Research Division Federal Reserve Bank of St. Louis Working Paper Series

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1 Research Divisin Federal Reserve Bank f St. Luis Wrking Paper Series Mnetary Plicy, Determinacy, and Learnability in a Tw-Blck Wrld Ecnmy James Bullard and Eric Schaling Wrking Paper A May 2006 FEDERAL RESERVE BANK OF ST. LOUIS Research Divisin P.O. Bx 442 St. Luis, MO The views expressed are thse f the individual authrs and d nt necessarily reflect fficial psitins f the Federal Reserve Bank f St. Luis, the Federal Reserve System, r the Bard f Gvernrs. Federal Reserve Bank f St. Luis Wrking Papers are preliminary materials circulated t stimulate discussin and critical cmment. References in publicatins t Federal Reserve Bank f St. Luis Wrking Papers (ther than an acknwledgment that the writer has had access t unpublished material) shuld be cleared with the authr r authrs.

2 Mnetary Plicy, Determinacy, and Learnability in a Tw-Blck Wrld Ecnmy James Bullard Eric Schaling y 29 May 2006 z Abstract We study hw determinacy and learnability f wrldwide ratinal expectatins equilibrium may be a ected by mnetary plicy in a simple, tw cuntry, New Keynesian framewrk under bth xed and exible exchange rates. We nd that pen ecnmy cnsideratins may alter cnditins fr determinacy and learnability relative t clsed ecnmy analyses, and that new cncerns can arise in the analysis f classic tpics such as the desirability f exchange rate targeting and mnetary plicy cperatin. Keywrds: Indeterminacy, learning, mnetary plicy rules, new pen ecnmy macrecnmics, exchange rate regimes, secnd generatin plicy crdinatin. JEL cdes E58, E61, F31, F41. Research Department, Federal Reserve Bank f St. Luis, bullard@stls.frb.rg. Any views expressed are thse f the authrs and d nt necessarily re ect the views f the Federal Reserve Bank f St. Luis r the Federal Reserve System. y Department f Ecnmics University f Jhannesburg, and CentER fr Ecnmic Research, Tilburg University, esc@eb.rau.ac.za. This paper was written while Eric Schaling was a visiting schlar at the Research Department f the Federal Reserve Bank f St. Luis. z This paper was presented at the third cnference f the Internatinal Research Frum n Mnetary Plicy at the ECB. The Frum is spnsred by the Eurpean Central Bank, the Bard f Gvernrs f the Federal Reserve System, the Center fr German and Eurpean Studies at Gergetwn University and the Center fr Financial Studies at Gethe University. Earlier versins were als presented at CentER, the University f Jhannesburg, Bnn University, the BIS, the Bank f England, De Nederlandsche Bank, the University f Cape Twn and the Suth African Reserve Bank. Helpful cmments by Jrdi Gali, Martin Ellisn, Albert Marcet, Vicente Tuesta and Ed Nelsn are gratefully acknwledged.

3 1 Intrductin 1.1 Overview New Keynesian macrecnmic mdels have becme a wrkhrse fr studying a variety f mnetary plicy issues in clsed ecnmy envirnments. An imprtant cmpnent f this e rt has been the develpment f the idea that equilibrium determinacy and learnability may be signi cantly in uenced by mnetary plicy chices. 1 Recently, simple extensins f the New Keynesian mdel t pen ecnmy envirnments have been develped. Our primary cncern in this paper is t prvide an analysis f the extent t which the ndings cncerning determinacy and learnability fr the clsed ecnmy New Keynesian framewrk may be altered when pen ecnmy cnsideratins are brught t bear. Our learnability criterin is that f Evans and Hnkaphja (2001). Our apprach t this questin is t adpt a simple framewrk fr a twcuntry wrld due t Clarida, Gali, and Gertler (2002). This framewrk prvides ne straightfrward extensin f the New Keynesian mdel t tw cuntries and allws cmparisn t the mre cmmn single cuntry and small pen ecnmy analyses as special cases. We fcus n the tw plar cases f xed and exible exchange rates, and ask the questin hw determinacy and internatinal mnetary plicy transmissin are a ected by the exchange rate regime. 1.2 Main ndings The main ndings under exible exchange rates are as fllws. Instrument rules which are fcussed n dmestic in atin and dmestic utput gaps lead t wrld determinacy and learnability cnditins which must be met in each ecnmy independently f whether they are met in the partner ecnmy. Fr targeting rules, this result has a natural cunterpart when plicymakers in 1 See, fr instance, Wdfrd (2003), Bullard and Mitra (2002), Bullard (2006), Evans and Hnkaphja (2003a,b), and Prestn (2003). 1

4 each cuntry pursue nn-cperative ptimal plicy under discretin. The chice f hw t implement the ptimality cnditin stemming frm the minimizatin prblem faced by the mnetary authrities can easily be made inapprpriately, leading t indeterminacy and expectatinal instability. On the ther hand, instrument rules which include respnses t internatinal ecnmic cnditins induce internatinal feedback between the tw ecnmies even when there wuld therwise be n such feedback. The separability f cnditins between cuntries breaks dwn. This secnd result again has a natural cunterpart in the case f targeting rules, in the situatin where the tw cuntries agree t try t pursue the gains frm cperatin which may exist in the mdel. Implementatin will again be an issue. We als nd that, if prperly implemented, a exible exchange rate regime has attractive insulatin prperties relative t a xed exchange rate regime (here mdelled as an exchange rate peg). We cnclude that determinacy and learnability cnsideratins can alter the evaluatin f mnetary plicy ptins in an internatinal cntext. 1.3 Recent related literature Batini, Levine, Justinian and Pearlman (2005) study indeterminacy in a tw-cuntry New Keynesian mdel. Their fcus is n the relatinship between many-perid frward-lking in atin frecast rules and indeterminacy cnditins. We d nt cnsider rules in this class in this paper. When frward-lking rules are cnsidered here, they arise frm the implementatin f certain ptimality cnsideratins and d nt invlve frecasts mre than ne perid int the future. De Fire and Liu (2005) study indeterminacy in a small pen New Keynesian ecnmy. Their mdel is smewhat di erent frm the ne we study. They cnclude that whether a given plicy rule can deliver determinacy will depend n the degree f penness in the small ecnmy, a result we als btain. A number f papers study classic pen ecnmy issues in the New Keynesian framewrk. Pappa (2004) and Benign and Benign (2004), fr exam- 2

5 ple, study the gains frm mnetary plicy crdinatin. Crsetti and Pesenti (2005) analyze self-riented r inward-lking natinal mnetary plicies in framewrks related t the ne studied here. While tuching n sme related themes, these papers d nt fcus n the determinacy and learnability issues we emphasize. Ellisn, Sarn, and Vilmunen (2004) study central bank learning in the tw-cuntry wrld f Aghin, Becchetta, and Banerjee (2001). They allw fundamental parameters in the ecnmy t fllw Markv switching prcesses, and central banks update their inference cncerning the current regime via Bayes rule. Zanna (2004) studies determinacy and learnability in the small pen ecnmy case fr a mdel due t Uribe (2003) which is again smewhat di erent frm the ne we study. 2 Zanna (2004) cntains results n learnable sunspt equilibria under cmmn factr representatins, a tpic we have nt addressed here. Wrking in parallel with us, Llsa and Tuesta (2005) study determinacy and learnability in a versin f the Clarida, Gali, and Gertler (2002) mdel we use. Whereas we emphasize the tw cuntry mdel they analyze the mdel frm the pint f view f the small pen ecnmy. Llsa and Tuesta (2005) study instrument rules mre extensively than we d, including di erent frms f Taylr-type rules as in Bullard and Mitra (2002). The Llsa and Tuesta (2005) discussin f dmestic in atin versus cnsumer price index in atin in the plicy rule parallels sme f ur analysis, and we cmpare ur results t theirs when apprpriate. 1.4 Organizatin We begin by presenting the basic mdel envirnment in the next sectin. We take up ur analysis f the e ects f plicy n determinacy and learnability by rst cnsidering instrument rules under exible exchange rates, simple descriptins f plicy that allw us t develp sme basic results 2 Bullard and Schaling (2006) als discuss purchasing pwer parity rules. 3

6 and intuitin, especially cncerning cuntry by cuntry determinacy and learnability cnditins. Plicymakers using rules in this class might break the natural separability f cuntry analysis in the mdel shuld they decide t react in part t internatinal variables when setting mnetary plicy, and we develp a versin f this situatin. We then turn t targeting rules (als under exible exchange rates), whereby the plicy rule is inferred frm an ptimizatin exercise undertaken by each mnetary authrity. The nature f the ptimizatin exercise will be imprtant fr ur ndings. The nal prtin f the paper takes up certain asymmetric situatins assciated with xed exchange rates. One f these is the case f ne cuntry pegging its exchange rate t a secnd cuntry which is fllwing an independent mnetary plicy. We discuss ur ndings and directins fr future research in the cnclusin. 2 A tw-cuntry New Keynesian mdel 2.1 Overview We emply the tw-cuntry mdel f Clarida, Gali, and Gertler (2002). This is ne natural extensin f the clsed ecnmy New Keynesian mdel t the pen ecnmy case in which tw large ecnmies are interacting, and s it prvides a gd starting pint fr the analysis f determinacy issues in the pen ecnmy. The mdel has a natural separatin between cuntries that Clarida, Gali, and Gertler (2002) discuss in sme detail. Rughly, after making certain adjustments t parameters accunting fr the degree f penness f each ecnmy, this versin f the pen ecnmy New Keynesian mdel is qualitatively the same as the standard, Clarida, Gali, and Gertler (1999)-style clsed ecnmy New Keynesian mdel. We explit this feature extensively in this paper. 2.2 Envirnment We can prvide nly a brief discussin f the micrfundatins f the mdel here interested readers shuld cnsult Clarida, Gali, and Gertler (2002). 4

7 The tw cuntries are labelled H and F: Preferences and technlgies are the same in bth cuntries. Each cuntry has an intermediate gds sectr which is subject t a Calv-style sticky price frictin alng with a nal gds sectr which is cmpetitive. Only nal gds are traded. Preferences fr cnsumptin are de ned ver an aggregate C t = C 1 H;t C F;t, with 0 1: The parameter is ften described as the degree f penness, because as! 0 (! 1) the freign (hme) ecnmy becmes vanishingly small, and all gds are prduced and cnsumed at hme (abrad). The mdel ecnmy is lg-linearized abut a steady state and described by ~y t = E t ~y t+1 1 [r t E t t+1 rr t ] ; (1) t = E t t+1 + ~y t + u t (2) where = ( 1) ; = ; = + ; = ; and = [(1 ) (1 )] =: The variable ~y t represents the dmestic utput gap, t represents dmestic prducer price in atin, and r t represents the shrt term nminal interest rate. The term rr t is the dmestic natural real interest rate (cnditinal n freign utput) given by rr t = E t y t+1 + E t y? t+1 where y t+1 is the rate f grwth f the dmestic natural level f utput and y t+1? is the rate f grwth f the level f freign utput. The term u t fllws an AR (1) prcess given by u t = u t 1 + u;t ;with 0 < 1; where u;t is an i:i:d: stchastic term. 3 The equatins (1) and (2) have ve fundamental parameters: The husehld discunt factr ; a parameter cntrlling the curvature in preferences ver cnsumptin ; a parameter cntrlling the curvature in preferences ver leisure ; the mass f agents r degree f penness ; and the prbability that a rm will nt be able t change its price tday ; which we smetimes refer t as the degree f price stickiness. The freign ecnmy is described analgusly as ~y? t = E t ~y? t+1?; 1 r? t E t? t+1 rr? t ; (3) 3 Fr simplicity we keep the serial crrelatin parameter the same fr all shcks in the mdel. 5

8 ? t = E t? t+1 +? ~y? t + u? t (4) where? = (1 ) ( 1) ;? =? ;? =? + ;? =? ; and = [(1 ) (1 )] =: In these equatins ~y? t is the freign utput gap,? t is freign prducer price in atin, and r? t is the freign nminal interest rate. The term rr? t is the freign natural real interest rate (cnditinal n dmestic utput), given by rr? t =? E t y? t+1 +? E t y t+1 where y t+1? is the rate f grwth f the freign natural level f utput and y t+1 is the rate f grwth f the level f dmestic utput. The term u? t is analgusly assumed t fllw an AR (1) prcess given by u? t = u? t 1 +? u;t with 0 < 1; where? u;t is an i:i:d: stchastic term. In equatins (3) and (4), the fundamental parameters ; ; ; ; and are all the same as in equatins (1) and (2), re ecting the maintained assumptin that the preferences and technlgies in the tw ecnmies are the same. The nly di erence is that in (1) and (2) has been replaced by 1 in (3) and (4). The nminal exchange rate e t beys cnsumer price index-based, r aggregate purchasing pwer parity, and is given by e t = (p C;t p? C;t) = (p t + s t ) (p? t f(1 )s t g) = p t p? t + s t where p t is shrthand fr the dmestic prducer price level p H;t, p? t is shrthand fr the freign prducer price level p? F;t, and where p C;t and p? C;t represent the hme and freign cnsumer price index, respectively. Finally, a simple expressin links the terms f trade t mvements in the utput gap: s t = (~y t ~y? t ) + (y t y? t ) (5) = (~y t ~y? t ) + s t where s t is the natural level f the terms f trade. 6

9 An advantage f this frmulatin is that the pen ecnmy e ects in this mdel cme thrugh the cmpsite parameters and? : The special cases where either! 0 r! 1 respectively place all the mass f agents in the hme r the freign ecnmy. In these cases, the hme r freign ecnmy behaves as if it were an islated, clsed ecnmy, while the partner behaves as if it were a small pen ecnmy. 4 An islated, clsed ecnmy crrespnds t the nes that have been extensively analyzed in the New Keynesian literature. 2.3 Determinacy issues As pinted ut by Jensen (2002), since Sargent and Wallace (1975) shwed that an interest rate peg rendered the price level indeterminate in a ratinal expectatins IS-LM-AS mdel, there has been a lt f research in the issue f designing mnetary plicy in rder t secure determinate ratinal expectatins equilibria. The mdel abve is ne where an interest rate peg wuld als lead t indeterminate equilbrium. T understand sme f the intuitin fr this result, cnsider a sunspt-driven increase in in atin expectatins, E t t+1. As this des nt a ect the nminal interest rate r t, the real interest rate falls. This stimulates demand and the utput gap via equatin (1). Thrugh the interactin f the IS and Phillips curves, this implies an increase in current in atin that is larger than the increase in expected in atin. As the increase in in atin expectatins is f arbitrary size, ne cannt pin dwn a unique nn-explsive ratinal expectatins equilibrium (REE). The ecnmy is cnsequently vulnerable t expectatins-driven uctuatins, a.k.a. sunspt uctuatins. T ensure determinacy and thus exclude the ptential fr ine cient, selfful lling uctuatins, sme restrictins are typically required n the behavir f the nminal interest rate. In the remainder f the paper we will analyze the mdel under di erent scenaris fr hw these interest rates are determined by plicymakers. We will begin with a simple speci catin that prduces 4 Clarida, Gali and Gertler (2001) and Gali and Mnacelli (2002) analyze the case f a small pen ecnmy using a similar framewrk. 7

10 simple intuitin, and later mve t mre cmplicated ptimal plicy speci- catins under a variety f assumptins n the nature f the ptimizatin plicymakers undertake. 3 Flexible exchange rates: instrument rules 3.1 Simple Taylr-type rules The dynamic system In this sectin we simply assume that the plicymakers in each cuntry fllw Taylr-type plicy rules given by fr the dmestic ecnmy, and by r t = ' t + ' y ~y t (6) r? t = '?? t + '? y ~y? t (7) fr the freign ecnmy, allwing the exchange rate t at. Imprtantly, the in atin terms in these rules refer t dmestic prducer price in atin (we discuss ther pssibilities belw). By substituting (6) and (7) int equatins (1) and (3), we can write the fur equatin system as fllws. First, de ne Z t = [~y t ; t ; ~y? t ;? t ] 0 alng with V t = [rr t ; u t ; rr? t ; u? t ] 0 : Then write the system as Z t = A 0 + BE t Z t+1 + X V t (8) where A 0 = 0, 5 B11 0 B = ; 0 B ' B 11 = ; + ' y + ' + + ' y 1? B 22 = 1 '?? + '? y +? '???? +? + '? ; y 5 We stay cnsistent with Bullard and Mitra (2002) in allwing fr cnstant terms. 8

11 where 0 is a 2 2 matrix f zeres, and X11 0 X = ; 0 X 22 with and 1 0 X 11 = 0 1?; 1 0 X 22 = ; 0 1 and where V t fllws a vectr AR (1) prcess with serial crrelatin given by the scalar : Determinacy Because the fur variables in this system are free in the terminlgy f Blanchard and Kahn (1980), we require all eigenvalues f B t be inside the unit circle fr determinacy. Since B is blck diagnal, this requirement means that the eigenvalues f B 11 and B 22 must be inside the unit circle. Frm a versin f Prpsitin 1 in Bullard and Mitra (2002), this implies that the fllwing tw cnditins must hld fr determinacy in this system: (' 1) + (1 ) ' y > 0 (9) and? ('? 1) + (1 ) '? y > 0: (10) These cnditins are versins f the Taylr principle 6 fr each cuntry and depend n the husehld discunt factr ; n the plicy parameters in the Taylr-type rules in the tw cuntries, and n the cmpsite parameters and? : We can write the cmpsite parameters as = [ + ( 1)] ; 6 See Wdfrd (2001) fr a discussin.? = [ + (1 ) ( 1)] : 9

12 Thus the cnditins (9) and (10) can be written as [ + ( 1)] (' 1) + (1 ) ' y > 0 (11) and [ + (1 ) ( 1)] ('? 1) + (1 ) '? y > 0: (12) The term in brackets is psitive, s that if ' y = '? y = 0; the cnditins state that each central bank has t mve nminal interest rates mre than nefr-ne in respnse t deviatins f in atin frm target. We have several remarks n cnditins (11) and (12). First, the cnditins fr the tw ecnmies are nt the same except in the special case where plicies are identical (in the sense that ' = '? and ' y = '? y) and = 1=2; which wuld be interpreted as the case that the tw ecnmies are equally pen. 7 Otherwise, the degree f penness di ers and this translates int a di erence in the tw cnditins. This means in particular that identical plicy in the tw cuntries, in the sense f identical values fr the Taylr-type plicy rule ce cients, may be enugh t meet ne determinacy cnditin but nt the ther. Secnd, the plicy parameters frm a single cuntry can nly in uence ne f the tw cnditins. Thus plicymakers frm each cuntry must separately meet cnditins fr determinacy: Determinacy cnditins fr wrldwide ratinal expectatins equilibrium are met, in sme sense, cuntry by cuntry. We interpret these ndings as fllws. If the hme cuntry plicymaker beys the Taylr principle while the freign plicymaker des nt, wrldwide equilibrium will be indeterminate. Shuld a sunspt variable begin t in uence expectatins, then the freign ecnmy will endure endgenus vlatility, but the hme cuntry will nt due t the blck diagnality f B which indicates that there is n feedback between the tw ecnmies. The intuitin is that any internatinal CPI in atin di erential will cause the nminal exchange rate t adjust, exactly setting the freign in atin prblem, and 7 If = 1 2, there is n hme bias in cnsumptin. 10

13 exactly insulating the hme cuntry. This result relies heavily n the idea that the tw Taylr rules react t dmestic prducer price in atin, which has n imprted cmpnent, as ppsed t cnsumer price in atin, which des have an imprted cmpnent. With CPI in atin in the plicy rules, r with a xed exchange rate, this will n lnger be the case. We discuss these pssibilities belw Learnability We nw turn t the learnability f ratinal expectatins equilibrium fr cases where that equilibrium is unique. We allw the expectatins in equatin (8) t initially be di erent frm ratinal expectatins. 8 The MSV slutin f equatin (8) is given by Z t = A + CV t where the cnfrmable matrix A is null and C = (I B) 1 X : We endw agents with a perceived law f mtin Z t = A + CV t (13) where A and C are cnfrmable. Using this perceived law f mtin and assuming time t infrmatin (1; rr t ; u t ; rr? t ; u? t ) 0 we can calculate E t Z t+1 = A + CV t : Substituting this int equatin (8) yields the actual law f mtin Z t = B (A + CV t ) + X V t = BA + (BC + X ) V t : 8 Prestn (2003) cnsiders deriving the fundamental equatins f mdels in this class assuming agents are learning. Under his interpretatin f the micrfundatins, the equatins are altered and lng-hrizn frecasts matter. We think it wuld be interesting t carry ut an analysis f this type fr the pen ecnmy case. 11

14 We then de ne a map T frm the perceived law f mtin t the actual law f mtin as T (A; C) = (BA; BC + X ) : Expectatinal stability is attained if the di erential equatin d d (A; C) = T (A; C) (A; C) is lcally asympttically stable at A; C. Results in Evans and Hnkaphja (2001) establish that under weak cnditins, expectatinal stability gverns stability in the real-time learning dynamics. We use Prpsitin 10.3 in Evans and Hnkaphja (2001) t calculate the cnditin fr expectatinal stability. Accrding t the prpsitin, the cnditin fr expectatinal stability is that the real parts f the eigenvalues f the matrices B and B are less than unity. Because 0 < 1; we need nly check the real parts f the eigenvalues f B. Als, because f the blck diagnality f B, the expectatinal stability cnditin can be calculated cuntry by cuntry, that is, via B 11 and B 22 ; and by a versin f Prpsitin 2 in Bullard and Mitra (2002) yields cnditins (11) and (12). This means that bth cuntries must meet the pen ecnmy versin f the Taylr principle in rder fr the wrld equilibrium t be learnable. It als means that the cnditins fr determinacy are the same as the cnditins fr learnability in the special case where bth cuntries fllw simple Taylr-type instrument rules. This is knwn nt t be true in general in mdels in this class with alternative instrument rules, but it prvides a gd benchmark Quantitative e ects As stressed by Clarida, Gali, and Gertler (2001, 2002), the nature f the plicy prblem faced by each cuntry in this pen ecnmy framewrk is ismrphic t the clsed ecnmy case, but there are nevertheless quantitative 9 An example f a case in which determinacy and learnability cnditins d nt cincide is when the plicy authrities use a Taylr-type plicy rule but react t lagged infrmatin n in atin and the utput gap. See Bullard and Mitra (2002). Fr a wider variety f Taylr-type instrument rules in a similar mdel, see Llsa and Tuesta (2005). 12

15 cnsequences. Figure 1 illustrates. Here the calibratin has been chsen s that the dmestic ecnmy cllapses t the ne studied by Wdfrd (2003) when the penness parameter! 0: Wdfrd s (2003) values have been widely used and prvide a simple benchmark. The discunt factr = 0:99: When! 0;! and we set this t Wdfrd s value f = 0:157: The ce cient wuld crrespnd t a value f = 0:024 in the Wdfrd calibratin. When! 0;! 0 s that! + ; and = ( + ) ; with = [(1 ) (1 )] =: We fllw Wdfrd (2003) and set t the nearly linear value 0:11: Given ther parameters, this means that = 0:745 t btain = 0:024: The gure plts (11) as a functin f ' and ' y using this calibratin fr values f between zer and unity. Since (12) is the same cnditin fr the freign cuntry with replaced by 1 ; ne can view the lines in Figure 1 as representing this cnditin as well. The line labelled = 0 represents the case when the hme cuntry is clsed and crrespnds t the cnditin frm Bullard and Mitra (2002, their Figure 1). The determinacy and learnability cnditin fr the freign cuntry wuld then crrespnd t the line labelled = 1 (that is, 1 wuld equal ne if = 0). 10 Thus the small pen freign ecnmy wuld have t chse its Taylr rule ce cients t the nrtheast f this line in the gure, while the large clsed hme ecnmy wuld nly have t chse its Taylr rule ce cients t the nrtheast f the line labelled = 0: Failure f either cuntry t abide by its cnditin wuld prduce indeterminacy and the pssibility f sunspt uctuatins in the wrld equilibrium. These lines are clser tgether if the degree f penness is intermediate between zer and ne, as illustrated by the lines labelled = 1=3 and = 2=3: Fr = 1=2; the cnditins fr determinacy and learnability in the tw cuntries wuld be identical. One f the main implicatins f Figure 1 is that the pen ecnmy lines with greater than zer all lie abve the clsed ecnmy line, s that cn- 10 Llsa and Tuesta (2005) fcus n the small pen ecnmy and depict the same line in their Figure 1 fr their dmestic in atin rule, which wuld crrespnd t this case. Their mdel is similar t the ne used here and has a similar calibratin. 13

16 Figure 1: The cnditins fr determinacy and learnability when each mnetary authrity uses a simple cntempraneus data Taylr rule. The mre pen ecnmy will have a steeper trade in the Figure. 14

17 ditins fr determinacy and learnability becme mre stringent when pen ecnmy cnsideratins are intrduced. A central bank analyzing its ecnmy as if it were clsed might mistakenly chse Taylr rule ce cients that are t small t deliver determinacy and learnability f equilibrium. 3.2 Instrument rules with internatinal variables Cnsumer versus prducer price in atin In Bullard and Schaling (2006) we shw that instrument rules which include respnses t internatinal ecnmic cnditins induce internatinal feedback between the tw cuntries where there wuld therwise be n such feedback. In this sectin we brie y summarize this argument. We begin by suppsing that each cuntry pursues a Taylr-type rule featuring cnsumer price index, r CPI, in atin instead f dmestic prducer price in atin. 11 This is intuitively plausible as in an pen ecnmy CPI in atin, nt dmestic prducer price in atin, is ften the variable f interest fr the mnetary authrity. The mnetary plicy rule in the hme cuntry is given by r t = ' C;t + ' y ~y t ; (14) and the mnetary authrity in the freign ecnmy pursues r? t = '?? C;t + '? y ~y? t (15) where is hme CPI in atin, and C;t = t + s t (16)? C;t =? t (1 )s t (17) is freign CPI in atin, and where s t is the terms f trade. 12 The in atin targets f the mnetary authrities implicit in these speci catins wuld then 11 This is als the secnd rule analyzed by Llsa and Tuesta (2005) fr their small pen ecnmy analysis. 12 In ur tw-cuntry mdel fllwing Clarida, Gali and Gertler (2002, p. 882) the hme cnsumptin price index can be written as P C;t = k 1 P 1. Using the de nitin f 15 H;t P F;t

18 be in terms f CPI in atin. Thus, respnding t CPI in atin is equivalent t having a cnventinal Taylr-type rule augmented by a third term which is the terms f trade. The terms f trade is in turn a re ectin f freign utput via equatin (5). The plicymakers in each cuntry are naturally reacting t develpments in the partner ecnmy because sme fractin f the gds being cnsumed at hme are being prduced abrad. Thus the plicymaker reactin t CPI in atin intrduces internatinal feedback between the tw cuntries that des nt exist under Taylr-type rules with dmestic prducer price in atin. As a cnsequence the key matrix B is n lnger blck diagnal (B 12 and B 21 are n lnger null). We stress that the lss f the blck diagnality f this matrix is induced by plicy alne. Plicymakers are reacting t cnsumer rather than prducer prices and this is creating internatinal linkages that wuld therwise nt exist. This means, in principle, that plicy parameters in ne cuntry will in uence all aspects 13 f wrldwide cnditins fr determinacy and learnability. The separability f these cnditins acrss brders breaks dwn in spite f exible exchange rates and PPP because the plicymakers are reacting t variables that have freign cmpnents. In sectin 5 we cnsider the case where the hme cuntry irrevcably pegs its exchange rate t the freign currency, which is anther rule that respnds t internatinal variables and changes the implied frm f the key matrix B. the terms f trade S t = P F;t =P H;t this equatin can be written as P C;t = k 1 P H;t S t, where k = (1 ) (1 ). Fr the freign cuntry ne gets PC;t = k 1 (PH;t )1 (PF;t ) = 1. k 1 PF;t 1 S t Taking lgs f these equatins yields pc;t = p t + s t and p C;t = p t (1 ) s t. Taking rst di erences and nrmalizing the initial (t 1) price levels t zer, these equatins can then be rewritten as the hme and freign CPI in atin equatins in the main text. 13 That is, all fur eigenvalues. 16

19 4 Flexible exchange rates: targeting rules 4.1 Overview In this sectin we assume that the central bank sets plicy ptimally. This means that the nminal interest rate is set accrding t a rule inferred frm an explicit ptimizatin exercise. 14 We investigate the benchmark case f discretin 15 and cnsider tw implementatin strategies f the rst-rder cnditin alng the lines f Evans and Hnkaphja (2003b) (hereafter EH). The varius implementatin strategies may r may nt prvide determinacy and learnability f ratinal expectatins equilibrium. In the next sub-sectin we fcus n the nn-cperative case in which each plicymaker sets mnetary plicy autnmusly. We will turn t the cperative case in Sectin Nn-cperative discretinary plicy The plicy prblem Imprtantly, as Clarida, Gali, and Gertler (2002) mentin, the crrect in atin variable fr the plicymaker fllwing a nn-cperative discretinary plicy is dmestic prducer price in atin. This means t will enter int the bjective fr the dmestic plicymaker. 16 Under discretin the mnetary authrity will chse a sequence f current and future shrt-term nminal interest rates t minimize lss de ned by L = (1 ) E t 1 X =t t 1 2 [ T 2 + ~y ~y T 2 ] (18) 14 Fr a recent discussin abut targeting versus instrument rules see Svenssn (2003), McCallum and Nelsn (2005), as well as Svenssn (2005). 15 Fr a discussin f determinacy issues fr ptimal rules in a clsed ecnmy where the timing prtcl is cmmitment, see Giannni and Wdfrd (2002a,b). 16 The reasn is that by targeting a cmbinatin f PPI in atin and the dmestic utput gap (in line with Clarida, Gali and Gertler 2002) where the weight n the latter, 0, is nt free but given by 0 = = 0, the plicymaker actually mimics targeting CPI in atin which in turn has its micr fundatins in scial welfare. 17

20 with and =, and where T and ~y T are target values which we will ften view as being zer. The parameter represents the price elasticity f demand fr intermediate gds in Clarida, Gali, and Gertler (2002). The minimizatin is subject t and where and ~y t = E t ~y t+1 1 (r t E t t+1 rr t ); (19) t = E t t+1 + ~y t + u t ; (20) rr t = E t y t+1 + E t y? t+1; u t = u t 1 + t : We can refrmulate the prblem abve as chsing the indirect cntrl variable f~y g 1 =t t minimize (18) where the central bank treats E t t+1 as given. We write the central bank s Lagrangian as 17 L = E t h X 1 =t 2 t (1 ) T 2 + ~y ~y T 2 i t ( E +1 ~y u ) where t and E t t+1 are state variables. The rst rder t = (1 ) ~y t ~y T + t = t = (1 ) t T t = 0: (22) Frm equatin (21) we have t = yields (1 ) ~y t ~y T. Using this result in (22) ~y t ~y T = t T : (23) 17 Fr a discussin f the relative merits f dynamic prgramming and the Lagrange methd see Schaling (2001). Fr applicatins f the latter t a nn-linear ptimizatin prblem, and a regime switching mdel see Schaling (2004) and Bullard and Schaling (2001), respectively. 18

21 It is well-knwn in the clsed ecnmy literature that there are a variety f strategies fr implementing cnditins like (23), and that these strategies can have di ering implicatins fr determinacy and learnability. We nw turn t tw implementatins fr the pen ecnmy mdel in rder t see hw these results may r may nt be altered An pen ecnmy expectatins-based ptimal rule Cmbining the rst-rder cnditin (23) with equatin (19) we btain E t ~y t+1 1 (rr t rr t ) ~y T = t T (where rr t is the ex ante real interest rate r t E t t+1 ). This can be written as rr t rr t = t T + E t ~y t+1 ~y T : Substituting fr t frm equatin (20) we btain rr t rr t = E t t+1 + ~y t + u t T + E t ~y t+1 ~y T : Eliminating utput via (19) yields r t rr t = 0;0 + ;0 E t t+1 + y;0 E t ~y t+1 + u;0 u t (24) where the ce cients are given by 0;0 = T + ~y T + 2 ; (25) ;0 = ; (26) y;0 = ; (27) u;0 = + 2 : (28) Equatin (24) is an example f a targeting rule, as discussed fr example in Wdfrd (2003, pp ). This rule is an pen ecnmy versin f 19

22 what Evans and Hnkaphja (2003b) call an expectatins-based ptimal rule. By cnstructin, it implements what Evans and Hnkaphja label ptimal discretinary plicy in every perid and fr all values f private expectatins. If! 0 ur (mre general) pen ecnmy rule cllapses t their versin. Setting the targets T and y T t zer, the wrld ecnmy can be written as Z t = A 0 + BE t Z t+1 + X V t ; where Z t = [~y t ; t ; ~y t? ;? t ] 0, and the key matrix B is given by B11 0 B = ; 0 B 22 where and B 11 = B 22 = " " 0? 0? +(? ) 2?? +(? )2 Because B is blck diagnal, determinacy cnditins will be have t be met cuntry by cuntry. A unique ratinal expectatins equilibrium exists since fr the dmestic ecnmy, and 0 < < < 1 # #?? + (? ) 2 < 1 fr the freign ecnmy. What we have in this sectin is di erent frm sectin n determinacy f instrument rules. Althugh in bth cases we have a B-matrix that is blck diagnal, under an Evans and Hnkaphja (2003b) style expectatins-based ptimal rule (adhered t in bth cuntries), we have uncnditinal determinacy f the tw-cuntry wrld ecnmy. There is n pssibility f indeterminacy f the wrld equilibrium like we had in sectin : 20

23 S, there is nthing like a Taylr principle that needs t be adhered t. Next, we turn t the learnability f the ratinal expectatins equilibrium. Because f the blck diagnality f B, the expectatinal stability cnditin can be calculated cuntry by cuntry, that is, via B 11 and B 22. By a versin Prpsitin 3 in Evans and Hnkaphja (2003b), we nd that fr all parameter values the REE f the tw-cuntry wrld ecnmy under wrld-wide adherence t pen ecnmy expectatins-based ptimal rules is stable under least squares learning by private agents. S, we nd that the EH (2003b) result that incrpratin f bserved private sectr expectatins int the plicymaker s ptimal rule can vercme expectatinal stability prblems carries ver t the tw-cuntry envirnment f Clarida, Gali and Gertler (2002) if the relevant rules are mdi ed t take due recgnitin f pen ecnmy e ects. Other implementatins f (23) are knwn t have pr prperties with respect t learnability and determinacy, hwever, and we nw turn t this case An pen ecnmy fundamentals-based ptimal rule A fundamentals-based plicy rule implementing (23) generates a di erent reduced frm. T btain an ptimal interest rate rule under ratinal expectatins cnjecture a slutin f the frm ~y t = a 1 + d 1 u t ; t = a 2 + d 2 u t ; 21

24 fr the dmestic ecnmy, with an analgus cnjectured slutin fr the freign ecnmy. The MSV slutin has a 1 = d 1 = a 2 = d 2 = 0;0 ( ;0 1) a 2 ; d 2 ( ;0 1) u;0 ; 0;0 (1 ) + ( ;0 1) ; u;0 (1 ) + ( ;0 1) : where 0;0 ; ;0 ; y;0 ; u;0 are given by (25) thrugh (28) respectively. The plicy feedback rule is then with and r t = 0 + u u t + rr t ; (29) 0 = 0;0 + ;0 a 2 + y;0 a 1 u = ;0 d2 + y;0 d1 + u;0 : This is smetimes called the fundamentals frm f the RE-ptimal plicy rule. It is knwn that this interest rate rule is assciated with indeterminacy in the clsed ecnmy case. 18 The wrld ecnmy can be written as Z t = A 0 + BE t Z t+1 + X V t ; with B blck diagnal, and B 11 = B 22 = ?; 1? +??; 1 ; : 18 See fr instance Wdfrd (1999, 2003) and Svenssn and Wdfrd (2003). 22

25 Determinacy requires ja 0 j < 1 and ja 1 j < 1 + a 0 in v 2 + a 1 v + a 0 = 0; the characteristic equatin fr B 11 and B 22 ; respectively. Fr the dmestic ecnmy (and analgusly fr the freign ecnmy), a 1 = ( + + ) and a 0 = : The cnditin ja 1 j < 1 + a 0 is never met under maintained assumptins and s wrldwide equilibrium is indeterminate, as in the dmestic ecnmy case discussed by Evans and Hnkaphja (2003). The MSV slutin will als be unstable in the learning dynamics. We cnclude that the methd f implementing (23) will matter in the pen ecnmy case just as it des in the clsed ecnmy. 4.3 Cperative discretinary plicy Overview As we have seen, blck diagnality breaks dwn if plicymakers put weight n internatinal variables in their plicy rules, r, in a targeting apprach, in their bjective functin. That is exactly what happens shuld plicymakers in each cuntry attempt t pursue the gains t cperatin which nrmally exist in this mdel. We nw turn t this issue. Clarida, Gali and Gertler (2002) study cperatin in the cntext f their New Keynesian mdel and are thus part f what Canzneri, Cumby and Diba (2004) call secnd generatin mdels f plicy crdinatin. Canzneri, et al., state that the gains frm crdinatin are larger in secnd generatin mdels than in rst generatin mdels. 19 Clarida, Gali, and Gertler (2002) shw in their Prpsitin 3 that gains t internatinal plicy cperatin will accrue t bth cuntries when > 1 and each cuntry fllws a rule dictated by the slutin t a jint ptimizatin prblem. We nw fllw Clarida, Gali, and Gertler (2002) and discuss the 19 Fr a survey f the lessns frm the rst generatin literature see Nlan and Schaling (1996). 23

26 prspects fr determinacy and learnability if each cuntry attempts t pursue the gains frm cperatin The plicy prblem Clarida, Gali, and Gertler (2002) de ne cperatin t mean that the tw central banks in the mdel agree t maximize a weighted average f the utility f the hme and freign husehlds under discretin. The weights are naturally and 1 : Bth gvernments refrain frm creating a surprise appreciatin, and hand ut emplyment subsidies that just set the mnplistic cmpetitin distrtin. The mnetary authrities jintly maximize an apprximatin t weighted husehld utility given by L = 1 2 E 0 1X t t=0 (1 ) 2 t + ~y t C 2 + (?t ) 2 +? 2 ~y?;c t 2~y t C ~y?;c t ; where = =; = =;? =? =; (1 ) (1 ) ; and ~y t C and ~y?;c t are the utput gaps de ned under cperatin as the deviatin, in percent, f utput frm the cperative steady state level fr the dmestic and freign ecnmy, respectively. 20 The rst rder cnditins fr this prblem can then be written in terms f standard utput gaps as ~y t = t +? t ; ~y t? =? t +?? t : 20 Fr mre details see Clarida, Gali, and Gertler (2002). 24

27 4.3.3 One implementatin Cmbining these cnditins with (1) and (3) gives ptimal cperative plicy rules where r t = #E t t+1 + (# 1) E t? t+1 + rr t ; r? t = #? E t? t+1 +?? (#? 1) E t? t+1 + rr? t ; # = 1 + (1 ) ; #? = 1 +? (1 ) : The wrld ecn- The dynamic system, determinacy, and learnability my can be written as Z t = A 0 + BE t Z t+1 + X V t ; where the key matrix B is B11 B B = 12 B 21 B 22 and and 1 1 (# 1) B 11 = 1 (# 1) 0 1 B 12 = 1 (# 1) (# 1) 1?; 1 (#? 1) B 22 =??; 1? (#? 1) ; 0?; 1 B 21 =??; 1 (#? 1) 0?; 1???; 1 (#? 1) ; ; : 25

28 Determinacy prperties will again depend n the eigenvalues f the matrix B: The lack f blck diagnality indicates that plicy in each cuntry will in uence determinacy prperties. The fur eigenvalues f B are given by and v 1; = v 2; = (1 + ) + (1 + ) ( 1) 2 ( [1 + ] [1 + + (1 + ) ]) 2 2 (1 + ) + ( + ) ( 1) 2 ( [ + ] [1 + + ( + ) ]) = =2 : These eigenvalues are independent f, the degree f penness. This is because the tw ecnmies are fllwing a cperative plicy which takes the size f each ecnmy int accunt. Determinacy des nt always hld. In particular, lim 1;!0 = 1; lim 2;!0 = 1: Unless the serial crrelatin in the shck is su ciently large, this cperative plicy will generate indeterminacy. 21 We use the baseline calibratin with the additin f = 7:88 implying a markup f abut 15 percent, and we reprt results fr values f. The cut value fr the serial crrelatin parameter is c 0:165: 22 Values less than this will create indeterminacy given the baseline calibratin. Shuld the shck prcess becme smething mre like white nise, ptimal plicy cperatin implemented in this way will be assciated with indeterminacy. 21 This is a versin f a similar result fr the clsed ecnmy in Evans and Hnkaphja (2003b). 22 Fr = 2; c 0:28: 26

29 Fr determinate cases, we veri ed numerically at baseline parameter values that expectatinal stability hlds. One might wnder if full cperatin is really a gd psitive mdel fr wrld mnetary plicy. In the internatinal plicy arena, we seem t bserve a variety f strategies in play. S far in the paper we have nly cnsidered certain types f symmetry in plicy, but there are als interesting asymmetric situatins. We nw turn t ne f these. 5 Fixed exchange rates: asymmetry in mnetary plicy 5.1 An exchange rate peg Overview In this sectin we suppse the hme cuntry targets its nminal exchange rate e vis-a-vis the freign cuntry. We assume the freign ecnmy sets its mnetary plicy based n its wn dmestic cnsideratins. The hme cuntry gives up its dmestic mnetary autnmy in return fr imprting mnetary stability frm the freign, anchr cuntry. This is a leading example f an asymmetric exchange rate regime, as nly the anchr cuntry s variables matter fr its interest rate (depending n the nature f the plicy adpted there), and the hme cuntry simply sets its interest rate t ensure it realizes a xed exchange rate. The hme cuntry in setting plicy takes freign mnetary cnditins int accunt, but the freign cuntry need nt incrprate the hme cuntry s cnditins in its wn mnetary plicy stance. This arrangement is similar t the regimes adpted by sme Eurpean cuntries prir t ecnmic and mnetary unin and t the present peg f the Chinese renminbi t the U.S. dllar. 27

30 5.1.2 The plicy prblem The hme cuntry minimizes (1 ) E t 1 X The minimizatin is subject t =t t 1 2 [ e e T ] 2 : (30) ~y t = E t ~y t+1 1 [r t E t t+1 rr t ] ; (31) t = E t t+1 + ~y t + u t ; (32) _ rr t = E t y t+1 + E t y? t+1; u t = u t 1 + t ; e t = e t 1 + s t s t 1 + t? t ; and s t = (~y t ~y t ) + s t : Fr ease f expsitin we nrmalize the initial levels f the nminal exchange rate and terms f trade at zer (e t 1 = s t 1 = 0), s that e t = s t + t? t : (33) In what fllws we nrmalize the exchange rate target at zer (e T = 0). Frm (30) the rst-rder cnditin then becmes e t = 0, which cmbined with (33) implies s t = ( t? t ): (34) The intuitin behind (34) is the fllwing. The nminal exchange rate beys CPI-based purchasing pwer parity and, after apprpriate nrmalizatin, is given by e t = t? t + s t. In rder t prevent uctuatins in e t, the hme central bank shuld manipulate the terms f trade s t, which it can a ect via the dmestic utput gap, in such a way as t set the GDP de atr-based in atin di erential. Thus we have (34). 28

31 Since the terms f trade can be a ected by the dmestic utput gap, which in turn is a ected by the hme nminal interest rate, the hme central bank shuld try t achieve a level f the hme utput gap given by ~y t = ( t? t ) + ~y? t s t : (35) Equatin (35) is btained by substituting the expressin fr the terms f trade int the rst-rder cnditin and rearranging The plicy rule Substituting (32) int (35), we btain the hme cuntry s ptimal mnetary plicy rule in terms f its indirect cntrl ~y t ~y t = E t t (? t + ~y t? ) (s t + u t ): (36) The hme interest rate reactin functin can be btained by cmbining (36) with (31) t btain r t rr t = 0 ;0E t t y;0e t ~y t+1 + 0?;0? t + 0?;0~y? t + 0 u;0 (u t + s t ) ; (37) where the ce cients are given by 0 ;0 = (1 + ) ; (38) 0 y;0 = ; (39) and 0?;0 = 0 u;0 = : (40) 1 + The rule (37) describes the ptimal hme mnetary reactin functin that implements its mnetary plicy f pegging the exchange rate t the freign anchr cuntry. 23 We substitute the hme cuntry s plicy rule (37) int (31). This implies ~y t = 1 (1 0 ;0)E t t+1 1 0?;0(? t + ~y? t ) 1 0 u;0 (u t + s t ) ; (41) Here the dependence f hme s ecnmic utcmes n the freign macrecnmy is evident frm the presence f the terms? t and ~y? t. 23 We stress that there may be ther ways t implement the rst rder cnditin fr the xed exchange rate. 29

32 5.1.4 The dynamic system, determinacy, and learnability Whether r nt a xed exchange rate regime is cmpatible with determinacy f wrldwide ratinal expectatins equilibrium depends n hw the freign, anchr cuntry implements mnetary plicy, and n any internatinal spillver e ects n the hme cuntry. We make the assumptin that the freign, anchr cuntry is inward-lking, and cncerned nly abut reacting t develpments in its wn ecnmy. We prceed with the mst straightfrward assumptin, namely that the freign in atin cuntry fllws a simple Taylr-type plicy rule. This allws us t easily study cases where the freign, anchr mnetary authrities are pursuing plicies either cnsistent r incnsistent with determinacy and learnability f wrldwide ratinal expectatins equilibrium. The wrld ecnmy can again be written in standard frm. The matrix B is given by B11 B B = 12 0 B 22 where B 22 is the matrix assciated with a simple Taylr rule in use in the freign cuntry. The eigenvalues there will depend n whether the freign cuntry is fllwing the pen ecnmy versin f the Taylr principle r nt, as discussed earlier in the paper. The eigenvalues f B 11 will als have t be less than unity fr determinacy. This matrix is given by ;0 B 11 = : ;0 The eigenvalues are zer and v = 1 + < 1: We cnclude that determinacy hlds under maintained assumptins prvided the freign, anchr mnetary authrities are fllwing the Taylr principle. Learnability hlds under the same cnditins. One may be able t imagine scenaris under which this result wuld break dwn, if the freign, anchr ecnmy had sme ther plicy. But this result 30

33 suggests there need nt be anything intrinsically unstable in the use f an exchange rate peg. 6 Cnclusin We have develped results n determinacy and expectatinal stability fr a simple pen ecnmy New Keynesian mdel due t Clarida, Gali, and Gertler (2002). We used this mdel with an eye tward cmparing the pen ecnmy ndings t knwn results fr clsed ecnmies under similar assumptins. We have shwn that even fr simple Taylr-type plicy rules, pen ecnmy cnsideratins will have quantitative e ects n determinacy and learnability cnditins. Clsed ecnmy analyses tend t understate the degree f aggressiveness the plicymaker must adpt t avid indeterminacy and expectatinal instability. Quantitative di erences f this type are alluded t by Clarida, Gali, and Gertler (2002) and are in accrd with the ndings f Llsa and Tuesta (2005). When central banks are inward-lking reacting t dmestic variables in their plicy rules and when exchange rates are ating, ur results indicate that determinacy and learnability cnditins fr wrldwide equilibrium must be met cuntry by cuntry. This is true whether we are cnsidering inward-lking instrument rules r targeting rules which are implied by nn-cperative plicy bjectives. Optimal plicy will require an implementatin, but the natural implementatins suggested in the clsed ecnmy literature imply the separability f determinacy and learnability cnditins acrss ecnmies. We interpret this nding as fllws. If ne cuntry ut f many adpts an instrument rule that is incnsistent with determinacy and learnability, r ne cuntry ut f many adpts an implementatin f an ptimal plicy which is incnsistent with determinacy and learnability, then wrldwide equilibrium will be indeterminate and expectatinally unstable. The remaining cuntries, even if they attempt t be very aggressive in prmting determinacy and learnability, will nt have an impact n this facet f the wrld equilibrium. This might be viewed as an undesirable aspect f 31

34 inward-lking plicies, even if they are judged ptimal n ther grunds. When mnetary authrities are actively respnding t internatinal variables, ur results indicate that determinacy and learnability cnditins fr wrldwide equilibrium are met by smething akin t an average f wrld mnetary plicy. This als ccurs fr targeting rules where mnetary authrities are attempting t pursue cperative plicies t achieve the available gains. Optimal cperative plicy will als require an implementatin, and the baseline implementatin frm the literature may nt be cnsistent with determinacy and learnability. Still, inclusin f reactins t internatinal variables allws the mnetary authrities frm a su ciently large ecnmy t mitigate the threats f indeterminacy and expectatinal instability psed by a partner cuntry that is pursuing a pr plicy, either thrugh an ad hc plicy r thrugh an inadvertently bad implementatin f an ptimal plicy. The ability t in uence these cnditins may be viewed as a desirable aspect f mnetary plicy in an pen ecnmy cntext. References [1] Aghin, P., P. Bacchetta, and A. Banerjee A Simple Mdel f Mnetary Plicy and Currency Crises. Eurpean Ecnmic Review 44: [2] Benhabib, J., and R. Farmer Indeterminacy and Sunspts in Macrecnmics. Chapter 6: in Taylr, J. B., and M. Wdfrd (Eds.). Handbk f Macrecnmics, Vlume 1 A. Elsevier. [3] Batini, N., P. Levine, A. Justinian and J. Pearlman Mdel Uncertainty and the Gains frm Crdinating Mnetary Rules. Paper Presented at the Third Cnference f the Internatinal Research Frum n Mnetary Plicy, ECB, May. [4] Benign, G., and P. Benign Designing Targeting Rules fr Internatinal Mnetary Plicy Cperatin. Eurpean Central Bank, Wrking Paper #

35 [5] Blanchard, O., and C. Kahn The Slutin f Linear Di erence Mdels under Ratinal Expectatins, Ecnmetrica 48(5): [6] Bullard, J The Learnability Criterin and Mnetary Plicy. Federal Reserve Bank f St. Luis Review 88(3): [7] Bullard, J., and E. Schaling New Ecnmy-New Plicy Rules? Federal Reserve Bank f St. Luis Review 83(5): [8] Bullard, J., and E. Schaling Mnetary Plicy, Determinacy, and Learnability in the Open Ecnmy Eurpean Central Bank Wrking Paper, N 611, April. [9] Bullard, J., and K. Mitra Learning Abut Mnetary Plicy Rules. Jurnal f Mnetary Ecnmics 49: [10] Canzneri., M., R. Cumby, and B. Diba The Need fr Internatinal Plicy Crdinatin: What s Old, What s New, What s Yet t Cme. Jurnal f Internatinal Ecnmics, frthcming. [11] Clarida, R., J. Gali, and M. Gertler The Science f Mnetary Plicy: A New Keynesian Perspective. Jurnal f Ecnmic Literature 37(4): [12] Clarida, R., J. Gali, and M. Gertler Optimal Mnetary Plicy in Open versus Clsed Ecnmies: An Integrated Apprach. American Ecnmic Review Papers and Prceedings 91: [13] Clarida, R., J. Gali, and M. Gertler A Simple Framewrk fr Internatinal Mnetary Plicy Analysis. Jurnal f Mnetary Ecnmics 49: [14] Crsetti, G., and P. Pesenti Internatinal Dimensins f Optimal Mnetary Plicy. Jurnal f Mnetary Ecnmics 52(2):