The Optimal Instrument Rule of Indonesian Monetary Policy

Transcription

1 The Opimal Insrumen Rule of Indonesian Moneary Policy Dr. Muliadi Widjaja Dr. Eugenia Mardanugraha Absrac Since 999, according o Law No. 3/999, Bank Indonesia (BI- he Indonesian Cenral Bank) se inflaion argeing as he goal of is moneary policy. A he ime, BI se moneary aggregaes M as is operaional insrumen. However, as BI considers ha M is more and more difficul o conrol, hey change is operaional insrumen ino nominal ineres rae. The changes are sipulaed in Law No.3/004. This paper discusses he opimal value of ineres rae as he operaional insrumen of Indonesian moneary policy, or known as he opimal insrumen rule. Insrumen rule is defined as single mahemaical expression indicaing how much value of ineres rae (as a policy insrumen) is he Cenral Bank supposes o se. Previous examples of insrumen rule are he well-known Taylor rule and McCallum rule. Insrumen rule in his paper is consruced by applying mahemaical model which is hen esed empirically by using economeric mehod. The period of esimaion for he policy insrumen in he model are quarerly moneary daa from The economeric findings explain ha, firs, even hough he seing of he nominal ineres rae policy has differen direcion from inflaion, he changes of cenral bank concern, eiher concern on inflaion sabiliy or oupu sabiliy, would no have large effec he nominal ineres rae policy. Therefore, i is ime for Bank Indonesia o concern more on he oupu growh, since i has only small impac o he decrease of nominal ineres rae. Second, he gap beween acual inflaion wih he arge inflaion conribues as high as 3% of nominal ineres rae increase. I means ha if he gap becomes percen wider, Bank Indonesia is supposed o se he increase of nominal ineres rae by 3 basis poins. In fac, he increase of Bank Indonesia nominal ineres rae as a shor erm insrumen policy is frequenly lower han he opimal nominal ineres rae as he resul findings of insrumen rule in his research. In addiion, Bank Indonesia should also be able o choose he correc iming o increase he nominal ineres rae, in order no o induce inflaionary volailiy bu o conrol inflaion.

2 Finally, Bank Indonesia inflaion arge is se oo low so ha i is difficul for BI o achieve i. This oo low inflaion argeing diminishes he credibiliy of BI moneary policy, since BI should revise i as he acual inflaion rises. Therefore, our suggesion is ha he arge is need o be more evaluaed and announced more frequenly, based on he real economy condiion.

3 . Inroducion In seing is moneary policy insrumen, every cenral bank guides on he purpose i would like o achieve. The role of Bank Indonesia, he Republic of Indonesia cenral bank, according o he Law No. 3 Year 004 is o achieve and mainain he sabiliy of he value of rupiah, he Indonesian currency. The sabiliy of he value of rupiah mean by he law is he sabiliy of he value of rupiah owards goods and services and also owards he foreign exchange. The rupiah sabiliy owards goods and services is measured by he inflaion rae, while is sabiliy owards foreign exchange is measured by he exchange rae. Moreover, Bank Indonesia faces difficul choice beween pressing he inflaion rae and simulaing economic growh. A growing economy is usually followed by he increases of aggregae demand, pushing he price of goods and services up. However, Bank Indonesia does no have o press he inflaion rae o is lowes level. There is an opimal rule of inflaion rae ha suppor he oupu growh in he economy. Therefore, besides argeing inflaion rae, Bank Indonesia mus also considering he oupu growh in seing he correc policy. In keeping he sabiliy of price of goods and services and he oupu growh, currenly many counries apply he inflaion argeing framework. The framework makes i compulsory for he cenral bank o se a quaniaive inflaion arge. The framework makes i compulsory for he cenral bank o be independen in seing he direcion and he magniude of oher macroeconomic variables, as well as choosing and creaing he policy insrumen. The choice of an opimal policy insrumen is always leading o he choice of using he ineres rae or he money supply. Nex, an opimal ineres rae he cenral bank has o deermine is a furher quesion o solve. Lieraures regarding he choice of an opimal moneary policy insrumen sar from Poole (970). In 0 h cenury, here are many rules arise regarding he choice of policy insrumen and magniude seing. Taylor (993) se a rule o deermine an opimal nominal ineres rae in order o respond inflaion rae, he expeced rae of inflaion and oupu gap. In addiion o he Taylor rule, here is anoher rule inroduced by McCallum (987, 988, 993). The deerminaion of unbiased opimal moneary policy insrumen holds specifically for each counry, as each counry has special characerisics in is economy. Technically, he deerminaion of unbiased opimal moneary policy insrumen depends on he magniude of macroeconomic parameers and he economic flucuaion. The economic flucuaion is 3

4 represened by he variances of srucural disurbance, affecing he magniude of macroeconomic parameers. In his paper, we develop a model consruced by Guender (003). The Guender model discusses he srucure of an economy and choosing an opimal ineres rae ha becomes he moneary policy insrumen. The model we develop in his paper differs from he Guender model in a way ha we explicily explain he exchange rae behavior. Afer ha, we esimae he model empirically by using Indonesian quarerly macroeconomic daa from 993: o 006: period. The main resuls obained in he paper are as follows: (i) Alhough he ineres rae deerminaion policy has differen direcion wih inflaion rae, he changes of focus of he cenral bank, wheher he cenral bank concern more eiher on inflaion sabiliy or oupu sabiliy, would no have significan impac on he policy ineres rae. Therefore, i is ime for he cenral bank o pay more aenion on oupu growh, since i has only lile impac on ineres rae decrease. (ii) The gap beween acual inflaion and he arge of inflaion conribues 3% of nominal ineres rae increase. I means ha if he gap becomes wider by %, he cenral bank supposes o increase he opimal ineres rae by 3 basis poins. We find ha he increase of Bank Indonesia nominal ineres rae, as a shor-erm insrumen policy, is usually of lower value han he opimal ineres rae generaed by he insrumen rule of our research. In addiion, Bank Indonesia mus be able o choose he righ iming o increase nominal ineres rae, in order no o simulae inflaion rae bu conrol inflaion rae. (iii) The arge of inflaion se by Bank Indonesia is oo low, causing difficulies for he bank o achieve i. Therefore, he se arge of inflaion needs more evaluaion, and he announcemen of he arge of inflaion needs o be done more ofen, by looking a he acual economy condiion, forward or backward.. Lieraure review There are some rules of moneary policy applied in many counries, among hem are he well-known Taylor rule and McCallum rule. The Taylor Rule can be expressed as follows: a a ( p * ) 0.5y R = r p 0.5 π ~ () 4

5 Here R is shor erm nominal ineres rae ha cenral bank uses as is insrumen or operaing arge. r is he long-run average real rae of ineres. a p is an average of recen inflaion * raes (or a forecas value), and π is he cenral bank s arge inflaion rae. Finally y~ is he measure of he oupu gap, he percenage difference beween acual and capaciy oupu values. The rule suggess ha moneary policy should be ighened (by increase) when inflaion exceeds is arge value and/or oupu exceeds capaciy. The rule proposed by McCallum can be expressed as follows: Here * ( x x ) * a b = x v 0.5 () b is he change in he log of he adjused moneary base, i.e. he growh rae of he base beween period - and. The erms * x is arge growh rae for nominal GDP, x being he change in he log of nominal GDP. * * x is specified as π y *, where * y is he long-run average of growh of real GDP. a v is he average growh of base velociy over he previous 6 quarers, v = x b being he log of base velociy. Guender (003) consruced a moneary policy insrumen using a srucural model explaining he economic behavior of a counry. The Guender model generaed an opimal insrumen rule of moneary policy for counries adoping he inflaion argeing policy. The rule is derived from a simple macroeconomic model in order o find a parameer gauging he opimal policy. Having reached he parameer, we are able o esimae an opimal ineres rae policy. Nex are equaions applied in he Guender model. Equaion (3) and (4) indicae he main behavior of he economy ogeher wih he cenral bank moneary policy. Equaion (5) indicaes he objecive funcion ha he cenral bank would like o achieve, and equaion (6) indicaes he opimal soluion of he cenral bank s goal. Those equaions are wrien as follows: y β v (3) = r E y β > 0, v N(0, ) Equaion (3), represening he IS relaion, explains ha oupu gap will increase a he same momen wih he increase of he expeced oupu gap for he nex period, and will go down o respond he increase of real ineres rae. v 5

6 π E π ay u (4) = a > 0, u N(0, ) u Equaion (4), represening a Forward-looking Phillips Curve, explains ha he curren inflaion rae is he posiive funcion of he nex period expeced inflaion and he oupu gap. T ( π π ) r = r λ (5) Equaion (5) represens he insrumen rule, where variable r is he real ineres rae ha he cenral bank should achieve in running he moneary policy. Variable r is he nominal ineres rae arge, λ is he policy parameer, achieved by deriving he cenral bank objecive funcion. Variable λ indicaes how quick he cenral bank adjuss is moneary policy unil he inflaion arge is reached. Min L = V y ) µ V ( π ) (6) ( Afer ha, equaion (6), he cenral bank objecive funcion, is he sum of variables, he variance of he oupu gap and he variance of he inflaion. The cenral bank chooses a parameer µ indicaing is concern, wheher he cenral bank concern more on he variabiliy of he oupu gap or inflaion. Parameer µ is an exogenous variable deermined by judgmen. v ( µ a ) * a λ = µ (7) β u Finally, equaion (7) is he soluion of equaion (6). The parameer λ * depends on he source of economic uncerainy (he variabiliy of oupu gap and inflaion) and also on he preference of policy maker in running moneary policy. By subsiuing equaion (7) o equaion (5), we will obain he opimal nominal ineres rae. In order o implemen he model on Indonesian economy and he way Bank Indonesia se is opimal ineres rae, we need o esimae equaion (3) and (4) in he model. The Guender model lays freedom o do empirical esing o gain he following opimal parameer: β (a coefficien relaing he ineres rae and oupu gap), a (a coefficien relaing inflaion and oupu gap), he sochasic disurbance variance of each equaion, and he cenral bank preference parameer µ. 6

7 3. The Model The goal of his research is o develop he Guender model unil we achieve an opimal nominal ineres rae for Bank Indonesia s arge of operaion. The characerisics of he model ha we applied are several. Firs, he insrumen used as an inermediae arge is he nominal ineres rae, leaving no space for a debae wheher money supply or ineres rae o be used as he chosen insrumen. Second, he model is consruced only for counries applying he inflaion argeing policy. Finally, he model assumes ha economic agens are forward looking in forming heir expecaion, applying he raional expecaion. However, he Guender model assumes a closed economy, so he model has no included he exchange rae flucuaion explicily. The exchange rae flucuaion is our improvemen over he Guender model. The model characerisics follow he curren world economy condiion, where many counries cenral bank apply he inflaion argeing policy and se he nominal ineres rae as he inermediae arge. Meanwhile, he raional expecaion heory is also a modern heory in explaining how people form heir expecaion, leaving he adapive expecaion heory behind. In explaining he cenral bank characerisics, besides he oupu and inflaion sabilizaion, he exchange rae sabilizaion could also be anoher main focus of cenral bank policy. The model applied in his research is o compile equaion (3) o (5) in a sysem of equaion and afer ha we add he following equaion (8): = Ee * ( r r ) w e γ (8) Variable e is he real exchange rae as a funcion of he difference beween real domesic ineres rae (r) and foreign ineres rae (r*). We ake he firs order condiion of cenral bank objecive funcion in equaion (6) o ge a parameer deermining he opimal ineres rae. By following he flow of he model, we can deermine wheher he acual Bank Indonesia ineres rae policy (called he BI Rae ) is higher or lower or close o he esimaed opimal value. In shor, we wrie down he sysem of equaion as follows: β IS Relaion. y r E y b( Ee e ) v =. π = E π ay u Forward Looking Phillips Curve T 3. r r λ( π π ) = Insrumen Rule 7

8 * 4. e Ee ( r r ) w = γ Ineres Rae Pariy Condiion The purpose of he sysem of equaion is o find he opimal soluion value for parameer λ. Having gained he esimaed value of parameer λ and he esimaed value of oher coefficiens, we will gain he esimaed value of he opimal cenral bank ineres rae. An esimaion problem wih a forward-looking model is he difference of ime period beween a dependen variable wih he equaion s error erm. The exisence of ime period differences cause esimaion bias on variance of errors. In fac, variance of errors is he main componen o gain he esimaed insrumen rule. To overcome he ime period difference problem, Rudd & Whelan (005) express he following forward looking equaion: in erm of: π f b = ω Eπ ω π γx (9) f b π = ω π ω π γx ε (0) Which are: π ( he acual inflaion a ime ), ε : (he error of expecaion), x : ( he oupu gap or unemploymen rae). According o he heory of raional expecaion, he error erm a equaion (0) canno be deermined a ime, so ha he coefficien ω f can be esimaed consisenly by using he same variable a ime period or before, as a coefficien for π. We esimae he coefficien ω f using he following mehod: Firs, we do a backward-looking esimaion o gain esimaed values of π owards he ˆ following equaion: ˆ π ˆ ˆ ˆ x = δπ δ δ3z () In equaion (), variable z is oher unknown variable simulaing inflaion. ˆ Second, we use he esimaed values of π on he second sage regression beween he curren inflaion π as he independen variable owards he expeced fuure inflaion ˆ (approximaed by π ), he lag of inflaion rae π nex regression equaion: f b = ω π ω π γx ε and he driving variable x, reaching he π ˆ () 8

9 We esimae he Forward Looking Phillip Curve by using he wo-sage regression mehod. We also use he same mehod o esimae equaion (3), (4) dan (8). 4. Solving he model The model is solved by using a pos-puaive soluion for he hree endogenous variables: y φ 0 φv φu φ3 = w (3) 0 φv φu φ3 π = φ w (4) e φ 30 φ3v φ3u φ33 = w (5) Readers may find he mahemaical derivaion for he opimal soluion in Appendix. he soluion of equaion (6) is he parameer λ, derived mahemaically wih he following sep: (i) Subsiue one equaion o anoher o ge he reduced form for oupu, inflaion and exchange rae. (ii) Deermine he coefficien of error erm and he inercep of each reduced form equaion of oupu, inflaion and exchange rae. (iii) Creae he equaion of oupu variance and inflaion variance by using he reduced form equaion. (iv) Take he firs order equaion for equaion (6) from he equaion of oupu variance and inflaion variance creaed in he previous sep (v) Generae he opimal value of parameer λ, whose value depends on oher parameers in he srucural equaion. The oher parameers are: he source of uncerainy in he economy (he oupu gap variabiliy and inflaion variabiliy) and he preference of he policy maker. (vi) Subsiue he opimal parameer λ ino equaion (5) o ge he value of opimal nominal ineres rae. Having included he ineres rae pariy equaion, he soluion for he objecive funcion is: Minimize L λ ( λa( β bγ )) [( µ a ) ( µ λ ( β bγ ) ) ( b µ a b ) ] = (6) v u w The soluion for he firs order condiion of equaion (6) is he opimal value of he following insrumen rule parameer: λ * a v w = µ ( µ a ) b β bγ u u (7) 9

10 Readers may see how equaion (7) differs from equaion (7). Equaion (7) explicily include he variance of errors of he exchange rae ( ), derived from he ineres rae pariy equaion. Equaion (7) saed ha he opimal moneary policy no only affeced by he flucuaion of oupu and inflaion, by also by he exchange rae flucuaion. We apply he consruced model o explain he behavior of Indonesian economy and he way Bank Indonesia is supposed o se he opimal ineres rae. In ha case, we need o esimae equaion (3), (4) and (8) empirically. The parameers o be esimaed from he hree equaions are: β (a coefficien relaing he ineres rae and he oupu gap), a (a coefficien relaing he inflaion and he oupu gap), γ (a coefficien relaing he exchange rae wih domesic and inernaional ineres rae pariy), he variance of sochasic disurbance for each equaion, and he cenral bank preference parameer µ. A necessary condiion for he esimaed model is ha i has a forward-looking explanaory variable. w 5. The Empirical Evidence To deermine he opimal ineres rae, we sar from doing esimaion owards hree srucural equaions, equaion (3), equaion (4) and equaion (8). The bes model we esimae is he one making parameers of he hree equaions saisically significan. The esimaion resuls by using saisical sofware EVIEWS are shown in Appendix. We do a wo-sage regression for each equaion. A he firs sage, we esimae he expeced value of each dependen variable, hen use he forecased expeced value a he firs sage as he proxy for he expeced value a he second sage. Rudd and Whelan (005) apply a wo-sage regression o avoid he model misspecificaion problem. We apply he logarihm ransformaion for each variable in he srucural equaion o make he value of esimaed variance homogenous and no more dependen on he uni of daa. The Forward Looking Phillips Curve equaion is being esimaed by using logarihmic CPI variable insead of inflaion daa, in order o generae he variance of error homogenous among equaions. The esimaed parameer value of equaion (3), (4), and (8) above is as follows: a : b : 0.75 β : 0.00 γ :

11 The hree esimaed srucural equaion can be formulaed as: =.00* r E y 0.75* ( Ee e ) v y 0 (8) π = E π 0.085* y u (9) = Ee.0353* * ( r r ) w e 0 (0) We use he sum squared residual (SSE) from each equaion o esimae variance of error erm of each srucural equaion, following he definiion: variance of error erm = SSE / (T-M). Variable T = he amoun of observaion and M = he amoun of esimaed parameer. The esimaed values of he hree variance of error are: v : u : w : 0.83 Nex, we subsiue he values of esimaed parameers and he value of variance of errors o ge he value of λ* in equaion (7), equal o Therefore, we conclude ha he insrumen rule as he guidance for Indonesian moneary policy based on daa: r T ( π π ) = r 0.38 * (8) Equaion (8) shows ha here is a roughly 3% deviaion of he difference beween inflaion arge and acual inflaion, for he opimal ineres rae from he long run ineres rae. The higher he difference beween inflaion arge and acual inflaion is, he wider he gap beween he long run ineres rae and he opimal ineres rae ha Bank Indonesia is supposed o achieve. As example, in May 008, Bank Indonesia se BI rae a 8.5%, increase by 5 basis poin from he previous period, 8%. If we follow he insrumen rule we generae in equaion (8), and assume ha he inflaion arge and he oupu growh arge have he same value, wih he inflaion arge as much as 6.5%, BI is supposed o se he ineres rae a 8.78% insead of 8.5%.

12 Table Several Values of Ineres Rae and Inflaion Based on he Insrumen Rule Variable Opimal Value Acual Value Opimal ineres rae Inflaion arge acual inflaion (yoy) previous period ineres rae Source : Bank Indonesia and esimaion resul The insrumen rule performed in equaion (8) emphasizes he imporance of achieving he inflaion arge. The insrumen rule provide space for he acual inflaion o be higher 0.8% han he inflaion arge, assuming ha he curren Bank Indonesia ineres rae policy were opimal. By ha assumpion, he increase of 5 basis poin ineres rae aken by yang Bank Indonesia may only decrease inflaion rae o he level 8.6%, no o is arge level; i.e. 5%. Our nex discussion will be based on wo simulaions. Firs, a simulaion ha explains he imporance of he cenral bank o focus o is goal, wheher he goal is oupu sabiliy or inflaion sabiliy. Second, a hisorical review comparing he se BI rae so far wih he opimal ineres rae generaed by he insrumen rule in equaion (8). The focus of he cenral bank is shown by he parameer µ in he objecive funcion L = V y ) µ V ( π ). The value µ = shows ha he cenral bank se he same weigh beween ( oupu sabiliy and inflaion sabiliy. The higher he value of parameer µ is, he more aenive he bank cenral owards inflaion sabiliy. The simulaion on many values of parameer µ and λ resuled on a linear funcion beween he wo parameers, as shown in Figure :

13 Figure The Linear Funcion of Parameer µ oward Parameer λ 0.5 λ = µ Noes: µ = a parameer indicaes he focus of a cenral bank on conrolling inflaion. The higher he value of he parameer indicaes ha he cenral bank prefer conrolling inflaion o promoing economic growh. λ = a parameer indicaes he funcion of he gap beween acual inflaion wih arge inflaion owards he difference beween opimal and acual ineres rae. Figure shows ha he higher he focus of he cenral bank owards inflaion sabiliy is, he larger he role of differenial proporion of inflaion arge and acual inflaion on opimal ineres rae. I means ha o achieve he inflaion arge, Bank Indonesia mus se a higher BI rae. The implicaion is ha, should Bank Indonesia se a oo low inflaion arge, i will have heavier burden o pay he ineres on Cerificae of Bank Indonesia (Serifika Bank Indonesia- SBI), he cenral bank securiies insrumen o do open marke operaion. Figure Inflaion, BI Rae and Opimal Ineres Rae Based on 6.5% Inflaion Targe y-o-y Period Augus 9 April 3, 008 3

14 Aug-05 6-Sep-05 4-Oc-05 -Oc-05 6-Dec-05 9-Jan-06 7-Feb-06 7-Mar-06 5-Apr-06 9-May- 6-Jun-06 6-Jul-06 8-Aug-06 5-Sep-06 5-Oc-06 7-Nov-06 7-Dec-06 4-Jan-07 6-Feb-07 6-Mar-07 5-Apr-07 8-May- 7-Jun-07 5-Jul-07 7-Aug-07 6-Sep-07 8-Oc-07 6-Nov-07 6-Dec-07 8-Jan-08 6-Feb-08 6-Mar-08 3-Apr Acual BI Rae Opimal Ineres Rae Inflaion Source: Figure shows a simulaion beween he BI rae, opimal ineres rae and acual inflaion since Bank Indonesia announced BI rae for he firs ime (Augus 9, 005) up o dae (April 3, 008). There are wo assumpions regarding how he figure is made. Firs, we assume ha Bank Indonesia se he same weigh beween oupu sabiliy and inflaion sabiliy (µ = ). Second, hey se inflaion arge a 6.5%. We may see from Figure ha he higher inflaion rae is, he wider he gap beween BI rae and he opimal ineres rae. 6. Conclusion The sep aken by Bank Indonesia o se he inflaion argeing policy framework following he worldwide moneary policy - is accurae. However, for he case of Indonesia, Bank Indonesia does no have an insrumen rule as a guidance for policy implemenaion ye. The purpose of his paper is o consruc a moneary policy rule for Indonesia, developed from he Guender opimal rule (003) and from he empirical esimaion of he model. Several conclusions from he empirical esimaion resul are as follows. Firs, he policy based ineres rae has differen direcion wih he inflaion rae. However, he changes of he focus of he cenral bank s policy, wheher hey concern more eiher on sabiliy inflaion or on oupu sabiliy, neiher have large nor significan impac on he changes of he ineres rae policy (BI rae in his case). Therefore, i is ime for Bank Indonesia 4

15 o pay more concern on he growh of oupu, since i has only small impac on he decrease of ineres rae. Second, he gap beween acual inflaion wih inflaion arge conribues as high as 3% o he increase of ineres rae. As he gap increases by %, he opimal ineres rae Bank Indonesia is supposed o se increases by 3 basis poins (0.3 %). The increase of BI rae as a shor-erm policy insrumen is mosly lower han he opimal ineres rae generaed by he insrumen rule of our research. In addiion, Bank Indonesia need o choose well-iming o increase he ineres rae, as well as concern on increasing a higher long-run ineres rae ha is valid in longer erm. Finally, he inflaion arge se by Bank Indonesia is relaively oo low, make i difficul o achieve. Therefore, Bank Indonesia needs o evaluae he arge and needs more ofen and regularly announce he inflaion arge, according o he pas and presen economic condiion, and he fuure expecaion. 5

16 References BEECHEY, MEREDITH, NARGIS BHARUCHA, ADAM CAGLIARINI, DAVID GRUEN and CHRISTOPHER THOMPSON (000), A Small Model of he Ausralian Macroeconomy, Economic Research Deparmen. Reserves Bank of Ausralia. Research Discussion Paper. DEBELLE, GUY and JENNY WILKINSON (00), Inflaion Targeing and The Inflaion Process: Some Lessons from an Open Economy, Economic Research Deparmen. Reserves Bank of Ausralia. Research Discussion Paper. GUENDER, ALFRED V. (003), Opimal Moneary Policy under Inflaion Targeing Based on an Insrumen Rule, Economic Leers.78 (003) LEITEMO, KAI & ULF SÖDERSTRÖM. (005), Robus Moneary Policy in A Small Open Economy, Bank of Finland Discussion Papers.0. MAJARDI, FAJAR (004), Pembenukan Model Makroekonomi Skala Kecil (SSMX), Bagian Sudi Sekor Rill. Direkora Rise Ekonomi dan Kebijakan Moneer. Bank Indonesia. RUDD, JEREMY & KARL WHELAN (005), New Tes of The New-Keynesian Phillips Curve, Journal of Moneary Economics. 5(005) Websie of Bank Indonesia a 6

17 Appendix Subsiue Phillips Curve eq(4) o insrumen rule eq (5) T (A) r r λ( E π ay u π ) = Subsiue eq (A) o IS Relaion eq (3) T (A) y = β ( r λ( Eπ ay u π ) E y b( Ee e ) v Subsiue eq (8) o eq (A) T * (A3) y = β ( r λ( Eπ ay u π ) E y b( γ ( r r ) w ) v Subsiue eq (A) o eq (A3) T (A4) y = β ( r λ( Eπ ay u π ) E y T * b ( γ ( r λ( Eπ ay u π ) r ) w ) v Reduced Form IS Relaion T ( ) = β ( r λ( Eπ u π ) E y T * b ( γ ( r λ( Eπ u π ) r ) w ) v (A5) y λ a( β bγ ) Puaive Soluions for endogenous variables: (A6) y = φ 0 φv φu φ3 w (A7) (A8) π = φ 0 φv φu φ3 e = φ 30 φ3v φ3u φ33 w w The Expeced Values (A9) E y = φ0 (A0) E π = φ0 (A) E e = φ30 Soluion for parameers in eq (6) (A) φ 0 = 0 (A3) φ = λa b ( β γ ) 7

18 (A4) (A5) λ φ = λ b φ3 = λa ( β bγ ) a( β bγ ) ( β bγ ) Subsiue eq () o eq (4) T * (A6) e = Ee γ ( r λ( Eπ ay u π ) r ) w Subsiue eq (6) and he expeced values o eq (9) T * ( ( 0 3 u ) r ) w (A7) φ γ r λ E π a( φ φ v φ u φ w ) e = 30 π Soluion for parameers in eq (8) (A8) (A9) (A0) φ φ φ γλa = λa ( β bγ ) γλ = λa b ( β γ ) λabγ = λa ( β bγ ) Subsiue eq (6) and he expeced values o eq () (A) π = φ0 a ( φ0 φv φu φ3w ) u Soluion for parameers in equaion eq (7) (A) (A3) (A4) φ φ φ a = λa ( β bγ ) = λa b = λ ( β γ ) ab a ( β bγ ) 8

19 9 The objecive funcion is: (A5) ( ) ( ) ( ) ( ) ( ) ( ) [ ] w u v b a b b a b a L Minimize µ γ β λ µ µ γ β λ λ = The policy maker is assumed o se he parameer value ha minimizes he loss funcion. The parameer opimal value of he insrumen rule is: (A6) ( ) = * u w u v b a b a µ µ γ β λ

20 Appendix EVIEWS oupu of esimaion of he IS Relaion equaion Dependen Variable: GDPGAP Mehod: Leas Squares Dae: 05/6/08 Time: :3 Sample(adjused): 993: 006:4 Included observaions: 55 afer adjusing endpoins Convergence achieved afer 3 ieraions Variable Coefficien Sd. Error -Saisic Prob. C AR() R-squared Mean dependen var Adjused R-squared S.D. dependen var 094. S.E. of regression Akaike info crierion.9955 Sum squared resid 5.33E09 Schwarz crierion.3755 Log likelihood F-saisic.0050 Durbin-Wason sa Prob(F-saisic) Dependen Variable: LOG(ABS(GDPGAP-GDPGAPF())) Mehod: Leas Squares Dae: 06/05/08 Time: 3:38 Sample(adjused): 993: 006:3 Included observaions: 55 afer adjusing endpoins Variable Coefficien Sd. Error -Saisic Prob. C LOG(ABS(USDF() USD)) 0.4*SBI *SBC R-squared Mean dependen var Adjused R-squared S.D. dependen var S.E. of regression Akaike info crierion Sum squared resid Schwarz crierion Log likelihood F-saisic Durbin-Wason sa Prob(F-saisic)

21 EVIEWS oupu of esimaion of he Phillips Curve equaion Dependen Variable: CPI Mehod: Leas Squares Dae: 05/6/08 Time: 3:07 Sample(adjused): 993:3 00:4 Included observaions: 38 afer adjusing endpoins Variable Coefficien Sd. Error -Saisic Prob. CPI(-) CPI(-) R-squared Mean dependen var Adjused R-squared S.D. dependen var S.E. of regression.6076 Akaike info crierion Sum squared resid Schwarz crierion Log likelihood Durbin-Wason sa.9076 Dependen Variable: LOG(ABS(CPI-CPIF())) Mehod: Leas Squares Dae: 05/6/08 Time: 3:0 Sample(adjused): 993:3 006:3 Included observaions: 53 afer adjusing endpoins Convergence achieved afer 9 ieraions Variable Coefficien Sd. Error -Saisic Prob. LOG(GDPGAP) AR() R-squared Mean dependen var Adjused R-squared S.D. dependen var S.E. of regression Akaike info crierion Sum squared resid Schwarz crierion Log likelihood Durbin-Wason sa Invered AR Roos.63

22 EVIEWS oupu of esimaion of he Ineres Rae Pariy equaion Dependen Variable: USD Mehod: Leas Squares Dae: 05/3/08 Time: 6:56 Sample: 993: 006:4 Included observaions: 56 Variable Coefficien Sd. Error -Saisic Prob. SING YEN R-squared Mean dependen var Adjused R-squared S.D. dependen var S.E. of regression Akaike info crierion Sum squared resid Schwarz crierion Log likelihood Durbin-Wason sa Dependen Variable: LOG(ABS(USD-USDF())) Mehod: Leas Squares Dae: 06/03/08 Time: :30 Sample(adjused): 993: 006:3 Included observaions: 55 afer adjusing endpoins Variable Coefficien Sd. Error -Saisic Prob. C ABS(SBI-FEDRATE) R-squared Mean dependen var Adjused R-squared S.D. dependen var S.E. of regression Akaike info crierion Sum squared resid Schwarz crierion Log likelihood F-saisic Durbin-Wason sa.585 Prob(F-saisic)