Currency crisis: unique equilibrium and transparency

Transcription

1 Currncy crss: unqu qulbrum and ransparncy Ch-Tng Chn Dparmn of Rsk Managmn and Insuranc, Mng Chuan Unvrsy Absrac Morrs and Shn (998) nroduc h global gam no h slf-fulfllng currncy crss modl and show ha an nformaonal vn would b a rggr for a currncy crss. Howvr, hr s no govrnmn s objcv xplcly spcfd n h modl. W consdr h macroconomc mark o spcfy h govrnmn s objcv n h global gam modl of currncy crss and us h spcfc govrnmn s objcv o oban h rang of h ru fundamnals undr whch a govrnmn should adop a ransparn polcy. W hav shown ha an nformaonal vn may rggr a currncy crss, and a govrnmn wll prvn a currncy crss by adopng a ransparn polcy whn h cos of h ransparn polcy s small nough. Kywords: Global gam; Informaonal vn; Currncy crss; Transparn polcy. JEL classfcaon: F3; D8 Plas snd all corrspondnc o: Ch-Tng Chn Dparmn of Rsk Managmn and Insuranc Mng Chuan Unvrsy Tap, Tawan Fax: ; Tl: x. 63; Emal: dbbyjn@za.mcu.du.w

2 . Inroducon Th frs-gnraon currncy crss modl clarly dscrbs h forgn xchang urmol n h 970s and arly 980s n dvlopng counrs such as Mxco (973-98), Argnna (978-98), Bolvan (98-985), Brazlan (983, 986, ), Chlan (97-974), Pruvan (976, 987), and Uruguayan (98). Ths currncy crss ar ncouragd by connuously xpansonary domsc polcs combnd wh fxd xchang ra. Salan and Hndrson (978), Krugman (979), Flood and Garbr (984), Obsfld (984), and Bur (987) apply h frs-gnraon currncy crss modl o xplan how a fxd xchang-ra polcy assocad wh xcssvly xpansonary pr-crss fundamnals push h conomy no crss. In hs approach, h currncy crss s an unavodabl oucom of ovrly xpansv domsc polcs ncompabl wh a fxd xchang ra. Ths ncompabl polcs rprsn a profabl opporuny for spculaors. Forgn rsrvs wll drop o zro rapdly and h currncy bgns o dprca a h sam m whn h spculaors aack on h fxd xchang ra. Th xprnc of Europ s Exchang Ra Mchansm (ERM) crss n and h Mxcan crss n h la 994 ndcas h fac ha currncy crss can ars vn wh sound macroconomc fundamnal (s Saxna (004)). In ordr o xplan why currncy crss occurs whou obvous chang n mark fundamnal, Obsfld (996; 997) dvlops scond-gnraon currncy crss modl ha gnras mulpl qulbra - on s h fxd xchang ra and h ohr s h floang xchang ra - for h sam fundamnal. I follows ha on agn s xpcaon s a sragc complmn, ponrd by Topks (979), o anohr s xpcaon (.., gvn anohr s xpcaon, on agn s xpcaon s h sam as anohr s). If all agns xpc ha h govrnmn can pg a fxd xchang ra, h govrnmn s cos of h fxd xchang ra s lowr han ha of h floang xchang ra and hn h govrnmn can manan h fxd xchang ra; on h conrary, f all agns xpc ha h govrnmn has o chang h xchang ra, h govrnmn s cos of h fxd xchang ra s hghr han ha of h floang xchang ra and hn h govrnmn canno ran h fxd xchang ra. As a rsul, hr ar wo qulbra: on s ha no agn has dvaluaon xpcaon and h fxd xchang ra s manand, and h ohr s ha all agns hav dvaluaon xpcaon and h govrnmn allows h xchang ra o chang. In such modl, an qulbrum shfs from h fxd xchang ra o h

3 floang xchang ra no bcaus somhng has happnd o h fundamnal, bu bcaus all agns blv ha h qulbrum has changd. Thrfor, h scond-gnraon currncy crss modl s also clamd as slf-fulfllng currncy crss approach. Th problm wh scond-gnraon currncy crss modl s ha dos no ndognously drmn h apparanc and occurrnc of a crss. To solv ha problm, Morrs and Shn (998) nroduc h global gam no h slf-fulfllng currncy crss hory. Thy show ha hr s a unqu qulbrum undr nosy prva nformaon. Bcaus an agn only obsrvs a nosy sgnal concrnng h ru fundamnals undr a nosy sgnal gam, hs agn canno ascran wha ohrs sgnals ar and canno hav dvaluaon xpcaon (or hav non-dvaluaon xpcaon) followng ohrs. Thus, h agn wll hav dvaluaon xpcaon (or hav non-dvaluaon xpcaon) basd on hs/hr own sgnal. Thrfor, hs ruls ou any possbly of mulpl qulbra, so hr s a unqu qulbrum. Morrs and Shn (998) hn prsn ha an nformaon vn causs an agn o obsrv a nosy sgnal concrnng h ru sa of a mark s fundamnal. Afr an nformaon vn o occur, all agns wll xpc ha h govrnmn hav o gv up h fxd xchang ra f h ru fundamnal s locad whn a spcfc rang, so ha h nformaon vn prcpas a currncy crss vn f h fundamnal s unchangd. Hnc, a nws vn, whch s no nrprd n xacly h sam way by dffrn agns, mgh b a rggr for a currncy crss. Basd on h global gam modl of currncy crss, a ransparn polcy s a crucal ssu o rduc h lklhood of currncy crss. Th ffcs of ransparn polcy n h global gam modl of currncy crss hav bn analyzd by Hnmann and Illng (00) and Mz (003). Thy assum ha a mor ransparn govrnmnal polcy ncrass h prcson of prva sgnals and hn dcrass nos n prva nformaon. Undr a global gam, dvlopd by Carlsson and van Damm (993), som knd of nos nruds no a gam nvolvng sragc complmns. Du o h nos, nformaon s ncompl: som componn of h payoff s randomly drmnd and no playr can obsrv h ru sa of h payoff. As a rsul, a playr obsrvs a nosy sgnal concrnng h ru sa of h payoff srucur only and basd on hs/hr own sgnal maks h dcson. Furhrmor, Morrs and Shn (00), Vaugrard (004), Goldsn and Pauznr (005) and Anglos, Hllwg, and Pavan (006) nroduc h global gam no h prcng db, fnancal conagon, bank runs and coordnaon falur hors, rspcvly.

4 Hnmann and Illng (00) and Mz (003) show ha ncrasd ransparncy can rduc h lklhood of currncy crss. Howvr, Hnmann and Illng (00, pp ) ndca ha h modl s no suabl o answr h quson undr wha condons spculav aacks should ndd b prvnd. Basd on Krugman (979), h sngl objcv of h govrnmn s o prvn currncy aacks. Th br h fundamnals, h mor rsourcs ar avalabl o dfnd h currncy and h hghr h hurdl for a succssful aack. Boh an ncras n ransacons coss (such as a Tobn ax) and h mposon of capal conrols wll rduc h lklhood of aacks. Th modl can b sn as a rducd form whou spcfyng govrnmn objcvs xplcly. Prvnng aacks may no ncssarly b good for h conomy. Whn fundamnals ar bad nough, a surrndr of an unsusanabl pg could b wlfar mprovng. Obsfld (996) gav an xplc srucur modlng govrnmn objcvs. To analys wlfar mplcaons of ransparncy by nroducng lack of common knowldg n such a s up could b promsng xnson of h currn analyss. Obvously, hr ar hr qusons no o answr: On s wha h govrnmn s objcv s; anohr s how h ransparn polcy affcs h socal wlfar; and h ohr s whn a govrnmn should adop a ransparn polcy. In gnral macro modls, h govrnmn s objcv s o maxmz h socal wlfar or o mnmz oal govrnmn s cos rsrcon on h macro mark condon. Basd on Kydland and Prsco (977) and Barro and Gordon (983), h govrnmn s cos can b sn as h rducon on h socal wlfar. Morrs and Shn (998), Hnmann (000), Hnmann and Illng (00), and Mz (003) do no xplcly spcfy h govrnmn s objcv. Ths papr provds a macro foundaon and xplcly spcfs h govrnmn s objcv for h xnsv-form gam xamnd by Morrs and Shn (998). By hs way, hr s h sam govrnmn s bhav bwn h global gam modl of currncy crss and h gnral macro modls. Morovr, Hnmann and Illng (00) and Mz (003) show ha a ransparn polcy can rduc h probably of a currncy crss whou xplc goal of h ransparn polcy. In hs papr, w consdr ha h govrnmn s objcv s o mnmz s cos ha s quvaln o maxmz h socal wlfar. W hn us h spcfc govrnmn s objcv o oban h rang of h ru fundamnals ha a govrnmn should adop a ransparn polcy. W fnd ha a govrnmn wll prvn a currncy crss by adopng a ransparn polcy whn h cos of h ransparn polcy s small nough. Howvr, vn f hr s no cos assocad wh a ransparn polcy, a govrnmn wll adop 3

5 ransparn polcy whn h fundamnal s locad whn a spcfc rang. Compard o h xsng lraur on h global gam modl of currncy crss, hs papr has svral sgnfcan conrbuons. Frs, hs papr xplcly spcfs h govrnmn s objcv for h global gam modl of currncy crss. Scond, hs papr xamns h wlfar ffc of h ransparn polcy. Thrd, hs papr obans h rang of h ru fundamnals ha a govrnmn should adop a ransparn polcy. To b mor spcfc, hs papr answrs h qusons ndcad by Hnmann and Illng (00, pp ). Th rs of hs papr s organzd as follows. Scon consdrs h macroconomc qulbrum o s up h govrnmn s objcv n h currncy crss global gam modl and shows ha h prfc nformaon gam lads o mulpl qulbra,.., a slf-fulfllng qulbrum. In scon 3 w show ha h global gam modl lads o a unqu qulbrum and prsn ha nformaon vn mgh b a rggr for a currncy crss. Scon 4 uss h spcfc govrnmn objcv o oban h rang of h ru fundamnal ha h govrnmn should dcd a ransparn polcy o avod a currncy crss. Fnally, h concludng rmarks ar prsnd n scon 5.. Th modl Ths papr analyzs h currncy-crss ssu n a small opn conomy whr h govrnmn has pggd h xchang ra a. Naur chooss h sa of fundamnal accordng o a unform dsrbuon ovr h un nrval. Whn h ru fundamnal s, all nvsors obsrv h ru sa of h fundamnal and hn xpc h ra of dprcaon. 3 A a lar m, h govrnmn dcds bwn a floang xchang ra rgm and a fxd xchang ra rgm o mnmz s loss funcon afr obsrvng h ralzd. W consdr a Mundll-Flmng-yp opn-conomy macro modl dvlopd by Krugman (996). In such a modl, oupu s dmand-drmnd, so ha h domsc goods mark clarng condon s: y p* p ) ( ), () ( whr y s h log of oupu a m, s h sa of h fundamnal, p * s h 3 In hs scon w s up a basc modl n whch s common knowldg and prfcly nformd o vrybody. Howvr, n h nx scon w assum ha hr xss som knd of nos so ha h ru s unobsrvabl; an ndvdual agn only obsrvs a sgnal (o b llusrad n mor dal n Scon 3). 4

6 log of h forgn prc lvl, p s h log of h domsc prc lvl a m, s h log of h xchang ra a m, s h domsc nrs ra a m, and s h xpcd ra of nflaon a m. Th conomy s assumd o b opn o capal movmn, wh an qualzaon of xpcd rurns. Thus, h forgn xchang mark clarng condon s: *, () whr * s h forgn nrs ra and ( ) s h xpcd ra of dprcaon a m. Suppos ha h govrnmn has an oupu arg y, and h fundamnal xchang ra f s h log xchang ra ha would lav oupu qual o s arg lvl n h absnc of any xpcd dprcaon. In hs modl, f would b rad as a fundamnal and would b chosn by h govrnmn f facd no crdbly concrns. From quaon (), w hav: f y p * p ) ( * ). (3a) ( Snc Mundll-Flmng-yp opn-conomy macro modl consdrs scky prcs, w hav p p and 0. Thus, h fundamnal xchang ra s: f y * ( p* p) a b, y * ( p * p) a, b 0. (3b) Suppos ha a b. Gvn quaons (), (), and (3a), h dvaon of oupu from a dsrd lvl s: ( y y) { [ ( a b )] ( )}. (4) Assum ha h dvaon of oupu from h dsrd lvl of h govrnmn would ncras h govrnmn s cos, and ha h govrnmn has o ncur h rpuaon cos c f abandons h pg. Th govrnmn s loss funcon L can b wrn as: L ( y y) I c, f h govrnmn abandons h pg, I (5a) 0 f h govrnmn dfnds h pg. Th govrnmn s opmzng bhavor s o mnmz s loss funcon gvn h mark-clarng condons on h macro-conomy by choosng h xchang ra. As a 5

7 consqunc, h govrnmn s objcv can b xprssd as: Mn s.. ( y ( y y) I c, y) { [ ( a b )] ( )}, ; f h govrnmn abandons h pg, I (5b) 0; f h govrnmn dfnds h pg, Basd on quaon (5b), f h govrnmn abandons h pg, hn h frs-ordr condon for h xchang ra s: ( ){ [ ( a b )] ( )} 0, (6a) From quaon (6a), h opmal xchang ra: ( a b ) ~, (6b) L ~, L(, ) b h govrnmn s loss funcon whn h govrnmn abandons h pg, h fundamnal s, and h xpcd xchang ra s quaon (6b) no quaon (5b), w hav:. Subsung L ~,, c, (6c) ( ) If h govrnmn dfnds h pg, h xchang ra s. (7a) Whn all nvsors do no xpc dvaluaon of h domsc currncy, h xpcd xchang ra s, (7b) Whn all nvsors xpc dvaluaon of h domsc currncy, h xpcd xchang ra s ~ f ( a b ). (7c) L L,, ) b h govrnmn s loss funcon whn h govrnmn abandons ( h pg, h fundamnal s, and h xpcd xchang ra s quaons (7a), (7b), and (6c) no quaon (5b), w hav: L(,. Subsung, ) [( a b ) ], (7d) L(,, a b ) {( )[ ( a b )]}. (7) Basd on quaons (6c), (7d) and (7), w can dfn wo possbl qulbra - namly, floang xchang ra qulbrum and fxd xchang ra qulbrum. Frsly, w dal 6

8 wh h floang xchang ra qulbrum. Whn all nvsors xpc dvaluaon of h domsc currncy ( ( a b ) ), h govrnmn abandons h pg f h govrnmn s loss of dfndng h pg s hghr han abandonng h pg (.., L (,, a b ) L( a b,, a b ). Gvn L(,, a b ) {( )[ ( a b )]} and L( a b,, a b ) c, s qu asy o nfr ha h condon for h govrnmn o abandon h pg s {( )[ ( a b )]} c. Scondly, w dfn h fxd xchang ra qulbrum. Whn all nvsors do no xpc dvaluaon of h domsc currncy ( ), h govrnmn dfnds h pg f h govrnmn s loss of abandonng h pg xcds dfndng h pg (.., L(,, ) L( a b,, ) ). Gvn L(,, ) [( a b ) ] and L( a b,, ) c, s qu asy o nfr ha h condon for h govrnmn o dfnd h pg s [ ( a b )] c. Gvn h condons for h floang xchang ra qulbrum and h fxd xchang ra qulbrum, w fnd wo crcal valus of - namly, and - ha sasfy h followng xprssons. {( )[ ( a b )]} c, (8a) [ ( a b )] c. (8b) To b mor spcfc, s h valu whr h govrnmn s ndffrn bwn dfndng h pg and abandonng wh h dprcaon xpcaon by all nvsors, whl s h valu whr h govrnmn s ndffrn bwn dfndng h pg and abandonng wh h non-dprcaon xpcaon by all nvsors. Fgur dscrbs how wo crcal valus and ar drmnd. In ha fgur, h L(,, a b ) locus xprsss h govrnmn s loss of dfndng h pg as h dprcaon xpcaon, whl h L(,, ) locus dscrbs h govrnmn s loss of dfndng h pg as h non-dprcaon xpcaon. In addon, h ~, L(, ) ln xprsss h govrnmn s loss of abandonng h pg. Gvn ha L ~,, c, ( ) h ~, L(, ) ln s horzonal. Th L(,, a b ) locus nrscs h ~, L(, ) ln a pon Q, whr h assocad lvl of s. Th L(,, ) locus nrscs h ~, L(, ) ln a pon Q, whr h assocad lvl of s. Gvn hs wo crcal valus, w hav h followng concluson: 7

9 . By rfrrng o Fgur, n h nrval, L(,, a b ) L(,, ) ~, L(, ) s ru. Thrfor, L (,, a b ) L( ~,, a b ) holds, and hs mpls only h floang xchang ra qulbrum holds: all nvsors xpc dvaluaon of h domsc currncy ( ( a b ) ) and h govrnmn abandons h pg ( ( a b ) ).. In h nrval, L (,, a b ) ~, L(, ) L(,, ) s ru. Thrfor, L (,, a b ) L( ~,, a b ) and L( ~,, ) L(,, ) hold, and hs mpls boh h floang xchang ra qulbrum and h fxd xchang ra qulbrum hold: on s ha all nvsors xpc dvaluaon of h domsc currncy ( ( a b ) ) and h govrnmn abandons h pg ( ( a b ) ); h ohr s ha all nvsors do no xpc dvaluaon of h domsc currncy ( ) and h govrnmn dfnds h pg ( ). 3. In h nrval, L(,, a b ) L(,, ) ~, L(, ) s ru. Thrfor, L(,, ) L( ~,, ) holds, and hs mpls only h fxd xchang ra qulbrum holds: all nvsors do no xpc dvaluaon of h domsc currncy ( ) and h govrnmn dfnds h pg ( ). c Q Q L( ~,, ) c L(,, a b ) {( )[( a b ) ]} L(,, ) { [( a b ) ]} Fgur : Th govrnmn s loss n common knowldg cas. 8

10 Spcfcally, h qulbrum s gvn by: ( a b ) f, ( a b ) or f, (9a) f. ( a b ) f, ( a b ) or f, (9b) f. Ths modl parons h spac of h fundamnal no hr nrvals. Frsly, whn h sa of h fundamnal s bad,.., qulbrum., h floang xchang ra s h unqu In hs suaon, all nvsors xpc dvaluaon of h domsc currncy and h govrnmn has o abandon h pg. fundamnal s nrmda,.., Scondly, whn h sa of h, hr ar mulpl qulbra: on s h floang xchang ra and h ohr s h fxd xchang ra. In hs suaon, h currncy crss may b rggrd whou any chang n h conomc fundamnal. ohr words, as h conomc sysm sars wh h fxd xchang ra, nohng happns o h fundamnal, bu all nvsors blv ha h qulbrum has changd and hy wll chang hr xpcaon from non-dvaluaon o dvaluaon som day, and hn h currncy pg falls. Ths rsul could xplan why currncy crss ar ralzd n assocaon wh no obvous chang n mark fundamnal. Thrdly, whn h sa of h fundamnal s good,..,, h fxd xchang ra s h unqu qulbrum. In hs suaon, all nvsors do no xpc dvaluaon of h domsc currncy and h govrnmn s abl o dfnd h pg. In 3. Global gam Snc hr s an nrmda rang of h fundamnal (.., ), for whch h fxd xchang ra and h floang xchang ra ar qulbra undr h prfc nformaon cas, h oubrak of currncy crss appars o b complly arbrary. W hn buld upon h slf-fulfllng currncy crss hory basd on h global gam dvlopd by Carlsson and van Damm (993) and show ha h ndrmnacy of qulbra can b complly rmovd. For hs purpos, wo furhr assumpons ar ndd. Frs, n a way ha dffrs from h prvous scon, hr w assum ha all 9

11 nvsors ar mprfcly nformd of h ru du o h prsnc of nos. Basd on h lack of common knowldg, ach nvsor only obsrvs a sgnal rahr han a ru valu. Scondly, hr s a connuum of nvsors ndxd by and dsrbud unformly on [ 0,]. Invsor rcvs a prva sgnal x n rlaon o h ru fundamnal. In hs global gam h ru s chosn by naur and, for smplcy, has a unform dsrbuon wh suppor on [ 0,]. Undr such an assumpon, nvsor obsrvs a sgnal s a small consan. x, whch s drawn unformly from h nrval,, whr Basd on h prva sgnal, an nvsor xpcs h ra of dprcaon. Morovr, nvsor obsrvs a prva sgnal x, whch s drawn unformly from h nrval,, so ha h condonal dsrbuon of gvn x has unform dsrbuon: f x, ( ) x h x (0a) 0 f x or x, whr, h( x ) s h condonal dnsy of gvn x. Dfn h crcal valu * such ha h govrnmn abandons h pg ( ~ ) f *, and h govrnmn dfnds h pg ( ) f *. Gvn ha nvsor obsrvs a rlavly bad sgnal x * (.., x *), as shown n Fgur a. In such a cas, all of h possbl conomc sa s locad whn h rang of h floang xchang ra. Hnc, f x *, nvsor has a full dvaluaon xpcaon and xpcs h xchang ra o b: x ~ ( a bx ) E[ x ] E[ x * ] d a bx. (0b) x x x x * ~ Fgur a: Th xpcd xchang ra undr rlavly bad sgnal. 0

12 x x * x ~ Fgur b: Th xpcd xchang ra undr mdum sgnal. ~ * x x x Fgur c: Th xpcd xchang ra undr rlavly good sgnal. Fgur b shows ha nvsor obsrvs a mdum sgnal x * (.., * x * x ), h ru conomc sa may b locad whn h rang of h floang xchang ra (.., [ x, *] ) or h rang of h fxd xchang ra (.., [ *, x ] ). As a rsul, f x *, nvsor has a paral dvaluaon * xpcaon and xpcs h xchang ra o b: * ~ x E[ * x * ] d d f ( x, *, ). (0c) x By rfrrng o Fgur c, s asy o fnd ha nvsor obsrvs a rlavly good * sgnal * x (.., * x ), all of h possbl s locad whn h rang of h fxd xchang ra. As a rsul, f xpcaon and xpcs h xchang ra o b: x * x, nvsor has a non-dvaluaon E[ * x ] d. (0d) x Basd on quaons (0a) - (0d), for any gvn sgnal xchang ra o b: x, nvsor xpcs h a bx f x * E[ x ] f ( x, *, ) f * x * (0) f * x

13 x * * * * * a bx f (, *, ) x Fgur 3a: Th rang of h sgnal undr far bad fundamnal. If h ru fundamnal s far bad * (.., * ), hn x *, as shown n Fgur 3a. In such a cas, (0b) ndcas ha all nvsors xpc ha h govrnmn wll abandon h pg, and as a rsul, E[ x a bx. ] Thrfor, f *, h aggrga xpcaon on xchang ra s: E[ x ] dx a b. (a) x * * * * * a bx f (, *, ) x Fgur 3b: Th rang of h sgnal undr rlavly bad fundamnal. Fgur 3b shows ha f h ru fundamnal s rlavly bad * * (.., * * ), h sgnals may b locad whn h rang of h full dvaluaon xpcaon (.., [, * ]) or h rang of h paral dvaluaon xpcaon (.., [ *, ] ). Thrfor, f * *, h aggrga xpcaon on xchang ra s: E[ x ] *, ) dx. (b) * a bx f ( x, d dx *

14 x * * * * * a bx f (, *, ) x Fgur 3c: Th rang of h sgnal undr rlavly good fundamnal. Fgur 3c shows ha f h ru fundamnal s rlavly good * * (.., * * ), h sgnals may b locad whn h rang of h paral dvaluaon xpcaon (.., [, * ] ) or h rang of h non-dvaluaon xpcaon (.., [ *, ] ). Thrfor, f * *, h aggrga xpcaon on xchang ra s: E[ x ] dx. (c) * f ( x, *, ) d dx * x * * * * f ( x, *, ) a bx * Fgur 3d: Th rang of h sgnal undr far good fundamnal. If h ru fundamnal s far good * (.., * ), hn x *, as shown n Fgur 3d. In such a cas, (0d) ndcas ha all nvsors xpc ha h govrnmn can dfnd h pg, and as a rsul, E[ x. ] Thrfor, f *, h aggrga xpcaon on xchang ra s: E[ x ] dx. (d) Basd on quaons (a) - (d), for any gvn ru fundamnal, h aggrga xpcaon on xchang ra s: 3

15 * (, *, ) ( a b ) ( a bx ) f ( x, *, ) dx dx * * f ( x, *, ) dx dx * f f f f * * * * * * () Equaon () ndcas h posror blf of h xchang ra, and w hn hav h followng govrnmn s loss funcons: L( ~,, (, *, )) c, (a) L(,, (, *, )) ))} { [ ( a b )] ( (, *,. (b) Accordng o (), (a) and (b), hr s a unqu *, whch s h qulbrum, such ha h govrnmn abandons h currncy pg f and only f *. * s characrzd by h quaon: ~, L ( *, ( *, *, )) L(, *, ( *, *, )). (3a) Bcaus an nvsor obsrvs a nosy sgnal concrnng h ru fundamnal only undr a nosy sgnal gam, h canno ascran wha ohr nvsors sgnals ar and hs nvsor canno choos h xpcd ra of dprcaon only bcaus ohrs do so, and h nvsor wll xpc ra of dprcaon basd on hs own sgnal. Bascally, hs ruls ou any possbly of mulpl qulbra and hr wll b a unqu qulbrum. Morrs and Shn (000) prov hs unqu qulbrum s rad lmnaon of domnad srags. In h slf-fulfllng currncy crss modl wh a global gam, hr s unqu qulbrum. Spcfcally, h qulbrum s gvn by: ~ f *, (3b) f *. Gvn quaon (3b), w hav h followng concluson:. In h nrval for *, all nvsors hav full dvalua xpcaon (.., ( a b ) ), and w hn hav: L(,, a b ) {( )[ ( a b )]}, ( ~,, a b ) c, and L(,, a b ) ( ~,, a b ), as shown n Fgur 4. L L As such, h govrnmn wll abandon h pg, ( a b ). 4

16 L(,, ) L(,, ) c L(,, ) L(,, a b) * * * Fgur 4: Th govrnmn s loss n h global gam.. In h nrval for * *, () ndcas ha h aggrga xpcaon on xchang ra s paral dvalua. L(,, (, )) ))} Undr such an nrval, ~, ar { [ ( a b )] ( (, and L(, (, )) c ru. On h on hand, n h nrval for * *, w hav L (,, (, )) L( ~,, (, )), as shown n Fgur 4. Th govrnmn wll abandon h pg, w hav ~. On h ohr hand, n h nrval for * *, L (,, (, )) L( ~,, (, )), as shown n Fgur 4. Th govrnmn wll dfnd h pg,. 3. In h nrval for *, all nvsors hav non-dvalua xpcaon (.., ), and w hav { [ ( a b )]}, L, ) c L(,, ) ( ~,, and L(,, ) L( ~,, ), as shown n Fgur 4. Th govrnmn wll dfnd h pg,. Fgur 5 conrbus an mporan mplcaon o h hory of currncy crss: an nformaon vn can prcpa a currncy crss. fundamnal s locad whn h spcfc rang, In h bgnnng, suppos ha h *, and all nvsors can obsrv h ralzd fundamnal so ha hr s common knowldg. Ths modl lads o mulpl qulbra: on s h fxd xchang ra and h ohr s h floang 0 5

17 xchang ra. Assum ha h qulbrum says a h fxd xchang ra. An nformaon vn hn causs an nvsor o obsrv a nosy sgnal concrnng h ru fundamnal. Ths modl lads o a unqu qulbrum undr a global gam. Snc 0 *, h govrnmn wll abandon h pg,.., ~. Hnc, a nws vn, whch s no nrprd n xacly h sam way by dffrn nvsors, mgh b rggr a currncy crss. common knowldg ( a b) ( a b) 0 * nosy sgnal ~ Fgur 5: An nformaon vn can prcpa a currncy crss. 4. Transparn polcy W now us h spcfc govrnmn objcv o oban h rang of h ru fundamnal for h ransparn polcy dcdd by h govrnmn. 6 Whn h ru fundamnal s, h govrnmn obsrvs and chooss ransparncy or non-ransparncy. obsrvs a sgnal Thr s a cos d assocad wh ransparncy, and nvsor x, whch s drawn unformly from h nrval, 0 0, whn h govrnmn chooss ransparncy. nvsor hn obsrvs a sgnal If h govrnmn chooss non-ransparncy, x, whch s drawn unformly from h nrval,, 0. An nvsor xpcs h ra of dprcaon. afr obsrvng h sgnal. If h govrnmn can choos ransparncy or non-ransparncy, hn h govrnmn s objcv can b xprssd as: Mn I H(,θ, I ) L(,θ, (, ( I ))) I d, d d d

18 I d 0 f f h govrnmn chooss ransparncy, h govrnmn chooss non ransparncy. 0 f I, ( Id ) (4) f I 0. Whr, H,, I ) s h govrnmn s loss funcon whn h govrnmn can choos ( d ransparncy or non-ransparncy. W nx us h spcfc govrnmn objcv, whch s o mnmz h govrnmn s loss funcon H,, I ), so as o oban h rang of h ru fundamnal ( d for h ransparn polcy dcdd by h govrnmn. L k * b characrzd by h quaon: ~, L( k*, ( k*, k )) L(, k*, ( k*, k )), k {0, }. Whn h govrnmn chooss ransparncy, 0, h govrnmn abandons h pg f and only f 0 *. Whn h govrnmn chooss non-ransparncy,, h govrnmn abandons h pg f and only f *. Accordng o (4), w can now oban h govrnmn s loss funcon. Frsly, h govrnmn chooss non-ransparncy,.., I d 0 and. Whn h govrnmn abandons h pg, quaons (a) and (4) ll us ha H,θ,0) L(,θ, (, )) c. ( Whn h govrnmn dfnds h pg and h aggrga xpcaon xchang ra s gvn by quaon (), w hav h followng govrnmn s loss funcon: H(,θ,0) L(,θ, { [ (, )) ( ) [ ( a b )], ( a b )] ( [ ( a b )], )}, f f f * ; * * ; *. (5a) Scondly, h govrnmn chooss ransparncy,.., I d and 0. Whn h govrnmn abandons h pg, quaons (b) and (4) ll us ha H,θ,) L(,θ, (, )) d c d. Whn h govrnmn dfnds h pg and ( 0 h aggrga xpcaon xchang ra s gvn by quaon (), w hav h followng govrnmn s loss funcon: H(,θ,) L(,θ, { [ (, )) d ( ) [ ( a b )] ( a b )] ( [ ( a b )] d, d, )} d, f f f * ; * * ; *. (5b) 7

19 H(,,) c H(,,0) H( ~,,0) H( ~,,) ˆ * * * 0 * Fgur 6: Th govrnmn s loss whou ransparncy cos. W hn consdr h spcal cas whou ransparncy cos (.., d 0 ), whch s llusrad n Fgur 6. As shown n Fgur 6, H( ~,θ,) H( ~,,0) c,. Basd on quaons (5a) and (5b), H(,θ,) H(,,0) holds f * or *. Suppos ha ˆ, ) ( ˆ, ) a ˆ. Fgur 6 shows ha ( 0 b H (,θ,) H (,,0) f ˆ * ; H (,θ,) H (,,0) f ˆ *. Sx nrsng fndngs ar obsrvd from h Fgur 6:. Whn *, Fgur 6 lls us ha H(,θ,) H(,,0) ( ~,θ,) H H ( ~,,0). Snc h govrnmn s loss undr ransparncy s qual o non-ransparncy n hs nrval, h govrnmn wll choos non-ransparncy.. Whn ˆ, Fgur 6 lls us ha H(,θ,) * H(,,0) ( ~,θ,) H H ( ~,,0). Th ransparn polcy ls h nvsors ascran ha h ru fundamnal s rlavly bad, and h xpcd xchang ra of h nvsors undr ransparncy s hghr han non-ransparncy. As a rsul, ncrasd ransparncy 8

20 rass h govrnmn s loss n h rlav bad sa and h govrnmn wll choos non-ransparncy. 3. Whn ˆ *, Fgur 6 lls us ha H(,,0) 0 H(,θ,) ( ~,θ,) H H ( ~,,0). Th ransparn polcy ls h nvsors ascran ha h ru fundamnal s rlavly good, and h xpcd xchang ra of h nvsors undr ransparncy s lowr han non-ransparncy. Howvr, h govrnmn s loss of h floang xchang ra s lowr han ha of h fxd xchang ra. No mar h govrnmn chooss ransparncy or non-ransparncy, h govrnmn wll abandon h pg and s loss wll b qual o c. As a rsul, h govrnmn wll choos non-ransparncy. 4. Whn *, Fgur 6 lls us ha H(,,0) 0* H( ~,θ,) H ( ~,,0) H(,θ,). Th ransparn polcy ls h nvsors ascran ha h ru fundamnal s rlavly good, and h xpcd xchang ra of h nvsors undr ransparncy s lowr han non-ransparncy. If h govrnmn chooss ransparncy, h govrnmn s loss of h fxd xchang ra s lowr han ha of h floang xchang ra; f h govrnmn chooss non-ransparncy, h govrnmn s loss of h floang xchang ra s lowr han ha of h fxd xchang ra. In such suaon, h ransparn polcy no only prvns h currncy crss bu also rducs h govrnmn s loss. As a rsul, h govrnmn wll choos ransparncy. 5. Whn * *, Fgur 6 lls us ha H( ~,θ,) H( ~,,0) H (,,0) H (,θ,). No mar h govrnmn chooss ransparncy or non-ransparncy, h govrnmn s loss of h fxd xchang ra s lowr han ha of h floang xchang ra. Th ransparn polcy ls h nvsors ascran ha h ru 9

21 fundamnal s rlavly good, and h xpcd xchang ra of h nvsors undr ransparncy s lowr han non-ransparncy. As a rsul, h govrnmn wll choos ransparncy. 6. Whn *, Fgur 6 lls us ha H( ~,θ,) H( ~,,0) H (,,0) H (,θ,). Th ransparn polcy ls h nvsors ascran ha h ru fundamnal s rlavly good, and h xpcd xchang ra of h nvsors undr ransparncy s lowr han non-ransparncy. No mar h govrnmn chooss ransparncy or non-ransparncy, h govrnmn wll dfnd h pg and s loss wll b qual o [ ( a b )]. As a rsul, h govrnmn wll choos non-ransparncy. c d c H( ~,,) H( ~,,0) ~ * * 0 ~ 0 H(,,) H(,,0) Fgur 7: Th govrnmn s loss wh rlavly small ransparncy cos. W hn consdr h spcal cas wh rlavly small ransparncy cos (.., d 0 ), whch s llusrad n Fgur 7. As shown n Fgur 7, H( ~,θ,) c d H( ~,,0) c,. Basd on quaons (5a) and (5b), undr mdum fundamnal, 0

22 H (,θ,) H (,,0) holds; ohrws, H (,θ,) H (,,0). Suppos ha ~ ~ ~ ~ { [ ( a b )] ( (, 0))} d { [ ( a b )] ( (, ))} and ~ ~ { [ ( a b0 )] ( ( 0, 0))} d c. Fv nrsng fndngs ar obsrvd from h Fgur 7:. Whn 0 *, Fgur 7 lls us ha H (,θ,) H( ~,θ,), H (,,0) H ( ~,,0) and H( ~,θ,) H ( ~,,0). No mar h govrnmn chooss ransparncy or non-ransparncy, h govrnmn wll abandon h pg, and h ransparn polcy rass h govrnmn s loss. As a rsul, h govrnmn wll choos non-ransparncy. ~. Whn 0* 0, Fgur 7 lls us ha H (,θ,) H( ~,θ,), H (,,0) H ( ~,,0) and H (,θ,) H ( ~,,0). If h govrnmn chooss ransparncy, h govrnmn s loss of h fxd xchang ra s lowr han ha of h floang xchang ra; f h govrnmn chooss non-ransparncy, h govrnmn s loss of h floang xchang ra s lowr han ha of h fxd xchang ra. In such suaon, h ransparncy polcy can prvn h currncy crss bu rass h govrnmn s loss. As a rsul, h govrnmn wll choos non-ransparncy. ~ 3. Whn *, Fgur 7 lls us ha H (,θ,) H( ~,θ,), H (,,0) 0 H ( ~,,0) and H (,θ,) H ( ~,,0). Th ransparn polcy ls h nvsors ascran ha h ru fundamnal s rlavly good, and h xpcd xchang ra of h nvsors undr ransparncy s lowr han non-ransparncy. If h govrnmn chooss ransparncy, h govrnmn s loss of h fxd xchang ra s lowr han ha of h floang xchang ra; f h govrnmn chooss non-ransparncy, h govrnmn s loss of h floang xchang ra s lowr han ha of h fxd xchang ra. In such suaon, h ransparn polcy no only prvns h currncy crss bu also rducs h govrnmn s loss. As a rsul, h

23 govrnmn wll choos ransparncy. ~ 4. Whn *, Fgur 7 lls us ha H (,θ,) H( ~,θ,), H (,,0) H ( ~,,0) and H (,θ,) H ( ~,,0). Th ransparn polcy ls h nvsors ascran ha h ru fundamnal s rlavly good, and h xpcd xchang ra of h nvsors undr ransparncy s lowr han non-ransparncy. As a rsul, h govrnmn wll choos ransparncy. ~ 5. Whn, Fgur 7 lls us ha H (,θ,) H( ~,θ,), H (,,0) H ( ~,,0) and H (,θ,) H (,,0). Th ransparn polcy ls h nvsors ascran ha h ru fundamnal s rlavly good, and h xpcd xchang ra of h nvsors undr ransparncy s lowr han non-ransparncy. No mar h govrnmn chooss ransparncy or non-ransparncy, h govrnmn wll dfnd h pg. As a rsul, h govrnmn wll choos non-ransparncy. c d H( ~,,) c H( ~,,0) H(,,) 0 * * H(,,0) Fgur 8: Th govrnmn s loss wh rlavly larg ransparncy cos.

24 W hn consdr h spcal cas wh rlavly larg ransparncy cos (.., d 0 ), whch s llusrad n Fgur 8. As shown n Fgur 8, H( ~,θ,) c d H( ~,,0) c,. Basd on quaons (5a) and (5b), H(,θ,) H(,,0), f h ransparncy cos s larg nough. Thr nrsng fndngs ar obsrvd from h Fgur 8:. Whn 0 *, Fgur 8 lls us ha H (,θ,) H( ~,θ,), H (,,0) H ( ~,,0) and H( ~,θ,) H ( ~,,0). No mar h govrnmn chooss ransparncy or non-ransparncy, h govrnmn wll abandon h pg, and h ransparn polcy rass h govrnmn s loss. As a rsul, h govrnmn wll choos non-ransparncy.. Whn *, Fgur 8 lls us ha H (,θ,) H( ~,θ,), H (,,0) 0* H ( ~,,0) and H (,θ,) H ( ~,,0). If h govrnmn chooss ransparncy, h govrnmn s loss of h fxd xchang ra s lowr han ha of h floang xchang ra; f h govrnmn chooss non-ransparncy, h govrnmn s loss of h floang xchang ra s lowr han ha of h fxd xchang ra. In such suaon, h ransparn polcy can prvn h currncy crss bu rass h govrnmn s loss. As a rsul, h govrnmn wll choos non-ransparncy. 3. Whn *, Fgur 8 lls us ha H (,θ,) H( ~,θ,), H (,,0) H ( ~,,0) and H (,θ,) H (,,0). No mar h govrnmn chooss ransparncy or non-ransparncy, h govrnmn wll dfnd h pg. As a rsul, h govrnmn wll choos non-ransparncy. In hs scon, w hav usd h spcfc govrnmn s objcv o oban h rang of h ru fundamnal ha h govrnmn should dcd h ransparn polcy o avod a currncy crss. W hav shown ha, vn f hr s no cos assocad wh ransparncy, h govrnmn wll choos ransparncy only whn h fundamnal s locad whn a spcfc rang. I s also found ha h govrnmn may prvn h crss by choosng ransparncy whn h ransparncy cos s small nough only. Somms, h ransparncy polcy can prvn h currncy crss bu rass h govrnmn s loss, and h govrnmn wll no choos ransparncy. 5. Concluson Carlsson and van Damm (993) nroduc prva sgnal no a gam nvolvng 3

25 sragc complmns and rfr hs prva nformaon modl as a global gam. Morrs and Shn (998) us a global gam sng o drv a unqu qulbrum from a currncy crss modl wh slf-fulfllng blfs bu do no xplcly spcfy h govrnmn s objcv. Ths papr provds a macro foundaon and xplcly spcfs h govrnmn s objcv for h xnsv-form gam xamnd by Morrs and Shn (998). Basd on our approach, w show ha wh common knowldg hr ar mulpl qulbra: on s h floang xchang ra and h ohr s h fxd xchang ra. In hs crcumsanc, a currncy crss may b rggrd whou any chang n h conomc fundamnal. To b mor spcfc, as h conomc sysm sars wh a fxd xchang ra, nohng happns o h fundamnal, bu all agns blv h qulbrum has changd and hy wll hav dvaluaon xpcaon som day, and hn h currncy pg fals. Ths rsul could xplan why currncy crss s ralzd n assocaon wh no obvous chang n mark fundamnal. Addonally, w assum an agn obsrvs a nosy sgnal concrnng h ru fundamnal only. An agn could no ascran wha ohrs sgnals ar, and so hs agn could no chang hs xpcaon only bcaus ohrs do so, and h agn would chang hs xpcaon basd on hs own sgnal. As a rsul, hr s only unqu qulbrum undr h currncy crss modl wh prva sgnal. Basd on h global gam, w also show an nformaon vn could prcpa a currncy crss. In h bgnnng, suppos ha all agns can obsrv h ralzd fundamnal, so ha h knowldg s common. Ths modl lads o mulpl qulbra: on s h floang xchang ra and h ohr s h fxd xchang ra. Assum ha h qulbrum says a h fxd xchang ra. An nformaon vn hn causs agn o obsrv a nosy sgnal concrnng h ru fundamnal. Undr h nosy sgnal gam, hs modl lads o a unqu qulbrum. If h fundamnal s locad whn a spcfc rang, all agns hav dvaluaon xpcaon and hn h govrnmn abandons h pg. Hnc, a nws vn ha s no nrprd n xacly h sam way by dffrn agns may rggr a currncy crss. Hnmann and Illng (00) and Mz (003) show ha ncrasd ransparncy can rduc h lklhood of currncy crss n h global gams. Howvr, Hnmann and Illng (00, p. 448) ndca ha [p]rvnng aacks may no ncssarly b good for h conomy. Whn fundamnals ar bad nough, a surrndr of an unsusanabl pg could b wlfar mprovng. Ths papr consdrs h govrnmn s objcv s o mnmz s cos and uss hs spcfc govrnmn s objcv o oban h rang of h 4

26 ru fundamnals ha h govrnmn should adop h ransparn polcy o avod a currncy crss. W show ha, vn f hr s no cos assocad wh ransparncy, h govrnmn adops h ransparn polcy whn h fundamnal s locad whn a spcfc rang. I s also found ha h govrnmn may prvn a currncy crss by adopng h ransparn polcy whn h cos of h ransparn polcy s small nough. Somms, h ransparn polcy could prvn a currncy crss bu would ras h govrnmn s loss, and hn h govrnmn would no adop h ransparn polcy. Rfrncs Anglos, G.-M., Hllwg, C. and Pavan, A., (006), Sgnalng n a Global Gam: Coordnaon and Polcy Traps, Journal of Polcal conomy 4, Azarads, C. (98), Slf-Fulfllng Prophcs, Journal of Economc Thory 5, Barro, R. and Gordon, D. (983), A Posv Thory of Monary Polcy n a Naural-Ra Modl, Journal of Polcal Economy 9, Boonprakakaw, J. and Ghosal, S. (000), Bank Runs and Nosy Sgnals, Unvrsy of Warwck. Bur, W. H. (987), Borrowng o Dfnd h Exchang Ra and h Tmng of and Magnud of Spculav Aacks, Journal of Inrnaonal Economcs 3, -39. Carlsson, H. and van Damm, E. (993), Global Gams and Equlbrum Slcon, Economrca 6, Cukrmann, A. and Lpp, F. (005), Endognous Monary Polcy wh Unobsrvd Ponal Oupu, Journal of Economc Dynamcs and Conrol 9, Easly, D. and O Hara, M. (99), Tm and h Procss of Scury Prc Adjusmn, Journal of Fnanc 47, Flood, R. P. and Garbr, P. M. (984), Collapsng Exchang-Ra Rgms: Som Lnar Exampls, Journal of Inrnaonal Economcs 7, -3. 5

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28 Currncy Aacks, Amrcan Economc Rvw 88, Morrs, S. and Shn, H. S. (000), Rhnkng Mulpl Equlbra n Macroconomc Modlng, NBER Macroconomcs Annual 5, Morrs, S. and Shn, H. S. (00), Coordnaon Rsk and h Prc of Db, Cowls Foundaon Dscusson Papr No. 4R. Obsfld, M. (984), Balanc-of-Paymns Crss and Dvaluaon, Journal of Mony, Crd, and Bankng 6, Obsfld, M. (994), Th Logc of Currncy Crss, Cahrs Economqus Monars 43, Obsfld, M. (996), Modls of Currncy Crss wh Slf-Fulfllng Faurs, Europan Economc Rvw 40, Salan, S. and Hndrson, D. (978), Mark ancpaon of govrnmn polcy an h prc of gold, Journal of Polcal Economy 86, Topks, D. M. (979), Equlbrum Pons n Nonzro-Sum n-prson Sub modular Gams, SIAM Journal on Conrol and Opmzaon 7, Vaugrard, V. E. (004), Informaonal Conagon of Suddn Sops n a Global Gams Framwork, Opn Economs Rvw 5,