Macroeconomic Volatility Trade-off and Monetary Policy Regime in the Euro Area (FEP Working Paper Nº 123, Faculdade de Economia da Universidade do Porto o, Março 2003)

1 FACULDADE DE ECONOMIA UNIVERSIDADE DO PORTO Faculdade de Economia do Po o - R. D . Robe o F ias - 4200-464 Po o - Po ugal Tel . +351 225 571 100 - Fax. +351 225 505 050 - h p://www. ep.up.p WORKING PAPERS DA FEP MACROECONOMIC VOLATILITY TRADE-OFF AND MONETARY POLICY REGIME IN THE EURO AREA Ál a o Aguia Manuel M. F. Ma ins In es igação - T abalhos em cu so - nº 123, Ma ço de 2003 www. ep.up.p FEP Wo king Pape no. 123, Ma ch 2003 1 Mac oeconomic Vola ili y T ade-o and Mone a y Policy Regime in he Eu o A ea Al a o Aguia and Manuel M. F. Ma ins CEMPRE*, Faculdade de Economia, Uni e sidade do Po o Abs ac This esea ch unco e s a well-de ined mone a y policy egime s a ing in 1986 in he agg ega e Eu o A ea. Bo h al e na i e solu ion-es ima ion me hods employed - op imal con ol cum GMM, and dynamic p og amming cum FIML - iden i y a egime o s ic in la ion a ge ing wi h in e es a e smoo hing. The unemploymen gap, p ope ly es ima ed as quasi eal- ime in o ma ion, is a ele an elemen in he in o ma ion se o he mone a y au ho i y, despi e no being included in i s p e e ences. The eme gence o he egime ela es o he imp o emen o he ola ili y ade-o be ween in la ion and unemploymen gap since he mid-80s. Addi ional imp o ing ac o s ha e been milde supply shocks and be e abili y o policymake s o se he in e es a e close o op imum. Keywo ds: Mone a y Policy Regime, Eu o A ea, Op imal Con ol, Dynamic P og amming, GMM, FIML. JEL classi ica ion: E52, E58, C32, C61. This pape is also a ailable om he Social Science Resea ch Ne wo k Elec onic pape Collec ion h p://pape s.ss n.com/abs ac _id=355700 * CEMPRE - Cen o de Es udos Mac oeconómicos e P e isão - is suppo ed by he Fundação pa a a Ciência e a Tecnologia, Po ugal, h ough he P og ama Ope acional Ciência, Tecnologia e Ino ação (POCTI) o he Quad o Comuni á io de Apoio III, which is inanced by FEDER and Po uguese unds. Please add ess co espondence o Al a o Aguia ([email p o ec ed]), Faculdade de Economia, Uni e sidade do Po o, Rua Robe o F ias 4200-464 Po o, PORTUGAL; +351225571254 (phone); +351225505050 ( ax). FEP Wo king Pape no. 123, Ma ch 2003 2 Mac oeconomic Vola ili y T ade-o and Mone a y Policy Regime in he Eu o A ea 1. In oduc ion* Along he las hi y yea s, he mac oeconomic pe o mance o he cu en Eu o A ea, in e ms o he main s abilisa ion policy objec i es, has changed ma kedly. Figu e 1 illus a es his change, showing i e yea s a e ages o he a iabili y o qua e ly in la ion and unemploymen gap (u-gap), o he agg ega e Eu o A ea be ween 1972:I and 2001:II. The mac oeconomic ola ili y pe o mance o he Eu o A ea has clea ly imp o ed since 1986, wi h low and sys ema ically dec easing a iabili y o bo h in la ion and u-gap. We in e p e his pic u e wi hin Taylo 's (1979) amewo k. The ansi o y Phillips ade-o be ween he le els o in la ion and unemploymen gap implies a pe manen ade-o be ween hei a iabili y a ound desi ed le els. As u he de eloped by Taylo (1994) and Fuh e (1997), he pe manen a iabili y ade-o is in e p e able as an e iciency policy on ie o he mone a y policy egime. This policy on ie - o en called Taylo cu e - is nega i ely sloped and con ex o he o igin. I s locus depends on he policy egime and on he a iabili y o he shocks hi ing he economy, and i s slope is a unc ion o he s uc u e o he economy, including he elas ici y o he ansi o y Phillips cu e. The op imal policy choice yields a speci ic combina ion in he e iciency on ie , which is a unc ion o he ela i e weigh a ached o in la ion and ac i i y gap ola ili y in he policymake 's loss unc ion. In his con ex , he dis ance be ween ac ual mac o pe o mance and he on ie may be in e p e ed as a measu e o he policy ine iciency. FEP Wo king Pape no. 123, Ma ch 2003 3 This pape in es iga es he con ibu ion o a new mone a y policy egime o he a ou able shi in he ola ili y ade-o o he Eu o A ea, obse ed since 1986 and ein o ced he ea e . In he p ocess, we mus isola e his ac o om he o he h ee possibly d i ing he implied shi o he Taylo cu e and/o he posi ion o he economy ela i e o ha e iciency on ie , namely: (i) changes in he s uc u e o he economy; (ii) shi s in he deg ee o smoo hness o shocks bu e ing he A ea; and (iii) imp o emen in he e iciency o mone a y policy. In o de o pu sue his app oach, we need o es ima e he Eu o A ea policymake 's p e e ences in a amewo k ha allows o simul aneous iden i ica ion o he A ea mac oeconomic s uc u e, he supply shocks, and policy e iciency.1 Two ecen s udies o he US case, Fa e o and Ro elli (2001) and Dennis (2001), seem o i hese equi emen s. They bo h use a small mac oeconomic model sugges ed by Rudebusch and S ensson (1999) o ep esen agg ega e supply and agg ega e demand, oge he wi h an in e es a e equa ion desc ibing condi ions o op imali y o he policymake 's ac ions. Such op imali y condi ions a e de i ed by Fa e o and Ro elli using op imal con ol, while Dennis uses dynamic p og amming, building on he use o in e se- con ol heo y by Salemi (1995). In e ms o econome ic es ima ion o he sys em, he wo app oaches - op imal con ol and dynamic p og amming - lead o wo di e en es ima o s, GMM and FIML, espec i ely. Gi en he balanced assessmen o s eng hs and weaknesses o hese wo me hods, we e ine and adap bo h he Fa e o and Ro elli (2001) and Dennis (2001) amewo ks o he Eu o A ea, and compa e he esul s. An impo an e inemen e e s o he u-gap se ies used in he es ima ion. Ins ead o using measu es a ailable om o icial sou ces a he ime o he esea ch, we build a quasi eal- ime es ima e o he u-gap, which is FEP Wo king Pape no. 123, Ma ch 2003 4 close o he in o ma ion a ailable o policymake s in eal- ime, i.e. a he ime o ac ual decisions. E en hough i s obse ed shi in ola ili y pa allels ha o he US, he Eu o A ea case has wo impo an pa icula i ies ha ende ou goal po en ially mo e complex. Fi s , he e was no o mal unique Eu opean mone a y policy egime un il he Eu opean Mone a y Union (EMU) in 1999, and, un il hen, he na ional mone a y au ho i ies ope a ed wi hin he e ogeneous mone a y policy ins i u ional amewo ks – Cukie man (1992, chap e 19). Second, he Eu o A ea ime se ies a e weigh ed a e ages o he 11 membe -s a es o ming he EMU, as published in he A ea Wide Model Da abase (AWMD) by he Eu opean Cen al Bank (ECB), possibly masking s uc u al he e ogenei y. In spi e o hese di icul ies, he da a and he e en s in he Eu opean mone a y in eg a ion h oughou 1979-1999 mo i a e ou hypo hesis ha he a iabili y ade-o imp o emen is concu en wi h he de ac o eme gence o a well-de ined mone a y policy egime in he agg ega e Eu o A ea in he mid-80s. Such egime would be associa ed o he leade ship o he exchange a e mechanism o he Eu opean Mone a y Sys em by Ge man mone a y policy. The Bundesbank ini ia ed a new egime in 1986, s abilising he in la ion a ge a 2 pe cen pe yea , a e ha ing g adually dec eased i since he beginning o he 80s. The exchange a e e en s and he nominal con e gence eco d in he Eu o A ea mo i a e ou claim conce ning he mone a y policy egime eme gence in 1986. In ac , a e Ap il 1986 he e we e almos no ealignmen s o exchange- a e pa i ies wi hin he exchange a e mechanism o he Eu opean Mone a y Sys em. E en he 1992-93 exchange a e c isis u ned ou o ha e no signi ican s uc u al consequences. Exchange FEP Wo king Pape no. 123, Ma ch 2003 5 a e s abili y, oge he wi h he libe alisa ion o capi al mo emen s – capi al con ols we e p ac ically ine ec i e a e 19862 -, explains why mone a y policy o indi idual coun ies has signi ican ly los au onomy a e 1986-87. Fu he mo e, nominal con e gence owa ds Ge many – especially in e ms o in la ion a es – had al eady been achie ed, in la ge pa , by he second hal o he 80s. In addi ion o he ecen his o ical eco d, he hypo hesis o a new in o mal mone a y egime since 1986 - an icipa ing he o mal 1999's EMU - is also compa ible wi h a gumen s pu o h p e iously in di e en con ex s. McCallum (1997) no ed ha in many episodes o mone a y his o y ins i u ional changes lag behind ac ual policy changes. Musca elli and T ec oci (2000) su eyed e idence o his hypo hesis, o which Musca elli e al. (2000) added new esul s. Doménech e al. (2002) p esen e idence ha led hem, in Doménech e al. (2001), o s udy a model o he EMU A ea wi h da a beginning in 1986:I. The es o he pape is ou lined as ollows. Sec ion 2 discusses an app op ia e op imising model o mone a y policy analysis in he Eu o A ea, desc ibes he da a and p esen s s uc u al s abili y es s. Sec ion 3 b ie ly explains wo al e na i e solu ion- es ima ion p ocedu es and compa a i ely discusses hei esul s. Finally, Sec ion 4 o e s some concluding ema ks. 2. A Model o Mone a y Policy Analysis in he Eu o A ea Ou s uc u al model de i es om a simple op imising amewo k o mone a y policy analysis, in which he loss unc ional o he cen al bank desc ibing i s in e empo al p e e ences is minimised subjec o he dynamic s uc u e o he agg ega e economy. This sec ion se s up he model o op imisa ion, which, in u n, is sol ed in FEP Wo king Pape no. 123, Ma ch 2003 6 sec ion 3. Thus i p esen s and iden i ies he dynamic economic s uc u e - an AD-AS sys em - and he loss unc ional - an in e empo al agg ega ion o quad a ic loss unc ions. Agg ega e Demand and Agg ega e Supply The s uc u e o he Eu o A ea agg ega e economy is modelled as a simple backwa d-looking agg ega e demand - agg ega e supply sys em simila o he one applied by Rudebusch and S ensson (1999) o US da a. Agg ega e demand is basically an IS equa ion exp essed in e ms o u-gap, and agg ega e supply an expec a ions augmen ed Phillips equa ion wi h he sho - e m ade-o be ween u-gap and in la ion. Rudebusch and S ensson's mo i a ion o using his model was h ee old: ac abili y and anspa ency o esul s; good i o ecen US da a; and p oximi y o many policymake s' iews abou he dynamics o he economy, and o he spi i o many policy-o ien ed mac o-econome ic models, including some used by cen al banks. In addi ion, we ha e h ee easons o ou own. Fi s , i has been widely used in ecen empi ical s udies o mone a y policy ules o egimes. Tha is he case, among many o he s, o Fa e o and Ro elli (2001), Dennis (2001), and, o Eu opean coun ies, Pee sman and Sme s (1999), Taylo (1999), and Aksoy e al. (2002). To be su e, he in ensi e use does no necessa ily mean ha his model e ec i ely ep esen s he s uc u e o ac ual de eloped economies - see Cukie man (2001). I e lec s, hough, i s sensible heo e ical and empi ical p ope ies, om which Goodha (2000) s esses he ealis ic inclusion o mone a y ansmission lags. Second, e en hough mos o he uses o he model ela e o he US, i is easonable o expec he s uc u e o he Eu o A ea o be b oadly simila , as bo h a e la ge and FEP Wo king Pape no. 123, Ma ch 2003 7 ela i ely closed economies - see Rudebusch and S ensson (2002). In suppo o his belie , Ag es i and Mojon (2001) ound ha he business cycle o he agg ega e Eu o A ea is simila o he US in se e al espec s, and Angeloni e al. (2002) show how he esponses o he A ea's ou pu and in la ion o mone a y ac ions a e qui e close o hose ypically epo ed o he US. In ac , bo h Pee sman and Sme s (1999) and Taylo (1999) ha e success ully es ima ed his model wi h agg ega e da a o a co e o EMU coun ies. Thi d, he unemploymen gap se ies ha we use has been compu ed wi hin a sys em ha ea u es a simila Phillips equa ion - speci ically, a backwa d-looking e sion o he one in Aguia and Ma ins (2002). We p oceed now wi h he iden i ica ion o he speci ic o mula ion o he Rudebusch and S ensson's AD-AS sys em ha bes i s he Eu o A ea agg ega e da a - qua e ly ime-se ies 1972:I-2001:II. Fo he pe iod 1970-1998, he da a sou ce is he A ea Wide Model Da abase (AWMD) published in Fagan e al (2001), whils o subsequen pe iods compa ible upda es a e aken om se e al issues o he ECB Mon hly Bulle in. The in la ion a e - π - is measu ed h ough he GDP de la o , and he nominal sho - e m in e es a e - i - is he qua e ly a e age o he 3-mon h in e es a e EURIBOR. Ou p oxy o exogenous supply shocks is he de ia ion o impo ed om domes ic in la ion - Im π , in pe cen age poin s. The unemploymen gap - x, in pe cen age poin s - is compu ed as a ime- a ying NAIRU minus he ac ual unemploymen a e. The unobse able NAIRU is compu ed om a backwa d-looking e sion o he unobse ed componen s model es ima ed by maximum likelihood wi h he Kalman il e in Aguia and Ma ins (2002). By using he il e upda ing equa ions om each pe iod, ins ead o he end o sample smoo he , we a e able o sui ably in e p e ou u- FEP Wo king Pape no. 123, Ma ch 2003 8 gap se ies as quasi eal- ime es ima es. In ac , each u-gap is an op imal es ima e in each ime pe iod, gi en he iden i ied model and he in o ma ion a ailable a ha pe iod.3 He e, we clea ly di e om Fa e o and Ro elli (2001) and Dennis (2001), which use es ima es o he gap ob ained a he ime o hei esea ch. Ou quasi eal- ime es ima es o he gap a e concep ually close o he policymake s' eal- ime pe cep ions abou he s a e o he economy. The assump ions abou he iming o in o ma ion ga he ing can be qui e ele an o policy analysis, as has been a gued in he li e a u e, and as can be illus a ed in ou case. In he li e a u e, he impo ance o using da a a ailable o policymake s in eal- ime in ex-pos e alua ions o mone a y policy has been p o usely shown, o he US case, by O phanides (2001a and 2002). Nelson and Nikolo (2001) also epo a pa e n o o icial eal- ime ou pu gap mispe cep ions in he UK du ing he 70s simila o he one iden i ied by O phanides o he US. In bo h cases, he au ho s inspec ed he in o ma ion ac ually used a he mee ings o mone a y policy commi ees.4 He e, howe e , we canno use p ope eal- ime in o ma ion, no only because he e is no Eu o A ea agg ega e eal- ime s a is ical da a o almos he whole sample pe iod, bu also because we e alua e he policy o a no ional cen al bank. Ins ead, we adop a quasi eal- ime app oach, as explained abo e.5 Figu e 2 illus a es, o ou case, he disc epancies be ween ex-pos and quasi eal- ime es ima es. I shows he u-gap se ies gi en by he Kalman smoo he (i.e. using o each pe iod he en i e sample in o ma ion) and he unsmoo hed se ies gi en by he Kalman il e (i.e. using o each pe iod he in o ma ion a ailable up o hen). The di e ence is in e p e able as he quasi eal- ime gap measu emen e o aced by policymake s. FEP Wo king Pape no. 123, Ma ch 2003 15 ela e o pe iods u he ahead. Second, expanding he ho izon would complica e he equa ion and b ing collinea i ies o he sys em, causing g ea di icul ies o es ima ion. We a gue, in addi ion, ha he ou -qua e o ecas ho izon seems o be in line wi h he o ecas ing needs and abili ies o eal wo ld policymake s - see, o ins ance, he mac oeconomic p ojec ions in IMF (2001), and in he G eenbook a ailable a each FED open ma ke commi ee mee ing as discussed in Pe ez (2001). Mo eo e , e idence om es ima ed policy ules sugges s ha ac ual policy in ol es o ecas ho izons o in la ion no beyond ou qua e s – see, o example, O phanides (2001b), and Boi in and Giannoni (2002). Equa ion (5) is join ly es ima ed wi h he sys em (1), gene a ing es ima es o he coe icien s desc ibing he mone a y policy egime - µ , λ , and π * - as well as o he agg ega e-demand and agg ega e-supply coe icien s, and he sys em's inno a ions. Because expec a ions a e eplaced by ac ual obse a ions, es ima ion uses GMM, as i seems easonable o assume ha policymake s use e icien ly he in o ma ion a ailable when o ming expec a ions. Following Fa e o and Ro elli's p ocedu es, we use ou lags o all he sys em's a iables as ins umen s, and base in e ence in a he e oescedas ici y and au o-co ela ion-consis en a iance-co a iance ma ix.11 Employing his me hod in he mo e es ic ed loss unc ion o s ic in la ion a ge ing wi h in e es a e smoo hing is s aigh o wa d, se ing λ o ze o in equa ion (5). An al e na i e o Fa e o and Ro elli's is he me hod ecen ly designed by Dennis (2001) - he ea e equi alen ly designa ed "dynamic p og amming cum FIML" and "Lag angean-FIML" - a e he in e se con ol s a egy used by Salemi (1995). This me hod uses he esul ha wi h a quad a ic objec i e unc ion and linea s ochas ic cons ain s he pos ula ed policymake op imisa ion p oblem i s in o he s ochas ic FEP Wo king Pape no. 123, Ma ch 2003 16 linea egula o p oblem - see Ljungq is and Sa gen (2000) -, and, as such, Chow's (1997) Lag angean solu ion can be employed. The app oach begins by w i ing he dynamic cons ain s in s a e-space o m: 110 ++ + + += ΕCBuAXXA (6) whe e u s ands o he con ol a iable - he in e es a e, i - and X is he ec o o s a e a iables. In ou case (see he Appendix o de ails) [] ' 12121321 ImπiiixxxX −−−−−−−− ∆= ππππ (7) The Lag angean solu ion consis s o in oducing a ec o o Lag ange mul iplie s, and se ing o ze o i s de i a i es in o de o he con ol and s a e a iables, hus ob aining a se o i s -o de condi ions. The mul iplie s and he de i a i es o he policymake objec i e unc ion wi h espec o he con ol and s a e a iables a e w i en as linea unc ions and, oge he wi h (6) and he i s o de condi ions, yield a solu ion o he policymake p oblem ha is an op imal s a e-con ingen linea policy ule gGXu += (8) This ule is compu able, o a speci ic se o alues o he model s uc u al pa ame e s, wi h simple calculus and algeb a - see he Appendix and Chow (1997, sec ions 2.3-2.4, pages 22-25). In ou speci ic case, G is a (1×11) ec o , and he op imal linea policy ule akes he o m Imπgigigxgxgxg gggggi 10291827165 34231210 +++++ + + +++= −−−− −−− π π π π (9) Once supplemen ed wi h an inno a ion, (9) joins he equa ions in (1) in a h ee equa ions sys em. Unde he assump ion o no mali y, he esiduals o his sys em a e used o compu e he da a log-likelihood unc ion, condi ional on he i s 4 obse a ions, which is hen maximised by nume ical me hods wi h espec o he model s uc u al FEP Wo king Pape no. 123, Ma ch 2003 17 pa ame e s - he agg ega e-supply and demand coe icien s, c1 h ough c10, and he policymake 's p e e ence pa ame e s, λ , and µ . The p ocedu e can be simila ly employed in cases o mo e es ic ed loss unc ions, such as one o s ic in la ion a ge ing wi h in e es a e smoo hing - in which case λ is se o ze o in he solu ion equa ions leading o he op imal linea policy ule, wi hou , howe e , changing i s o m. Dennis' app oach consis s o a sequence o s eps in ol ing a componen o dynamic solu ion and ano he o es ima ion. A each s ep, he solu ion componen consis s in using he Lag angean me hod o sol e o he op imal linea policy ule, gi en ce ain alues o he model coe icien s - c1 h ough c10, λ and µ . Then, in he es ima ion componen , his op imal eed-back ule joins he agg ega e-demand and agg ega e- supply equa ions, in a h ee equa ions sys em, om which he model s uc u al coe icien s a e e-es ima ed, by maximum likelihood. Solu ion and es ima ion a e sequen ially epea ed un il bo h con e ge in o a se o es ima es o he s uc u al pa ame e s o he model.12 Since his app oach does no gene a e a di ec es ima e o π *, we compu e i as he sample a e age o he nominal in e es a e minus he es ima e o he eal equilib ium in e es a e - which is gi en by c1/(- c5) in sys em (1). In addi ion o es ima ing he mone a y policy egime, and he Phillips coe icien , measu ing he ade-o be ween he le els o u-gap and in la ion, bo h amewo ks o e some in o ma ion conce ning he ola ili y o he supply shocks, gi en by he s anda d de ia ion o he agg ega e-supply equa ion. Mo eo e , he s anda d e o o he op imising in e es a e equa ion can be seen as an indica ion o he abili y o policymake s o main ain in e es a es close o op imum, and, hus, o main ain he FEP Wo king Pape no. 123, Ma ch 2003 18 economy close o he Taylo cu e. This in e p e a ion is, howe e , subjec o cau ion, as in e se con ol heo y a ibu es his e o o speci ica ion impe ec ions. Eu o A ea 1972-1985 e sus 1986-2001 We now apply compa a i ely he es ima ion p ocedu es jus desc ibed o he case o he agg ega e Eu o A ea. Mo i a ed by he mac oeconomic eco d o he A ea, b ie ly e iewed in sec ion 1, we compa e he esul s be o e and a e 1986. Table 1 summa ises he esul s o ou baseline loss unc ion - lexible in la ion a ge ing wi h in e es a e smoo hing. The le -hand side shows ha , o 1972:I- 1985:IV, bo h p ocedu es es ima e an in la ion a ge somewha abo e 9 pe cen age poin s and a eal equilib ium in e es a e a bi below 1 pe cen age poin , bu ail o es ima e easonable and p ecise coe icien s associa ed o he de ia ions o he gap and in la ion om hei a ge s. The igh -hand side highligh s he change in mone a y policy and mac oeconomic condi ions a e 1986, e ealing ha he in la ion a ge seems o ha e allen below 3 pe cen age poin s, while he eal in e es a e o equilib ium has isen subs an ially o a ound 4.5 pe cen age poin s. Howe e , as in he i s sub-sample, bo h p ocedu es ail o gene a e sensible and p ecise es ima es o λ and µ . Hence, we conclude ha a egime o lexible in la ion a ge ing wi h in e es a e smoo hing is no compa ible wi h he agg ega e Eu o A ea da a, nei he be o e no a e 1986. In able 2 we inspec whe he a loss unc ion wi h s ic in la ion a ge ing and in e es a e smoo hing is mo e app op ia e o desc ibe he Eu o A ea case - a hypo hesis ha seems compa ible wi h he s a u es o he ECB, as men ioned in sec ion 2. Be o e 1986 he weigh o in e es a e smoo hing is no p ecisely es ima ed, a s anda d con idence le els, and he p e ious esul s in e ms o in la ion a ge and equilib ium FEP Wo king Pape no. 123, Ma ch 2003 19 eal in e es a e a e b oadly con i med. The e is some e idence agains he egime o s ic in la ion a ge ing du ing he 1972-1985 pe iod. In ac , he s anda d e o o he esiduals o he op imising in e es a e equa ions is, in bo h p ocedu es, la ge han in able 1 and, u he mo e, he J- es e eals ha he momen s o hogonali y condi ions o GMM es ima ion a e now ejec ed a one pe cen signi icance. In con as o he p e ious esul s, he igh -hand side o able 2 shows ha a mone a y policy egime o s ic in la ion a ge ing wi h in e es a e smoo hing can be well iden i ied and es ima ed o he sample pe iod beginning in 1986. The Eu o A ea in la ion a ge is es ima ed qui e p ecisely a 2.7 pe cen age poin s by bo h p ocedu es, and he equilib ium eal in e es a e is es ima ed - also wi h acco dance be ween p ocedu es - a 4.5 pe cen age poin s. The weigh o in e es a e smoo hing in he policymake 's loss unc ion is s a is ically signi ican a less han 5 pe cen in bo h p ocedu es - e en hough wi h a la ge disc epancy in he es ima es, which is u he discussed below. The esul s a e hus compa ible wi h he hypo hesis o mula ed in sec ion 1 - ha he eme gence o a well-de ined mone a y policy egime a ge ing a low in la ion a e is pa o he explana ion o he imp o emen in he Taylo ade-o obse ed in he agg ega e Eu o A ea since 1986. Using he sub-sample 1986:I-2001:II, we iden i y he agg ega e egime as one s ic ly a ge ing he in la ion a e a 2.7 pe cen age poin s, wi h a signi ican elemen o policy ins umen smoo hing. No ably, his egime iden i ica ion seems o be qui e obus , as i is con i med by he wo al e na i e p ocedu es employed.13 The acco dance be ween ou esul s om he wo me hods may shed some ligh on he disc epancies ound in he o iginal applica ions o he US by Fa e o and Ro elli (2001) and Dennis (2001). The disc epancies be ween hei esul s FEP Wo king Pape no. 123, Ma ch 2003 20 include di e en in e ence ega ding he weigh o he ou pu gap in he policymake 's objec i e unc ion, and di e en in la ion a ge s and equilib ium eal in e es a es. In iew o ou esea ch, maybe such disag eemen s ha e a isen no om he di e en p ocedu es, bu a he om di e ences in sample pe iods, discoun ac o s, and ou pu gap se ies. As o he o he h ee ac o s o ola ili y imp o emen in he Eu o A ea, we ha e al eady checked in sec ion 2 ha he e has been no signi ican change in he agg ega e economic s uc u e in he 80s. In u n, he supply shocks seem o ha e been milde in he second sample pe iod, as he s anda d de ia ion o he Phillips equa ion esidual dec eased by a ound 40 pe cen . Also, he e is some e idence ha he abili y o he no ional policymake o un in e es a es close o hei op imal pa h has imp o ed a e 1986. In ac , wi h a ema kable consis ency, he s anda d de ia ion o he Eule equa ion esidual ell by 42 pe cen , and ha o he op imal linea policy ule ell by 43.5 pe cen . This in e p e a ion, howe e , should be conside ed en a i e, no only because con ol heo y asc ibes a model speci ica ion meaning o he de ia ion o he con ol a iable om i s op imal pa h, bu also because he esiduals ha e di e en meanings ac oss he sub-samples, as he e is no clea policy egime be o e 1986. Taking now a close look a he iden i ied egime o s ic in la ion a ge ing a e 1986, we ind wo s ong indica ions ha he u-gap, in spi e o no being a inal objec i e, has been conside ed aluable in o ma ion o mone a y policy in he agg ega e Eu o A ea. Fi s , i he lagged u-gaps a e excluded om he ins umen se in he GMM es ima ion, esul s a e qui e di e en . No ably, he in e es a e smoo hing weigh is no p ecisely es ima ed, he Phillips elas ici y looses i s signi icance, se e al es ima es change subs an ially, and he s anda d e o o he esidual o he Eule FEP Wo king Pape no. 123, Ma ch 2003 21 equa ion doubles i s alue. Second, as able 3 shows, he op imal linea policy ule ob ained h ough he dynamic p og amming cum FIML app oach indica es ha he policy ins umen eac s subs an ially o he u-gaps. In ac , op imal in e es a es eac sligh ly mo e o each addi ional pe cen age poin o u-gap han o an addi ional poin o he in la ion a e, bo h in he cumula ed sho - un - 0.215 e sus 0.203 - and in he long- un - 2.323 e sus 2.190. Table 3 also shows a clea change in he op imal linea policy ule om he i s o he second sub-sample pe iod - a dec ease in he explana ion o he in e es a e by i s pas and an inc ease in i s eac ion o bo h in la ion and he u-gap. The be e abili y o he op imal linea policy ule o eplica e he second momen s o ac ual in e es a es in he second sample pe iod also indica es he p o ound di e ence be ween he wo e as, as ega ds he exis ence o a de ec able policy egime. Howe e , he op imal linea eed- back ule o 1986:I-2001:II s ill exhibi s a qui e la ge sensi i i y o he policy ins umen o i s pas . The magni ude o his au o- eg essi e e ec is coupled wi h he la ge es ima e o he in e es a e smoo hing weigh ob ained wi hin his me hod - dynamic p og amming cum FIML -, and explains some o he disc epancy be ween in e es a es i ed by he wo app oaches, appa en in igu e 3. No ably, he se ies gene a ed by Lag angean-FIML lags bo h ac ual and Eule -GMM i ed a es h oughou he whole sub-sample, hus exposing he impo ance o he au o- eg essi e elemen o he op imal policy ule in gene a ing he good Lag angean-FIML i . Hence, igu e 3 calls o a close examina ion o he dispa i y be ween he es ima ed weigh s o in e es a e smoo hing in he policymake loss unc ion – µ = 2.210 in Lag angean-FIML e sus µ = 0.013 in Eule -GMM –, which is he majo disc epancy be ween he esul s o he wo me hods. FEP Wo king Pape no. 123, Ma ch 2003 22 In gene al, di e ences in he esul s could de i e om he a ibu es o he econome ic echniques employed in each p ocedu e. Howe e , mo e speci ic di e ences could be mo e di ec ly linked o he disag eemen in he es ima es o µ . Fo example, Sode lind e al. (2002) sugges ha i would be he case o he ho izon unca ion speci ic o he Op imal Con ol cum GMM. Nex , we specula i ely o e wo addi ional speci ic easons, one ela ed o expec a ions and he o he o s a iona i y. In he Eule -GMM app oach he policymake ’s expec a ions a e eplaced by ac ual alues o in la ion, while in he Lag angean-FIML app oach he op imal linea ule is s a e con ingen , he e o e depending only upon obse ed a iables. I he obse ed smoo h pa h o he ac ual in e es a e me ely e lec s he ine i able smoo hness o policymake s’ o ecas s - like Goodha (2000) a gues -, hen he Eule -GMM me hod, yielding a smalle es ima e o he impo ance o in e es a e smoo hing, ends up es ima ing unde lying p e e ences concep ually close o he heo e ical loss unc ion. The o he possible explana ion is ela ed o he di e en ea men o non- s a iona i ies by he wo me hods. The Eule equa ion imposes, by cons uc ion, ha he ela ionship be ween he in e es a e and i s ecen pas depends solely on he discoun ac o - which is calib a ed, no es ima ed. In u n, he Lag angean compu a ion o he op imal policy ule does no es ic he lagged in e es a e coe icien s, hus admi ing non-s a iona y esul s. In ac , he me hod always inds an op imal linea policy ule, e en when he sys em does no each a s eady-s a e – Chow (1997, page 25). S a iona i y can be checked h ough exp essions (6, wi hou inno a ions) and (8) abo e, om whe e he op imal dynamic pa h o he s a e- ec o is ) ~ ~ () ~ ~ ( 1CgBXGBAX +++= + (10) whe e . ~ and, ~ , ~ 1 0 1 0 1 0CACBABAAA −−− === FEP Wo king Pape no. 123, Ma ch 2003 23 The s a e ec o con e ges o an equilib ium – a unique s a iona y dis ibu ion - i and only i he maximum absolu e alue o he cha ac e is ic oo s o ma ix ) ~ ~ (GBA + is s ic ly smalle han uni y – Ljungq is and Sa gen (2000, chap e 4). We ecall ha G is he ec o o he op imal policy ule coe icien s, and GB ~ e lec s he deg ee o smoo hing in he op imal pa h o he in e es a e. Table 4 epo s he maximum eigen alues o he wo sub-samples and he wo policy egimes conside ed in ou es ima ions. E en hough he smalle one co esponds o he mos p ecisely es ima ed egime and sub-sample, he absolu e alues a e all close o one, i.e. e y much on he bounda y be ween s a iona i y and non-s a iona i y. This does no seem o be a p oblem in o he mone a y policy s udies - close o ou s in he use o dynamic p og amming bu wi h calib a ed ins ead o es ima ed policy p e e ences - ha o en epo maximum eigen alues e y close o uni y.14 Howe e , we suspec ha in cases like ou s, whe e dynamic p og amming is linked o he es ima ion o all he pa ame e s, such quasi non-s a iona i y migh gene a e nume ical p oblems in es ima ing policymake s' p e e ences, including he ele ance o in e es a e smoo hing. 4. Concluding Rema ks The empi ical esea ch in his pape unco e s a well-de ined mone a y policy egime s a ing in 1986 in he agg ega e Eu o A ea, in spi e o he ins i u ional p e alence o na ional mone a y policies un il 1999. Rema kably, bo h al e na i e solu ion-es ima ion me hods employed - op imal con ol cum GMM and dynamic p og amming cum FIML - iden i y a egime o s ic in la ion a ge ing wi h signi ican in e es a e smoo hing, wi h a a ge a ound 2.7 pe cen age poin s. The unemploymen gap, al hough no showing up as an a gumen in he objec i e unc ion o he no ional mone a y au ho i y, FEP Wo king Pape no. 123, Ma ch 2003 24 is a ele an elemen o he in o ma ion se used in policy o mula ion. Thus, ou cu en emphasis in quasi eal- ime in o ma ion conce ning he gap is well jus i ied, bu so i is i s eplacemen by eal- ime da a as i becomes a ailable o u u e esea ch conce ning he analysis o ECB policymaking. The eme gence o he egime in 1986 has been concu en wi h an appa en imp o emen o he ola ili y ade-o be ween in la ion and unemploymen gap since he mid-80s. The esul s, always acco ding o bo h me hods, also indica e ha o he imp o ing ac o s ha e been milde supply shocks and some inc ease in he abili y o policymake s o se he in e es a e close o i s op imal pa h. Simila conclusions abou he ac o s o ola ili y imp o emen - al hough da ed ea lie in he 80s - ha e a isen in he esea ch o he US case by Fa e o and Ro elli (2001) and Dennis (2001). A s uc u al b eak in he mid-90s may also ha e played a ole in educing ola ili y, bu i is oo soon o isola e i s causes and e ec s - a leas wi hin ou amewo k. The unca ion o he 1986-2001 sub-sample a 1995 - no epo ed in sec ion 3 - esul s in an imp ecise es ima ion o he loss unc ion pa ame e s, especially wi h Eule -GMM, which is mo e sensi i e o small sample p oblems. S ill, he Lag angean-FIML es ima e o he weigh o in e es a e smoo hing does no change ma kedly, and he inclusion o unemploymen as a policy objec i e is clea ly ejec ed. The es ima e o he in la ion a ge , in u n, is highe in 1986-1995 han in 1986-2001. Hence, a he momen we can only conjec u e ha he mid-90s s uc u al b eak de ec ed in he AD-AS sys em is ela ed o a educ ion in he desi ed le el o in la ion, bu no o a signi ican change o he emaining ea u es o he policy egime. We con i m ha in e es a e smoo hing is an open p oblema ic issue, no only wi h ega d o heo e ical explana ions bu also conce ning empi ical es ima ion. The wo FEP Wo king Pape no. 123, Ma ch 2003 31 No es (con inued) Goodha (1998 and 2000); (i ) conce ns wi h epu a ion and c edibili y - Goodha (1996); and ( ) conce ns wi h he ze o bound o nominal in e es a es - Rudebusch (2001). 10 Applied o he Eu o A ea, his may seem a odds wi h he Bundesbank eco d o explici mone a y a ge s since 1974, and wi h he ECB o mal i s pilla o policy, which is a mone a y agg ega e g ow h a ge ing - see ECB (1998). Bu , in ac , he Bundesbank beha ed much mo e as an in la ion a ge e han a money a ge e - see Von Hagen (1995) and Be nanke and Miho (1997) -, he ole o money a ge s being mos ly poli ical, as a gued by Von Hagen (1999). In wha ega ds he ECB, se e al ecen s udies ha e ound no e idence ha money has been ele an in i s policy decisions - Miho (2001) and Begg e al. (2002). 11 We use And ews and Mohanan's (1992) p e-whi ening and a Ba le Ke nel o weigh he au o-co a iances, wi h a bandwi h es ima ed wi h And ews' (1991) es ima o . We employ he wo-s ep es ima o , which is a one-s ep weigh ing ma ix e sion o GMM. Co a iance es ima ion is di icul in cases, like ou s, o se ially co ela ed momen condi ions and small samples - see Hansen e al. (1996) and he o he a icles in ha special edi ion o he Jou nal o Business and Economic S a is ics ( ol. 14, n. 3). Ou choice o GMM es ima o d aws la gely om Flo ens e al.'s (2001) Mon e Ca lo esul s indica ing ha he wo-s ep es ima o gene a es es ima es close o maximum likelihood and is no s ongly biased in he es ima ion o o wa d-looking Taylo ules. 12 Richa d Dennis' GAUSS code has been an in aluable basis o ou s', which implemen s he nume ical solu ion by linea app oxima ions desc ibed in Chow (1997). FEP Wo king Pape no. 123, Ma ch 2003 32 No es (con inued) 13 We ha e also checked he sensi i i y o he esul s o possibly ea lie da es o eme gence o he well-de ined mone a y policy egime. 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