Linking real activity and financial markets: the first steps towards a small estimated model for Canada

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1 Linking real aciviy and financial markes: he firs seps owards a small esimaed model for Canada Céline Gauhier and Fuchun Li 1 1. Inroducion The crudes feaure of many models reamen of financial markes is ha hey aggregae all financial markes ino only wo: he marke for money and he marke for everyhing else. This aggregaion allows us o summarise asse marke equilibrium in a single LM curve bu hides he srucure needed o achieve a good undersanding of how financial markes and he real economy are inerrelaed. Anoher weakness of mos models ha purpor o describe he ransmission mechanism is heir failure o pass he simple es of generaing a differen seady sae rae of inflaion in response o a series of moneary policy acions. 2 Such models wih an unique seady sae rae of inflaion are very difficul o reconcile wih he uni roo es resuls found in he empirical lieraure. 3 One goal of his paper is o idenify permanen shocks causing inflaion o reach a new seady sae rae of growh. A second goal is o model equilibrium values of financial variables hrough heir long-run relaionships wih real variables in a racable macroeconomic model. Over he pas wo decades, here has been a growing ineres in developing racable macroeconomic models wih ransparen heoreical foundaions. As wrien in Garra e al (21): There are wo main heoreical approaches o he derivaion of long-run, seady sae relaions of a core macroeconomic model. One possibiliy is o sar wih he iner-emporal opimisaion problems faced by represenaive households and firms and solve for he long-run relaions. [ ] An alernaive approach [ ] is o work direcly wih he arbirage condiions which provide iner-emporal links beween prices and asse reurns in he economy as a whole. [ ] The srengh of he iner-emporal opimisaion approach lies in he explici idenificaion of macroeconomic disurbances as innovaions (shocks) o processes generaing ases and echnology. However, his is achieved a he expense of ofen srong assumpions concerning he form of he underlying uiliy and producion funcions. In conras, he approach ha Garra e al (21) and he presen paper adop, focuses on long-run heory resricions and leaves he shor-run dynamics largely unresriced (in he conex of a VECM model), hus providing a much more flexible modelling sraegy. Our aim is o combine Garra e al s (21) approach wih King e al s (1991) mehodology allowing he idenificaion of permanen shocks in a coinegraed sysem. Crowder e al (1999), Dhar e al (2), Jacobson e al (21) and Cassola and Morana (22) all follow his roue and show he degree of srucure ha may be assigned o a simple vecor auoregression (VAR) framework characerised by coinegraion if one embraces sufficien idenifying resricions. The building blocks of he model consis of hree coinegraing relaions: (1) a money marke equilibrium relaion, (2) an arbirage relaion beween shor- and long-erm bonds, and (3) a long-run relaion beween he sock marke and real oupu. This las relaion allows he idenificaion of a supply shock as he only shock permanenly affecing he sock marke and a demand shock leading o significan ransiory sock marke overvaluaion. We also idenify a nominal shock defined as he only shock having a permanen impac on he level of inflaion. In fuure work, we will sudy he Corresponding auhor: CGauhier@bank-banque-canada.ca. The auhors wish o hank Sco Hendry, Pierre S-Aman, David Tessier and Carolyn Wilkins for helpful commens on a previous version of he paper and Alejandro Garcia for his echnical assisance. The views expressed herein are hose of he auhors and do no necessarily reflec hose of he Bank of Canada. More deails on his poin are made in Selody (21). This is also a very difficul issue as inflaion is expeced o become saionary in a successful inflaion argeing environmen. BIS Papers No

2 behaviour of a moneary policy reacion funcion consising in reversing any idenified nominal shock causing inflaion o permanenly deviae from he arge. Our paper is organised as follows. The heoreical foundaions of he model are presened in Secion 2. The coinegraion analysis and specificaion es resuls are given in Secion 3. Secion 4 presens he economeric formulaion of he core model. Secion 5 analyses he impulse response funcions. A conclusion follows. 2. The heoreical foundaions of he model In his secion, we describe he long-run relaions used as he building blocks of our model. We base our core model on Blanchard (1981), who develops a simple model of he deerminaion of oupu, he sock marke and he erm srucure of ineres raes. The model is an exension of he IS-LM model. However, whereas he IS-LM model emphasises he ineracion beween he ineres rae and oupu, Blanchard s model emphasises he ineracions beween oupu and four markeable asse values. These are shares which are iles o he physical capial, privae shor- and long-erm bonds issued and held by individuals, and money. Linking he real economy and he sock marke We assume ha here are wo main deerminans of spending. 4 The firs is he value of shares in he sock marke. I may affec spending direcly hrough he wealh effec on consumers, or indirecly hrough is impac on he borrowing capaciy of consumers and invesors (he credi channel effec); deermining he value of capial in place relaive o is replacemen coss, i affecs invesmen. The second is curren income, which may affec spending independenly of wealh if consumers are liquidiy-consrained. Toal spending is expressed as: d = αsm + βy ; α > ; β > (1) All variables are real, d denoes spending, sm is he sock marke value, and y is income. 5 We can see equaion (1) as a forward-looking aggregae spending curve wih sm being a funcion of he presen value of expeced fuure profis, he laer being a funcion of expeced fuure oupu. Hence, aggregae spending is implicily a negaive funcion of acual and expeced ineres raes and a posiive funcion of acual and fuure expeced oupu. Oupu adjuss o spending over ime: y = σ ( d y ) = σ ( αsm by ); σ > ; b 1 β (2) where a do denoes a ime derivaive. Since oupu growh is a saionary variable and he level of oupu and he sock marke price are boh I(1) variables, equaion (2) can be seen as an error correcion equaion posiively linking he shor-run dynamics of oupu o deviaions of he sock marke from he real economy. Such a long-run relaion beween oupu and he sock marke implies ha ransiory changes in oupu canno permanenly affec he level of he sock marke. Money marke equilibrium Porfolio balance is characerised by a long-run relaion beween money, oupu, ineres rae and inflaion: M p = cy hi βπ ; c > ; h > ; β > (3) where i denoes he shor-erm nominal rae, y is real income, M and p denoe he logarihms of nominal money and he price level, and π is he level of inflaion. The parameer c is posiive because an increase in oupu shifs he money demand for ransacion purposes upwards; an increase in he 4 5 Blanchard also includes a balanced budge change in public spending as a hird deerminan of oal spending. No sochasic error erms are included in his secion o simplify he presenaion. 254 BIS Papers No 22

3 ineres rae and an increase in inflaion boh increase he opporuniy cos of holding money, which decreases real balance. Given ha all he variables in equaion (3) are beer characerised as I(1) variables, if deviaions of real money from is deerminans are ransiory, hen his equaion represens a coinegraing relaionship. Arbirage beween shor- and long-erm bonds The expecaions hypohesis is perhaps he bes known and mos inuiive heory of he erm srucure of ineres raes. If lr is he nominal yield o mauriy of a discoun bond and i is he period- one-period rae, he expecaions hypohesis in he absence of uncerainy implies ha n 1 n (1+ lr ) = (1+ i + i ) (4) i = This is an arbirage condiion ensuring ha he holding-period yield on he n-period bond is equal o he yield from holding a sequence of one-period bonds. Taking logs of boh sides and recalling ha ln(1 + x) x for small x, yields a common approximaion: n 1 1 lr = i + i (5) n i = The long-erm yield is equal o he average of one-period yields. Hence, a permanen shock o he shor-erm yield will, in he long run, be refleced one for one in he long-erm yield, once he shock is correcly perceived as permanen by he financial markes. This defines a hird coinegraion relaionship. 3. Coinegraion analysis We esimae a monhly VECM over he period wih six endogenous variables and one exogenous variable and wo lags. 6 The endogenous variables are he following Canadian variables: real gross domesic produc (GDP) a basic prices, 7 he over 1-year markeable bond rae, he overnigh rae, 8 a broad money aggregae (CPI deflaed M2++), 9 he real sock marke price (CPI deflaed Torono Sock Exchange (TSE)), and he CPI year-over-year inflaion rae. Given he srong economic links beween Canada and he Unied Saes, we incorporae as an exogenous variable he real US indusrial producion index, one available monhly proxy for US aciviy. This will allow simulaion of differen US scenarios. Uni roo ess indicae ha all variables can be reaed as I(1) variables. We add a dummy equalling one from 1993 onwards o capure he change in he rend of inflaion afer he adopion of an inflaion arge in Based on he heoreical foundaions of he core model described in he above secion, we expec o find hree coinegraing relaions in he esimaed VECM (as described by equaions (2), (3) and (5)). The coinegraion ess correced for he presence of one exogenous variable, as proposed by Pesaran e al (2), are presened in Table 1. The L-max es indicaes he presence of hree coinegraion vecors, supporing our a priori expecaions based on Blanchard s model, while he Trace es sugges only wo vecors Two lags minimise he Hannan-Quinn and Schwarz informaion crieria and are sufficien o remove he correlaion in residuals. We use monhly daa because he Bank of Canada has adoped a fixed acion dae schedule eigh imes a year. A series of specificaion ess have been done and will be included in he nex version of his paper. This series has been merged wih real GDP a facor cos for he period As noed in Selody (21), a good moneary policy insrumen mus be under he direc or close conrol of he cenral bank. M2++ includes muual funds, whose imporance increased coninuously in consumer porfolios over he 199s, and which are relaively liquid. Using a broad aggregae like M2++ in he model avoids inerpreing a precauionary porfolio adjusmen from muual funds o money as inflaionary. Moreover, Longworh (23) finds ha, since 1992, boh core inflaion and M2++ have been remarkably sable. BIS Papers No

4 Table 1 Coinegraion ess 1 L-max Trace H : r = L-max (.1) Trace (.1) The criical values correced for he presence of one exogenous variable are aken from Table T.3 in Pesaran e al (2). To discriminae beween our coinegraion ess, we looked a he -values of he α coefficiens for he hird vecor, as suggesed in Hendry and Juselius (21); when hese are small, say less han 3., hen one would no lose grealy by excluding ha vecor as a coinegraion relaion in he model. Given ha many of hese -values are greaer han 3. for all hree vecors and ha our heoreical model also suggess hree vecors, we proceed under he assumpion ha here are hree coinegraing vecors in our model. The Johansen (1992) procedure allows us o idenify he number of coinegraing vecors. However, in he case of exisence of muliple coinegraing vecors, an ineresing problem arises: α and β are only deermined up o he space spanned by hem. Thus for any non-singular marix ζ conformable by-produc: Π = αβ = αζζ 1 β In oher words, β and β ζ are wo observaionally equivalen bases of he coinegraing space. The obvious implicaion is ha before solving such an idenificaion problem, no meaningful economic inerpreaion of coefficiens in coinegraing space can be proposed. The soluion is imposing a sufficien number of resricions on parameers such ha he marix saisfying such resricions in he coinegraion space is unique. Such a crierion is derived in Johansen (1992) and discussed in Hamilon (1994). Our resricions are based on Blanchard s model and sugges more han a sufficien number of consrains on he coinegraion space. The overidenificaion resricions can herefore be esed. The resuls are in Table 2. Table 2 Tesing resricions on he coinegraing vecors 1 The LR es, χ 2 (1) = 7.2, p-value =.72 inf y onr m sm Ir y US 2.41 (.27) 1.18 (.8) 2.41 (.27) Sandard errors are given wihin parenheses. The resriced core model is srongly acceped wih a p-value of.72. These resuls are consisen wih he heoreical foundaions presened in Secion 2. The firs coinegraing relaion corresponds o he money marke equilibrium, and he second o an approximaion of he pure expecaions hypohesis 256 BIS Papers No 22

5 based on an arbirage relaion beween shor- and long-erm bonds, while he hird relaion links real aciviy wih he real sock marke. The coefficiens of he coinegraing relaion canno usually be inerpreed as elasiciies even if he variables are in logs, since a shock o one variable implies a shock o all variables in he long run. Hence he coefficiens do no in general allow for a ceeris paribus inerpreaion (see Lukepohl (1994)). Inerpreing he coefficiens in he firs coinegraing relaion is hus meaningless. However, given ha he las wo coinegraing relaions involve only wo variables, we do no need he ceeris paribus inerpreaion. The second long-run relaion specifies ha a permanen 1% increase in he shor-erm ineres rae is associaed wih he equivalen increase in he long-run ineres rae. The hird coinegraing relaion suggess ha a 1% permanen increase in oupu (or a 1% increase in poenial oupu) is associaed wih a permanen 1% increase in he sock marke. Ineresingly, his las relaion also implies ha ransiory changes in real oupu can only lead o ransiory changes in he level of he sock marke. The economy is in a long-run equilibrium when hose hree coinegraing relaionships are respeced, ha is, when here is no gap beween money, oupu, inflaion and he overnigh rae (or no money gap), he overnigh rae is equal o he long rae (no ineres rae gap), and he sock marke level is consisen wih poenial oupu (no sock marke gap). Graph 1 illusraes he money gap 1 over he sample period. The wo surges in inflaion, in 1981 and 1991, were preceded by an increasing money gap around wo years before. I is also ineresing o noe ha since he Bank of Canada adoped an explici inflaion arge in 1991, he money gap has been much more sable, deviaing only slighly from equilibrium and for shor periods of ime in 1995 and 2. This is in line wih he resuls in Longworh (23), who repors ha, since 1992, boh core inflaion and M2++ have been remarkably sable. The ineres rae gap is defined as he yield spread (he long minus he overnigh rae), well known as a good moneary policy sance measure. Wih his definiion of he ineres rae gap, he shor rae is a is neural level, or a is long-run equilibrium value, when i is equal o he long rae. According o his definiion, he Bank of Canada was resricive a he end of he 198s o achieve he following disinflaion and was accommodaive for mos of he 199s excep for a shor period in The overnigh rae was back below equilibrium a he end of 22 by almos 2%. The sock marke gap in Graph 2 illusraes periods of mis-valuaion of he sock marke. 11 Our resuls show ha he sock marke led he 1981 and 1991 recessions and became srongly undervalued (close o 4%) afer he 1981 recession. I became relaively less depressed afer he 1991 recession (around 2%), bu ook longer o recover; he marke go back o is fair value only in Graph 2 also shows ha he sock marke was abou 2% overvalued before he 1987 crash and undersho by abou 1% aferwards. The marke was overvalued for mos of he period, excep for he srong correcion following he Asian crisis in By far he mos significan deparure from equilibrium happened a he beginning of 2 when he sock marke appeared o have been close o 6% higher han wha was jusified by fundamenals. Finally, he bubble burs and he marke overreaced again. Graph 2 suggess i was abou 1% undervalued a he end of 22. These resuls are in line wih Dupuis and Tessier (23), who esimae a hree-variables VECM linking he US sock marke o dividends and he long-erm ineres rae. 4. Economeric formulaion of he core model The hree long-run equilibrium relaionships can be wrien in he following form: m = c 11 + c 12 y + c 13 onr + c 13 inf + ξ 1+1 (6) lr = c 21 onr + ξ 2+1 (7) 1 11 The gaps in his secion are simply defined as he error correcion erm from he coinegraing relaions. Gaps based on permanen componens of he variables will be presened in Secion 5. Noe ha he permanen componens of he variables have ye o be idenified before we can ell if a posiive error correcion erm is due o he sock marke being oo high or oupu oo low (or boh). This is done below. BIS Papers No

6 sm = c 31 y + ξ 3+1 (8) The hree long-run relaions of he core model, equaions (6), (7) and (8), can be wrien as ξ = β z 1 c (9) US where z = (inf, y, onr, m, sm, lr, y ), c = (c 11, c 21, c 31 ), ξ = (ξ 1, ξ 2, ξ 3), and c13 c12 c β = Le x = (inf, y, onr, m, sm, lr ). We base our analysis on he following condiional error correcion model: (1) s 1 x = a αξ + Γ z + b y + u i = 1 i i US x (11) where a is a 6 1 vecor of fixed inerceps, α is a 6 3 marix of error correcion coefficiens, b is a 6 1 vecor represening he impac effecs of changes in US oupu on x, and u x is a 6 1 vecor of disurbances assumed o be IID(, Σ x ), wih Σ x being a posiive definie marix. From equaions (9), (1) and (11), we have y y y 1 s 1 i = 1 i i y US x = a + α c α β z + Γ z + b y + u (12) y where β z 1 is a 3 1 vecor of error correcion erms. This specificaion implies he economic heory s long-run predicions by consrucion. The esimaions of he parameers in equaion (12) are obained by using he esimaion procedure of vecor error correcion models wih exogenous I(1) variables (Pesaran e al (2)). 5. Shock analysis The impac of a change in US indusrial producion The response funcions o a permanen increase of 1% in US indusrial producion are shown in Graph 4. Small inflaion pressures are generaed as oupu is boosed by almos.2% on impac. Ineres raes are increased by around 25 basis poins o keep demand in line wih shor-run supply. The Canadian sock marke is negaively affeced by he higher ineres rae. I neverheless increases by.12% in he long run, in line wih he permanen increase in oupu. 12 Broad aggregae money is negaively affeced in he shor run by he sligh increases in inflaion and real ineres raes. Only oupu is significanly affeced in he long run. Idenificaion of he permanen shocks Given he presence of hree coinegraing vecors and six endogenous variables, here are hree sochasic rends or permanen shocks o be idenified. 13 The firs permanen shock, ε π, labelled an inflaion shock, is he only shock having a permanen impac on inflaion. According o he monearis view, he long-run money growh and inflaion rae are ulimaely se exogenously by moneary auhoriies. So he inflaion shock relaes o cenral bank moneary policy. A posiive inflaion shock US indusrial producion represens abou 15% of US oal GDP. Under he assumpion ha a permanen increase of 1% in US indusrial producion ranslaes ino an increase of.15% in US oal GDP, our resuls sugges ha a.15% increase in US GDP is associaed wih an increase of abou.12% in Canadian GDP. Deails on idenificaion in he presence of exogenous variables will be published in a fuure version of his paper. 258 BIS Papers No 22

7 reflecs he cenral bank s decision o permanenly increase he inflaion rae. Hence, he srucural inflaion shock is idenified by assuming ha he long-run sysem has he following recursive srucure: inf + s y + s onr + lim s m + s sm + lr + s s τ τ τ = τ τ τ s τ τ τ τ τ ε τ 33 ε τ43 ε τ53 τ63 π y d Noe ha τ ij is he long-run response of he ih endogenous variable o he j elemen in he vecor of srucural disurbances ε. The resricions τ 12 = and τ 13 = mean ha only an inflaion shock, ε π, affecs he long-run level of inflaion. The mainsream view would predic ha he decision o change inflaion permanenly has no permanen impac on real variables and hus ha [τ 21 τ 41 τ 51 ] =. However, economic heory provides no clear-cu predicions on ha quesion. In several heoreical models, he superneuraliy resul due o Sidrausky (1967) breaks down as inflaion can have eiher posiive or negaive effecs on real variables such as consumpion and invesmen, depending on he exac assumpions concerning preferences. Addiionally, in hese models he real ineres rae may or may no be independen of inflaion in he long run (see Orphanides and Solow (199) for a survey). Some recen empirical resuls (see, for example, Rapach (23) and Gauhier e al (23)) find suppor for he Mundell-Tobin effec, suggesing ha an unexpeced increase in inflaion has a permanen negaive impac on he real ineres rae. We le he daa alk on his poin by leaving unconsrained he parameers in [τ 21 τ 31 τ 41 τ 51 τ 61 ]. Mos heoreical models define supply shocks as being governed by echnology innovaions deermining he echnical capaciy of he economy. We hus idenify a supply shock as a shock allowed o have a permanen effec on oupu bu no on inflaion. The long-run effecs on all he oher real variables are lef unconsrained. Noe ha all shocks are allowed o impac all he variables in he shor run. In paricular, a supply shock is expeced o decrease inflaion in he shor run. The hird srucural shock is a shock having no permanen impac eiher on oupu or on inflaion. This shock is labelled a demand shock. The inflaion shock A posiive inflaion shock reflecs he cenral bank s decision o permanenly increase he inflaion rae. 14 Given he insrumen used by he cenral bank, his can only be achieved by decreasing he overnigh rae. Graph 5 shows ha our resuls are consisen wih his view. To achieve a ypical unexpeced inflaion increase of around.3% in he long run, he cenral bank has o decrease he overnigh rae by abou 25 basis poins. Given he expecaions hypohesis of he erm srucure in our core model, he long rae is persisenly depressed as well. The bank s inervenion leads o a small oupu simulus in he shor run. The shock also significanly hurs he sock marke and decreases real broad aggregae money in he shor run. The permanen significan negaive effec of inflaion on ineres raes may be explained hrough he Mundell effec: an unexpeced increase in inflaion decreases real wealh, which increases savings. Real ineres raes mus hen fall o resore goods marke equilibrium. Our resuls are also consisen wih he focus on sabilising oupu in he 197s and he beginning of he 198s even a he cos of higher inflaion. Furhermore, hey are in line wih he need o persisenly increase he ineres rae in disinflaion periods and in he firs years of inflaion argeing in order o gain credibiliy. Rapach (23) 14 Of course, such a shock can always be reversed by a negaive inflaion shock of he same size, if he cenral bank decides o do so. BIS Papers No

8 also finds ha an unexpeced permanen increase in inflaion is associaed wih permanenly lower long-run real ineres raes in every indusrialised counry in a sample of 14, including Canada. 15 When inflaion is forecas o deviae permanenly from he acual arge of 2%, he hisorical esimaed reacion funcion (he equaion for he overnigh rae) may be adjused using he esimaed impac over ime of he ypical permanen inflaion shock in such a way as o eliminae he expeced long-run deviaion from arge. The supply shock The ypical supply shock increases he producive capaciy of he economy by around.9% in he long run. Inflaion is pushed downwards in he shor run as producion coss are decreased (Graph 6) bu goes back o is iniial level in he long run. The cenral bank has, over he sample, accommodaed he shock by decreasing ineres raes o eliminae he excess supply in he goods marke and bring inflaion back o arge. 16 The sock marke leads oupu and overshoos somewha. Broad money is higher in he shor run because of he accommodaive sance of moneary policy and remains higher in he long run because of boh higher money demand for ransacion purposes and higher real value of he sock marke. A demand shock 17 The demand shock increases inflaion, oupu and he sock marke in he shor run. Shor and long ineres raes increase in he shor run as expeced. This can be seen as he resul of a sandard exbook open marke operaion wih a disinflaionary objecive. When inflaion and oupu urn ou o be higher han expeced, an inflaion argeing cenral bank has o increase ineres raes. I is ineresing o noe ha since a demand shock has no permanen impac on oupu, he significan sock marke surge in he firs monhs following he shock slowly dissipaes as invesors realise ha higher profis canno be susained wihou a permanen increase in produciviy. The permanen posiive impac on he overnigh rae implies ha he so-called demand shock induces, on average, a higher equilibrium ineres rae. This, again, is consisen wih he need o persisenly increase he ineres rae in disinflaion periods and in he firs years of inflaion argeing in order o gain credibiliy. Furhermore, as prediced by he long-run heory of growh models, any shock ha persisenly lowers he share of produc going ino invesmen is associaed wih higher real ineres raes in he long run. 18 For example, fiscal shocks crowding ou invesmen persisenly will be associaed wih persisenly higher ineres raes. Oupu gap An oupu gap is easily obained from our model as he difference beween acual oupu and he hisorical conribuion of permanen shocks o oupu (deermining poenial oupu). Poenial oupu and he oupu gap are ploed in Graphs 8 and 9 respecively. According o hese resuls, he Canadian economy was in excess demand before boh he 1982 and he 1991 recessions and was in excess supply for mos of he 199s. The gap was closed a he end of 1999 and he economy urned Noe ha a permanen inflaion shock represens an unexpeced persisen deviaion of inflaion from is deerminisic rend. This source of increase in inflaion is associaed in he long run wih a decrease in ineres raes. Tha, of course, does no mean ha expeced changes in inflaion have he same effec on ineres raes. In some SDGE models wih adjusmen coss on capial (see Neiss and Nelson (21, p 23) for an example), produciviy shocks would decrease he neural rae in he shor run. This provides furher incenives o decrease he acual ineres rae afer a produciviy shock. Oher demand shocks having only ransiory effecs may also be idenified. King e al (1991) esimae a significan coinegraion relaionship negaively linking he raio of invesmen o oupu and he real ineres rae in he Unied Saes and idenify wha hey call a real ineres rae shock wih long-run properies very similar o our demand shock. They also idenify wha hey call a balanced-growh shock, which is very similar o our supply shock increasing oupu permanenly while leaving he raios of invesmen and consumpion o oupu as well as he real ineres rae and inflaion unchanged in he long run. 26 BIS Papers No 22

9 o excess demand for he following wo years. The economy was back in excess supply (hough close o zero) a he end of 22. Wha may be more surprising is he period over which supply shocks conribued o increasing oupu permanenly. Graph 8 suggess ha i sared around 1985 and lased unil 1996, he year Chairman Greenspan firs alked of irraional exuberance. From 1996 unil he end of 2 and he srong sock marke correcion, he economy was demand-driven and poenial would have been growing a a rae lower hen he deerminisic rae. 19 This resul, in line wih Dueker and Nelson (22) and he laes economic developmens, cass some doubs on he purpored new economy in he second half of he 199s. 6. Conclusion We have esimaed a small monhly VECM o sudy he ineracions beween he real and financial secors of he Canadian economy. To ake ino accoun he high degree of economic inegraion beween Canada and he Unied Saes, he US indusrial producion index has been included as an exogenous variable. Idenificaion of permanen shocks in a VECM wih exogenous variables represens a echnical conribuion o he lieraure. Our principal resuls are: (1) he idenificaion of a long-run relaion beween he sock marke and real oupu which allows he idenificaion of a supply shock as he only shock permanenly affecing he sock marke and a demand shock leading o significan ransiory sock marke overvaluaion; (2) he money gap defined as he error correcion erm from he firs coinegraing relaion has been much more sable since he adopion of inflaion arges in Canada. The nex sep in his projec is o sudy he behaviour of a reacion funcion ha would reverse any idenified nominal shock causing inflaion o persisenly deviae from he arge. The model could also be used o build a financial condiion index for Canada using he sock marke and money gaps from he core model ogeher wih he deviaion of he acual real ineres rae from he neural ineres rae recommended by he proposed reacion funcion. This index could also possibly be compleed wih he deviaion of he Canadian exchange rae from equilibrium provided in Gauhier and Tessier (22) and esed agains hose proposed in Gauhier e al (23). This is lef for fuure research. 19 I should be noed, however, ha a shif in he deerminisic rend in oupu is esimaed in Hence, he growh of poenial in he second half of he 199s is lower compared wih a relaively higher growh in rend. Depending on our judgmen on he source of his shif, he sory can be compleely differen. If he higher deerminisic oupu growh is aribued o supply shocks, hen poenial oupu would have increased coninuously in he 199s and he Canadian economy would currenly be in considerable excess supply. Neverheless, given he deerminisic naure of his shif and he recen economic developmens, we proceed under he assumpion ha his change in rend should be considered as demand-driven, implying ha poenial oupu and he oupu gap are well approximaed by Graphs 8 and 9. The fac ha poenial has been below he higher growh rend for he las seven years is also an indicaion ha he higher rend should be seen as ransiory. BIS Papers No

10 Graph 1 Money gap Graph 2 Sock marke gap 262 BIS Papers No 22

11 Graph 3 Ineres rae gap BIS Papers No

12 Graph 4 Responses o a permanen increase in US indusrial producion.15 Permanen US shock o inflaion.4 Permanen US shock o oupu Permanen US shock o onr Permanen US shock o M Permanen US shock o sock marke Permanen US shock o long rae BIS Papers No 22

13 Graph 5 Impulse responses o an inflaion shock.8 Inflaion shock o inflaion.5 Inflaion shock o oupu Inflaion shock o onr Inflaion shock o M Inflaion shock o sock marke Inflaion shock o long rae BIS Papers No

14 Graph 6 Impulse responses o a supply shock.4 Supply shock o inflaion 1.5 Supply shock o oupu Supply shock o onr Supply shock o sock marke Supply shock o M Supply shock o long rae BIS Papers No 22

15 Graph 7 Impulse response o a demand shock.3 Demand shock o inflaion.3 Demand shock o oupu Demand shock o onr Demand shock o sock marke Demand shock o M Demand shock o long rae BIS Papers No

16 Graph 8 Poenial oupu BIS Papers No 22

17 Graph 9 Oupu gap Graph 1 Money gap (based on permanen componens) BIS Papers No

18 Graph 11 Sock marke gap (based on permanen componens) Graph 12 Transiory componen of inflaion 27 BIS Papers No 22

19 References Ahmed, S and J Rogers (2): Inflaion and he grea raios: long-erm evidence from he US, Journal of Moneary Economics, 45, pp Angeloni, I, G Coenen and F Smes (23): Persisence, he ransmission mechanism and robus moneary policy, European Cenral Bank Working Paper Series, 25. Blanchard, O J (1981): Oupu, he sock marke, and ineres raes, American Economic Review, 71, pp Blanchard, O J and D Quah (1989): The dynamic effecs of aggregae demand and supply disurbances, American Economic Review, 79, pp Cassola, N and C Morana (22): Moneary policy and he sock marke in he euro area, European Cenral Bank Working Paper Series, 119. Coenen, G (22): Inflaion persisence and robus moneary policy design, European Cenral Bank, mimeo. Cogley, T and T Sargen (21): Evolving pos-world War II inflaion dynamics, NBER Macroeconomics Annual, 16. Crowder, J, D L Hoffman and R H Rasche (1999): Idenificaion, long-run relaions, and fundamenal innovaions in a simple coinegraed sysem, The Review of Economics and Saisics, vol 81, pp Dhar, S, D Pain and R Thomas (2): A small srucural empirical model of he UK moneary ransmission mechanism, Bank of England Working Paper Series. Dueker, M J and C R Nelson (22): Business cycle derending of macroeconomic daa via a laen business cycle index, Federal Reserve Bank of S Louis Working Paper 22-25A. Dupuis, D and D Tessier (23): The US sock marke and fundamenals: an hisorical decomposiion, Bank of Canada Working Papers, Garra, A, K Lee, M H Pesaran and Y Shin (23): A long-run srucural macroeconomeric model of he UK, The Economic Journal, 113, pp Gauhier, C, C Graham and Y Liu (23): Financial condiion indexes for Canada, Bank of Canada, mimeo. Gauhier, C, F Pelgrin and D Schweisguh (23): The long-run relaionship beween inflaion and real sock prices: is here neuraliy?, Bank of Canada, mimeo. Gauhier, C and D Tessier, (22): Supply shocks and real exchange rae dynamics: Canadian evidence, Bank of Canada Working Papers, Goodfriend, M (1993): Ineres rae policy and he inflaion scare problem: , Federal Reserve Bank of Richmond Economic Quarerly, Winer, pp Hamilon, James D (1994): Time series analysis, Princeon Universiy Press, Princeon. Hendry, David F and Kaarina Juselius (21): Explaining coinegraion analysis: par II, Energy Journal, vol 22, issue 1, pp Jacobson, T, P Jansson, A Vredin and A Warne (21): Moneary policy analysis and inflaion argeing in a small open economy: a VAR approach, Journal of Applied Economerics, 16, pp Johansen, S (1992): Coinegraion in parial sysems and he efficiency of single-equaion analysis, Journal of Economerics, 52, pp King, R G, C I Plosser, J H Sock and M W Wason (1991): Sochasic rends and economic flucuaions, American Economic Review, 81, pp Longworh, D (23): Money in he Bank (of Canada), Bank of Canada Technical Repors, 93. Lucas, R E (1976): Economeric policy evaluaion: a criique, in K Brunner and A Melzer (eds), The Phillips curve and labor markes, Norh-Holland, Amserdam. BIS Papers No

20 Lukepohl, H (1991): Inroducion o muliple ime series analysis, Springer-Verlag. (1994): Inerpreaions of coinegraing relaions, Economeric Reviews, 13, pp Lukepohl, H and H-E Reimers (1992): Impulse response analysis of coinegraed sysems, Journal of Economic Dynamics and Conrol, 12, pp Neiss, K S and E Nelson (21): The real ineres rae gap as an inflaion indicaor, Bank of England Working Paper Series. Orphanides, Ahanasios and Rober M Solow (199): Money, inflaion and growh, Handbook of moneary economics, vol 1, Norh-Holland, Amserdam, Oxford and Tokyo, disribued in he Unied Saes and Canada by Elsevier Science, New York, pp Pesaran, M H, Y Shin and R J Smih (2): Srucural analysis of vecor error correcion models wih exogenous I(1) variables, Journal of Economerics, 97, pp Rapach, D E (23): Inernaional evidence on he long-run impac of inflaion, Journal of Money, Credi and Banking, 35, pp Selody, J (21): Principles for building models of he moneary policy ransmission mechanism, Bank of Canada, mimeo. Sidrausky (1967): Inflaion and economic growh, Journal of Poliical Economy, 75, pp Sims, C (198): Macroeconomics and realiy, Economerica, 48, pp Sock, J (21): Commen, NBER Macroeconomics Annual, 16. Wickens, M R (1996): Inerpreing coinegraed vecors and common sochasic rends, Journal of Economerics, 74, pp Wickens, M R and R Moo (21): Esimaing shocks and impulse response funcions, Journal of Applied Economerics, 16, pp Yang, M (1998): On idenifying permanen and ransiory shocks in VAR models, Economics Leers, 58, pp BIS Papers No 22