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1 constor Mak Your Publications Visibl. A Srvic o Wirtschat Cntr zbwlibniz-inormationszntrum conomics Natividad-Carlos Fidlina B. Working Papr xchang-rat ovrshooting: An analysis or intrmdiat macro Discussion Papr School o conomics Univrsity o th Philippins No Providd in Coopration with: Univrsity o th Philippins School o conomics (UPS) Suggstd Citation: Natividad-Carlos Fidlina B. (04) : xchang-rat ovrshooting: An analysis or intrmdiat macro Discussion Papr School o conomics Univrsity o th Philippins No This Vrsion is availabl at: Standard-Nutzungsbdingungn: Di Dokumnt au constor dürn zu ignn wissnschatlichn Zwckn und zum Privatgbrauch gspichrt und kopirt wrdn. Si dürn di Dokumnt nicht ür öntlich odr kommrzill Zwck vrvilältign öntlich ausstlln öntlich zugänglich machn vrtribn odr andrwitig nutzn. Sorn di Vrassr di Dokumnt untr Opn-Contnt-Liznzn (insbsondr CC-Liznzn) zur Vrügung gstllt habn solltn gltn abwichnd von disn Nutzungsbdingungn di in dr dort gnanntn Liznz gwährtn Nutzungsrcht. Trms o us: Documnts in constor may b savd and copid or your prsonal and scholarly purposs. You ar not to copy documnts or public or commrcial purposs to xhibit th documnts publicly to mak thm publicly availabl on th intrnt or to distribut or othrwis us th documnts in public. I th documnts hav bn mad availabl undr an Opn Contnt Licnc (spcially Crativ Commons Licncs) you may xrcis urthr usag rights as spciid in th indicatd licnc.

2 UP School o conomics Discussion Paprs Discussion Papr No Octobr 04 xchang-rat Ovrshooting: An Analysis or Intrmdiat Macro by Fidlina B. Natividad-Carlos Prossor Univrsity o th Philippins School o conomics UPS Discussion Paprs ar prliminary vrsions circulatd privatly to licit critical commnts. Thy ar protctd by Rpublic Act No. 893 and ar not or quotation or rprinting without prior approval.

3 xchang-rat Ovrshooting: An Analysis or Intrmdiat Macro Fidlina B. Natividad-Carlos* Abstract Whil xchang rat dynamics is an important topic in opn conomy macroconomics th standard tool commonly usd to introduc xchang rat dynamics - th Dornbusch (976) sminal papr along with phas diagram - is not wll-suitd or undrgraduat studnts as most o thm do not hav yt a background on dynamic macroconomic analysis. This papr attmpts to provid a graphical dvic a panl IS*-LM* diagram which can b usd to tach intrmdiat macroconomics studnts about Dornbusch s ida o xchang rat dynamics. In addition it also attmpts to bridg th gap btwn undrgraduat taching and graduat taching o xchang rat dynamics by showing th corrspondnc btwn th conomy s adjustmnt path in th IS*-LM* diagram and that in th phas diagram. Ky words: undrgraduat taching graduat taching xchang rats xchang rat dynamics sticky prics intrst parity opn conomy macroconomics iscal policy montary policy. JL classiication cods: A50 A30 F30 F40 * Prossor School o conomics Univrsity o th Philippins 0. Th author is gratul to HPDP or inancial support.

4 . Introduction xchang-rat ovrshooting is an important phnomnon acting housholds businsss and govrnmnts. I intrmdiat-lvl macroconomics studnts ar to b prpard in undrstanding th policy issus concrning this phnomnon thy must b providd with a tool to undrstand th mchanics o xchang-rat dynamics. Th pionring and th most popular work in th litratur on ovrshooting is th Dornbusch (976) papr. It is an important and intrsting xtnsion o th Mundll-Flming modl a static small opn conomy IS-LM modl as it allows or pric adjustmnt ovr tim and rational xpctations ormation. Dornbusch (976 txt) assums prct capital mobility and substitutability which togthr imply uncovrd intrst rat parity (UIP) a rgrssiv xchang-rat xpctations schm that can b mad consistnt with prct orsight 3 a mony dmand unction and quilibrium in mony markt ixd incom vn in th short run a dmand or domstic goods unction sluggish pric adjustmnt that dpnds on a masur o transitory xcss dmand or domstic goods ovr ixd incom and a small conomy undr lxibl xchang rats which taks orign variabls as givn. Givn ths assumptions Dornbusch shows that whn incom is ixd and supply-dtrmind vn in th short-run and whn th pric lvl is a non-jumping or sluggish variabl th xchang rat will unambiguously ovrshoot its nw long-run quilibrium valu in rspons to an unanticipatd incras in th mony supply. With th pric lvl sticky and incom ixd an incras in th mony supply crats an Th Mundll-Flming modl is on o th stapls in intrmdiat macroconomics. Also s Boyr and Young (00). Th Dornbusch modl is also rrrd to as th Mundll-Flming-Dornbusch modl (or instanc s Obstld and Rogo (996)). 3 Prct orsight is th dtrministic/crtainty analogu o rational xpctations.

5 xcss supply at th initial domstic intrst rat and consquntly th domstic intrst rat must all to maintain mony markt quilibrium. At th sam tim an incras in th mony supply causs th xpctation o dprciation o th stady-stat xchang rat sinc thr is prct orsight. Th all in th domstic intrst rat causs incipint capital inlows which in turn causs th xchang rat to actually dprciat. To compnsat holdrs o domstic assts or th all in th domstic intrst rat th instantanous xchang rat dprciation must xcd th long-run dprciation i.. th xchang rat must ovrshoot its long-run quilibrium valu. Thus in an intrdpndnt systm whr th pric lvl is constraind not to mov immdiatly in rspons to som disturbanc it is th xchang rat and othr jump-variabls that bar th burdn o instantanous adjustmnt. Howvr whn incom is dmand-dtrmind and varis in th short run xchang-rat ovrshooting is no longr an invitabl consqunc o unxpctd montary xpansion as shown in Dornbusch (976 appndix). Spciically sinc an incras in th mony supply tmporarily stimulats incom and an incras in incom in turn causs an incras in mony dmand th dcras in th domstic intrst rat ncssary to maintain mony markt quilibrium is dampnd. Thus th instantanous xchang-rat adjustmnt is rducd. I incom xpansion is suicintly high thn th domstic intrst rat riss and th instantanous xchang-rat rspons is that o undrshooting. Th ssnc o th litratur (or th intuition bhind xchang-rat ovrshooting) is bst dscribd by Coopr (985 pp. vii-viii): that xchang rats can ovrshoot thir long-trm quilibrium valus in rspons to som nw disturbanc. It is yt anothr illustration in conomics o L Chatlir s principl that whn lxibility is constraind in som part o an intrdpndnt systm thos variabls that ar lxibl will rspond at irst to an vn gratr xtnt than thy would i constraind variabls wr also rly lxibl. In Dornbusch (976) th variabl which is constraind to adjust immdiatly is th pric lvl and on o th variabls

6 3 that can adjust rly is th xchang rat. Whil xchang rat dynamics is an important topic in opn conomy macroconomics th standard tool commonly usd to tach xchang rat dynamics (th Dornbusch (976) modl) - th phas diagram - is not wll-suitd or undrgraduat studnts as most o thm do not hav yt a background on dynamic macroconomic analysis. Thus th main objctiv o this papr is to attmpt to provid a graphical xposition o th Dornbusch (976 appndix) modl. Spciically it will attmpt to provid a graphical dvic - a panl diagram whr th irst thr panls not only dscrib th thr markts (orign xchang markt mony markt and goods markt) in th modl but also show th undrpinning o th last panl (th so-calld IS*-LM* diagram) - which can b usd to tach intrmdiat macroconomics studnts about xchang rat dynamics. Th advantag o a panl diagram is that givn a disturbanc on would asily s th dynamic (short-run transitional and long-run) cts on th dirnt markts as wll as on dirnt variabls. 4 This papr will also attmpt to bridg th gap btwn undrgraduat taching and graduat taching o xchang rat dynamics by showing th corrspondnc btwn th conomy s adjustmnt path in th IS*-LM* diagram and that in th phas diagram. In particular it will show that th transitional adjustmnt path in th IS*-LM* modl is th locus o IS*-LM* intrsctions as th pric lvl changs ovr tim and that such path corrsponds to th transitional adjustmnt path th saddl path in a phas diagram. Th rmaindr o this papr is organizd as ollows. Sction irst prsnts th building blocks o th Dornbusch (976 appndix) modl and shows thir corrsponding graphical rprsntation a panl IS*-LM* diagram - and thn discusss th dynamic proprtis o th 4 Anothr our-panl diagram - consisting o orign xchang markt diagram PPP diagram IS-LM diagram and y d y s diagram - is that o Harvy (007). Th PPP diagram dos not sm to b ncssary bcaus whthr PPP holds can b inrrd rom th stady-stat proprtis whil th y d y s diagram is not a good rprsntation o pric adjustmnt ovr tim.

7 4 modl. Sction 3 uss th panl IS*-LM* diagram to xamin th cts o a disturbancs montary xpansion and iscal xpansion. Sctions 4 and 5 show that th rsults o th gussand-vriy mthod usd in sction ar th sam as thos whn prct orsight is imposd dirctly but that it is advantagous to mploy a rgrssiv xpctations schm as a guss about xchang rat xpctations and vriy it only latr (that indd it is an ducatd guss) rathr than to impos prct orsight dirctly bcaus it maks possibl to draw on o th schduls in th orign xchang markt diagram and mor importantly th conomy s adjustmnt path right away as thir corrsponding quations can b obtaind radily without irst rsorting to som othr tchniqu or solving a systm o dirntial quations. Finally sction 6 givs th summary and conclusions.. Th Modl Th modl ollowing Dornbusch (976 appndix) is that o a small opn conomy undr lxibl xchang rats whrin prct capital mobility and substitutability prvail output or incom is variabl goods prics ar sticky and xchang-rat xpctations can b consistnt with rational xpctations.. Building Blocks Th building blocks o th modl ar: (.) i i uncovrd intrst parity ( UIP) (.) ( ) xchang-rat xpctations.3 m p y i LM (.4) y u y ( p p IS (.5) p ( y y) pric adjustmnt whr i ( i ) is domstic (orign) intrst rat is th log o xchang rat masurd as domstic currncy pr unit o orign currncy xchang rat m is th log o xognous mony supply p ( is th xpctd rat o rat o chang in th p ) is th log o domstic (orign) pric lvl m pis th log o ral mony supply y is th log o ral incom or output

8 5 p p is th log o th ral xchang rat q or th rlativ pric o domstic goods. Thus all variabls xcpt i and i ar in natural logarithms. All paramtrs ar positiv and 0. A bar on top o variabl indicats long-run quilibrium valu. Forign variabls i and p ar bcaus th conomy is assumd to b small takn as givn and thror xognous. y is also assumd xognous as it is assumd to b qual to th log o xognous ull mploymnt lvl o output y F. Not that th quations dscribing th modl ar xactly th sam as thos in th Dornbusch (976 appndix) modl xcpt that in this papr it is assumd or simplicity but without loss o gnrality that invstmnt is xognous and dos not dpnd on th domstic intrst rat (s.4).. Stady-Stat Th conomy is in a long-run quilibrium or in a stady-stat whn 0 and p 0 implying that th stady-stat valus o variabls ar givn by (.) i i (.) p m y i (.3) p p (/ )( u ( ) y) (.4) y y whr (.) is obtaind rom (.) (.) rom (.3) and (.3) rom (.4). and (3.4) ollows rom th assumption that y y F. Thus whil incom is dmand-dtrmind and varis in th short run it is assumd to b xognously ixd in th long-run..3 A Panl IS*-LM* Diagram Th modl (.) to (.5) which ar rlations dscribing th asst markt (orign xchang markt and th mony markt) and th goods markt is illustratd graphically in Figur and th dtails ar discussd blow. Forign xchang markt diagram. Th orign xchang markt is dscribd by th UIP

9 6 condition (.) and th assumption about xchang-rat xpctations (.). mbodid in th UIP condition ar th assumptions o prct inancial capital mobility across countris and prct inancial capital substitutability rom th point o viw o invstors which nsur th xpctd rat o rturn on domstic-currncy-dnominatd domstic asst R (qual to th domstic intrst rat i ) and th xpctd rat o rturn on orign-currncy-dnominatd orign R (qual to th orign intrst rat i plus th xpctd rat o chang in th xchang rat ( ) ar prctly alignd. 5 (.) also shows that whnvr th intrst dirntial i i is ngativ (positiv) holdrs o domstic (orign) assts must b compnsatd by th xpctation o utur domstic (orign) currncy apprciation i.. Th xpctd rat o chang in th xchang rat < (>) 0. is assumd to dpnd ngativly on th dviation o th logarithm o short-run xchang rat rom its long-run quilibrium valu (.). This mans that i th short run xchang rat is abov (qual to; blow) its long run quilibrium valu th xpctation is that th xchang rat will b alling (constant; rising) or th domstic currncy will b apprciating (constant; dprciating) ovr tim. This mans that (.) is a rgrssiv xpctations schm. To illustrat th orign xchang markt notic that th LHS o (.) is R (..) R i and that th RHS o (.) is R which whn combind with (.) yilds th downward sloping R schdul (..) R i ( ( )) or in slop-intrcpt orm 5 Th UIP condition is ( i) ( i ) / whr is xpctd xchang rat. It can b rwrittn as approximatd by (.). i i (( ) / ) i.(( ) / ) and assuming that i (( ) / ) is small nough it is

10 7 (.. ) i R v.intrcpt slop. (.) an ducatd guss or a guss about which can b vriid latr is an important componnt o th modl and a convnint on bcaus without it on cannot graph th R schdul at th outst and no urthr dynamic analysis can b mad. Th R schdul is vrtical at th domstic intrst rat. Th R schdul is downward sloping bcaus or givn and i an incras in or a domstic currncy dprciation will crat an xpctation o a subsqunt domstic (orign) currncy apprciation (dprciation) and rduc R. Ths schduls ar shown in Figur (a) th orign xchang markt diagram. At th intrsction o th R and R schduls th UIP condition (.) holds and xpctations satisy (.). Th R schdul shits to th lt as i dcrass whil th schdul shits to th right as incrass and/or i incrass. Not that th R schdul will R coincid with th 0 lin only i i i i as in Figur (a). Mony markt diagram. Th mony markt is summarizd by th LM quation (.3) which assums that mony markt quilibrium (MM) holds i.. ral mony supply is qual dmand or ral mony balancs L whr L is assumd to b a positiv unction o output and a ngativ unction o domstic intrst rat. Figur (b) th mony markt diagram shows th m pschdul as a horizontal schdul and th l (= ln L) unction th RHS o (.3) as a downward sloping schdul. At th point o intrsction btwn th m pand l schduls MM holds i.. (.3) holds. 6 Th m pschdul shits as m or p changs whil th l schdul shits as y changs. Not that th siz o th shit o th l schdul as y changs is larg whn paramtr is larg. 6 Such point corrsponds to a point on th upward sloping LM schdul in a y-i diagram.

11 8 Asst markt quilibrium (AM) and th LM* schdul. Th LM* (or th opn conomy LM) schdul is drivd rom th rlations dscribing th asst markt. Thus combining (.) (.) and (.3) yilds th quation or th LM* schdul (3.) ( ) ( y y) ( p p) or in slop-intrcpt orm (3. ) i ( m p ) ( ) y v.intrcpt slop which shows th (y ) combinations or which th assts markt clars i.. both th mony markt and th orign xchang markt clar and xchang-rat xpctations conorm with (.). Thus th LM* schdul is actually th AM schdul. Th LM* schdul can b obtaind graphically as ollows. As y incrass l incrass and th l schdul shits up and i incrass to maintain mony markt quilibrium. Th incras in i in turn causs th R schdul to shit to th right thrby causing R < R at th initial and must all (th domstic currncy must apprciat) to incras to maintain UIP. This mans that at any point on th LM* schdul mony markt quilibrium and UIP hold and xpctations ar takn into account and that along th LM* schdul th rlationship btwn and y is ngativ (s Figur 3(a)). Not that th siz o th all in is also actd by paramtr : th all in will b larg whn is larg i.. LM* is stp. Th LM* schdul shits to th right as incrass i incrass or ( m p) incrass. Goods markt diagram. Th goods markt is dscribd by th IS* (or opn conomy IS) quation (.4) and th pric adjustmnt quation (.5). (.4) assums that goods markt quilibrium (GM) holds i.. output quals th dmand or domstic output D whr D is a positiv unction o output or ral incom and th ral xchang rat or th rlativ pric o

12 9 domstic goods. 7 Figur (c) is an opn conomy Kynsian cross diagram whr th d (= ln D ) schdul th RHS o (.4) is drawn as upward sloping and lattr than th 45 o lin sinc its slop is lss than. Th 45 o lin is th y d lin and thus is also th y lin. quilibrium output is givn by th crossing o d schdul and th y lin. Thus at th point o crossing GM (.4) holds and that point corrsponds to a point on th IS* schdul. Th d schdul shits up as u and/or p p changs. Not that th siz o th shit o th d schdul whn changs is larg whn paramtr is larg. Th inal quation o th modl (.5) indicats that th pric lvl adjusts only slowly ovr tim. Spciically pric adjustmnt is proportional to th dviation o output rom its long run quilibrium valu. (.5) whos implications ar yt to b drivd cannot b linkd/ mbddd yt in Figur. Goods markt quilibrium (GM) and th IS* schdul. Th IS* schdul is simply th opn conomy IS (.4) which can b writtn in dviation orm as 8 (3.) ( p p) ( y y) or in slop-intrcpt orm (3. ) p p u y. v. intrcpt slop Th IS* schdul shows th (y ) combinations or which th goods markt clars (s Figur (d)). Thus it can also b calld th GM schdul. Th IS* schdul can b drivd graphically as ollows (s Figur (b)). As 7 Not that hr th goods markt is not actd dirctly by i as invstmnt is assumd to b xognous but th goods markt acts th mony markt through y. u in (.4) capturs th cts o xognous aggrgat dmand such as xognous invstmnt and iscal policy. 8 Th IS* schdul is th sam as IS schdul in a y-i diagram which is vrtical sinc invstmnt is xognous.

13 0 incrass p p incrass nt xports incras th dmand or domstic goods incrass and thus th ln D schdul shits up and y incrass to maintain goods markt quilibrium. This mans that at any point on th IS* schdul goods markt quilibrium holds and that along th IS* schdul th rlationship btwn and y positiv. Not that th siz o th incras in y is also actd by paramtr : th incras in y will b larg whn is small i.. th IS* schdul is stp. Th IS* schdul shits to th right as p dcrass or incrass. p incrass or u Th IS*-LM* diagram. Figur (d) th IS*-LM* diagram is an opn-conomy IS-LM diagram drawn in a y diagram rathr than in a y i diagram. A shown abov it is actually a GM - AM diagram. Krugman and Obstld (988) and Krugman Obstld and Mlitz (0 Krugman and Obstld (988) rr to this diagram as th DD-AA diagram; howvr do not us a our-panl diagram. 9.4 quilibrium Adjustmnt and Prct Forsight Long-run quilibrium and short-run quilibrium. Th conomy s short-run quilibrium occurs at th intrsction o IS* and LM* schduls; at this point all markts clar. I th IS*- LM* intrsction lis on th y F lin and at th sam tim th R R intrsction lis on th 0 lin thn th conomy is also in a long-run quilibrium whr thr is no tndncy or both th pric lvl and th xpctd xchang rat to chang. Short-run quilibrium and adjustmnt: th SP schdul as th locus o IS*-LM* intrsctions as p changs. At any point in tim th conomy is in short-run quilibrium i.. on a point o intrsction btwn th IS* (or GM) schdul and LM* (or AM) schdul. 9 On th inconsistncis which on inds in idntiying modls in th opn macroconomy Boyr and Young (00) rmark that Obstld and Rogo (996) us th xprssion th Mundll-Flming-Dornbusch modl at last svn tims in thir graduat txtbook but th sam xprssion is not to b ound in th undrgraduat txtbook by Krugman and Obstld (988 and latr ditions) which mploys th mchanism idntical to that in th so-calld th Mundll-Flming-Dornbusch modl as th cntral mchanism in thir ky ramwork which thy call th DD-AA modl.

14 Using th IS* and LM* quations in dviation orm (3.) and (3.) yilds a (4) ( ) ( p p) a or in slop-intrcpt orm a a p p a a (4 ) / ( ) whr a 0 / ( ) 0 as / ( ). and a a (4) is th ky quation o th modl and illustratd as th schdul labld SP. It dtrmins or givn and p th short-run quilibrium valu o as a unction o p. It is th ky quation bcaus as shown blow it is th quation or th adjustmnt path and thus it is th on which dtrmins th siz o xchang-rat jump at t = 0 and also th on which dscribs th rlation btwn and p during adjustmnt. (4) using (3.) or ( p p) can b rwrittn quivalntly as a (5) ( ) ( y y) / or in slop-intrcpt orm a a y y / / (5 ) v.intrcpt slop which dtrmins or givn and y th short-run quilibrium valu o as a unction o y. Thus (4) or (5) is th quation or th locus o IS*-LM* intrsctions. Graphically th locus o points o IS*-LM* intrsction in y diagram labld SP (s Figur 3(a)) corrsponds to a locus in p diagram which is also labld SP (s Figur 3(b)). Figurs 3(a) and 3(b) show th cas whr a > 0. Not that whn a is positiv (zro; ngativ) or quivalntly whn / ( ) is lss than (qual to; gratr than) unity th SP

15 schdul in p diagram is downward sloping (horizontal; upward sloping) whras th SP schdul in y diagram is upward sloping (horizontal; downward sloping). Not also that both SP schduls in p diagram and in y diagram shits up whn ithr m or i incrass (and thror both p and incras) or whn ithr p or u dcrass (and thror p incrass). Th SP schdul in th p ( y ) diagram shits to th right (lt) whnvr thr is an incras in and/or p thrby changing th conomy s long-run quilibrium position. During adjustmnt rom short-run to th nw long-run quilibrium or whn th pric lvl is changing ovr tim both th IS* and LM* schduls ar shiting ovr tim but th conomy is always on an IS*-LM* intrsction and thror always on th SP schdul. Thus th SP schdul ((4) or (5)) is th graphical rprsntation o th conomy s convrgnt adjustmnt path. Dynamics o p and along th adjustmnt path and convrgnc. Th quation dscribing th dynamics o p along th adjustmnt path can b obtaind using th assumd pric adjustmnt (.5) (3.) or ( y y) and (4) or ( ) p ( ) ( p p) ( y y)using (.') a ( ) a ( p p) a a ( p p) a ( p p) a ( )using (4) which yilds (6.) p v( p p) a a ( a ) a v a whr and a a / ( ) 0.

16 3 (6.) shows that p will b incrasing (constant; dcrasing) ovr tim whnvr p is blow (qual to; abov) p. (6.) can b solvd to yild th tim path o p (6.) p( t) p ( p(0) p)xp vt which shows that p will convrg towards p at th rat v. Th tim path o using (4) and (6.) is givn by a (7.) vt vt ( t) ( p(0) p)xp ( (0) )xp a indicating that will convrg towards also at th rat v. Along th SP schdul th dynamics o is givn by (7.) v( ) implying that th domstic currncy will b apprciating (constant; dprciating) ovr tim or as long as is abov (blow) its long-run lvl. 0 Consistncy with prct orsight. xpctations would b consistnt with prct orsight i th xpctd rat o chang in th xchang rat is qual to th actual rat o chang in th xchang rat = () i.. i in (.) is qual to v in (7.). quating and v a a ( a ) a a a a a a a a 0 ( a a ) ( a a a a ) yilds an quation that is quadratic in (8.) ( a a ) ( aa aa ) 0 with solution 0 Th quations dscribing th bhavior o othr variabls i and y during adjustmnt can b similarly obtaind (s Appndix availabl upon rqust).

17 4 (8.) / ( a a ) [( ( a a )) 4( a a a a )] (4) is th quation or th uniqu SP schdul or adjustmnt path providd that (8.3) / ( a a ) [( ( a a )) 4( a a a a )] v 0. is th conomy s spd o adjustmnt and convrgnc will b astr th lowr is th highr is and th highr is. Adjustmnt procss. Th conomy s procss o adjustmnt can b dscribd using Figur 3(a) or 3(b). At any point in tim all markts clar i.. thr is short-run quilibrium (s (4)). This mans that th conomy is always on th SP schdul. Th adjustmnt procss is also illustratd in Figur 4 which is th sam as Figur 3(b) with th p 0 locus in it. Th p 0 locus shows th (p ) combinations or which th goods markt is in quilibrium and th pric lvl dos not chang. At any point to th lt (right) o and abov (blow) th p 0 schdul y is abov (blow) y and thus th pric lvl is rising (alling). Th p 0 locus is positivly slopd and paralll to th 45 o lin bcaus an incras in crats an xcss dmand and p will hav to incras qui-proportionatly to rstor quilibrium sinc an incras in p acts aggrgat dmand only through th ral xchang rat and not through intrst rat. Long-run quilibrium is a point on th vrtical y F lin or on th p 0 locus. Spciically long-run quilibrium occurs at th point whr th IS* and LM* schduls and th vrtical y F lin intrsct (i.. whn y y yf and thus p 0) or altrnativly at th point whr th SP intrscts th p 0 locus. This occurs at point C. Sinc th smi-rducd orm pric adjustmnt quation is p a( ) a ( p p) th p 0 locus is givn by ( ) ( p p) or in slop-intrcpt orm p () p. In th cas th p 0 may ithr coincid with or b paralll to th 45 o lin. v.intrcpt slop

18 5 Considr point B a point on th SP schdul but abov th p 0 locus. At this point p will b rising ovr tim and thus both th IS* and LM* schduls ar shiting with th points o intrsction tracing th lin with sris o arrows rom point B to point C. Th path rom point B to point C is th locus o points o intrsction btwn th IS* schdul and th LM* schdul as p changs ovr tim. Thus th conomy s adjustmnt path is th SP schdul in Figurs 3(a) (3(b) and 4. As shown blow th SP schdul is th sam as th stabl arm o th saddlpoint in a modl whr prct orsight is imposd dirctly. A dtaild discussion o th adjustmnt procss is covrd in th nxt sction. 3. cts o Disturbancs 3. Montary xpansion Assum that th conomy is initially in a long-run quilibrium. All initial positions ar labld A whil all initial valus ar labld with th subscript (s Figurs 5a and 5b or th ovrshooting cas and Figurs 6a and 6b or th undrshooting cas). Now considr a montary xpansion in th orm o an incras in m at t = 0 a disturbanc which acts long-run quilibrium pric lvl. Stady-stat cts. Th stady-stat cts o a montary xpansion shown as th movmnt rom A to C in Figurs 5a and 6a using (3.)-(3.4) ar (8.) di / dm di / dm 0 (8.) dp / dm (8.3) d / dm dp / dm (8.4) dy / dm dy / dm 0 F and by implication d( dp p ) / dm 0. In th long run mony is nutral (s 8.4) and acts and p quiproportionatly (s (8.) and (8.3)). This mans that an x% incras in th mony supply will lad to an x% incras in th pric lvl and an x% domstic currncy dprciation but will lav th rlativ pric or ral xchang and thror output unchangd

19 6 implying that th rlativ purchasing powr parity (PPP) holds. Thus th modl is montarist/classical in th long-run. Impact cts. Assum th cas whr a > 0 i.. th cas whr SP schdul in th p diagram is downward sloping. Th impact cts or th cts which occurs at t = 0 ar shown as th jump rom A to B in Figur 5a and 5b th ovrshooting cas. conomic agnts bcaus thy ar ndowd with prct orsight s th montary xpansion and know that it will lad to a long-run domstic currncy dprciation. Thy rspond accordingly by altring thir xpctations which causs th R schdul to shit up by an amount qual to d (= ). With i unchangd yt UIP no longr holds but this may not b possibl bcaus i may chang. To s why notic that an incras in m rsults in an incras in ( m p) sinc p dos not chang at t = 0 i.. th ( m p) schdul shits up by an amount qual to dm. At th sam tim th incras in will sinc p is sticky and p is xognously ixd lad to a ral dprciation an incras in nt xports and incras in th dmand or domstic output and thus th d schdul shits up; to maintain GM y must incras. This incras in y in turn will incras l and shit up th l schdul. I at th initial i th incras in ( m p) is gratr than th rsulting incras in l d( m p) dl dy d d d( m p) dl / ( )... 0 dm dy d d dm dm dm dm/ dm /( ) at thinitiali or th v. shit o th ( m p) schdul > th v. shit o th l schdul thn will b an xcss supply o mony at th initial i; to maintain mony markt quilibrium i must all. I i dcrass th R schdul shits to th lt and with i rmaining th sam UIP will b maintaind i < 0 i.. i thr is an xpctation o a subsqunt domstic currncy apprciation (constant xchang rat; domstic currncy dprciation) so as to compnsat holdrs o domstic assts. Such an xpctation will b cratd only i d > d i..

20 7 ovrshoots initially. In Figur (d) th LM* schdul shits up bcaus th ( m p) schdul shits up and also bcaus th R schdul shits up but th IS* schdul rmains th sam. Sinc th asst markt is in continuous quilibrium th conomy jumps rom A on LM* to point B on LM*. At point B th has risn but is gratr than th nw i is lowr y is highr and p which has not changd yt is lowr than th nw p. Using (4) whn t = 0 a (9) ( (0) ) ( p(0) p) a Th rsulting xchang rat jump is d(0) d a (9.) d p 0 dm dm a / ( ) dm and thus th xtnt o ovrshooting/undrshooting is (9.) d(0) d a d p dm dm a dm / ( ) / ( ) whr th numrator o a / ( ) has alrady bn intrprtd abov. Clarly th impact cts shows that th modl xhibits Kynsian proprtis in th short-run in th sns that mony acts output and in this modl lik in th Mundll-Flming modl montary policy is ctiv in inluncing output in th short-run undr conditions o lxibl xchang rats and prct capital mobility. Transitional dynamics. Atr th jump th conomy movs continuously along th adjustmnt path rom point B to point C in Figurs 5a and 5b. This happns bcaus at point B y > y y causing p to ris ovr tim which in turn causs othr variabls to chang ovr F

21 8 tim. Thus during transition dynamics is drivn by p. Spciically rising p ovr tim lads to alling ( m p) and downward shiting ( m p) schdul ovr tim. Rising p also causs alling q( p p ) and downward shiting d schdul alling y and thus alling l and downward shiting l schdul. In th ovrshooting cas this mans that i will b rising and corrspondingly th R schdul is shiting to th right and sinc thr is no chang in i < 0. Sinc with prct orsight xpctations ar slulilling subsqunt adjustmnt is indd charactrizd by actual apprciation 0. Adjustmnts continu until th nw stady-stat is rachd at point C. Othr cass. Th prvious analysis assums that a > 0. It can b shown that i a < (=) 0 thn th SP schdul is p upward sloping (horizontal). Following a montary xpansion will jump but will undrshoot (nithr ovrshoot nor undrshoot) at t = 0; during transition < (=) 0 i.. adjustmnt is charactrizd by an xpctation o and an actual domstic currncy dprciation (constant xchang rat). This is so bcaus whn a < (=) 0 i.. whn / ( ) < (=) 0 th incras in ( m p) is lss than (qual to) th rsulting incras in l at th initial i or th v. shit o th ( m p) schdul < (=) th v. shit o th l schdul and an xcss dmand or mony (nithr an xcss supply o or dmand or mony) is cratd at th initial i; to maintain mony markt quilibrium i must ris (rmain th sam). An incras in (An unchangd) i with i rmaining th sam rquirs > (=) 0 or th UIP condition to b maintaind. But such an xpctation o a subsqunt domstic currncy dprciation (constant xchang rat) can only b cratd i undrshoots (nithr ovrshoots nor undrshoots) th nw. In this cas th transition is charactrizd by actual dprciation (constant xchang rat) > (=) 0 and a rising pric lvl. Th undrshooting ovrshooting cas is shown in Figurs 6a and 6b.

22 9 Limiting cas o 0. I 0 thn givn a montary xpansion thr will b no incras in mony dmand vn whn thr is a rsulting incom xpansion and th rsult will b xchang rat ovrshooting as in th Dornbusch (976 txt) ovrshooting modl. Figur. A panl IS*-LM* diagram R 0 lin y F lin GM: IS* A R A AM: LM* i i R( i) R (a) Forign xchang markt y yf y y (d) IS*-LM* diagram m-p l d y 45 0 lin: y lin d A (m-p) l A i i i (b) Mony markt y yf y (c) Goods markt

23 0 Figur a. Graphical drivation o th LM* schdul R R R LM*: i ( m p ) ( ) y v.intrcpt slop m-p l i i R(=i) R y y y (m-p) l l i i i Figur b. Graphical drivation o th IS* schdul IS*: p p u y v. intrcpt slop d y y y y 45 o lin: y lin d d y y y

24 Figur 3. SP as th locus o IS*-LM* intrsctions (ovrshooting cas) ' C B IS* schduls SP ' B C F ' (a) y LM* schduls s y y y y y (b) SP p p' p p y Figur 4. Th SP schdul and th 0 p locus (ovrshooting cas) ' A B C p 0 SP p p' p p y

25 Figur 5a. cts o a prmannt montary xpansion (ovrshooting cas) ' R R =R 0 lin B C A R =R R ' y F lin C A B IS* IS* =IS* LM* LM* LM* m-p l i ' i i i i R B (m-p) d y y yf y y ' y y B 45 o lin: y lin d d =d AC (m-p) =(m-p) l l =l AC i ' i i i i y yf y y ' y y Figur 5b. cts o a prmannt montary xpansion: IS*-LM* diagram vs. phas diagram (ovrshooting cas a > 0) ' C A B IS* IS* =IS* LM* LM* LM* ' A B C p 0 SP SP y y y y y F ' (a) y p p' p p (b)

26 3 Figur 6a. cts o a prmannt montary xpansion (undrshooting cas a < 0) y F lin R R =R 0 lin ' C A B R =R R ' C A B IS* IS* =IS* LM* LM* LM* m-p l i i i i ' i R B (m-p) d y y yf y y ' y y B 45 o lin: y lin d d =d AC (m-p) =(m-p) l l =l AC ' i i i i i y yf y y ' y y ' Figur 6b. cts o a prmannt montary xpansion: IS*-LM* diagram vs. phas diagram (ovrshooting cas a > 0) y F lin C A B IS* IS* =IS* LM* LM* LM* ' B A C p 0 SP SP y yf y y ' y y (a) p p' p p (b)

27 4 3. Fiscal xpansion Th our-panl IS*-LM* diagram can also b usd to analyz th cts o othr disturbancs. In th cas o ral disturbancs (disturbancs in aggrgat dmand such as changs in p or u in th IS* quation) and thror iscal disturbancs (capturd by u) it can b shown that thr ar no transitional dynamics sinc quilibrium pric lvl is not actd by ths disturbancs; th systm simply jumps rom th initial stady stat to th nw stady stat. Thus th Dornbusch ramwork and thror th modl prsntd hr prsrv th Mundll-Flming rsult that iscal policy is inctiv undr conditions o prct capital mobility and lxibl xchang rats. 4. Assuming A Prct-Forsight Consistnt Rgrssiv xpctations Schm and th Mthod o Undtrmind Coicint (Guss and Vriy Mthod) Dornbusch by assuming a prct-orsight-consistnt rgrssiv xchang-rat xpctations schm ( in (.) and spciid in (.)) and a pric adjustmnt ovr tim (.5) ssntially turnd th static Mundll-Flming modl into a dynamic modl. H uss a rgrssiv xpctations schm (.) as a guss and latr vriis that it can b consistnt with rational xpctations providd that th xchang-rat xpctations coicint satisis a uniqu rlationship among all th paramtrs o th modl. As thr is no uncrtainty in th modl rational xpctations ar quivalnt to prct orsight and prct orsight implis that th xpctd rat o chang in th xchang rat is th sam as th actual rat o chang in th xchang rat i... This papr has applid th sam procdur and as shown abov th advantag o having a guss such as (.) and vriying it only latr (that indd it is an ducatd guss) is that it is possibl to draw th R schdul in th orign xchang markt diagram and mor Th our-panl IS*-LM* diagram can also b usd to analyz th cts o a chang in th orign intrst rat.

28 5 importantly th saddl path (Dornbusch s QQ schdul) or th conomy s adjustmnt path right away as thir corrsponding quations can b obtaind radily without irst rsorting to som tchniqu or solving a systm o dirntial quations. 5. Imposing Prct Forsight Dirctly I instad o assuming a prct-orsight consistnt rgrssiv xpctations schm prct orsight that th xpctd and th actual rat o chang in th xchang rat ar th sam - is imposd dirctly into th modl i.. (.) is rplacd by (. ) thn quation is drivd rom th ntir modl or consistncy with prct orsight and th modl now has two dynamic quations th quation and th p quation which constituts a systm o dirntial quations. 3 (.5) ar It can b shown that th rducd-orm short run static quations o th modl (.) to (0.) ( i( t) i ) a ( ( t) ) a ( p( t) p) (0.) ( y( t) y) ( ( t) ) ( p( t) p) and that th dynamic quations ar (.) a ( ( t) ) a ( p( t) p) (.) p a( ( t) ) a( p( t) p) whr a ij s ar as dind bor. (0.) obtaind using th IS (.4) and th LM (.3) shows th i that is consistnt with th simultanous claring o mony and goods markts whil (0.) is obtaind using th IS (.4) Not that th assts markts ar in continuous quilibrium. Spciically in th short run i is th quilibrating actor in th mony markt and in th 3 S Bhandari (98).

29 6 orign xchang markt th xchang rat. Not that that th goods markt is always in quilibrium du to th assumption that short run incom or output is dmand-dtrmind. (.) bcaus o prct orsight assumption is drivd rom th ntir modl (or rom UIP (.) and (0.)) i.. drivd rom th condition o short run quilibrium in all markts. Thus th IS th LM th UIP condition and th prct orsight assumption yilds th quation. Th quation or p is obtaind using an assumd atur o th modl (.5) and (0.). Th dirntial quations in and in p (.) and (.)) along with th rducd orm short-run static quations or i and y ((0.) and (0.)) ully dscrib th conomy s motion ovr tim contingnt upon som st o initial conditions. Howvr (.) and (.) do not xplicitly show th systm s dynamic proprtis. It is thror ncssary to driv th quantitativ and/or th qualitativ solution to ths dynamic quations. Qualitativ solution: phas diagram. (.) and (.) constitut a systm o two irstordr linar dirntial quations with constant coicints whos solution can b ound using a phas diagram. Using th quation (.) and stting qual to zro givs a a (.) ( t) p p( t) a a which th quation or th 0 locus. It is downward sloping (horizontal; upward sloping) as a 0. Using (A4.) again (.) d / d a 0 implying that all points abov (blow) th 0 locus whr is positiv (ngativ) is incrasing (dcrasing) as dnotd by th vrtical arrows pointing upward (downward). Th 0 locus shits as and/or p changs. Using th p quation (.) and stting p qual to zro givs

30 7 (3.) a a t p p t a a ( ) ( ) p p() t which is th quation or th p 0locus. It is upward sloping with slop qualing sinc a a. Using (.) (3.) dp / dp a 0 implying that at all points to th lt (right) o th p 0locus whr p 0 > (=;<) 0 p is incrasing (dcrasing) as dnotd by th horizontal arrows pointing rightward (ltward). Th p 0locus shits/rotats as ithr p or i changs but not whn m changs sinc th p 0locus is simply p p and d dp dm (s (.) (.) and (.3)). Combining th sts o horizontal and vrtical arrows givs an ida about th trajctoris and in particular th totally unstabl path and th saddl path (s Figur 7). Figur 7. Phas diagram or th modl with prct orsight imposd dirctly (ovrshooting cas) p 0 ' B A C 0 SP p p' p p Th phas diagram or th modl in which prct orsight is imposd dirctly (Figur 7) is th standard diagram showing th p 0 and 0 loci and th stabl arm o th saddlpoint. Th phas diagram in a modl which assums a rgrssiv xpctations schm dos not hav th 0 locus as it is not ncssary in driving th adjustmnt path.

31 8 Quantitativ solution. 4 Considr irst th natur o th modl s stationary quilibrium. Dirntiating th p quation (.) with rspct to tim and using th quation (.) to substitut out or and th p quation (.) or ( ( t) )) yilds (4) p ( a a ) p ( a a a a )( p( t) p) 0 which is a scond-ordr dirntial quation in p. Th charactristic quation associatd with (4) is (4.) r a a r aa aa ( ) ( ) 0 and th charactristic roots o (4) ar givn by (4.) r r ( a a) ( a a) 4( aa aa) / ( ) dt( A) rr aa aa 0 and A is th whr tr( A) r r a a matrix o coicints associatd with (.) and (.). Sinc dt( A) rr 0 thn whatvr is th sign o tr( A) r r th two roots ar ral and opposit in signs. This nsurs that th prct-orsight stationary quilibrium o th modl is a saddl point and that thr xists a uniqu path convrging to that point. Now lt r 0 and r 0. Providd that v thn (4.3) ( a a) ( a a) 4( aa aa) r v 0. It can b shown that th condition that th coicint associatd with th positiv root must b zro which is satisid whn a (9 ) ( (0) ) ( p(0) p) ( a r) 4 Tchniqus or solving a systm o irst-ordr linar dirntial quations can b ound in Gandolo (980) and Dixit (980).

32 9 along with th condition that p cannot jump at t 0convrts th gnral solution to (.) and (.) into particular or boundd solution which should b xactly th sam as (7.) and (6.) rspctivly with v is rplacd by r. Thus providd that v thn indd r and consquntly all th rsults whn a rgrssiv xpctations schm is assumd quation or th saddl path (4) tim paths o and p ((7.) and (6.)) dynamics o and p along th saddl path ((7.) and (6.)) and th xchang rat jump as wll as th xtnt o ovrshooting/undrshooting rsulting rom a montary xpansion ((9.) and (9.)) ar idntical to th rsults whn prct orsight is imposd dirctly (s Bhandari (98) and Appndix (availabl upon rqust )). 6. Summary Th pionring and th most popular work in th litratur on ovrshooting is th Dornbusch (976) papr. It is an important and intrsting xtnsion o th Mundll-Flming modl a static small opn conomy IS-LM modl as it allows or pric adjustmnt ovr tim and rational xpctations ormation. Whil xchang rat dynamics is an important topic in opn conomy macroconomics th standard tool commonly usd to tach xchang rat dynamics - th phas diagram - is not wll-suitd or undrgraduat studnts as most o thm do not hav yt a background on dynamic macroconomic analysis. Th main objctiv o this papr has bn to attmpt to provid a graphical xposition o th Dornbusch (976 appndix) modl. Spciically it has attmptd to provid a graphical dvic - a panl diagram whr th irst thr panls not only dscrib th thr markts (orign xchang markt mony markt and goods markt) in th modl but also show th undrpinning o th last panl (th so-calld IS*-LM* diagram) - which can b usd to tach intrmdiat macroconomics studnts about xchang rat dynamics. Th advantag o a panl diagram is that givn a disturbanc on would asily s th dynamic (short-run transitional

33 30 and long-run) cts on th dirnt markts as wll as on dirnt variabls. This papr has also attmptd to bridg th gap btwn undrgraduat taching and graduat taching o xchang rat dynamics by showing th corrspondnc btwn th conomy s adjustmnt path in th IS*-LM* diagram and that in th phas diagram. In particular it has shown that th transitional adjustmnt path in th IS*-LM* modl is th locus o IS*-LM* intrsctions as th pric lvl changs ovr tim and that such path corrsponds to th transitional adjustmnt path th saddl path in a phas diagram. Furthrmor this papr has shown that th rsults o th guss-and-vriy mthod ar th sam as thos whn prct orsight is imposd dirctly but that it is advantagous to mploy a rgrssiv xpctations schm as a guss about xchang rat xpctations and vriy it only latr (that indd it is an ducatd guss) rathr than to impos prct orsight dirctly bcaus th ormr tchniqu it maks possibl to draw not only on o th schduls in th orign xchang markt diagram but also mor importantly th conomy s adjustmnt path right away as thir corrsponding quations can b obtaind radily without irst rsorting to som othr tchniqu or solving a systm o dirntial quations.

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