Frequency of Central Bank Evaluation in an Inflation Targeting Regime: the Brazilian Experience

Transcription

1 Frequency of Cenral Bank Evaluaion in an Inflaion Targeing Regime: he Brazilian Experience Paulo Springer de Freias Banco Cenral do Brasil and UnB SBS Q.3, Bl. B, Ed. Sede, 9 o andar Brasília, DF, Brazil paulo.freias@bcb.gov.br Absrac This paper analyses he opimal frequency for Cenral Bank evaluaion in an inflaion-argeing regime, applied o he Brazilian economy. Seing a frequency of accounabiliy is an imporan issue in he design of an inflaion-argeing regime, since i allows he maching of conflicing arges beween he moneary auhoriy and he governmen: while he governmen cares abou inflaion and employmen, he Cenral Bank should be concerned only abou inflaion. Through sochasic simulaions, i was possible o conclude ha he Cenral Bank should be evaluaed every wo or hree years. However, here are lile losses involved in he curren Brazilian regime, where he Cenral Bank is evaluaed in he end of every calendar year. Only in case of very frequen evaluaions, like a every wo quarers, he social welfare loss would be significan, wih high oupu gap and inflaion variances. Keywords: Inflaion argeing, moneary policy, accounabiliy of he Cenral Bank JEL classificaion: E52, E58

2 Frequency of Cenral Bank Evaluaion in an Inflaion Targeing Regime: he Brazilian Experience, Paulo Springer de Freias I - Inroducion The objecive of his paper is o evaluae he opimal frequency of Cenral Bank evaluaion in an inflaion-argeing regime, wih applicaion for he Brazilian case. Opimaliy refers o esablishing a frequency of evaluaion ha is compaible wih he minimizaion of a loss funcion, whose argumens are inflaion and oupu gap variances. Regarding he frequency of evaluaion, in he Brazilian inflaionargeing regime, he performance of he Cenral Bank is assessed in he end of every calendar year. The Cenral Bank will have a posiive evaluaion in case he observed inflaion lies wihin he admied olerance inerval 1. Oherwise, he Governor of he Cenral Bank will have o wrie an open leer explaining he reasons of missing he arge and describing he measures ha will be aken in order o make inflaion come back o he arge. The accounabiliy of he Cenral Bank is a common feaure of he exising inflaion argeing regimes, alhough here is a wide variaion in assessing he performance of he Cenral Banks 2. Since in he Brazilian case an evenual punishmen will depend exclusively on he behavior of he inflaion, i is reasonable o assume ha, independenly of he preferences of he Cenral Bank, moneary police will be conduced in a way o minimize he probabiliy ha observed inflaion is ou of he olerance inerval. Therefore here is a poenial conflic of ineress: on one side, he Cenral Bank, in spie of deciding he basic ineres rae in all periods, should be only direcly concerned wih he deviaion beween acual inflaion and he arge in he period where evaluaion occurs, ha is, i should be mainly concerned wih year-end oucomes. On he oher hand, he governmen should be worried no only wih Banco Cenral do Brasil and Universidade de Brasilia. The auhor wishes o hank Gil Riella for his valuable compuaional suppor. Inerpraaion and any remaining errors are my own responsibiliy. This paper expresses only he opinion of he auhor and in no hose of he Banco Cenral do Brasil. 1 In Brazil, he olerance inerval is plus or minus 2.5 pp around he cenral arge esablished for 2003 and 2004.

3 inflaion oucomes during he whole year bu also wih he variance of oupu gap. I is possible, herefore, ha he Cenral Bank conducs moneary policy in an inefficien way, from he poin of view of he governmen. However, he conflicing objecives beween governmen and Cenral Bank should no necessarily generae inefficiency. Clarida e al. (1999) show ha, when oupu gap variance has a sricly posiive weigh in he loss funcion, i is opimal o make a gradual convergence of inflaion o he arge. Baini and Haldane (1999) also argue ha oupu variance depends on he horizon of he inflaion arge. Inuiively, hrough he ransmission mechanism of police moneary via aggregae demand, variaions in he ineres rae lead o variaions in he oupu gap. If he frequency of evaluaion is very high, he Cenral Bank will be forced o generae high volailiy in he nominal ineres rae, increasing he volailiy of oupu gap. If he evaluaion of he Cenral Bank is made a longer inervals, here is a smaller probabiliy ha abrup aleraions in he ineres rae are necessary and, hence, oupu variabiliy should be smaller. For England, Baini and Nelson (2000) esimaed an opimal horizon beween 8 and 19 quarers. In his way, by choosing he frequency of evaluaion of he Cenral Bank, he governmen can generae inflaion and oupu oucomes ha maximize is own uiliy funcion. The main exercise of his paper will be o esimae he opimal frequency of Cenral Bank evaluaion for he Brazilian case, given differen weighs for inflaion and oupu gap variance in he governmen's loss funcion. This paper will have wo secions, besides he Inroducion and he Conclusion. Secion 2 presens he Baini and Haldane (1999) model for inflaion, exchange rae and oupu gap deerminaion and describes he sochasic simulaion used o find he opimal ineres rae rule. In a few words, i was assumed ha he Cenral Bank ses he ineres rae according o a Taylor ype rule. For each evaluaion frequency, he parameers of he ineres rae equaion are chosen in order o minimize he expeced inflaion variance. Secion 3 presens he resuls. I could be found ha he opimal parameers of he Taylor rule are no very sensiive o he frequency of evaluaion, excep in he case where he Cenral Bank is evaluaed a every wo quarers. A his frequency, he reacion of he Cenral Bank o inflaion deviaions should be sronger han under longer frequencies. The opimal frequency for 2 Bernanke e al. (1999) summarizes differen regimes of inflaion argeing. 2

4 evaluaion varies beween 8 and 12 quarers, alhough he loss of uiliy is small if he evaluaion is made on an annual basis, as i is currenly done in Brazil. Finally, he Conclusion summarizes he main resuls and presens suggesions for fuure research. II - The srucural model and he sochasic simulaion The Baini & Haldane (1999) model will be used for deerminaion of he oupu gap, inflaion and exchange rae. According o his model, price rigidiies enable moneary police o have real effecs in he shor run. Such rigidiies arise as a consequence of overlapping wage adjusmens. The reduced form of he model is given by: (1) y = 1 y 1+ α 2E y+ 1+ α 3 ( i 1 E 1π ) + α 4z 1 α + ε h (2) π = + χ 0 E ( π + 1) + (1 χ 0 ) π 1 + χ1( y + y+ 1) + µ [(1 χ 0 ) x + χ 0E ( x 1)] + ε f e (3) e = Ee+1 ( i i ) + ε π The firs equaion corresponds o he IS curve and saes ha he oupu gap - y - depends on is own value lagged one period; on he expecaion of oupu gap in he following period; on he ex-ane real rae of ineres of he previous period, i -1 - E π ; on he rae real exchange rae, z; and on an error erm. I is expeced α 3 o be negaive and he oher parameers o be posiive. Observe ha here is no consan in his IS curve, wha is consisen wih he equilibrium real ineres rae being equal o zero 3. This is equivalen o say ha he model and he simulaions will refer o deviaions wih respec o he mean values of he variables. The second equaion is he Phillips curve, ha says ha he curren inflaion - π depends on expeced and previous inflaion; on he oupu gap; on he variaion of he radable goods prices denominaed in local currency - x - which corresponds o he sum of he logarihms of he variaion of nominal exchange rae and of foreign inflaion; and on an error erm. Observe ha, unlike wha happens wih he IS curve, 3 Equilibrium real ineres rae - r* - is obained by making oupu gap equals o zero. Making y=0 in * * (2) and rearranging one ges: r = α 4z α3, where z* is he equilibrium real exchange rae. If z* is zero, r* will also be zero. If here were a consan erm in (1), i would be added o he numeraor of he above formula. 3

5 he resricion of no inercep in he Phillips curve is no only a maer of redefining measuremen unis. This resricion is a heoreical necessiy o ensure long run vericaliy of he Phillips curve. The hird equaion presens he nominal exchange rae deerminaion by he uncovered ineres rae pariy condiion. Tha is, expeced exchange rae depreciaion - E e +1 - e - should depend on he difference beween domesic and foreign nominal ineress - i and i f -, respecively; and on an error erm. This equaion does no explicily include a measuremen of counry risk. Alhough he counry risk is an imporan facor o explain he behavior of exchange rae movemens for emergen economies, his simplificaion does no aler he core of his paper: firsly, because since he model deals only wih deviaions in relaion o he mean, variaions in Brazil risk may be incorporaed ino he forecas error; secondly, i is no he objecive of his paper o model he counry risk. Equaions 1-3 above incorporae he main channels of he ransmission mechanism of moneary police. Firsly, he presence of he lagged erm for inflaion in he Phillips curve allows for changes in he nominal ineres rae o aler he real ineres rae. From he IS curve (1), an increase in he real ineres rae causes a reducion in he oupu gap (reminding ha α 3 is negaive) and, according o he Phillips curve (2), leads o a reducion in he inflaion rae. This is he aggregae demand channel. The oher mechanism in his model is he exchange rae one. From he exchange rae equaion (3), an increase in he domesic ineres rae causes an appreciaion of he exchange rae and pressures inflaion downwardly hrough reducion of radable goods prices. For he simulaions ha hey will be presened, i will be used he parameers calibraed by Bonomo and Brio (2001), reproduced in he able below: Parameers α 1 0,93 α 2 0,06 α 3-0,44 α 4 0,08 χ 0 0,85 χ 1 0,09 µ 0,1 4

6 Observe ha, according o he calibraion done by Bonomo and Brio (2001), inflaion has a large forward-looking componen, wih a coefficien of 0.85, while he oupu gap is more backward-looking, wih coefficien of Since oupu gap is very sluggish, he period necessary for he ransmission mechanism o be effecive should be longer. Because of his characerisic, in he shor run, he whole impac of moneary police on inflaion should be hrough he exchange rae channel. The variance covariance marix esimaed by Bonomo and Brio (2001) is given by: 0, Σ= (4) Where he columns and lines refer o he residual of he oupu gap, of he inflaion and of he exchange rae, respecively. In spie of here being conemporaneous correlaion among he error erms, i is assumed ha hey are no auo-correlaed. These equaions enable an endogenous deerminaion of inflaion, oupu gap and exchange rae. Therefore, i is sill missing an equaion for he ineres rae. I is assumed ha he Cenral Bank decides he ineres rae under discreion. To simplify he analysis, i is assumed moneary policy follows a Taylor rule, whose parameers are opimally chosen: = 1 1 ( i γ i + 1 γ )[ γ π γ y ] (5) Tha is, i is assumed he Cenral Bank makes decision on ineres rae based on one-lagged inflaion, ineres rae and oupu gap 4. The vecor γ = {γ 1, γ 2, γ 3 } is chosen by he Cenral Bank in order o maximize is uiliy funcion. As explained in he Inroducion, he objecive of he Cenral Bank is o minimize he probabiliy of acual inflaion laying ou of he pre-esablished olerance inerval in he evaluaion period, say, +s. Thus, he objecive of he Cenral Bank can be wrien as: 4 There are oher specificaions for he Taylor rule (see Taylor, 2000) ha keeps he simpliciy of he formula above. Tha is, he Cenral Bank may se ineres rae according o a linear combinaion of oher macroeconomic variables, like exchange rae or expeced inflaion, insead of realized inflaion. 5

7 * * max Pr ob ( δ π π + δ) (6) γ1, γ 2, γ 3 π + s + s + s where δ is inerval of olerance around he cenral arge. For a symmerical disribuion of errors, as assumed in his simulaion 5, he probabiliy above is maximized when he Cenral Bank chooses he ineres rae ha saisfies: E π +s = π +s Therefore, he Cenral Bank will choose an ineres rae ha minimizes he difference beween expeced inflaion and he arge. Due o he well-known problems of minimizing differences, he Cenral Bank should acually minimize he square of errors, ha is: * min [ E π + s π + s ] γ, γ, γ Finally, since all variables are being expressed as deviaions from he mean, i is reasonable o work wih a arge consan a zero. Besides, as he objecive funcion is quadraic and he resricions (equaions 1 o 3 and 5) are linear, one can apply he cerainy equivalence principle 6 and rewrie he loss funcion of he Cenral Bank as: 2 [ ( π ) ] min E + s γ, γ, γ (7) The final problem is he deerminaion of he s above, ha is, o which horizon he Cenral Bank should look a. A simplifying assumpion was made saing ha, in he evaluaion ime, he Board of he Cenral Bank looses is mandae if 5 I is assumed ha he error erms are normally disribued and here is no uncerainy regarding he parameers of he model. Therefore, he inflaion forecas error will be a linear funcion of he error erm in he Phillips curve - ε π and he error erms in he IS and exchange rae equaions - ε y and ε e, respecively. Since i is a linear funcion of normally disribued errors, he forecas error will also be normally disribued. 6 Esrella and Mishckim (1999) show he equivalence principle for a model similar o he one used here. However, i is necessary o assume ha here is no uncerainy regarding he parameers of he model. When he cerainy equivalence principle can be applied, he Cenral Bank is indifferen beween minimizing he expeced square of he deviaions or he square of he expeced deviaions. 6

8 realized inflaion falls ou of he olerance inerval. Therefore, he Board should choose s in such a way o coincide wih he firs ime when hey are appraised. For example, if he evaluaion is made every 2 periods, s=2, and so forh. Tha is, if he Cenral Bank is evaluaed every wo quarers, moneary policy will be conduced in order o minimize he deviaion beween expeced inflaion and he arge in he following wo quarers. The dynamics of he model is he following: a he end of each period, he Cenral Bank chooses he ineres rae and, afer aking his decision, he shocks are revealed for he whole sociey. Afer each shock, economic agens reassess heir expecaions regarding he fuure rajecory of ineres rae, inflaion, oupu gap and exchange rae. Since i is a linear model of raional expecaions, he soluion of he sysem was obained hrough he Blanchard-Kahn (1980) decomposiion and he non pre-deermined variables was inflaion, oupu gap and exchange rae. I is assumed ha he economy is in he seady sae a =0. As he ineres rae se a =1 depends only on variables observed in he previous period, i =1 = 0, regardless of he shocks occurred in his period. Hence, i does no make sense o evaluae he Cenral Bank every period and he minimum frequency of evaluaion should be of wo periods. Afer all, a =2, he ineres rae will reac o he shocks observed in =1 and will have a conemporaneous effec on inflaion, mainly horugh he exchange rae channel. The firs sep o find he Taylor rule ha minimizes (7) was o generae 150 series of 13 periods each, defining he shocks for inflaion, oupu gap and exchange rae. Those shocks were generaed according o he variance-covariance marix (4). Thus, for each Taylor rule and for each sequence of shocks, he Cenral Bank chooses a sequence of 13 ineres raes. As his exercise was repeaed 150 imes for each Taylor rule, i was possible o calculae he variance of inflaion for each period. The opimal Taylor rule should correspond o he values of he vecor γ = {γ 1, γ 2, γ 3 } ha minimizes (7). I was no possible, however, o do his opimizaion direcly using he sofware Malab, because he resuls did no converge. Therefore, i was necessary o span he whole space of possible values of γ, in inervals of 0,20 and, laer on, for smaller grids, reaching inervals of 0,05. By doing his exercise, i was obained he variance of inflaion for all possible combinaions of γ 1 (he coefficien of he nominal 7

9 ineress) ranging from 0 o 1; γ 2 (he inflaion coefficien) ranging from 1 o 5 7 and γ 3 (he oupu gap coefficien) ranging from 0 o 3. Once one obained he opimal variances of inflaion and oupu gap, according o he Cenral Bank loss funcion, he Governmen's loss funcion can be calculaed by he formula below: L g = T j= s * 2 2 ρ [ λe ( π π ) + (1 λ) E y ] (8) j j j where: π is he inflaion rae;π* is he inflaion arge; y is he oupu gap, defined as he difference (in logarihms) beween he acual and poenial oupu; λ [0,1] is he weigh aribued o inflaion variabiliy compared o oupu gap variabiliy; ρ is he ineremporal discoun facor 8. Thus, for each value of λ, he opimal frequency of evaluaion of he Cenral Bank should be he one ha minimizes (8). III - Resuls The Table below exhibis he coefficiens of he Taylor rule ha opimize each frequency of evaluaion: Table 1: Coefficiens of he Taylor rule by Frequency of Evaluaion Coefficiens Period of Evaluaion 2 4 and γ 1 (ineres rae) γ 2 (inflaion) γ 3 (oupu gap) As i can be seen, excep for evaluaion done a every wo periods, he coefficiens for he oher frequencies are very similar and, in he case of γ 2, he 7 Coefficien γ 2 should be greaer han 1 in order o ensure sysem sabiliy. Inuiively, if γ 2 1, he Cenral Bank plays an accommodaive moneary policy, leing real ineres rae fall when inflaion is rising. This behavior lead o higher aggregae demand, wha pressures inflaion upwardly. 8 This is he mos common loss funcion found in he lieraure, alhough here are oher specificaions. In general, here are erms penalizing deviaions of inflaion from he arge and oupu gap deviaions, 8

10 response of nominal ineres rae o inflaion, he value was very close of 1.5, he one found by Taylor (1993). In all cases, ineres rae is opimally se wihou aking ino consideraion is previous value (γ 1 = 0). Finally, as expeced, he reacion of ineres rae o deviaions of inflaion o he arge is sronger when evaluaion is made a every wo quarers. In his case, due o he fac ha he oupu gap is very auoregressive, here is no enough ime for moneary police o affec inflaion hrough he aggregae demand channel. Therefore, he only way for ineres rae o offse he shocks will be hrough he exchange rae channel. Char 1: Oupu Gap Variance by Evaluaion Frequency 0,008 0,007 0,006 0,005 0,004 0,003 0,002 0, Quarer Frequency = 2 Frequency = 4 and 6 Frequency = 8 Frequency = 12 Char 1 raifies he hypohesis presened in he inroducion ha i is possible o have a cerain conrol of oupu gap variance, even if he Cenral Bank has he sole objecive o minimize he deviaion of inflaion o he arge. Each loccus shows he variance of oupu gap for a specific evaluaion frequency. This variance is he resul of a moneary policy, which follows he Taylor rule ha opimizes he uiliy of he Cenral Bank. Since he Taylor rules ha opimize he frequencies from 4 o 12 periods are very similar, i is sraighforward ha he variances associaed wih hese rules are also similar. The variances are more differen when one considers he woperiod frequency, hough. From he 5 h quarer on, i is more eviden ha he oupu gap variance falls monoonically wih he increase in he inerval of evaluaion. The similariy of he oupu gap variance in he firs wo quarers among he differen alhough hese erms are no necessarily quadraic. I is also found loss funcions involving penalies 9

11 Taylor rules can be aribued o he exising lags in he ransmission mechanism of moneary policy hrough he aggregae demand channel. In he firs periods, he behavior of oupu gap is mosly deermined by he realizaions of he error erm of he IS curve and are only marginally affeced by moneary police. Char 2 exhibis he variance of inflaion by each Taylor rule. The behavior was similar o he one observed for he oupu gap. Along ime, he variances associaed wih he wo-period evaluaion frequency ge furher apar from he variances associaed wih oher frequencies. I should be observed ha an excessive reacion of ineres rae o he deviaions of inflaion o he arge does no necessarily reduce he variance of inflaion. Afer all, in he Taylor rule associaed wih he woperiod frequency, he coefficien of inflaion is almos 3 imes bigger (4.4 versus abou 1.55) han he coefficiens for inflaion associaed wih oher frequencies. Neverheless, he variance of inflaion afer hree quarers is higher under he woperiod frequency. As here is no ineres rae smoohing (coefficien γ 0 = 0 in he Taylor rule), he smaller inflaion variance under longer periods of evaluaion may be explained by he fac ha he Cenral Bank also responds o deviaions of he oupu gap. Tha is, when reacing o he oupu gap, he Cenral Bank can also reduce inflaion variance. Char 2: Inflaion Variance by Frequency of Evaluaion 0,004 0,0035 0,003 0,0025 0,002 0,0015 0,001 0, Quarers Frequency = 2 Frequency = 4 and 6 Frequency = 8 Frequency = 12 Table 2 below exhibis he loss of he governmen by differen weighs (λ) aached o inflaion and oupu gap variances. The losses were calculaed using he variances found above. I was assumed a semi-myopic sociey, ha considers only he for ineres rae and exchange rae variaion. 10

12 firs 13 periods o evaluae he loss. This limiaion o 13 periods was due, mainly, o compuaional coss. However, from he rends presened in chars 1 and 2, i seems likely ha he ordering of inflaion and oupu gap variances should no be affeced when longer horizons are inroduced in he loss funcion. The resuls shown refer o a discoun rae (ρ) of 0.99, bu hey are robus o differen values of ρ 9. As i can be seen, varying λ from 0 o 0.8, ha is, in a range ha encompasses a zero weigh o inflaion variance o a weigh ha is relaively large, he opimal frequency of evaluaion is 3 years. If λ is beween 0.8 and 1, which corresponds o a sociey ha is exremely averse o inflaion, i is opimal o evaluae he Cenral Bank a inervals of wo years. 9 The ordering of preferences did no change for ρ higher han

13 Table 2: Value of he Governmen's Loss Funcion by λ and by Frequency of Evaluaion λ (weigh Frequency of Evaluaion for inflaion) 2 4 and The resul above indicaes ha he frequency of evaluaion of he inflaionargeing regime in Brazil is sub-opimal. However, as able 3, shows, he loss associaed wih his sub-opimaliy is very small in relaive erms. This able shows he incurred loss (in %) when i is used an evaluaion frequency differen from he one ha minimizes he governmen's loss funcion, for each λ. For evaluaions done a each 4 quarers, like in he Brazilian regime, he loss ranges from 15% when λ = 0 o less han 1% when λ = 1. I is possible ha oher aspecs no capured in he model, like he credibiliy of he Cenral Bank, favor shorer frequencies of evaluaion. Bu i is clear from he resuls ha evaluaions done a very high frequency should lead o welfare losses. 12

14 Table 3: Relaive Loss by λ and by Frequency of Evaluaion (in %) λ ( weigh Frequency of Evaluaion of inflaion) 2 4 and Conclusions This paper esimaed opimal Taylor-ype rules for differen frequencies of Cenral Bank evaluaion, using he model of Baini and Haldane (1999) and he parameers calibraed by Bonomo and Brio (2001). I was observed ha, for evaluaions beween 4 and 12 quarers, he opimal Taylor rules were very similar. The coefficien referring o he reacion of ineres rae o deviaions of inflaion from he arge is around 1.5 and he coefficien referring o he reacion of ineres rae o oupu gap deviaion is close o 1. When evaluaion is made a every wo quarers, he opimal Taylor rule implies a reacion of ineres rae o deviaions of inflaion abou hree imes more inense han in he oher cases. The main explanaion for such discrepancy should be relaed o he lags associaed wih he aggregae demand channel of moneary policy ransmission mechanism: wih very frequen evaluaions, he ineres rae can only offse he effecs of he shocks hrough he exchange rae channel and, herefore, he moneary policy should be more reacive o inflaion deviaions from he arge. Seing an appropriae frequency of evaluaion was shown o be an insrumen capable of aenuaing he differen objecives of he governmen and of he Cenral Bank. More specifically, while he governmen is concerned wih he variances of 13

15 inflaion and oupu gap, he Cenral Bank has he only objecive of guaraneeing ha acual inflaion lies inside a pre-esablished olerance inerval. By assessing he Cenral Bank performance a longer periods, i is possible o reduce he oupu gap variance and, consequenly, o induce moneary policy o generae macroeconomic oucomes ha are more compaible wih wha he governmen considers opimal. The sochasic simulaions showed ha he governmen can minimize is funcion loss by making evaluaions a every 12 quarers, when he weigh aached o inflaion variance in is loss funcion ranges from 0 o 0.8. If he governmen is exremely averse o inflaion (λ > 0,8), he opimal frequency of evaluaion is around 2 years. However, he curren Brazilian sysem, where he performance of he Cenral Bank is assessed in he end of he calendar year, does no impose significan welfare loss: he loss varies from 15%, when λ =0, o less han 1% for λ =1. A naural exension of his work would be o es he robusness of he resuls. This can be made by repeaing he procedure for oher specificaions of he IS and Phillips curves or by using oher ypes of ineres rae rules, like he ones where he ineres rae is se according o expeced inflaion. Anoher possible exension would be o inroduce he credibiliy of he Cenral Bank ino he analysis. This may cause a shorening in he opimal period for Cenral Bank evaluaion. The inuiion is ha, wih very disan evaluaions in ime, he Cenral Bank can guide moneary police in order o aend oher objecives (for example, shor-run populariy) in he periods where here is no evaluaion, increasing he probabiliy of no achieving he arge for inflaion. 14

16 References: Baini, N. and Haldane, FOR Forward-Looking Rules goes Moneary Policy, in Taylor, J.B. Moneary Policy Rules, Universiy of Chicago Press. Baini, N. and Nelson, E Opimal Horizons goes Inflaion Targeing, Bank of England Working Paper Series no Bernanke, B, Laubach, T, Mishkin, F S and Posen, A.S Inflaion Targeing: Lessons from Inernaional Experience, Princeon Universiy Press. Blanchard, O. and Kahn, C The Soluion Linear Difference Models under Raional Expecaions, Economerica vol. 48, no. 5, pp Bonomo, M. and Brio, R Regras Moneárias e Dinâmica Macroeconômica no Brasil: Uma Abordagem de Expecaivas Racionais (Moneary rules and Macroeconomic Dynamics in Brazil: A Raional Expecaions Approach), Ensaio Econômico No. 410, Fundação Geúlio Vargas, Rio de Janeiro, Brazil. Clarida, R., Galí, J. and Gerler, M The Science of Moneary Policy: A New Keynesian Perspecive, Journal of Economic Lieraure, vol. 37, December, pp Esrella, A. and Mishkin, F Rehinking he Role of NAIRU in Moneary Policy: Implicaions of Model Formulaion and Uncerainy, in Taylor, J.B. Moneary Policy Rules, Universiy of Chicago Press. Taylor, J.B Discreion versus Policy Rules in Pracice, Carnegie-Rocheser Seriaes on Public Policy, vol. 39(0), pp Taylor, J.B The Moneary Transmission Mechanism and he Evaluaion of Moneary Policy Rules, Working Paper Series of he Cenral Bank of Chile no.87, December. 15