DYNAMIC RISK SHARING IN THE UNITED STATES AND EUROPE. Pierfederico Asdrubali * European University Institute, Florence. and

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1 DYNAMIC RISK SHARING IN THE UNITED STATES AND EUROPE By Perfederco Asdrubal * European Unversy Insue, Florence and Soyoung Km ** Unversy of Illnos a Urbana-Champagn December Prelmnary verson JEL Classfcaon: Key Words: Rsksharng, Consumpon Smoohng, VAR, European Moneary Unfcaon, Shock Absorpon, Redsrbuon, Transory Shocks Absrac Ths paper uses a panel VAR model o mprove upon he exsng leraure on nerregonal rsk sharng channels (e.g. Asdrubal, Sorensen and Yosha, 1996) n several respecs. Frs, endogenzes he oupu process whn a mul-equaon framework, capurng he dynamc feedback beween oupu and varous rsk sharng channels. Second, n conras o prevous research's analyss of sac rsk sharng n he presence of exogenous oupu shocks, uses mpulse response funcons o race he role of each rsk sharng channel over me, n he presence of dfferen srucural shocks (emporary vs. perssen and oupu vs. rsk sharng channels). Thrd, he paper exends he rsk sharng channels ypcally analyzed, by consderng he consumpon smoohng role of changes n he nomnal exchange rae and relave commody prces across regons. As a resul, s able o beer address such polcy ssues as wheher publc rsk sharng has been a subsue or a complemen for fnancal marke dversfcaon acves, or wheher he rsk sharng role of exchange rae movemens n Europe has been relavely unmporan. * Fnance and Consumpon Char, European Unversy Insue, va de Roccen 9, San Domenco d Fesole (FI), Ialy; phone: +(055) , fax: +(055) , emal: asdrubal@ue. ** Deparmen of Economcs, 225b DKH, 1407 W. Gregory Dr., Urbana, IL 61801, phone: (217) , fax: (217) , e-mal:km11@uuc.edu 1

2 1. Inroducon The European Unon lke any oher moneary unon enals vrually no role for regonal moneary polcy, and a much lmed scope also for regonal fscal sablzaon. Hence he moneary unfcaon process has revved he aenon o sablzaon mechansms able o nsure agans he rsk of dosyncrac oupu shocks among he regons of a currency area.. Sala-Marn and Sachs (1992) denfed one such mechansm n he fscal federals srucure of counres lke he Uned Saes; hey calculaed ha he ax/ransfer sysem n he US smoohes up o 40% of an ncome shock o a sae, and much less n Europe. 1 Anoher channel of rsk sharng had long been denfed by he fnance leraure: porfolo dversfcaon. Snce Arrow and Debreu's work on equlbrum conngen clams was clear ha ncome accrung from cross-regonal asse ownershp provdes an mporan hedgng agans dosyncrac conngences. French and Poerba (1991) were among he frs o documen he (scarce) exen of such rsk sharng n a few ndusral counres, and van Wncoop (1994) confrmed he nernaonal rsksharng puzzle for he OECD. These analyses were relavely unconneced unl Asdrubal, Sørensen and Yosha (1996) (henceforh ASY) usng a varance decomposon mehod negraed all he rsksharng channels n a unque framework, and were able o calculae ha an oupu change n a US sae s smoohed on average for 39% by nersae asse ncome, for 13% by fscal rsksharng, and for 23% by cred markes hrough nerregonal lendng and borrowng. 2 Sørensen and Yosha (1998) (henceforh SY) repeaed he analyss for he OECD and confrmed French and Poerba (1991) s home bas resul, whle revealng ha all nernaonal smoohng abou 30% of a shock o a counry s oupu -- akes place hrough domesc cred markes (and mosly hrough budge defcs, as Arreaza, Sørensen and Yosha (1997) have documened). Several papers have refned ASY s mehodology, 3 and a map s beng creaed of he scope and capably of shock absorpon of several counres, and regons heren. The paern ha seems o emerge s one of scarce nernaonal rsksharng, where home bas prevals and smoohng akes place essenally hrough 1 von Hagen (1992) for he US and Bayoum and Masson (1994) for he US and Canada found somewha smaller numbers, due o dfferen economerc echnques employed. 2 I s no clear n he leraure wheher cred marke smoohng s acually a form of rsksharng, snce akes place afer he realzaon of he shock. See a bref dscusson n Ahanasouls and van Wncoop (1998). 3 For example, Alberola and Asdrubal (1997) added rsksharng hrough mgraon; Asdrubal (1998) dsngushes rsksharng from neremporal smoohng; Del Negro (1998) analyzes shocks o permanen raher han curren oupu; Ahanasouls and van Wncoop (1998) separae ou he unpredcable oupu shocks; Mélz and Zumer (1999) add addonal regressors. Oher papers, such as Pellegrn (1998), and Dedola, Usa and Vannn (1999) apply he seup o dfferen counres. 2

3 domesc savng; and rcher nerregonal rsksharng, where he role of capal markes can somemes be preponderan. 4 The leraure menoned above shares mos of he same assumpons (e.g., exogeney of oupu) and revolves around a basc seup (essenally sac), whch allows a smple quanfcaon of rsksharng channels, bu also leaves some mporan quesons unanswered. Wha knds of shocks have he larges mpac on consumpon? How long does ake o absorb a gven shock o oupu? Does depend on he rsksharng channels? Wha s he dynamc role of each rsk sharng channel? Wha are he relaons among dfferen rsk sharng channels? Are hey subsues or complemens? I s somewha surprsng gven he economerc srucure of he ssue a hand ha he leraure has so far negleced he use of dynamc and smulaneous economerc models. To address hese quesons, hs paper uses a dynamc and smulaneous economerc model, namely a panel Vecor Auoregresson (VAR) framework, o generalze he sochasc processes of he relevan se of varables. As a consequence, some lmaons of he sac leraure are overcome, and new ssues can be addressed. Frs, he model endogenzes he oupu process whn a mul-equaon framework, capurng he dynamc feedback beween oupu and varous rsk sharng channels. Second, n conras o prevous research's analyss of sac rsk sharng n he presence of exogenous oupu shocks, uses mpulse response funcons o race he role of each rsk sharng channel over me, n he presence of dfferen srucural shocks (emporary vs. perssen, shocks o oupu vs. shocks o rsk sharng channels). Thrd, he paper exends he rsk sharng channels ypcally analyzed, by consderng he consumpon smoohng role of changes n he nomnal exchange rae and relave commody prces across regons. As a resul, s able o beer address such polcy ssues as wheher publc rsk sharng has been a subsue or a complemen for fnancal marke dversfcaon acves, or wheher he rsk sharng role of exchange rae movemens n Europe has been relavely unmporan. We es our mehodology on hree groups of counres/regons: he saes of he USA, he 23 OECD counres, and he 15 European Unon members for whch Naonal Accouns daa are avalable. Boh for he US and for he OECD (and EU15), we fnd ha he dynamcs of rsksharng are much rcher han he smple sac model could foreshadow. Some smoohng channels, lke capal markes, exer her effec mosly on mpac, and hen declne rapdly; some ohers, lke he ax/ransfer sysem, connue o absorb oupu shocks years afer hey h; sll oher channels, lke he cred markes, sar havng a ds- 4 Alberola and Asdrubal (1997) found ha capal markes and cred markes n Span smooh 23% of an oupu shock each. These fgures rse respecvely o 63% and 20% for Ialy and 48% and 56% for he UK (Dedola, Usa and Vannn 1999). 3

4 smoohng effec afer wo years, hereby offseng any nal bufferng acon. Anoher example of he complexy of rsksharng dynamcs comes from he analyss of real exchange rae changes n response o oupu shocks: whle on mpac he real exchange rae exhbs a ds-smoohng effec, over me moves owards a neural effec. Moreover, f we decompose s movemens no changes n he nomnal exchange rae and changes n relave prces, we fnd ha he former are responsble for he nal ds-smoohng, snce prces adjus slowly. As prces cach up, he effec of he nomnal exchange rae on he real exchange rae s neuralzed. As for he ssue of exogeney of oupu, we fnd ha mos of he changes n oupu a annual horzon are caused by shocks o GDP, no by oher srucural shocks, ncludng consumpon. In addon, usng a VAR sysem wh long-run (LR) resrcons, we are able o dsngush he responses o permanen and emporary GDP shocks; we fnd ha mos of he changes n oupu a annual horzon are caused by permanen GDP shocks. However, hese resuls also sem from he mporan fac ha shocks o smoohng channels (ncludng consumpon) are mosly offse by he oher smoohng channels (also ncludng consumpon) a annual horzon; for example, a change n he srucure of fnancal markes affecng cross-regonal ncome flows ends o be offse by changes n he smoohng role of savng. We wll derve polcy mplcaons from hs subsuably of smoohng channels, as well as from he ds-smoohng role of real exchange raes. The paper s organzed as follows. Secon 2 summarzes he framework used so far o esmae rsk sharng channels, and hen explans he VAR modelng and he emprcal mehodology. Secon 3 dscusses he daa and he basc resuls. Secon 4 dscusses he exended models, whch quanfy he role of addonal smoohng channels. Secon 5 summarzes he resuls and concludes. 2. Mehodology 2.1. The foundaons of rsksharng ess Mos of he leraure on rsk sharng consders a world of endowmen economes --- ndexed by --- lasng nfne perods ndexed by. Each economy s populaed by a represenave rsk-averse consumer who maxmzes hs expeced VNM uly n he face of an exogenous sochasc oupu process, GDP. Under CRRA preferences, can be shown ha, f markes for conngen clams are complee, 5 every represenave agen wll nsure hs fuure 5 Marke compleeness s a suffcen, bu no necessary condon for full rsksharng. Several auhors have shown ha even f only a lmed number of socks are raded nernaonally, under ceran spannng condons full rsksharng can sll be acheved; for example, Duffe and Huang (1985). 4

5 ncome sream n any conngency. Thus, full rsksharng ensues, mplyng ha each economy's consumpon wll comove wh aggregae, raher han domesc, oupu. Namely, C = µ Y (0.1) where me, and C represens consumpon of ndvdual n perod, Y sands for aggregae oupu a µ s a facor whch represens counry s power n he rsksharng arrangemen. Ths resul has a few srong emprcal mplcaons warranng economerc esng. Frs, ndvdual consumpon growh mus be equal across counres, and hus mus also be equal o aggregae oupu (or consumpon) growh when rsksharng s full. Ths has been esed by Backus, Kehoe, and Kydland (1992) and Obsfeld (1994), who rejeced he nernaonal rsksharng proposon, gvng rse o he so called quany anomaly, or nernaonal rsksharng puzzle. A second mplcaon s ha consumpon shouldn comove wh dosyncrac varables, such as domesc oupu or employmen. For hs reason, anoher group of emprcal mplemenaons of he full rsksharng hypohess focused on he analyss of he covarance of consumpon wh dosyncrac varables (for example domesc oupu) n varous specfcaons, nerpreng he resul as a measure of rsksharng: he hgher he correlaon beween GDP (gross domesc produc) and C (oal consumpon), he lower he amoun of rsksharng aaned n he economy. 6 Furher ess on hs lne should measure wheher dosyncrac oupu shocks affec ndvdual consumpon regardless of he sochasc process governng domesc oupu. No many sudes have deal wh hs ssue. ASY esmae separaely saes wh "hgh-perssence" and saes wh "low-perssence" shocks, and separae predcable from unpredcable shocks usng lagged sae and regonal oupu as predcors. Del Negro (1998) consders dfferen sochasc processes governng oupu, whle Ahanasouls and van Wncoop (1998) dsenangle he effecs of unpredcable shocks usng a predcon regresson The sac model of rsksharng channels The sudy of rsk sharng channels bulds on he es of he second mplcaon above, by addng o he analyss he correlaon beween GDP and addonal naonal accouns measures: GNP (gross naonal produc), defned as GDP plus ne facor ncome paymens from abroad; GDI (gross dsposable ncome) defned as GNP plus axes pad o and mnus ransfers receved 6 As Hayash, Alonj and Kolkoff (1996) poned ou, any equaon ha regresses consumpon on ncome s mplcly esng for rsksharng. 5

6 from nernaonal organzaons (or, n he case of regons, from he Governmen); C (oal consumpon) defned as GDI mnus oal savngs. Noe ha we modfed some defnons of componens of Naonal Accouns o be conssen wh heorecal conceps of rsk sharng. Dealed explanaons of acual daa are provded n Secon 3.1. If one consders -- n every perod -- he followng deny: GDP GDP = GNP GNP GDI GDI C C (0.2) and hen manpulaes by akng logs and dfferences, mulplyng hrough by log GDP mnus s mean and akng expecaons, one arrves a he relaon: β k + β g + β c + β u = 1 (0.3) where β k, he coeffcen n he regresson of log GDP log GNP on log GDP, s nerpreed as he percenage of smoohng of a GDP shock carred ou by capal markes (.e., hrough ne facor ncome paymens); β g, he coeffcen n he regresson of log GNP log GDI on log GDP, s nerpreed as he percenage of smoohng of a GDP shock carred ou by nernaonal ransfers; β c, he coeffcen n he regresson of log GDI log C on log GDP, s nerpreed as he percenage of smoohng of a GDP shock carred ou by cred markes (.e., ne lendng abroad and domesc nvesmen); fnally coeffcen n he regresson of log C on log GDP β u, he, s nerpreed as he percenage of smoohng of a GDP shock ha remans unsmoohed. In pracce, he followng SUR panel sysem s esmaed: log GDI log C log GDP log GNP = ν log GDI log C, u u log GNP = ν = ν = ν, c, k, g + β log GDP + β c + ε k g u + β log GDP log GDP + β log GDP + ε + ε + ε c k g (0.4) 6

7 where ν,. are me fxed effecs. A panel esmaon for hs sysem corresponds o a weghed average over me of cross-seconal regressons. Furher deals and resuls can be found n he research papers menoned n he Inroducon, and n parcular n ASY and SY. Even hough he above framework encompasses several nce feaures of a relavely general endowmen economy, does no address several mporan ssues of a dynamc producon economy, buffeed wh varous srucural shocks (n addon o exogenous oupu shocks). Frs, he model s slen on he exac naure of he oupu changes ha exogenously cascade on he res of he economy. One mporan mplcaon of equaon (0.1) suggess ha ndvdual consumpon wll be proporonal o oupu regardless of he sochasc process governng domesc oupu. Therefore, an economerc es s warraned o esmae wheher ndvdual consumpon vares, dependng on he naure of he shock ha caused he oupu change; for nsance, whle a emporary unpredcable shock should elc complee smulaneous smoohng, a perssen predcable shock would enal some consumpon change as opmal response. Second, he above framework gnores he possbly of endogenous oupu changes due o varous srucural dsurbances. For example, n he presence of preference shocks, he proporonaly of consumpon o oupu may fal even under complee markes. 7 To examne rsk sharng due o exogenous oupu changes, we should conrol for endogenous oupu componens due o oher srucural shocks. In addon, he rsk sharng properes n he presence of shocks oher han exogenous oupu changes may be an anoher neresng ssue. A VAR framework seems he naural way o address hese ssues. A VAR model reas all varables n he sysem, ncludng oupu, as endogenous, and allows dynamc feedback among hose varables. In addon, a VAR framework s able o explcly subrac he exogenous srucural shocks and o race he dynamc effecs of srucural shocks. As a consequence, we can dsngush he effecs of dfferen knds of shocks (perssen vs. emporary, ancpaed vs. unancpaed, shocks o each rsk sharng channel), and a he same me address he endogeney problem arsng n a specfcaon lke (0.4), by fully accounng for he feedback from each componens of oupu or each rsksharng channel ono oupu. An mporan aspec of (0.4) s ha he model s essenally sac, n he sense ha he rsksharng measure s compued as weghed average of cross-seconal regressons. The VAR, usng mpulse responses o shocks, races he rsksharng reacon o a well-defned shock over me, esmang how long akes each rsksharng channel o absorb a well-defned shock. 7 SY argue ha, alhough ase shocks may be mporan o explan he lack of full rsksharng (as suggesed by Sockman and Tesar (1995)), he varance decomposon measure n equaon (0.4) s robus o such 7

8 2.3. Dynamc Smulaneous Analyss of Rsk Sharng In hs secon we wll generalze he economerc specfcaon of models lke (0.4) n order o address he 3 novel ssues we have n mnd: dynamc responses o shocks, dfferng responses dependng on he naure of he shock, and endogeney of he oupu process. Models lke (0.4) can be generalzed by allowng dynamc (conemporaneous and lagged) feedback among all varables, namely log GDP, log GDP log GNP, log GNP log GDI, log GDI log C, and log C. In he followng, we acheve ha by employng a VAR framework Srucural Panel VAR Frs we pool he daa and esmae he followng reduced form panel VAR. y = c + B(L)y -1 + u, (0.5) where c s an n 1 consan marx, y s an n 1 daa vecor, B(L) s a marx polynomal n he lag operaor L and var(u )= Σ. Insead of explcly nroducng he me fxed effec n he model, we consruc daa seres as devaons from aggregae values. 8 Based on he esmaes of he reduced form VAR, we recover he followng srucural form equaon. We assume he economy s descrbed by he srucural form equaon G 0 y = d + G(L) y -1 + e (0.6) where G 0 s he n n conemporaneous srucural parameer marx wh 1 s n he dagonal, G(L) s a marx polynomal n he lag operaor L, d s an n 1 consan marx, and e s an n 1 srucural dsurbance vecor. e s serally uncorrelaed and var(e )=Λ. Λ s a dagonal marx whose dagonal elemens are he varances of srucural dsurbances, so srucural dsurbances are assumed o be muually uncorrelaed. If (G 0 LG(L)) s nverble, he srucural form equaon can also be wren n he followng movng average represenaon. shocks. However, hey do no consder he case n whch ase shocks feed back on oupu, whch would bas her esmaes. 8 One reason ha we do no nroduce he me fxed effec explcly s o avod he well-known bas n he case of boh fxed effec and lagged ndependen varable. Refer o Hsao (1986) 8

9 y = d* + G(L)*e (0.7) where d* = (G 0 LG(L)) -1 d, G(L)* = (G 0 LG(L)) -1 G(L), and G(0)* = G 0-1. There are several ways of recoverng he parameers n he srucural form equaon from he esmaed parameers n he reduced form equaon. Ths paper employs wo dfferen mehods. The frs mposes resrcons on he conemporaneous srucural parameers G 0 whle he second mposes resrcons on he long run srucural parameers G(1) *. In he frs mehod, followng Sms (1980), we posulae a recursve srucure on he conemporaneous parameers G 0 n order o recover he parameers n he srucural form equaon. In he second mehod, followng Blanchard and Quah (1989), we assume a recursve srucure n he long run srucural parameer G(1) * The Sysem wh SR resrcons Frs, we esmae he model wh conemporaneous resrcons. The daa vecor s { log GDP, log GDP - log GNP, log GNP - log GDI, log GDI - log C}. Agan, noe ha all varables are devaons from he growh rae of own regonal aggregaes. In all esmaons n hs paper, we oban log C as he dfference beween log GDP and he sum of all oher varables usng he naonal ncome deny. Lke prevous researchers, we nerpre he sze changes n log GDP log GNP, log GNP log GDI, and log GDI log C n reacon o exogenous shocks changng log GDP as measures of rsk sharng acheved by capal markes, nernaonal ransfers, and cred markes, respecvely, and he sze of changes n unsmoohed par. Our denfyng resrcons based on equaon (0.6) are: log C as he L N M g g g g g g = d + G( L) L NM OL Q P NM loggdp log GNP loggdi loggdp log GNP loggdp log GDI loggdp log GNP log GDI log C 1 1 loggnp 1 1 loggdi 1 1 logc 1 O QP + L M NM e O QP GDP, e e e k, g, c, O P QP (0.8) Tha s, we assume a recursve srucure on he conemporaneous srucural parameers. Though hs sysem does no consder some conemporaneous feedback among varables, does no 9

10 mpose any resrcons on dynamc (lagged) feedback among hem. In ha sense, hs sysem s more general han he sac model descrbed above, whch does no consder any (dynamc) lagged neracons of hs sor. Usng he sac sysem, prevous sudes examned how log GDP s smoohed by dfferen channels of rsk sharng by regardng log GDP as exogenous. Insead, we examne how e GDP s smoohed by dfferen channels of rsk sharng by regardng e GDP as exogenous. Our measure of exogenous oupu change s more general snce n our sysem e GDP s consruced as condonal on nformaon abou he hsory of all varables n he sysem. In pracce, he sysem n (0.4) s a specal case of our specfcaon, wh he coeffcens g 32, g 42, g 43, g 52, g 53, g 54 and G(L) all equal o zero. On he oher hand, we nerpre e k,1, e g,2, and e c,3, as shocks o each rsk sharng channel, ha s, shocks o capal marke, shocks o nernaonal ransfers, shocks o cred marke. They are surprses n rsk sharng channels, condonal on all lagged varables n he sysem and on conemporaneous oupu (and some oher rsk sharng channels). By racng he mpulse responses of all varables, we can examne wheher each rsk sharng channel s a subsue or a complemen for he ohers. For example, we can nvesgae how much he role of oher rsk sharng channels such as cred channel decreases (or ncreases) gven GDP when here s an unexpecedly large ncrease n rsk sharng hrough he capal marke. In hs respec, he ncluson of he conemporaneous value of GDP n hose equaons s mporan snce we can conrol for s changes. Regardng he conemporaneous resrcons among hose rsk sharng channels, we rely on he naural properes and nerpreaons of each channel. Frs, we assume ha he cred channel s conemporaneously affeced by all ohers snce consumers would decde how much o save afer consderng he rsk sharng done by oher channels such as nernaonal ransfers and capal marke smoohng. Second, he orderng beween nernaonal ransfers (or federal governmen ransfers) and capal marke mgh be more conroversal, bu we assume ha capal marke smoohng comes frs because federal ncome axes are based on capal ncome oo, so ha mus be known before he ax s leved. A any rae, we examne he robusness of our resuls under alernave denfyng assumpon n Secon 4. We esmae he model usng no only yearly daa bu also quarerly daa when hey are avalable. By usng quarerly daa, he resrcons are on quarerly neracons. In such a case, our denfyng assumpons become weaker because we allow neracons among varables whn a year, and our measure of e GDP becomes more exogenous. 10

11 Sysem wh LR resrcons We use he same daa vecor as ha n he sysem wh SR resrcons. Our denfyng resrcons based on equaon (0.7) are: L NM loggdp loggdp log GNP loggnp log GDI log GDI log C O QP * = d + L N M g g * 21 * * 31 g32 * * * g g g OL M Q P NM e GDP, e e e k, g, c, O P QP (0.9) Noe ha he 5 5 marx on he RHS s he long run srucural coeffcens, G(1). Therefore, e GDP represens he srucural shocks ha may affec all varables n he long run; e K1, e K2, e K3, and e K4 are srucural shocks ha do no affec he level of regonal oupu n he long run. Then, we can aach some neresng srucural nerpreaons o he shocks. e GDP s he permanen shock o GDP; oher srucural shocks can enavely be nerpreed as emporary shocks o GDP snce s dffcul o jusfy any LR recursve srucure among rsk sharng channels. However, hey urned ou o be smlar o shocks o each rsk sharng channel (Refer o Secon 3.). Also noe ha our resrcons are only on he long run srucural coeffcens and we do no mpose any oher resrcons on G(L) *. Therefore, all varables are endogenously deermned by consderng all conemporaneous and lagged neracons. Agan, a model lke (0.4) can be consdered as a specal case of our sysem snce does no allow conemporaneous and lagged neracons. In he followng secons, we examne mpulse responses of log GDP, log GDP log GNP, log GNP log GDI, log GDI log C, and log C o each srucural shock o analyze he dynamc rsk sharng properes under each srucural shock. 3. Basc Resuls 3.1. Daa and Esmaon Our analyss of nernaonal rsksharng whn OECD (and EU) counres uses Naonal Accouns daa for 23 counres from 2 sources: he Inernaonal Moneary Fund's Inernaonal Fnancal Sascs Yearbook, varous ssues and CD, supplemened, where avalable, by he monhly ssues (perod ); and he OECD's Sascal Compendum on CD, for boh annual daa (perod ) and quarerly daa (perod 1980-I IV). Our varables are derved from he Naonal Accouns as follows: GDP (gross domesc produc) 11

12 GNP (gross naonal produc) = GDP + ne facor ncome from abroad GDI (gross dsposable ncome) = GNP + ne ransfers from abroad 9 C (oal consumpon) = GDI - (deprecaon + fxed nvesmens + nvenory change + rade balance) As for he Uned Saes, our daa are he same as hose consruced by ASY, and we refer o her daa appendx for a dealed descrpon. However, we augmened he daase wh he sae CPI seres, consruced by Del Negro (1998). The ls of varables s: GSP (gross sae produc) SI (sae ncome) = GSP + ne facor ncome from oher saes DI (sae dsposable ncome) = SI - federal axes + federal ransfers C (sae consumpon) = DI - (nvesmen + nersae rade balance) I s mporan o pon ou ha he US daa lack measures of nvesmen a he sae level, so ha s mpossble o dsenangle nersae smoohng from domesc smoohng. In esmang VAR equaons, we ncluded 2 lags and a consan erm n all equaons. 10 All varables are n real per capa erms, and are consruced by deflang nomnal values by domesc CPI, and dvdng by populaon. Each varable s hen subraced from he aggregae measure. The aggregae measure of each varable's growh rae s consruced based on domesc growh raes, where he wegh s drven by he relave sze of GDP n In he exended model, we use nomnal exchange raes, defned as he amoun of naonal currency exchanged for one US dollar a md-year or md-quarer The Uned Saes Fgure 1 repors mpulse responses wh wo sandard error bands over 5 years n he sysem wh he SR resrcons. Each column shows he mpulse responses of all neresed varables o each srucural shock. The name of each srucural shock s noed a he op of each column whle he names of he respondng varables are noed a he far lef of each row. GSP KAP, GOV, CRE, and C represen log GSP, log GSP log SI, log SI log DI, log DI log C, and log C, respecvely. Therefore, hey depc he changes n GSP, capal marke smoohng, smoohng by Federal Governmen, cred marke smoohng, and unsmoohed par. Noe ha our daa do no allow o separae capal deprecaon and reaned earnngs from sae ncome, so ha our KAP measures smoohng hrough hese wo 9 Ne ransfers from Naonal Accouns are unavalable n IFS sources. 10 Usng hgher lags does no change resuls much n mos cases. 12

13 channels besdes capal marke smoohng. 11 The scales of all he graphs n each column are he same. Frs, we examne he effecs of exogenous GSP shocks (n he frs column n Fgure 1). To examne he exac numbers, we also repor he responses n Table 1 (1). For Table 1(1), we normalze he sze of he shocks so ha he sum of oal changes n GSP over me s 100. In addon, we also repor he exac numbers wh sandard error n he parenhess n Table 1 (1). In Table 1 (2), we repor cumulave mpulse responses n order o examne he cumulave role of each rsk sharng channel over me. Table 1. Impulse Responses o e GDP n he Sysem wh SR resrcons, U.S. Saes 1) Impulse Responses GSP KAP GOV CRE C 0 year 74.9 (1.6) 34.7 (1.3) 7.3 (0.8) 20.9 (2.5) 12.0 (2.3) 1 year 22.4 (2.3) 3.1 (1.4) 7.1 (0.8) 6.1 (2.5) 6.1 (2.3) 2 year 2.9 (2.1) -1.6 (1.4) 1.3 (0.9) -9.4 (2.5) 12.5 (2.3) 3 year -0.1 (1.3) -0.1 (0.6) -0.2 (0.4) -3.7 (1.1) 3.9 (1.0) 4 year 0.1 (0.7) -0.2 (0.3) -0.3 (0.2) -0.4 (0.5) 1.0 (0.6) 2) Cumulave Impulse Responses GSP KAP GOV CRE C 0 year 74.9 (1.6) 34.7 (1.3) 7.3 (0.8) 20.9 (2.5) 12.0 (2.3) 1 year 97.3 (3.1) 37.9 (2.0) 14.4 (1.2) 27.0 (3.3) 18.1 (3.1) 2 year (4.1) 36.3 (2.5) 15.7 (1.4) 17.6 (4.1) 30.6 (4.0) 3 year (4.8) 36.2 (2.7) 15.4 (1.5) 13.9 (4.5) 34.4 (4.6) 4 year (5.1) 36.0 (2.7) 15.1 (1.5) 13.5 (4.6) 35.4 (4.9) From he mpulse responses of GSP, we can nfer he naure of he shocks. On mpac, GSP ncreases sharply and also shows a posve response n he nex year. From wo years afer he shocks, GSP s no much dfferen from zero. As shown n he scale, he mpac ncrease n GSP s 74.9% of oal GSP ncreases, and he ncrease n he nex perod s abou 22.4%. In response o such an exogenous shock o GSP, a large capal marke smoohng (34.7%) s found on mpac, bu n he nex perod, a lle smoohng (3.5%) s found, and laer he capal marke does no play much role. Overall capal marke smoohng conrbues abou 36.0% of oal GSP changes. In he frs wo perods, smoohng by he Federal governmen s sgnfcan, 7.3% and 7.1%, respecvely. Overall, he conrbuon s more han 15.1%. Cred marke conrbues 20.9% on mpac, abou 6.1% n he nex perod. However, n he second and 11 In any case, SY have llusraed how hose wo channels are unlkely o affec he capal smoohng measure. 13

14 hrd years afer he shocks, a sgnfcan negave conrbuon s found, -9.4% and 3.7%, respecvely. Overall, cred marke smoohes 13.5 % of oal GSP shocks. Consumpon (UNS) ncreases up o hree years afer he shocks. Overall, 35.4% of he GDP changes are unsmoohed. The mpulse responses show dfferen dynamc roles of he dfferen rsk sharng channels. Mos smoohng by capal marke occurs on mpac whle smoohng by cred marke occurs over me and s posve nally bu negave laer. The resuls are conssen wh our nerpreaons of he capal marke smoohng; however, he behavor of cred marke smoohng s somewha dffcul o be explaned clearly. Capal marke smoohng nsures unceran fuure conngences. Pars of capal marke smoohng such as capal gans and dvdends may occur almos on mpac when here are unexpeced changes n expeced curren and fuure ncome, hough some oher componens, such as neres paymens, may accrue wheher he ncome change s expeced or no. Therefore, a subsanal par of smoohng by capal marke s acheved on mpac when he naure of he shock s revealed. 12 However, s no so easy o explan he cred marke smoohng based on radonal heores of consumpon smoohng. We may regard he cred marke smoohng (a leas par of ) as neremporal rade. Followng radonal heory on consumpon smoohng or neremporal rade, n he presence of AR-1 oupu growh rae shocks wh a posve AR-1 coeffcen, consumpon growh rae n he frs perod should be more volale han oupu growh rae whle consumpon growh rae n he laer perod should be less volale han oupu. However, we fnd he oppose regardng he relave volaly of consumpon and oupu, even hough he GSP dynamcs n our model s smlar o he AR-1 oupu growh rae shocks wh a posve AR-1 coeffcen. Ths problemac relave volaly beween consumpon and oupu s known as Deaon s paradox. We sugges hree possble explanaons for hs behavor of consumpon. Frs, we rely on mperfec nformaon of consumers. Suppose he GSP shocks are a mxure of permanen and emporary shocks n he level of GSP. When a shock hs, consumers don know whch shock s realzed, so nally hey smooh a lle (or lend). However, n laer perods, consumers realze ha he shocks s very perssen, (as shown n he resuls for he longrun resrcons below), and borrow n he face of an ncreasng permanen ncome level. Alernavely, we may nerpre ha consumers smooh he growh rae of consumpon, nsead of he level of consumpon. In such a case, he dynamcs are conssen wh consumpon growh 12 Noe ha he role of capal marke s very small n he one year afer he shock. Even hough we fnd a subsanal ncrease n GSP (22%), s already expeced n he one year afer he shock. (I s already 14

15 rae smoohng. Snce he GSP s hgher for he frs wo perods, consumers save for he frs wo perods. In he nex wo perods, consumers use he savng. As a resul, consumpon s smoohed over he four perods. 13 Fnally, all hese problems may be properes of a producon economy subjec o producvy shocks or oher srucural shocks generang such GSP dynamcs, regardng whch we do no have a full-fledged heory. Fnally, mos smoohng by he Federal Governmen occurs whn wo years. I suggess ha smoohng by he Federal Governmen seems o be based on he curren value (and possbly one perod lagged value) of GSP. In general, hese resuls are conssen wh prevous sudes by ASY, Del Negro (1998), and ohers, n ha hey reveal ha a large fracon of a shock s smoohed across saes n he US, and ha he role of prvae markes as compared o he ax/ransfer sysem s preponderan for rsksharng. However, mpulse responses convey a more nformave pcure on he evoluon over me of smoohng responses. The frs orgnal resul s ha akes some me o absorb a shock, even wh auomac sablzers lke cross-sae capal ncome paymens or axes. In he former case, he adjusmen lag of abou 3 years may be due o he srucure of cross-sae paymens n he US (neres paymens may no accrue annually, as n zero-coupon bonds), o capal deprecaon or reaned earnngs (boh ncluded n he measure of sae ncome). As for fscal smoohng, ceran axes (and subsdes) may refer o evens occurred years before (e.g., refunds). The cred marke channel presens an addonal feaure deservng aenon: 2 years afer he shock on average, cred flows have a ds-smoohng role, ha s hey flow owards he sae h wo years before by a posve shock. As a resul, he cumulave response of cred markes s lower han he mpac response, and lower han had been prevously esmaed n oher sudes. Snce hs channel measures boh nersae and nrasae smoohng, s possble ha as menoned above -- neremporal smoohng consderaons may affec he behavor of savngs over me. Nex, we examne he mpulse responses of shocks o each rsk sharng channel (n he second, hrd, and fourh columns n Fgure 1). Frs, he posve shocks o cred marke and Federal governmen paymen sysem does no affec oher varables much excep for own varable and consumpon. Tha s, an ncrease n savng or federal governmen ne ransfers does no affec oher rsk sharng channels. Also noe ha GSP does no change much. As a resul, he ncrease n savng or Federal governmen ne ransfers jus decreases he unsmoohed par (C). refleced n he capal marke smoohng n he frs perod.) We sll fnd some posve role of capal marke one year afer he shocks, whch may reflec neress and oher prearranged paymens. 15

16 However, he shocks o capal marke do affec all varables sgnfcanly. Frs, an ncrease n ne facor ncome decreases savng -- and smoohng hrough savngs -- sgnfcanly. The sze of he mpac ncrease and he mpac decrease are smlar, whch mples ha an ncrease n he capal marke channel crowds ou he cred marke channel almos perfecly. We also fnd a small decrease n Federal governmen ne ransfers. Overall, an ncrease n ne facor ncome s almos perfecly offse by decreases n oher channels on mpac. As a resul, consumpon does no change a all on mpac. In he nex perod, GSP ncreases and mos par of he ncrease s smoohed by he cred channel. Probably hs effec s due o he mpac on producvy of fnancal ncome. Ths s an example of a feedback from rsksharng channels o oupu ha was negleced by prevous sudes, and ha may help assess he relave mporance of hese channels for smoohng purposes; ndeed, f a change n capal markes s desablzng for oupu, hs may promp o reconsder her overall role n smoohng dsurbances. The above resuls on shocks o each rsk sharng channel have anoher neresng polcy mplcaon. The Federal Governmen s aemp o ncrease rsk sharng whn U.S. saes va axes and ransfers s crucal, n ha oher relavely prvae marke mechansms canno subsue hem auomacally. For example, suppose he Federal Governmen reduces he overall level of axes and ransfers n a parcular year. In such a case, marke mechansms do no help o make up for he los ncome nsurance. On he oher hand, he capal marke s falure n hedgng ncome n a parcular year s mosly rescued by he cred marke channel, hough here may be some dfferences n erms of permanen ncome. 14 Fgure 2 repors he mpulse responses o permanen shocks o GSP n he sysem wh LR resrcons. In general, we fnd smlar quanave resuls o hose n he model wh SR resrcons. Ths may mply ha mos of he shocks o GSP denfed n he model wh SR resrcons are permanen shocks. In response o GSP shocks, compared o he sysem wh SR resrcons, smoohng by capal markes and he Federal Governmen plays a slghly larger role whle smoohng by cred markes plays a slghly smaller role. The unsmoohed par becomes slghly smaller. Snce e GSP n he sysem wh SR resrcons may be a mxure of emporary and permanen shocks o GSP, he larger role played by capal markes and smaller role of cred markes confrm wha oher auhors, such as ASY, suggesed, namely ha, cred markes are less suable han capal markes o deal wh perssen (or permanen) shocks. Indeed, when negave 13 Suppose ha cred channel does no change a all. Then, he frs wo perod consumpon would be far hgher han he nex wo perod consumpon. 14 The sharp conras beween Federal Governmen and capal marke s robus under dfferen denfyng assumpons. For example, when we change he orderng of KAP and GOV, sll we fnd a smlar resul, 16

17 shocks are perssen, lenders may reduce loans, whereas when posve shocks perss, hey may decde o ransfer he boon on consumpon. Impulse responses o oher srucural shocks are also smlar o hose n he sysem wh SR resrcons. Though we do no aemp o nerpre hose srucural shocks n he prevous secon, hey may be nerpreed as shocks o each rsk sharng channels. Gven hs smlary wh he SR model, we may conclude ha he resuls on shocks o rsk sharng channels seem o be que general OECD and Europe We repor he resuls for 23 OECD counres and 15 EU counres 15, usng OECD daa. Snce resuls for he model wh LR resrcons and he model wh SR resrcons are qualavely smlar, we only repor he resuls for he model wh SR resrcons. Fgure 3 and Table 3 repor resuls for 23 OECD counres whle Fgure 4 and Table 4 repor resuls for 15 EU counres. Table 3. Impulse Responses o e GDP n he Sysem wh SR resrcons, OECD 23 1) Impulse Responses GDP KAP GOV CRE C 0 year 71.5 (1.9) 0.7 (0.5) -0.2 (0.3) 32.0 (1.9) 38.9 (1.7) 1 year 23.7 (2.8) -0.7 (0.5) -0.4 (0.3) -1.0 (2.0) 25.8 (2.4) 2 year 3.5 (2.9) -0.6 (0.5) -0.4 (0.3) -7.1 (1.8) 11.6 (2.3) 3 year 1.0 (2.0) 0.0 (0.4) 0.2 (0.2) -1.5 (1.0) 2.3 (1.7) 4 year 0.5 (1.2) 0.2 (0.2) 0.2 (0.1) 0.0 (0.6) 0.1 (1.2) 5 year -0.1 (0.5) 0.1 (0.1) 0.0 (0.0) 0.0 (0.2) -0.2 (0.6) 2) Cumulave Impulse Responses GDP KAP GOV CRE C 0 year 71.5 (1.9) 0.7 (0.5) -0.2 (0.3) 32.0 (1.9) 38.9 (1.7) 1 year 95.1 (3.9) 0.1 (0.8) -0.6 (0.5) 31.0 (2.7) 64.7 (3.2) 2 year 98.6 (5.6) -0.5 (1.1) -1.0 (0.6) 23.9 (3.2) 76.3 (4.7) 3 year 99.6 (6.8) -0.5 (1.4) -0.8 (0.7) 22.4 (3.4) 78.6 (5.7) 4 year (7.3) -0.3 (1.5) -0.6 (0.7) 22.5 (3.3) 78.6 (6.3) 5 year (7.5) -0.2 (1.6) -0.6 (0.7) 22.4 (3.3) 78.4 (6.6) Table 4. Impulse Responses o e GDP n he Sysem wh SR resrcons, EU 15 1) Impulse Responses hough changes n ne facor ncome end o subsue for changes n Federal Governmen ne ransfers slghly. 17

18 GDP KAP GOV CRE UNS 0 year 72.4 (2.5) 2.3 (0.7) -0.3 (0.5) 36.3 (2.3) 34.1 (2.1) 1 year 18.9 (3.7) -0.8 (0.8) -0.9 (0.5) -0.5 (2.6) 21.0 (2.7) 2 year 2.8 (3.4) -1.3 (0.9) -0.8 (0.5) -7.8 (2.5) 12.7 (2.5) 3 year 3.0 (2.0) -0.5 (0.6) 0.2 (0.3) -2.1 (1.3) 5.5 (1.8) 4 year 2.2 (1.5) -0.1 (0.4) 0.4 (0.2) -0.7 (0.9) 2.7 (1.4) 5 year 0.7 (0.9) 0.0 (0.3) 0.1 (0.1) -0.5 (0.4) 1.1 (1.0) 2) Cumulave Impulse Responses GDP KAP GOV CRE UNS 0 year 72.4 (2.5) 2.3 (0.7) -0.3 (0.5) 36.3 (2.3) 34.3 (2.1) 1 year 91.2 (4.8) 1.5 (1.3) -1.2 (0.8) 35.8 (3.6) 55.1 (3.8) 2 year 94.0 (6.6) 0.3 (1.8) -2.0 (1.0) 28.0 (4.3) 67.8 (5.3) 3 year 97.1 (7.6) -0.3 (2.1) -1.8 (1.1) 25.8 (4.6) 73.3 (6.4) 4 year 99.3 (8.3) -0.4 (2.3) -1.4 (1.1) 25.1 (4.6) 76.0 (7.2) 5 year (8.3) -0.4 (2.5) -1.3 (1.2) 24.7 (4.7) 77.0 (7.8) Resuls for 23 OECD and 15 EU counres are qualavely smlar, and boh are somewha dfferen from he resuls for he U.S. saes. Agan, n response o he e GDP shocks, GDP responds mosly for he frs wo years, hough he response s a lle more delayed and we fnd larger ncreases wo and more years afer he shocks. In conras o he U.S., capal marke and nernaonal ransfers do no play a very sgnfcan role. Among 23 OECD counres, he esmaes of eher channel are no sascally sgnfcan. Among he 15 EU counres, smoohng hrough nernaonal ransfers s no sascally sgnfcan whle capal marke smoohng plays a small posve role on mpac (2.3%) and no sgnfcan role overall. Among hese counres, mos smoohng s acheved hrough he cred channel (overall abou 22-25%). We fnd a smlar dynamc behavor of cred smoohng o ha among he U.S. saes. On mpac, a sgnfcan posve smoohng s found whle a sgnfcan negave smoohng s found for wo and hree years afer he shock. Overall 77-79% of GDP changes are no smoohed, whch s far larger han he sze of he unsmoohed par among he U.S. saes. These resuls confrm he nernaonal rsksharng puzzle, bu reveal ha he dynamc response of nernaonal cred markes o GDP shocks s exremely smlar o ha of domesc cred markes n he US: an nal smoohng va lendng and borrowng s followed, afer abou 3 years, by plan ds-smoohng. The alernance beween smoohng and ds-smoohng helps explan why dfferen auhors have faled o agree on he "sac" measure of cred markes rsksharng. Unforunaely, oher conclusons on he smlary beween he US and he nernaonal paern of cred marke smoohng would be unwarraned, because we canno 15 They are Ausrala, Belgum, 18

19 separae domesc nvesmen from nersae lendng and borrowng n he U.S saes and we canno compare nernaonal provson of cred separaely. More mporanly, however, sysemac dfferences beween domesc and nernaonal smoohng seem o dsappear n he case of cred markes: o fnd he reason for he exsence of he nernaonal rsksharng puzzle, as opposed o domesc rsksharng, we should perhaps look elsewhere. The responses o shocks o each rsk sharng channel are smlar o he U.S. n some cases, bu slghly dfferen n ohers. Frs, an ncrease n savng does no change nernaonal ransfers or ne facor ncome, as n he U.S. Second, an ncrease n ne facor ncome decreases savng as n he U.S. However, he sze of he decrease n savng s abou half he sze of he ncrease n ne facor ncome. Tha s, a rse n ne facor ncome crowds ou savng only by half. Fnally, now an ncrease n nernaonal governmen ransfers also decreases savng, whch s no observed n he U.S. sae case. The sze of decrease n savng s even larger han he ncrease n he nernaonal ransfers on mpac. Therefore, polcy mplcaons are que dfferen from he U.S. sae case. The cred marke channel now subsues for nernaonal governmen ransfers even more han does for he capal marke channel. In order o beer undersand whch componens of savng are manly responsble for hese resuls, we now urn o analyze how savng s decomposed no domesc gross nvesmen and he rade balance. 4. Exended Sysem 4.1. Componens of Savng n OECD and EU Counres Snce he cred marke (or savng) s he only rsk sharng channel ha works sgnfcanly among OECD and EU counres, we furher examne s role n deal. We dvde savng no four componens capal deprecaon (DEP), ne fxed nvesmen (NFINV), nvenores (INVT), and rade balance (TB). 16 We use he followng orderng n our recursve sysem: DEP, NFINV, TB, INVT. Frs, we nclude nvenores las snce hey are compued as resduals by defnon. Second, we nclude capal deprecaon, because apples o las year s capal formulaon. Thrd, we assume ne fxed nvesmen affecs he rade balance conemporaneously (no vce versa) snce people may decde he domesc use of savng frs, and hen decde s foregn use. Fgure 5 and 6 repor he mpulse responses o each srucural shock n he sysem wh SR resrcons n 23 OECD and 15 EU counres, respecvely. In response o e GDP shocks, DEP 16 From Naonal Accouns denes, S = I +X-M, where S s naonal savng, I s gross oal nvesmen (furher decomposable no ne fxed nvesmen, nvenory nvesmen and capal deprecaon), X represens expors and M 19

20 decreases slghly n he frs wo years, NFINV ncreases a lo n he frs hree years, TB ncreases sgnfcanly n he frs perod, bu decreases laer, and INVT ncreases n he frs wo perods bu decreases n he nex wo years. Among hese, NFINV plays he mos sgnfcan role n he frs perod, absorbng abou 15 % of oal GSP changes, and overall abou 25% of oal GDP changes. TB smoohes abou 5-10% n he frs perod, bu ds-smoohes abou 5-10% n each of he second and he hrd perod, so ha overall ds-smoohes abou 5-10%. INVT smoohes abou 10-13% on mpac, bu n he hrd and fourh year ds-smoohes abou 5%, averagng a 5-7% overall. These resuls shed lgh on he domesc (as opposed o nernaonal) exen of cred smoohng among OECD counres. Of he oal 36% smoohng on mpac occurrng hrough hs channel, he bulk (abou 30%) akes place domescally, ha s, whou any nernaonal rsksharng. If we consder overall smoohng, of he oal 25% smoohng, a whoppng 35% s acheved domescally (manly hrough gross fxed nvesmens) on mpac, wh he rade balance even playng an overall ds-smoohng role. The above breakdown also helps explan he mng paern of cred smoohng. I s apparen ha boh nvenores and he rade balance are responsble for he ds-smoohng behavor of he cred channel afer he hrd year. Whle he volaly of nvenores s hardly a surprse, he rade balance appears o behave accordng o neremporal paerns predced by he heory n case of an oupu shock ha urns ou o be perssen. The behavor of he rade balance, herefore, comes o he forefron as one of he man culprs of he mng of he cred marke response; hs s a novel resul ha had been overlooked by prevous analyses. Nex, we examne he mpulse responses o oher srucural shocks. Frs, abou wohrds of an nal ncrease n ne facor ncome s offse by a decrease n he rade balance. We also observe a lle ncrease n deprecaon. In he nex perod, a subsanal par of he ncrease n ne facor ncome s offse by he decrease n nvenores. Second, he mos par of he ncrease n nernaonal governmen ransfers s offse by a decrease n rade balance. Thrd, he mos par of he ncrease n capal deprecaon s offse by he decrease n he oher hree channels of savng. The sze of he decrease n each channel s smlar. Fourh, he mos par of he ncrease n ne fxed nvesmen s offse by he decrease n rade balance. Ffh, some of he ncrease n rade balance s offse by he decrease n nvenores. Fnally, an ncrease n nvenores does no affec oher rsk sharng channels (due o our denfyng assumpon), bu he followng year a lle decrease n nvenores s observed, whch s offse by an ncrease n he rade balance. In mpors of goods and servces. We exclude ne facor ncome and nernaonal ransfers from savng snce hey are already separaed as he dfference beween GDP and GNP, and GNP and GDI. 20

21 summary, shocks o each rsk sharng channel are offse by change n rade balance n mos cases. 17 The logc behnd hs resul s ha, as alernave means o smooh ncome ncrease, he dscrepancy beween savng and nvesmen shrnks, and he sze of he rade balance auomacally declnes The Role of Relave Prce across Counres The varables used n our rsksharng regressons are deflaed usng own sae (counry) s CPI. 18 Bu snce sae (naonal) prces may respond as well o oupu shocks, s mporan o examne wheher he resuls we obaned above were drven by he relave dynamcs of prces. There are sound heorecal reasons o expec boh a smoohng and a ds-smoohng effec of relave prces. Cenerng he dscusson on relave supply shocks, as we have done up o now, open-economes real exchange rae models, as n Obsfeld (1985), sugges ha posve producvy shocks creae an excess supply whch reduces relave prces; on he conrary, when dfferences beween radable and non-radable secors are consdered, as n he Balassa- Samuelson hypohess, posve producvy shocks, whch manly benef radable secors, resul n relave prce ncreases. To examne he role of relave prces n rsk sharng, we need o exend he basc model. In he case of he U.S. saes, he smoohng role of prces can be derved by consderng nomnal consumpon deflaed by he naonal CPI ndex (P), whch we denoe consumpon deflaed by he sae CPI ndex, as n he orgnal deny n (0.2), as apples o he US, we oban * C, nsead of nomnal C above. By appendng hs new erm no GSP C * GSP = C, (0.10) * SI SI DSI DSI C C and he sysem of equaons (0.4) becomes: 17 Ths resul s robus under alernave denfyng assumpons. 18 In he case of U.S. saes, he resuls n Secon 3 used varables deflaed by aggregae U.S. CPI snce he resuls are smlar o hose usng varables deflaed by each sae s CPI and each sae s CPI s avalable only from

22 log SI log C log C log DSI * log GSP log DSI log SI log C log C = ν u* * + β u* = ν = ν = ν = ν p c k g + β + β p c log GSP k f u* log GSP + β log GSP log GSP + β log GSP + ε + ε + ε + ε + ε c p k g (0.11) The dfference beween hs sysem and he prevous one les n he las wo equaons. In parcular, he par correspondng o he unsmoohed componen n (0.4) corresponds now o he las wo equaons, so ha β β = β p + u* u. Noe ha he orgnal unsmoohed componen u β s now decomposed no wo pars, he frs of whch measures he smoohng effec of prces. To see hs more clearly, from he defnons of C and * C follows ha, n logs: log C log C * = ( log P log P ) (0.12) Subsung hs expresson above, follows ha, when relave prces (he rgh erm n (0.12)) ncrease (fall) n response o a posve shock n sae oupu, β p wll be negave (posve), mplyng a smoohng (dsmoohng) effec of prces. More specfcally, β p n (0.11) reflecs he percenage of smoohng acheved by he adjusmen of relave prces. Therefore, he effec of prce adjusmens on global smoohng can be recovered by performng hs modfcaon o he sysem. 19 In he VAR specfcaon, herefore, we nclude anoher recursve equaon, whose lefhand sde varable s log CPI (he sae consumer prce ndex). Snce he CPI daa for each U.S. sae s avalable only from 1969, we esmae over In he case of OECD and European counres, he exsence of dfferen currences mples ha nomnal exchange raes, besdes prces, can vary n response o an oupu shock, and exhb eher a smoohng or a ds--smoohng behavor. In fac, hs s a way of descrbng he enre debae on opmaly of he EMU as a currency area ha has been akng place boh n he leraure and n polcy crcles. 20 Operaonally, we have o nclude wo addonal varables, log E (he nomnal exchange rae) and log CPI. Followng he same seps as above, we oban a 19 For deals on hs procedure, see Alberola and Asdrubal (1997). 22

23 recursve sysem wh wo addonal equaons, one measurng he response of relave prces, he oher reflecng he reacon of he nomnal exchange rae o oupu and oher shocks. Agan, all varables are devaons from own regonal aggregaes. Regardng he denfyng resrcons, we nclude he new varables as he las ones n equaons (0.8) and (0.9). Tha s, he new varables are assumed o be affeced by all varables n he sysem wh SR resrcons whle he shocks o he new varables do no affec any basc varables n he long run. Table 5 repors he resuls. We repor only resuls from he sysem wh SR resrcons snce resuls from he one wh LR resrcons are smlar. We do no repor he responses of real varables, snce response of real varables are smlar o he basc sysems. For he OECD and EU counres, we also repor he mpled real exchange rae changes due o exchange rae and CPI changes. Table 5. Impulse Responses of log CPI, log E, and log RER o e GSP. US Saes CPI OECD 23 CPI EU 15 CPI OECD 23 EXC EU 15 EXC OECD 23 RER EU 15 RER 0 year 1.1 (0.6) (2.6) (3.2) (8.4) (11.4) year 1.7 (0.5) 4.0 (3.6) 4.9 (4.4) (8.9) (13.9) year 0.0 (0.6) 18.3 (4.0) 15.4 (5.2) (9.1) (13.4) year 0.3 (0.3) 23.1 (4.0) 19.0 (5.2) 12.0 (7.4) -0.1 (10.3) year 0.2 (0.2) 23.5 (3.9) 20.6 (5.0) 26.7 (5.7) 21.3 (9.1) year 0.0 (0.1) 21.7 (3.7) 19.7 (4.8) 26.9 (4.6) 24.9 (7.2) Frs of all, n he U.S. saes, n response o shocks o GSP, he CPI growh rae ncreases over wo years, hereby slghly smoohng oupu shocks. However, he ncreases are relavely small; a 1% ncrease n he growh rae of GSP (over a few years) ncreases less han 0.04% overall. Such a small relave prce change does no seem o have much rsksharng effecs across U.S. saes. In conras, n OECD and EU counres, he CPI growh rae decreases for he frs year, bu ncreases for he second year and afer, whle he exchange rae growh rae decreases for he frs hree years bu ncreases laer. As a resul, he real exchange rae growh rae decreases for mos years up o four years afer he shocks. The resul on CPI s clearly o be nerpreed as a sluggsh response of prces, whch declne (ncrease) nally afer a posve (negave) oupu shock, o hen gradually rse (fall) o smooh a remarkable fracon of he oupu shock overall (a whoppng 77% for OECD). Ths novel resul appears o lend wegh o he Balassa-Samuelson hypohess of a prce sysem 20 See for example Echengreen.(1997). 23