Taylor rules for monetary policy in a closed economy

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1 Taylor rules for moneary policy in a closed economy Peros Varhaliis Ahens Universiy of Economics & Business Firs Draf: February 211 Absrac This paper sudies moneary sabilizaion policies in a DSGE model wih Calvo ype nominal xiies and imperfec compeiion. We model Moneary policy o follow alernaive Taylor-ype rules. We nd ha he moneary auhoriy can guaranee he join sabilizaion of in aion and oupu hrough he baseline Taylor rule (Taylor 1993) wih srong enough reacion o in aion and no reacion o he oupu gap. Moreover, we nd ha he join sabilizaion of in aion and oupu requires neiher he esimaion of unobservable variables nor he opimal choice of reacion coe ciens. Given ha reacion coe ciens always guaranee Blanchard-Kahn condiions a good moneary policy can be implemened hrough an operaional Taylor ype rule which responds o observed arges already known wih cerainy a he ime of moneary policy acion. Keywords: Taylor Rules, Counercyclical Moneary Policy JEL Classi caions: E52, E58 I am graeful o my advisor Aposolis Philippopoulos for inspiring and guiding me o his opic. I would like o hank Vanghelis Vassilaos for helpful commens and suggesions. I grealy appreciae helpfull commens by paricipans a he 3rd Workshop in Macroeconomics a Ahens Universiy of Economics and Business. All errors are mine. I acknowledge nancial suppor from he Greek Minisry of Educaion and he EU under he Iraklios II research fellowship program. Address for correspondence: Peros Varhaliis, Economics Deparmen, Ahens Universiy of Economics & Business, Paissiwn sree, Ahens, Greece. pvarhaliis@aueb.gr 1

2 1 Inroducion In recen years Taylor-ype rules have considered a widespread acknowledgemen for he analysis of pracical policy issues as well as for he assesmen of several heoreical open debaes. In his paper, we sudy moneary policy sabilizaion issues in a DSGE model wih nominal xiies (Calvo-ype) and imperfec compeiion. Following recen empirical lieraure such as Smes & Wouers (23) and Rabanal & Tuesa (21) who nd ha he reacion funcion of Cenral Banks can be summarized by Taylor-ype rules and recen heoreical models such as Schmi-Grohé & Uribe (27) who show ha simple Taylor rules can implemen opimal policy of Ramsey ype, we model he moneary auhoriy o follow simple Taylor-ype rules. Our scope is o analyze he e ecs of alernaive moneary sabilizaion policies so we keep scal policy simple and we assume ha he moneary auhoriy worries abou in aion and oupu. Our measure of sabilizaion is he uncondiional second momen of in aion and oupu. In his model, i was prooved ha he moneary auhoriy can avoid he rade-o beween in aion and oupu sabilizaion, so he goal of he moneary auhoriy is o sabilize joinly in aion and oupu. We focus on hree key moneary policy issues: i) We ask wheher moneary policy should reac or no o he oupu gap. Several auhors argue agains counercyclical moneary policy mainly because he bes operaing arge for he oupu is unobservable and ofen misspeci ed. Thus, a srong counercyclical reacion o a misspeci ed operaing arge for oupu causes inrinsic volailiy in he economy which can be avoided. ii) We ask which is he bes operaing arge for oupu, given ha moneary policy responds counercyclically. We nd ha his is he naural level of oupu, i.e. he oupu ha will prevail under exible prices. However, we nd ha counercyclical moneary policy generaes a rade-o beween he goals of moneary policy (sabilizaion of in aion and oupu) under all he operaing arges we examine and menioned in he relevan lieraure excep from he naural oupu. iii) We sudy if a moneary policy wih good sabilizaion properies can be implemened hrough an operaional Taylor rule. Several auhors argue ha simpliciy and operaionaliy are crucial for he successfull implemenaion of moneary policy. Such a rule is of ineres because i requires minimal informaion from he par of he policy maker, as he policy insrumen (he nominal ineres rae in our case) can be se as a funcion of easily observed macroeconomic indicaors and i makes he communicaion of he moneary policy arges o he public simple. Moreover, Orphanides (2) poins ou ha no only are he expecaion of in aion and he naural oupu measured wih saisical errors bu also curren in aion and oupu can be measured wih serious errors from real ime daa. Based on his criique, we use he di erence rule, proposed by Schmi-Grohe & Uribe (27), in which he 2

3 policy insrumen is se as a funcion of variables already known wih cerainy when moneary policy akes acion and we relax heir opimal choice of reacion coe ciens o nd if an operaional Taylor rule su ces o sabilize he economy. Hopefully, we nd ha his rule can replicae and in some cases overperform all Taylor rules we examine and acually i can yield resuls very close o he sric in aion argeing policy which is near opimal in his model. The remainder of he paper is organized in ve secions. Secion 2 presens he model, he decenralized equilibrium and policy. Secion 3 presens he calibraion and he long-run soluion of he model. Secion 4 discusses alernaive moneary policies and he key resuls of he paper and secion 5 concludes. In echnical appendix you can nd he analyical derivaion of he model equilibrium described in Secion 2, compuaional issues and some addiional resuls (graphs and ables). 2 The Model 2.1 Households There is a represenaive household indexed by j. Household j yields uiliy from a consumpion index C (j) ; real money balances m (j) and disuiliy from hours worked N (j) : 1X U (C (j); m (j) ; N (j)) (1) = The funcional form of uiliy is given by U (j) = [C(j)]1 1 + [m(j)]1 1 j maximizes (1) by facing each period is nominal budge consrain: N (j) : Household P C (j) + P X (j) + B (j) + M (j) = R 1 B 1 (j) + M 1 (j) + W N (j) + R k K 1(j) T l (j) + (j) (2) B 1 are privae nominal bonds, R 1 is he gross nominal ineres rae, (j) are nominal pro s, T l (j) are governmen lump-sum axes, M 1 are money holdings, K 1 is capial, W and R k are nominal wage and he reurn on capial respecively. Capial accumulaes according o: K (j) = (1 ) K 1 (j) + X (j) (3) is a consan depreciaion rae. Finally, C (j) and X (j) are consumpion and invesmen 3

4 Dixi-Sigliz (1977) aggregaors over all di ereniaed goods i 2 [; 1] : Z 1 C (j) = [C (i; j)] 1 1 di (4) Z 1 X (j) = [X (i; j)] 1 1 di is he elasiciy of subsiuion among he di ereniaed goods i: Household allocaes is consumpion among goods i by maximizing (4) subjec o a given expendiure Z (j) R 1 P (i) C (i; j). As in Schmi-Grohé & Uribe (27) we assume ha household solves an idenical problem in order o allocae is invesmen among di ereniaed goods i (see appendix). Solving hese problems we obain he demand for good i : P (i) X (i; j) + C (i; j) = (X (j) + C (j)) (6) P R 1 where P = P (i) di is he aggregae price level. Household j rs order condiions from he uiliy maximizaion problem are: 1 C +1 (j) P = E R C (j) (7) P +1 C (j) = E h(1 ) + r k +1 (5) i C +1 (j) (8) and he rasversaliy condiion. [m (j)] C (j) = R 1 (9) R N (j) C (j) = w (1) 2.2 Governmen Governmen solves an idenical problem wih household j o allocae is expendiure among di ereniaed goods i : Z 1 G = G (i) 1 1 di (11) 4

5 Thus, demand for good i from governmen is given by: P (i) G (i) = G (12) Governmen nances governmen expendiures by seignorage revenues and lump-sum axes so he governmen budge consrain in nominal erms is given by: P T + M = M 1 + P G (13) Policy follows simple policy rules analyzed in nex secion. 2.3 Moneary Policy We assume ha he Cenral Bank follows simple Taylor-ype feedback rules following recen lieraure (see Clarida, Gali & Gerler 21, Schmi-Grohe & Uribe 27, Gali 28). We consider Taylor ype rules and compare hem o he baseline Taylor rule: log R R = log + y log Y Y (14) where ; Y are he operaing arges se by he Cenral Bank. We consider alernaive operaing arges for he sabilizaion of he economy. 2.4 Fiscal Policy We focus on moneary policy issues so we keep scal policy simple. Thus, he scal auhoriy ses he governmen spending oupu raio (s g periods: G Y ) equal o is seady-sae value for all s g = sg (15) 2.5 Firms We assume a coninuum of monopolisic rms i 2 [; 1] : Every period each rm i faces a Calvo ype nominal xiy. Thus, i faces an exogenous probabiliy ha canno se is price, so when i ses is new price P (i) a period anicipaes ha may keep i xed wih probabiliy k1 for he nex k periods: Firm i maximizes he sum of expeced pro s for he nex k periods: 1 In he appendix we solve rm i s pro maximizaion problem wih indexaion o rend in aion, so he fracion of rms which canno reopimize updae heir prices o seady-sae in aion, see Ascari (24) for a relevan discussion. 5

6 subjec o: 1X max k E fq ;+k (P (i)y +k (i) +k(y +k (i)))g P (i) k= where Y d P Y +k (i) = (i) Y+k d (16) P +k C + X + G is aggregae demand,q ;+k is he sochasic discoun facor and (::) is he minimum cos funcion derived in he appendix. We assume perfec compeiion in facor markes and an idenical Cobb-Douglas producion funcion Y (i) = A K a (i) N 1 for all rms i: The soluion of he pro maximizaion problem is given by he price seing rule: ( 1X P k E Q (i) ;+k Y d P +k k= +k P (i) 1 a (i) +k ) = (17) We proove in he appendix ha he marginal cos is only a funcion of he facor inpus prices because of he consan reurns o scale echnology, so he nominal marginal cos is idenical across all rm i s: +k = MCn +k (i) = MCn +k Firms behaviour can be summarized by equaion (17) and he demand for labour and capial: [Demand for Labour] : w = MC (1 a)a K (i) a N (i) a (18) [Demand for Capial] : r k = MC aa K (i) a 1 N (i) 1 a (19) 2.6 Aggregaion and Price Dispersion Yun (1996) shows ha in order o obain a relaion fo aggregae oupu in erms of he aggregae facor inpus, we need o denoe wo auxiliary indices. Thus, we aggregae (16) across i: Z 1 Y (i) di = Z 1 ( P (i) P Y d ) di (2) 6

7 In (2) we denoe he auxiliary indices Y R 1 Y (i) di = A K a N 1 a and R P 1 P (i) 1 di : Imposing he equilibrium condiion Y = Y s = Y d relaion beween he auxiliary and he consisen aggregae oupu index: we ge a Y = h P 1 P i Y = h P 1 P i A K a N 1 a (21) Ascari (24) nds ha price dispersion resuls a loss of oupu when seady-sae gross in aion is higher han uniy. Also, he shows ha a rs order approximaion of his model around a posiive in aion seady-sae may yield implausible dynamic behaviour for he endogenous variables. To avoid a counerfacual dynamic behaviour of his model Yun (1996) assumes ha he fracion of rms which canno reopimize in period updae heir price o seady-sae in aion. In appendix, we solve he pro maximizaion problem of rm i under indexaion o rend/seady-sae in aion, however our resuls holds independen of he indexaion o rend in aion. 2.7 Decenralized Equilibrium: h i A decenrelized equilibrium is a vecor of prices P = P R k W R ; a vecor of allocaions for household H = K s N s C M d a vecor of allocaions for rms F = h i, h i h i such Y K d N d and a vecor of allocaion for governmen M s G ha: a) Household chooses H in order o maximize is uiliy subjec o heir budge consrain (2) given he vecor of prices P, heir iniial nominal wealh R 1 B 1 + M 1, capial iniial endowmen K 1 and policy: b) The fracion of monopolisic rms 1 choose a new price P in period in order o maximize a sequence of pro s subjec o a sequence of demands for heir di ereniaed producs (16), given he vecor of prices P and heir echnology. The oher fracion canno rese heir prices so hey se heir previous period price (or hey updae heir prices each period wih seady sae in aion level ; we solve for eiher case in appendix). c) Moneary auhoriy sais es every period is budge consrain (13) by seing is insrumens (see below). e) The vecor of prices P is such ha all markes clear: [Goods Marke] : Y = G + X + C 7

8 [Labour Marke] : N s = N d [Capial Marke] : K s = K d [Bonds Marke] : B = [Money Marke] : M s = M d When moneary auhoriy uses as is insrumen he nominal ineres rae i commis o saisfy he money demand which arises a any given level of he nominal ineres rae. The decenralized equilibrium given policy can be summarized by 13 equaions and 13 endogenous variables 2 h Y C N X r k MC w K m i and one exogenous variable [A ] : Households: ( 1 C +1 = E R C 1 +1 ) (22) C = E h(1 ) + r k +1 i C +1 (23) w = N C (24) Firms: m C = R 1 R (25) 2 In appendix we ransform he nominal variables in raios following Schmi-Grohe & Uribe (27). We de ne hree new variables, gross in aion P P P 1 ; price dispersion P and an auxiliary variable P P : 8

9 1X >< k E k= >: or wih indexaion Q ;+k 6 4 ky i=1 +i 7 5 Y +k 1 MC +k 8! ky >= +i = (26) i= 9 9 >; 1X k k >< E Q ;+k D +k k 1 P +k ky k= >: i=1 +i >= 1 MC +k >; = w = MC (1 a)a K a N a (27) r k = MC aa K a 1 N 1 a (28) Consrains & Indices: Y = C + X + s g Y (29) Y = 1 A K a N 1 a (3) K = (1 )K 1 + X (31) 1 = + (1 ) ( ) 1 (32) or wih indexaion 1 = () 1 + (1 ) ( ) 1 = 1 + (1 ) (33) or wih indexaion = () 1 + (1 ) 9

10 + m = m 1 + s g Y (34) Moneary policy ses he nominal ineres rae [R ] according o (14) and scal policy ses he governmen oupu raio s g = sg consan and equal o is seady-sae value. 3 Calibraion & Long-Run Soluion In his sudy we aim o discuss moneary policy issues for Euro area. We consider Euro area as a closed economy, so we calibrae he srucural parameers of our model by mainly following Andrés & Domenech (26) who sudy a similar model for Euro area. Srucural Parameers Descripion Parameer Value Time Preference.9926 Risk Aversion Coef. 1 Depreciaion Rae.21 Price Rigidiy Parameer 3/4 Price Elasiciy of Demand 6 Share of Capial a 1/3 Elasiciy of Real Money Balances 3.42 Labour Elasiciy 1 Table 1 Moneary policy ses he long-run nominal ineres rae R = 1:1237 such ha seady sae in aion is = 1:2 :25. We assume ha he governmen spending o oupu raio is s g G Y = :2; a value very close o he Euro-zone average: Table 2 shows he seady-sae values of he endogenous variables: 1

11 Seady-Sae Values (Quarerly) Y C N X r k MC w k m s l Table 2 We simulae he model around his seady-sae using sandard mehods (i.e. Klein 1998). We assume ha he economy ucuaes around his seady-sae due o produciviy shocks which follow an AR(1) process: wih sandard deviaion a = :62 and persisence a = :8: log (A ) = a log (A 1 ) + a (35) 4 Policy Resuls Following recen moneary lieraure ([5],[7],[8],[12],[13] and [14]) we seek for Taylor-ype rules which saisfy wo crieria. Firs, he Taylor rule should be implemenable such ha he moneary auhoriy always guaranees a unique locally sable equilibrium (see appendix-sabiliy), all he Taylor rules and reacion coe ciens are chosen so as o always saisfy his crierion. Second, we prefer aylor-ype rules which are simple and operaional. A simple Taylor rule ses he nominal ineres rae as a funcion of a small number of easily observed macroeconomic indicaors. Moreover, he operaional arges/macroeconomic indicaors should require he minimal informaion from he par of policy maker (see Schmi-Grohe and Uribe 27). 4.1 Baseline Taylor Rule: Reac o he oupu gap or no? We de ne as he baseline Taylor rule, he reacion funcion (14) when he operaing arges for in aion and oupu are se equal o heir seady-sae values (Y = Y; = ) : This means a yearly in aion rae equal o 2% which is consisen wih ECB long-run in aion arge. In his benchmark case we ask wheher he moneary auhoriy should follow a counercyclical moneary sance. We examine his simple case of he Taylor rule because : i) i is he proposal made by Taylor 1993, ii) i is realisic and simple because he Cenral Bank reacs o a long-run operaing arge for he oupu and does no need o adjus each period is arge, iii)oher measures which are examined in nex secion are unobservable and require oo 11

12 much informaion in order o be implemened. We nd ha counercyclical moneary policy generaes a rade o beween in aion and oupu sabilizaion, so i sabilizes oupu bu a he cos of large in aion volailiy (his is imporan,as Woodford (23) shows, because in aion volailiy deerioraes welfare). If moneary policy swiches on he counercyclical reacion o he baseline rule (14) equal o y = :5 which is a value consisen wih empirical esimaes for ECB, see Gerlach & Schnabel (2), he sandard deviaion of oupu will be reduced from :163 o.93 bu in aion volailiy will increase from :5 o :71 (see Table 1 in he appendix). In his model policy inervenion is jusi ed by he presence of wo fricions, i.e. saggered prices and imperfec compeiion. In he baseline Taylor rule, moneary policy should reac only o deviaions of he acual in aion from is arge in order o replicae he exible price equilibrium, while should no respond o he oupu gap because i generaes in aion volailiy. The message from his exercise is ha moneary policy should focus on undoing he disorion which arises from he saggered price mechanism and avoid counercyclical reacion o he oupu gap. 4.2 Alernaive Operaing Targes for Oupu In his secion we examine alernaive operaing arges for oupu. There are several operaing arges proposed in he relaed lieraure, in his secion we show ha he resul of he previous secion holds for he majoriy of he operaing arges proposed in he lieraure and ha he bes operaing arge is he naural oupu (de ned below), however he gains are no quanaiaively signi can. So, we compare he second momens of in aion and oupu when he operaing arge for oupu is respecively he naural oupu which is he oupu ha will prevail under exible prices and imperfec compeiion ( rs row in Table 3), he e cien level of oupu which is he oupu ha will prevail under exible prices and perfec compeiion (second row), las period oupu so moneary policy responds o he growh rae (hird row) and he baseline case i.e. seady-sae oupu. We se he counercyclical policy response y equal o.5, which is he value proposed by Taylor and also i is very close o he acual empirical esimaes for Euro area 3. A summary of resuls are presened a Table 3. In erms of he join sabilizaion of in aion and oupu i is beer o reac o he naural oupu, while he wors scenario is when he Cenral Bank reacs o seady-sae oupu. Moreover, he e cien level of oupu desabilizes in aion and leads o a burs of mean in aion. This is 3 However, empirical ndings are no clear for he acual counercyclical reacion of he ECB wih y varies wihin he range from o 3, depending on he speci caion and he daa available o he economerician. So we examine he whole se for he policy parameer space y ; 2 (; 3). In he appendix you can nd a gure illusraing ha he sabilizaion ordering of he operaing arges for oupu remains he same for he whole policy space as for y = :5: 12

13 an expeced resul, because he e cien level of oupu is always higher han he he disored level of oupu so he nominal ineres is always lower han is seady-sae value and mean in aion is very large. Table 3:Alernaive Operaing Targes De niion y = :5 Sandard Deviaions Naural Oupu Y T Y n sd (Y ) = :16 sd ( ) = :4 E cien Oupu Y T Y eff sd (Y ) = :161 sd ( ) = :7 Las Period Oupu Y T Y 1 sd (Y ) = :124 sd ( ) = :18 Long-Run Oupu Y T Y sd (Y ) = :93 sd ( ) = :71 Noes: In he case where he operaing arge is he e cien level of oupu he mean in aion is exremely large (= 1:235). Thus, e cien counercyclical moneary policy requires a lo of informaion and does no o er quaniaively imporan sabilizaion of he economy. While when he operaing arges are se equal o easily observed measures of oupu (long-run or previous period oupu) he losses in erms of higher volailiy of in aion are quaniaively larger. 4.3 Sric In aion Targeing The analysis in secions (4.1) and (4.2) yields wo imporan resuls concerning counercyclical moneary policy. Firs, counercyclical moneary policy increases signi canly he volailiy of in aion for several operaing arges for oupu. Second, he correc choice of he operaing arge for oupu requires oo much informaion 4 from he par of he policy maker while i only achieves small improvemen in he join sabilizaion of oupu and in aion. In our seup, i is beer no o responding o he oupu gap. So, he polar case of sric in aion argeing is ineresing because i is simple and easy o communicae o he public as well as in his seup guaranees he bes sabilizaion resuls. In order o achieve he sric in aion argeing case hrough he Taylor rule we se! 1 and y = : Thus, acual in aion is always equal o 4 For a Cenral Bank o respond o he naural oupu needs a srucural model and esimaion from real ime daa. 13

14 is arge while he sandard deviaion of oupu falls o.157. Thus, sric in aion argeing no only achieves zero volailiy of in aion bu also he minimum volailiy of oupu among he policies we examined. 4.4 Operaional Taylor rule In his secion we examine he sabilizaion properies of an operaional Taylor-ype rule. Recens leading academic papers as Orphanides 21, McCallum 1999 and McCallum & Nelson 1999 dispue he abiliy of policy makers o observe he operaing arges suggesed by he heoreical models i.e. naural or seady sae oupu. In addiion, hey show ha policy insiuions may esimae wih saisically signi can errors curren in aion and oupu from real ime daa. Below, we analyse he performance of an operaional Taylor rule proposed by Schmi-Grohé & Uribe (27), in which he nominal ineres rae is se as a funcion of previous periods growh raes: R log = log R 1 R 1 R 2 + log 1 Y 1 + y Y 2 Taylor rule (36) requires informaion ha is already known in period wih cerainy. We simulae he model when he policy reacion coe ciens are chosen opimally as in Schmi- Grohé and Uribe (27) = :77; :75 & y = :2 : However, an operaional Taylor rule should require minimal informaion from he par of he policy maker. Thus, we relax opimaliy assumpion and choose some sandard values for he reacion coe ciens which guaranee local sabiliy (see he gure in appendix). In Table 4 we observe ha rule (36) performs beer han all he Taylor rules ha we examine and very close o he case of sric in aion argeing. Addiionally, he Cenral Bank does no need o choose opimally he reacion coe ciens in order o achieve he join sabilizaion of in aion and oupu. (36) 14

15 Table 4: Operaional versus Theoreical Taylor SGU 27 (Opimal) SGU 27 (Sandard) Theoreical Taylor sd (Y ) = :156 sd ( ) = :1 sd (Y ) = :151 sd ( ) = :4 sd (Y ) = :16 sd ( ) = :4 5 Conclusions Noes: Sandard means = ; = 1:5 & y = :1. As heoreical Taylor rule we de ne equaion (14) when he operaing arge for oupu is he naural oupu and he reacion coe ciens = 1:5 & y = :5 In his paper we aim o sudy he sabilizaion properies of moneary policy in a closed economy. We examine moneary policies which can be implemened by Taylor ype rules. Moneary policy goal is he join sabilazion of in aion and oupu from heir policy arges. Our crierion o evaluae alernaive moneary policies is he volailiy of in aion and oupu. Our main coclusions are: Firsly, moneary policy can guaranee he join sabilizaion of in aion and oupu hrough he baseline Taylor rule wih a srong enough reacion o in aion and no reacion o he oupu gap. Secondly, a counercyclical moneary sance o almos all alernaive operaing arges for oupu ha we examine, generaes a rade-o beween oupu and in aion sabilizaion excep he case where he moneary auhoriy reacs o deviaions from he naural oupu (i.e. he oupu ha will prevail under exible prices). This resul con rms he proposal ha moneary auhoriy should focus on in aion argeing. Thirdly, we nd ha he join sabilizaion of in aion and oupu requires neiher he esimaion of unobservable variables nor he opimal choice of reacion coe ciens. Given ha reacion coe ciens always guaranee Blanchard-Kahn condiions a good moneary policy can be implemened hrough simple and operaional Taylor ype rules ha respond o easily observed arges already known a he ime of moneary policy acion. References [1] Andrés, Javier and Rafaél Domenech,26.Auomaic Sabilizers, scal rules and Macroeconomic Sabiliy European Economic Review 5,

16 [2] Ascari, Guido 24.Saggered Prices and Trend In aion: Some Nuisances Review of Economic Dynamics 7, [3] Calvo, Guillermo, 1983.Saggered Prices in a Uiliy Maximizing Framework Journal of Moneary Economics 12, [4] Clarida,Richard,Gali,Jordi and Mark Gerler,1999.The Science of Moneary Policy:A New Keynesian Perspecive Journal of Economic Lieraure 37, [5] Gali Jordi,28.Moneary Policy,In aion and he Business Cycle:An Inroducion o he New Keynesian Framework Princeon Universiy Press. [6] Gerlach, Sefan and Ger Schnabel, 2.The Taylor rule and ineres raes in he EMU area Economic Leers 67, [7] McCallum, Bene, 1999.Issues in he Design of Moneary Policy Rules in J. B. Taylor and M. Woodford, Handbook of Macroeconomics, Norh-Holland. [8] McCallum, Benne and Edward Nelson, 1999.Performance of Operaional Policy rules in an Esimaed Semiclass Srucural Model in J. B. Taylor, Moneary Policy Rules, Universiy of Chicago Press. [9] Orphanides, Ahanasios, 21.Moneary policy Rules Based on Real-Time Daa American Economic Review 91, [1] Rabanal, Pau and Vicene Tuesa, 21.Euro-Dollar Real Exchange Dynamics in an Esimaed Two-Counry Model: An Assessmen Journal of Economics Dynamics and Conrol 34, [11] Schmi-Grohé,Sephanie and Marin Uribe,26.Opimal Simple and Implemenable Moneary and Fiscal Rules:Expanded Version NBER Working Paper [12] Schmi-Grohé,Sephanie and Marin Uribe,27.Opimal Simple and Implemenable Moneary and Fiscal Rules Journal of Moneary Economics 54, [13] Smes, Frank and Raf Wouers, 23.An Esimaed Dynamic Sochasic General Equilibrium of he Euro Area Journal of European Economic Associaion 1, [14] Woodford, Michael, 23.Ineres Raes and Prices: Foundaions of a Theory of Moneary Policy, Princenon Universiy Press. 16

17 [15] Yun,Tack,1996.Nominal Price Rigidiy, money supply endogeneiy, and business cycles Journal of Moneary Economics 37,