Trend-Cycle Interactions and the Subprime Crisis: Analysis of US and Canadian Output

Transcription

1 Regensburger DISKUSSIONSBEITRÄGE zur Wirschafswissenschaf Universiy of Regensburg Working Papers in Business, Economics and Managemen Informaion Sysems Trend-Cycle Ineracions and he Subprime Crisis: Analysis of US and Canadian Oupu Max Soloschenko *, Enzo Weber ** December 5, 01 Nr. 470 JEL Classificaion: C3, E3 Keywords: unobserved componen, rend, cycle, idenificaion, subprime crisis * Universiy of Regensburg, Deparmen of Economics and Economerics, Regensburg, Germany. max_soloschenko@web.de. ** Universiy of Regensburg, Deparmen of Economics and Economerics, Regensburg, Germany. enzo.weber@wiwi.uni-regensburg.de, phone: , and Insiue for Employmen Research (IAB).

2 Trend-Cycle Ineracions and he Subprime Crisis: Analysis of US and Canadian Oupu Max Soloschenko * Enzo Weber ABSTRACT In he following paper a simulaneous unobserved componens model is applied o US- American and Canadian oupu daa in order o examine he causal srucure of rend and cycle shocks and he way i changes over ime. The main focus is placed on he analysis of he subprime crisis impac on he rend and cycle componens. The srucural model is idenified by means of heeroscedasiciy. During he subprime crisis for boh counries we deermine he srong increase of he srucural rend variance compared o he previous period. This underlines he permanen effec and, hus, srucural problems as a poenial cause. Moreover, he boh componens are more volaile in he USA han in Canada. A furher similariy beween boh counries is he complee disappearance of he srucural cycle shock volailiy. JEL codes: C3, E3 Keywords: unobserved componens, rend, cycle, idenificaion, subprime crisis. * Universiy of Regensburg ( max_soloschenko@web.de) Universiy of Regensburg and Insiue for Employmen Research (IAB) ( enzo.weber@wiwi.uni-regensburg.de)

3 INTRODUCTION 1 1 INTRODUCTION The subprime crisis led o he mos severe slump in he world economy since he Grea Depression of he 1930s. On he empirical side, i would be of paricular ineres o ascerain which shocks led o a near worldwide economic collapse. This paper akes up Weber's (011) srucural framework, and augmens and applies i o US-American and Canadian oupu daa. The main focus lies on an examinaion of he rend and cycle componens as well as heir causal srucure. For his purpose, he aggregae oupus of boh counries are decomposed ino cyclical and rend componens and he ineracion beween heir srucural innovaions is deermined. Anoher imporan poin consiues he analysis of he course of he subprime crisis in boh counries and is effec on he rend and cycle. By including Canada, i will be ineresing o see wheher he US resuls can be confirmed, given he counry's radiionally srong economic inegraion wih he USA. The following quesions will be addressed: were he wo componens, rend and cycle, driven by permanen or ransiory shocks, or indeed boh? Do he same innovaions in he USA and Canada influence rend and cycle? In addiion, i will also be clarified wheher he respecive componens are affeced purely by heir own shocks or if spillovers also play a significan role. I will be shown ha during he subprime crisis rend and cycle were driven in boh counries by permanen shock alone, bu ha differen explanaions for his are required. Moreover, he srong negaive correlaion of oupu componens for Canada and he USA will be confirmed. Furhermore, wih regards o rend and cycle, he USA has a higher volailiy han Canada. The underlying paper makes use of he class of unobserved componens (UC) models in is empirical analysis. In he firs UC models, uncorrelaed rend and cycle componens were assumed (Harvey 1985, Clark 1987). In laer developmens, such as hose by Balke and Wohar (00) and Morley e al. (003), his assumpion was relaxed and subsequenly exended by Weber (011) in he framework of simulaneous unobserved componens (simuluc) models, which capure he concurren causaliy srucure of rend and cycle shocks. These auhors have esablished ha i is possible o ake ino accoun he correlaion beween he permanen rend and ransiory cycle innovaions, while mainaining he idenifiabiliy of he srucural model. In his paper he idenificaion of he simuluc model is achieved hrough heeroscedasiciy, i.e. he necessary informaion is aken from he differing variances of he srucural shocks. Addiionally, in he following paper, drif breaks will be

4 THEORETICAL PART inroduced o he srucural model in accordance wih criicism levelled by Basisha (007). Moreover, he exisence and number of breaks will be endogenously deermined and saisically verified. In heir influenial work, Sock and Wason (1988) commen on he inerconnecion beween rend and cycle as follows: Mulivariae empirical analysis suggess ha rend variaions and business cycle movemens appear o be relaed. One inerpreaion of his link is ha business cycle flucuaions migh be caused by innovaions in growh. An alernaive explanaion equally consisen wih he empirical resuls is ha cyclical flucuaions cause changes in long run growh. In he firs case (ha is, if causaliy goes from rend o cycle) RBC heory can be aken as a plausible explanaion. This heory regards business cycles as a reacion o changes in he prospecs for long-erm economic growh (see Presco 1987). The causal effec from cycle o rend canno, however, be ruled ou in any case. As an explanaion, one can sugges e.g. an expansive fiscal policy, which leads o a posiive demand effec in he shor-run, bu has a negaive effec (because of he raising ax and ineres raes) on he poenial oupu in he long-run (see Clark 1987). Furhermore, he simuluc model makes i possible o disinguish empirically beween he respecive componens as well as causaliy direcions. As will be shown laer, he impac direcion can change wih ime or even run in boh direcions. This paper is organised as follows: The second secion presens he model specificaions and deals wih he idenificaion problem. Secion hree hen applies he heoreical framework o he indusrial producion (IP) of he seleced counries, inerpres he resuls and examines robusness. Lasly, a shor overview of he key findings is provided. THEORETICAL PART.1 MODEL SPECIFICATION The saring poin is a simuluc model, Weber (011), which represens he seasonally adjused log oupu y as he sum of a sochasic rend τ and a cyclical componen c : (1) y =τ + c. The individual componens can be represened as follows:

5 THEORETICAL PART 3 η Q q q () τ τ µ µ D q k ~ η k ~ = = ε 1, η ~ N(0, σ η ) (3) c = b c b pc p k ~ η k ~ ε 1443, ε ~ N (0, σ ε ) ε,. Thus, he rend is a random walk wih drif and he cycle is an AR(p) process. The laer can be regarded as a saionary ransiory deviaion from he sochasic rend. Hereafer, he erm cycle will be used as a synonym for he ransiory par of he oupu flucuaions. The drif erm µ represens he seady-sae growh rae of he economy. Moreover, we inroduce he possibiliy of a (or if need be several) drif break(s) (see Perron and Wada 005). For his purpose, a dummy variable, q D, is employed, being equal o one afer he break in ime T and zero before. Q denoes he number of drif breaks. For he empirical analysis, he poenial break dae is deermined endogenously. The decomposiion of he composie shocks ( η and ε ) in equaions () and (3) was firs inroduced by Weber (011) and faciliaes capuring he causaliy srucure beween he wo componens. Thus, ~ η and ~ ε denoe srucurally uncorrelaed rend and cycle shocks (henceforh: srucural shocks). Accordingly, rend and cycle innovaions ( η and ε ) and, hus, rend and cycle can be hi by rend- as well as cycle-specific shocks. The parameers k 1 and k 1 are spillover coefficiens, which describe he simulaneous ineracion beween he wo unobserved componens, τ and ~ E( η ) = 1 and ~ E( ε ) = 1, as well as k 0 and k c. The simulaneous sysem is normalised by. REDUCED-FORM AND IDENTIFICATION In order o verify he idenificaion of he simuluc model, he reduced-form mus be deduced. Those is calculaed by subsiuing he equaions () and (3) ino equaion (1) and solving for he endogenous variable. Thus, an auoregressive inegraed moving average (ARIMA(p,d,q)) process is obained. The ARIMA represenaion in he convenional form and noaion akes he following form: Q q q (4) B ( L) y = c+ = c D + A( L) u, u ~ N(0, σ ), q 1 u where u consiss of boh srucural shocks. A (L) is a p-dimensional lag polynomial. Is

6 THEORETICAL PART 4 coefficiens a i, where i = 1K,, p, as well as is variance σ u can be calculaed from he heoreical auocovariance equaions. The AR-coefficiens from he cycle equaion, i = 1K,, p, are direcly idenified by he auoregressive parameers from (4). Furhermore, he MA par delivers exacly p + 1 nonzero auocovariances γ ( 0), K, γ ( p). The necessary condiion for idenificaion is fulfilled when he number of unknown parameers from he srucural form is equal o he number of equaions in he sysem. If we ake AR() as an example, he equaion comparison shows ha he simulaneous srucure is no idenified, because, for he idenificaion of four k ij (where i, j= 1, ), one equaion is missing (see Morley e al. 003 ). Furhermore, as Weber (011) has shown, in his case, raising he AR order would no help, because an AR(3) model does no fulfil he sufficien rank condiion. In he aforemenioned paper, his problem is solved by means of heeroscedasiciy. This approach considers several regimes (wih differen volailiy) for he daa generaing process of he srucural simuluc shocks ( ~ η and ~ ε ). The srucural variances (say, hose of he firs regime) are normalised o 1, so ha ~ Eη ( Ι ) = 1 ( ~ Ι ) 1 σ ~ ε 1= Eε 1 = holds. r (where b i, σ ~ η and 1= Ι denoes he se of informaion belonging o he r h regime r = 1,..., s ) and s indicaes he number of volailiy regimes. The variances of he ~ ~ furher regimes σ ~ η = ( η ) and ~ = ( ε ) l E Ιl σ ε, where l =,..., s, are parameers ha l E Ιl need o be esimaed. If variance breaks have indeed aken place, hese esimaions will be differen from one. As one can see, his separaion ino several regimes increases he number of he unknown 1 coefficiens by wo a each sep: σ and ~ ηl σ (where ~ εl l =,..., s ). However, p + 1 addiional auocovariances for each furher variance regime can be obained from he MA par of he reduced form. 1 I follows logically from his ha for p, he necessary summing-up condiion for he idenificaion of four k ij and he wo addiional variances σ and ~ ηl σ per ~ εl regime is fulfilled. A his poin he heeroscedasiciy implicaions of he reduced-form parameers should be briefly addressed. As can be seen from equaion (4), a change in he variance of he srucural 1 The proporional break in he srucural shocks ( σ ~ = σ ~ ) implies he following: he "new" auocovariances ηl εl γ l ( 0), K, γ l ( p) ( l denoes regime) are linearly dependen from heir firs-regime counerpars and consequenly deliver no addiional informaion o idenify he simulaneiy. On op of ha, hese "new" auocovariances will be only presen if he variance breaks are disproporionae o one anoher.

7 EMPIRICAL PART 5 shocks implies a break in he MA parameers ( a i ) as well as in he residual variance ( σ u ), bu no in he consan (c) or in he AR coefficiens b ). Had hese been affeced, a change in he drif and in he AR cycle coefficiens would have been observed as a consequence. ( i 3 EMPIRICAL PART 3.1 DATA We seleced he USA and Canada (CA) for he empirical analysis. While US oupu has already been analysed closely by Weber (011), we add he perspecive on he subprime crisis. An empirical sudy of Canadian aggregae oupu represens enirely new errain. This paper, as well as he above one, uses IP as a measure of oupu. 3. TECHNICAL ASPECTS OF THE ESTIMATION Firs of all, IP indices are logged and muliplied by 100. In he nex sep, he ADF-Tes is applied o he modified series in order o check for he presence of uni roos. Wih he help of an ARIMA(p,1,p) model for each counry, he lag lengh is specified and he iniial values for he opimisaion of he simuluc likelihood are deermined. The opimal lag lengh is seleced using Akaike (AIC) and Schwarz (SC) crieria. Subsequenly, he residuals are examined for he presence of auocorrelaion. Given he complexiy of he srucural model under consideraion, only lag lenghs from 1 o 4 were aken ino accoun. 3 The exac dae of he change in variance regimes is deermined as follows: firs of all, we look a hisorical evens ha could poenially explain a break. This economic analysis is bolsered by a visual inspecion of he firs differences. Then an endogenous search is carried ou by looking for he specificaion wih he larges likelihood. On op of ha, he presence of breaks in he MA coefficiens and variances is also esed. The esimaion of he ARIMA models and he subsequen ess were performed using R.10.1 saisical sofware, while he simuluc models were esimaed in GAUSS 9. 4 See Weber (011) for deails. 3 Boh he informaion crierion and he residual analysis found he lag lengh of 4 redundan. 4 In he firs sep of he Kalman filer, he iniial values for he condiional expecaion and he condiional variance are required. In his case, he rend sars wih he firs observaion of he series, while he cycle is iniialised a zero. The saring poin for he cycle variance is he variance of he IP growh raes. The rend variance sars a , which represens an exremely large variance, as is expeced of a random walk process.

8 EMPIRICAL PART EMPIRICAL ANALYSIS: USA SPECIFICATION The framework consruced by Weber (011) is aken as a saring poin for he US esimaion and exended for he specific purposes of his paper. The applied ime series runs from 1947:1 o 011:3. Furhermore, a drif break is included so as o avoid possible disorions. Log IP muliplied by 100 (hereinafer referred o as IP ) and is firs differences are ploed in Fig. 1. FIG. 1: US log real IP (x100) and he firs differences As he firs differences in Fig. 1 show, here are a leas wo possible break poins ha could be eligible for he USA: he early 60s and he mid-1980s. The hird one ha is, he beginning of he subprime crisis consiues a novel elemen of his paper. The subsanial flucuaions, which sar a he end of he fories and las unil he beginning of he sixies, indicae several consecuive recessions: 1948(I)-1949(IV), 1953(II)-1954(II), 1957(III)- 1958(II), 1960(II)-1961(I). 5 Labone und Makinen (00) race hese economic slumps back o overly resricive moneary policy: "In all of hese episodes, moneary policy can be characerized in hindsigh as following a paern of oo much ighening of policy before he recession, followed by an easing of policy during he recession. The over ighening of moneary policy is cleares in he hree cases ( , , 1960) where inflaion was already low." The recession of plays an imporan role in ha respec. The Fed's decision o increase he rae of ineres in 1959, combined wih resricive fiscal policy, are viewed as a cause for his economic slowdown. However, he cenral bank's immediae move owards expansionary policy subsequenly led o a quick economic recovery. This recession was followed by he second larges economic boom ever measured by he NBER 5 NBER recessions

9 EMPIRICAL PART 7 and is clearly visible in he firs differences. The search for he bes likelihood value indicaed January 1961 as a poenial break poin. This is very close o he break poin suggesed for he US GDP growh by Keaing and Valcarcel (011). February 1984 is aken as he second mos likely break poin. This dae is also commonly used as he beginning of he Grea Moderaion for he US GDP series in he relevan economeric lieraure (see McConnell and Perez-Quiros 000 / Kim and Nelson 1999). As previously menioned, he beginning of he subprime crisis, ha is, spring/summer 007, is aken as marking he hird break. Given ha his paper examines IP (a real variable), he acual saring poin should reflec he momen when he real secor succumbed o he crisis. As can be seen from he firs differences, srong flucuaions sar in summer 008 and peak in Sepember of he same year (a he same ime as he bankrupcy of Lehman Brohers). This suppors he value suggesed by he larges likelihood, and hus June 008 was seleced as he exac dae of he change in regimes. As Rigobon (003) has poined ou, a sligh misspecificaion of volailiy regimes would no impair idenificaion and consisency. Before he acual simuluc esimaion, he seleced break poins were verified in an ARIMA(,1,) model by he Wald ess of he null hypohesis of he sabiliy of he variances and MA coefficiens. All hree of he break poins are clearly significan, meaning ha he necessary idenificaion condiion is indeed fulfilled. Aside from ha, a drif break was inegraed in January 1974, in keeping wih he larges likelihood value, as can also be seen from he IP ime-series in Fig. 1. From an economic perspecive, he drif break can be explained by he oil crisis, which began in he fourh quarer of 1973 and is in line wih he drif break poins suggesed for he US real GNP and GDP (see Perron 1989 / Perron and Wada 005). I should also be noed ha he specificaion wih wo drif breaks could no be corroboraed. The second poenial dae of he break in drif was se a he end of he "docom" bubble (November 001). The recovery phase afer he Inerne bubble is he larges economic boom ha has been measured by he NBER o dae ESTIMATION AND RESULTS The esimaed parameers from he rend and cycle equaions, as well as he respecive six variances of he hree addiional regimes, are presened in equaions (5) o (9). Sandard errors from he inverse Hessian are given in parenheses. Addiionally, due o he poenial disorion of he Wald es (e.g. Dufour 1997 / Nelson and Sarz 007), LR ess were performed for he relevan coefficiens.

10 EMPIRICAL PART 8 (5) τ = τ ~ η ~ (0.109) (0.11) (0.66) (0.557) (6) c = 1.086c c ~ η ~ (0.091) 1 (0.084) (0.7) (0.545) ε ε (7) (8) (9) σ ~ = , η η 3 (0.114) σ ~ = 0. 70, η 4 (0.078) σ ~ = , (0.514) σ ~ = ε ε 3 (0.068) σ ~ = σ ~ ε 4 = 0 ( ) (0.00) The sandard errors clearly indicae ha all coefficiens excep σ are significan. The ~ε 3 high significance of he spillover parameers k 1 and k 1 from he equaions (5) and (6) deserves paricular aenion, for i confirms he srengh of he applied idenificaion approach. A he same ime, he model wih hree breaks is over-idenified wih wo degrees of freedom, which is due o he fac ha he covariance marices deliver welve deermining equaions for en unknown parameers. Thus, using he LR es, i is possible o es boh spillover coefficiens for breaks direcly in he simuluc model. In his case, he null hypohesis of no break finds clear suppor for all hree break poins. Hence, i is obvious ha only he variances and he MA coefficiens display breaks, bu no he spillovers. In he firs regime where boh variances are normalized o 1 he simuluc sysem is srongly influenced by he srucural cycle shock ( ~ ε ). I his he cycle more han wice as srongly as he srucural rend innovaion does, and even prevails in is effec on he rend componen ( k 1 =. 097 ). Hence, he negaive correlaion (-0.934) beween η and ε can be explained primarily hrough k 1. The second spillover coefficien k 1= reflecs he convenional approach, which sees he correlaion as a causal effec from rend o cycle. Therefore, i can be inerpreed as he real persisen shock, which drives business cycles, jus as he RBC heory posulaes. I should be noed here ha k 1 denoes he permanen effec of he srucural cycle shock, while k 1 describes he ransiory influence of he srucural rend innovaion. The volailiy of he composie shocks, η and ε, is approximaely equal. According o he esimaed resuls, he drif levelled off from (before he break) o (afer he break, µ = 0. 14) and is also in line wih he paern from he IP series. The LR es has shown ha 1 µ is marginally insignifican on he 5% level. Noneheless, he

11 EMPIRICAL PART 9 curren specificaion was preserved, because of he criicism levelled by Perron and Wada (005) and Basisha (007). 6 In he second regime he variance of he srucural cycle shock dropped by 75% and ha of he srucural rend shock by 56%. In he hird regime he variances declined even furher. Compared o he firs regime, he variabiliy of he srucural rend shock sank by more han 70%, and for he srucural cycle shock by 97%. The variance reducion of almos one hundred percen in he case of he srucural cycle disurbance has he following implicaions for he sysem. The dominan posiion in he sysem has shifed o ~ η. Consequenly, he negaive correlaion beween he composie shocks can be aribued o k 1= and mus be seen as a causal effec from rend o cycle. Taking an economic inerpreaion ino consideraion, he business cycles in he hird regime can be mosly explained by real permanen shocks. This idea is refleced in a range of economic heories, such as he RBC heory. In he fourh regime, he variance of he srucural rend innovaion rises fivefold, while he volailiy of he srucural cycle shock remains immaerial. This is in line wih he heory, according o which he subprime crisis was caused (in he case of real esae and he financial secor) or exacerbaed (in he case of labour marke) by srucural problems in sysem-relevan secions. I should be noed ha he curren esimaion is in line wih Weber's (011) resuls, despie he inclusion of he highly volaile Global Financial Crisis, which cerainly confirms he robusness of he applied model. In conras o previous sudies, which focussed on composie shock analysis, he srucural framework used in his paper makes i possible o deermine and invesigae he source of hese disurbances. The following can be said regarding he volailiy reducion of η and ε wih respec o one anoher. The relaion of sandard deviaions amouned o 0.98 wihin he firs regime (see Table 1 in he appendix). Hence, despie he fac ha before he firs break he variance of each componen was mosly driven by srucural cycle innovaions, boh composie shocks displayed equal volailiy in relaion o one anoher. In he second regime, he variances of he srucural shocks declined, wih he resul ha he volailiy of each componen also decreased. However, he relaion of sandard deviaions remains almos equal. In he hird regime, he almos complee disappearance of srucural cycle variance led o furher decline of he η and ε variances, which were driven almos enirely by he srucural rend shock. Afer he hird break (ha is, during he subprime crisis) he srucural rend 6 Moreover, he omission of he parameer would no have led o any noeworhy changes.

12 EMPIRICAL PART 10 variance increased fivefold, and hus he relaion of composie sandard deviaions rose even furher. In essence, he increase of he relaion from 0.98 o 1.84 can be inerpreed as "moderae", because he spillover coefficiens in boh equaions preven he variances from drifing furher apar. The reducion of σ ~ εl (where l =,3,4. ) decreased (hrough k 1 ) is conribuion o he rend variance. A he same ime, he sligh drop/rise found in σ (where l =,3,4. ) moderaed he reducion of cycle variance (hrough k 1 ). In sum, i is clear ha here is a decrease in he volailiy of boh composie shocks due o he considerable reducion in he variabiliy of he srucural cycle shock ( σ ). However, he drop in cycle volailiy was by far less sharp han ha of he srucural cycle innovaion. ~ εl ~ ηl Figure plos he filered unobserved rend and cycle componens: FIG. : Filered IP rend and cycle (USA) As shown in Fig., he filered rend remained very volaile unil he beginning of he sixies. Moreover, i can be seen ha each recession had an obvious effec on is course. In he second regime, where he variance of he srucural cycle shock has declined by 75%, he rend becomes less noisy. Noneheless, one can sill see srong variaions induced by boh oil crises. From he year 1985 onwards, he rend becomes smooher and he "do-com" bubble represens he sole volaile period. Afer ha, one can see he severe drop in he rend induced by he subprime crisis. All of his makes a convincing case for he suggesed break poins. The filered cycle is shown on he righ-hand side of Fig.. As he lag polynomial has no complex roos, he cycle shows no ypical "periodic" behaviour. The moderaion of he cycle beween he firs regime and he subprime crisis reflecs he drop in he volailiy of he srucural cycle shock. The cycle behaviour also clearly demonsraes ha he recen financial

13 EMPIRICAL PART 11 crisis has affeced is course more srongly han all previous crises. A closer look a boh componens shows ha hey display opposie movemens, which can be seen especially during he subprime crisis. I can be explained as follows. A negaive shock causes a sharp decline in he poenial oupu. However, due o rigidiies, he producion iself does no immediaely follow his developmen. The "posiive" cycle only parially counerbalances he negaive rend and he ne effec is a decrease in oupu. The abrup plumme of he cycle a few periods laer implies ha producion follows poenial oupu. Tha seep drop shows he effec of he crisis on he cycle componen, while he previous increase indicaes a gap beween he rend and he acual producion, jus as he RBC heory posulaes. As will become apparen laer, he explanaions pu forward above are equally valid for Canada. 3.4 EMPIRICAL ANALYSIS: CANADA SPECIFICATION The monhly seasonally adjused Canadian IP index was obained from he Inernaional Financial Saisics (IMF) and runs from 1957:1 o 011:5. I is presened on he lef-hand side of Fig. 3 FIG. 3: Canadian log real IP ( 100) and firs differences. AIC and SC crieria from he ARIMA(p,1,p) model prefer a lag lengh of for he cycle esimaion. The AR and MA roos of he characerisic equaion lie ouside he uni circle. In he differences on he righ-hand side of Fig. 3, wo break poins are visible: he beginning of 1985 and The firs dae when volailiy undoubedly decreased can be raced back o he Grea Moderaion and is very close o he break poin suggesed for he US GDP (see McConnell und Perez-Quiros 000) and IP (see Weber 011). For his esimaion, he ime

14 EMPIRICAL PART 1 poins ha provide he larges likelihood were seleced: February 1985 and January Taking a closer look a he differences from he year 1985 onwards, one can recognise a drop in heir ampliude in 1991/199. This (raher) sligh sabilisaion of he variaions is followed by a noable reducion in he volailiy in 1995, which is congruen wih he resuls from Sock und Wason (003), who demonsraed ha a srong decrease in volailiy occurred in he midnineies. From an economic poin of view, his is consisen wih he decision made by he Bank of Canada and he Canadian governmen in February 1991 o se ou a pah for inflaion reducion, which foresaw a decrease in inflaion o % by he end of Tha led o lower inflaionary expecaions and, hus, o more securiy in he markes. In he firs "Moneary Policy Repor" produced by he Bank of Canada (1995), his issue was commened upon as follows: "Since 1991, he Bank has been commied o specific inflaion-conrol arges along a pah o price sabiliy, and his commimen has begun o bear frui. The decline of underlying inflaion o raes beween 1 1/ and per cen during he las hree years has been a key facor behind Canada s improved economic performance." As was he case for he US, June 008 was seleced as he hird break in variance. In addiion, a visual examinaion of he differences makes i possible o predic a he ouse ha he subprime crisis hi Canada markedly less severely han he USA. As shown in Fig. 3, he drif break in he mid-sevenies could also be relevan for Canada and, as in he case of he US, he firs oil crisis could be considered a poenial explanaion. July 1974 was chosen for he esimaion. This dae is very close o he break poin (April 1973) Basisha (007) suggesed for Canadian GDP ESTIMATION AND RESULTS The esimaed parameers from he simuluc model for Canada are given in equaions (10) o (14). Due o he fac ha he unresriced esimaion for he srucural rend variance wihin he second regime was equal o 1.001, i was se o 1. (10) τ = τ ~ η ~ (0,119) 0.14 (0,344) (0,57) (11) c = 0.589c c ~ η ~ (0,083) (0,043) (0,3) ε (0,466) ε (1) (13) σ =, ~ η 1 ( ) σ ~ = , η 3 (0,040) σ ~ = 0. 4 ε ε 3 (0,068) σ ~ = (0,011)

15 EMPIRICAL PART 13 (14) σ ~ = , η 4 (0,14) σ ~ ε 4 = 0 ( ) Given ha longer ime series were no available for Canada and ha he model complexiy remains subsanial, a 10% significance level is considered appropriae. The esimaion for he spillover coefficiens k 1 and k 1 is saisically significan according o he sandard errors. However, he LR es only suppors he validiy of he former a he 10% level. 7 Here, as in he US case, he chosen variance breaks were verified in an ARIMA(,1,) model using he Wald es. I was no possible o confirm sabiliy of he variances or of he MA coefficiens in any of he cases. As he Wald es in he ARIMA(,1,) model found he hird break significan only a he 10% level, is presence was checked again wihin he simuluc model. η 4 = ε 4 The LR es clearly rejeced he null hypohesis σ ~ σ ~ = 0 a he 5% level and, in doing so, confirmed he significance of he fourh regime. As menioned earlier, i is possible o es he parameers k 1 and k 1 for breaks because of he model s overidenificaion. The LR es was no able o rejec he null hypohesis of parameer sabiliy for all hree break poins. Therefore, i is obvious ha only variances and he MA coefficiens break, bu no he spillover parameers. I should be noed ha here is no proporional break in he variances ( σ ~ = σ ~ where l =,3,4. ) and, consequenly, no violaion of he (sufficien) idenificaion ηl εl condiion. The sum of boh AR coefficiens amouns o approximaely 0.8 for Canada, jus as i was he case for he US, which suggess nearly equal cycle persisence. In he firs regime, he simuluc sysem is influenced equally by boh srucural shocks ( ~ η and ~ ε ). I is clear ha each componen is srongly affeced by is own shock. Moreover, each shock s influence is sronger upon is own componen, i.e. he srucural cycle shock his he cycle componen more han he rend componen and vice versa. Thus, i is obvious ha he cycle can also have permanen effecs, jus as rend can ac in a ransiory fashion. Following 1 he resuls, he drif break parameer ( µ ) was esimaed as -0.30, meaning ha he rend flaened ou by more han 50% afer he break occurred. The slope of he rend before and afer he break, as well as he resuls of addiional LR es verificaion, is similar o he US 7 Wih regard o he significance of 1 k he following can be saed. If one shorens he sample for he es purpose and hen subsequenly expands i sep by sep, one ges he following resuls: p-value declines, while here are only marginal changes in he parameer value.

16 EMPIRICAL PART 14 case. The model esimaion wihou he drif break did no lead o any significan parameer change excep, of course, for he consan ( µ = 0. 9 ). In he second regime, he variance of he srucural rend shock remained unchanged, while ha of he srucural cycle innovaion declined by nearly 80%. Thus, he srong negaive correlaion beween he composie shocks can be raced back almos enirely o he spillover of he srucural rend innovaion from he cycle equaion ( k 1 ). This, jus as in he US case, suppors he RBC heory, according o which business cycles are caused by real permanen shocks (supply shocks). In conras o he US resuls, he explanaion of he Grea Moderaion in Canada can be seen in he drasic disappearance of genuine cycle volailiy. The magniude of he rend shock remained consan and led o volailiy reducion in he enire sysem. This consellaion (ha is, a sharp decrease of he cycle volailiy accompanied by unalered rend volailiy) poins owards he "good policies" hypohesis as a more likely explanaion of he Grea Moderaion phenomenon in Canada. In he hird regime, he variabiliy of boh srucural shocks decreased by over 90% compared o he firs regime. As one can see, here was an adjusmen of boh srucural innovaion conribuions o he negaive correlaion in he hird regime. In he fourh regime, he variance of he srucural rend innovaion rose fivefold, while he volailiy of ~ ε disappeared, jus as was he case for he US. Consequenly, only k 1= conribues o he negaive correlaion. The equal increase of rend volailiy, combined wih he complee insignificance of he srucural cycle shocks in boh counries, poins a he presence of a single source of he slump. Regarding he volailiy reducion, he following saemen can be made (see Tab. in he appendix). In he firs regime, he relaion of he sandard deviaions of he composie shocks η and ε amouned o This suggess a greaer volailiy of he cycle componen, which can be raced back primarily o k. Furhermore, boh shock influences are higher in he cycle equaion han in he rend componen. As can be seen in Tab., he relaion rose from regime o regime, while he volailiies of he composie innovaions declined seadily. The reason for his raher "moderae" change in he relaion is he ransmission coefficien of he srucural rend innovaion from he cycle equaion ( k 1 ). In sum, i can be said ha he sysem volailiy declined over ime and ha his reducion should be aribued o boh composie shocks. For Canada he volailiy of he esimaed rend and cycle componens was driven for he mos par by srucural rend innovaions.

17 EMPIRICAL PART 15 The unobserved rend and cycle componens for he Canadian IP, filered in he simuluc model, are presened in Fig. 4. As one can see, he rend s behaviour remained relaively erraic up o he year 1995, and from hen on became fairly smooh. The highes variabiliy can be seen in he early and mid-eighies. These facs cerainly speak in favour of he chosen break daes. As menioned previously, he decline in volailiy during he mid-nineies is in line wih he findings of Sock and Wason (003), who suggesed exacly he same dae as a poenial break poin for Canadian GDP growh raes. This, combined wih he filered componens presened in Fig. 4, indicaes ha he volailiy reducion process conneced o he Grea Moderaion in Canada occurred less abrup han in he USA. The reducion in volailiy of Canadian IP was a process, which presumably lased from abou he mid-eighies o he mid-nineies. The main reason for he volailiy decrease during he 1990s was he reducion of he srucural rend variance. This lagged volailiy decline of σ ~η 3 coincided wih he "rehinking" of moneary policy, which he Bank of Canada underook in he early 1990s (see secion 3.4.1). As Davis and Kahn (008) have poined ou, his "moneary policy urning poin" had already aken place in he USA around No only is i in line wih he seleced break daes for boh counries, bu i also brings he "good policies" hypohesis o he fore as he mos likely explanaion of he Grea Moderaion phenomenon. Compared o boh oil crises, he impac of he subprime crisis on he rend was raher insubsanial. Moreover, i should be noed ha, in conras o he filered rend for he US IP, he Canadian filered rend exhibis less variabiliy. FIG. 4: Filered IP rend and cycle (Canada) The 1973 and oil crises are boh clearly visible in he filered cycle, bu he laer evidenly hi he cycle componen more srongly. As already menioned, he srong flucuaions from he mid-eighies o he mid-nineies can be largely aribued o he shor-

18 USA VS CANADA 16 erm effec (ransiory) of he rend innovaions ( k 1 ). This fac indicaes ha he negaive correlaion can be seen as a causal effec from rend o cycle. Moreover, he cyclical movemens undoubedly mirror he aforemenioned decline in volailiy in he mid-nineies. The reducion in he cycle flucuaions beween he second and hird break reflecs he decline of boh srucural variances. The effec of he subprime crisis was approximaely equal o ha of each of he oil crises. 4 USA VS CANADA The major objecive of his paper was o analyse he impac of he subprime crisis on he oupus of he US and Canada using Weber's (011) simuluc model. The main emphasis was placed on he examinaion of he influencing facors ha have been driving he rend and cycle componens in he pas few decades and especially during he subprime crisis. Furhermore, he separaion ino several regimes made i possible o sudy he way in which he effecs and causaliy of individual componens change over ime. The implemened srucural framework allowed for idenificaion and esimaion of he rend and cycle causal srucure. The applicaion of he simuluc model o he US and Canada's IP reveals one similariy, ha is, he enire disappearance of he srucural cycle shock volailiy. Moreover he wo counries show differen shock coefficien relaions in he firs regime. Alhough in Canada each componen is dominaed by he respecive "specific shock", US rend and cycle are driven more srongly by srucural cycle innovaions. A he same ime, however, i was possible o confirm srong negaive correlaion across all regimes. Aside from he subprime crisis, anoher even manifesed iself in boh ime series: he Grea Moderaion. In he US daa, i showed iself in a sharp decline of boh srucural volailiies, while in Canada only he volailiy of he srucural cycle shock decreased. The srong reducion of srucural cycle volailiies in boh counries suggess ha he "good policies" hypohesis is likely o be a plausible explanaion of he Grea Moderaion phenomenon. However, for he USA, he "good luck" hypohesis can also be considered a poenial explanaion, since he decline of is srucural rend variance was quie sharp. All in all, he IP differences ogeher wih he esimaed volailiies indicae ha he Grea Moderaion process in Canada lased longer han in he USA, ha is, unil he mid-1990s. Generally, boh componens exhibi higher volailiy in he USA han in Canada.

19 USA VS CANADA 17 Wih regard o he shocks during he subprime crisis, he following can be poined ou. Agains he previous period, here was a fivefold increase in he variance of he srucural rend innovaion from he middle of he year 008 onwards, and his resul holds rue for boh counries. Expressed in absolue erms, he variance of he srucural rend shock rose considerably more srongly in he USA han in Canada. As a resul, he Unied Saes exhibis higher volailiy of he composie shocks, and hus also of is wo componens. The filered componens from he simuluc model illusrae his poin (see Fig. and 4). The fac ha he subprime crisis had is origins in he USA obviously plays a par here. In general, almos all real economic variables GDP, unemploymen, IP, ec. reaced significanly more srongly o he crisis in he USA han in Canada. Srucural problems in he USA, especially hose in banking, finance, real esae and fiscal secors and no leas in he labour marke, can be pu forward as he main reason for his. Moreover, he high level of privae secor deb, combined wih he low savings rae, will have also played a subsanial role. In conras o he Unied Saes, he Canadian economy was in a relaively solid condiion when he crisis sruck. As Cross (011) has argued, consumpion (due o much lower privae secor deb and a flexible labour marke), and he quick acions of he Canadian cenral bank, ogeher wih governmen economic simulus programmes, no o menion he sable banking secor, 8 were paricularly able o alleviae he crisis. Noneheless, he Canadian economy was srongly hi by he global crisis, wih he resul ha expors and invesmens in paricular decreased sharply. As can be seen from he Canadian filered rend componen, he upward rend was disored by he subprime crisis and i has no (ye) compleely reurned o he old pah ha would have been reached absen he crisis. This indicaes a permanen effec and, hus, he exisence of durable srucural causes. For boh counries i was possible o confirm he exisence of srong negaive correlaion beween he componens during he subprime crisis. Moreover, in eiher case his can be seen as a causal effec from rend o cycle, and no vice versa. The subprime crisis is conspicuous in he IP ime series, which is direcly relaed o he srong impac i had on real variables. The "do-com" bubble and he subsequen recession can be cied here as a couner-example, as hey scarcely show up in he IP daa. Tha bubble had very lile real background and herefore played only a minor role in his invesigaion. Transiory effecs (such as fiscal policy) appear o have had lile influence on he IP componens during he subprime crisis and are hus hardly percepible in he underlying daa and he model. I remains o be seen if he laes 8 In he Global Compeiiveness Repor published by he World Economic Forum he Canadian banking sysem was praised as he soundes and, hus, he mos sable in he world.

20 LITERATURE CITED 18 high-volailiy-regime keeps is characer or if volailiy revers afer he subprime urbulence. The recen more seady growh raes in boh counries may suppor he laer supposiion. Fuure research on his decisive quesion appears highly promising. LITERATURE CITED BALKE, N.S., M.E. WOHAR (00): Low-Frequency Movemens in Sock Prices: A Sae-Space Decomposiion. Review of Economics and Saisics, 84, BASISTHA, A. (007): Trend-cycle correlaion, drif break and he esimaion of rend and cycle in Canadian GDP. Canadian Journal of Economics, Vol.40, No., CLARK, P.K. (1987): The cyclical componen of U.S. economic aciviy. Quarerly Journal of Economics, 10, CROSS, P. (011): How did he recession and recovery compare wih previous cycles? Canadian Economic Observer, Saisics Canada. DUFOUR, J-M. (1997): Some Impossibiliy Theorems in Economerics wih Applicaions o Srucural and Dynamic Models, Economerica, Vol. 65, No. 6, DAVIS, S.J., J.A. KAHN (008): Inerpreing he Grea Moderaion: Changes in he Volailiy of Economic Aciviy a he Macro and Micro Levels. Journal of Economic Perspecives, Vol., No. 4, HARVEY, A.C. (1985): Trends and Cycles in Macroeconomic Time Series. Journal of Business and Economic Saisics, 3, KEATING, J.W., V.J. VALCARCEL. (01): Greaer Moderaions, Working Papers Series in Theoreical and Applied Economics, Universiy of Kansas, Deparmen of Economics, No KIM, C.-J., C. R. NELSON (1999): Has he U.S. Economy Become More Sable? A Bayesian Approach Based on a Markov-Swiching Model of Business Cycle. Review of Economics and Saisics, Vol. 81, No. 4, LABONTE, M., G. MAKINEN (00): The Curren Economic Recession: How Long, How Deep, and How Differen From he Pas? CRS Repor for Congress. MCCONNELL, M., G. PEREZ-QUIROS (000): Oupu Flucuaions in he Unied Saes: Wha Has Changed Since he Early 1980s? American Economic Review, 90, MORLEY, J.C., C.R. NELSON, E. ZIVOT (003): Why Are he Beveridge-Nelson and Unobserved- Componens Decomposiions of GDP So Differen? Review of Economics and Saisics, 85,

21 APPENDIX 19 NELSON, C.R., R. STARTZ (007): The Zero-Informaion-Limi Condiion and Spurious Inference in Weakly Idenified Models, Journal of Economerics, Vol. 138, No. 1, PERRON, P. (1989): The Grea Crash, he Oil Price Shock, and he Uni Roo Hypohesis, Economerica, Vol. 57, No. 6, PERRON, P., T. WADA (009): Le s Take a Break: Trends and Cycles in US Real GDP. Journal of Moneary Economics, 56, PRESCOTT, E.C. (1987): Theory ahead of business cycle measuremen. Federal Reserve Bank of Minneapolis, Carnegie-Rocheser Conference on Public Policy. RIGOBON, R. (003): Idenificaion hrough Heeroskedasiciy. The Review of Economics and Saisics, November 003, 85(4), STOCK, J.H., M.W. WATSON (1988): Variable Trends in Economic Time Series. Journal of Economic Perspecives, Vol., No. 3, STOCK, J.H., M.W. WATSON. (003): Has he Business Cycle Changed? Evidence and Explanaions. Federal Reserve Bank of Kansas Ciy, Proceedings of he Symposium on Moneary Policy and Uncerainy. WEBER, E. (011): Analyzing U.S. Oupu and he Grea Moderaion by Simulaneous Unobserved Componens. Journal of Money, Credi and Banking, Vol. 43, No. 8, APPENDIX Regime Correlaion Relaion of STD 1 (1947m1-1960m1) (1961m1-1984m1) (1984m - 008m5) (008m6-011m3) TAB. 1: Correlaion coefficiens and he relaions of sandard deviaions of he composie shocks (USA) Regime Correlaion Relaion of STD 1 (1957m1-1985m1) (1985m m1) (1995m1-008m5) (008m6-011m5) TAB. : Correlaion coefficiens and he relaions of sandard deviaions of he composie shocks (CA)