Mundll-Flming I: Sup In ISLM, w had: E ( ) T I( i π G T C Y ) To his, w now add n xpors, which is a funcion of h xchang ra: ε E P* P ( T ) I( i π ) G T NX ( ) C Y Whr NX is assumd (Marshall Lrnr condiion) incrasing in h ral xchang ra: εp * P
Mundll-Flming II: Sup No ha P is h domsic pric lvl, P * h forign pric lvl, and ε h nominal xchang ra (i.. h pric of forign currncy xprssd in domsic currncy). Now w look a h nominal sid of h conomy: M D L P, ( i Y ) W also assum saic xpcaions and prfc capial mobiliy which in his conx mans * ha: i i
Mundll-Flming III: Floaing Exchang Ra Saic xpcaions mans ha fuur xpcaions ual h currn sa. So, wih a floaing xchang ra, w nd up wih wo uaions: Y E( Y, i * εp π, G, T, P M ( * L i, Y ) P Noic ha h LM* curv is vrical and h IS* (boh graphd in xchang ra vrsus oupu spac) curv is upward sloping. * )
Mundll-Flming IV: Floaing Exchang Ra Monary xpansion wih a flxibl xchang ra: Mony supply incrass Tmporary fall in domsic inrs ra Capial ouflow Fall in dmand for domsic currncy Dprciaion Oupu xpansion Fiscal xpansion wih a flxibl xchang ra: Govrnmn xpndiurs incras Tmporary ris in domsic inrs ra Capial inflow Incras in dmand for domsic currncy Apprciaion Grar domsic dmand bu lowr n xpors offs ach ohr
Mundll Flming V: Floaing Exchang Ra Why is h fiscal xpansion xacly offs by apprciaion and dclin in n xpors? Suppos no hn for a givn M and P, Y would b highr Thn in ordr for mony dmand o ual mony supply, h domsic inrs ra would hav o b highr which gos agains h assumpion of prfc capial mobiliy.
Mundll Flming VI: Fixd Exchang Ras Two changs nd o b mad for h modl of fixd xchang ras: (.) ε ε (2.) M is now ndognous in ordr o mak sur ha h xchang rmains fixd (i is bough and sold by h cnral bank o rain h xchang ra arg).
Mundll-Flming VII: Fixd Exchang Ra So, wih a fixd xchang ra, w nd up wih hr uaions: Y M P ε ε E( Y ( *, Y ) L i, i * π, G, T, εp * ) P Now h LM* curv is rplacd by a horizonal xchang ra curv and h IS* (boh graphd in xchang ra vrsus oupu spac) curv is upward sloping.
Mundll-Flming VIII: Fixd Exchang Ra Monary xpansion wih a fixd xchang ra: Mony supply incrass Tmporary fall in domsic inrs ra Capial ouflow Fall in dmand for domsic currncy Incipin Dprciaion Cnral bank buys back mony o rsor h xchang ra Fiscal xpansion wih a flxibl xchang ra: Govrnmn xpndiurs incras Tmporary ris in domsic inrs ra Capial inflow Incras in dmand for domsic currncy Apprciaion Monary auhoriy prins mony, rsoring xchang ra Two sourcs of dmand incras: fiscal and monary
Dornbusch I: Sup Rurn on a domsic bond: i Exchang ra pric of forign currncy: i.. if US is h hom counry and Swdn h forign counry, hn h xchang ra would b ha i cos /7 of a dollar dividd by on dollar or us /7. Rurn on a forign bond: Taking logs: log ε i ε [ * ] [ *] * i i ε ε
Dornbusch II: Sup So, w g uncovrd inrs pariy: i * i Undr wha assumpions will his hold? Covrd inrs pariy: rplac h fuur spo ra wih h currn fuur ra. Essnially, his MUST hold. If i dosn, why no? Scond uaion: mony dmand m p i φy
Dornbusch III: Sup Dfiniion of ral xchang ra: p * p In hory, h ral xchang ra should hav a pric of for radabl goods. Why? Empirically, w don s his. Dmand is drmind by h ral xchang ra rlaiv o h full mploymn REX: y d [ p p ] y [ ] y δ * δ
Dornbusch IV: Sup Inrpraion of ral xchang ra: h ral pric of forign o domsic goods (i.. h pric of forign TV xprssd in domsic currncy o pric of domsic TV). Ral xchang ra of is calld PPP (Purchasing Powr Pariy). Dornbusch modl allows for dviaions from PPP.
Dornbusch V: Sup Moivaion for assumpion ha dmand for a counry s oupu is a dcrasing funcion of h ral xchang ra (.) Monopoly powr by hom firm in own marks (so pric adusmn dosn lad o infini or zro dmand) (2.) Hom-producd radabls goods ar mor imporan o h hom counry (3.) Domsic dmand swichs from forign radabls o domsic non-radabls.
Dornbusch VI: Sup Dornbusch modl is fully dynamic; shows priod by priod pric adusmn. Assumpion: pric adusmn happns according o an xpcaions-adusd philips curv: Whr p~ is h pric lvl ha would occur if h pric lvl clard: ~ p p * [ ] d y y ( ~ p p ) p ~ p ψ
Dornbusch VII: Sup Firs diffrncing h dfiniion of, w g: ~ p ~ ( p * ) ( p ) p * Plugging his ino h pric adusmn philips curv, w g: p Now ha w hav spcifid h modl, w will rviw h main uaions: noic ha his modl can much br look a h im pah of xchang ra dynamics in comparison wih h Mundll-Flming modl which can only b usd o analyz changs from on long-rm uilibrium o anohr. p~ [ ] d y y p ψ
Dornbusch VIII: Sup, p, y, i Thus, w hav four unknowns ( ) and h following uaions: Uncovrd Inrs Pariy: i * i Mony Dmand: m p i φy Domsic Tradabls Dmand: y d y δ [ ] Pric Adusmn: p [ ] d y y p ψ
Dornbusch IX: Graphical Soluion Firs, from h dfiniion of h ral xchang ra, w g [ p p ] p * p * p [ p ] Thn, combining h mony dmand uaion wih h pric adusmn uaion, w g: This is on of wo uaions whos dynamics w will nd h ohr is h nominal xchang ra. [ y y] ( ) d ψ ψδ
Dornbusch X: Graphical Soluion Firs, w normaliz h paramrs o zro: p* y i* 0 Thn, using uncovrd inrs pariy, w g: i From mony dmand, w can solv for h inrs ra: i p φy m
Dornbusch XI: Graphical Soluion Now w nd o g rid of all ndognous variabls bsids nominal and ral xchang ras (i.. pric and oupu). W can rplac oupu using h dmand uaion (and normalizing): y ( ) ( ) y δ δ Similarly, w can g pric from h dfiniion of h ral xchang ra (normalizd): p * p p
Dornbusch XII: Graphical Soluion Rplacing h xprssions for pric and oupu ino h inrs ra uaion, w g: Rplacing h inrs ra xprssion from uncovrd inrs pariy, w g: ( ) [ ] ( ) φδ φδ φδ m m i [ ] ( ) φδ φδ m
Dornbusch XIII: Graphical Soluion So, w hav wo uaions of moion, ach of which ar funcions of wo dynamic variabls: Th uaion of moion for h ral xchang ra: ψδ ( ) And h uaion of moion for h nominal xchang ra: [ φδ ] ( φδ m )
Dornbusch XIV: Graphical Soluion Firs, w sar wih solving for h long-run uilibrium: 0 [ φδ ] ( m ) 0 φδ Bu sinc in uilibrium, w hav, w g: m So h schdul is a vrical lin a and h schdul is a sraigh lin wih slop and inrcp φδ m φδ
Dornbusch XV: Graphical Soluion Now w draw h phas diagram and look a sabiliy propris of h uilibrium. and > < 0 < > 0 [ φδ ] ( φδ m ) > 0 > [ φδ ] ( φδ m ) < 0 < Ths parns imply somhing calld saddl-pah sabiliy: convrgnc o h long-run uilibrium is only along a uniu saddl pah. Elswhr in h spac, w g divrgnc. Morovr, his is no ral conomic rason o xpc h conomy o b on h saddl pah.
Dornbusch XVI: Graphical Soluion Now considr a on-im prmann incras in h mony supply a monary shock. In h long run, sinc p * p p and also m hn w hav, p m. As a rsul, in h long run, an incras in h mony supply from m o mˆ will lad o an incras in h pric lvl o mˆ and givn ha h long-run ral xchang ra mus rmain consan, an incras in h long-run xchang ra by h amoun mˆ m
Dornbusch XVII: Graphical Soluion Wha abou in h shor run? In h shor run, sinc prics ar sicky, so p 0 m which mans ha h ral xchang ra, nominal xchang ra combinaion ar on h lin givn by: 0 0 m Th iniial nw nominal and ral xchang ra combinaion ar givn by h inrscion of h abov lin and h nw saddl pah (which inrscs h nw long run uilibrium and has a slop of lss han h xchang ra curv which islf has a slop lss han ).
Dornbusch XVIII: Graphical Soluion Thus, as long as h xchang ra curv is posiivly slopd ( φδ > 0 ), hr will b ovrshooing of h nominal xchang ra. Wha is h inuiion for his? An incras in h mony sock lads o an incras in ral mony balancs bcaus prics ar fixd. If h φδ xchang umpd o is nw uilibrium wih p fixd, ha would caus a ral dprciaion of h currncy and hus oupu would incras by φδ. If h abov condiion is saisfid, hn ral mony supply will b grar han ral mony dmand and h domsic inrs ra will hav o fall.
Dornbusch XIX: Graphical Soluion If h domsic inrs ra falls, hn hr should b an accompanying xpcd apprciaion of h nominal xchang ra in ohr words, h xchang has o dprcia mor han implid by h xpansion of h mony supply and hn i mus apprcia slowly afrwards as prics incras.
Dornbusch Modl XX: Analyical Soluion W sar wih h ral-sid diffrnc uaion which is us an uaion wih ral ndognous variabls: ψδ ( ) ψδ [ ]( ) [ ]( ) [ ] 2 ψδ ψδ ( ) 2 N ψδ [ ] N ( )
Dornbusch Modl XXI: Analyical Soluion Now aking h uaion for h nominal sid of h conomy, which dos dpnd upon h ral sid, w g: [ ] ( ) φδ φδ m [ ] ( ) φδ φδ m [ ] ( ) φδ φδ m ( ) [ ]( ) φδ m
Dornbusch Modl XXII: Analyical Soluion Iraing forward, w g: Imposing h no bubbls condiion (which ruls ou pahs xcp h saddl pah): [ ] ( ) φδ lim m 0 lim
Dornbusch Modl XXIII: Analyical Soluion Rwriing: Now, assuming a consan mony supply, w firs no ha: [ ] ( ) φδ m
Dornbusch Modl XXIV: Analyical Soluion Coninuing o solv: Rplacing for h ral xchang ra: [ ] ( ) φδ m [ ]( ) [ ] ψδ φδ m [ ] ( ) ψδ ψδ ψδ
Dornbusch Modl XXV: Analyical Soluion Finally, w arriv a h uaion for h saddl pah: Now w look a shocks: m [ φδ ]( ) ψδ Suppos ha a da zro, h mony supply unxpcdly incrass from m o m'
Dornbusch Modl XXVI: Analyical Soluion From bfor, w know ha prics ar suck in h shor run so ha: 0 0 p0 0 m W also hav drivd h uaion for h saddl pah: 0 [ φδ ]( ) 0 m' ψδ W hav wo uaions and wo unknowns so ha w can solv for h iniial and.
Dornbusch Modl XXVII: Analyical Soluion Plugging h iniial condiion uaion ino h saddl pah uaion, w g: 0 Solving for h iniial ral xchang ra, w g: 0 [ φδ ]( ) 0 m m' ψδ ψδ ' φδ ψδ ( m m) W can also solv for h iniial nominal xchang ra: 0 ψδ m ' φδ ψδ ( m m)
Dornbusch Modl XXVIII: Analyical Soluion Sinc, by assumpion, > φδ, w find ha > m' 0 In ohr words w g ovrshooing > φδ of h nominal xchang ra! No ha w can coninu o solv for ohr priod valus by iraing forward on h ral xchang ra uaion and hn plugging h ral xchang ra ino h uaion for h nominal xchang ra.