Ruhr Economic Papers. Ansgar Belke and Yuhua Cui. New Evidence from Taylor Rule Based VECMs #85

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1 Ansgar Belke and Yuhua Cui New Evidence from Taylor Rule Based VECMs #85 Ruhr Economic Papers UNIVERSITÄT D U I S B U R G E S S E N

2 Ruhr Economic Papers Published by Ruhr-Universiä Bochum (RUB), Deparmen of Economics Universiässraße 150, Bochum, Germany Technische Universiä Dormund, Deparmen of Economic and Social Sciences Vogelpohsweg 87, Dormund, Germany Universiä Duisburg-Essen, Deparmen of Economics Universiässraße 12, Essen, Germany Rheinisch-Wesfälisches Insiu für Wirschafsforschung (RWI Essen) Hohenzollernsrasse 1/3, Essen, Germany Ediors: Prof. Dr. Thomas K. Bauer RUB, Deparmen of Economics Empirical Economics Phone: +49 (0) 234/ , Prof. Dr. Wolfgang Leininger Technische Universiä Dormund, Deparmen of Economic and Social Sciences Economics Microeconomics Phone: +49 (0) 231 / , Prof. Dr. Volker Clausen Universiy of Duisburg-Essen, Deparmen of Economics Inernaional Economics Phone: +49 (0) 201/ , Prof. Dr. Chrisoph M. Schmid RWI Essen Phone: +49 (0) 201/ , Ediorial Office: Joachim Schmid RWI Essen, Phone: +49 (0) 201/ , Ruhr Economic Papers #85 Responsible Edior: Volker Clausen All righs reserved. Bochum, Dormund, Duisburg, Essen, Germany, 2009 ISSN (online) ISBN The working papers published in he Series consiue work in progress circulaed o simulae discussion and criical commens. Views expressed represen exclusively he auhors own opinions and do no necessarily reflec hose of he ediors.

3 Ruhr Economic Papers #85 Ansgar Belke and Yuhua Cui UNIVERSITÄT D U I S B U R G E S S E N

4 Bibliografische Informaion der Deuschen Naionalbibliohek Die Deusche Naionalbibliohek verzeichne diese Publikaion in der Deuschen Naionalbibliografie; deailliere bibliografische Daen sind im Inerne über hp://dnb.d-nb.de abrufbar. ISSN (online) ISBN

5 Ansgar Belke and Yuhua Cui* US Euro Area Moneary Policy Inerdependence New Evidence from Taylor Rule Based VECMs Absrac This paper analyses he moneary policy inerdependence beween he European Cenral Bank () and he eral Reserve () for he period Two models are specified: a parial Vecor Error Correcion Model (VECM) and a general VECM. In he parial VECM, we look for a long-run inerdependen relaionship beween he ineres raes of he wo currency areas and specify he Taylor Rule erms as exogenous variables. In he general VECM, we regard all variables as endogenous, and look for long-run equilibrium relaionships among hem, which may reveal moneary policy inerdependence beween he wo cenral banks. Weak exogeneiy is checked in boh models in order o esablish a possible leader-follower relaionship. The empirical resuls of boh models indicae inerdependence beween he and he, bu only he general VECM esifies a leader-follower paern beween he wo cenral banks. According o his paern, he does follow he. JEL Classificaion: E43, E58 Keywords: Moneary policy, inerdependence, European Cenral Bank, eral Reserve, Taylor rule, VECM February 2009 * Ansgar Belke, Universiy of Duisburg-Essen and IZA Bonn; Yuhua Cui, Universiy of Hohenheim. We are graeful for valuable commens from he paricipans in he All China Economics (ACE) Inernaional Conference 2007 in Hong Kong, especially Hugh Mecalf, Niklas Porafke, Louis Yeung, and Lili Yan. We are also graeful for he valuable commens from Daniel L. Thornon a he Eighh Annual Missouri Economics Conference 2008, a he eral Reserve Bank of S. Louis, and Hamdi Raissi, Chrisoph Hanck and Ahmed El Ghini a he 2nd Inernaional Workshop on Compuaional and Financial Economerics 2008, Neuchâel, Swizerland. All correspondence o Ansgar Belke, Universiy of Duisburg-Essen, Campus Essen, Deparmen of Economics, D Essen, Germany, ansgar.belke@uni-due.de.

6 1. INTRODUCTION Since January 2008, he U.S. eral Reserve () has enaced a series of ineres rae cus on is arge rae as a reacion o he curren subprime crisis. The federal funds rae has been decreased from 4.25 per cen a he beginning of 2008 o a range of 0 o 0.25 per cen a he end of las year. In he firs half of 2008, he cu in he U.S. ineres rae has fuelled speculaions ha he European Cenral Bank () would be forced o sofen is posiion as a moneary policy hawk as well. However, he day afer he U.S. ineres rae cu in January 2008, he made clear ha i would no bow easily o pressure for euro area ineres rae cus 1, which highlighed he conras beween he and he. Towards he big pressure of ineres rae cuing, he even raised he ineres rae in July by 25 basis poins. The noable increase of is main ineres rae in July apparenly conradiced a popular argumen ha he follows he in is moneary policies bu was probably iner alia due o much higher srucural rigidiies in he euro area (Belke and Gros, 2002). However, in he las quarer of 2008, he siuaion urned ino a compleely opposie side: wihin hree monhs, he sharply cu is ineres rae by a oal 175 basis poins. The ineres rae developmens across he Alanic in 2008 bring an old debae back ino aenion: does he follow he in is moneary policy? Is here any comovemen paern beween he wo cenral banks? 2 Since he inroducion of he euro, here has been always some discussion on a 1 See news on January 23, 2008, Financial Times (FT.com), resiss pressure o cu ineres raes. 2 For a recen survey on relevan sudies on he issue of US-euro area moneary policy inerdependence see, for insance, Eijffinger (2008). 4

7 possible leader-follower relaionship beween he and he, paricularly a he early sage of he inroducion of he euro. The reacion of he o he moneary and economic shocks was described as slow and some researchers and economiss poined ou ha here migh be a ime lag effec, or more precisely a leader-follower relaionship beween he moneary policies of he and he (see, e.g., Belke and Gros, 2005; Ullrich, 2006). Comparing wih he, he is widely regarded more quick-reacing o he marke and economic shocks or changes. Due o he special insiuional characers, he change of he policy raes made by he was apparenly slower han he one by he corresponding o he same economic or marke urmoil. The cause of he original hypohesis of leader-follower relaionship comes from a lag-effec on he cenral bank policy raes beween he and he FED, which is illusraed in he figure 1 below. FIGURE 1 Moneary Policy Raes of he and he. Main Refin FED Funds Targe /1/1999 5/1/1999 9/1/1999 1/1/2000 5/1/2000 9/1/2000 1/1/2001 5/1/2001 9/1/2001 1/1/2002 5/1/2002 9/1/2002 1/1/2003 5/1/2003 9/1/2003 1/1/2004 5/1/2004 9/1/2004 1/1/2005 5/1/2005 9/1/2005 1/1/2006 5/1/2006 9/1/2006 1/1/2007 5/1/2007 9/1/2007 1/1/2008 5/1/2008 9/1/2008 Noe: 1 The daa were obained from he homepages of he and he respecively. From figure 1 we can see ha a he early sage of euro, in he period of 1999 o mid- 2002, here was an obvious rough paern beween he and he, on which he 5

8 leader-follower argumen based. However, his paern did no coninue afer he end of 2002, insead, he reacion of he became more simulaneous wih he during he period 2003 o mid Afer mid-2004, he reacion of he o he economic shocks backslid and a leader-follower paern appeared again ill he end of Due o he complexiy of he paerns over he differen periods, i appears o us more appropriae o furher invesigae an inerdependen relaionship beween he and he, raher han o esify only for a leader-follower paern over he corresponding ime span. An invesigaion of moneary policy inerdependence beween he and he has wo folds: on one hand, here could be conemporaneous inerdependence, which presens a long-run equilibrium relaion, or co-movemen, beween he wo ineres raes (Scoi 2006, p.18); on he oher hand, according o he developmens of wo ineres raes in he pas years, a possible leader-follower paern could exis beween he wo cenral banks, and more concreely, he may follow he in making is moneary policy. Differen mehodologies have been used for esing he leader-follower relaionship beween he and he, as well as he inerdependence beween hem. The Granger-causaliy es was used by Garcia-Cervero (2002) and Belke and Gros (2002, 2005) for esifying a leader-follower relaionship. Ullrich (2005) esimaed linear equaions wih OLS mehod o es for he inerdependence, by incorporaing he ineres rae of one cenral bank ino he oher bank s reacion funcion; Breuss (2002) also esimaed a linear equaion bu wih he Generalised Mehod of Momens (GMM) o invesigae wheher he follows he policy seps of he. In our analysis, we employ a parial Vecor Error Correcion Model (VECM) and a general VECM o es for inerdependence and a possible leader-follower relaionship 6

9 beween he wo cenral banks. Based on he special feaures of he parial VECM and he general VEC model, we are able o idenify inerdependence in he long-run coinegraing equaions and evidence of shor-run ineres rae smoohing dynamics in he error correcion framework (Judd and Rudebusch, 1998). Boh he parial VECM and he general VECM pay good aenion o he non-saionariy of he ime series variables, which has been oo ofen ignored in earlier Taylor Rule esimaions (Gerlach-Krisen, 2003). Hence, ineres rae rules esimaed using he coinegraion approach are, in conras o he radiional Taylor rule sable in sample and end o forecas beer ou of sample. In addiion, in he parial and general VECM frameworks, we are able o es for a leader-follower paern by checking weak exogeneiy of he ineres raes in he sysem. In order o explain he inerdependence of moneary policies across he Alanic, we need o know how he moneary policy decisions are made in he euro area and as well as in he U.S. The Taylor reacion funcion (Taylor, 1993) has been jusified by many researchers o be an appropriae framework for describing he moneary policies of he and he 3, according o which ineres raes are deermined by ime-varying variables like inflaion rae, oupu gap and lagged values of he ineres raes. Therefore, in our esimaions, he Taylor Rule represens he basic framework for boh of he economeric models. The remainder of his paper is srucured as follows. In secion 2, we give a brief explanaion of he Taylor Rule which provides a heoreical framework for he empirical esimaions in he following secions. In secion 3, we presen he economeric mehods and he empirical models. The daa and variables are described in secion 4. The 3 See, e.g., Gerdesmeier and Roffia (2004) for he, and Judd and Rudebusch (1998) for he. 7

10 empirical resuls are summarized in secion 5 wih corresponding economic explanaions of he findings. The las secion concludes. 2. THEORY OF THE TAYLOR RULE Since i was published in 1993, he Taylor rule (Taylor, 1993) has been widely acceped o describe he moneary policies in differen counries, paricularly for he and he. A general ime-varian Taylor Rule reacion funcion wihou coefficien specificaion could be expressed as: i T = π + a o + a π π 0 1( *) * = β + β π + β o ε + r + ε (1) where i T is he Taylor Rule rae, r * is he equilibrium real policy rae, π is he inflaion rae over he previous four quarers, π * is he arge inflaion rae, o is he percen deviaion of real GDP from a arge (oupu gap), and ε is a error erm. a 0 and a 1 are coefficiens of original equaion, where boh of a 0 and a 1 are greaer han zero. For he derived equaion, β 0 = r * a1π *, β 1 = 1+ a1, and β 2 = a0. All parameers are expeced o be greaer han zero. The empirical esimaion of he Taylor Rule ofen relaes he nominal ineres rae o is own lags. This approach, as Judd and Rudebusch (1998, p.2) poined ou, allows he possibiliy of a gradual adjusmen of he nominal ineres rae o achieve he rae recommended by he Taylor Rule. Similarly, a Taylor reacion funcion proposed by Clarida e al. (1998, 2000) was also modified by incorporaing ineres rae smoohing for he euro area. A ypical dynamic Taylor reacion funcion wih ineres rae smoohing can be 8

11 derived from he equaion i T = ( 1 ρ ) i + ρi 1 + ε, where i is he nominal ineres rae, ρ is he smoohing parameer (see, e.g., Judd and Rudebusch, 2005; Ulrich 2005; Belke and Pollei, 2007). The ineres rae is hen dependen on he inflaion rae and he oupu gap, and plus is own lags: T i = (1 ρ) i + ρi 1 = (1 ρ)( β + β π + β o ) + ρi = A + A π + A o + A i ε ε 1 + ε, (2) where A 0 is he new consan and A 1, A 2, and A 3 are he new coefficiens of π, o and i 1 respecively, and A = 1 ρ) β = (1 ρ)( r * a π*) 0, 0 ( 0 1 > A = 1 ρ ) β = (1 ρ)(1 + a ) 0, 1 ( 1 1 > A2 = ( 1 ρ ) β2 = (1 ρ) a0 > A 3 = ρ > 0. 0, and Mos of he empirical ess on he Taylor Rule have corroboraed he posiive signs of A 0, A 1, A 2, and A 3. 4 Hence, we expec ha an increase of he inflaion rae or he oupu gap will resul in rising ineres rae, and he higher he lagged ineres rae is, he higher is he curren ineres rae. In addiion o his dynamic model, some oher macroeconomic variables have been 4 The resuls of posiive signs of hese parameers are mainained in he Taylor Rule esimaions for boh of he and he. For he, see he work of Judd and Rudebusch (1998); for he, see he works of Elefheriou, e al. (2006), Gerlach-Krisen (2003), and Gerdesmeier and Roffia (2004). For a survey of specificaions of Taylor reacion funcions as simple rules for moneary policy see, for insance, Clarida, Galí and Gerler (1999), pp. 1695ff. 9

12 considered o be included ino he Taylor reacion funcions as well. Elefheriou e al. (2006), for insance, summarize differen Taylor Rule specificaions for he moneary policy in he exising lieraure. According o hem, he inflaion rae, he oupu gap, and he lagged ineres rae are he mos preferred variables in he Taylor Rule esimaions. We will sricly follow his preferred specificaion in our analysis. 3. EMPIRICAL MODELS Many sudies and empirical esimaions on he Taylor reacion funcions have ignored he non-saionariy feaure of he ime series variables (Gerlach-Krisen, 2003). In our analysis we ake ino accoun he possible non-saionariy in he variables, and carry ou uni roos for all he ime series variables implemened. The precondiion for he coinegraion es, which is an essenial par of he VECM, is ha all he variables should be non-saionary a heir level, bu become saionary a he same order, for example, in our esimaions, hey are expeced o be inegraed of order one, or I(1). When his precondiion is saisfied, we are able o carry ou coinegraion ess among he level variables, and hen esimae he degree of inerdependence and check for a leader-follower relaionship in he parial and he general VECM frameworks. a. Coinegraion Tes If a linear combinaion of he non-saionary variables, which for example are all I(1), is saionary, hen he variables are said o be coinegraed (Granger 1986, p. 215). In his case, he linear combinaion of he variables presens a long-run equilibrium relaionship among he variables (Granger 1986, p ). In our empirical analysis, he coinegraion es is a precondiion for an applicaion of he empirical framework of he 10

13 VECMs. As we incorporae he Taylor Rule variables ino he parial and he general VECMs, he coinegraion ess are carried ou among hese variables. When he number of variables is larger han wo, here migh be more han one coinegraing equaion (Engle and Granger 1987, p. 254). Hence, i is necessary o es for he coinegraing rank, i.e. he number of coinegraing relaions among he variables. In he esimaions, we firs check for he coinegraing rank and hen use he resuls of he coinegraing rank as a pre-deermined condiion for furher esimaions in he parial and he general VECM framework. b. Parial VECM As shown in Figure 1, here is an obvious co-movemen beween he wo ineres raes, which could be inerpreed as a possible long-run equilibrium relaion. This longrun relaionship can be esed by he coinegraion es and expressed in a coinegraing equaion. If he coinegraing equaion exiss, we can use a parial VECM o capure he long-run relaion beween he ineres raes in he coinegraing quesion, ogeher wih a shor-run dynamic reacion funcion based on he Taylor Rule. In our parial VECM framework, we deal wih wo endogenous variables, i.e. he U.S. and he euro area ineres rae, and four exogenous variables, i.e. he inflaion raes and he oupu gaps in boh currency areas. A reduced form of he parial VECM can be wrien as below 5 : i = ') i 1 + Γ1 i Γp 1 i p+ 1 + B0 ( αβ x + ε (3) 5 For a more deailed explanaion of he parial VECM see Johansen (1992). For a pracical applicaion see, for insance, Woo (1999). 11

14 where i is he vecor of endogenous variables, i = ( i, i )' ; x is he vecor of exogenous variables, x = ( π, o, π, o )'. β is he coinegraion vecor, which specifies he long-run equilibrium relaion. α is he error correcion vecor, which represens he shor-run adjusmen when he economy deviaes from he equilibrium level, and α β = Π. j (j = 1,, p - 1) is a marix of he srucural coefficiens for dynamic ineresing smoohing process. B j is he coefficien marix on he exogenous variables. In case of significance of he coefficiens in B j we have o rejec he hypohesis ha he Taylor Rule does no hold. is a 2-dimensional error vecor. Under he parial VECM, he error erms in he vecor are whie noise errors. For a beer undersanding of he funcions of he coefficien, we display each individual equaion as below: i i = a + a ( i 10 = a + a ( i γ i ) + ϕ i ϕ i + η i η i + b π + b o + b π + b o i i i i (4) 1 + γ1i 1 ) + ϕ21 i ϕ2 i i i + η21 i η2i i i + b21π + b22o + b23π + b24o + ε2 + ε For esing inerdependence, we need o check he significance of he coefficiens in he vecor β. Since one of he coefficiens in he vecor β has been pre-defined as 1 (see he erm ( i 1 + γ 1i 1 ) in equaion (4)), we only need o consider he coefficien γ 1. If γ 1 is significan, hen he null hypohesis of no inerdependence can be rejeced. For esablishing a leader-follower paern, we need o check for weak exogeneiy by looking a he significance of he coefficiens in he vecor α ( α = ( a 11, a )) in equaion ' 21 (4). In he case of he parial VECM, if he U.S. ineres rae is weakly exogenous, hen here is one way causaion from he U.S. ineres rae o he euro ineres rae. I indicaes ha he follows he. According o Johansen (1992), he hypohesis of weak 12

15 exogeneiy of an endogenous variable for he parameers of ineres α and β is equivalen o imposing a zero on he corresponding coefficiens in he vecor α. In oher words, he hypohesis of weak exogeneiy canno be rejeced, if he variables can be characerized as a pure random walk independen of he coinegraion/error correcion erm. In he parial VECM, he hypohesis of weak exogeneiy of he U.S. ineres rae i is H 0 : a 21 =0. If H 0 canno be rejeced, i means he U.S. ineres rae is weakly exogenous, and he U.S. ineres rae leads he euro ineres rae, or in oher words, he follows he. If in addiion o a 21 =0, he coefficiens 21 2i are all equal o zero, he U.S. ineres rae does no depend upon he lagged values of he euro ineres rae and, hus, he U.S. ineres rae, i, can be considered o be srongly exogenous (Paerson, 2001, p. 674). c. General VECM As Maddala (2001, p. 375) poined ou, he classificaion of variables ino endogenous and exogenous is someimes arbirary. Due o he anicipaed Taylor Rule long-run equilibrium relaionship, he Taylor Rule variables, which appear in he parial VECM are more reasonable o be reconsidered as endogenous variables, raher han exogenous variables. Hence, we move on o he general VECM and assume all he variables are endogenous, i.e. hey are deermined wihin he sysem, raher han predeermined ouside of he sysem. Based on he Taylor Rule, we include six endogenous i, i variables in he esimaions: he ineres raes in wo currency areas ( inflaion raes and he oupu gaps in wo currency areas ( π, π, o, o ), he ). A 13

16 reduced form of he general VECM can be wrien as 6 : y = α β y + Γ + + Γ y 1... p 1 y ( p 1) ε (5) where, y is he vecor of endogenous variables, y = ( i, π, o, i, π, o ). ε is he error vecor. β is he coinegraion marix, α is he error correcion marix, and α β = Π. j (j = 1,, p - 1) is a (6 X 6) marix for coefficiens on lagged endogenous variables. We re-wrie he model in a marix-vecor form for a beer illusraion of he ess: i i π π o o A A A = A A A A21B A 22 B A 23 B A24B A 25 B A26 B ' 11 B i γ 11,1.. γ 1 B22 i γ 12,1.. γ 1 B 23 π γ 13,1.. γ 1 + B24 π 1 γ 14,1.. γ B 25 o γ 1 15,1.. γ B26 o 1 γ16,1.. γ 61,1 62,1 63,1 64,1 65,1 66,1 i γ 1 11, i γ 1 12, π γ 1 13, π γ 1 14, o γ 1 15, o 1 γ 16, p 1 p 1 p 1 p 1 p 1 p 1.. γ.. γ.. γ.. γ.. γ.. γ 61, p 1 62, p 1 63, p 1 64, p 1 65, p 1 66, p 1 i ( p 1) ε1 i ( p 1) ε 2 π ( p 1) ε3 + π ( p 1) ε 4 o ( p 1) ε 5 o ( p 1) ε 6 (6) Some pre-assumpions are made according o he heory of he Taylor Rule. Based on he Taylor Rule, we can assume ha, in he long-run, he ineres rae in each counry is deermined by he domesic inflaion rae and he oupu gap, plus he ineres rae from he oher counry. This assumpion implies ha some of he coefficiens (in our case B 15, B 16, B 23, B 24 ) in he marix β should be pre-defined as zero. In marix form, hese consrains can be expressed as: 1 B21 B12 1 B 13 0 β = (7) B B 25 0 B26 6 For deails see Engle and Granger (1987) and Johansen (1992). 14

17 A check for weak and srong exogeneiy of he endogenous variables is also carried ou for he general VECM, wih a similar hypohesis as in he parial VECM. Insead of a single coefficien in he error correcion vecor α in he parial VECM, he hypohesis of weak exogeneiy of he U.S. ineres rae in he general VECM, for insance, is A 12 =0 and A 22 =0. If, in addiion, he coefficiens of he lagged values of oher variables are zero, hen he U.S. ineres rae is srongly exogenous o he sysem. Analogous checks are carried ou also on all he oher endogenous variables. 4. DATA AND VARIABLES In view of he moneary policy decision imeframes on boh sides of he Alanic, we use monhly daa in our esimaions (see also Breuss, 2002; Scoi, 2006; Ullrich, 2005; Gerdesmeier and Roffia, 2004). The daily realizaions are no preferred in our analysis, alhough hey were seleced by some oher researchers a he early sage of research work for he moneary policy. The daily realizaions of he daa may have he maximum informaion, bu mos of he news on a daily basis comes presumably from financial markes (Belke and Gros, 2005). The sample period for he empirical esimaions is from 1999M1 o 2006M12. All he raw daa are seasonally adjused wih Census X-12- ARIMA mehod 7. Since he seven-year-long ime span in he esimaions can presen a complee ineres rae cycle, his sample period seems o be sufficien o gain reliable esimaes. We decided o leave ou he years 2007 and 2008 from our sample. We did so for wo 7 The Census X-12-ARIMA mehod is generally adoped by he and he (, 2000). 15

18 reasons. Firsly, he sandard heory of he Taylor rule implicily assumes ha he equilibrium real rae is sable over ime, whereas in fac i will move abou. Secondly, a cenral bank will someimes need o change is policy rae simply in order o leave moneary condiions unchanged. Expressed differenly, cenral banks can only fix he shor nominal rae. However, wha a paricular level of his rae implies for moneary condiions will depend on shor-run inflaion expecaions and on he equilibrium real rae needed o balance ou he economy. Mos likely, he laer have changed significanly in he face of he cos and credi shocks experienced during he urbulences of he financial crisis of 2007/08. This has led iner alia o an exraordinarily high degree of model uncerainy (Tucker, 2008). We do no argue ha i is ime now o limi oneself o qualiaive analysis. However, we do hink i is oo early o be able o model srucural breaks adequaely in his conex. In his paper, we follow Gerdesmeier and Roffia (2004) and use he EONIA rae as a proxy for he moneary policy rae, and follow Judd and Rudebusch (1998) o use he Funds rae for he U.S. moneary policy rae. Boh he EONIA rae and he Funds rae are marke raes which are srongly influenced by he moneary policies. The euro area inflaion rae is measured by he year-o-year percenage change in he harmonized index of consumer prices (HICP) for he euro area. The U.S. inflaion is calculaed on he basis of consumer price index (CPI): Euro HICP HICP 12 US CPI CPI 12 π = 100*( ), and π = 100*( ). HICP CPI 12 The oupu gasp are derived from he indusrial producions for boh currency areas as follows: 12 16

19 IP IPrend o = 100*( ), IPrend where, IPrend presens he poenial long-erm rend of oupu which is obained by using a Hodrick-Presco Filer. While ineres raes, inflaion and he oupu gap are likely o be saionary in large samples, he resuls in he lieraure sugges ha, in order o draw correc saisical inference, i is desirable o rea hem as non-saionary in he relaively shor sample sudied here a priori (Gerlach-Krisen, 2003). However, in order o feel legiimized o implemen he coinegraion es, we explicily check all he variables for uni roos. For his purpose, we conduced a baery of uni roo ess. 8 The resuls of he ADF ess including a consan bu no drif (because he graphs of all series do no show a clear rend) are summarized as an example in Table 1 below. TABLE 1 Uni Roo Tes Resuls Tes Descripion ADF Tess, SIC Crierion (p-values) (H0: Series has a uni roo.) Level Firs Difference EONIA Euro Area Inflaion Rae * 0 Euro Area Oupu Gap Funds Rae U.S. Inflaion Rae U.S. Oupu Gap Noes: 1 Sample (adjused): Jan Dec Based on ADF es equaions wih a consan bu no rend. 8 We carried ou ADF ess, KPSS ess and Phillips Perron ess. The resuls are available on reques. 17

20 A closer inspecion of Table 1 reveals ha, excep he euro area inflaion rae which is rejeced o have a uni roo nearly a he 1% significance level, all variables appear o conain a uni roo a he usual significance levels. Wha is more, hey appear o be saionary afer firs differencing hroughou. In case of he ambiguous resuls for he euro area inflaion rae we would like o argue ha i has been subjec o much debae (and is sill so) wheher in limied samples he price level is I(1) or I(2) and, hence, he inflaion rae is I(0) or I(1). Moreover, saionariy is a sample propery and differencing in case of saionariy of a variable is beer han no differencing when i is non-saionary. In oher words, from an empirical poin of view i is ofen advanageous o approximae a nearuni roo wih a uni roo, even hough i is significanly differen from one (Juselius, 2006, pp. 31ff., Juselius and MacDonald, 2004). All in all, hus, i does make sense o consider also he euro area inflaion rae as nonsaionary a he level. In oher words, our uni roo es resuls have saisfied he precondiion for a furher coinegraion es which is essenial for he parial and general VECM esimaions. 18

21 5. RESULTS a. Coinegraion Tes Resuls The resuls of he coinegraing rank ess are summarized in Table 2. TABLE 2 Coinegraing Rank (CR) Tes Resuls wih Differen Lag Selecions. Lag Selecion on i (PVECM) or y (GVECM) CR of Parial VECM CR of General VECM lag = lag = lag = lag = lag = lag = Lag = lag = lag = lag = lag = lag = lag = 12 2 no applicable Noes: 1 Sample (adjused): Jan Dec The es resuls are subjec o he seleced lag lengh. Alhough we display he resuls for up o lag=12, based on he heory of he ineres rae smoohing, we would propose a lag lengh no higher han As poined ou by Judd and Rudebusch (1998, p.7), he error-correcion framework is useful for he 19

22 The rank es resuls corresponding o lag=2 (i.e. rank is 1 for he parial VECM and 2 for he general VECM) can be well explained by economeric and economic heory. For a parial VECM wih wo endogenous variables (i.e. k=2), he maximum coinegraing rank r should be 1, because he coinegraing rank r among he k endogenous variables should be 0 r k-1 (Engle and Granger 1987, p. 254). For he general VECM esimaion, he es resuls are comparable wih he analysis in he previous secion, where we expeced only wo long-run coinegraing relaions among he variables. Therefore, we selec a lag lengh of 2 as he assumpion for boh he parial and he general VECMs, and he coinegraing ranks for he parial VECM is 1, and 2 for he general VECM. b. Esimaion Resuls of he parial VECM Based on he coinegraion ess, we seleced a lag order of wo for our esimaions. In order o carry ou he parial VECM esimaions, we need o make an assumpion regarding he deerminisic rend underlying he daa. Five possible deerminisic rends are conained in Johansen procedure (Johansen 1995, pp ). Based on he economeric echniques on selecing he deerminisic rend (Paerson 2001, pp ), we choose he assumpion of having no deerminisic rend on level daa bu inercep in coinegraing equaions. In Table 3, we presen our esimaion resuls, dividing our presenaion of he laer in hree pars. The firs par delivers he esimaed coefficiens for he long-run coinegraing consideraion of he ineres rae smoohing process. The lag considered in he Taylor reacion funcion for ineres smoohing is widely acceped o be one, as shown in he equaion (2). Therefore, in our esimaions, we will no consider long lags. Here we assume he highes possible lag lengh as 3. This assumpion is consisen wih our esimaion resuls of boh of he parial and he general VECMs. 20

23 equaion; he second par delivers he esimaed coefficiens for he shor-run error correcion process, wih he firs column presening he reacion funcion of he euro ineres rae (in differencing erm), and he second column presening he reacion funcion of he U.S. ineres rae (also in differencing erm); he las par liss ou he regression saisics for each equaion. Le us now urn o he inerpreaion of he resuls. The srong significance of he coefficien in he vecor β, i.e. he coefficien of, indicaes conemporaneous inerdependence beween he ineres raes (see he firs par in Table 3). Addiionally, hese figures also indicae ha he adjusmen of he owards economic shocks has smaller seps han ha of he. These resuls underline he view ha comparing wih he, he is more conservaive and less acive in making is moneary policy decisions. The wo esimaed coefficiens in he vecor α (see he firs row of he second par in Table 3) boh appear significan and heir signs are negaive. In he shor run, boh ineres raes adjus o he errors, which consiss of he deviaions from he equilibrium level. The adjusmen magniudes of he wo ineres raes are similar: abou 12% for he and 15% for he. The high significances of he error correcion parameers also indicae a clear rejecion of he hypoheses of weak exogeneiy of boh ineres raes. Hence, i is no clear a his sage of analysis wheher here exiss a leader-follower relaionship beween he wo cenral banks. i 1 21

24 TABLE 3 Esimaion resuls of he parial VECM Coinegraing Eq: CoinEq1 ( ) i 1 1 i *** C ** Error Correcion: i i CoinEq *** *** i ** i i *** 1 i π *** *** o ** π *** *** o *** *** R-squared Adj. R-squared Sum sq. resids S.E. equaion F-saisic Log likelihood Akaike AIC Schwarz SC Mean dependen S.D. dependen Noe: 1 Sample (adjused): Jan Dec * significan a 10 per cen; ** significan a 5 per cen; *** significan a 1 per cen. Seen on he whole, he remaining esimaion resuls reveal a paern of he reacion funcion which is quie close o he Taylor Rule expecaion (see he second par in Table 3). The coefficiens of he ineres raes lagged one monh are significan in each equaion respecively, which indicaes ineres rae smoohing in boh reacion funcions. The high degree of significance of he coefficiens of he inflaion rae and he oupu gap show ha boh ineres raes can be explained well by he Taylor Rule. However, as shown in 22

25 he firs column, he reacion funcion of he follows he Taylor Rule more closely, wih posiive signs on domesic inflaion rae and oupu gap. Alhough i is no clear for a leader-follower relaionship, he s moneary policy obviously is affeced by he changes of he U.S. inflaion rae and oupu gap. Similarly, he economic changes from he euro area also have an impac on he s moneary policy decision, bu he s consideraion concenraes more on he inflaion rae of he euro area (see he second column in Table 3). A series of diagnosic ess are carried ou for he parial VECM. 10 The es resuls reveal ha he esimaed parial VECM does no fi very well wih he observaions. A high goodness of fi is indicaed by he empirical realizaions of he R-squared and adjused R-squared values, and also by he AR roos graph and Granger causaliy Wald es saisics. However, he LM ess show he possible residual serial correlaions. Addiionally, he presence of heeroskedasiciy also indicaes ha he variance of he coefficiens ends o be underesimaed. We ried differen alernaive specificaions of he parial VECM, bu canno ge rid of he problems. Hence, we proceed by rying o ge beer resuls by moving all he exogenous variables ino he coinegraing relaions and keeping all he variables as endogenous in he general VECM esimaion. c. Esimaion Resuls of he general VECM We carried ou he esimaion ess for he general VECM wih he same rend assumpions as for he parial VECM. The resuls under he consrains of equaion (6) in secion 3 are summarized in Table The resuls of he diagnosic ess are available on reques. 23

26 Coinegraing Equaions Coin. Eq1 ( 1 ) Coin. Eq2 ( 2 ) i *** i π *** 0 o *** 0 π *** o *** C *** *** TABLE 4 Esimaion Resuls of VEC model Variables Equaions i i π o π o Coin. Eq1 ( 1) *** *** * CoinEq2 ( 2) *** *** i *** ** ** i ** i *** * i * π ** π o *** *** o *** * π *** π *** ** *** *** o o R-squared Adj. R-squared Sum sq. resids S.E. equaion F-saisic Log likelihood Akaike AIC Schwarz SC Mean dependen S.D. dependen Noe: 1 Sample (adjused): Jan Dec * significan a 10 per cen; ** significan a 5 per cen; *** significan a 1 per cen. 24

27 As already in Table 3, Table 4 presens he esimaion resuls in hree pars. The firs par delivers he resuls of he long-run equilibrium relaions among he endogenous variables. The second par delivers he resuls for he shor-run error correcion process. In he second par, each column corresponds o an equaion in he general VECM. The firs wo columns are he reacion funcions of he euro and he U.S. ineres raes in firs differences, he remaining columns correspond o he equaions of inflaion raes and oupu gaps in boh currency areas. Below he coefficiens summary, he hird par of he able liss he regression saisics for each equaion. The significance of mos coefficiens conained in vecor β indicaes long-run equilibrium relaionships among he variables. However, only in he second coinegraing equaion he coefficien of he ineres rae (he coefficien of i 1 ) is significan. Therefore, here exiss only one possible inerdependen relaionship beween he wo ineres raes and he Taylor rule erms. Conradicory o wha we have expeced from our long-run Taylor rule based assumpions, he long-run equilibrium relaions beween he variables revealed by he esimaion resuls do no fi he Taylor Rule exacly. Alhough he magniude of he esimaed coefficien parameers fall wihin he heoreical range, bu he signs on he coefficiens of he Taylor Rule erms - inflaion and he oupu gap, are mosly conradicory o he heory. 11 Neverheless, he inerdependen relaionship beween he ineres raes is clearly corroboraed by he resuls. In he coinegraing 11 As we see in secion 2, he signs for he Taylor Rule erms should be opposie o he ineres rae. In he case of he VEC model, hey should be negaive, because he ineres raes and he Taylor Rule erms appear on he same side of he equaion in he coinegraing equaion. 25

28 equaion 2, he esimaed parameer for coefficien B 21, is -3.43, so if here is 1% increase on he U.S. ineres rae, hen conemporaneously here will be abou (1/3.43)*100%=29% increase on he ineres rae. This resul is very close o he resul of he parial VECM (35%). The possible explanaion for a smaller magniude is he impac of he inflaion rae and he oupu gap in he coinegraing equaion. The esimaion resuls for he shor-run coefficiens deliver clear evidence of weak and srong exogeneiy on some endogenous variables. The U.S. ineres rae and he euro area inflaion rae appear o be weakly exogenous o he model, while he oupu gaps of boh areas appear o be srongly exogenous. Wha concerns us mos is he apparen weak exogeneiy of he U.S. ineres rae. As he coefficiens A 12 and A 22 are boh saisically insignifican, he hypohesis of weak exogeneiy for he U.S. ineres rae i canno be rejeced. Hence, he U.S. ineres rae is raher a variable pre-deermined ouside of he model, and he decision of he ineres rae is dependen on he U.S. ineres rae. In his sense, we could say he follows he in making moneary policy decisions. As in he parial VECM esimaions, we carry ou a series of diagnosic ess on he esimaed model. 12 The resuls show a good fi of he model o he observaions. The R- squared and Adjused R-squared values are also beer han hose we obained from he parial VECM esimaions. The more imporan aspec is ha he residual ess show no serial correlaion or heeroskedasiciy in he error erms. In his sense, he general VECM explains he daa beer han he parial VECM. 12 The resuls of he diagnosic ess are available on reques. 26

29 6. CONCLUSIONS In his paper, we analyze he moneary policy inerdependence beween he and he for he ime period ranging from 1999 o Two alernaive models are employed in he esimaions, he parial VECM and he general VECM. Boh models are based on he dynamic Taylor Rule reacion funcion. Unlike he resuls obained by some oher researchers 13, we find ou clear moneary policy inerdependence beween he and he. However, a leader-follower relaionship is only shown in he resuls of he general VECM. The empirical resuls of he parial VECM indicae a srongly significan long-run equilibrium relaion (inerdependence) beween he wo cenral banks ineres raes. Alhough he es for weak exogeneiy failed o reveal a clear leader-follower relaionship, he s moneary policy obviously is affeced by he economic shocks impacing on he U.S. inflaion rae and oupu gap. This resul could explain why he was facing a big pressure of cuing ineres rae due o he subprime crisis in he U.S. in he firs half of 2008, i.e. ou of he esimaed sample. On he oher hand, he economic shocks from he euro area also have an impac on he s moneary policy decision, bu he apparenly aaches greaer imporance o he inflaion pressure in he euro area. One weak aspec of our parial VECM is ha he diagnosic ess reveal possible residual serial correlaion and heeroskedasiciy of he error erms which we are no able o ge 13 The resuls in he lieraure on esing inerdependence and a leader-follower paern beween he and he vary among he researchers. For example, Belke and Gros (2005) found neiher a clear follower paern nor inerdependence; Ullrich (2005) found a follower paern bu no evidence o inerdependence; Scoi (2006) found evidence of synchronizaion bu no follower behavior; Ehrmann and Frazscher (2005) found ha he euro area and he U.S. have become generally more inerdependen afer he adven of EMU. 27

30 rid of and which migh indicae remaining misspecificaions, or incompleeness of he model. Hence, we move on o he esimaion of a general VECM model, and leave he furher exploraion of he parial VECM open o fuure research. The esimaion resuls of he general VECM also indicae long-run inerdependence beween he wo ineres raes. The numerical equilibrium relaions beween he and he esimaed in boh of he parial VECM and he general VECM are very close. In he parial VECM, a 1% change in he U.S. ineres rae will be accompanied by a 0.35% change in he euro area ineres rae, while in he general VECM, his elasiciy urns ou o be 0.29%. Comparing wih he, he appears o be more conservaive and less acive in adjusing is moneary policy decisions owards economic shocks. The weak exogeneiy es in he general VECM reveals a clear leader-follower relaion among he and he, according o which he follows he in is moneary policy. Our resul is consisen wih he lieraure. Based on a vecor error correcion model imposing long-run coinegraion beween he relevan ineres raes, for insance, Chinn and Frankel (2005) conclude ha, alhough financial inegraion has increased a lo, he direcion of he effecs runs predominanly from he USA o he euro area. The inroducion of EMU has no alleviaed his asymmery. Mos recenly, he sharp ineres rae cus by he in he las quarer of 2008 corroboraed he argumen ha he, alhough no willing o admi i, does indeed follow he. Moreover, Eijffinger (2008) imposes a long-run coinegraing relaionship upon boh he euro area and he US shorerm and long-erm ineres raes, using a vecor error correcion specificaion. Also in his sudy, for boh he shor-erm and he long-erm ineres rae, he coinegraing relaionship runs from he U.S. o he euro area. 28

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