Taylor Rules and Inflation Targeting do not Work with Systematic Foreign Exchange Market Intervention. Víctor Olivo. Banco Central de Venezuela

Transcription

1 Talor Rules and Inflaon Targeng do no Work wh Ssemac Foregn xchange Marke Inervenon Vícor Olvo Banco Cenral de Venezuela Absrac Ths paper examnes how he ssemac aemp o nfluence drecl he pah of he nomnal exchange rae due o fear of floang affecs he conduc of monear polc under a Talor rule and nflaon argeng The paper demonsraes ha mplemenng a Talor rule or an nflaon-argeng scheme smulaneousl wh polces ha r o moderae he rae of deprecaon of he nomnal exchange rae ma resul n an nconssen monear polc In addon, he paper shows n a relavel smple framework he close heorecal connecon beween a Talor rule and nflaon argeng Ths arcle does no reflec he opnon of he Cenral Bank of Venezuela Professor Sephen Mller Unvers of Nevada a Las Vegas made mporan conrbuons o prevous versons of he paper An remanng errors are he sole responsbl of he auhor

2 - Inroducon Inflaon argeng became wdel popular among cenral banks durng he 990s The frs wave of cenral banks ha adoped nflaon argeng n he frs half o hs decade was manl from ndusralzed counres In he lae 990s, however, several Lan Amercan cenral banks embarked on nflaon argeng Currenl, he cenral banks of Chle, Mexco, Brazl and Colomba pracce nflaon argeng Jonl wh he spreadng of nflaon argeng, here has been an exploson on he leraure ha covers dfferen praccal and heorecal aspecs of hs monear polc regme Bofnger 00, however, pons ou ha n conras o monear argeng ha was appled b cenral banks afer nensve academc dscusson, nflaon argeng was frs pu n pracce b cenral banks and hen researchers began o produce he heorecal suppor Mos of he leraure avalable on nflaon argeng has focused on counr experences wh he scheme Lederman and Svensson, 995, Bernanke e al 999; mplemenaon of nflaon argeng as nflaon forecas argeng Svensson, 996; analss of he responses o dfferen shocks, consequences of model unceran, effecs of neres rae smoohng and sablzaon, comparson wh nomnal GDP argeng, and mplcaons of forward-lookng behavor Svensson, 997; sudng nflaon argeng n he conex of monear polc rules Svensson, 998; examnng he effcenc of nflaon argeng n relaon o Talor rules n closed economes Ball, 997 and open economes Ball, 998 Alhough nflaon argeng currenl reflecs he monear polc sraeg of choce of hose counres ha wan o provde he econom wh a nomnal anchor whle avodng he excessve rgd of hard or sof pegs, Calvo and Renhar 000 argue

3 ha man counres ha sa he allow her exchange rae o floa acuall do no Those auhors conen ha an epdemc case exss of fear of floang The man purpose of hs paper s o sud how he ssemac aemp o nfluence drecl he pah of he nomnal exchange rae due o fear of floang affecs he conduc of monear polc under a Talor rule and nflaon argeng The paper demonsraes ha mplemenng a Talor rule or an nflaon-argeng scheme smulaneousl wh polces ha r o moderae he rae of deprecaon of he nomnal exchange rae ma resul n an nconssen monear polc In addon, he paper shows n a relavel smple framework he close heorecal connecon beween a Talor rule and nflaon argeng Ths s an mporan ssue, because as we menoned prevousl, nflaon argeng has been spreadng rapdl n counres ha ma be experencng smulaneousl fear of floang The paper s organzed as follows Secon examnes he relaonshp beween a Talor rule and nflaon argeng n a closed econom Secon 3 exends he analss o an open econom In parcular, focuses on he effec on a Talor rule and nflaon argeng of adopng smulaneousl an exchange rae regme based on a crawlng peg Ths analss mplcl assumes mperfec capal mobl, so he monear auhor can exer some degree of conrol over he domesc neres rae Secon 4 examnes he effec on a Talor rule and nflaon argeng of ssemac nervenon n he foregn exchange marke o curb he volal of he nomnal exchange rae whou pursung an arge for ha varable Secon 5 concludes - Talor Rules and Inflaon Targeng: Closed conom The closed econom model developed here closel follows Ball 997 I consss of a dnamc IS funcon, and a Phllps curve In conras o Ball, I subsue he real 3

4 neres rae r usng he Fsher ex pos relaonshp, and solve he model for he nomnal neres rae I measure all varables as devaons wh respec o her respecve means n logarhms In hs model, akes wo perods for monear polc o affec nflaon hrough changes n he neres rae -- one perod for polc o affec oupu, and one perod for oupu o affec nflaon The model ncludes he followng equaons: IS curve: = r λ ε Phllps curve: = η Fsher ex pos relaon: = r 3 Subsung hs relaon no equaon produces: = λ ε, a = η a For perod, he model s wren as follows: = λ ε, b 4

5 = η b Talor Rule The ransmsson mechansm of monear polc assumed n he model mples ha he polcmaker mnmzes he followng expeced quadrac loss funcon n erms of oupu and nflaon varance: L = c 4 Subsung he assumed srucure of he econom n he loss funcon elds: L = c λ [ ], and 4a L = c λ [ λ ] 4b Mnmzng L wh respec o and solvng for produces: λ = [ ] [ ] c c 5 Hence, hs model generaes an opmal polc rule, Talor rule, where s parameers depend on he srucure of he econom and he wegh ha he polcmaker assgns o oupu varabl n he loss funcon c When he polcmaker assgns no wegh o oupu flucuaons c=0, he neres rae rules reduces o: 5

6 λ = 6 Src Inflaon Targeng Ths secon demonsraes ha nflaon argeng mplcl mples an neres rae rule Ball 997 defnes src nflaon argeng as a polc ha mnmzes he varance of nflaon around s average level: = 0 7 Usng equaon updaed wo perods causes equaon 8 o equal: 0 = 8 Subsung equaons b and b no hs expresson resuls n: λ = 0 9 Solvng hs expresson for, produces: λ = 0 The prevous equaon equals he Talor rule wh c=0 e, quaon 5 Hence, src nflaon argeng maches a Talor rule where he polcmaker gves zero wegh o oupu varance Because he Talor rule s he opmal rule n hs model, src nflaon argeng s also an opmal rule for he parcular case ha c=0 6

7 Alhough he polcmaker assgns a zero wegh o oupu flucuaons, he mplc polc rule sll responds o hs varable due o he srucure of he model Flexble Inflaon Targeng Inflaon argeng more generall equals a paral adjusmen rule where expeced nflaon n perod equals a fracon of expeced nflaon n perod Tha s; = θ Once agan, usng equaon updaed wo perods, equaon equals: = θ Subsung equaons b and b no hs expresson and re- arrangng erms leads o: θ λ = 0 3 Solvng for produces: θ λ θ = [ ] [ ] 4 If we defne: θ = c 5 c or θ = c, and subsue no equaon 4, hen equaon 5 emerges Ths mples ha flexble nflaon argeng s, n general, he opmal polc rule n hs model The value of θ 7

8 mplcl depends on he wegh ha he polcmaker assgns o oupu volal n he loss funcon c A larger value of θ, ha s a more gradual pah oward he nflaon arge, assocaes wh a larger c gven he value of 3- Talor Rules and Inflaon Targeng: Crawlng Peg Ths secon develops a model smlar o ha of Ball 998, bu assumes ha he exchange rae follows a crawlng peg Combnng a Talor rule or nflaon argeng wh a crawlng peg ma seem srange a frs, bu ha polc sraeg currenl reflecs he Hungaran and Israel suaons IMF-IFS, Ma 00 In he open econom model, I nroduce he logarhm of he real exchange rae q no he IS funcon and he change of he nomnal exchange rae e - e - no he Phllps funcon The rae of he crawl Ω s specfed as a fracon of he dfferenal beween domesc and foregn nflaon, where he laer s normalzed o zero 0 Ω Thus, he model seup s as follows: IS curve: = r λ q ε 6 Phllps curve: = ψ e e η 7 Fsher ex pos relaon: = r 8 Crawlng peg rule: 8

9 e e = * = Ω ; 0 9 Defnon of he real exchange rae: q ; q = e e 0 q = q Ω Subsung he prevous defnons no equaons 6 and 7 elds: = Ω λ q ε, = ψω η 3 Movng one perod ahead leads o: = Ω λ q ε, a = ψω η 3a In hs model he nroducon of he crawlng peg rule manans he wo-perod lag wh whch monear polc affecs nflaon Ths s due o he fac ha he crawlng rule breaks he explc connecon beween he exchange rae and he neres rae The neres rae, however, sll affecs he behavor of he exchange rae ndrecl hrough s effec on he amoun of nervenon necessar o manan he crawlng rule 9

10 Talor Rule As before, he loss funcon equals: = c L 4 Subsung he equaons of he model no he loss funcon produces: ] [ ] [ Ω Ω = q c L ψ λ, and hen 5 ]} [ ] [ { ]} { Ω Ω Ω Ω = q q c L λ ψ ψ λ 6 Mnmzng L wh respec o and solvng for leads o: ] [ ] [ Ω Ω Ω = q c c ψ ψ λ 7 Agan, he opmal polc n hs model equals a Talor rule Now, he parameers of he polc rule depend posvel on he rae of he crawl Ω The case where c=0 elds he followng neres rae rule: ] [ ] [ Ω Ω Ω = q ψ ψ λ 8 Src Inflaon Targeng As n he closed econom model, src nflaon argeng mples ha: 0

11 = 0 9 Ths leads o: ψ Ω = 0, or 30 ψ Ω[ ψω ] [ Ω λ q ] = 0 30a Solvng for resuls n: λ ψω Ω ψω = [ ] [ ] q 3 Src nflaon argeng equals he opmal Talor rule wh c=0 Flexble Inflaon Targeng As n he closed econom case, a gradual nflaon argeng s defned as follows: = θ 3 quaon 3 can be re-wren as follows: ψ Ω = θ, or 33 [ ψω θ ][ ψω [ 33a Solvng for elds: Ω λ ] q ] = 0

12 λ θ ψω = [ ] q Ω ψω[ θ ψω] { } 34 If we defne: θ ψω = c ψω c ψω or θ =, c and subsue hs expresson no equaon 34, we oban equaon 7 Therefore, flexble nflaon argeng s, n general, an opmal polc Noe ha when c=0, hen equaons 8, 3 and 34 are all dencal Talor Rules and Inflaon Targeng under a Crawlng Peg Regme The prevous resuls show ha he parameers of he nomnal neres rae rule depend posvel on he rae of he crawl Ω Seng a relavel low value of Ω o reduce nflaon owards some arge value, dmnshes he response of he neres rae for a gven devaon of oupu and nflaon wh respec o her respecve means In addon, as long as he crawlng peg regme produces an apprecaon of he real exchange rae, he las erm of he polc rule also ndcaes a lower neres rae for gven devaons of oupu and nflaon The reduced response of he neres rae, n urn, generaes pressures on nflaon b rsng aggregae demand, and on nernaonal reserves as ncreases he amoun of nervenon n he foregn exchange marke necessar o suppor he crawlng rule Hence, n a crawlng peg regme he neres rae rule or s nflaon argeng counerpar ma generae an neres rae oo low o manan he peg Ths s a resul ha one can nuvel expec If a polcmaker ha observes a posve gap beween acual and arge nflaon

13 chooses o reduce he rae of deprecaon of he nomnal exchange rae hrough drec nervenon n he foregn exchange marke, hen she wans o avod a drec ghenng of monear polc o close hs gap 4- Talor Rules and Inflaon Targeng: Ssemac Foregn xchange Marke Inervenon Ths secon develops an analss of he effec on Talor rules and nflaon argeng of ssemac nervenon of he monear auhor n he foregn exchange marke o moderae he rae of deprecaon of he nomnal exchange rae In conras o he crawlng peg model, hs secon focuses on he case where polcmakers do no have an explc arge for he nomnal exchange rae, bu b rng o conrol wha he perceve as hgh raes of deprecaon no relaed o fundamenals, drec nervenon n he foregn exchange marke become ssemac In hs model he amoun of nervenon s an exogenous varable We specf a model smlar o ha of Ball 998, bu assume ha he rae of deprecaon of he nomnal exchange rae depends negavel on he neres rae and he ssemac nervenon of he monear auhor n he foregn exchange marke The model ncludes he followng equaons: IS curve: = r λ q ε 35 Phllps curve: = ψ e e 36 Fsher ex pos relaon: = r η Thus, n hs model he amoun of nervenon n he foregn exchange marke s an endogenous varable ha depends on he neres rae 3

14 37 Nomnal exchange rae adjusmen: e e = τ γfx υ 38 Defnon of he real exchange rae: q * = e ; = 0 39 Subsung he prevous defnons n he equaons of he basc model and movng one perod ahead, elds he followng: = τ λ e γfx ε ν 40, and = ψτ ψγfx η ψν 4 Talor Rule In conras o he prevous model, he presen monear polc affecs boh oupu and nflaon wh one perod lag Hence, n hs case, he loss funcon o mnmze s he followng: L = c 4 Mnmzng L wh respec o and solvng for subjec o he assumed srucure of he econom produces: cλ τ ψτ = c τ ψτ c τ c τ ψτ e c τ ψτ c τ ψτ cγ τ ψ γτ fx c τ ψτ 43 Noce ha n 43 he neres rae responds o he lagged value of he nomnal 4

15 exchange rae and o he level of nervenon n he foregn exchange marke Ball 998 holds ha In open economes, nflaon arges and Talor rules are subopmal unless he are modfed n mporan was Dfferen rules are requred because monear polc affecs he econom hrough exchange-rae as well as neres-rae channels p The neres-rae rule assumng zero nervenon n he foregn exchange marke -- dffers from a sandard Talor rule, because ncludes he exchange rae lagged one perod Ths erm capures he effec of he exchange rae on nflaon ha Ball 998 consders s he source of subopmal of he sandard Talor rule n open economes The case where c=0 generaes he followng Talor rule: = ψτ ψτ γ fx τ 44 Src Inflaon Targeng In hs case, we defne src nflaon argeng as follows: = 0 45 Subsung equaon 36 no he nflaon argeng defnon resuls n he followng expresson: ψτ ψγfx =0 46 Solvng for elds an expresson equvalen o equaon 44: = ψτ ψτ γ fx τ 47 In equaons 44 and 47 he lagged exchange rae erm does no appear, so as Ball How equaon 43 compares o Ball s rule based on a monear condon ndex n erms of opmal s beond he scope of hs paper 5

16 998 argues, src nflaon argeng ma no be opmal n an open econom Wheher he reacon of he neres rae rule o foregn exchange nervenon s conssen wh nflaon argeng s analzed below Flexble Inflaon Targeng As dscussed b Ball 998, n hs model monear polc can conrol nflaon perod b perod In hs conex he defnon of flexble nflaon argeng =θ does no deermne a unque polc rule Hence, s no possble o denf he Talor rule equvalen o flexble nflaon argeng n hs model Ball 998 proposes, however, ha argeng long-run nflaon defned as L = ψe makes possble o oban an operave defnon of flexble nflaon argeng Subsung hs defnon of nflaon n equaons 40 and 4 elds: L = τ λ [ ψ ] e γfx ε ν 48 L L = η 49 The defnon of flexble nflaon argeng s now cas n erms of long-run nflaon: L L = θ 50 Makng he approprae subsuons no equaon 50 and solvng for produces: θ λ θ L = [ ] [ ] τ τ τ τ ψ γ [ ] e [ fx ] τ τ 5 If we defne: 6

17 θ = c c or θ = c, and subsue hs expresson no equaon 5, we oban an equaon equal o he one derve b mnmzng he expeced loss funcon L L = c respec o subjec o he assumed srucure of he econom The value of θ s equal o ha derved n he closed econom model Wha s mporan o hghlgh, however, s ha hs resul does no change he fac ha nervenon n he foregn exchange marke appears as a varable n he neres rae rule Talor Rules and Inflaon Targeng wh Ssemac Inervenon n he Foregn xchange Marke quaons 43, 44, and 47 show ha ssemac nervenon n he foregn exchange marke o decrease he rae of deprecaon of he nomnal exchange rae reduces he response of he neres rae o devaons n oupu and nflaon from her mean values In conras o he crawlng peg case, nervenon n he foregn exchange marke appears as an explc varable n he Talor rule nsead of affecng s parameers Agan, he reduced response of he neres rae s a resul ha one can nuvel expec If a polcmaker ha observes a posve gap beween acual and arge nflaon chooses o moderae he rae of deprecaon of he nomnal exchange rae hrough drec nervenon n he foregn exchange marke, hen she wans o avod a drec ghenng of monear polc o close hs gap Ths dmnshed response of he neres rae, however, generaes pressures on he nflaon rae b ncreasng aggregae demand and on he nomnal exchange rae o deprecae, hus reducng he credbl of he an-nflaon sance of monear polc Therefore, polcmakers concerned wh he effecs of he behavor of he exchange rae on he nflaon arge should adop a monear polc sraeg ha adjus he neres rae o changes n he nomnal exchange rae, and avod drec nervenon n he foregn exchange marke wh 7

18 Inervenon n he foregn exchange marke under nflaon argeng has receved some aenon lael In an nflaon argeng semnar organzed b he Bank of Mexco March 4-5, 00, a panel dscusson was held abou hs opc The parcpan from he Cenral Bank of Chle argued ha cenral banks ha choose o nervene n he foregn exchange marke n he conex of nflaon argeng should no compromse he credbl of he polc regme In general, he panel agreed ha non-ssemac and pre-defned n me and amoun nervenon o aenuae flucuaons of he exchange rae due o facors no drecl relaed o fundamenals can occur along wh nflaon argeng Ver occasonal nervenons n a conex where fundamenals are robus, ma sgnal o economc agens he polcmakers percepon ha srong movemens of he nomnal exchange rae are no jusfed For example, polcmakers n counr A ma decde o nervene n he foregn exchange marke for a ver shor me and n a lmed amoun, f he perceve ha a fnancal crss n counr B s causng a srong deprecaon of s currenc ha he do no hnk accords wh he fundamenals of counr A s econom Also, rules o conrol volal of he nomnal exchange rae should be desgned and monor carefull o avod ssemac nervenon and s consequences on he conssenc of monear polc The problem for nflaon argeng emerges when wha should be occasonal nervenons urn ssemac, because s no possble o dsngush when fundamenals and non-fundamenals facors are drvng he foregn exchange marke 5- Conclusons Ths paper uses a model smlar o ha developed b Ball 998 o analze how he aemp o nfluence drecl he behavor of he nomnal exchange rae affecs he conduc monear polc under a Talor rule and nflaon argeng In secon 3, I exend Ball s 998 model o an open econom wh a crawlng exchange rae regme In hs case, he polcmakers have explc arges for he nomnal 8

19 exchange rae ha requre a ceran endogenous level of nervenon In hs model, he parameers of he opmal nomnal neres rae rule depend posvel on he rae of he crawlng peg Ω Ths mples ha seng a relavel low value of Ω o reduce nflaon owards some arge value, decreases he level of he neres rae for a gven devaon of oupu and nflaon wh respec o her means Ths, n urn, generaes pressures on aggregae demand and nernaonal reserves In secon 4, I exend Ball s 998 model o nclude ssemac nervenon of he monear auhor n he foregn exchange marke o moderae he rae of deprecaon of he nomnal exchange rae In hs case, polcmakers do no have nomnal exchange rae arges, bu n rng o conrol wha he consder hgh raes of deprecaon, her nervenon acons become ssemac We show ha nervenon reduces he response of he neres rae o devaons n oupu and nflaon from her mean values Ths decreased response of he neres rae generaes pressures on aggregae demand and he nomnal exchange rae o deprecae, hus reducng he credbl of he an-nflaon sance of monear polc The man concluson of he paper s ha a conflc exss beween he mplemenaon of a Talor rule or nflaon argeng, and ssemac nervenon n he foregn exchange marke Polcmakers should know ha such poenal conflcs ma arse n aemps o mplemen an ndependen monear polc whle smulaneousl rng o conrol he behavor of he nomnal exchange rae Thus, our resuls formalze he noon ha a monear polc based on a Talor rule or nflaon argeng requres a farl clean flexble exchange rae regme Ths s a relevan ssue because as Calvo and Renhar 000 pon ou fear of floang s a generalzed problem The argue, however, ha n man counres neres rae polc s replacng foregn exchange nervenon as he preferred means of smoohng exchange raes 3 Neverheless, he empaon o nervene 3 In an nflaon argeng regme excessve response o exchange rae flucuaons ma also generae some problems Ths subjec, however, s ousde he scope of hs paper 9

20 drecl o reduce volal ma sll be presen Calvo and Renhar 000 hold: In he conex of less-han-freel-floang exchange raes, purchases and sales of nernaonal reserves are rounel a means for smoohng exchange rae flucuaons ofen, alongsde neres rae polc, as dscussed p 0 Recenl, some economss argue, however, ha non-ssemac nervenon n he foregn exchange marke ma be compable wh nflaon argeng On hs ssue, cenral banks ha have adoped nflaon argeng should evaluae carefull, gven he specfc characerscs of her respecve economes, nervenon sraeges ha do no erode he credbl of he monear polc regme In parcular, cenral banks adopng nflaon argeng whou a srong repuaon ma sfle he effecveness of he scheme, f he embark ver earl n exchange rae smoohng hrough drec nervenon n he foregn exchange marke References -Ball, Laurence 997 ffcen Rules for Monear Polc Naonal Bureau of conomc Research, Workng Paper Polc Rules for Open conomes Naonal Bureau of conomc of conomc Research, Workng Paper Bernanke Ben; Thomas Laubach; Frederc Mshkn; Adam Posen 999 Inflaon Targeng: Lessons from he Inernaonal xperence Prnceon Unvers Press -Bofnger, Peer 00 Monear Polc: Goals, Insuons, Sraeges and Insrumens Oxford Unvers Press -Calvo, Gullermo, Carmen Renhar 000 Fear of Floang Unpublshed manuscrp Unvers of Marland -Inernaonal Monear Fund 00 Inernaonal Fnancal Sascs Ma 0

21 -Lederman Leonardo; Lars O Svensson dors 995 Inflaon Targes Cener for conomc Polc Research -Rudebusch, Glenn; Lars O Svensson 999 Polc Rules for Inflaon Targeng Publshed n Monear Polc Rules, John B Talor, edor The Unvers of Chcago Press -Svensson, Lars O 996 Inflaon Forecas Targeng: Implemenng and Monorng Inflaon Targes Naonal Bureau of conomc Research, Workng Paper Inflaon Targeng: Some xensons Naonal Bureau of conomc Research, Workng Paper Inflaon Targeng as a Monear Polc Rule Naonal Bureau of conomc Research, Workng Paper Talor, John B 994 The Inflaon/Oupu Varabl Trade-off Revsed Publshed n Goals, Gudelnes, and Consrans Facng Monear Polcmakers: Proceedngs of a Conference held n June 994, Jeffre Fuhrer, edor Federal Reserve Bank of Boson