Uncertainty and the Taylor rule in a simple model of the euro-area economy *

Transcription

1 This draf: 2 February, 998 Uncerainy and he Taylor rule in a simple model of he euro-area economy * by Ger Peersman a and Frank Smes b a Universiy of Ghen, Belgium b European Cenral Bank, Frankfur and Cenre for Economic Policy Research, London Absrac This paper explores he Taylor rule defined as an insrumen rule linking he cenral bank s policy rae o he curren inflaion rae and he oupu gap as a benchmark for analysing moneary policy in he euro area. Firs, i presens evidence ha ineres raes in Germany and he euro area can be described by a Taylor rule wih ineres rae smoohing. Second, i analyses he sabilisaion properies of he Taylor rule in a closed economy model of he euro area, esimaed using aggregae daa from five EU counries. An opimised Taylor rule performs quie well compared o he unconsrained opimal feedback rule. Finally, he robusness of hese resuls o esimaion error in he oupu gap and model uncerainy is examined. * A previous version of his paper was circulaed under he ile The Taylor rule: a useful moneary policy guide for he ECB?. We hank Lars Svensson, John Taylor, Shamik Dhar, Giorgia Giovanei and paricipans a he workshop on Moneary policy of he ESCB: Sraegic and implemenaion issues, held in Milan on 6-7 July 998, he CEPR/CREi/DGXII/EUI Conference on The poliical economy of fiscal and moneary policy in EMU held in Barcelona on 7/9 December 998 and seminars a he BIS and he IIES in Sockholm for very useful commens. We hank Ger Schnabel for superb assisance wih he daa. The paper was wrien while he second auhor was a he BIS. The views expressed are solely our own and no necessarily hose of he BIS or he ECB.

2 . Inroducion In his paper we explore he usefulness of he Taylor rule -- defined loosely as an insrumen rule linking he cenral bank s insrumen (he shor-erm ineres rae) o he curren inflaion rae and he oupu gap -- as a benchmark for analysing moneary policy in he euro area. Such insrumen rules have he advanage ha hey are simple and ransparen as hey explicily relae he policy insrumen o curren economic condiions. They have, however, wo imporan disadvanages. Firs, hey may be oo resricive as he number of variables in he feedback lis is ypically limied. Second, hey may no be robus o changes in he srucure of he economy. For hese wo reasons, cenral banks, including he ECB, would never wan o commi o such simple insrumen rules. The need o be able o change policies flexibly in response o new informaion and/or srucural changes in he economy pus a premium on cenral bank discreion. Neverheless, simple insrumen rules like he Taylor rule could be a useful benchmark, provided ha heir sabilisaion properies prove o be reasonably robus o changes in he underlying economy. To bring some evidence o bear on wheher his is he case, we develop hree secions. In Secion 2, we firs review some evidence on recen ineres rae behaviour in Europe. In paricular, following Clarida, Galí and Gerler (998) (CGG), we analyse wheher a Taylor rule can reasonably describe he Bundesbank s ineres rae policy in he las wo decades. More speculaively, we also analyse wheher average ineres raes in he euro zone can be described by such a rule. Such an hisorical analysis is of ineres for wo reasons. Firs, he Bundesbank arguably is a model cenral bank for he ECB. If he Taylor rule is a good descripion of Bundesbank policy, hen i may also be an appropriae benchmark for he ECB. Second, if in he recen pas average ineres raes in he euro area can be described by a Taylor rule, hen using such a rule as a benchmark has he advanage of coninuiy. By and large we confirm he resuls of CGG ha a forward-looking version of he Taylor rule wih ineres rae smoohing is able o rack German and European shor-erm ineres raes quie well since 979. While a hisorical analysis of ineres rae behaviour in Europe may sugges he usefulness of he Taylor rule, i does no answer he normaive quesion wheher he Taylor rule is a good benchmark o discuss policy in he newly esablished single currency area. To make progress on his quesion, we need o analyse he sabilisaion properies of he Taylor rule in a model of he euro area economy. Obviously i is difficul o come up wih a In December 998 he ECB Council announced a sabiliy-oriened moneary policy sraegy. I consiss of a quaniaive definiion of he price sabiliy objecive as an increase of he area-wide harmonised index of consumer prices of below 2%. In addiion, a wo-pillar sraegy -- a reference value for he growh of a broad money aggregae and a broad-based assessmen of he oulook for inflaion -- was announced o explain moneary policy decisions. This sraegy was designed o communicae he long-run commimen o price sabiliy, while allowing for enough shor-run flexibiliy o face he many uncerainies relaed o he esablishmen of he new currency. 2

3 convincing aggregae model of he euro area economy when he single currency has jus been creaed. Neverheless, in Secion 3.. we esimae a version of he closed-economy model presened in Rudebusch and Svensson (998) using a weighed average of oupu and inflaion in five euro counries as a measure of aggregae oupu and inflaion and he real German policy rae as a measure of he common moneary policy. We argue ha his model may approximae he working of moneary policy in he euro area. Par of his jusificaion is given in Appendix. There we show ha once one conrols for changes in bilaeral exchange raes and ineres rae differenials, a rise in he German real ineres rae has similar effecs on oupu in each of he five counries. Moreover, he exernal ransmission channel hrough he DM-dollar exchange rae does no appear o be significan. While hese resuls need o be aken wih more han he usual degree of cauion, we consider hem as supporing he view ha, overall, he euro area will funcion as a relaively closed economy. Moreover, o he exen ha differences in he impac effec of he common moneary policy on he oher counries are miigaed by he cross-border effecs, he effecs will be relaively uniform across he whole euro area. We hen use he EU5 model o compare he performance of a simple Taylor rule wih various oher insrumen rules and he opimal feedback rule in Secion 3.2. Our measure of comparison is a sandard loss funcion which capures he fac ha he cenral bank dislikes oupu, inflaion and ineres rae variabiliy. Our resuls are similar o he ones obained by Rudebusch and Svensson (998). We find ha a Taylor rule performs quie well compared o he opimal feedback rule, alhough he feedback on he oupu gap is larger han suggesed by Taylor (993). Finally, in secion 4 we analyse he robusness of he resuls o various forms of uncerainy. Given he imporance of he oupu gap in he Taylor rule and he fac ha ypically he confidence band around esimaes of he oupu gap is quie large, we firs analyse he impac of esimaion error in he oupu gap on he Taylor rule s sabilisaion properies (Secion 4.). Consisen wih recen research by Aoki (998), Orphanides (998), Rudebusch (998) and Smes (998), we find ha esimaion error reduces he opimal feedback coefficien on oupu in a simple Taylor rule. However, i does no affec is relaive performance. In Secion 4.2 we ask how sensiive he Taylor rule is o model uncerainy. As in Esrella and Mishkin (998) and Rudebusch (998), we find ha he esimaed parameer uncerainy has only negligible effecs on he efficien feedback parameers. Moreover, he sabilisaion properies of a simple Taylor rule wih coefficiens of.5 on inflaion and. on oupu as recenly proposed by Taylor (998a) appear quie robus o changes in he parameers of he esimaed economy as long as he basic closed economy srucure is mainained. 3

4 2. Taylor rules from he pas In his secion we firs briefly review he work of CGG. They argue ha he Bundesbank s moneary policy reacion funcion can be cas in erms of a forward-looking Taylor rule wih ineres rae smoohing. In addiion, we look more broadly a ineres raes in he eleven euro zone counries. CGG argue ha cenral bank behaviour in he G3 counries can be described by a forward-looking version of he Taylor rule wih ineres rae smoohing as in he following equaion: a () i = ρ )[ i + β( E[ π + n I ] π ) + β2e[ z I ] + ρ i + µ (, where i is he cenral bank s policy rae, i is he equilibrium nominal ineres rae, π is he a inflaion arge, π +n is he annual inflaion rae a ime +n, z is he oupu gap (he log difference beween acual and poenial oupu), and µ is an i.i.d. disurbance represening exogenous shocks o he shor rae. E is he expecaion operaor and I is he informaion available o he cenral bank a he ime i ses he policy ineres rae. The erm in square brackes capures he arge ineres rae of he cenral bank. In his simple Taylor-like specificaion he arge rae is solely a funcion of curren or expeced inflaion and he curren oupu gap. For his insrumen rule o lead o an effecive sabilisaion of he inflaion rae β needs o be greaer han one and β 2 posiive, so ha he real policy rae rises whenever inflaion is above arge and/or oupu is above poenial. The parameer ρ capures he degree of ineres rae smoohing or he speed wih which he acual policy rae adjuss o he arge rae. To esimae he parameers of equaion (), we rewrie he policy rule in erms of realised variables as follows: a (2) i = ( ρ ) β + ( ρ) βπ + n + ( ρ) β2z + ρ i + ε where Suppose a a = i β π and ε = ( ρ) [ β ( π + n E [ π + n I ]) + β( z E[ z I ])] + µ. u is a vecor of variables wihin he cenral bank s informaion se ( u I ), hen β [ ] = u E ε. These momen condiions can be used o esimae he parameers in (2). Table presens he esimaion resuls using monhly daa covering he period 979:-997:2. For he baseline specificaion he horizon of he inflaion forecas is one year ahead ( n = 2 ). Several resuls are worh menioning. Firs, alhough our sample period is somewha longer and he insrumen se larger, our baseline resuls are close o he baseline resuls in CGG. The parameers on expeced inflaion and oupu are significanly greaer han respecively one and zero, bu significanly lower han he values of.5 and.5 posulaed by 4

5 Taylor (993). The laer resul is, however, no robus and depends, for example, on he mehod used for derending indusrial producion (see specificaion 8 and 9 of Table ). 2 Second, in conras o he closed economy Taylor rule in which here is no explici policy feedback on he exchange rae, he resuls of he second and hird specificaion in Table show ha over he sample period he German policy rae rose significanly in response o a depreciaion of he rade-weighed exchange rae. 3 This is consisen wih previous findings using differen mehodologies (e.g. Clarida and Gerler (996) and Bernanke and Mihov (997)), as well as wih a careful reading of he Monhly Repors of he Bundesbank (see, for example, Tsasaronis (994)). I is also consisen wih he simple heoreical analysis in Gerlach and Smes (998) and Ball (998) who emphasise he imporance of he exchange rae channel in open economies and is implicaions for he opimal moneary policy rule. Third, in conras o CGG we find ha curren inflaion remains significan when we add i o he baseline specificaion (specificaion 6). Insead, wo-year-ahead annual inflaion is no (specificaion 7). This sheds some doub on CGG s inerpreaion of (2) as an inflaion-forecas rule from which he relaive weighs on inflaion versus oupu sabilisaion in he cenral bank s preferences can be deduced. 4 As mos esimaes sugges ha cenral banks affec inflaion wih a lag ha is longer han one year, he forecas horizon should more likely be 2 years ahead. 5 In fac, specificaion 6 suggess ha he policy rae responds o a measure of curren rend inflaion, wih he rend being calculaed as a 24-monh cenred moving average of inflaion. This is consisen wih he imporance many cenral banks aach o measuring core inflaion. Is purpose is o purge purely emporary facors from he curren inflaion rae as hese canno be influenced anyway. Finally, Graph examines he sabiliy of he Bundesbank s policy reacion funcion during he whole pos-breon Woods period by esimaing he parameers of (2) wih a moving window of years. Alhough he Bundesbank regained is moneary policy independence and sared announcing moneary growh arges immediaely following he breakdown of he Breon Woods sysem in 974, here is evidence of insabiliy in he esimaed equaion beween mos of he 97s and he period following 979. The wide 2 The magniude of he parameers also changes when we esimae he reacion funcion using quarerly daa of GDP insead of indusrial producion (see specificaion in Table ). 3 In his specificaion he arge rae includes a fourh erm, β e 3, where e is he log difference of a nominal (real) rade-weighed exchange rae in percenage poins. 4 See, for example, Svensson (997) for a derivaion of such a rule in a simple heoreical model. CGG argue ha he significance of he oupu gap in he reacion funcion in spie of he inclusion of he inflaion forecas proves ha he Bundesbank cares abou oupu sabilisaion. 5 See, for example, Black, Macklem and Rose (997) and Baini and Haldane (998) for a numerical analysis of he opimal forecas horizon in inflaion forecas argeing rules. 5

6 confidence bands during he 97s sugges a misspecificaion of he equaion. In paricular he coefficien on inflaion is very volaile and even negaive in he early period. Wih he adopion of he Maasrich Treay in he early 99s he process of moneary convergence in he EU counries acceleraed. I may hus make sense o look a average ineres rae behaviour in he EU counries in he 99s as an indicaor of he European moneary policy sance. Gerlach and Schnabel (998) show ha a simple Taylor rule applied o a weighed average of he oupu gap and he inflaion rae in he eleven euro counries can explain he fall in he average 3-monh ineres rae over he period quie well. 6 One excepion is he period of exchange marke urmoil in lae 992 and early 993 when ineres raes rose quie dramaically in a number of ERM counries o defend he fixed exchange rae pariy. The lower panel of Table repors he resuls of esimaing equaion (2) on quarerly weighed average daa for he eleven euro-area counries. Somewha surprisingly he resuls are very similar o he resuls obained for Germany. Graph 2 plos he average hreemonh ineres rae ogeher wih he forward-looking arge rule. In sum, he evidence presened in his Secion suggess ha a Taylor rule wih ineres rae ineres rae smoohing can rack shor-erm ineres raes in Germany and he euro area as a whole quie well. While his evidence complemens similar evidence for he Unied Saes and oher relaively large economies, he analysis remains ex pos and does no necessarily say much abou how well a Taylor rule may work for he fuure ECB. To his we urn in he nex secion. 3. The Taylor rule in an aggregae model for he EU5. One of he obvious problems wih analysing opimal moneary policy in he euro area is ha i is difficul o predic how he economy and he ransmission mechanism will work under he new moneary regime. Neverheless, he esablishmen of he ESCB is no a compleely new policy environmen as a gradual process of moneary convergence has preceded i. In paricular, France and Germany and some of heir smaller neighbours have had fixed exchange raes wih occasional pariy adjusmens since he end of he Breon Woods sysem. In his secion we use a simple model of he ransmission process in hese counries o analyse more formally he performance of a simple Taylor rule. The model is similar o ha esimaed by Rudebusch and Svensson (998) for he Unied Saes. As our measures of oupu and inflaion we ake a weighed average of real GDP and he CPI in Germany, France, Ausria, Belgium and he Neherlands. The moneary policy indicaor used o esimae he 6 To calculae he ineres rae ha is consisen wih a Taylor rule, hey assume coefficiens of.5 and.5 on respecively inflaion and he oupu gap, a consan inflaion arge of 2 percen and a consan equilibrium real ineres rae of 3.55%. The laer is derived from a cross-counry regression which filers ou he effec of changes in he real exchange rae. 6

7 effecs of a change in he common moneary policy sance is he real German day-o-day rae. 7 This aggregae EU5 model may be a useful approximaion of he working of he euro economy as a whole in a number of respecs. Firs, while wo large euro counries, Ialy and Spain, are excluded from he aggregae model, he five counries included sill accoun for almos wo hirds of GDP in he EMU area. Second, he counries included have had a hisory of fixed bilaeral exchange raes, wih he German Bundesbank de faco playing he anchor role. 8 As a resul, he ransmission of he German ineres rae on aggregae oupu and inflaion under a fixed exchange rae regime may be as close as one can ge o a hisorical descripion of he effecs of a common moneary policy in EMU. Third, he model akes ino accoun ha in erms of openness he euro area as a whole will be more like he Unied Saes han like any of is individual members. The raio of expors of goods o euro area-wide GDP is abou 4% and by and large comparable o ha of he Unied Saes and Japan. The disaggregaed analysis of he ransmission mechanism in Appendix confirms his hypohesis. Two resuls from his analysis need o be highlighed. Firs, we find ha once one conrols for changes in bilaeral exchange raes and ineres rae differenials he oupu effecs of a rise in he German real rae are similar in he five counries (wih he possible excepion of Belgium). Second, he exernal exchange rae approximaed by he DM/USdollar exchange rae has only negligible effecs on aggregae oupu. Thus, in conras o recen esimaion resuls in Dornbusch e al. (998) we find ha he coefficien on he exernal exchange rae in an implici Moneary Condiions Index (MCI) for he ECB would be close o zero. I is neverheless obvious ha he aggregae EU5 model can only be a rough approximaion of he ransmission process in he euro area. Firs, while we argue in Appendix ha he oupu effecs of moneary policy in hese five counries are similar, his may no be he case for he oher euro area counries. Indeed, in Appendix we find some evidence ha he impac of a common moneary policy shock on Ialian oupu may be significanly larger han in hese counries. Second, he bilaeral exchange raes were no compleely fixed during he esimaion period. The omission of changes in bilaeral exchange raes or ineres rae differenials may bias he esimaion of he aggregae model. Third, i is hard o predic how inflaion will respond o he oupu gap under he new policy regime. Implicily we assume ha he euro area-wide Phillips curve will resemble he one in he EU5 counries over he las wo decades. Finally, no only is he moneary regime changing, a he same ime many oher 7 Also Ialy has been a long-sanding member of he ERM. We decided agains including Ialy in he esimaion of he aggregae model because is inflaion behaviour over he esimaion period was very differen. Oher counries paricipaing in EMU are excluded eiher because of problems wih daa availabiliy (Ireland) or because hey sared paricipaing in he ERM only recenly (Spain, Porugal, Finland). See also Taylor (998). 8 See, for example, he references in Gros and Thygesen (992) and De Grauwe (997). 7

8 echniques. 9 The esimaed model has he following form: srucural changes are aking place which may have an impac on he ransmission process. For all hese reasons, he resuls of his secion need o be reaed very cauiously. The res of his secion is srucured as follows. In Secion 3. we esimae a simple aggregae model for he EU5 based on Rudebusch and Svensson (998). In Secion 3.2 we analyse he performance of various opimal insrumen rules in he esimaed model. 3.. An esimaed aggregae model for he EU5 In his secion we esimae a simple aggregae model for he EU5 along he lines of Rudebusch and Svensson (998). The main difference wih he laer paper is ha we simulaneously esimae he model and he oupu gap using unobservable componen (3) π π + = α( L) π + βz + ε + (4) z z+ = ϕz + ϕ2z + λ( i π ) + ε+ (5) p p y y+ = µ + y + ε + p (6) y = y + z, where π is an EU5 weighed average of quarerly inflaion in percenage poins a an annual rae; π is four-quarer inflaion in Germany; i is he quarerly average German day-o-day p rae in percenage poins a an annual rae; y is a weighed average of he log of unobserved poenial GDP in percenage poins and z is he unobserved oupu gap, i.e. he log difference beween acual real GDP ( y ) and poenial GDP in percenage poins. Equaion (3) can be inerpreed as a Phillips-curve which relaes inflaion o he lagged oupu gap and o lags in inflaion. The second equaion is he reduced form of an aggregae demand equaion which relaes he oupu gap o is own lags and o a lagged real ineres rae, which is approximaed by he difference beween he nominal day-o-day rae and average inflaion over he previous four quarers. Equaion (5) assumes ha poenial oupu follows a random walk process wih consan drif. Finally, equaion (6) is an ideniy ha defines he oupu gap. In Appendix 2 we show how his model can be wrien in sae space form and esimaed using he Kalman filer and maximum likelihood mehods. Table 2 repors he 9 See Smes (998). This esimaion mehodology exends he work by Kuner (994) and Gerlach and Smes (997). 8

9 esimaion resuls wih quarerly daa over he period 975:-997:4. For comparison we also add he esimaion resuls for he same model esimaed for he Unied Saes over he same period. As can be seen all he parameers have he expeced sign and are significan. I is useful o compare he EU5 esimaes wih he US ones. While he effec of he real policy rae on he oupu gap is almos he same in boh cases (λ=-.), we esimae he slope of he Phillips-curve o be seeper in EU5 han in he US (β=.33 insead of.). The EU5 oupu gap is somewha more persisen han he US one, bu does no exhibi he hump-shaped paern of he US oupu gap. In conras, he inflaion process is much less persisen in he EU5 han in he US. The sum of he α-parameers is.74 in he EU5 case versus.92 in he US case. One inerpreaion for he fac ha we can easily rejec a uni roo in he inflaion process in he EU5 is ha during his period agens in he EU5 pu a posiive weigh on he consan inflaion arge (which equals he average inflaion rae over he sample) in forming heir inflaion expecaions. One imporan issue for he analysis of opimal Taylor rules is wheher his weigh will be differen in he EMU area. This will in par depend on he repuaion of he new cenral bank. Everyhing else equal lower aniinflaionary credibiliy will resul in a higher persisence of inflaion. Implicily we assume ha he ECB will inheri he credibiliy of he EU5 cenral banks. If his urns ou no o be he case and, for example, he weigh on he ECB s inflaion arge is less han implici in he EU5 model, hen one implicaion for he opimal Taylor rule would be ha he cenral bank will have o lean more agains inflaion and oupu (see he resuls of secion 4.2). Graph 3 compares he effecs of a emporary one-percenage poin rise in he real policy rae during 8 quarers on he oupu gap and inflaion in he EU5 and he US. Consisen wih he discussion above, one can see ha he effecs on EU5 oupu are less in magniude, bu more persisen han in he US, while he effecs on inflaion are sronger. This again suggess ha according o hese esimaes he oupu cos of reducing inflaion is less in Europe han i is in he US. Comparing hese resuls wih he resuls of he disaggregaed analysis in Graph A. and A.2. of Appendix, i is likely ha he oupu effecs would be larger if he aggregae daa had included Ialy. Turning o he esimaes of he variances of he shocks, we find ha he variance of he inflaion shocks is very similar o ha in he US. However, esimaed supply shocks are relaively less imporan, while demand shocks are more imporan in he EU5 compared o he US. Graph 4 plos he one-sided and wo-sided esimaes of he EU5 oupu gap ogeher wih a wo sandard-deviaions confidence band. Consisen wih he findings of Gerlach and Smes (997) he confidence band around he esimaes of he oupu gap is quie wide, bu somewha less so han for he US (Smes, 998). Typically, he sandard deviaion of he See, for example, he discussion in McLean (998). In Secion 3.4 we analyse he robusness of he sabilisaion properies of he Taylor rule o larger oupu effecs of a moneary policy shock. 9

10 oupu gap is a bi less han one percen. According o hese esimaes he EU5 was a he end of 997 sill facing a negaive oupu gap of 2% which is marginally significanly differen from zero How well does he Taylor rule perform? Insrumen rules and he loss funcion In order o analyse how well an opimised Taylor rule performs in he EU5 model esimaed in he previous secion, we consider he following loss funcion, 2 (7) E L ) γ Var( π ) + ( γ ) Var( z ) + νvar( i i ). ( = The cenral bank cares abou variabiliy in he deviaions of annual inflaion from a consan inflaion arge, variaions in he oupu gap and changes in he shor-erm ineres rae. As all variables are demeaned before he analysis, equaion (7) implies ha he inflaion arge equals he mean inflaion rae over he sample. In his secion we assume ha he cenral bank akes he model esimaed in secion 3. as given and observes he curren sae of he economy, including no only curren and pas inflaion and ineres raes, bu also he curren and pas oupu gap. The cenral bank s ask is hen o se is policy insrumen, i, in such a way as o minimise he loss funcion (7) subjec o he dynamics of he economy described by equaions (3) o (6). We consider seven insrumen rules. The benchmark rule is he unresriced opimal feedback rule. Given he linear-quadraic naure of he opimal conrol problem he opimal rule is linear in each of he seven sae variables. In addiion, we consider six resriced insrumen rules. The firs four of hese are all varians of he popular Taylor rule. The firs resriced rule is he simple Taylor rule (T), and consrains he feedback of he policy rae o he curren annual inflaion rae and he curren oupu gap, (T) i = g π + g z π z. The second resriced rule is a forward-looking Taylor rule (FT). In such a rule he cenral bank responds o an inflaion forecas raher han o curren inflaion. Following RS, we assume he cenral bank responds o a consan-ineres-rae inflaion forecas, i.e. he inflaion forecas is calculaed under he assumpion of a consan ineres rae. The forecas horizon is assumed o be 8 quarers. (FT) i = g π + g e π z z 2 This discussion follows Rudebusch and Svensson (998). They show how his loss funcion is equivalen o a more sandard ineremporal loss funcion wih a discoun rae equal o one.

11 The hird and fourh resriced rules (TS) and (FTS) correspond o he previous wo rules, bu allow for ineres rae smoohing by including he lagged ineres rae in he feedback lis, i.e. (TS) i = g π π + g zz + gii e (FTS) i = g π + g zz + gii π. Finally, he las wo resriced rules (F) and (FS) are pure inflaion-forecas rules wih and wihou smoohing, i.e. (F) i = g π e π e (FS) i = g π + gii π. For each of hese rules he feedback parameers are opimised so as o minimise he uncondiional variance of he period loss funcion in equaion (7) (see Appendix 2). In addiion, we also repor he performance of he original Taylor rule (OT) and a modified Taylor rule wih a somewha larger response o oupu (MT), i.e. (OT) i =.5π +. 5z. (MT) i =.5π +. z. Resuls The upper panel of Table 3 gives he feedback parameers for each of he nine insrumen rules, he corresponding sandard deviaions of he goal variables, he value of he loss funcion and he ranking among he rules considered. Following Rudebusch and Svensson (998), we assume for he benchmark case ha he cenral bank pus equal weigh on inflaion and oupu deviaions ( γ =. 5 ) and a weigh of.25 ( ν =. 25) on he ineres rae smoohing componen. The opimal feedback rule in he esimaed EU5 model is given by (8) i =.34π +.7π +.9π 2 +.5π 3 +.7z +.2z +. 56i. This rule implies a quie srong response o he curren oupu gap wih policy raes increasing more han one for one wih increases in he oupu gap. No surprisingly, wih a weigh of.25 on he ineres rae smoohing componen, he opimal feedback rule also implies a significan feedback on he lagged ineres rae.

12 The imporance of he oupu gap is also obvious in he resriced insrumen rules. We find ha he weigh on he oupu gap in he simple Taylor rule is as large as he weigh on inflaion and equals abou.5. In oher words, while he weigh on inflaion is close o he weigh proposed by Taylor (993), he opimal weigh on he oupu gap is hree imes as large (i.e..5 insead of.5). This resul is consisen wih he findings of Ball (997) who using a small calibraed model of he US economy argued ha an efficien weigh on he oupu gap should be much larger han he.5 proposed by Taylor (993). The hird and fourh row in Table 3 give an indicaion of he cos of following a Taylor rule wih lower weighs on oupu. Using he original Taylor rule (OT) increases a ypical deviaion of he oupu gap by almos 3 percenage poins and a ypical deviaion of inflaion from arge by abou 2 percenage poins. Using a weigh of. reduces hese losses considerably. 3 Obviously, he opimal feedback coefficiens in he Taylor rule will also depend on he weighs in he objecive funcion. Graph 5 plos he efficien Taylor rule parameers as a funcion of he weighs on oupu relaive o inflaion and he weigh on he ineres rae smoohing componen. In his graph he symbol O on he lef side of he solid curves sands for sric oupu argeing, i.e. γ =, while he symbol I on he righ side sands for sric inflaion argeing, i.e. γ =. 4 The middle curve corresponds o a weigh on ineres rae smoohing, ν, equal o.25 as in he benchmark case. The upper and lower curves correspond o respecively a smaller and greaer weigh on ineres rae smoohing in he loss funcion. A couple of observaions are worh making. Firs, for a given weigh on ineres rae smoohing i appears ha he opimal feedback coefficien on he oupu gap is no much affeced by he relaive weigh on oupu versus inflaion sabilisaion. A higher weigh on inflaion does increase he response o inflaion considerably. Again, his reflecs he crucial role of he oupu gap in aemps a inflaion sabilisaion in his model. In conras, he weigh on ineres rae smoohing does affec he opimal response o oupu quie significanly. As ineres rae smoohing becomes more imporan he coefficien on he oupu gap falls quie considerably. Over he sample period he sandard deviaion of changes in he German policy rae was.68. If his is a good indicaor of he ineres rae smoohing objecive of a cenral bank, i suggess ha he implici weigh on ineres rae smoohing should lie beween he cases of ν =. 25 and ν =. 5 depiced in Graph 5. In view of he considerable weigh on ineres rae smoohing in he objecive funcion, allowing for a response o he lagged ineres rae in he resriced insrumen rule, improves he performance of he Taylor rule quie considerably. While he long-run feedback on inflaion is no much affeced, ineres rae smoohing allows for an even sronger response 3 In a recen paper John Taylor seems o acknowledge ha his original proposal may be inefficien and considers rules wih a weigh on oupu of. (Taylor, 998). See, for example, also McCallum and Nelson (998). 4 A weigh in beween is wha Svensson (997) calls flexible inflaion argeing. 2

13 o he oupu gap in he medium-erm. As is clear from Table 3, a Taylor rule wih ineres rae smoohing (TS) comes very close o he opimal feedback rule in his EU5 model. Allowing he cenral bank o respond o a consan-ineres rae inflaion forecas raher han curren inflaion does no paricularly improve he performance of he Taylor rule. While he opimal feedback coefficien on he oupu gap falls somewha and ha on he inflaion forecas rises, he losses are very comparable. The crucial role of he oupu gap in he ransmission mechanism of moneary policy is mos obvious when comparing he Taylor rules wih he simple inflaion forecas rules. The laer perform clearly much worse han he simple Taylor rule. As here are only wo shocks in he economy, i is no very surprising ha in his economy, one can no improve very much upon a simple Taylor rule by using inflaion forecass raher han curren inflaion. Obviously, in a more realisic seing filering ou emporary shocks from more permanen ones by using a inflaion forecas will be opimal given he considerable lags in he ransmission process. 5 In sum, if he model esimaed for he EU5 in secion 3.. is a reasonably good approximaion of he way he euro-area economy will work, hen he resuls in his secion sugges ha a simple Taylor rule wih a relaively srong feedback on he oupu gap would perform quie well in sabilising he economy in he face of macroeconomic shocks. How do hese resuls relae o he exising lieraure on opimal moneary policy rules? These resuls on he sabilisaion properies of he Taylor rule are quie similar o he findings in Rudebusch and Svensson (998). One difference wih he RS resuls is ha hey find a much sronger feedback on inflaion. This can be explained by he higher persisence of inflaion in he esimaed US model. Lower inflaion persisence which may be inerpreed as higher credibliy of he inflaion arge implies ha he cenral bank will need o lean relaively less agains changes in inflaion. There is more evidence ha a simple Taylor rule wih a relaively srong feedback on he oupu gap performs quie well in he US economy. Earlier work include he sudies by Henderson and McKibbin (993) and Levin (996). More recenly Levin e al (998) examined he performance of a Taylor-like rule in a range of models for he US economy. 6 Similarly o our findings hey find ha such a rule ouperforms simple inflaionforecas rules. In addiion, hey find ha no much can be gained from including oher informaion (such as lagged variables, foreign variables or he exchange rae) in he feedback rule. [pu also reference o McCallum and Nelson (998)]. The overall posiive resuls ha have been found for he US economy conras wih he less favourable resuls researchers have found for smaller, more open economies. 5 See Baini and Haldane (998) on a lucid discussion of why forward-looking rules while simple in form may perform very well. 6 One difference wih he findings in his paper is ha hey find ha a srong persisence in he policy rae is opimal. This resul is in par due o he fac ha i is he long-erm ineres rae ha maers in he aggregae demand equaion. 3

14 Black, Macklem and Rose (997) and Baini and Haldane (998), for example, find ha inflaion forecas rules have he abiliy o perform much beer han simple Taylor rules in respecively he Bank of Canada s QPM-model and a calibraed model of he UK economy. Similarly, De Brouwer and O Regan (997) find ha including he exchange rae and foreign variables improves he performance of he Taylor rule in a model for he Ausralian economy. These resuls are no very surprising. While in closed economies he curren oupu gap and inflaion may be close o sufficien saisics o describe he sae of he economy, his is unlikely o be he case for more open economies. The mos imporan difference is probably he imporance of he exchange rae channel, which is, for example, emphasised in Svensson (997c) and Baini and Haldane (998). Indeed, he imporance of his channel in relaively open economies is refleced in a significan response o he exchange rae as, for example, illusraed in he esimaed reacion funcion for he Bundesbank in Table. However, hese resuls do no necessarily urn around he posiive resuls concerning he Taylor rule of his secion. As long as he underlying paradigm of a relaively closed economy wih he main ransmission channel working hrough he oupu gap is reasonable for he euro-zone economy, a Taylor rule would appear o be a useful benchmark. 4 Uncerainy and he robusness of simple Taylor rules 4.. The effec of esimaion error in he oupu gap In ligh of he crucial role of he oupu gap in he efficien Taylor rules of he previous secion, an imporan quesion ha needs o be addressed concerns he impac of esimaion error in he oupu gap on he efficien feedback parameers and he performance of he Taylor rule. Several auhors, including Kuner (994), Saiger e al (996) and Gerlach and Smes (997) have shown ha indicaors of capaciy uilisaion such as he oupu gap or he NAIRU are esimaed wih a considerable margin of uncerainy. Given he iniial aggregaion problems and he lack of reliable hisorical daa, his is likely o be even more rue for he measuremen of an EMU-wide oupu gap. One counerargumen is ha he variabiliy of he EMU-wide oupu gap will be less han ha of he individual counries because some of he idiosyncrasies will be averaged ou. In his secion, we analyse he effec of esimaion error in he oupu gap on he efficien insrumen rules and heir performance in he esimaed model of secion 3.. To address his quesion we follow Smes (998) who argues ha esimaion error in he oupu gap may in par explain why he acual cenral bank response o movemens in he oupu gap is less han opimal conrol exercises sugges.. The loss funcion and he dynamics of he economy are again given by equaions (3) o (7). However, now we assume, consisen wih he esimaed model, ha oupu gaps are no direcly observed, bu need o be esimaed. In oher words, wo of he sae variables, z and z are unobserved. 4

15 Curren and pas growh raes of real GDP, y, are observed, bu could be due o eiher a change in he growh of poenial oupu or a change in he oupu gap, so ha he cenral bank faces a signal exracion problem. The Kalman filer which was used in secion 3.. o esimae he model gives he opimal esimae of he oupu gap given he observed daa and he srucure of he economy. The middle panel of Table 3 gives he resuls of he opimal conrol exercise when we ake he esimaed uncerainy of he oupu gap ino accoun. 7 As emphasised in Esrella and Mishkin (998) and shown by Chow (97) esimaion errors in he sae variables do no affec he opimal unconsrained feedback rule in a linear-quadraic framework. As a resul of his cerainy equivalence heorem, he only difference beween he opimal linear feedback rule in panel and 2 of Table 3 is ha in he laer case he feedback is on he esimaed sae variables raher han on he acual sae variables. 8 However, he loss funcion is affeced as he policy feedback on measuremen error in he oupu gap will filer hrough ino he economy and increase he variabiliy of he goal variables. Indeed, he loss under he opimal feedback rule increases from.3 o.6. More ineresing are he resuls concerning he resriced feedback rules. The relaive ranking of he differen rules is no affeced. However, comparing panel and 2 of Table 3, i is obvious ha in he simple Taylor rule, he weigh on oupu falls from.58 o.4 and he weigh on inflaion increases from.53 o.65. The effec of measuremen error is o pu less weigh on he variable ha is measured wih error and more on he variable ha is perfecly observed. 9 Graph 6 plos he Taylor rule coefficiens as a funcion of he uncerainy in he oupu gap. The opimal response o he oupu gap in a simple Taylor rule falls a an increasing rae as he sandard deviaion of he esimaion error in he oupu gap increases, while he opimal response o inflaion rises. In boh cases he opimal feedback parameer is sill relaively high a he esimaed sandard deviaion (around.8 percen). However, increasing he sandard deviaion beyond is esimae resuls in a rapid drop of he feedback parameer. A sandard deviaion of.3 would in his model be consisen wih a coefficien of.5 on oupu, as suggesed by Taylor (993). I becomes opimal no o respond o he oupu gap when is sandard deviaion is larger han.5 percen. Graph 5 shows ha he negaive effec of higher esimaion error on he Taylor rule coefficiens is robus o various weighs in he objecive funcion. The dashed lines give he opimal Taylor rule coefficiens for various weighs aking he esimaed oupu gap uncerainy ino accoun. In almos all cases he efficien Taylor rule coefficien on oupu falls, bu how much depends on he weighs in he objecive funcion. I is worh noing ha alhough he effec of he esimaed oupu gap uncerainy is o move he efficien Taylor rule 7 See Appendix 2 for some of he echnical deails. 8 This resul is someimes called a separaion heorem. See Chow (97) for a discussion. 9 See Saiger e al (996). 5

16 parameers in he direcion of he values suggesed by Taylor (993), i is clear ha one needs eiher larger han esimaed oupu gap uncerainy or a srong ineres rae smoohing objecive o explain why acually esimaed feedback parameers on oupu are around.5. However, from he hird and fourh row in he middle panel of Table 3 i is obvious ha he loss of having a lower feedback parameer on oupu (.5 or.) is much less when one akes ino accoun he measuremen error in he oupu gap. In sum, esimaion error in he oupu gap can parly explain why cenral banks in pracice respond less o he oupu gap han suggesed by opimal conrol exercises which do no ake ino accoun his uncerainy. In he exreme, high uncerainy may resul in a zero response o he oupu gap. Wih he esimaed sandard deviaion of he EU5 oupu gap, a quie srong feedback is sill opimal. I is an empirical quesion wheher esimaes of he EMU-wide oupu gap are subjec o much larger confidence bands. These resuls correspond wih oher recen research ha has analysed he effecs of measuremen error in boh oupu gaps and inflaion on he opimal feedback coefficiens in a Taylor rule. Boh Rudebusch (998) and Orphanides (998) analyse measuremen error in inflaion and he oupu gap in a very similar model for he Unied Saes. Boh of hem documen ha here are significan revisions in US esimaes of inflaion and he oupu gap and show ha aking his measuremen error ino accoun reduces he efficien feedback parameers and brings hem more in line wih he original Taylor rule ones. Aoki (998) performs a heoreical analysis in a simple, bu opimising model of he US economy. Consisen wih he previous resuls, he shows ha noise conained in he daa offers a reason for policy conservaism The effec of uncerainy abou he ransmission mechanism In Secion 3 we have argued ha a simple model of he ransmission mechanism for a relaively closed economy may be a useful saring poin for analysing moneary policy in he euro area. However, he uncerainies remain large. In par, his is a generic problem facing cenral banks. In spie of decades of economic research on his issue, here is sill a considerable degree of uncerainy abou he precise effecs on oupu and inflaion of changes in he moneary policy sance. 2 In he case of euro area, he fac ha moneary policy may impac he economy of he differen naions differenly, he associaed aggregaion problem, he absence of aggregae hisorical daa and he poenial for a srucural break under he new regime make an analysis of he euro area-wide ransmission mechanism even more complicaed. In his secion, we make a preliminary and necessarily limied aemp a assessing he impac of parameer uncerainy on he opimal policy rules considered in his paper. 2 For an overview of some of he empirical research on he ransmission mechanism in he European conex, see Kieler. and Saarenheimo (998). 6

17 Following he original work of Brainard (967), a number of auhors, including Svensson (997b), Clarida e al (997b), Cecchei (997), Esrella and Mishkin (998) and Wieland (997), have recenly analysed he effec of parameer uncerainy on opimal moneary policy rules using simple mosly heoreical models of he ransmission mechanism. 2 There is, however, lile aemp o quanify he effecs of parameer uncerainy in an empirical model. Such quanificaion is imporan because only in he special case where none of he parameers are correlaed can one unambiguously show ha higher uncerainy abou he ransmission mechanism will resul in a more cauious response of he cenral bank o he economy s sae variables. 22 In his secion we use wo admiedly limied ways of assessing he impac of model uncerainy on opimal policy behaviour and he performance of he Taylor rule in paricular. Firs, following he lieraure discussed above we analyse he opimal Taylor rule if we ake ino accoun he esimaed variance-covariance marix of he parameer esimaes as a measure of model uncerainy. The lower panel of Table 2 presens he resuls. 23 We basically confirm he resuls of Esrella and Mishkin (998) and Rudebusch (998) who show ha parameer uncerainy only marginally reduces he efficien feedback parameers in he insrumen rules. This is rue for boh he opimal linear feedback rule and he simple Taylor rule. Moreover, even doubling he esimaed sandard deviaions of he parameers does no significanly change his resul. In sum, convenional parameer uncerainy does no seem o maer very much for he efficien insrumen rules. However, he esimaed parameer uncerainy of he EU5 model may no ake ino accoun he poenial for model uncerainy ha arises from he fac ha he ransmission in he oher EMU counries may be differen or from srucural breaks due o he esablishmen of he new moneary regime. While a full analysis of he robusness of simple Taylor rules o such model uncerainy deserves a separae paper, Graph 7 presens some suggesive evidence. In his graph we plo he efficiency fronier of boh he opimal linear feedback rule and he efficien simple Taylor rule (T) for four differen versions of he EU5 model. In each case he symbol MT corresponds o he oucome of he Modified Taylor rule wih a feedback coefficien of.5 on inflaion and. on he oupu gap. The solid lines correspond o he esimaed model. The lines indicaed by Model correspond o a similar model wih a reduced slope of he Phillips curve (β is.5 insead of.33). In oher words, compared o he esimaed model, he sacrifice raio is higher and similar o he one esimaed for he Unied 2 See also Blinder (998). A paricularly innovaive paper is Wieland (997). He analyses he radeoff faced by he cenral bank beween cauion and experimenaion. 22 Recen papers ha conain a quaniaive assessmen of he effecs of parameer uncerainy are Esrella and Mishkin (998), Rudebusch (998), Sack (998), Shuerim (998) and Salmon e al (998). 23 Some of he echnical deails can again be found in Appendix 2. 7

18 Saes. As noed in Rudebusch (998), a seeper slope of he Phillips curve will reduce he feedback coefficien on he oupu gap while increasing he one on inflaion. The lines indicaed by Model 3 correspond o a model in which he oupu effecs of an ineres rae rise are much higher (λ is.5 insead of.). A higher ineres rae sensiiviy will generally reduce he feedback coefficiens on boh oupu and inflaion. Finally, he lines wih shor dashes (Model 2) correspond o a model in which he persisence of inflaion is greaer (α() is.85 insead of.74). Excep in he laer case, he resuls of Graph 7 seem o indicae ha he modified Taylor rule does relaively well in sabilising oupu and inflaion compared o he efficiency fronier. The gains from moving o he fronier are ypically less han basis poins in erms of a reduced sandard deviaion of inflaion and he oupu gap. More subsanial gains can be achieved when inflaion is much more persisen han esimaed in he EU5 model. In his case an efficien Taylor rule would do much beer and could poenially reduce he sandard deviaion of inflaion by more han 2 basis poins. The reason for his is ha when shocks o inflaion are highly persisen i pays for he cenral bank o be much more aggressive. In his paricular case he efficien Taylor rule parameers are.9 on inflaion and.8 on he oupu gap if he cenral bank cares equally abou oupu and inflaion. Mos evidence seems, however, o sugges ha inflaion persisence has fallen as inflaion has been come down. Overall, he evidence presened here suggess ha he relaively good performance of a simple Taylor rule wih coefficiens of.5 on inflaion and. on oupu is robus o small variaions in he parameers of he esimaed model. This is consisen wih ess of he robusness of simple Taylor rules in he US models. Levin e al (998), for example, find ha he Taylor rules hey consider are quie robus across he differen models of he US economy hey analyse. One possible excepion ha we idenified is when he inflaion process urns ou o be much more persisen han esimaed in he EU5 model. In ha case opimal Taylor rules are sill performing quie well, bu he feedback parameers need o be much higher han he ones ypically suggesed. Of course, he significance of hese resuls is somewha reduced by he fac ha we did no consider radically differen models of he euro area economy. 5. Conclusions The need o be able o change policies flexibly in response o new informaion and/or srucural changes in he economy pus a premium on cenral bank discreion. Neverheless, simple policy guidelines can be useful in wo respecs. Firs, hey can be used inernally as a benchmark o assess policy decisions which are based on he wides informaion se available. The availabiliy of a benchmark pus some discipline on he cenral bank s saff o explain why is analysis deviaes from wha he benchmark suggess. Second, 8

19 when made public hey can also be used as a communicaion device o explain policy decisions o he general public. In his paper we have argued ha i may be worh considering a simple guideline like he one suggesed by Taylor (993) as a benchmark for analysing moneary policy in he euro area. Our jusificaion is basically hreefold. Firs, as he rule explicily links he curren policy rae o he curren sae of he economy as capured by he curren rend inflaion rae and he curren oupu gap, i is easy o calculae and undersand. This simpliciy helps he communicaion of he cenral bank. Second, here is increasing evidence ha he policy behaviour of successful cenral banks can be usefully described by varians of he Taylor rule. 24 In Secion 2 of his paper we presen some evidence ha also in Europe movemens in shor-erm ineres raes can be approximaed by such a rule. In par, hese wo reasons explain why so many privae secor economiss use a Taylor rule o analyse policy decisions. Third, he benefis of having a benchmark rule will, of course, depend on how robus he abiliy of he rule o sabilise inflaion and oupu is o changes in he srucure of he economy. Obviously, if opimal policy deviaes frequenly and persisenly from he benchmark and/or he rule needs o be revised frequenly, he advanages of having such a benchmark will quickly disappear. 25 In secion 3 of he paper we argue ha o a firs degree he euro area economy can be modelled as a relaively closed economy along he lines of Rudebusch and Svensson (998). Using his esimaed model we show ha simple Taylor rules do a raher good job in sabilising oupu and inflaion. In Secion 4 we show, in addiion, ha esimaion error in he oupu gap does no significanly affec he performance of he Taylor rule, alhough i does reduce he opimal feedback coefficien on he oupu gap. We also find ha he performance of he Taylor rule is robus o small changes in he parameers of he model. Overall, his is consisen wih research on simple policy rules using models for he US economy. In spie of he generally favourable resuls concerning he sabilisaion properies of a Taylor rule in a relaively closed economy, here remain a number of issues which need o be resolved. Firs, quesions remain abou he appropriae choice of he feedback coefficiens in he Taylor rule, in paricular on he oupu gap. Second, mos empirical sudies of cenral bank behaviour reveal ha cenral banks smooh ineres raes and only gradually move owards he policy suggesed by a Taylor rule. The reasons for ineres rae smoohing need o be beer undersood. In an innovaive sudy, Sack (998) finds ha in a siuaion where he cenral bank learns abou he policy muliplier by observing he reacion of he economy o recen ineres rae changes, i may be opimal o move gradually over ime. 24 For an ineresing hisorical analysis of US moneary policy hrough he lenses of he Taylor rule, see Taylor (998). 25 The imporance of robusness in he design of moneary policy rules has ofen been sressed by Ben McCallum (See, e.g. McCallum (997)). 9