An extended dynamic IS-LM model of exchange rate adjustments and movements

Transcription

1 An xndd dynamic IS-LM modl of xchang ra adjusmns and movmns Piji Wang Univrsiy of Plymouh and IÉSEG Economics Working Papr No. 4 May 4 Absrac: This papr proposs a modl of xchang ra adjusmns in an xndd IS-LM analyical framwork. I maks inquiris ino h adjusmn and voluion pah of h xchang ra owards is nw long-run quilibrium lvl following a chang in mony supply. Tradiional monary modls of xchang ra drminaion and adjusmns play primarily wih h LM componn of h IS-LM framwork in discr sps. Th nw modl incorporas h IS componn ha is xndd o dal wih an xrnal scor in an opn conomy volving coninuously. Effcs of inrs ra pariy and purchasing powr pariy ar hn scruinizd, assuming nihr flxibl nor sicky prics. JEL No: F3, F37 Ky words: xchang ra, monary policy, inrs ra pariy, purchasing powr pariy

2 . Inroducion Th forign xchang mark is crucial o inrnaional conomic co-opraions. I facilias inrnaional rad and ransacions. Nonhlss, disurbancs gnrad in on par of his inrlinkd global conomy can also b ransmid and magnifid hrough h forign xchang mark as on of h dirc and major channls o impac on h financial marks around h world. Exchang ra bhavior, which is cnral o consiuion of an ordrly forign xchang mark, should hrfor b scruinizd o br our undrsanding of xchang ra drminaion and adjusmns. Monary modls of xchang ra drminaion hav prvaild for h floaing xchang ra priod undr h sing ha prics ar no fixd. Major monary modls of xchang ra drminaion includ h flxibl pric modl of Frnkl (976), h sicky pric modl of Dornbusch (976) and h ral inrs ra diffrnial modl of Frankl (979). On of h mos famous faurs of h Dornbusch (976) modl is ovrshooing of h xchang ra in is adjusmn procss owards h nw quilibrium prinn o h nw and changd conomic fundamnals. Du o is prominnc and influnc, h ovrshooing proposiion has bn sd mpirically ovr im. Alhough Dornbusch (976) covrs boh mony mark and goods mark, ovrshooing can b gnrad by incorporaing uncovrd inrs ra pariy and a kind of xchang ra xpcaions formaion ino h LM quaion. Tha is, all radiional monary modls of xchang ra drminaion and adjusmns play primarily wih h LM componn of h IS-LM framwork. This prsn sudy pus forward a modl of xchang ra adjusmns in an xndd and dynamic IS-LM analyical framwork. I incorporas h IS componn ha is xndd o dal wih an xrnal scor in an opn conomy ha volvs coninuously. Effcs of inrs ra pariy (IRP) and purchasing powr pariy (PPP) can b scruinizd in his framwork as im gos by. Th modl ss no nw quilibrium

3 xchang ra xplicily, and i assums nihr flxibl nor sicky prics. Th goods pric movs and adjuss naurally, corrsponding wih h movmns and adjusmns in h inrs ra and h xchang ra. Th rs of h papr is organizd as follows. Th nx scion prsns h consruc and paradigm of his sudy. Scion 3 provids an illusraing cas and calibras h modl, whil Scion 4 summarizs his sudy.. Th modl W propos a modl of xchang ra adjusmns in an xndd IS-LM analyical framwork o dal wih an xrnal scor in an opn conomy. This involvs an xchang ra-inrs ra plan, in addiion o an incom-inrs ra plan. Th IS-LM analyical framwork compromiss of h following wo quaions for claring h mony mark and goods mark: m p ηy λr () αy r g q () whr m is and for mony ha is qual o mony supply in quilibrium, p is pric of goods, y is incom, r is inrs ra, g is govrnmn spnding, and q is ral xchang ra, and, λ,,, and ar posiiv cofficins. All h variabls ar in logarihms. In paricular, λ is h inrs ra smi-lasiciy of h and for mony, is h aggrga inrs ra smi-lasiciy of savings and invsmn, and is h ral xchang ra snsiiviy of rad balanc. Th ral xchang ra, by dfiniion, is: q f p p (3) whr is xchang ra and p f is forign pric of goods in logarihms. Th IS-LM sysm in h inrs ra-incom plan ras h ral xchang ra, alongsid and for mony and govrnmn xpndiur, as xognous or as a policy insrumn for alring h lvl of inrs ras and incom. W xnd and map h IS-

4 LM sysm o h inrs ra-xchang ra plan, so h ral xchang ra, as wll as h nominal xchang ra and pric, bcoms ndognous. W dpar furhr from h convnional IS-LM analysis in h inrs ra-incom plan hr. In h convnional IS-LM framwork, an incras in mony supply by would rduc h inrs ra by in quaion (), wih no chang in pric and incom. Corrspondingly in quaion λ (), q is rquird o b rducd by λ, givn no chang in incom and govrnmn spnding, which in urn indicas is rducd by h sam dgr, givn no immdia chang in pric. A rducion in q or mans apprciaion of h domsic currncy, which is implausibl. W qusion his judiciousnss. A domsic inrs ra ha is lowr han h world lvl of inrs ras would rsul in h domsic currncy o apprcia. Bu i would ak on yar for h domsic currncy o apprcia by according o inrs ra pariis, furhr assuming ha h domsic inrs ra rmains unchangd a his lowr lvl for on yar., λ W propos ha, rad balanc is affcd by no only h xchang ra bu also h vlociy of chang in xchang ras, i..: αy dq r g q ( ) d whr is a posiiv cofficin. So, i is no rquird for q o b rducd by λ immdialy o aain h nw mporary quilibrium in h goods mark, q could incras as wll. Th shif is ffcd by h vlociy of xchang ra changs, which maks h sysm dynamic manwhil. Bringing quaion (3) ino quaion ( ) lads o: d d dp d f r p p αy g (4) 3

5 Assum ha h sysm is in quilibrium a, wih m m, p p, y y, r r, and g g ; and h quilibrium inrs ra is s o qual h world lvl of inrs ras * r r. Givn an incras in mony supply a im +, h mony mark quilibriums bfor and afr h incras in mony supply ar: m p ηy λr (a) m (b) p ηy λ r Th domsic inrs ra, corrsponding o h monary xpansion, is rducd by: r r (5) according o quaion (), sinc h pric is fixd in h shor-rm and oupu is no supposd o b affcd, i.., p y y p,. Th domsic inrs ra assums a funcion form wih which i riss gradually in rvring o h world lvl of inrs ras: r λ r * (6) Thn h pric of goods riss in h sam way as follows: p p (7) for h mony mark o clar coninuously. Th goods mark quilibriums bfor and afr h incras in mony supply ar: f r p p αy g (4a) d dp f r p p αy g (4b) d d wih y y and g g. Subracing quaion (4a) from quaion (4b) yilds: d d * dp r r p p (8) d 4

6 5 Givn quaion (6), quaion (7) and d dp, h abov can b r-arrangd o: λ λ d d (9) which is a firs-ordr linar diffrnial quaion and has a gnral soluion of:, C λ C d λ d d () C is solvd by aking h boundary condiions ino considraion: λ λ C () Conclusivly, h xchang ra movs and volvs as follows:, λ λ λ () I is apparn ha,. Th faurs of h modl and ach of is lmns ar discussd in h nx scion.

7 3. Th faurs of h modl Prior o discussing h faurs of h modl and ach of is lmns, w addrss h issu in modling which is lf unsolvd in h abov quaion. W focus on h voluion pah of h xchang ra afr h shock in his sudy, and lav and subjc i o acual figurs. Findings in h mpirical liraur imply ha unsolvd is no prdicabl or can b modld. For xampl, Lvin (994) finds a monary xpansion ha iniially lowrs inrs ras can produc ihr ovrshooing or undrshooing of h xchang ra. H has documnd xchang ra undrshooing in an arlir sudy (Lvin 989). Cavaglia (99) also conradics h xchang ra ovrshooing hypohsis. On h ohr hand, Kigul and Dauhajr (988) show h xchang ra is likly o ovrshoo in hir cass. Bjørnland (9) finds ha a conracionary monary policy shock has a srong ffc on h xchang ra. Th domsic currncy apprcias on impac bu i aks - quarrs for h ffc o maximiz. In addiion o h argumn on ovrshooing or undrshooing, a numbr of sudis hav indicad ha h ovrshooing modl is ouprformd by random walk modls in xchang ra forcass. Hwang s (3) rsuls suggs ha h random walk modl ouprforms h Dornbusch and Frankl modls a vry forcasing horizon. Similarly, Zia and Cupa (8) find ha naïv modls ouprform h Dornbusch modl. Furhrmor, many hav dpard far away from h original sing of immdia rsponss upon an incras in mony supply. For xampl, Vrschoor and Wolff () invsiga h ffc a h 3-, 6-, and -monh horizons o find ou whhr xchang ras ovrshoo using h Mxican daa. Mussa (98) has inspcd xchang ra movmns ovr 6 monhs o s if h currncy ovr dprcad. In Bjørnland (9) cas, h domsic currncy apprcias on impac bu i aks - quarrs for h ffc o maximiz. Such dparur is ypifid 6

8 o a magnifid dgr by Hinlin and Krolzig () who hav dcd dlayd ovrshooing -3 yars afr a monary policy shock. Th scond rm on h righ hand sid of quaion () incrass gradually from a o whn. Th hird rm is h iniial shock ffc, which fads away vnually as. Givn h iniial ffc is domsic currncy dprciaion o varid dgrs, as vidn in h abov rviwd sudis,. Thrfor, h hird rm dcrass ovr im. Th fourh rm sars a a and approachs whn. I is concav or has a minimum valu, which can b provd as follows., λ givn ha h lasiciy or snsiiviy paramrs ar smallr han uniy. Thn, λ if ; and λ if. So, i is rquird o prov ha is concav or has a minimum for and is convx or has a maximum for. Tchnical proofs ar as providd in Appndix A. Givn h proofs, h fourh rm dcrass firs and hn incrass, fauring iniial apprciaion of h domsic currncy afr h monary shock. {Figur } {Figur } Finally, w inspc h ovrall parn in xchang ra voluions, combining h faurs of individual lmns. Th domsic currncy would apprcia iniially afr h shock, and hn dprcia owards is nw long-run quilibrium ra if. Th 7

9 xchang, saring a, dcrass and rachs is minimum min a m, shown in Appndix B. Tha is, h domsic currncy would apprcia iniially afr h shock, and hn dprcia owards is nw long-run quilibrium ra. Th domsic currncy would furhr dprcia from max afr h iniial shock, and hn apprcia owards is nw long-run quilibrium ra if. Th xchang ra rachs is maximum max a, m fauring dlayd ovrshooing in pro-ovrshooing mpirical sudis whr h im horizons rang from on quarr o four quarrs. Prviously i is sad ha is rquird for h xchang ra o convrg. Bu byond mahmaical modling, won b much smallr ha, givn ha hy ar boh snsiiviis of rad balanc o xchang ra variabls. Hnc, would prvail in h xndd IS-LM framwork, whil no ruling ou complly. So h dominan parn in xchang ra voluions afr h shock is ha h domsic currncy apprcias iniially prior o gradual dprciaion owards is nw long-run quilibrium lvl. Ths ar xhibid in Figur wih h parns in ach lmn of quaion () and h ovrall parn in xchang ra adjusmns and voluions. Th abov onsrad parn of xchang ra voluion is consisn wih ha in a rcn sudy of Wang (3). Upon an incras in mony supply, h inrs ra falls wih IRP aking ffc iniially, wih which h currncy apprcias, and hn h sicky pric riss gradually from h mdium-rm and ovr h long-run, in which h currncy dprcias. H has onsrad hr cass ha iniially rvrsly shoos, ovr shoos and undr shoos rspcivly. All of hm mak rvrs movmns afr h iniial shock in h shor-rm, b h iniial rspons ovrshooing, undrshooing or rvrs shooing. Unlik Wang (3) who assums a shor-rm xchang ra arg in 8

10 addiion o a long-run quilibrium xchang ra, our modl ss no shor-rm arg a all and no nw long-run quilibrium xchang ra xplicily. I ls h opn conomy volvs islf. Th dsign of our modl is also cohrn wih, bu xnds, h join dynamics of xchang ras and inrs ras of Andrson al. () who apply h affin class of rm srucur modls o xchang ra movmns as diffusion procsss. Th voluion pah of xchang ras in our modl gos byond h horizon whn IRP ffcs hav diminishd o a ngligibl xn. 4. Th faurs of h xndd IS-LM framwork and IRP and PPP ffcs Th modl and is faurs ar drivd from h xndd IS-LM framwork. This scion onsras h pah of xchang ra adjusmns and movmns on h xchang ra-inrs ra plan in h xndd IS-LM framwork, oghr wih h corrsponding adjusmns and movmns on h radiional incom-inrs ra plan. Ths ar xhibid in Figur. Th righ sid panl is h radiional IS-LM analysis on h incom-inrs ra plan. LX is h LM curv mappd o h xchang ra-inrs ra plan. Whn mapping h LM curv ono h xchang ra-inrs ra plan, h curv is horizonal sinc h xchang ra is no a variabl for h LM curv. IX is h IS curv mappd o h xchang ra-inrs ra plan. Thr ar wo horizonal axs; on is for h xchang ra, and h ohr for h vlociy of xchang ra changs. Th vlociy axis has wo scions, on for d d and on for. Th curv is flar d d whn r is far away from * r and spr whn r is closr o * r, rflcing h IRP ffc. For r *, i mans h largr h inrs ra diffrnial, h grar h r dcras in h xchang ra, or h apprciaion of h domsic currncy. No ha a shif of h IX curv is by changs in p, y, g and d dp. Wih y y and g g, h IX 9

11 curv will shif only if hr is a chang in p or dp dp. Givn p p and d d, h IX curv shifs lfwards by upon h shock. dp d and p p as, h oal disanc h IX curv has ravld lfwards is whn h sysm has sld down a h nw quilibrium. Th cross poins of h corrsponding LX and IX curvs in hir shifs xhibi h pah of xchang ra adjusmns and movmns. Th shif of h IS curv on h incominrs ra plan is by changs in q dq d, which can also b xprssd in h nominal xchang ra and prics: q dq f d dp p p (3) d d d A, p p f = p p f = q, d d λ, and dp d, so h shif of h IS curv upon h shock is: q (4) λ Th downwards movmn of h IS curv is nabld by h ngaiv figurs of λ, allowing h domsic currncy o dprcia upon h shock, i.., allowing h nominal xchang ra o incras. Whil masurs h swifnss of mony mark adjusmns o aain h nw quilibrium, rflcs h dynamics in goods mark adjusmns in moving o h mporal quilibrium and hn aaining h nw quilibrium. If, goods mark adjusmns rspond o h lvl of h xchang ra only. A sizabl rlaiv o

12 fds dynamics ino h sysm h vlociy of xchang ra changs movs h goods mark oo. Morovr, guarans coninuiy in goods mark adjusmns. Th xchang ra would ohrwis b rquird o jump in h wrong dircion immdialy. Th mony mark paramr plays a rol for h IRP ffc; and h goods mark paramrs joinly play a par for h PPP ffc. Th domsic currncy would apprcia o a grar xn and h apprciaion priod would las longr wih a smallr. This is bcaus h domsic inrs ra rvrs o h world lvl of inrs ras wih a slowr spd, kping mor sizabl inrs ra diffrnials for a longr im. According o quaion (6) and uncovrd IRP: E (5) * τ rτ r dτ dτ, λ λ τ τ Th IRP ffc is grar and lass longr wih a smallr. Manwhil, h domsic pric would incras mor slowly wih a smallr. I aks a longr im for h xchang ra o incras by h full amoun ffcd by h monary xpansion. In ohr words, i aks a longr im for h xchang ra o rach is nw quilibrium ra incras by h sam prcnag as h incras in mony supply. Ohrwis wih a largr, h domsic currncy would apprcia o a smallr xn and h IRP ffc disappars mor quickly. Th domsic pric would ris mor rapidly and i aks a shorr im for h xchang ra o rach is nw quilibrium ra. According o quaion () and quaion (7), h dparur of h xchang ra from is pr shock quilibrium or PPP ra is:

13 , λ q λ p p p p λ p p q f f f (6) Th firs rm on h righ hand sid is h pr shock quilibrium or PPP ra, which h xchang ra would rvr o or rach. Th scond rm is h iniial shock ffc ha dis away whn im gos by. Th hird rm is concav. I sars a zro, dcrass and bcoms ngaiv, and hn incrass o zro again. Thrfor, h largr h paramr and h closr h paramrs and, h fasr h xchang ra would rach is PPP ra. Also h dparur of h xchang ra from is PPP ra would b smallr during h adjusmn cours. 5. A manifs xampl Th las financial crisis has providd us wih h rar opporuniis o inspc h parns in xchang ra movmns following an xpansionary monary policy. Th innion o xpand h monary bas in mos conomis during h crisis priod was almos solly o prvn h conomy from sliding ino rcssion or, a bs, o kp h conomy as i was, wih h oucom of virually vry inrvnion bing jus ha. Th scals of monary policy inrvnion hav bn normous and unprcdnd. Th policy ool adopd by mos monary auhoriis around h dvlopd world is h mos dirc amongs h hr major policy ools larg scal opn mark purchass of

14 bonds and gils or quaniaiv asing (QE). Unlik convnional monary xpansions whr changs in a fw ohr conomic variabls may influnc xchang ras as much as mony supply dos, h ffc of QE on xchang ras and xchang ra movmns graly dwarfs ha of any ohr conomic variabls. For his rason, QE ffcivly isolas h impac of ohr conomic variabls on xchang ra movmns from ha of monary xpansions, offring an immacula nvironmn in which h ffc of monary xpansions on xchang ra adjusmn and movmn is sudid. Th firs round of QE in h US, QE, is usd for cas analysis. QE sard in Dcmbr 8 whn h Fdral Rsrv announcd i would purchas up o $ billion in agncy db and up o $5 billion in agncy morgag-backd scuriis on Novmbr 5, 8. Alhough h purchass sprad ovr a priod, ha priod was fairly shor. Th announcmn ffc would b also considrabl, which Gagnon al. () scruiniz for QE in dail. Th xchang ra usd in h sudy is h US dollar ffciv xchang ra providd by h US Fdral Rsrv. Th ffciv xchang ra is r-arrangd so ha an incras in i corrsponds o h dprciaion of h US dollar vis-à-vis h currncis of is rading parnrs, h sam way as dircly quod bilaral xchang ras. Figur xhibis US dollar ffciv xchang ra movmns sinc h sar of QE in a on-yar fram, by which im h rs of h dvlopd conomis had also bgun implmning hir own QE programs and hir ass purchass bcam sizabl. For xampl, h MPC of h UK announcd a 75b ass purchas plan ovr a hr-monh priod in March 9; by h Novmbr MPC ming ass purchass wr xndd o b (cf. Joyc al. for h dsign and opraion of QE in h UK). During his priod, h ECB also adopd som kind of QE, albi on a much smallr scal, including a 6b corpora bond purchas program mad known in May 9. Obsrving Figur 3, US dollar ffciv xchang ra movmns in QE fi h horical curv dlicaly wll. Th US dollar ffciv xchang ra incrasd from an 3

15 indx numbr of around 8 a h bginning of Dcmbr in 8 o 9 by h middl of h monh, causing 9 prcn dprciaion. Thn h US dollar mbarkd on a rvrs movmn cours and on March 9, 9, h indx dcrasd o lss han 6, amouning o mor han prcn of accumulad apprciaion in narly a quarr im priod. Afrwards, h US dollar kp dprciaing and by Dcmbr 9, h US dollar ffciv xchang ra rachd 4. Th US dollar dprciad by narly 9 prcn rlaiv o is posiion a yar ago, masurd by is ffciv xchang ra. Thr ar wo priods whn h xchang ra dvias from h voluion pah on h horical curv. On is around h nd of March 9 whn h Bank of England, following h announcmn on March 5, purchasd is firs larg chunk of corpora bonds, lasing for hr wks. This sms o b a counr ffc of QE by ohr conomis; h US dollar xchang ra soppd monoonic rising bu flucuad, for abou hr wks. Th scond priod is h nd of May and Jun 9, which coincidd h mov of h ECB and rflcd anohr counr ffc of QE in ohr conomis. Ths dviaions, conribud by ohr conomis QE, ar fairly mods nonhlss. {Figur 3} I has bn obsrvd ha h US dollar dprciad upon h xpansion of mony supply, bu hr wr no signs of ovrshooing of xchang ras. Th iniial dprciaion was pulsaing for acual ass purchass as wll as for h announcmn. This kind of iniial dprciaion following an xpansionary monary policy is prvaln in h mpirical liraur, faurd largly by undrshooing of xchang ras, bu alludd implicily by h palpabl failur o ndors xchang ra ovrshooing as wll. Rvrs movmns of h xchang ra in h shor-rm, howvr, wr manifs in QE. Th US dollar dprciad inviably afrwards in h long-run and h xchang 4

16 ra movd inviably in a dprciaing mannr. Th displayd parn in US dollar ffciv xchang ra adjusmns and movmns mirror h horical analysis of his papr rmarkably agrably. 6. Summary A modl of xchang ra adjusmns in an xndd IS-LM analyical framwork has bn proposd in his papr, o analyz h adjusmn and voluion pah of h xchang ra following a chang in mony supply. Th proposd modl incorporas h IS componn ha is xndd o dal wih an xrnal scor in an opn conomy on h xchang ra-inrs ra plan, in addiion o h radiional IS-LM analysis on h incom-inrs ra plan. Assuming nihr flxibl nor sicky prics, ffcs of inrs ra pariy and purchasing powr pariy can b and ar scruinizd wih his analyical framwork. Th dominan parn in xchang ra voluions following an xpansionary monary policy is found o b ha h domsic currncy apprcias iniially afr h shock, prior o gradual dprciaion owards is nw long-run quilibrium lvl ha is h pr monary xpansion quilibrium ra plus h prcnag incras in mony supply. This parn in xchang ra adjusmns and movmns is rsuld from h join and squnial ffcs of IRP and PPP. This parn in h voluion pah of xchang ra adjusmns and movmns has manifsd by h rcn xampl of h US QE in on of h mos raling pochs of h las financial crisis. Th acual xchang ra movmns fi h horical curv dlicaly wll. 5

17 Rfrncs Andrson, B., Hammond, P.J. and Ramzani, C.A. (), Affin modls of h join dynamics of xchang ras and inrs ras, Journal of Financial and Quaniaiv Analysis 45, Bjørnland, H.C. (9), Monary policy and xchang ra ovrshooing: Dornbusch was righ afr all, Journal of Inrnaional Economics 79, Cavaglia, S. (99), Prmann and ransiory componns in h im sris of ral xchang ras, Journal of Inrnaional Financial Marks, Insiuions and Mony, -44. Dornbusch, R. (976), Expcaions and xchang ra dynamics, Journal of Poliical Economy 84, Frankl, J.A. (979), On h mark: a hory of floaing xchang ras basd on ral inrs diffrnials, Amrican Economic Rviw 69, 6-6. Frnkl, J.A. (976), A monary approach o h xchang ra: docrinal aspcs and mpirical vidnc, Scandinavian Journal of Economics 78, -4. Gagnon, J., Raskin, M., Rmach, J. and Sack, B. (), Larg-scal ass purchass by h Fdral Rsrv: did hy work? Quaniaiv Easing Confrnc, h Fdral Rsrv Bank of S. Louis. Hinlin, R. and Krolzig, H.M. (), Effcs of monary policy on h US dollar/uk pound xchang ra is hr a dlayd ovrshooing puzzl? Rviw of Inrnaional Economics, Hwang, J.K. (3), Dynamic forcasing of sicky-pric monary xchang ra modl, Alanic Economic Journal 3, 3-4. Joyc, M., Tong, M. and Woods, R. (), Th Unid Kingdom s quaniaiv asing policy: dsign, opraion and impac, Quarrly Bullin Q3, Bank of England. Kigul, M.A. and Dauhajr, A. (988), A dynamic modl of h opn conomy wih sluggish oupu, Inrnaional Economic Rviw 9,

18 Lvin, J.H. (989), On h dynamic ffcs of monary and fiscal policy undr floaing xchang ras: simulaions wih an ass mark modl, Wlwirschaflichs Archiv 5, Lvin, J.H. (994), On sluggish oupu adjusmn and xchang ra dynamics, Journal of Inrnaional Mony and Financ 3, Mussa, M. (98), A modl of xchang ra dynamics, Journal of Poliical Economy 9, Vrschoor, W.F.C. and Wolff, C.C.P. (), Exchang risk prmia, xpcaions formaion and nws in h Mxican pso/us dollar forward xchang ra mark, Inrnaional Rviw of Financial Analysis, Wang, P.J. (3), Rvrs shooing of xchang ras, Economic Modlling 33, Zia, S. and Gupa, R. (8), Modling and forcasing h Mdical-Rand xchang ra, ICFAI Journal of Monary Economics 6, Endnos In rlaiviy, ohr conomis inrs ras convrg/rvr o h domsic inrs ra for a larg opn conomy. Excp for, in which cas, sinc Lim Lim Appndix A S: d d (A) I rachs a minimum or maximum a im m : 7

19 8 m (A) No whn and whn, so m R ++ and is always viabl. A = m, h scond drivaiv is: d d m (A3) Thrfor, whhr h scond drivaiv is posiiv or ngaiv is dcidd by h sign of. Sinc: (A4) Thrfor:

20 d d m (A5) So, is concav for and is convx for. Appndix B Exprss quaion () in a condnsd way:, (B) whr λ. S: d d (B) Th xchang ra rachs a minimum or maximum valu a m, which can b solvd by: m (B3) A = m, h scond drivaiv of h xchang ra wih rspc o is: 9

21 d d m (B5) Th sign of h scond drivaiv is h sam as h sign of, which in urn has h sam sign as: 3 (B6) Thrfor: m d d (B7) Th xchang ra rachs is minimum min a m if. Tha is, h domsic currncy would apprcia iniially afr h shock, and hn dprcia owards is nw long-run

22 quilibrium ra. Th xchang ra rachs is maximum max a m if. Howvr, max. Th domsic currncy would furhr dprcia from afr h iniial shock, and hn apprcia owards is nw long-run quilibrium ra. This is almos h ovrshooing cas of Dornbusch (976), xcp ha h domsic currncy dos no dprcia byond h nw quilibrium ra immdialy, i aks som im. This is h cass in pro-ovrshooing mpirical sudis whr h im horizons rang from on quarr o four quarrs.

23 Figurs (a) Parns in hr rms xchang ra in logarihm (b) Parns in xchang ra adjusmn and movmn in logarihm.4 Exchang ra asjusmn and movmn xchang ra (c) Exchang ras Figur. Exchang ra adjusmn and movmn

24 r IX T3 IX T IX T IX T IS N LM N LX N LX O N IX N IX O r * IS T IS O LM O LM T LX T Evoluion pah of h xchang ra T T T λ y Figur. Exndd IS-LM framwork 3

25 UK QE sars ECB bond purchass Exchang ra adjusmn and movmn US$ ffciv xchang ra Projcd xchang ra Figur 3. Exchang ra adjusmns and movmns: acual and projcd 4