Monetary transmission and controllability of money in Europe: a structural vector error correction approach. P.J.G. Vlaar and H.

Transcription

1 Moneary ransmission and conrollabiliy of money in Europe: a srucural vecor error correcion approach P.J.G. Vlaar and H. Schuberh This paper was presened a he conference on General Equilibrium and Moneary Transmission, held a De Nederlandsche Bank, Amserdam, 4-6 November The oher papers presened a his conference are also published as DNB Saff Repors. DNB Saff Repors 1999, No.36 De Nederlandsche Bank

2 1999 De Nederlandsche Bank NV Corresponding auhor: P.J.G. Vlaar Aim and scope of DNB Saff Repors are o disseminae research done by saff members of he Bank o encourage scholarly discussion. Ediorial Commiee: Marin M.G. Fase (chairman), Peer van Bergeijk, Peer Koeze, Marga Peeers, Bram Scholen, Job Swank, Ber Groohoff (secreary). Subscripion orders for DNB Saff Repors and requess for specimen copies should be sen o: De Nederlandsche Bank NV Exernal Relaions and Informaion Deparmen Weseinde 1 P.O. Box AB Amserdam The Neherlands Inerne:

3

4 Moneary ransmission mechanism and conrollabiliy of money in Europe: a srucural vecor error correcion approach P.J.G. Vlaar and H. Schuberh

5

6 MONETARY TRANSMISSION AND CONTROLLABILITY OF MONEY IN EUROPE: a srucural vecor error correcion approach * P.J.G. Vlaar** and H. Schuberh*** ABSTRACT In his paper, a srucural vecor error correcion model is esimaed o invesigae hree essenial prerequisies for a successful moneary argeing sraegy: sabiliy, conrollabiliy and predicabiliy. Firs, mulivariae coinegraion echniques are used o idenify wo coinegraion relaions, ha are idenified as a long run money demand funcion and he Fisher effec for he long-erm ineres rae. Idenificaion of he srucural model is achieved by imposing conemporaneous and long-erm resricions. I is found ha alhough money demand seems o be sable and alhough excess money holdings have an inflaionary impac, money argeing seems quesionable as moneary conracion, embodied in a posiive shock o he shor erm ineres rae, significanly increases money holdings. The impac on inflaion is significanly negaive in he shor run. The size of his effec is relaively small however. Keywords: conrollabiliy, money demand, generalized common rends model J.E.L. Code: C32, E41, E52 *An earlier version of his paper was presened a seminars a he Oeserreichische Naionalbank and De Nederlandsche Bank, he Bocconi Universiy Banca D Ialia workshop on Moneary policy of he ESCB: Sraegic and implemenaion issues, ESEM 1998 and he Conference on general equilibrium and moneary ransmission a De Nederlandsche Bank. The auhors graefully acknowledge helpful commens by he paricipans of hese seminars, in paricular Josef Baumgarner, Günher Coenen, Shamik Dhar, Neil Ericsson, Marin Fase, Carlo Favero, Renao Filosa, Franz Hof, Kaarina Juselius, Chrisopher Sims, Frank Smes, Harald Uhlig and Peer van Els. **De Nederlandsche Bank, Economeric Researsch and Special Sudies Deparmen, POB 98, 1000 AB Amserdam, The Neherlands, P.J.G.Vlaar@dnb.nl. ***Oeserreichische Naionalbank, Economic Sudies Division, POB 61, A-1010 Vienna, Ausria, Helene.Schuberh@oenb.a

7 -

8 - 1-1 INTRODUCTION The discussion abou he appropriae moneary policy sraegy in sage III of European Moneary Union (EMU) has simulaed research on money demand. The main focus in his field is on he sabiliy properies of an EMU-wide money demand funcion. Several sudies have provided suppor for he exisence of an EMU-wide long-run money demand funcion wih sable income and ineres elasiciies over differen ime periods, for differen money measures, counry groupings and conversion mehods. Aggregae demand for money is usually shown o be more sable han is counerpars in he EU-counries. This is usually ascribed o a specificaion bias in naional money demand funcions, which may reflec omied variables ha capure currency subsiuion effecs (Kremers and Lane, 1990). Then, sabiliy of area-wide money demand mirrors he fac, ha his specificaion bias is reduced hrough aggregaion. 1 Mos of he sudies on EU-wide money demand were carried ou wihin a single equaion seing (e.g. Kremers and Lane, 1990; Monicelli, 1995; Fase and Winder, 1997). 2 For boh economic and echnical reasons, a mulivariae approach is o be preferred however. On he economic side, sabiliy of he money demand funcion is only one precondiion for money argeing o be appropriae. In order o be successful, a sufficien degree of conrollabiliy of he money sock via a policy variable and a predicable effec of excessive money growh on fuure inflaion are also of crucial imporance. These aspecs can only be analyzed in a mulivariae seing. From a echnical poin of view, he mulivariae approach is o be preferred as i allows o es for muliple coinegraing relaionships, and is more efficien if no all variables bu money are weakly exogenous wih respec o he long run parameers. Moreover, he procedure allows o explicily es for weak exogeneiy, hereby prevening simulaneiy biases. Conrollabiliy is non-rivial as he cenral bank is assumed o have only indirec conrol over he money sock, via he shor-erm ineres rae (is main policy insrumen or operaional arge). In he long run, he money sock is assumed o be demand deermined. Consequenly, he moneary auhoriies are only able o conrol he money sock in as far as hey can conrol he variables deermining money demand. As we assume a broad moneary aggregae o be he relevan money measure, he crucial quesion is, wheher he differen indirec ransmission chan- 1 Tha currency subsiuion may no be he main facor behind he sabiliy of EU-wide money demand funcions, was poined ou by Arnold (1994). He argues ha if naional money demand insabiliy were primarily due o shocks operaing in a desynchronized paern in sage II, esimaes of aggregaed money demand funcions overesimae money demand sabiliy in sage III, as far as hese shocks will be synchronized in sage III. Hence, he validiy of arewide money demand funcions is sill conroversial. 2 An excepion for European aggregaes is Fagan and Henry (1997), who apply he mulivariae coinegraion echnique o es for muliple long-run relaions. Afer finding suppor for one coinegraing relaionship hey coninue wih single equaion models. A recen applicaion o German daa is he join analysis of money demand, he erm srucure of ineres raes and he long-run Fisher effec (Hubrich 1997).

9 - 2 - nels are srong enough o ensure an overall negaive effec of a shor-erm ineres rae innovaion on broad money despie he posiive response of ineres rae bearing componens of broad money o a shor-erm ineres rae shock. The presen paper invesigaes wheher on he aggregaed European Union (EU) level, demand for broad money is sable and conrollable and wheher excess money growh (in excess of he quaniy demanded) predics fuure inflaion. This is done wihin a Srucural Vecor Error Correcion Model (S-VECM), a special case of he Srucural Vecor AuoRegression (S-VAR) model, ha has become a popular ool in analyzing he effecs of moneary policy surprises (Sims, 1992; Gali, 1992; Clarida and Gali, 1994; Kasumovich, 1996; Bagliano and Favero, 1997). The S-VECM mehod is a wo sep procedure. In he firs sep, he long run relaionships in he daa are deermined by means of mulivariae coinegraion echniques (Johansen, 1988, 1991; Johansen and Juselius, 1992, 1994). The sabiliy and predicabiliy aspecs will be analyzed in his firs sep. In he second sep, he residuals from he firs sep (he reduced form model) are expressed in erms of uncorrelaed srucural shocks in order o separae exogenous policy acions from endogenous movemens in policy variables (due o developmens in he economy). The idenificaion problem involved is solved by imposing resricions (based on economic heory) on eiher he conemporaneous or he long-run effec of he srucural innovaions on variables in he sysem (Vlaar, 1998). The dynamic effecs of he srucural shocks on he variables are subsequenly shown by means of impulse response funcions. In order o invesigae conrollabiliy, one srucural shock will be idenified as being a policy induced shor-erm ineres rae shock. The oher srucural shocks will be idenified as being an exchange rae shock, a real demand shock, a real supply shock, a fiscal policy shock, and a nominal shock respecively. The paper is organized as follows: Secion 2 reviews he channels by which variaions of he operaional arge may affec he money sock. Secion 3 discusses some echnical issues. Firs, he economeric mehods are oulined, summarizing he resuls of Vlaar (1998). Then, he daa are described. Secion 4 presens a reduced form vecor error correcion model for he EU, idenifying a long-run money demand funcion and a long-run Fisher effec. Secion 5 oulines a small macroeconomic model ha underpins he shor-run and long-run resricions used o idenify he srucural shocks. Furhermore, he esimaes of he srucural model are presened, and he impulse response funcions are shown. The final secion (Secion 6) summarizes and inerpres he main resuls.

10 - 3-2 MONETARY CONTROL The raionale behind moneary argeing is ha excess money growh, i.e. money growh exceeding he growh of money demand, will ulimaely lead o inflaion. Consequenly, he suiabiliy of a money growh arge hinges on a leas hree imporan aspecs: sabiliy, conrollabiliy and predicabiliy (Mishkin, 1992). Sabiliy refers o a sable measurable relaionship (preferably wih small forecas errors) beween money demand on he one hand and predicable macroeconomic variables on he oher. This precondiion is necessary in order o be able o se reasonable arges. Conrollabiliy refers o he abiliy of he moneary auhoriies o influence money growh if he moneary arges are no likely o be me. Predicabiliy refers o he relaionship beween excess money growh and fuure inflaion. An inermediae arge (money growh) is only useful if i provides a clear signal regarding he ulimae arge (price sabiliy). Crucial o he conrollabiliy of he money sock is he choice of he operaional arge of he moneary auhoriies and he definiion of he moneary aggregae chosen as inermediae arge variable. Conrollabiliy can be viewed from wo angles. In sandard exbook models of he money view of he ransmission process, moneary policy is analyzed in erms of changes in nominal reserves ha exer an influence on nominal money hrough he money muliplier. Conrollabiliy is hen assured if he money muliplier is sufficienly sable. 3 However, in pracice almos all cenral banks use a shor-erm ineres rae as heir main operaional arge. Therefore, numerous sudies measure moneary policy shocks as innovaions o he shor-erm ineres rae (Sims, 1992; Kasumovich, 1996; Bernanke and Mihov, 1997; Bagliano and Favero, 1997). 4 If he shor-erm ineres rae is he operaional arge of he moneary auhoriies, he money sock is demand deermined. The direc channel hrough which he shor-erm ineres rae influences he money sock, is he subsiuion effec: Wih narrow money as an inermediae arge, an increase of he cenral bank rae decreases demand for money, since he shor-erm ineres rae measures he opporuniy cos of holding money. Since demand for narrow moneary aggregaes usually proves o be less sable han for broad money (Fase, 1994), in he discussion abou he appropriae moneary sraegy he main focus is on broad moneary aggregaes. In ha case, he subsiuion effec migh become posiive, as he shor-erm ineres rae acs as an own ineres rae for he ineres bearing iems in broad money aggregaes. 3 A model of moneary conrol for he US ha uses oal reserves as moneary policy insrumens is presened in Thoron When using a shock o he shor-erm ineres as a moneary policy measure, in several VAR-sudies (e.g. Sims 1992), he iniial response of inflaion is posiive ( price puzzle ).

11 - 4 - Conrollabiliy problems can be alleviaed by a leas hree indirec channels. Firs, he income effec: Given price and wage rigidiies, a rise in he cenral banks rae decreases real income, and hence dampens demand for money. Second, according o he expecaions heory of he erm srucure, long-erm ineres raes reflec a weighed average of fuure shor-erm ineres raes. Consequenly, a rise in shor-erm raes should lead o higher long-erm raes as well, hereby furher reducing money demand. Third, a moneary conracion should lead o a lower price level, hereby reducing he demand for nominal money holdings. On he oher hand, conrollabiliy could be impaired for mainly wo oher indirec links. Firs, if moneary policy affecs he erm srucure via inflaionary expecaions, an ineres rae increase migh also reduce long-erm nominal ineres raes and hereby increase money demand. Wih broad moneary aggregaes, also a wealh effec becomes imporan. Ignoring revaluaion effecs 5, real wealh will increase in he course of a rise in official ineres raes, reflecing emporary higher curren accoun surpluses in response o a decline in he domesic demand for goods and a fall in prices. Increased wealh increases demand for money. The overall effec on conrollabiliy can no be prediced on beforehand. 3 TECHNICAL ISSUES 3.1 Economeric mehods used In order o invesigae he moneary ransmission mechanisms, a srucural vecor error correcion model (S-VECM) will be used. The S-VECM mehod is a wo-sep procedure. In he firs sep, a reduced form VECM is esimaed by means of he now familiar procedures of Johansen (1988, 1991) and Johansen and Juselius (1992, 1994): k = + X + 1 αβ 1 i= 1 X µ Γ X + e, (1) i i where X is an n-dimensional vecor of variables ha are inegraed a mos of order one; represens he firs difference operaor: x = x x 1; e is an n-dimensional vecor of reduced form residuals which is assumed o be normally disribued wih expecaion zero and 5 Revaluaion effecs are ignored because of he way, he wealh daa are consruced. See Secion 3.2. If revaluaion effecs are aken ino accoun, an ineres rae increase should - due o he devaluaion of financial asses - exer a negaive impac on real financial wealh, hereby easing he conrollabiliy problem.

12 - 5 - variance Ω ; µ is a parameer vecor of consans; he Γ i marices denoe parameers for shor run dynamics; and α and β are full column rank marices of order ( n r) where r is he coinegraing rank. The β -marix deermines he long run equilibrium relaionships beween he variables (one of which is assumed o be a money demand relaionship), whereas he α -marix represens he influence of disequilibria on he variables in he sysem (predicabiliy will be invesigaed by looking a he elemen of α represening he influence of excess money holdings on inflaion). As X conains only saionary variables, i can also be expressed in a vecor moving average represenaion (Johansen, 1991): X = Ci ( µ + e i ) = C( L)( µ + e ) (2) i= 0 where L denoes he lag operaor. The CL ( ) marix polynomial can be separaed ino componens associaed wih long-run (C(1)) and shor-run informaion (C * (L)) respecively: * CL ( ) = C( 1) + C( L)( 1 L) where C( 1 ) represens he sum of he moving average parameers. This marix is called he oal impac moving average marix as i gives he ulimae effec of a shock o he reduced form residuals on he level of he endogenous variables. I can be shown ha he rank of C( 1 ) is equal o n-r. By accumulaing he differences i follows ha: 0 + C(1)( + ei ) + i= 1 * X = X µ C ( L) e (3) The second sep comprises he idenificaion of he srucural model. Thereo, he reduced form disurbances e are expressed in erms of he srucural innovaions ε, which can be given an economic inerpreaion: e = B 0 ε (in our case including a policy induced ineres rae shock). Here, B 0 is a non-singular (n n) marix and ε is a vecor of srucural innovaions wih expecaion zero and variance I n, an n-dimensional ideniy marix. In order o idenify he srucural model, resricions have o be imposed on he B 0 marix. From he relaionship beween he variances of he reduced form residuals and he srucural innovaions i follows ha BB 0 0 =Ω. This relaionship imposes n(n+1)/2 independen non-linear

13 - 6 - resricions on B 0, leaving n(n-1)/2 elemens free. Consequenly n(n-1)/2 addiional independen resricions have o be imposed in order o exacly idenify he srucural model. These resricion have o come from economic heory as hey are no esable. I is also possible o impose more han n(n-1)/2 resricions in which case he overidenifying resricions are esable (Amisano and Giannini, 1997). Assuming he addiional resricions are all linear zero resricions, hey can be expressed in he following general implici form: R vec ( B 0 ) = 0, (4) where R denoes a ( g n 2 ) marix, imposing he g independen resricions on B 0 and vec() denoes he column sacking operaor. In he case of only conemporaneous resricions, he R marix is a selecion marix wih only nonzero elemens for he resriced elemens of B 0. Long run resricions are relaed o he oal impac marix C( 1 )(see Equaion 3). If he j-h srucural innovaion is supposed o have no impac on variable i in he long run, his can be achieved by resricing he i,j elemen of C() 1 B 0 o be zero. Wihin resricion scheme (4) hese long run resricions can easily be incorporaed. In accordance wih he common rends lieraure (Sock and Wason, 1988; King, Plosser, Sock and Wason, 1991; Warne, 1993), he space spanned by he srucural innovaions will be spli ino he (n-r)-dimensional common rend space, and he r-dimensional coinegraing space. The innovaions ha lie in he common rend space (he common rends or permanen shocks) each have a permanen impac on a leas one variable in he sysem, whereas he impac of he disurbances in he coinegraing space (he ransiory shocks) dies ou in he long run. This is accomplished by imposing zeros in r columns of C() 1 B 0. As he rank of C( 1 ) is n-r, his already implies r(n-r) independen resricions. In convenional common rends models, he muual idenificaion of he common rends (ransiory shocks) is subsequenly achieved by imposing a recursive ordering wihin he common rend (coinegraion) space. Our specificaion is much more flexible however. In order o achieve idenificaion wihin he common rend space any se of (n-r)(n-r-1)/2 independen linear zero resricion on eiher he conemporaneous or he permanen impac will do. Especially for relaively large sysems, his flexibiliy is imporan as a recursive ordering of long run impacs migh be oo resricive from an economic poin of view. Similarly any se of r(r-1)/2 independen linear zero resricions on he conemporaneous impacs can be used o muually idenify he ransiory shocks. Moreover, our common rends model is more flexible in ha i allows for overidenifying resricions.

14 - 7 - Afer rewriing he implici resricion formulaion (Equaion 4) in explici form, he srucural model can be esimaed by maximum likelihood (Amisano and Giannini, 1997). The effecs of he srucural innovaions on he sysem variables is subsequenly shown by means of impulse response funcions (dynamic mulipliers). These funcions show he dynamic effecs of a one sandard deviaion shock o he srucural innovaions on he endogenous variables. The asympoic disribuion of he impulse response funcions in case of only conemporaneous resricions is given in Lükepohl and Reimers (1992). The inroducion of long run resricions considerably complicaes he disribuion however, as hese resricions on B 0 are funcions of he VECM parameers. As a consequence, he convenien block-diagonaliy of he covariance marix of model parameers wih he parameers of he mean on he one hand and hose of B 0 on he oher is desroyed. In Vlaar (1998) i is shown ha he asympoic disribuion of he impulse responses can sill be compued from he covariance marix ha neglecs he sochasic naure of he resricions however, provided ha a correcion is compued relaed o he parial derivaive of B 0 wih respec o he VECM parameers. 3.2 The Daa The sudy analyses aggregaed quarerly daa of 14 European counries (European Union wihou Luxembourg) over he sample period 1979-I up unil 1996-IV. We exended he daase used in Fase and Winder (1997) hrough The variables included are seasonally unadjused daa for annualized quarerly inflaion (π), shor-erm ineres rae (i s ) 7, long-erm ineres rae (i l ), real oupu (y), real wealh (w), and real money sock (M3 harmonized, m). Excep ineres raes, all variables are expressed in percenage logs. These variables are chosen because of heir imporance in a money demand relaionship. Financial wealh is included as broad money holdings are no only moivaed by ransacion purposes - for which real oupu is he appropriae scale variable bu also by porfolio allocaion moives. I can offer an explanaion for he sharp increase of he area wide M2 and M3 o GDP raio in he 1980s (Fase and Winder, 1993, 1997). Ne financial wealh of he non-moneary privae secor is defined as he sum of debs by he governmen and he foreign secor. The foreign deb is hereby approximaed by he accumulaed curren accoun surpluses from 1956 on, assuming zero deb in In he lieraure on area-wide money demand, conversion wih curren or wih base-year exchange raes or purchasing power pariies have been applied o conver naional variables in a 6 A deailed descripion of he daa se can be found in Fase and Winder (1997). 7 Due o lack of daa on own-ineres raes for all counries under consideraion, he hree-monh inerbank rae has been used.

15 - 8 - common currency. 8 For he consrucion of area-wide variables on nominal and real oupu, financial wealh and M3H, naional variables were convered ino DM wih he purchasing power pariies of he year Afer convering naional variables o a common currency, hey have been aggregaed across counries. Aggregaion a a base-year rae has he advanage ha he growh raes of oupu, money, wealh and he inflaion rae are weighed averages of he corresponding variables of he individual counries and are no influenced by changes of he exchange rae of he counries currencies (vis à vis he DM). 9 The area-wide price index has been calculaed as he raio of nominal and real gross domesic produc. The price index was used o deflae aggregaed nominal wealh and nominal M3H. The shor-erm and long-erm ineres raes have been aggregaed wih he real GDP weighs of individual counries in areawide oupu. 4 THE REDUCED FORM MODEL s l The reduced form VECM (Equaion 1) is esimaed wih X = ( π, i, i, y, w, m) being a vecor of endogenous variables inegraed of order d, where d This firs sep in he esimaion procedure reveals he long run equilibrium relaionships beween he variables, one of which is assumed o be a money demand relaionship. The model allows for linear rends in he daa, bu i is assumed ha here are no rends in he coinegraing relaions. A vecor of deerminisic erms conaining a second se of cenered seasonal dummies and an impulse dummy (D923) which is one in 1992:3 and zero oherwise is included in order o reduce auocorrelaion. The impulse dummy accouns for he EMS exchange rae crises of auumn The second se of seasonal dummies sars in 1983 and accouns for he changed seasonal paern since hen, especially in inflaion. To es for he opimal lag lengh, he Akaike, Schwarz and Hannan-Quinn informaion crieria were employed, see Table 1. The Schwarz crierion indicaed a lag lengh of 1, whereas he Akaike and Hannan-Quinn crieria recommended more lags. Based on ess for auocorrelaion, he lag lengh was fixed a wo. Table 1 Preliminary lag lengh analysis 8 The mehod o conver naional variables ino a common currency is conroversial, as shown by he differen choices in he lieraure. Kremers and Lane (1990) use purchasing power pariies, while Monicelli and Srauss- Kahn (1991) use curren exchange raes. 9 For a deailed discussion of mehodological and aspecs of aggregaion see Winder (1997). 10 The compuaions were done in PcFiml 9.0 (Doornik and Hendry, 1997) and a modified version of he Ras package Malcolm (Mosconi, 1997).

16 - 9 - lags Akaike Hannan-Quinn Schwarz AR(1) AR(5) () () (0.10) (0.14) (0.37) (0.19) (0.56) (0.49) Noe: AR(1) and AR(5) refer o he LM ess based on auxiliary regressions of he residuals on he original variables and one respecively one o five lagged residuals. The saisics are expressed in F-form, p-values are in parenhesis. Subsequenly, he maximum likelihood procedure of Johansen (1988) is applied o es for he number of coinegraing vecors. Table 2 repors he λ-race and λ-max saisics (wih and wihou he correcion for he number of esimaed parameers) ogeher wih he 95% criical values. The wo race ess suppor a coinegraion rank of eiher 2 or 3, whereas he λ-max ess indicae a rank beween 1 and 3. The rank saisics were also calculaed wihou he deerminisic componens. 11 Using hese daa, only he uncorreced λ-max saisics indicaed a rank of hree whereas he oher hee saisics indicaed a rank of wo. Table 2 Tes for coinegraion rank 95%-Criical 95%-Criical λ-race Value λ-max Value H 0 λ-race (using T-nk) λ-max (using T-nk) r = ** 120.0** ** 51.18** 39.4 r = ** 68.83* * r = * * r = r = Noe: * (**) denoes significance a he 5% (1%) level As saisical argumens were no clear enough o decide on he number of coinegraing relaionships, economic argumens were used as well. Specific hypohesis regarding weak exogeneiy and saionariy have been esed o derive an economic meaningful inerpreaion of he muliple coinegraion vecors boh under he assumpion of a rank of wo and under a rank of hree, see Table 3. Wihin he six variable sysem, one coinegraing relaionship should represen a long run money demand funcion. Oher candidaes for saionariy migh be he shor or 11 As our dummy variables are saionary in he sense ha hey do no shif permanenly, he asympoic disribuion should no be affeced by he dummy variables.

17 long erm ineres rae, inflaion, a erm srucure relaionship or a real ineres rae. Given he fac ha a rend in he coinegraing relaionships is no allowed, combinaions wih eiher wealh or oupu seem less plausible on economic grounds. The null hypohesis of saionariy is clearly rejeced for all model variables, including he ineres raes and inflaion, even under a rank of hree. Saionariy of he real long-erm ineres rae is no rejeced a he 8% level assuming a rank of hree, and a he 2% level assuming a rank of wo. The saionariy es for he yield spread provides srong evidence agains he expecaions heory of he erm srucure, even under a rank of hree. 12 Given he lack of a plausible economic inerpreaion for a hird coinegraing relaionship and he ambiguous saisical resuls, a rank of wo was imposed. Regarding weak exogeneiy wih respec o he long run parameers, real wealh and inflaion sand ou. The weak exogeneiy of wealh suppors he resuls of Fase and Winder (1997) in he sense ha he significan impac of wealh on money hey found in heir single equaion model can no be aribued o a simulaneiy bias. Weak exogeneiy of inflaion would seriously impair a moneary argeing sraegy as i would imply absence of an inflaionary impac of excessive money growh, hereby frusraing predicabiliy. Given he economic imporance of inflaion and he rejecion of exogeneiy under a rank of hree, inflaion was no a priori resriced o be weakly exogenous for he long run parameers. Table 3 Tes for weak exogeneiy and saionariy π i s i l y w m l i π l s i i r = 2 Weak exogeneiy 0.94 (0.625) () () 6.66 (0.036) 1.02 (0.60) 9.66 (0.022) Saionariy () () () () () () (0.024) () r = 3 Weak exogeneiy (5) () () 7.81 (0.050) 3.88 (0.28) () Saionariy () () () () () () 6.62 (0.085) () Noe: p-values in parenhesis. Based on he resuls in Table 3, he second coinegraing vecor (column of β), he firs being he long-run money demand equaion, was resriced o represen a relaionship beween he long-erm ineres rae and inflaion. The usual way o idenify he coinegraing vecors is o impose r-1 resricions (plus a normalizaion) on every coinegraing vecor in he sysem. However, as all he variables included are a priori expeced o play a role for money demand, we did no wan o resric he β-vecor ha is relaed o money demand. Idenificaion is insead 12 The hypohesis of saionariy of he real shor-erm ineres rae is also clearly rejeced.

18 achieved by resricing he α-marix. The firs coinegraing vecor, which is normalized on real money, is idenified as a long run money demand equaion by resricing he α-coefficien for real money in he second coinegraing vecor o be zero. Consequenly, all long run informaion ha is imporan for real money is provided by he firs coinegraing vecor. As he resuls indicaed a negligible effec of inflaion on real money demand and an income elasiciy close o one, he inflaion and real oupu elasiciies were resriced. Afer imposiion of weak exogeneiy of real wealh and idenificaion of he real money demand equaion, he hypohesis ha he real long erm ineres rae - reflecing a long run Fisher equaion - was saionary could no longer be rejeced. Therefore, saionariy of he real rae was imposed. The resuling model is shown in Table 4. Table 4 Esimaion resuls of he reduced form model LR es of resricions: χ 2 () 8 = [0.062] β s.e. α s.e. π (0.067) (0.102) i s (0.290) (0.020) (0.031) i l (0.339) (0.017) (0.027) y (0.044) (0.069) w (0.019) m (0.031) - Noe: sandard errors in parenhesis, p-values in squared brackes. The resuling long-run money demand equaion has a leas wo ineresing feaures: The firs is he significan role, financial wealh plays as a deerminan of he demand for money, reflecing he porfolio allocaion moive. This confirms he resuls of Fase and Winder (1997) who show ha wealh has a significan impac on he demand for area-wide M2 and M3. The oher ineresing resul refers o he relaive size of he highly significan elasiciies of he shor and longerm ineres rae. The significance of he shor-erm ineres rae, which is a proxy for he own ineres rae of moneary componens of M3H, also poins o he imporance of porfolio selecion moives for broad moneary aggregaes. The fac ha he posiive semi-elasiciy of he shor-erm ineres rae is higher han he negaive semi-elasiciy of he long-erm ineres rae indicaes possible problems wih conrollabiliy of he money sock. This finding differs from he resuls of he few sudies on EMU-wide money demand, simulaneously insering a longerm and a shor-erm ineres rae ino he money demand equaion.

19 For boh, M2 and M3, Fase and Winder (1997) found higher negaive long-erm ineres rae elasiciies han he posiive shor-erm ineres rae elasiciies. When including a shor-erm and a long-erm ineres rae ino he long-run demand for M3H funcion, Fagan and Henry (1997) find ha he shor-erm ineres rae is no significan. These findings hold for EU7 and EU14. Table 4 also shows he loading coefficiens α wih he respecive sandard errors. All he coefficiens have he expeced sign. Excess money, defined as money holdings in excess of he long run equilibrium, increases inflaion, ineres raes and oupu, and has a negaive impac on real money holdings. A relaively high real long-erm ineres rae signals rising inflaion, whereas ineres raes and real oupu are negaively affeced. The inflaion effec reflecs he anicipaion of bond marke paricipans o fuure inflaion. Mos of he α-coefficiens are significanly differen from zero. Especially for inflaion, his is remarkable as i was shown o be weakly exogenous if no oher resricions were imposed (Table 3). The significan impac of excess money on inflaion is paricularly imporan as his is a necessary precondiion for money growh o be a useful indicaor for fuure inflaion. Table 5 Residual analysis vecor es π i s i l y w m AR(1) (0.703) AR(5) (0.051) Normaliy (0.082) (0.713) (0.135) (0.871) (0.658) (0.051) (0.790) (0.782) (0.026) (0.032) (0.621) (0.022) (0.271) (0.130) (0.033) (0.448) (0.367) (0.053) (0.053) ARCH(4) (0.743) (0.851) (0.923) (0.235) (0.901) (0.932) Noes: p-values in parenhesis; The ess are compued for fixed β. The normaliy es are based on ransformed skewness and kurosis parameers, see Doornik and Hansen (1994). The ARCH(4) saisic ess for fourh order ARCH-like heeroskedasiciy. Table 5 shows some residual diagnosics for he final model. In he equaions for he long-erm ineres rae, real income and real wealh, single equaion misspecificaion ess show some indicaion for auocorrelaion of order 5 a he 5% significance level, bu no a he 1% level. The assumpion of normaliy is accepable for all equaions wih he possible excepion for he one on he long-erm ineres rae. ARCH-like heeroskedasiciy seems no presen in he daa. As

20 he vecor ess for misspecificaion reveal neiher auocorrelaion, nor a rejecion of normaliy, he specificaion was deemed accepable. Figure 1: Sabiliy of Sp(bea) Significance level = 95% R_model Z_model Normcval In order o invesigae he sabiliy of money demand, recursive regressions have been performed. Figure 1 shows he sabiliy of he idenified β marix (Hansen and Johansen, 1993). Sabiliy is no rejeced a he 95% level according o he so-called R-model, in which he shor erm dynamics is kep consan. According o he Z-model, in which he all parameers are recursively esimaed, some insabiliy is deeced unil he second half of 1989 and during However, especially he Z-model migh be unreliable a he beginning of he sample as i suffers from a lack of degrees of freedom due o he many parameers o be esimaed. Moreover, i should be kep in mind ha he es saisics involved assume ha, a each poin of he recursive esimaion, he iming of he srucural change is known. Consequenly, he sequence of srucural break ess, as shown in he figure is oo conservaive, as possible breakpoins are deeced condiional on he daa. If a significance level of 99% would have been used insead, he Z- model would no have been rejeced from he second half of 1989 on. Figure 2 shows recursive coefficiens for he hree freely esimaed elemens in he money demand funcion for he R- model. The wealh coefficien is remarkably sable over ime, whereas he ineres rae semielasiciies seem o grow slighly over ime. In all sub-samples he coefficien of he shor erm ineres rae in money demand relaionship is higher in absolue value han he one for he longerm rae. All in all, he money demand relaionship seems o be reasonably sable.

21 Figure 2: Recursive bea, R-model Significance level = 95% Real wealh Shor erm ineres rae Long erm ineres rae THE STRUCTURAL MODEL 5.1 Theoreical consideraions In order o apply a S-VECM policy analysis, exogenous shocks have o be separaed from movemens in he variables due o endogenous responses o curren developmens in he economy. This involves an idenificaion problem ha mus be solved, based on a heoreical model. Therefore, he following open economy macroeconomic model is se up. y = ( 1 σ ) l + u wih s l u = 0 + u 1 σ + ε s (5) w p = ω 0 σ l + u (6) l l l s w l l = λ + λ ( w p ) (7) 0 w = E w (8) 1 l, e where w l, e = p ω 0 σ lλ σ λ l w u σ λ l w y d = δ + δ l ( w p ) δ ( δ i + (1 δ ) i E π + ) + δ q + δ ( m m ) + δ ε + ε 0 w l i s s s l 1 q m * g g d (9) q i l s + p p = α q 1 + ε (10) f q l, f = i + E s + s ) (11) ( 1 l, f f i 0 + = ι + E ( π ) 1 (12)

22 m * = y + µ w + µ i µ i µ ε w i s s i l l d d (13) m + p * = η 0 + m 1 + p 1 + η( m m 1 + π ) (14) i s l * = i + ( Eπ + π + 1) ρ g ( d y ) s i ρ π 1 + ε (15) π (16) * * n + 1 = π + ε 1 P 1 B (17) 1 W = W + CA + P ca = ϕ ca ϕ ( y y ) + ϕ q ca d s 1 y q (18) b = y + + γ q ( b 1 y 1 ) g γ 0 + ε (19) p = 1 ) E 1 ( θ p + θp (20) e e Excep ineres raes, lower case leers denoe variables in logarihm, muliplied by 100. denoes he expecaions operaor condiional on informaion known a ime. E The supply side of he model is a simplified version of he model in Hoffman and Rasche (1996). Equaion 5 is a sandard aggregae producion funcion relaing he log of real oupu s s supply ( y ) o he log of employmen ( l ) and a permanen supply shock ( ε ) wih drif. l Equaion 6 is a marginal produciviy condiion equaing he log of real wage ( w p ) o a linear funcion of log of employmen. Equaion 7 is a labor supply funcion, relaing labor supply o real wage. According o Equaion 8 nominal wages are se in he previous period in such a way ha labor supply and demand are expeced o be equal in he nex period. d Real oupu demand ( y ) is linearly relaed o he oal real wage sum (Equaion 9). Moreover, s l i is assumed o decrease in he long-erm real ineres rae ( δ si + ( 1 δ s ) i Eπ + 1 ) 13 and o increase in he real exchange rae ( q ). Furhermore we assume ha an excess of he acual nominal money holdings ( m ) over he desired money holdings ( m * ) affecs real demand in he shor run. Curren periods deparures from he long run equilibrium in he money marke, ha are formulaed in buffer sock models, are based on commonly acceped microeconomic principles, such as ransacion coss (Mizen, 1997). Finally, real oupu demand is supposed o be subjec o ransiory real demand shocks ( ε d ) and governmen shocks ( ε g ). 13 Boh he long-erm and he shor-erm ineres rae are included in Equaion 9 o accoun for he fac ha he mos imporan ineres rae in ransmiing moneary impulses o he real economy differs beween he counries considered.

23 Equaion 10 formulaes he real exchange rae as being a mean revering process (α is assumed o be smaller han 1) subjec o exchange rae shocks ( ε q ). Wheher he mean reversion of he real exchange rae is due o domesic price adjusmens, foreign price adjusmens or changes in he nominal exchange rae is no imporan for our analysis. Long-erm nominal ineres raes are assumed o be deermined by he uncovered ineres rae l, f pariy condiion (Equaion 11), where i denoes he foreign long-erm ineres rae. The ex ane real foreign ineres rae (Equaion 12) is assumed o be consan. Given he assumed saionariy of he real exchange rae his implies also he saionariy of domesic real long-erm ineres raes, which is in accordance wih our resuls for he reduced form model. The direc channel hrough which an ineres rae innovaion affecs real balances is formalized in Equaion 13 which specifies he real desired money holdings. In he long run i is deermined by real oupu ( y ), he long-erm ineres rae (i l ), real ne financial wealh ( w ) and a shorerm ineres rae ( i s ), reflecing he own ineres rae of moneary componens. In line wih he empirical resuls, an income elasiciy of 1 has been imposed. The inclusion of wealh is in line wih Friedman s heory ha money is considered as one of various alernaive asses wihin wealh. In he shor run, desired money holdings are negaively affeced by a real demand shock (ε d ), which accouns for he effecs of he business cycle on precauionary money holdings (Friedman, 1971; Den Buer and Fase, 1981; Fase and Winder, 1993, 1997). Acual money holdings (Equaion 14) are in he long run compleely demand deermined, bu may in he shor run deviae from desired holdings due o sluggish adjusmens of he acual money sock. We expec he moneary auhoriies o raise shor-erm ineres raes ( i s ) relaive o he longerm rae (i l * ), if expeced fuure inflaion ( E π +1 ) exceeds he arge inflaion rae ( π +1 ) (Equaion 15). 14 This kind of reacion funcion is similar o he one inroduced in Juselius (1997). In our model he cenral bank reacs o an increase in he deb o GDP-raio ( d y ) as well, however. This reflecs he fac ha several cenral banks were no compleely independen during he sample period. The higher he governmen deb, he higher he pressure on he cenral bank o lower ineres raes, hereby reducing he financing coss for he governmen and pushing up nominal GDP growh. The arge inflaion rae ( π * +1 ) serves as a nominal anchor in he model (Equaion 16). I is assumed o follow a random walk subjec o nominal shocks ( ε ). n 14 This is in line wih he resuls of Bernanke and Mihov (1997) and Schächer and Sokman (1995), who demonsrae ha he Deusche Bundesbank reaced o he desired rae of inflaion raher han o he deviaion of money supply from he arge range.

24 The shocks o he arge are asumed o be known beforehand consequenly are expeced o have only limied real effecs. The real privae financial wealh (W) Equaion 17 is an ideniy, reflecing he way he daa are consruced. Real wealh increases wih real curren accoun surpluses ( CA ) and wih real budge deficis ( B ). The laer is formulaed as a funcion of he las period s budge defici, a change in oupu and a fiscal policy shock (ε g ) (Equaion 19). Noice, ha here is no revaluaion of financial asses in he model. The curren accoun is assumed o be a funcion of he oupu gap ( y y ) and he real exchange rae (Equaion d s 18). To inroduce some nominal rigidiies, we use he price-seing Equaion 20 as in Mussa (1982) and Clarida and Gali (1994). The price level in period is a weighed average of he marke clearing price expeced in period -1 o prevail in period, ( E 1 p e ), and he price ha would acually clear he oupu marke in period ( p e ). When θ = 1, prices are fully flexible and oupu is supply deermined. When θ = 0, prices are fixed and predeermined one period in advance. Wihin his model, he movemens in he main macro variables are he resul of six exogenous disurbances: an exchange rae shock, a shor-erm ineres rae shock, a real demand shock, a real supply shock, a fiscal policy shock and a nominal shock. 5.2 Idenifying resricions To idenify he srucural shocks, resricions on he impac of he shocks on he model variables are imposed, based on he heoreical model oulined above. Following Gali (1992), we combine conemporaneous resricions such as specified in Blanchard (1989) and long-run neuraliy idenifying resricions such as pioneered by Shapiro and Wason (1988) and Blanchard and Quah (1989). Conemporaneous idenifying resricions are usually jusified wih he exisence of decision and informaional lags in economic policy (Gali, 1992) and/or wih feaures of Keynesian models such as wage and price rigidiies (Blanchard, 1989; Giannini, Lanzaroi and Seghelini, 1995). Long-run zero resricions on long-run mulipliers for he srucural shocks are advanageous over he shor-run echnique, since economic heory has usually more o say abou he long-run han abou he shor-run effecs of disurbances. In idenifying he sochasic processes, we ake ino accoun ha our n dimensional sysem wih r coinegraing relaionships feaures ( n r) independen sochasic rends (Sock and

25 Wason, 1988). Since in our model, r = 2, wo of he shocks are specified as having only ransiory effecs. In our model, hese shocks are he real exchange rae shock ε q and he real demand shock ε d. In order o muually idenify hese wo shocks only conemporaneous resricions can be used. These resricions are always somewha arbirary, he more so for infrequenly sampled daa. We will impose he resricion ha real demand shocks are accommodaed by he moneary auhoriies is such a way, ha he iniial real shor-erm ineres rae effec is zero. In order o idenify he four independen common rends boh conemporaneous and long-run resricions can be used. The firs se of long-run resricions allows us o sor ou he demand shocks from one supply shock. Following Blanchard Quah (1989) and in accordance wih our model, we assume ha only real supply shocks have a long run effec on oupu. We resric all shocks excep he real supply shock o have no long-run impac on oupu. In he seady-sae equilibrium, real oupu is hen only driven by is own shock. This classificaion of shocks is consisen wih a wide range of macroeconomic heories, hough i may be argued ha demand disurbances may have long-run effecs on oupu, e.g. hrough is effec o he seady sae level of capial. Bu as Blanchard and Quah (1989) argue, hose effecs may be small compared o he effecs of supply disurbances on oupu. In accordance wih Equaion 15 of our model, he fiscal policy shock is idenified by assuming ha i is he only shock ha affecs he slope of he erm srucure of ineres raes in he long run. This is in line wih empirical research (Goldsein and Woglom, 1992; Correira-Nunes and Semisiois, 1995; Van Els and Vlaar, 1996) ha excessive deficis increase he erm premium. The usual explanaion for his phenomenon are increased defaul premia on he governmen deb or rising inflaion risk premia. As real long-erm ineres raes urned ou o be saionary, our explanaion is lower shor-erm ineres raes due o Governmen pressure on he cenral bank. Anoher implicaion of he moneary policy equaion is ha only changes in preferences regarding inflaing and changes in he governmen deb have a lasing effec on inflaion. This condiion disinguishes he moneary policy shock from he nominal shock. The resuls are summarized in he Tables 6 and 7. The model imposes 17 independen resricions, so he model is over-idenified.

26 Table 6 Conemporaneous Resricions (B 0 ) Exchange rae shock Shor-erm ineres rae shock Real demand shock s π B ( i ) 0 Real supply Shock Fiscal policy shock Nominal shock i s B 0 ( π ) i l y w m Table 7: Long-run Resricions (B ) Exchange rae shock Shor-erm ineres rae shock Real demand shock Real supply Shock Fiscal policy shock Nominal shock π i s B i l i l ( i s ) y w 0 0 m 0 0 B 5.3 Esimaion resuls The wo over-idenifying resricions ha are imposed on he common rend space are no rejeced by he daa as he likelihood raio es has a value of 4.89 which is only significan a he 8.7% level. The resuling conemporaneous impac marix ( B 0 ) has he following form: B = wih asympoic -values:

27 B 0 = Mos of he iniial impacs are significan for he variables ha are direcly relaed o he shocks. An exchange rae shock (Column 1) has an immediae significan impac on inflaion. The fac ha real wealh is no affeced is due o he weak exogeneiy of real wealh. This saisical arifac can only be jusified in economic erms by assuming ha he decrease in real wealh due o he increase in prices is exacly compensaed by increasing curren accoun surpluses or Governmens deficis. The moneary policy shock (Column 2) significanly increases shor-erm ineres raes, alhough he iniial impac of a real demand shock (Column 3) on shor-erm ineres raes is even larger (16 verses 26 basispoins). Bu, where he laer shock is characerized by a significan increase of oupu, a moneary policy shock significanly decreases oupu, hereby signaling significan liquidiy effecs. The iniial effec of moneary conracion on inflaion is negligible. The effec of a moneary policy shock on real wealh seems o be oo high. Real money holdings are significanly increased afer he moneary conracion, probably because of he posiive subsiuion effecs and wealh effecs, hereby impairing conrollabiliy in he very shor run. By far he mos imporan source for movemens in oupu is he real supply shock (Column 4). The impac of a fiscal policy shock (Column 5) on real wealh is no significanly differen from zero. This can parly be explained by he immediae price increase. The significance of his shock on nominal wealh is higher. Finally, he nominal shock (Column 6) increases inflaion, alhough his effec is jus no significan. 5.4 Impulse response funcions In Figures 3 o 8, he impulse response funcions of he six model variables and six relevan auxiliary variables, ogeher wih he asympoic 95% confidence inerval, are given. The auxiliary variables are all linearly relaed o he model variables. These are: (1) he price level s l (0.25 π ); (2) real shor-erm ineres rae ( i π ); (3) real long-erm ineres rae ( i π ); (4) excess money supply ( β 1 B i ); (5) nominal wealh ( w π ); (6) nominal money sock ( m π ). The excess money supply represens acual minus long run desired real money holdings. I is compued from he coinegraing vecor represening he long run real money demand. As he excess money holdings are in excess of desired holdings, apar from shor-erm effecs due o real demand shocks, his money is more likely o be spen which migh lead o inflaion. The nominal wealh variable is included as absence he revaluaion of wealh,

28 changes in nominal wealh equal changes in curren accouns plus governmen deficis. The nominal money sock is of direc ineres for conrollabiliy. One reason o include he exra impulse response funcions is ha i is no possible o deduce confidence inervals for hem by jus looking a he original variables. An exchange rae shock (Figure 3) only significanly affecs inflaion in he very shor run. Already afer hree quarers, he inflaion effec is back o zero. Given he ample evidence ha PPP only holds in he very long run, his resul can hardly be due o a complee recovery of he real exchange rae. Possibly, price adjusmens ake place almos immediaely afer an exchange rae shock for some goods (for insance primary goods) whereas he prices of oher impored goods are hardly adjused a all (due o sunk coss or menu coss). Alhough inflaion is back o zero afer hree quarers, he price level remains a a significanly higher level. Nominal wealh is significanly increased by he shock. This can no be explained by he increased price level as here are no revaluaion effecs in he daa. Insead, i migh be explained by he emporarily improved erms of rade due o he exchange rae shock. This migh also explain he significan decrease in excess money as he improved erms of rade migh posiively affec he business cycle, hereby reducing precauionary money holdings. The almos significan negaive response of long-erm ineres raes on an exchange rae shock is hard o explain. Alhough i is consisen wih he assumpion of uncovered ineres pariy (Equaion 11) coupled wih saionary real exchange raes (Equaion 10), he lack of a significan negaive response of inflaion laer on (which could indicae a gradual appreciaion) makes his argumen implausible. All in all he characerizaion of his shock as an exchange rae shock is no very convincing. However, i is hard o hink of an alernaive as he combinaion of very significan and large immediae price increases coupled wih insignifican oupu effecs and declining ineres raes is hard o explain by any heory. A moneary policy shock (Figure 4) significanly increases shor erm ineres raes by abou 15 basispoins for hree quarers, afer which he shock gradually dies ou. In response, long erm ineres raes rise by abou he same amoun. Inflaion is hardly affeced conemporaneously, bu is significanly negaively affeced in he second period, afer which inflaion reurns o preshock levels. The overall effec on he price level is only limied o 0.11% and is no significanly differen from zero. 15 Oupu is only negaively affeced in he firs period, indicaing 15 However, if he conemporaneous response of inflaion is resriced o zero which is accepable according o he chi-square disribued likelihood raio saisic of 5.43 wih hree degrees of freedom he price effec is significanly differen from zero. Apar from some of he confidence inervals, he impulse response funcions are hardly affeced by his exra resricion.