvdng by the sze of county, a, and the domestc pce level, p t, we obtan a constant n eal tems wth nomnal exchange ate shocks coespondng to devatons fom puchasng powe paty: Blackwell Publshes Ltd 999

9 690 Chstan Zmmemann One mght wonde whethe ths specfcaton of the ntenatonal tansacton technology makes sense. Nowadays, mpotes and expotes often hedge the exchange ate sk though swaps o othe nstuments. In the pesent model economy they do not; and f they do, they hedge only wth domestc agents. The sk s then stll bone wthn the county. One may magne the domestc epesentatve agent as a famly of thee: a consume, a poduce, and an exchange ate nsue. The latte caes the exchange ate sk of the othe two, but on aggegate the sk s stll n the famly. Indeed, exchange ate nnovatons coespond ultmately only to an ntenatonal eallocaton of assets. On the poduces sde, the poblem n each county s whee w t s the labo wage and q t s the pce of captal. It follows mmedately fom the fst-ode condtons that n the steady state: Ths mples, wth the fst-ode condtons of the households: c - m w = - n m, so that È Ê ( a / a )( p + ( -p )( p / p ) e ) y + ( a / a )( p + ( -p )( p / p ) e ) y E0 ÂÁ t Î t= 0 Ë ( + t ) È Ê ( p ( pjt/ pt ) ejt + ( -p )) yjt + ( p ( pkt/ pt ) ekt + ( -p )) ykt ˆ = E0 ÂÁ t. Î t= 0 Ë ( + ) q -q max zk t t nt -wn t t - t + d qk t t { kt, nt," t } k c n qqy ( -q) y =, x = dk, w =. + d n = ( -q) y = j j j jt t jt jt k k k kt t kt kt ( -q)( / m). + ( -qm ) - dq( -m) /( + d) The tems of tade, the ato of the pce of mpots to the pce of expots, can be computed fom the equlbum pce of mpots elatve to the domestc good dvded by an expot pce ndex. The elatve pce of each mpot good s defned fo each pa of countes as the ato of magnal utltes: pejt pjt + ( -p ) pt pjt = pt Gyt yj t yk t Gyt yj t yk t = ( ) -,, -,, - È (,, -,, -) b yj t Î yt, - + j Ê y t- ˆ = b w, Á, w Ë yj, t- Uct pt = (, nt ). c t - n m n - m, ( ) [ ], t ˆ Blackwell Publshes Ltd 999

10 INTERNATIONAL BUSINESS CYCLES 69 Fo each county, the aggegate tems of tade p * t ae then defned by p * t y p + y p = y + y jt jt kt kt jt kt a j yjt + ak ykt ( - p ) e ( p / p )+ p a y ( p ) e ( p / p )+ p a y [ ] + [ - ] j jt jt t j j jt k kt kt t k k kt. In the steady state, the tems of tade and the exchange ate ae equal to one, by hypothess. Usng ths fact and the long-tem equlbum of the tade balance, one can nfe the steady-state equlba fo y, y j, and y k : y y y j j j k j = Ê Ê - j Ë Á ˆ Ê ˆ + Á + Ê ˆ + b w w w b w b w w Á Ë w Ë w k Ê Ê = w + w Áb w Á Ë w Ë = Ê b w Ë w Fnally, we defne the tade aggegates n the followng way (note that whle the tade balance s zeo n the steady state, t can be dffeent fom zeo ove the cycle): Ê eal expots: Áp Ë eal mpots: p jt y jt + p kt y kt, k Ê eal tade balance: Áp Ë ˆ Ë Ê - Ê j ˆ k + j Á + Ê ˆ + w w b w b w Á Ë w Ë w Ë + ( - a a p ) pjt j kt k jt jt p p kt kt p e ˆ a y Ê p p e ˆ + + ( - ) Ë a y, j ˆ k + ( - a p ) pjt j kt jt jt p p p e ˆ a y Ê p + + ( - ) Ë p e -pjt yjt -pkt ykt. t + Ê b w Ë w t ˆ What s happenng n ths economy? Agents eact n an optmal way to exogenous shocks. Poductvty shocks geneate poductvty dffeentals, whch nduce the eallocaton of (physcal) captal to the advantaged county. Ths stong esponse of nvestment, stonge than that of poducton, leads to vey pocyclcal mpots, somewhat pocyclcal expots and a countecyclcal tade balance. Exchange ate shocks geneate esponses of a dffeent natue: they affect the ntenatonal allocaton of wealth. Indeed, a shock changes the expenses and ecepts elated to the taded goods. As mpots have been detemned befoe the ealzaton of ths shock, any change n pces affects the budget constant n a way that has to be compensated n the next peods. Futhemoe, these shocks have a hgh degee of pesstence that exacebates ths effect. Fo example, a county expeences a depecaton of ts cuency. Its mpots, whch ae n fxed quanttes, suddenly become moe expensve. A defct towads the est of the wold esults, whch must be compensated ove the next peods because of the ntetempoal budget constant though lowe mpots and hghe expots. Ths mpact of exchange ate shocks on tade s moe dect than the poductvty shocks and s theefoe the souce of nceased volatlty fo ˆ y, ˆ ˆ t y, y. t kt ˆ a a k y kt Blackwell Publshes Ltd 999

11 692 Chstan Zmmemann mpots and expots. Hghly volatle tade s the stylzed fact we ae lookng fo wth ths model economy. 4. Paametezaton I use the condtons of the compettve equlbum as well as esults fom mco studes to detemne some of the paametes o steady-state values of the above model. Let us fst look at paametes common to all countes n the model economy. Along wth Kydland and Pescott (982) and most of the subsequent lteatue, I set b = /( + ) = 0.99, d = 0.025, c/y = 0.75, and the captal stock to 0 tmes quately output. The poducton functon paamete q coesponds, n the steady state, to the shae of captal ncome to total ncome, q = ( + d)q(k/y). We mpose that the tme to buld fo captal, J, s equal to thee quates. Gven that the pce of captal s q = 3 S 3 j=( + ) j- and that k/y = 0, we have that q = We choose the shae of total tme devoted to maket wok, n, to be 30%, and then detemne z such that steady-state output s one (wthout loss of genealty). It s then staghtfowad to establsh the value of m fom the household s fst-ode condtons: m =. + ( +q) [( - n ) / n ]( yc / ) Set the cuvatue of the utlty functon, g, at -. That s a lttle moe cuved than the logathmc functon. The last paamete common to all economc aeas (by assumpton) s the elastcty of substtuton among goods. Set s = /( + ) =.5, as n Backus et al. (994), and as suggested by Whalley (985). The pesent esults ae senstve to ths elastcty, whch s futhemoe not well establshed empcally; and thee ae good easons to beleve t s hghe see Zmmemann (994). I wll theefoe consde altenatve values. Tunng now to the county-specfc paametes, we fst detemne the nne w such that steady-state values of the y j match the aveage mpot shaes fom the data. To ths pupose, we mpose thee constants on the homogenety of the Amngton aggegato and sx constants elated to the steady-state unt pce fo the p j (these last constants ae equvalent to mposng that w j y j - = y j ). The w j ae then detemned by the followng elatons: w by y = by + y + y The Appendx descbes how the mpot shaes have been detemned. Fo the peod , the aveage y j ae, n pecentage of output (the fst ow and column coespond to Euope, the second to Noth Ameca, the thd to Japan): È Î yj y yk y, w j =, w k =. by + y + y by + y + y j k j k j k Assumng a steady-state zeo tade balance, the asymmetes n ths matx mply that the elatve szes of the economc aeas ae 42.8% fo Euope, 43.2% fo Noth Ameca, and 4.0% fo Japan. Ths s vey close to the actual aveage elatve szes fo ths peod, espectvely 4.4%, 43.0%, and 5.6%. Blackwell Publshes Ltd 999

12 INTERNATIONAL BUSINESS CYCLES 693 The law of moton of the technology shocks s establshed fom the Solow esduals of the poducton functon wthout captal nput, the latte movng vey lttle ove the busness cycle, as agued by Backus et al. (992). B z (L) s set to the dentty matx and A z (L) s estmated by egessng the Solow esduals wth the lagged esduals n all thee aeas. The egesson esduals ae then used to detemne V z.the esults ae A z È = , 0, 000V Î z È = Î The spllove matx A z has egenvalues of.005, 0.853, and 0.648, whch may lead to an unstable gowth path. We theefoe modfy a z33 to 0.830, such that the egenvalues ae , 0.852, and Note that the tansmsson of the shocks s qute asymmetc, so Japan has a much smalle mpact on the othe countes than they have on Japan. Ths can be explaned by the smalle sze of Japan see Zmmemann (997). The thee economc aeas have been chosen to make the paametezaton of the exchange ate movements moe staghtfowad. Indeed, Noth Ameca and Japan ae aeas wth vtually one cuency each, the US dolla and the yen. Fndng the laws of moton s then a matte of compang these two cuences wth the vaous Euopean ones and takng aveages. These laws ae smla to those of the technologcal nnovatons, although wth vey dffeent values. Agan, B e (L) s set to the dentty matx. It s found that A e s not sgnfcantly dffeent fom a dagonal matx. We theefoe egess the devatons fom the puchasng powe paty wth the past values wth an AR() setup. The esults ae n Table 5. The paamete values used fo these smulatons ae sze-weghted aveages of the Euopean cuences wth the US dolla and the yen. The pesstence paametes ae espectvely and and the standad eos ae 5.3% and 4.40%. The coelatons of the nnovatons ae set such that they geneate standad devatons fo the exchange ate between the dolla and the yen of 4.80%. The shae of mpoted goods blled n foegn cuency, p, s vey dffcult to assess. Fo example, Webe (993) epoted that, n the case of the fome West Gemany, about 80% of expots wee blled n DM. Howeve, between 43% (980) and 53% (988) of all mpots wee blled n DM: Not only ae the vaous p not equal fo all, but they may also vay acoss t. Futhemoe, Webe found that vehcle cuences wee qute mpotant. Fo the Geman case, about 7% of all mpots came fom the Unted States, but between 22% and 32% wee blled n US dollas. O, % of all mpots came fom Fance, but only 3.5 4% wee blled n Fench fancs. Fo paametezaton puposes, howeve, we have to take a stand. I choose hee that half of all mpots ae blled n foegn cuency, coespondng oughly to the Geman case just descbed: ", p = 0.5. Ths s the last paamete we need to detemne. Ths model economy can be ewtten as a socal planne s poblem wth shocks to the esouce constant stemmng fom the exogenous exchange ate movements. Usng the budget constant (n eal tems) and the tade balance, t s possble to wte a esouce constant whee exchange ate movements eallocate esouces fom one county to anothe, wth pces p t, p jt, p kt, p jt, and p kt endogenously detemned usng the fst-ode condtons of the maket equlbum. We can then use the Kydland and Pescott (982) technque of maxmzng the weghted sum of the epesentatve agents utltes by means of a quadatc appoxmaton. The weghts coespond to the sze, a, of the espectve countes. The model economy s then Blackwell Publshes Ltd 999

13 694 Chstan Zmmemann Table 5. Popetes of Devatons of Exchange Rates fom Puchasng Powe Paty, 973.I 99.II Aganst US$ Aganst yen SD of SD of Coelaton Pesstence nnovaton (%) Pesstence nnovaton (%) of nnovaton Austala (.62) (.30) Austa (.6) (.54) Canada (.30) (.5) Fnland (.74) (0.42) Fance (.29) (.28) Gemany (.47) (.49) Italy (.27) (0.03) Japan (.55) Noway (.66) (.62) Swtzeland (.60) (0.05) UK (.55) (0.34) US (0.57) t-statstcs ae shown n paentheses unde the hypothess of unt pesstence. 3 t m -m max  b Âa ct ( - nt ) g, g ÏÔ nt, ct, sjct, Ô t= Ìyt, yjt, ykt, ÓÔ " t, " Ô = [ ] s.t., "t, " s.t., "t, " s.t., "t c c J q -q a j È Ê pjt + s = z k n + ( - j ) Á J p e ˆ  jt - y Î p a Ë t t jt t t t j= a k È Ê pkt p e ˆ + ( -p k ) kt - y kt -( p jt -) y jt -( p kt -) y kt, a Î Ë t J t +  sjt = ( w yt + wj yj, t- + wk yk, t-), J j= k + = ( -d ) k + s, t t t, jt s.t., "t, "j < J s = s j, t+ j+, t, Blackwell Publshes Ltd 999

14 INTERNATIONAL BUSINESS CYCLES 695 s.t., "t s.t., "t z = z + A ( L) z + e,, t+ z t z t+ e = e + A ( L) e + e,. t+ e t e t+ The a coespond to the szes of the economc aeas mpled fom the mpot shaes. Gven that the vaables ae all n pe capta tems, the socal planne s theefoe maxmzng the sum of the utltes of all agents. Two hunded hstoes of 74 peods each, as n the data, ae computed ntoducng andom shocks on the technology paamete and on the exchange ate. Fo each hstoy, the sees ae detended wth the flte ntoduced by Hodck and Pescott (980). 2 The esultng statstcs ae then aveaged ove the 200 hstoes. 5. Busness Cycle Popetes of the Expemental Economy The paametezaton descbed above poduced the statstcs pesented eale n Tables 2 4 ( Benchmak economy ). In secton 2, ten facts about the busness cycle wee lsted; they ae evewed hee to assess the pefomance of the smulated economy: Consumpton s less volatle than output n all aeas. The hghe volatlty of consumpton n Japan emans an empcal fact to be explaned. Investment s much moe volatle than output n all aeas. Expots and mpots have a standad devaton close to two-thds of that of nvestment. They ae oughly equal n the data. The standad devatons of the tade balance ae n the ange of the data. The volatlty of the tems of tade s hghe than n the data, except fo Japan. Investment s moe coelated to output than consumpton, as n the data. Impots ae ndeed moe pocyclcal than expots. As n the data, the tade balance s negatvely coelated wth output. The tems of tade ae not negatvely coelated wth output, although close to zeo. The coss-coelatons of output ae not hghe than that of consumpton. Some featues of the data ae not eplcated. But the ncluson of exchange ate vaablty has mpoved the pefomance of the model, as we see by unnng a smulaton wthout these exchange ate movements (lowe pats of Tables 2 4). The fluctuatons of the exchange ates gve most of the vaablty to all ntenatonal vaables and add some to nvestment. Consumpton and especally output ae much less affected. But the model s able, wth exchange ate shocks, to geneate fluctuatons n tade aggegates close to o even stonge than those n the data. The volatlty of the tems of tade has not been attaned n any othe ntenatonal eal busness cycle model, fo example the models descbed n Backus et al. (995). Also, the ncluson of exchange ate shocks has gven a bette eplcaton of the fact that the coelaton of output wth nvestment s hghe than wth consumpton. The countecyclcalty of the tems of tade s not acheved, but s gettng close to zeo wth these nomnal shocks. Note also that they allow us to avod the almost pefect coelatons between mpots and output as well as between nvestment and output. Howeve, ths model does a pooe job fo the coelatons of output wth expots. One eason could be that the elastcty of substtuton s too low, as agued n Zmmemann (994). Blackwell Publshes Ltd 999

15 696 Chstan Zmmemann Some addtonal expements have been pefomed to assess the obustness of the model and the accuacy of some paametes. Removng the vaatons n the Solow esduals ( Constant technology ) leaves only nomnal shocks and vey few busness cycle statstcs coespond to the data. Inteestngly, nvestment s stll vey volatle. A tadtonal explanaton fo the hgh volatlty of nvestment n such models s that an ncease n poductvty (mostly a technologcal nnovaton) nduces mpot of nvestment goods. It seems that exchange ate movements can nduce smla flows of nvestment by alteng the poductvty n monetay tems wthout dectly changng t n eal tems. Zmmemann (994) agues that the elastcty of substtuton of.5 may be too low. Zmmemann (997) shows that ths paamete has qute an nfluence on the moments of the tade vaables. It s not dffeent hee. All statstcs, apat fom the volatltes of output and consumpton, ae vey senstve to movng s between 0.5 and 4. So vtually any standad devaton of expots and mpots seems attanable wth some elastcty. Howeve, the coelatons of mpots wth output become apdly unealstc when movng the elastcty hghe than.5. Note, howeve, that consumpton s moe volatle than output n Japan, as n the data, wth s = 4. Fo othe moments, hghe elastctes yeld statstcs close to those of the data, fo example the expots output coelaton, the tems of tade output coelaton, o the volatltes of the tade vaables. The coss-coelatons of output and consumpton, howeve, ae much less affected. Fom ths, I conclude that mpovng futhe the pefomance of ths model s not only a matte of fndng the tue elastcty of substtuton. Anothe paamete that s dffcult to pn down s the shae of mpots blled n foegn cuency, p. As can be seen when two exteme cases ae compaed (p = 0 and p = ), many statstcs vay consdeably. I used p = 0.5, whch may not be appopate as the dscusson of the paametezaton showed. The volatltes of the tade vaables o even consumpton could easly fall n the ange of the data wth p close to zeo, but the coelatons then become less ealstc. 6. Conclusons Stochastc exchange ate movements have been ntoduced nto an ntenatonal eal busness cycle model wth thee countes, n ode to account fo the hgh volatlty of expots, mpots, the tade balance, and the tems of tade obseved n the data. The smulatons wee able to eplcate these featues much bette than models wthout exchange ate shocks, whle also mpovng othe comovements. The esults ae, howeve, qute senstve to some of the paametes, such as the elastcty of substtuton between the taded goods and the shae of mpots blled n foegn cuency. But t s possble that the pefomance of the model can be mpoved wth moe accuate paamete values. Appendx: Souces of the Data All data used fo the paametezaton and fo the busness cycle popetes of the data came fom the OECD database. Some othe souces have been used to ncease the numbe of countes used to aggegate the Euopean aea: the IMF database fo Austa and Fnland, the Statstsk Sentalbyå fo Noway. Data on tems of tade and fo the detemnaton of mpot shaes also come fom the IMF. Fo the busness cycle statstcs, the countes buldng up the Euopean aggegate ae Austa, Fance, Fnland, Gemany, Italy, Noway, Swtzeland, and the UK. The Noth Amecan aggegate s composed by Canada and the US. These data wee agge- Blackwell Publshes Ltd 999

16 INTERNATIONAL BUSINESS CYCLES 697 gated usng the tables fom Summes and Heston (988) on eal output and ntenatonal pces fo 985. Each of the output sees (GDP, GNP fo the US, Japan, and Gemany) s multpled to gve the Summes and Heston fgues. The Euopean GDP s futhemoe adjusted by a constant multplcatve facto to account fo the sze of all Euopean OECD countes. The othe sees ae multpled by the same natonal coeffcents as GDP and then aggegated acoss countes. The tems of tade ae a weghted sum of the ndvdual tems of tade, whee the weght s the county shae to total output at each quate. The tems of tade ae calculated as the ato of unt values of mpot to unt values of expot (f not avalable, the espectve deflatos). The statstcs fo all sees ae fnally computed afte applyng the Hodck and Pescott (980) flte fom 973.I to 99.II, that s 74 peods. Fo the smoothng paamete, we used 600, as usual. The tables fom Summes and Heston (988) have also been used fo calculatng the Wold aggegates of Table. Fo the Solow esduals, the same GDP sees was used as fo the busness cycle statstcs, wth the addton of Sweden to the Euopean aggegate. The Solow esduals wee computed leavng captal constant, owng to the geneal lack of data on quately captal level. The employment data (cvlan employment) ae fom OECD and natonal statstcal offces fom 73.I to 9.II. Refeences Amngton, Paul, A Theoy of Demand fo Poducts Dstngushed by Places of Poducton, IMF Staff Papes 27 (969): Backus, Davd K., Patck J. Kehoe, and Fnn E. Kydland, Intenatonal Real Busness Cycles, Jounal of Poltcal Economy 00 (992): , Dynamcs of the Tade Balance and the Tems of Tade: the J-Cuve? Amecan Economc Revew 84 (994):84 03., Intenatonal Busness Cycles: Theoy and Evdence, n Thomas Cooley (ed.), Fontes of Busness Cycle Reseach, Pnceton: Pnceton Unvesty Pess (995): Baxte, Maanne and Alan C. Stockman, Busness Cycles and the Exchange-Rate Regme: Some Intenatonal Evdence, Jounal of Monetay Economcs 23 (989): Camchael, Benoît, Exchange Rate Detemnaton n a Two-County Model wth Lqudty Shocks, Unvesté Laval Wokng Pape 940 (994). Cumby, Robet E. and Mauce Obstfeld, Intenatonal Inteest Rate and Pce Level Lnkages and Flexble Exchange Rates: A Revew of Recent Evdence, n John F. Blson and Rchad C. Maston (eds.), Exchange Rate Theoy and Pactce, Chcago: Unvesty of Chcago Pess (984):2 5. Fnn, May G., The Equlbum Appoach to Nomnal and Real Exchange Rates, Fedeal Reseve Bank of Rchmond Wokng Pape (996). Gelach, H. M. Stefan, Wold Busness Cycles unde Fxed and Flexble Exchange Rates, Jounal of Money, Cedt and Bankng 20 (988): Hodck, Robet and Edwad C. Pescott, Post-Wa US Busness Cycles: An Empcal Investgaton, Gaduate School of Industal Admnstaton Wokng Pape, Canege Mellon Unvesty (980). Kydland, Fnn E. and Edwad C. Pescott, Tme to Buld and Aggegate Fluctuatons, Econometca 50 (982): Pak, Gonyung, The Role of Detendng Methods n a Model of Real Busness Cycles, Jounal of Macoeconomcs 8 (996): Schlagenhauf, Donald and Jeffey M. Wase, A Monetay, Open-Economy Model wth Captal Moblty, Insttute fo Empcal Macoeconomcs Dscusson Pape 67, Fedeal Reseve Bank of Mnneapols (992). Blackwell Publshes Ltd 999

17 698 Chstan Zmmemann Schlagenhauf, Donald and Jeffey M. Wase, Lqudty and Real Actvty n a Smple Open- Economy Model, Jounal of Monetay Economcs 35 (995):43 6. Stockman, Alan and Lnda L. Tesa, Tastes and Technology n a Two-County Model of the Busness Cycle: Explanng Intenatonal Comovements, Amecan Economc Revew 85 (995): Summes, Robet and Alan Heston, A New Set of Intenatonal Compasons of Real Poduct and Pce Levels: Estmates fo 30 Countes, , Revew of Income and Wealth 34 (988): 25. Webe, Axel A., Exchange Rates, Taget Zones and Intenatonal Tade: The Impotance of the Polcy Makng Famewok, pesented at the Konstanz Semna on Monetay Theoy and Monetay Polcy (993). Whalley, John, Tade Lbealzaton Among Majo Wold Tadng Aeas, Cambdge, MA: MIT Pess (985). Zmmemann, Chstan, Technology Innovatons and the Volatlty of Output: An Intenatonal Pespectve, Cente fo Reseach on Economc Fluctuatons and Employment Wokng Pape 34, Unvesté du Québec à Montéal (994)., Intenatonal Real Busness Cycles among Heteegeneous Countes, Euopean Economc Revew 4 (997): Notes. See, fo example, the fgues n Cumby and Obstfeld (984). 2. Ths flte has been ctczed ecently. Howeve, Pak (996) shows that moment senstvty ognatng n the flte s symmetc between the actual and the smulated data. Blackwell Publshes Ltd 999