Economics Discussion Paper

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1 Economcs Dscusson Paper EDP-057 Busness Cycle Lnkages for he G7 Counres: Does he Lead he World? By Dense R Osborn, Pedro J Perez and Maranne Senser Aprl 005 Correspondance emal dense.osborn@mancheser.ac.uk School of Socal Scences, The Unversy of Mancheser Oxford Road Mancheser M3 9PL Uned Kngdom Combnng he srenghs of UMIST and The Vcora Unversy of Mancheser

2 Busness Cycle Lnkages for he G7 Counres: Does he Lead he World? by Dense R Osborn Unversy of Mancheser Pedro J Perez Unversy of Valenca Maranne Senser Unversy of Mancheser Aprl 005 Keywords: nernaonal busness cycles, smooh ranson models, G7 counres JEL Codes: C3, E3, F0 Ths paper s prelmnary; please do no quoe whou permsson of he auhors. Ths research was suppored hrough a European Communy Mare Cure Fellowshp (programme Improvng Human Research Poenal and he Soco-Economc Knowledge Base IHP-MCFI-99-). The frs auhor graefully acknowledges fnancal asssance from The Mnsero de Cenca y Teconología (SEC ). The second and hrd auhors graefully acknowledge fnancal asssance from he Economc and Socal Research Councl (UK) under gran L Ths research does no reflec necessarly he vews of he fundng bodes.

3 ABSTRACT Ths paper emprcally models he relaonshp beween quarerly busness cycle movemens n he and he oher G7 counres, ncludng an analyss of he wh a European (E5) aggregae. By usng a nonlnear smooh ranson vecor auoregressve framework, he possbly of asymmerc busness cycle lnkages s explored. Dfferen ypes of possble busness cycle lnkages are represened hrough hree nonlnear VAR models for each counry wh he, where hese represen common busness cycle regmes, -led (bu no common) regmes and counry-specfc (or dosyncrac) regmes. In general, hgh annual growh s found o lead o a dsnc busness cycle regme n oher G7 counres compared wh average or low growh. Tess ndcae ha quarerly growh paerns are mporan for oher counres prmarly n he lower regme, wh domesc auoregressve lags hen somemes nsgnfcan.

4 Inroducon Inernaonal busness cycle flucuaons consue a fascnang, and mporan, opc of macroeconomc research. Whle early conrbuons examned he exen of busness cycle correlaons across major ndusralsed counres (see, for example, Ars and Zhang, 997; Backus, Kehoe and Kydland, 995), a number of recen sudes have sough o documen he exsence of a world and/or European busness cycle (ncludng Ars, Krolzg and Toro, 004; Lumsdane and Prasad, 003; Kose, Orak and Wheman, 003) or o model nernaonal neracons (for example, Pesaran, Schuermann and Wener, 003). However, here s also evdence ha hese nernaonal busness cycle relaonshps may no be consan over me, possbly due o ncreased economc negraon n Europe (Ars and Zhang, 997, 999; Inklaar and Haan, 00). Neverheless, he hypohess ha he busness cycle lnkages of mporan European counres wh he have lessened due o European negraon has been called no queson, due o he apparenly closer correlaons beween he and European counres a he begnnng of he weny-frs cenury han durng he 990s (Doyle and Faus, 00; IMF, 00; OECD, 00; Perez, Osborn and Senser, 003). I seems, herefore, ha European negraon provdes a bes only a paral answer o he changng lnkages beween he and oher mporan world economes. Ths paper focuses on busness cycle asymmeres n nernaonal busness cycle lnkages hrough he use of a nonlnear sysem of equaons for he bvarae relaonshp beween quarerly growh n he and ha of oher G7 counres. In he lgh of European economc negraon, we also examne he relaonshp beween he and an aggregae seres for he European Unon. In conras o he many sudes ha consder nernaonal busness cycle movemens n a lnear framework, our nonlnear model perms he crosscounry lnks o be asymmerc, n he sense hey can aler as a funcon of he regme, whch s defned n erms of annual growh. As he domnan counry n he world economy, our analyss focuses on he role of he, and we nvesgae wheher regmes n growh affecs each of he oher G7 counres. More specfcally, n he conex of regmes deeced n a smooh ranson vecor auoregressve (STVAR) sysem, we examne hree possbles for regmes n growh, namely: ha he counry (or he E5) has common regmes wh he, ha he regmes dffer bu are neverheless led by he, and ha he regmes are counry-specfc. The only sudy of whch we are aware ha examnes smlar ssues n a nonlnear framework s Phllps (99). However, ha analyss s based on a Markov swchng nonlnear model and s more

5 resrcve n assumng ha he dynamcs are consan over regmes. Our preference for he STVAR approach s based on he flexbly wh whch he underlyng regmes can be defned, ncludng he possbly of nermedae (or mulple) regmes ha arse from he use of a connuous regme ndcaor. Alhough smooh ranson models are wdely appled n her unvarae form, nonlnear STVAR sysems are relavely rare. Perhaps closes o our applcaon s Anderson and Vahd (00), who esmae bvarae STVAR sysems for oupu growh and he erm srucure of neres raes n each of he G7 counres. Oher applcaons of hese models nclude Huh and Lee (00), Wese (999) and Rohman, van Djk and Franses (00). Wh he excepon of Anderson and Vahd (00), hese sudes assume ha he same ranson funcon drves he regmes n all equaons of he STVAR. However, one of he key quesons n our analyss s he relaonshp beween he regmes n growh and ha of he oher G7 counres, so ha he naure of he ranson funcon(s) s gven a parcular focus below. The nex secon deals our model specfcaon and he esmaon procedure, ncludng he nerpreaon of he hree ranson funcons employed n our analyss. Secon 3 deals our resuls, presenng evdence of nonlneary n he bvarae relaonshps, as well as dscussng he mplcaons of he esmaed models. Fnally, Secon 4 offers some conclusons.. STVAR Models We model he quarerly growh n (seasonally adjused) real GDP from 970:I o 00:I, as shown n Fgure ; deals of he seres are gven n he Daa Appendx. As noed above, our bvarae models examne he relaonshps beween he and he European Unon (represened by he aggregae seres E5), and beween he and each of he G7 counres. Our frs sep s o esmae a wo counry lnear VAR for he growh rae of he and each of he oher counres (or he E5). We examned he Akake, Schwarz (Bayesan) and Hannan-Qunn lag lengh selecon crera, o a maxmum lag of 6. On he bass of hese resuls, we adoped a VAR() specfcaon for he subsequen modellng. The E5 seres s an aggregae for he 5 counres ha were members of he European Unon pror o he enlargemen of May 004. The Akake s he leas parsmnous of hese crera and, usng a common sample for all esmaons, hs ndcaed one or wo lags, excep for Ialy and Japan where hree lags were ndcaed. However, boh Schwarz and Hannan-Qunn ndcaed one or wo lags for he Ialy/ and Japan/ models. To ease comparson across models, we adoped wo lags n all cases. 3

6 The remander of secon frs dscusses he naure of he STVAR models examned, before urnng o he praccal ssues of nonlneary esng and STVAR model esmaon. Fnally, we dscuss he nerpreaon of hypohess ess we conduc on he coeffcens of he esmaed models.. The ST-VAR Model for Busness Cycle Lnkages Based on he wo lags of he lnear specfcaon, he STVAR model we employ has he form: X = α F = α 3 F = ( z ) = β β 3 α = ( z ) α 4 β 4 δ 4 X ε = = = δ X β 3 δ X = = δ X ε where represens he quarerly growh rae and X s he growh rae n he oher counry. The dsurbances ε = (ε, ε ) are assumed o be whe nose wh E(ε ε ) = Ω. In hs model, regmes are capured hrough he logsc ranson funcons F F ( z ) [ ˆ = exp{ γ ( z c) / σ } ] ( z ) = [ exp{ γ ( z c ) / ˆ σ }] whch sasfy 0 F (z ). As s clear from (), hese regmes are defned by he values of he ranson varables z, z, and he logsc form ensures ha hey are connuous and monooncally ncreasng funcons of he ranson varables. For nerpreaon purposes, s convenen o dsngush he regmes ha apply a he exremes, where F (z ) = 0 and F (z ) =. We laer refer o hese as he lower and upper regmes, respecvely. Snce he nercep and all coeffcens of an equaon n () can change as a funcon of he ranson varable, hs model allows he possbly ha he dynamcs of growh vares over regmes. Neverheless, an advanage of hs smooh ranson framework over one wh bnary regmes (such as he Markov swchng model, used by Phllps, 99) s ha s suffcenly flexble o allow a mxure of regmes, where 0 < F (z ) <. For example, F (z ) = 0.5 when z = c, so ha hs value delvers a model wh coeffcens gven by an equal weghng of he dsnc coeffcens ses ha apply n he wo exreme regmes. The slope parameer γ n () dcaes he slope of he ranson funcon, wh F (z ) approachng a bnary ndcaor varable, wh hreshold value c, as γ. Convenonally for hese models, and o ad () () 4

7 comparson across models, he exponenal erm n () s sandardsed by he sample sandard devaon of he correspondng ranson varable, σˆ ( =, ). In order o examne he role of he n he nernaonal propagaon of busness cycle movemens, we consder hree possbles for z and z as follows:. Common regmes. Common regmes are capured by resrcng he equaons of () so ha he same ranson funcon s used for each equaon, namely F (z ) = F (z ). As he larges economy n he world, we regard as a pror more plausble ha hese regmes orgnae from he han he oher counry, so ha he ranson varable n hs case depends on he busness cycle, bu he parameers c and γ are obaned hrough a jon esmaon of he wo equaons.. -led regmes. Alhough hs case specfes z = z o depend on growh, he values of γ, γ and c, c are no resrced o be dencal n he wo ranson funcons of (). Thus, we allow he busness cycle o deermne he regmes of he oher counry, bu hese regmes are no dencal across counres. 3. Counry-specfc regmes. We allow each counry o have s own dosyncrac busness cycle regmes. Snce he frs equaon of () refers o he and he second equaon o anoher G7 counry or he E5, z depends on growh, whle z depends on he counry s own growh rae. Snce we model GDP growh, he busness cycle measures we employ for he ranson varable(s) are based on hs varable. However, s unclear wheher quarerly, sxmonhly or annual growh raes provde he approprae measure of busness cycle movemens 3. We nally consdered each of hese, bu for all counres he annual growh rae gave he sronges evdence of nonlneary. Furher, snce annual growh s a relavely smooh seres, he regmes may be expeced o capure general movemens n economc growh. Therefore, we use annual GDP growh as he ranson varable n all models consdered here.. Nonlneary Tess, Model Specfcaon and Esmaon Pror o underakng nonlnear modellng, we employ ess of he null hypohess of lneary, usng wh he lnear VAR as he baselne. As spel ou n, for example, Wese (999) or Rohman e al. (00), hs can be consdered as a es of he null hypohess H 0 : γ = γ = 0 n (). However, some parameers of () are undenfed under hs null hypohess, and hs 3 As usual, hese growh raes were measured as he dfference over one, wo or four quarers (as approprae) of he logarhm of real GDP. 5

8 problem can be avoded by akng a Taylor seres approxmaon o he ranson funcon. We use a lnear approxmaon o conserve degrees of freedom n hs VAR conex, so ha he approxmang model s X = α = α = θ z 3 θ = 0 β 0 z 3 = β = θ z θ z = = δ X δ X 3 and he es for nonlneary s a es of he sgnfcance of he erms nvolvng z, z n (3). = θ =, θ z, We conduc a es for nonlneary n he sysem, whch consders he jon null hypohess H 0 : θ j = 0 (j = 0,, 4; =, ) n (3). Le Ω = e ' T and Ω z X ˆ 0 X ε ε e / be he esmaed varance-covarance marces of resduals from he resrced and unresrced sysems, respecvely. Then, under he null hypohess of lneary, he lkelhood rao sasc { log Ωˆ ˆ 0 log Ω } ˆ = (3) U U e e '/ T LR = T s asympocally dsrbued as χ wh 0 degrees of freedom. We follow he proposal of Sms (980) and replace T by T - c, where c s he number of parameers esmaed per equaon n he unresrced sysem 4. Alhough based on a frs-order Taylor seres approxmaon, hs es s a naural exenson o he vecor case of he nonlneary es recommended by Teräsvra (994) for unvarae smooh ranson models. Each STVAR model s esmaed by nonlnear leas squares. In order o oban relable sarng values, parcularly for he γ and c parameers n (), we nally underake a grd search over a range of possble sarng values. To be more precse, we esmae each equaon of (3) by ordnary leas squares over a grd of values of γ =,,, 000, 00,, 0,000. For he locaon parameer c, we rm he exreme 5% of observaons from eher end of he observed dsrbuon of values for z and hen ake 00 equally spaced pons. For he common regmes model, he grd search jus oulned s underaken over he parameers of he sngle ranson funcon n he conex of he sysem of wo equaons. Each se of parameers delvers an mpled ranson funcon and, condonal on hs funcon, ordnary leas squares (separaely for each equaon) s used o oban correspondng 4 In pracce, we esmae he unresrced model usng wo observaons less hen he resrced model, snce each z s a lagged annual dfference, resulng n wo addonal sarng observaons beng requred compared wh he resrced model. The sample sze T used n compung he es sasc s ha for he unresrced model. 6

9 esmaes of all oher coeffcens n (). The se of values ha mnmses Ωˆ log provdes he nal values for a nonlnear esmaon underaken over all parameers, ncludng hose of he ranson funcon(s). For he -led regmes and counry-specfc regmes models, dsnc ranson funcons are used n each equaon and hence he prelmnary grd search over he parameers of he relevan ranson funcon s performed separaely for each equaon. The nal values used for he (sysem) nonlnear esmaon are hose ha mnmse he resdual sum of squares of he equaon..3 Hypohess Tess n he STVAR Models The models usng ranson funcons n boh equaons, namely he frs wo cases dscussed n Secon., are nesed. Consequenly, (condonal on he presence of nonlneary n he equaons) a convenonal lkelhood rao sasc for he valdy of he resrcons s vald. We conduc such a es for common regmes below 5. To focus on he dfferen regmes mpled by F (z ) = 0 and F (z ) =, () can be equvalenly reparameerzed as [ ] ( ) [ ] ( ). ) ( ) ( X z F X z F X X z F X z F ε φ φ α φ φ α ε φ φ α φ φ α = = = = = = = = = = (4) In order o consder he role of n leadng growh n oher G7 counres, our prncpal neres focuses on he second equaon of (4). For a gven ranson funcon F (z ), causaly ess can be conduced for he role of quarerly growh n he separae regmes hrough ess of (5) 0, = = r φ r φ 5 Anderson and Vahd (998) presen a es for common nonlneary based on a Taylor-seres approxmaon o he ranson funcon. However, snce we have used only a frs-order approxmaon, we prefer o base he es on esmaed nonlnear models. We do no use he es of Vahd and Engle (997) for codependen cycles, snce hs s based on a lnear specfcaon. 7

10 whch s compued separaely for r = 0,. In a smlar way, he mporance of auoregressve erms n he separae regmes can be examned as a es of φ r φ 3 = r 4 = 0, (6) whch s agan consdered for he separae regmes r = 0,. The hypoheses of (5) and (6) examne he possbly dsncve roles played by quarerly and domesc growh raes over regmes. In order o nvesgae wheher such dfferences may apply, we also examne regme nvarance for quarerly growh hrough he jon es φ = 0 0 = φ, φ φ. (7) Smlarly, consancy of he auoregressve lags s examned hrough φ = = φ3, φ4 φ4 (8) whle he correspondng es for nvarance of he nerceps over regmes consders α 0 = α. (9) Snce hese ess of (7)-(9) examne only sub-ses of coeffcens, hey do no consue overall ess for he presence of nonlneary 6, and hence hey can be conduced usng he convenonal (asympoc) χ dsrbuon. We also perform analogous causaly and nvarance ess o hose of (5) o (9) for he equaon n each sysem. Alhough parameersed here n erms of he represenaon of (4), equvalen lnear resrcons exs n erms of (). All hese es are conduced as Wald ess Resuls Before we urn o he esmaed models, Table repors subsanal evdence of nonlneary n he bvarae VAR models, wh he es sascs sgnfcan a 0 percen n all cases. For France and E5, he use of lagged annual growh as he ranson varable n boh 6 Noe ha we canno perform a es ha all coeffcens n (4) vary over regmes, snce hs consues a es for he presence of nonlneary and hence (snce hey are regme-dependen) he coeffcens are no denfed under he null hypohess. Each of hese ess on sub-ses of coeffcens s vald, condonal on he presence of nonlneary relang o oher coeffcens. 7 As a check, we esmae boh () and (4), wh he ess performed usng he approprae resrcons on he parameers of each. 8

11 equaons leads o more sgnfcan rejecon of nonlneary han he use of own growh as he ranson. On he oher hand, for Japan he oppose s rue. In he cases of Canada, Germany he UK and, o a lesser exen, Ialy, he smlar sgnfcance of he wo ses of resuls n Table makes dffcul o denfy he approprae ranson varables. Based on hese resuls, we esmae STVAR models for he hree cases of common busness cycle regmes, -led regmes and counry-specfc regmes, as dscussed n Secon.. The focus n he fnal wo subsecons s he naure of he mpac of he oupu growh on he oher G7 counres and Europe (secon 3.) and wheher he economy can be consdered closed wh respec o oher counres (secon 3.3). 3. Overvew of Esmaed STVAR Models Pror o consderng he mplcaons of he esmaed STVAR models, Table summarses her sysem goodness-of-f accordng o he log deermnan of he esmaed dsurbance covarance marx and presens he resuls of he es for common regmes. Noe ha snce he same number of parameers are esmaed n he models wh -led regmes and counryspecfc regmes, he log deermnan values can be compared for hese models. A comparson across he models wh dfferen numbers of parameers s provded by mnmsng AIC/SIC, for whch he values are also presened. Consder, frs, he es for common regmes for he wo esmaed STVAR specfcaons nvolvng F ( 4 - ). For he European aggregae, ogeher wh Ialy and Japan, he evdence agans common regmes s no very srong. However, (accordng o he log-deermnan and AIC, bu no BIC for Ialy) counry-specfc regmes provde a beer f han ones based on growh for Ialy and Japan, a fndng n accordance wh he resuls of Table. Taken n conjuncon wh AIC/BIC, he resuls for E5 n Table pon o a common regmes model for he and he European aggregae. The models nvolvng Canada, France, Germany and he UK rejec common regmes for hese counres wh he (a he 5 percen level), agans an unresrced -led regme. Neverheless, n each of hese cases, log Ωˆ ndcaes ha, when -led unsynchronsed regmes and counry-specfc regmes are compared, growh provdes he ranson varable for hese counres. AIC also pons o hese -led models, alhough BIC prefers he more parsmonous common-regme model for France. Therefore, whle Table pons o he regmes n mos G7 counres beng deermned by growh, he common regmes specfcaon s no suppored srongly overall. The 9

12 esmaed ranson funcons (Table 3) ndcae why hs s he case. The ranson funcon F ( 4 - ) for he equaon, wheher used n a common regmes model or no, ypcally has a hreshold value c around. percen growh over a year; as seen from Fgure, hs value approxmaes average annual growh. However, he esmaed hreshold value for growh n he equaon for oher G7 counres, c, s generally hgher, a around 3-5 percen. Therefore, whereas he busness cycle regmes for he can be nerpreed as above and below average annual growh, he regmes relevan for oher counres dsngush hgh growh, where F ( 4 - ) =, from average and low growh. These commens are renforced by Fgures 3 and 4 whch plo he values of he ranson funcons over me for he common-regmes and -led models. (Noe ha, n he laer case, he ranson funcon shown for he s ha from he bvarae model wh E5.) No surprsngly, and wh he sngle excepon of he UK model, he ranson funcon values are smlar for all common-regmes models n Fgure 3. The upper regme occurs less frequenly for non- counres n Fgure 4, alhough here s a subsanal proporon of such observaons for France and he E5. Alhough obaned from dsnc models, he smlary of he regmes n Fgure 4 for Ialy, Canada, Japan and (o a lesser exen) Germany and he UK s also noeworhy. The above commens abou he ranson funcon for he non- counry generally carry over o he models wh counry-specfc regmes, where he ranson funcon ndcaes regmes of hgh versus average/low growh (see Fgures and 5). The noable excepon, however, s Japan, where he hreshold value of zero s compable wh regmes of busness cycle expanson and recesson, wh a mxure of hese applyng when 4 JP - s a relavely small (posve or negave) value. The modes values of he esmaed slope γ for hs model furher ndcaes ha mxures of he wo regmes can apply n Japan. Wh he sngle excepon of he counry-specfc regmes case for Japan jus menoned, he esmaed ranson funcons are seep, wh large esmaed γ. Consequenly, he regmes are effecvely bnary and few observaons n Fgures 3 o 5 are nermedae beween regmes. 3. The Impac of Growh on G7 Counres Table 4 shows, n summary form, he coeffcens of he esmaed lnear and STVAR models. To conserve space, we show he esmaed φ ( =, or 3, 4) of (4) as a sum, ogeher wh he p-value for he jon es ha he wo ndvdual coeffcens are zero. Thus, we separaely 0

13 consder he coeffcens capurng causaly effecs from he and auoregressve ones, whle also showng he resuls of he hypohess ess of (5) and (6). In a lnear VAR sysem, lags of growh have posve effecs on oher counres, wh hs causaly beng sgnfcan a 5 percen n all cases excep France (margnally) and Japan. The dealed esmaon resuls (no shown) ndcae ha boh he frs and second lags of growh have posve and generally sgnfcan (a he 5 percen level) effecs on Germany, Ialy, UK and E5. Indeed, for all European counres (ncludng France), he frs and second lags are approxmaely equal n value and sgnfcance, ndcang ha he effecs of growh ake some me o be fel n Europe. Perhaps surprsngly, he auoregressve lags are no sgnfcan for Canada, Germany, Japan or he UK. The combnaon of sgnfcan coeffcens and nsgnfcan auoregressve lags for Canada, Germany and he UK n hese lnear VARs pons o a crucal role for he n deermnng oupu growh for hese counres. Before consderng regme-dependen causaly n he STVAR conex, s approprae o examne whch coeffcens vary over regmes, hrough he hypohess ess of (7) o (9). Irrespecve of he model consdered, Table 4 provdes no evdence of regmespecfc effecs of quarerly growh on eher Ialy or Japan. In all oher cases excep Germany, he -led growh model rejecs regme-nvarance for hese coeffcens. However, n he model for Germany, here s srong evdence ha he nercep vares wh he regme n annual growh. Furher, many models, and especally hose for -led growh, mply ha he effecs of domesc condons (capured hrough he auoregressve lags) vares over he regmes n growh. Before urnng o furher dscusson of specfc G7 counres, consder he nonlnear neracons of he and E5, whch (accordng o Tables and ) are more adequaely capured by models based on regmes han one wh counry-specfc regmes. Boh he common regmes and -led regmes ell a smlar sory for he naure of he mpac of he on Europe. Tha s, he E5 auoregressve dynamcs are relavely unmporan n he lower regme, bu are sgnfcan and posve n he upper regme. Therefore, even f he coeffcens of quarerly growh do no change over regmes (and here s lle evdence of hs n he preferred common regmes model), growh n Europe s more self-susanng n he upper regme han n he lower one. In erms of he -led regmes model and across all counres excep Japan, he causaly from quarerly growh ndcaed by he lnear VAR derve prmarly from he lower regme n he STVAR specfcaon. Ineresngly, he mplcaon from he lnear VAR

14 ha growh s no sgnfcan (a 5 percen) for France s conradced n he -led specfcaon, where he effecs are sgnfcan and posve n he lower regme. The models for Canada, Germany and he UK also show a smlar paern n he upper regme, wh a large ncrease n he nercep when growh s hgh, wh all oher coeffcens hen eher nsgnfcan of an unexpeced negave sgn 8. The nerpreaon s ha hgh growh over a year (greaer han he respecve hreshold) has a consan posve mpac on quarerly growh n hese counres, wh he precse value of recen quarerly or domesc growh beng rrelevan. The causaly mplcaons of he -led regmes model are ha quarer-o-quarer paerns n growh are mporan only n he lower regme, wh recen domesc growh playng a relavely modes role. Ths does no apply n he upper regme. Thus, oher G7 counres and he E5 end o rack paerns n quarerly growh only when condons (as ndcaed by annual growh) are no very srong. The only excepons relae o Ialy and Japan, whch may reflec he nonlneary es resuls of Table, whch mply ha regmes n hese cases may be counry-specfc. Due o he close lnks beween Canada and he, he model wh counry-specfc regmes delvers smlar mplcaons for he effec of growh on Canada as he -led regmes model. In he case of Japan, all model specfcaons n Table 4 merely serve o renforce he concluson ha hs counry has no been nfluenced by he over he perod. For Ialy, on he oher hand, he man effec of regmes s ha he auoregressve coeffcens play a more mporan role n he upper regme, wh hs effec beng sronges when he regmes are defned by domesc growh. 3.3 Is he Economy Closed? The fnal queson we examne s wheher he economy s nfluenced by growh n oher G7 counres. To hs end, Table 5 shows he esmaed equaon for he lnear VAR and he -led regmes model. Snce a ranson funcon s employed n all STVAR models, he equaon s largely unchanged across he STVAR specfcaons and hence (o conserve space) we presen only hs case. The lnear VARs largely suppor he proposon ha he economy s unaffeced by world condons. Indeed, alhough some European counres (France, Ialy and he E5) are found o have a sgnfcan effec on growh, hese effecs are negave. In he lower 8 The apparenly perverse large and sgnfcan negave oal (auoregressve or ) effecs for Germany and he UK n he upper regme may be a consequence of he relavely small number of observaons n hs regme.

15 regme of he STVAR model, he auoregressve coeffcens are hghly sgnfcan, wh he small oal coeffcen n he able reflecng a relavely large posve coeffcen a lag one and a correspondng negave one a lag wo. Ineresngly, he paern of quarerly growh havng a negave mpac on he noed for he lnear VAR now apples for all oher counres n he lower regme. These effecs are, however, mued n he upper regme. Judged by he lack of sgnfcance of boh he and oher counry coeffcens, quarerly (log) oupu s que well descrbed by a random walk wh drf when n he regme of above average growh. Table 5 esablshes ha he nonlneary n he equaon derves prmarly from he auoregressve dynamcs, whch aler n a sgnfcan way over regmes. The posve auoregressve coeffcens n hs upper regme end o renforce condons of above average growh. In neher regme does growh elsewhere n he G7 have a sgnfcan and posve mpac on he. Ths s he case for he Europe as a whole (E5), as well as for ndvdual counres. 4. Concludng Remarks Our analyss consders he naure of nonlneary n he bvarae relaonshps beween he and oher G7 counres. Alhough our model s effecvely unvarae and he nonlneary n oupu growh has been prevously esablshed (see, among ohers, Hamlon, 989; Teräsvra and Anderson, 99), he nvesgaon of he nonlnear naure of he dependence of oher counres on he s new. Usng a Markov swchng framework, Phllps (99) concludes ha regmes are common and due o world-wde shocks, bu hs s no confrmed by our analyss. Wh he excepons of he common regmes suppored for he and aggregae for he European Unon and he counry-specfc regmes ndcaed for Japan, we fnd ha regmes n he generally deermne he regmes n he oher G7 counres. Our resuls also ndcae ha he auoregressve dynamcs whn hese counres alers wh he regme. Where auoregressve dynamcs are mporan for non- counres, hese dynamcs ypcally apply only n he upper regme of relavely hgh annual growh. In conras, he causaly effecs of quarerly growh on oher counres ofen apples only n he lower regme. Therefore, whle he leads he world n erms of regmes, s paerns of quarer o quarer growh raes are parcularly mporan for oher counres when growh 3

16 s no hgh. Thus, he prmary fndng of hs sudy can be summarsed as mplyng ha lower growh from he may be more readly ransmed nernaonally han hgher growh. Our resuls may also explan he apparen ransmsson of he recesson of 000 o Europe, whch has been nvesgaed n a number of sudes, ncludng Doyle and Faus (00), IMF (00), OECD (00) and Perez e al. (003). Tha s, annual growh was srong hrough much of he 990s, bu hen declned sharply a he end of he decade. Thus correlaons n he busness cycle paerns beween he and Europe may no have srong durng he 990s, bu may have rsen wh he mpled swch o he lower regme a he end of hs perod. REFERENCES Anderson, H.M. and Vahd, F. (998), Tesng mulple equaon sysems for common nonlnear componens, Journal of Economercs, 84, -36. Anderson, H.M. and Vahd, F. (00), Predcng he probably of a recesson wh nonlnear auoregressve-leadng ndcaor models, Macroeconomc Dynamcs, 5, Ars, M.J. and W. Zhang (997), Inernaonal busness cycles and he ERM: s here a European busness cycle?, Inernaonal Journal of Fnance and Economcs,, -6. Ars, M.J. and W. Zhang (999), Furher evdence on he nernaonal busness cycle and he ERM: s here a European busness cycle?, Oxford Economc Papers, 5, 0-3. Ars, M., Krolzg, H.-M. and J. Toro (004), The European busness cycle, Oxford Economc Papers, 56, -44. Backus, D.K., Kehoe, P.J. and Kydland, F.E. (995), Inernaonal busness cycles: Theory and evdence, n T.F. Cooley (ed.) Froners of Busness Cycle Research, Prnceon Unversy Press, Prnceon NJ, pp Doyle, B.M. and J. Faus (00), An nvesgaon of co-movemens among growh raes of he G-7 counres, Federal Reserve Bullen, 88, pp Hamlon, J.D. (989), A new approach o he economc analyss of nonsaonary me seres and he busness cycle, Economerca, 57, Huh, H-S. and Lee, S-H. (00), Asymmerc oupu cos of lowerng nflaon: Emprcal evdence for Canada, Canadan Journal of Economcs, 35,, pp

17 Inklaar, R. and J. de Haan (00), Is There Really a European Busness Cycle?: A Commen, Oxford Economc Papers, 53, 5-0. Inernaonal Moneary Fund (00), Inernaonal Lnkages: Three Perspecves, World Economc Oulook, Ocober, Kose, M.A., C. Orak and C.H. Wheman (003), Inernaonal busness cycles: World, regon and counry-specfc facors, Amercan Economc Revew, 93, Lumsdane, R.L. and Prasad, E.S. (003), Idenfyng he common componens n nernaonal economc flucuaons, Economc Journal, 3, 0-7. OECD (00), OECD Economc Oulook, June, pp Perez, P.J., D.R. Osborn and M. Ars (003), The nernaonal busness cycle n a changng world: volaly and he propagaon of shocks, Cenre for Growh and Busness Cycle Research, Unversy of Mancheser, Dscusson Paper 37. Perez, P.J., D.R. Osborn and M. Senser (003): Busness cycle afflaons n he conex of European negraon, Dscusson Paper 9, Cenre for Growh and Busness Cycle Research, Unversy of Mancheser. Pesaran, M.H., T. Schuermann and S.M. Wener (003), Modellng regonal nerdependences usng a global error-correcng macroeconomerc model, Journal of Busness and Economc Sascs,, 9-8 (wh dscusson). Phllps, K.L. (99), A wo-counry model of sochasc oupu wh changes n regme, Journal of Inernaonal Economcs, 3, -4. Rohman, P., van Djk, D. and Franses, P.H. (00), Mulvarae STAR analyss of moneyoupu relaonshp, Macroeconomc Dynamcs, 5, Sms, C.A. (980), Macroeconomcs and realy, Economerca, 48, -48. Teräsvra, T. and Anderson, H.M. (99), Characerzng nonlneares n busness cycles usng smooh ranson auoregressve models, Journal of Appled Economercs, 7, S9- S36. Vahd, F. and Engle, R.F. (997), Codependen cycles, Journal of Economercs, 80, pp.99-. Wese, C.L. (999), The asymmerc effecs of moneary polcy: A nonlnear vecor auoregresson approach, Journal of Money Cred and Bankng, 3,, pp

18 Daa Appendx We model he frs dfference of seasonally adjused quarerly real GDP. All daa are obaned from he OECD or IMF daabases. We aemped o use comparable seres for each counry, bu n some cases, o oban longer samples, dfferen sources were used. For all he counres excep Ialy and Germany, bu ncludng he E5 aggregae, GDP s from he Man Economc Indcaors daabase of he OECD. Concreely our measure of GDP s: GDP volume ndex seasonally adjused (he code ypcally s counry_nagvvo0_ixobsa) For Germany, he seres GDP (PAN BD from 99) CONA, (wh Daasream code BDGDP D) was used. Ths seres comes from he OECD Naonal Accouns and was correced o ake no accoun he jump n 99, due o German reunfcaon. For Ialy, a GDP volume ndex from he IMF s used (3699BVRZF ) he seres was correced n 970 and 966 for a jump and an ouler respecvely. The samples perods for our daa are: DEU 970:- 00: A 970:- 00: FRA 970:- 00: CAN 970:- 00: ITA 970:- 00:4 JPN 970:- 00: E5 970: -00: UK 970:- 00: 6

19 Table : Sysem Lneary Tess VAR for wh z = z = 4 - z = 4 - z = 4 X - Canada France Germany Ialy Japan UK E Noes: Resuls are shown as p-values. The es employs he degrees of freedom adjusmen suggesed by Sms (980). 7

20 Table : Goodness-of-F Crera for Nonlnear Models log Ωˆ Common regmes -led regmes Counry-specfc regmes Tes for common regmes AIC Common regmes -led Regmes Counry-specfc regmes BIC Common regmes -led regmes Counry-specfc regmes Canada France Germany Ialy Japan UK E * -9.53* -0.88* -9.07* * * -8.88* * * * * * * * Noes: The es for common regmes compares he models wh common regmes and wh -led regmes, and s compued as a lkelhood rao es ha he parameers of he ranson funcons n he wo equaons of () are dencal. The resul of hs es s presened as a p- value. * ndcaes he preferred nonlnear specfcaon by AIC/BIC. 8

21 Table 3: Esmaed Transon Funcons Canada France Germany Ialy Japan UK E5 Common Regmes Model c γ Led Regmes Model -Equaon Transon c γ Oher-Equaon Transon c γ Counry-Specfc Regmes Model -Equaon Transon c γ Oher-Equaon Transon c γ

22 Table 4. Esmaed Equaons for G7 Counres and Europe Coeffcens Canada France Germany Ialy Japan UK E5 Lnear Model Inercep (.007) (.08) 0.00 (.80) (.00) (.065) 0.00 (.004) Growh (.064) (.00) 0.39 (.003) 0.4 (.573) (.00) 0.9 (.00) Own Growh 0.39 (.38) 0.40 (.00) (.086) (.449) -0.5 (.68) (.00) Common Regmes Model Lower Regme Inercep (.33) (.006) 0.00 (.534) 0.00 (.356) (.04) (.94) (.005) Growh (.0) 0.34 (.098) 0.88 (.549) 0.44 (.07) -0.4 (.65) (.00) 0.3 (.40) Own Growh (.04) (.349) 0.04 (.03) 0.07 (.455) (.890) (.968) -0.6 (.0) Upper Regme Inercep (.003) (.006) (.05) (.647) (.47) (.03) Growh (.008) (.747) 0.33 (.07) 0.56 (.063) 0.96 (.339) (.00) 0. (.8) Own Growh (.679) (.03) (.74) -0.4 (.556) Regme-Invarance Tess Inercep Growh Own Growh Led Regmes Model Lower Regme Inercep (.006) 0.00 (.008) (.0) (.85) (.96) (.00) Growh Own 0.95 Growh (.07) Upper Regme Inercep 0.00 (.008) 0.09 (.486) (.00) (.05) 0.64 (.06) (.884) (.45) -.40 (.067) 0.93 (.030) (.469) 0.39 (.34) 0.4 (.760) (.876) (.5) (.59) (.03) (.00) (.966) (.007) (.76) (.00) 0.3 (.74) (.076) 0.05 (.075) Growh (.905) Own Growh (.34) Regme-Invarance Tess Inercep Growh Own Growh

23 Table 4 (connued) Coeffcens Canada France Germany Ialy Japan UK E5 Counry-Specfc Regmes Lower Regme Inercep (.004) (.003) (.79) (.05) (.743) (.06) (.00) Growh (.008) Own 0.84 Growh (.00) Upper Regme Inercep 0.00 (.98) (.036) (.007) (.003) (.59) (.00) (.09) (.00) 0.94 (.75) (.04) (.09).30 (.05) (.00) (.04) (.848) (.700) (.00) (.44) 0.69 (.76) (.03) (.458) (.849).496 (.070) (.043) (.034) (.456) 0.66 (.0) (.98) Growh (.05) Own Growh (.09) Regme-Invarance Tess Inercep Growh Own Growh Noes: The able refers o he non- equaon n a lnear VAR or, for he nonlnear models, o he second equaon of (4). For he and own counry coeffcens, he value presened s he sum of he correspondng coeffcens, wh he p-value gven n parenheses for he jon es ha boh ndvdual coeffcens are zero. The esmaed nercep s also shown wh p-value n parenheses. The regme nvarance ess consder he null hypohess ha he correspondng coeffcens do no vary over regmes. The nvarance ess are compued as Wald ess and he resuls presened as p-values.

24 Table 5. Esmaed Equaons Coeffcens Canada France Germany Ialy Japan UK E5 Lnear Model Inercep (.00) Growh (.034) (.004) (.009) 0.37 (.004) (.05) 0.36 (.05) (.04) Oher Cry. Growh (.800) -0.5 (.09) 0.05 (.49) (.00) 0.9 (.508) (.3) (.09) -Led Regmes Model Lower Regme Inercep (.) (.07) 0.00 (.7) (.047) (.7) 0.00 (.48) (.04) Growh 0.07 (.073) 0.06 (.0) (.00) 0.00 (.07) (.00) 0.43 (.00) 0.7 (.049) Oher Cry. Growh -0. (.85) (.4) (.0) (.5) -0.7 (.667) (.038) Upper Regme Inercep (.00) (.00) (.00) (.00) (.004) (.00) (.004) Growh 0.98 (.505) 0.97 (.60) 0.40 (.68) 0.68 (.40) 0.7 (.89) 0.05 (.38) 0.60 (.38) Oher Cry. Growh (.78) (.00) 0.96 (.34) (.356) 0.84 (.7) 0.08 (.594) (.45) Regme Invarance Tess Inercep Growh Oher Cry Noes: The able refers o he equaon n a lnear VAR or, for he _led regmes model, o he frs equaon of (4). For he and oher counry coeffcens, he value presened s he sum of he correspondng coeffcens, wh he p-value gven n parenheses for he jon es ha boh ndvdual coeffcens are zero. The esmaed nercep s also shown wh p-value n parenheses. The regme nvarance ess consder he null hypohess ha he correspondng coeffcens do no vary over regmes. The nvarance ess are compued as Wald ess and he resuls presened as p-values.

25 Fgure. Quarerly GDP Growh 3

26 Fgure. Annual GDP Growh 4

27 Fgure 3. Transon Funcons for Common Regmes Models 5

28 Fgure 4. Transon Funcons for -Led Regmes Models Noe: The ranson funcon shown for he relaes o he bvarae model wh E5. 6

29 Fgure 5. Transon Funcons for Counry-Specfc Regmes Models Noe: The ranson funcon shown for he relaes o he bvarae model wh E5. 7