Decomposing G7 Business Cycle

Transcription

1 Dcomposing G7 Businss Cycl Sungjin Cho Jangryoul Kim In his papr, w hav simad a modl ha incorporas wo ky faurs of businss cycls, co-movmn among conomic variabls and swiching bwn rgims of xpansion and rcssion, o aggrga quarrly daa for h G7 counris. Two common facors, inrprd as rflcing h prmann and ransiory componns of h businss cycl in h rgion, and simas of urning poins from on rgim o h ohr wr xracd from h daa by using h Kalman filr and maximum liklihood simaion approach of Kim(994). Esimaion rsuls confirm a fairly ypical sylid fac of businss cycls - rcssions ar spr and shorr han rcovris, and boh co-movmn and rgim swiching ar found o b imporan faurs of h businss cycl in hos counris as a whol. Th wo common facors produc snsibl rprsnaions of h rnd and cycl, and h simad urning poins agr qui wll wih indpndnly drmind chronologis. I also urns ou ha h dgr of synchroniaion bwn h G7 and h Koran conomy has significanly incrasd afr h Asian currncy crisis of 997. Kywords: Businss cycls, Asymmry, Co-movmn, Prmann and ransiory componns. Inroducion Two main faurs of businss cycl, i.., co-movmn among conomic variabls hrough h cycl and asymmry in h voluion of h cycl, hav bn xnsivly xamind in liraur sinc h work of Burns and Michll(946). Rcn dvlopmn in conomric mhodology has prompd a rsurgnc of inrs in and xplici analysis of hos faurs by modrn im sris chniqus. Wih a viw o capuring h asymmric naur of businss cycl, wo yps of modls wr proposd. Th firs kind, pionrd by Hamilon(989), divids h businss cycl ino wo phass, ngaiv rnd growh and posiiv rnd growh, bwn which h sochasic rnd oupu swichs according o a lan sa variabl. This wo phas businss cycl

2 5 implis ha, sinc h rgim swich occurs in h growh ra of h rnd or prmann componn of oupu, a ngaiv sa rsuls in an oupu loss ha is prmann, vn if oupu swichs back o h xpansion growh phas. Th scond kind, having is roos in h work of Fridman(964, 993) and formally dvlopd by Kim and Nlson(999), characris rcssions as a mporary pluck down of oupu by larg ngaiv ransiory shocks. Tha bing h cas, rcssions ar nirly ransiory dviaions from rnd, no movmns in h rnd islf, and h rsuling oupu loss is mporary. Th ohr rgulariy of businss cycl, co-movmn, has also bn formally invsigad sinc h work of Sock and Wason(99). Th basic insigh of h dynamic facor modl proposd by Sock and Wason is ha h businss cycls ar masurd by a common unobsrvd facor xracd from ky variabls rflcing conomic aciviy. By mploying four monhly coincidn indicaor sris usd o consruc h Dparmn of Commrc(DOC) composi indx, hy show ha h common facor implid by h modl corrsponds closly o h DOC indx. In mor rcn sudis, h wo faurs of businss cycl ar analyd simulanously sinc h work of Dibold and Rudbusch(996). Thy provid mpirical and horical suppor for co-movmn and asymmry as imporan faurs of businss cycl and suggs ha h wo faurs should b analyd simulanously. Along his lin of rsarch, many rgim swiching common facor modls ar dvlopd, such as in Chauv(998), Kim and Yoo(995), and Kim and Nlson(998) o nam a fw. In hos synhic modls, h common facor is dfind as an unobsrvd variabl ha summaris h common cyclical movmns of a s of coincidn macroconomic variabls, as in Sock and Wason(99). Manwhil, i is also subjc o discr shifs so ha i can capur h asymmric naur of businss cycl phass, as in Hamilon(989). Dspi h succss in obaining much sharpr infrncs on h sa of h conomy, mos of h liraur mploying synhic modl focuss on ihr h Hamilon or Fridman yps of asymmry. Two xcpions would b Kim and Murray() and Crra and Saxna(3), who incorpora boh yps of asymmry by subjcing boh h common prmann and ransiory facors o rspciv rgim swiching. () Using US monhly daa, () Kim and Pigr() also considr h wo yps of asymmry, bu hy assum ha h rgim shifs in prmann and ransiory facors ar govrnd by a singl lan variabl.

3 Dcomposing G7 Businss Cycl 3 Kim and Murray() find ha mos of variaions of h US coincidn variabls during rcssions is du o h common ransiory componns. Crra and Saxna(3) also inroduc wo facors and xamin by how much h oupu of six Asian counris rcovrd from h currncy crisis in 997. In his papr, w consruc a modl ha incorporas h following hr faurs: comovmn among conomic variabls, swiching bwn rgims of booms and slump, and h rcssions of boh prmann and ransiory naur. Mos prvious rsarch using h synhic modls has ypically usd daa from h US, and fw sudis of ohr conomis hav bn undrakn. () In viw of h conomic and financial urmoil h G7 counris ar undrgoing, i is worhwhil o undrsand h naur of businss cycl in hos counris. W sima, hrfor, h modl o quarrly daa of h whol G7 counris, and xamin h rlaiv imporanc of h prmann and ransiory componns of h businss cycl in hos counris as a whol. Esimaion rsuls confirm a fairly ypical sylid fac of businss cycls - rcssions ar spr and shorr han rcovris, and boh co-movmn and rgim swiching ar found o b imporan faurs of h businss cycl in h rgion. Th wo common facors produc snsibl rprsnaions of h rnd and cycl, and h simad urning poins agr wll wih indpndnly drmind chronologis. This papr is organid as follows. Scion prsns h rgim-swiching dynamic facor modl, which allows for a common pak-rvring componn ha swichd indpndnly of h common growh componn. Scion 3 discusss h mpirical rsuls. Finally, scion 4 offrs concluding rmarks.. Modl Spcificaion W follow h dynamic facor modl dvlopd by Kim and Murray() and applid o Asian counris by Crra and Saxna(3). W assum ha ach individual im sris Y i, for i =,..., N could b rprsnd as () Mills and Wang(3) xamind h asymmry of h UK businss cycl, bu hy inroduc only h common prmann facor which is subjc o h Hamilon-yp asymmry.

4 4 5 (.) Y = γ C + ν + λ x + ω i i i i i whr C and x ar common prmann and ransiory componns, n i and w i ar idiosyncraic prmann and ransiory innovaion rms, (g i, l i ) ar facor loadings for prmann and ransiory facors, rspcivly. Following Kim and Nlson(999) and Kim and Murray(), w diffrnc h variabls o handl h ingraion problm of h obsrvd sris and wri h modl in h following diffrncd man-dviaion form: (.) y = γ c + λ x + η i i i i (.3) c = φ c + µ + µ S + υ, µ >, µ < (.4) x = ψ x + ψ x + τs + u, τ < (.5) η = ψ η + ψ η + i i i, i i, i whr c is h dmand common prmann facor. W pu u ~ iidn (, s n ), u ~ iidn (, s u (S )), and i ~ iidn (, s i ). No ha h ransiory innovaion u is allowd o b sadpndn, i.., s u (S ) = s u ( S ) + s u S. (3) Equaion (.3) rproducs Hamilon(989) rgim swiching of h common prmann componn in which μ drmins h growh ra of h prmann componn during xpansion (i.., S = ) and μ + μ drmins h growh ra of h prmann componn during conracion (i.., S = ). Equaion (.4) modls h Fridman(964, 993) rgim swiching of h common ransiory componn whos man is ro during xpansion (i.., S = ). and ngaiv (τ < ) during conracion (i.., S = ). Th lan variabls S and S follow muually indpndn wo-sa Markov procsss, aking on valu ro in xpansion and on in conracion. Transiion probabiliy marics for S and S ar P and P, rspcivly, givn by: (3) Varianc of prmann innovaions (σ ν ) and ha of ransiory innovaions in h conracion rgim (σ u ) ar fixd a on so ha h facor loading cofficins ar idnifid.

5 Dcomposing G7 Businss Cycl 5 p (.6) P = p p p q q, P = q q. Th assumpion ha h common idiosyncraic facor η i follows an AR() procss in quaion (.5) is h sam as in Crra and Saxna(3). (4) In drmining h AR lag lnghs for wo common facors, w hn follow Kim and Murray() o considr four cass in which ach facor is spcifid as ihr AR() or AR(). Afr running a fw diagnosic chcks, w sld wih h spcificaion abov. Th modl comprising quaions (.) (.6) allows us o invsiga h rol of h prmann and ransiory componns as wll as idiosyncraic shocks ovr h businss cycl. To sima h modl paramrs as wll as h unobsrvd componns, w cas h modl ino a sa-spac rprsnaion wih Markov-swiching and us h approxima maximum liklihood algorihm in Kim(994). Appndix prsns h daild dscripion of h sa rprsnaion of our modl. 3. Empirical Rsuls 3.. Daa and Esimaion W us hr quarrly im sris on oupu, consumpion, and invsmn, xpcing ha hy ar rprsnaiv of aggrga conomic condiions in h G7 counris. Ths sris ar ral GDP, ral priva final consumpion, and gross priva fixd capial formaions. (5) All sris ar sasonally adjusd volums indxs wih h yar as h bas yar. Th sampl priod is from 96Q o Q4. Graphs of h hr sris ar shown in <Figur >, whr h dod lins rprsn h log-lvls of variabls and h solid lind ar for h log-diffrncd muliplid by. W nd o chck if h hr sris ar individually ingrad. Alhough w do no rpor h dails hr, h s rsuls provid srong vidnc ha ach sris conains a uni roo. (4) W also usd h AR() spcificaion for idiosyncraic facors, bu h rsuls wr qualiaivly h sam. (5) Daa sris wr obaind from h quarrly naional accoun scion of h OECD saisical daabas. Th xac link is: hp://sas.ocd.org/indx.aspx?daascod=qna.

6 6 5 (a) GDP (b) Consumpion (c) Invsmn <Figur > Tim Sris of h Thr Variabls

7 Dcomposing G7 Businss Cycl 7 <Tabl > Esimas of Dynamic Facor Modl common prmann facor φ μ μ p p σ ν.969 (.).97 (.5) -.93 (.75).954 (.3).96 (.) - common ransiory facor ψ ψ τ q q σ u σ u.4 (.4) -.48 (.36) -.9 (.33).93 (.4).734 (.77) (.4) idiosyncraic componn ψ i ψ i γ i λ i σ i Δy -.3 (.49).384 (.4). (.).48 (.).34 (.6) Δy -.39 (.38) -.86 (.39). (.).45 (.8).34 (.8) Δy (.4) -.5 (.53).9 (.).559 (.5).76 (.6) Log-liklihood valu No: Th ordr of h variabls in y i is GDP, priva consumpion, and invsmn. Sandard rrors ar in parnhss. Thrfor, w us h firs diffrncs of h variabls in logs (muliplid by on hundrd) as is implid by h modl s ou in Equaions (.) o (.6). Also, as in h modl, all sris ar dmand by subracing h sampl man from ach diffrnc. Sandard sochasic growh modls wih capial accumulaion imply ha oupu, consumpion, and invsmn shar a common socsuhasic rnd. Basd on his insigh along wih h prmann incom hypohsis, Kim and Pigr() idnify consumpion wih h pur sochasic rnd (wihou ransiory variaions) and impos h coingraing rsricions among h hr variabls. In his papr, w follow Crra and Saxna(3) and do no impos his rsricion in ordr o allow for possibl liquidiy consrains ha would rndr a las som fracion of consumpion dpndn upon ransiory incom. Th simaion rsuls ar prsnd in <Tabl >. Th simad modl sms succssful in

8 8 5 xracing informaion abou flucuaions in conomic aciviy. Th rsuls suppor h prsnc of asymmric businss cycls ha swich bwn wo diffrn sas. For h common prmann componn, h sa has posiiv and significan man whil h sa has a significanly ngaiv man. Similar rsuls ar obaind for h common ransiory facor, in ha h sa has man ro and h sa has significanly ngaiv man, rspcivly. Ths rsuls imply ha boh h Fridman and Hamilon yp rgim swichs ar imporan in xplaining h businss cycls in h daa w considr. Th ransiion probabiliis associad wih h xpansion and conracion rgims of h common prmann facor ar.954 and.96, rspcivly, which imply ha h avrag duraions of h wo rgims for h prmann componn ar 4-5 yars. For h common ransiory facor, howvr, h rsuls ar qui diffrn: h avrag duraion of xpansion phas is abou 3 quarrs, whil ha of conracion rgim is lss han on yar. Ovrall, h simas of ransiion probabiliis and sa-dpndn mans imply h following: ovr h businss cycl, conracions ar on avrag boh spr and shorr han xpansions, which is consisn wih h findings in h liraur (.g., Kim and Nlson(998) for h US and Mills and Wang(3) for h UK). (6) Howvr, h swichs bwn rgims for h prmann facor ar infrqun. Moving o h boom panl of <Tabl >, h ngaiv AR cofficins for invsmn and consumpion indica ha h idiosyncraic componns of hs sris xhibi ngaiv srial corrlaion, whil h GDP sris bhavs diffrnly wih posiiv idiosyncraic auocorrlaion (i.., ψ 3 + ψ > ) wih a lag. Esimas of facor loadings show ha all hr variabls ar pro-cyclical wih posiiv facor loadings for boh h prmann and ransiory componns, in agrmn wih convnional viws of h businss cycl. Of h hr sris, invsmn has h highs wighing on h wo common facors, suggsing ha his sris is h mos snsiiv coincidn variabl. If h facor loadings for h ransiory componn ar all ro, our modl collapss o a dynamic facor modl which rlgas all variaions in daa o a rgim-swiching common growh componn. As w canno s h join hypohsis ha hs ransiory facor loadings ar all ro du o h non-sandard naur of h problm, (7) w s whhr h facor (6) No ha q > q and τ > for h ransiory componn. (7) Undr h null hypohsis ha λ i = for all i, h paramrs associad wih common ransiory

9 Dcomposing G7 Businss Cycl 9 (a) Common Prmann Facor, C (b) Growh Ra of Common Prmann Facor, Δc (c) Common Transiory Facor, x <Figur > Exracd Common Prmann Facor componn ar no idnifid. Sinc h disribuion of h s saisic in h prsnc of such nuisanc paramrs ha xis only undr h alrnaiv hypohsis is unknown for h sa spac modl w ar daling wih, w s insad h individual hypohsis ha λ i = for on i.

10 3 5 loadings for h ransiory componn ar individually significan. Th asympoic -raios for hs paramrs indica ha hy ar all individually significan a h % lvl. This confirms ha ha h common ransiory facor should no b ignord in xplaining h daa. (8) Figur (a) and (b) plo h xracd common prmann facor in lvls and firs diffrncs, rspcivly. (9) W argu ha h prmann facor sris rflcs h movmns of ponial GDP (up o h facor loading). Tha bing h cas, h panl (b) xhibis four priods of major slowdowns: h wo oil criss in 973 and 979, h 999- rcssion, and h subprim financial crisis in la 7, during which h growh ra of prmann facor sharply dcrass. Ohr findings in panl (b) ar h scular slowdown in ponial growh ovr h 7s and h sagnaion of ponial growh sinc hn, xcp h la 9s in h mids of h nw conomy. Figur (c) plos h xracd Markov swiching common ransiory facor, which can b inrprd as cyclical or rnd-dviaing componn of h businss cycl. This sris clarly shows h high volailiy of h 98s and h rlaiv sabiliy of h 99s, rflcing h Gra Modraion in h 99s. Also, h plos for h ransiory facor idnify a brif rcssion around 98. On possibly imporan finding is ha a considrabl, if no all, fracion of h impac on h G7 conomy causd by h rcn subprim crisis is ransiory pluckdowns: h magniud of h pluck-down in h ransiory componn is much largr han ha in h prmann componn, and all h mor so if w considr h wo facor loadings for GDP. On way o masur h imporanc of h wo common facors is o compar hir abiliy o mimic acual businss cycl pak-rough das. <Figur 3> plos h filrd probabiliis ha h conomy is in rcssionary rgims, along wih h acual businss cycl chronology ovr h sampl priod. () Panl (a) shows h rcssion probabiliy Pr[S j = Ω T ] or h (8) On inrsing finding is ha h loading of ransiory facor for consumpion is significanly posiiv, albi small, in conras o h prdicion of h prmann incom hypohsis. As sad arlir, w viw his as suggsing ha liquidiy consrains rndr a las som fracion of consumpion dpndn upon ransiory incom. (9) Sock and Wason(99) and Kim and Murray() discuss dails on how o consruc h lvl of h common prmann facor. () Th conracion das ar: 6:Q3-63:Q, 64:Q-65:Q, 69:Q3-7:Q, 73:Q4-75:Q, 79:Q-8:

11 Dcomposing G7 Businss Cycl 3 (a) Conracion in h Prmann Facor (b) Conracion in h Transiory Facor <Figur 3> Smoohd Probabiliis of Conracion prmann facor, whil panl (b) plos ha for h ransiory facor. Ovrall, h plos show mor frqun pluck-downs in h ransiory facor han in h prmann facor: if w us h.5 rul o drmin whhr h conomy is in conracion, () h simad probabiliis for h prmann facor calls 3 rcssions whil h ransiory componn givs 7. Th hr rcssions from h mid-9s o in h rfrnc cycl, howvr, ar dcd by nihr h simad rcssion probabiliis for h prmann nor hos for h ransiory facors. For a mor formal comparison of h wo facors, w again mploy h.5 rul o dclar Q4, 84:Q4-86:Q4, 89:Q-93:Q3, 95:Q-96:Q, 98:Q-99:Q, :Q4-:Q. () According o h.5 rul, h conomy is viwd in conracion if h smoohd probabiliy of rcssion is grar han.5, i.., Pr[S j = Ω T ] >.5., j =,.

12 3 5 modl-drmind rcssion priods and valua h rsuling daing prformanc by h Quadraic Probabiliy Scor(QPS) of Dibold and Rudbusch(989), dfind as: (3.) QPS = (Pr[ Sj = Ω T ] D ), j=, T whr D is a (,) dummy for h OECD rcssion daing. Th closr his masur is o ro, h br is h modl fi o h businss cycl chronology. W obain a QPS scor of.58 for h rcssion das calld by h prmann facor only, whil h QPS for h ransiory facor is much lowr.377, hus confirming h addiional imporanc of ransiory componn idnifying businss cycl phass. 3.. Synchroniaion wih h Koran Businss Cycl In his subscion, w xamin h dgr of businss cycl synchroniaion bwn h G7 and h Koran conomy. W firs obain h prmann and cyclical componns of h Koran businss cycl. () W hn masur h dgr of synchroniaion bwn h wo conomis. For ach common facor, w calcula wo masurs of synchroniaion: h corrlaion cofficins bwn h simad componns of h wo conomis, and hos bwn h smoohd probabiliis of conracion. In so doing, w can chck if h dgr of synchroniaion masurd by corrlaion cofficins shows any significan changs across h pr- and pos h Asian currncy crisis in 997. <Tabl > blow rpors h rsuls. Srikingly, i urns ou ha h dgr of synchroniaion is much highr in h pos-998 ra han bfor. For insanc, whn w focus on h changs in h prmann componn, h corrlaion bwn Koran and h G7 rgion ovr h whol and h pr-998 priod ar mr.36 and.383, rspcivly. In h pos-998 ra, howvr, h corrlaion cofficin <Tabl > Businss Cycl Synchroniaion wih Kora Corrlaion bwn whol priod pr-998 pos-998 Trnd growh ra Δc Prob{S = } Cyclical flucuaion x Prob{S = } () S Kim() for h dails of h modl and daa usd for h Koran conomy.

13 Dcomposing G7 Businss Cycl 33 incrass o.6, suggsing posiiv dgr of synchroniaion afr h Asian currncy crisis. This finding is robus across all cass considrd in <Tabl >, rgardlss of whhr w calcula corrlaion bwn conracion probabiliis or w focus on h synchroniaion of cyclical componn. On conclusion is clar: h pos-998 incras in h businss cycl synchroniaion bwn Kora and h G7 rgion, probably su o h srucural rform pursd in Kora sinc hn. 4. Conclusion In his papr, w hav simad a modl ha incorporas wo ky faurs of businss cycls, co-movmn among conomic variabls and swiching bwn rgims of xpansion and rcssion, o aggrga quarrly daa for h G7 counris. Two common facors, inrprd as rflcing h prmann and ransiory componns of h businss cycl in h rgion, and simas of urning poins from on rgim o h ohr wr xracd from h daa by using h Kalman filr and maximum liklihood simaion approach of Kim(994). Esimaion rsuls confirm a fairly ypical sylid fac of businss cycls - rcssions ar spr and shorr han rcovris, and boh co-movmn and rgim swiching ar found o b imporan faurs of h businss cycl in h rgion. In paricular, a considrabl fracion of rcssions ar xplaind by movmns in h common ransiory componn. As a whol, h wo common facors combind produc snsibl rprsnaions of h rnd and cycl, and h simad urning poins agr wll wih indpndnly drmind chronologis. As an applicaion of h rsuls, w xamin h dgr of businss cycl synchroniaion wih Kora. I urns ou ha h dgr of synchroniaion, masurd by corrlaion cofficins bwn common componns or conracion probabiliis, has significanly incrasd sinc h Asian currncy crisis. Associa Profssor, School of Economics, Soul Naional Univrsiy 599 Gwanak-ro, Gwanak-gu, Soul 5-746, Kora Phon: Fax: sungcho@snu.ac.kr

14 34 5 Corrsponding Auhor, Profssor, Dparmn of Inrnaional Economics and Law, Hankuk Univrsiy of Forign Sudis 7 Imun-dong, Dongdamun-gu, Soul 3-79, Kora Phon: Fax: kjryoul@hufs.ac.kr Appndix Th modl in quaions (.)-(.6) can b xprssd in sa-spac rprsnaion, comprising h masurmn and ransiion quaions as follows: Masurmn Equaion y i c = γ λ λ γ λ λ γ λ λ n x x 3 3 Transiion Equaion: n x x = 3 3 β β τ φ ψ + + S S ψ ψ ψ ψ ψ 3 3 ψ ψ n x 3 3 x + v u 3

15 Dcomposing G7 Businss Cycl 35 Covarianc Marix of h Disurbanc Vcor: E v u v u 3 3 = σ ν σ σ σ u 3 σ Rfrncs Burns, A. F., and W. A. Michll(946): Masuring Businss Cycls, Nw York, NBER. Crra, A., and S. Saxna(3): Did Oupu Rcovr from h Asian Crisis? IMF Working Paprs 3/48, Inrnaional Monary Fund. Chauv, M.(998): An Economric Characriaion of Businss Cycl Dynamics wih Facor Srucur and Rgim Swiching, Inrnaional Economic Rviw, 39, Dibold, F. X., and G. D. Rudbusch(989): Scoring h Lading Indicaors, Journal of Businss, 6, (996): Masuring Businss Cycls: A Modrn Prspciv, Rviw of Economics and Saisics, 78, Fridman, M.(964): Monary Sudis of h Naional Burau, Th Naional Burau Enrs Is 45 h Yar, 44 h Annual Rpor, NBER, 7-5. (993): Th Plucking Modl of Businss Flucuaions Rvisid, Economic Inquiry, 3, Hamilon, J. D.(989): A Nw Approach o h Economic Analysis of Nonsaionary Tim Sris and h Businss Cycl, Economrica, 57, Kim, C. J.(994): Dynamic Linar Modls wih Markov Swiching, Journal of Economrics, 6, -. Kim, C. J., and C. Murray(): Prmann and Transiory Componns of Rcssions, Empirical Economics, 7, Kim, C. J., and C. R. Nlson(998): Businss Cycl Turning Poins, a Nw Coincidn

16 36 5 Indx, and Tss for Duraion Dpndnc Basd on a Markov Swiching Modl of h Businss Cycl, Rviw of Economics and Saisics, 8, 88-. (999): Fridman s Plucking Modl of Businss Flucuaions: Tss and Esimas of Prmann and Transiory Componns, Journal of Mony, Crdi, and Banking, 3, Kim, C. J., and J. Pigr(): Common Sochasic Trnds, Common Cycls, and Asymmry in Economic Flucuaions, Journal of Monary Economics, 49, 89-. Mills, T. C., and P. Wang(3): Mulivaria Markov Swiching Common Facor Modls for h UK, Bullin of Economic Rsarch, 55, Kim, M. J., and J. S. Yoo(995): Nw Indx of Coincidn Indicaors: A Mulivaria Markov Swiching Facor Modl Approach, Journal of Monary Economics, 36, Kim, J.(): Th Lgacy of Two Criss: Th Cas of Kora, manuscrips, Sock, J. H., and M. W. Wason(99): A Probabiliy Modl of h Coincidn Economic Indicaors, in K. Lahiri, and G. H. Moor(ds.), Lading Economic Indicaors: Nw Approachs and Forcasing Rcords, Nw York, Cambridg Univrsiy Prss,