Demand Shocks, Credibility and Macroeconomic Dynamics

Transcription

1 Dmand Shocks, Crdibiliy and Macroconomic Dynamics José García-Solans* and Carmn Marín-Marínz** Univrsidad d Murcia Jun 2013 Absrac: In his papr w build and simula an opn macroconomic modl o invsiga h dynamic adjusmn of domsic oupu, inflaion and ral xchang, and h incurrd social losss afr an xrnal and prmann dmand shock. Rsuls ar snsiiv o h spd of inflaion adjusmn includd in h xpcaions mchanism of priva agns. W uncovr h opimal valu of his paramr wihin h rang considrd in our simulaions, and suggs ha cnral banks should announc his rsul in ordr o improv h inflaionary xpcaions mchanism and o minimis social losss. JEL Classificaion: E1, E3, E4 and E5 Kywords: Inflaion arging, monary plicy ruls, inflaion xpcaions, dynamic adjusmns. (*), (**) Dparamno d Fundamnos dl análisis conómico Faculad d Economía y Emprsa Univrsidad d Murcia. Campus d Espinardo Murcia solans@um.s and carmnma@um.s 1

2 1. Inroducion. Th on going global financial crisis has pushd goods and facor marks ino long lasing disquilibria, which ndors imporan conomic and social losss in boh indusrial counris and mrging mark conomis. As a rsul, h nd for naional auhoriis o dispos of racabl macroconomic modls o driv usful sabilizing policy acions is prssing. Th spcializd liraur has providd abundan macroconomic modls of high horical qualiy orind o policy guidanc in opn conomis, mos of hm in h srand of h Nw Kynsian opn conomy approach; s, for insanc, Clarida, Gali and Grlr (2001), Gali and Monaclli (2005) and Gali (2008). Howvr, h analyical complxiy of hs modls maks hm low suiabl for pracical purposs. Carlin and Soskic (2010) rid o ovrcom hs drawbacks by building a simplifid nw Kynsian modl of an opn conomy, in which inflaion arging by h cnral bank and raional xpcaions in h forign xchang mark play a crucial rol. Thy drivd graphically h rsponss of h cnral bank and h rajcory of h main variabls o a variy of shocks. Howvr, h Carlin and Soskic (2010) s papr lacks consisncy in h assumd xpcaions mchanism, on h grounds ha whras h forign xchang mark and h cnral bank xhibi raional xpcaions, h bhaviour of agns of h labour mark is guidd by a vry simpl adapiv xpcaions rul. Morovr, hs auhors adop ad hoc assumpions concrning h lags wih which h ral inrs ra impacs on oupu. Lvin (2004) buil a simpl drminisic modl o ascrain h impac of wo yps of xrnal shocks on a numbr of imporan conomic variabls. Th main limiaion of his framwork is h assumpion of prfc forsigh in xpcaions of boh h xchang ra and h ra of inflaion. Finally, Nunkirch and Tillmann (2012) valuad how cnral banks rspond o inflaion dviaions from arg, bu hir rsric hir analysis o a closd conomy. 2

3 In his papr w ry o ovrcom hs difficulis by building a gnral quilibrium modl for a small opn conomy, in which bhaviour of all agns, including workrs and firms, ar govrnd by h sam lvl of raionaliy. In a firs sp, w assum ha agns hav rady and fr accss o informaion and ha marks work smoohly. Undr ha scnario, h cnral bank racs acivly in ach priod by dciding and applying h lvl of h inrs ra ha minimizs h social losss crad by a variy of shocks. In a scond sp, w build a modl whr boh h goods and labour marks suffr imprfcions and rigidiis ha lad o sluggish adjusmn in h ra of inflaion. In his conx, h cnral bank follows an announcd monary policy rul, and priva agns xpc ha h inflaion ra will progrss gradually owards h inflaion arg. On h basis of hos assumpions and ruls, w driv a modl for a small opn conomy composd of hr dynamic quaions: aggrga dmand, aggrga supply and h voluion of h ral xchang ra. In ordr o vrify h dynamic rsuls prdicd by our framwork, w inroduc a prmann dmand shock and simula h modl o driv h dynamic rsponss of h ra of inflaion, domsic oupu and h ral xchang ra, and compu h nsuing social losss undr alrnaiv assumpions abou inflaion xpcaions. W find ha in cas of prfc raionaliy, implmnaion of h opimal monary rul avoids any dparur of oupu and inflaion from hir longrun quilibrium lvls, minimizing, by his way, social losss. Howvr, undr h lss prfc scnario, in which boh h cnral bank and priva agns follow mpirical ruls, h dynamic rsuls crucially dpnd on h xpcd spd of inflaion adjusmn. W also obain ha h minimum lvl of social losss is associad wih a spcific lvl of ha paramr. Consqunly, i urns ou ha cnral banks wih inflaion arging sragis should clarly announc no only hir inflaion arg bu also h approxima spd a which hy innd o progrss o i in a muli yar plan. Th papr is organizd as follows. Scion 2 ss ou h modl for a small opn conomy wih flxibl xchang ra, and drivs h long run 3

4 quilibrium valus and h ransiion dynamics of ach ndognous variabl undr h assumpion ha h cnral bank follows a sabl inflaionarging rul. Th soluion of h modl and h analysis of is dynamic propris ar prsnd in h Appndix o h papr. Scion 3 simulas h dynamic adjusmns riggrd by a posiiv prmann dmand shock and compus h social losss for svral valus of cnral bank crdibiliy. Finally, scion 4 summariss h main rsuls and drivs som policy prscripions. 2. Th opn conomy modl wih flxibl xchang ra. In his scion, w build and solv a srucural gnral quilibrium modl ha illusras h way diffrn xrnal shocks affc h ndognous variabls. W xnd h simpl IS MP AS framwork laborad by Jons (2008) for a small opn conomy wih flxibl xchang ra. Monary auhoriis ar concrnd wih oupu and inflaion sabilisaion, which implis ha, afr h occurrnc of xrnal shocks or, alrnaivly, afr obsrving h ffcs of shocks on inflaion, h cnral bank modifis h nominal inrs ra o minimis social losss. W assum a radiional aggrga supply funcion in which domsic oupu dpars from is saionary lvl (ponial oupu) ihr bcaus inflaion is no corrcly forsn, or bcaus xrnal supply shocks hi h conomy. Th variabls of h modl ar prsnd in logs xcp for inrs ras and h ra of inflaion. 2.1 Raional bhaviour and h opimal monary rul In a firs approach, w assum ha boh h monary auhoriis and h priva scor ar raional agns ha opimis hir bhaviour. Th modl is composd of h following quaions: 4

5 ( y y) 2 + ( π π ) 2 L = ψ (1) y y = b i ( R i r ) b NX q + d (2) ( y y) + s π = π + ν (3) Equaion (1) is a cnral bank s on priod loss funcion ha pnaliss dviaions of oupu and inflaion from hir args; π is h argd inflaion ra announcd by h cnral bank. Paramr Ψ is h rlaiv wigh aachd by h cnral bank o oupu sabilisaion. Valus man ha h cnral bank is mor snsiiv o dviaions of inflaion han o oupu gaps; and h convrs is ru for valus. Equaion (2) is h opn conomy IS funcion, prsnd as pr cn dviaion of h aggrga dmand wih rspc o h ponial oupu. Th variabl R sands for h ral inrs ra r is h marginal produciviy of capial o which h ral inrs ra is dmd o convrg in h long run. Variabl q is h ral xchang ra (RER) gap, xprssd as h diffrnc bwn h (log of h) currn RER and h (log of h) long run lvl of his variabl, which is normalisd o zro. Morovr, h RER is masurd as h pric of h domsic oupu in rms or h forign on. Consqunly, q is xprssd as: q = + p p M, whr p M is h log of h world pric lvl, is h log of h nominal xchang ra xprssd as h pric of h domsic currncy in rms of h forign on and p is h log of h domsic pric lvl. In h long run, h ral xchang ra achivs is sady sa valu, which implis ha q = 0. Cofficins and ar h lasiciy of domsic invsmn wih rspc o h ral inrs ra, and h lasiciy of n xpors wih rspc o h ral xchang ra, rspcivly. Finally, d is an xognous paramr ha has wo componns: h firs on is (h log of) h auonomous dmand ovr h lvl of ponial oupu, including priva consumpion and 5

6 invsmn, govrnmn xpndiurs and n xpors. Th scond componn is a dmand shock normally disribud wih zro man and varianc qual oσ. In h saionary sa, i is vrifid ha y = y and d = 0. 2 d Equaion (3) is h inflaion surpris aggrga supply, whr paramr ν masurs h snsiivnss of inflaion o producion prssurs capurd by h oupu gap, and s is a supply shock ha is ranslad o inflaion, 2 disribud normally, (, ) N σ. 0 s W assum ha h cnral bank obsrvs h occurrnc of shocks and movs subsqunly h nominal inrs ra o minimis social losss undr h rsricion of h aggrga supply funcion (9). Th soluion is found by minimising social losss undr h aggrga supply consrain; ha is, by minimising h following Lagrangan funcion: Min [ s ] 2 2 ( y y) + ( π π ) + ρ π π ( y y) y, π L = ψ ν (4) Th rsul provids h opimal rad-off bwn inflaion and oupu gaps: ψ π π = ( y y) (5) ν By subsiuing (5) ino (3), w obain h opimal oupu gap: ν ( y y) = ( π π s ) 2 ν + ψ (6) Joining (6) wih (3), w g: 2 ν ψ π = π + π 2 2 ν + ψ ν + ψ ψ + s 2 ν + ψ (7) 6

7 Equaion (7) is h racion funcion of h cnral bank ha drmins h opimal inflaion ra for givn valus of π, s and h ra of inflaion xpcd by priva agns. Raional agns know his racion funcion and us i o driv hir xpcd ra of inflaion. So, by aking raional xpcaions in (7), i is asy o obain: π = π (8) By subsiuing (8) ino (6) and (7), w g: ν ( y y) = s 2 ν + ψ (9) ψ π π = ν + ψ s 2 (10) Equaions (9) and (10) rval ha whras inflaion and oupu ar affcd by supply shocks, hy ar no ouchd by dmand disurbancs sinc h lar ar insananously nuralisd by h cnral bank hrough variaions in h nominal inrs ra. Th opimal inrs ra is, consqunly, sa dpndn and can b drivd by subsiuing h quaions (9) and (10) ino h IS schdul (quaion (2)). Th rsul is: β i = βd + ( ν 2 +ψ ν b NX )s + β ( b i b NX )π + βb NX ( λi M + π M ) βb NX q 1 + βb i r (11) Whr β = b 1 + λ i b NX In h saionary sa, h following condiions ar saisfid: d = s = 0, π = π, q = 0 7

8 By inroducing hs condiions in (11), i is asily vrifid ha h nominal inrs ra saisfis h Fishr condiion in h saionary sa: i = r + π (12) Sinc h cnral bank can nuralis h impac of dmand shocks on oupu and inflaion hrough appropria variaions in h nominal inrs ra during h sam priod hy hi h conomy, dmand shocks do no inflic social losss. Th sory is diffrn for supply shocks, sinc hy modify h opimal valu of boh oupu and inflaion. Th impac of supply shocks on social losss will las as much as h shocks, and can b calculad by subsiuing quaions (9) and (10) ino h social loss funcion (quaion (1)): 2.2 Th modl undr mpirical ruls Th assumpion ha all conomic agns, including h cnral bank, bhav raionally is jus ncssary o quip h modl wih horical consisncy. W will hn sick o his gnral samn along h whol modl dvlopd in his papr. Howvr, givn ha a) knowldg is imprfc, ha b) nws flow o agns wih lags ha ar uncrain in boh innsiy and lngh, and ha c) many marks work infficinly, h abiliy of h cnral bank o larn an conrol h conomy is no so srong as assumd abov. Indd, h assumpions ha cnral banks assss immdialy h naur and siz of h shocks, and ha hy can implmn h acions ha xacly and insananously dlivr h dsird rsuls ar unsound. Thos supposiions lack boh ralism and policy rlvanc. For h sam okn, undr conomic scnarios whr prics adjus wih imporan inria, w ar simply no allowd o xpc ha h ra of inflaion will rach immdialy h inflaion ra argd by h cnral bank. For opraional rasons and policy rlvanc, w nd o adop alrnaiv and mor ralisic assumpions compaibl wih horical consisncy. As far as h bhaviour of h cnral bank is concrnd, w assum ha i follows h following policy rul, which is a simplifid vrsion of h Taylor s 8

9 quaion 1 : i = r + π + m( π π ), (13) whr h cofficin m masurs h avrsion of h cnral bank o inflaion. As rgards his quaion, wo rmarks ar in ordr. Firs, h cnral bank movs and mainains h nominal inrs ra ou is long rm lvl such im as h ra of inflaion dpars from h argd lvl; ha is, in so much as h inflaion diffrnial, ( π π ), diffrs from zro. Scond, h cnral bank is also indircly concrnd wih h oupu lvl, and consqunly wih conomic aciviy, o h xn ha h inflaion diffrnial is linkd o h oupu gap hrough h aggrga supply funcion. Consqunly, h paramr m also ransmis som cnral bank s worry abou conomic aciviy. As rgards inflaion xpcaions, w assum a mchanism ha combins flxibly inria wih raionaliy. On h on hand, agns ar raional in h sns ha hy can calcula corrcly h saionary inflaion ra on h basis of h srucur of h modl and h informaion dlivrd by h cnral bank. On h ohr hand, hy ar awar ha adjusmns procd wih inria, which lad hm o includ h inflaion ra of h las yar in hir xpcaions schm. Consqunly: π +1 = π +θ ( π π ) ; 0 θ 1 (14) whr π +1 accouns for h xpcd ra of inflaion for priod +1 wih h informaion s of priod, and h paramr θ masurs h spd a which h inflaion ra is xpcd o approach is saionary lvl. Undr zro spd, θ = 0, agns bliv ha inflaion movs vry slowly, and xpcaions jus rproduc h ra of h currn priod ( π +1 = π ) whras 1 Of cours, h assumpion ha h cnral bank can conrol h domsic nominal inrs ra rquirs ha h risk prmium rmains sabl and/or wih variaions ha can b nuralisd by h cnral bank. 9

10 full spd, θ =1, indicas h hop ha h final rsul will b achivd during h nx priod ( π +1 = π ). For inrmdia valus of paramr θ, xpcaions ar drmind by boh h prvious inflaion ra (backward looking lmn) and h long run inflaion ra (forward looking facor). Equaion (13) can b wrin as follows: ( π π ) π i + 1 = r + π + m + 1 π ; ha is: ( π π ) R = r + + m π + 1 π (15) By insring (14) in (15), w obain h monary policy rul in rms of ral inrs ras: ( m + θ )( π π ) R = r + 1 (16) Th aggrga dmand (AD) schdul By inroducing (16) in (2), w obain: i ( m + )( π π ) bnxq d y y = b θ 1 + (17) Obsrv now ha: q M ( ) + π π = q (18) W assum ha, for givn lvls of h xpcd nominal xchang ra and h risk prmium, h ra of nominal xchang ra apprciaion is 10

11 proporional o h gap bwn h domsic and forign nominal inrs ras 2 : λ M ( i i ) 1 =, λ >0 (19) Joining (19) and (18) wih (17), and aking ino accoun h monary policy rul, i is asy o rach: ( y y) = bnx b ( π π ) bnx q 1 + d δ (20) ( + λm)( π π ) δ q = q (21) ( m + θ 1 ) + b ( + λm) b = b 1 i M NX ( i M r ) ( λ)π δ = π + λ 1+ Equaion (20) is h aggrga dmand (AD) schdul, which is downward slopping in h spac (π, y), and quaion (21) shows h dynamics of h RER. Th aggrga supply (AS) schdul To driv h aggrga supply in h spac (π, y), w us h xpcaions mchanism (14) o driv π and subsiu h xpcd ra of inflaion ino quaions (3): ( θ ) π + ν ( y y) + ( θ ) + s π π = π (22) 2 From h uncovrd inrs ra pariy (UIP) rlaionship, i follows ha an incras in h diffrnc bwn h domsic and h forign nominal inrs ra riggrs capial inflows ha apprcia h domsic currncy sufficinly o cra h xpcd ra of dprciaion ha rsors UIP. 11

12 Th compl AD/AS modl Th whol modl is composd of h following quaions: AD: ( y y) = bnx b ( π π ) bnx q 1 + d δ (20) AS: π π = ( θ ) π + ν ( y y) + ( θ 1) π + s Dynamics of h RER: q q + ( 1+ λm)( π π ) δ 1 1 (22) = 1 (21) ( m + θ 1 ) + b ( + λm) b = b 1 i M NX ( i M r ) ( λ)π δ = π + λ 1+ Th Appndix o his papr xplains h soluion of h modl and drivs h sabiliy condiions. I is worh rmarking ha h quilibrium quaions of inflaion and oupu can b inroducd in h social losss funcion o calcula h valu of h spd of inflaion adjusmn ha minimiss social losss. W do no mak such a calculaion hr for rasons of spac, bu w prform insad som simulaions ha uncovr h opimal valu of h paramr θ wihin h rang considrd in our simulaions. 3. Shor run rsuls and dynamic adjusmn L us analys h shor run impac and h dynamic adjusmn afr a prmann dmand shock 3 ha aks plac a momn : Δd For analyical convninc, w us hr h dynamic quaion of AD (quaion (24)) wih h inflaion ra as h xplanaory variabl. Morovr, wihou loss of gnraliy, in his scion w assum ha h supply shock is zro and ha h xpcd inflaion ra is alrnaivly givn by h wo xrm cass of our gnral mchanism. Ths assumpions allows us o concnra on h dynamic propris of h AS and AD schduls. Th 3 Dmand shocks hav bn prdominan in indusrial conomis along h las dcads, and according o García Solans, Rodríguz Lópz and Torrs (2011), hy xplain mos of h variabiliy of rad imbalancs of hos counris. 12

13 gnral xpcaions hypohsis will b usd mor flxibly in h simulaion xrciss ha w prform blow. Consqunly, h modl vrsion ha w mploy in his scion is composd of h hr following quaions: AD: ( δ q ) y + d + bnx 1 π = π + 1 y (20 ) b b AS: = π + ν ( y) y π (22 ) RER: q q + ( 1+ λm)( π π ) δ = 1 (21) L s sar wih h simpl adapiv cas, π = π 1. Th graphical analysis is prsnd in Figur 1, whr h iniial quilibrium is drmind by poin A in h inrscion of h shor run AD and AS schduls. This quilibrium saisfis h saionary sa condiions. As can b sn in quaion (20 ), h dmand shock incrass h inrcp of AD. Consqunly, his schdul shifs upwards o AD 1, and h shor run quilibrium movs o B in priod 1. Th rsul is an incras in boh oupu and inflaion. Th incras in h ra of inflaion of h currn priod cras nw shifs in h following on. On h on hand, h aggrga supply movs upwards bcaus, as indicad in quaion (22 ), inflaion incrass h inrcp of h aggrga supply of on priod lar, AS 2. On h ohr hand, h incras in h inflaion ra of h currn priod apprcias h RER of priod 1(quaion (21)), which in urn movs h aggrga dmand downwards in priod 2, o h posiion AD 2. As a rsul, quilibrium rachs poin C in priod 2, indicaing hn an incras in inflaion coupld wih a conracion of oupu. Th incras in h ra of inflaion in priod 2 pus in moion nw shifs of boh schduls, and so on and so forh. Dynamic adjusmns will prsis as far as h inflaion ra divrgs from h sady sa lvl (π ). Thy will procd along a spiral pah ha nds in poin A, as rprsnd in h graph. In accordanc wih h mahmaical analysis, h graph shows ha dmand 13

14 shocks affc h pair (π, y) in h shor run and during h ransiion priod as wll. Morovr, h graph illusras ha h long run valus of hs variabls ar no alrd by iniial dmand impulss. Figur 1. Shor run impac and dynamic adjusmn afr a prmann dmand xpansion. π = π 1 π AS 2 π 1 C B AS π A AD 1 AD AD 2 y y 1 y L s now shif o h cas in whichπ = π, and analys h rsuls wih h hlp of Figur 2. Th shor run impac dos no chang wih rspc o h prcding xrcis and, consqunly, i is locad in poin B. Th incras in h inflaion ra in priod 1 shifs AD downwards in priod 2, bu dos no mov AS bcaus, undr h nw xpcaions mchanism, his schdul is dprivd of dynamics. Th AD schdul will procd coming down (a a dcrasing spd) as far as h currn ra of inflaion xcds is long run quilibrium valu. Consqunly, h shor run quilibrium poin will follow h arrows pah indicad in h graph. Again, w vrify ha h AD shock producs ral ffcs in h shor run and during h adjusmn priod, bu i dos no modify h long run quilibrium of oupu and inflaion. 14

15 Figur 2. Shor run impac and dynamic adjusmn afr a prmann dmand xpansion. π = π π AS π 1 π A C B AD 1 AD AD 2 y y 1 y 4. Simulaion and compuaion of social losss L us now simula h ffcs of a prmann xpansionary dmand shock. For his purpos, w giv h main paramrs rasonabl numrical valus for his yp of aggrga modls: 1 ; 0,02 ; 0,1 ; 0,1 ; 0,8 ; 0,8 ; 1 and 2. Morovr, wihou loss of gnraliy, w assum ha, 0 and ha h dmand shock occurs whn h conomy is in h saionary sa, ha is, and 0. Th conomy dpars from a saionary sa and is hi by a prmann dmand shock, 0,1. In h following graphs w show svral simulaions for diffrn valus of h paramr, h spd a which agns hop ha h ra of inflaion will convrg o h inflaion ra argd by h cnral bank. Figurs 3, 4 and 5 prsn h im pahs of domsic oupu, h inflaion ra and h ral xchang ra, rspcivly. Each figur includs four simulaions obaind wih four diffrn spds: wo xrm valus, 0 and 1, mbddd in simulaions 1 and 4, and wo inrmdia valus, ( 0,3 ; 0,7), includd in simulaions 2 and 3. 15

16 Figur 3: Oupu Gap 1,08 1,06 1,04 1,02 1 0,98 0,96 Tha = 0 Tha = 0,3 Tha = 0,7 Tha = 1 0,033 0,031 0,029 0,027 0,025 0,023 0,021 0,019 0,017 0,015 Figur 4: Inflaion Ra Tha = 0 Tha = 0,3 Tha = 0,7 Tha = 1 16

17 0,18 Figur 5: Ral Exchang Ra 0,16 0,14 0,12 0,1 0,08 0,06 0,04 0,02 0 Tha = 0 Tha = 0,3 Tha = 0,7 Tha = 1 Figur 3 dpics h adjusmn of domsic oupu. Th dmand shock dos no alr h long run quilibrium of his variabl, bu h mchanism of inflaion xpcaions modifis snsibly h adjusmn rajcoris. Undr h simpl adapiv schm,, mbodid in simulaion 1, h im pah draws incrasingly miigad oscillaions around h long run quilibrium lvl. Onc w nlarg h xpcaions mchanism by including incrasing valus of paramr, oscillaions dampn and h im pah of oupu volvs owards hyprbol curvs. Figur 4 draws four im pahs of h ra of inflaion dpnding on h valus accordd o paramr. Simulaions show rsuls in lin wih hos dpicd for domsic oupu. Th long run quilibrium is complly drmind by h cnral bank arg i.. i is no affcd by h dmand shock bu h im rajcoris ar vry snsiiv o h valus of. Again, oscillaions miiga as h valu of incrass, and urn ino hyprbol curvs for valus of ovr a crain hrshold. 17

18 Figur 5 dpics h four dynamic adjusmns corrsponding o h RER. Th rajcoris ar snsiiv o changs in h paramr in a similar way as for oupu and inflaion. Howvr, h RER always convrgs owards an apprciad long run lvl. Th rason is ha h RER mus apprcia o crowd ou h iniial xpansion in h aggrga dmand. Figur 6 draws h im pahs of h pair oupu inflaion for h four assumd valus of h paramr. Th xrm cas of adapiv xpcaions,, gnras a spiral in accordanc wih h oscillaions of oupu and inflaion in Figurs 1 and 2. Th opposi xrm,, cras h pah capurd by h sraigh lin. Finally, h wo inrmdia cass giv ris o curv rajcoris which convxiy dcrass wih paramr. Finally, figurs 7 and 8 draw h social losss crad by h dmand shock for h four spds of inflaion adjusmn considrd in his mpirical analysis. Figur 7 porrays h rsuls for h oupu sabilizaion paramr qual o on half ( 0,5), and Figur 8 draws h graphs corrsponding o 1,5. Two conclusions follow from hs figurs. Firs, boh h rajcoris and h oal amoun of social losss ar snsiiv o h spd of inflaion adjusmn, bu no o h wigh aachd o oupu sabilisaion. Scond, wihin h rang of valus of paramr, h valu 0,3 minimiss h oal amoun of social losss. 18

19 0,035 Figur 6: Equilibrium Dynamics 0,033 0,031 0,029 0,027 0,025 0,023 0,021 0,019 0,017 0,015 Tha = 0 Tha = 0,3 Tha = 0,7 Tha = 1 0,003 Figur 7: Social Losss (Psi = 0,5) 0,0025 0,002 0,0015 0,001 0,0005 Toal Losss 0,0085 0,0075 0,0065 0,0055 0,0045 0,0035 0,0025 0,0015 0,0005 0,0005 Tha = 0 Tha = 0,3 Tha = 0,7 Tha = 1 0 Tha = 0 Tha = 0,3 Tha = 0,7 Tha = 1 19

20 0,009 Figur 8: Social Losss (Psi = 1,5) 0,008 0,007 0,006 0,005 0,004 0,003 0,025 0,02 0,015 0,01 0,005 Toal Losss 0,002 0,001 0 Tha = 0 Tha = 0,3 Tha = 0,7 Tha = 1 0 Tha = 0 Tha = 0,3 Tha = 0,7 Tha = 1 5. Concluding rmarks In his papr w hav buil an opn macroconomic modl o invsiga h dynamic adjusmn of oupu, inflaion and h ral xchang ra, and h inducd ffcs on social losss, afr an xognous shock in h aggrga dmand. W solvd and simulad h modl o assss h rol of boh h inflaion xpcaions mchanism and h monary ruls in h dynamic adjusmns. Undr h scnario in which h cnral bank and priva agns follow consisn mpirical ruls, w obaind ha h im pahs of h hr ndognous variabls ar vry snsiiv o h spd of inflaion adjusmn xpcd by priva agns. Among h s of simulaions, ha found wih 0,3 provids h highs spd of convrgnc of h hr ndognous variabls o hir saionary sas. Th rason is ha in ha cas agns ar wll awar of h sluggish progrss of h ra of inflaion owards h valu argd by h cnral bank and form corrcly hir inflaion xpcaions. Th ral xchang ra always convrgs owards an apprciad long run 20

21 lvl in ordr o crowd ou h xcss dmand crad by h prmann posiiv dmand shock. W compld our simulaions by driving h dynamic pahs of social losss, and compud h losss accumulad along h whol adjusmn priod for h four valus of paramr θ. W found again ha 0,3 provids h bs rsul. From h prcding findings w driv an implicaion vry usful o improv h mpirical working of inflaion arging (IT) sragis. In addiion o announcing clarly a muli yar inflaion arg as a ky pillar of IT as suggsd, for insanc, by Mishkin and Savasano (2002) cnral banks should ransmi o agns h opimal spd of inflaion adjusmn. By doing so, hy would provid crucial informaion o improv h inflaionary xpcaions mchanism and, consqunly, o minimis social losss. 21

22 APPENDIX Th whol modl is composd of h following quaions: AD: (A1) AS: 1 (A2) Dynamics of h RER: 1 (A3) 1 1 (A4) (A5) Solving for h ndognous variabls of h sysm: (A6) (A7) (A8) In h sady sa, y. Morovr, givn ha in h long run h Fishr ffc and h law of on pric ar boh saisfid, from (A5), h simplificaion ha 0 is drivd. (A9) (A10) (A11) To analyz h dynamic sabiliy of h modl, from (A7) and (A8) h undrlying sysm of dynamic quaions is drivd: 1 1 (A12) 22

23 (A13) (A14) (A15) So h marix srucur of h firs ordr Taylor xpansion around h sady sa is: Δπ Δq π π q q (A16) Namd A h wo by wo prvious marix, w driv is characrisic quaion so ha (A17) Solving h prvious drminan w g h characrisic quaion (A18) (A18) Tha quaion (A18) has all cofficins posiiv guarans ngaiv ignvalus and consqunly h sabiliy of h sysm. 23

24 Rfrncs Carlin, W. and D. Soskic (2010), A Nw Kynsian Opn Economy Modl for Policy Analysis, CEPR Discussion papr sris, Nº Clarida, R., Gali, J. and M. Grlr (2001), Opimal monary policy in opn vrsus closd conomis: an ingrad approach, Amrican Economic Rviw Paprs and Procdings, 91(2): Gali, J. (2008): Monary Policy, Inflaion and h Businss Cycl, Princon Univrsiy Prss. Gali, J. and T. Monaclli (2005), Monary policy and xchang ra volailiy in a small opn conomy, Rviw of Economic Sudis 72: García Solans, J., Rodríguz Lópz, J. and J.L. Torrs (2011), Dmand Shocks and Trad Balanc Dynamics, Opn Economic Rviw 22: Lvin, J. (2004), A modl of Inflaion Targing in an Opn Economy, Inrnaional of Financ and Economics, 9: Mishkin, F.S. and M. Savasano (2002), Monary Policy Sragis for Emrging Mark Economis: Lssons from Lain Amrica, Comparaiv Economics Sudis, 44, Nº 2,3, Palgrav Macmillan. Nunkirch, M. and P. Tillmann (2012), Inflaionn Targing, Crdibiliy and Non Linar Taylor Ruls, MAGKS Join Discussion Papr Sris in Economics, N