Estudios de Economía Aplicada ISSN: Asociación Internacional de Economía Aplicada.

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1 Esudios d Economía Aplicada ISSN: scraria.cnica@rvisa-a.n Asociación Inrnacional d Economía Aplicada España Bby, M.; Halls, S.; Hnry S., G.B.; Marc, A. Expcaions Formaion and h 1990s ERM Crisis Esudios d Economía Aplicada, vol., núm., agoso, 004, pp Asociación Inrnacional d Economía Aplicada Valladolid, España Availabl in: hp:// How o ci Compl issu Mor informaion abou his aricl Journal's hompag in rdalyc.org Scinific Informaion Sysm Nwork of Scinific Journals from Lain Amrica, h Caribban, Spain and Porugal Non-profi acadmic projc, dvlopd undr h opn accss iniiaiv

2 E STUDIOS DE ECONOMÍA APLICADA V OL. -, P ÁGS Expcaions Formaion and h 1990s ERM Crisis BEEBY M, HALL S. (*), HENRY S. G.B. and MARCET, A. * Imprial Collg, London and NIESR. Souh Knsingon Campus, London SW7 AZ. Tlf.: (44)(0) s.g.hall@imprial.ac.uk ABSTRACT Th ERM crisis of 199 appars o b du o a sris of ngaiv oupu shocks followd by dvaluaion. This sylisd fac dos no sm o conform o h "scond-gnraion" crisis modl basd on h REH. W show ha by adoping boundd raional larning, h modl yilds a rad- off bwn h siz and prsisnc of shocks lading o dvaluaion, a finding which, maks h modl mor clarly applicabl o hs crisis pisods. Kywords: currncy criss, larning, xpcaions. Formación d xpcaivas y crisis dl S.M.E n la década d los novna RESUMEN La crisis dl Sisma Monario Europo aparnmn fu dbida a una sri d «shocks» d ofra ngaivos sguidos d dvaluacions. Es hcho silizado no parc congrun con los modlos d crisis d «sgunda gnración» basados n la hipósis d xpcaivas racionals (Racional Expcaions Hypohsis, REH). En s arículo, mosramos qu adopando un modlo d aprndizaj racional limiado, s obin un compromiso nr l amaño y la prsisncia d los «shocks» qu conducn a la dvaluación, un rsulado qu hac qu l modlo sa más claramn aplicabl a sos pisodios d crisis. Palabras Clav: crisis monaria, aprndizaj, xpcaivas. Clasificación JEL: D450, D80, G150. Arículo rcibido n abril d 004 y aprobado n junio d 004. Arículo disponibl n vrsión lcrónica n la página rf.: -07. ISSN (onlin) ISSN (prin)

3 16 Bby M, Hall S., Hnry S. G.B. and Marc, A. 1. INTRODUCTION Th consnsus viw abou h causs of h ERM criss in 199 and 1993 is ha hs can b xplaind by h so-calld scond gnraion modl of currncy criss. (Eichngrn and Wyploz (1993), and (1995)). Indd, hs modls wr dvlopd wih h xprss purpos of accouning for h ERM criss, which h firs-gnraion modls wr hough o b incapabl of doing. According o h scond-gnraion modl, currncy cris ar no drivn by fundamnal facors such as h dplion of a naion's currncy rsrvs, as mphasisd in firs gnraion modls, bu ar ssnially slf-fulfilling, xpcaions drivn, procsss. Scond- gnraion, lik firs-gnraion modls, plac havy mphasis on h Raional Expcaions Hypohsis (REH), bu h characrisic of h scond-gnraion modl is ha i inroducs xplici govrnmn incnivs concrning h coss and bnfis of mainaining a currncy pg, and of h alrnaiv - ha of a ralignmn. Th analysis i advancs is ssnially an xnsion of h Barro-Gordon closd-conomy modl of monary policy sing o h opn conomy, wih wo rgims; pgging and floaing. Taking h spcial cas of a dvaluaion only, which is sricly h only cas w ar concrnd wih hr, h RE soluion for currncy changs (qual o inflaion in hs simpl modls), is a wighd avrag of xchang ra bhaviour in h wo rgims, h wighs bing h probabiliy ha oupu shocks xcd or fall shor of a criical hrshold valu. This quaion is quadraic in h oupu shock; so wo quilibria ar possibl, dpnding on h siz of h shock. (Obsfld (1994)). Wih his faur of mulipl quilibria, currncy criss in such modls ar sn ssnially as bing producd by h xognous oupu shock which shif h conomy from on quilibrium or rgim, o anohr. In h high xpcd dprciaion cas, hr is a compiivnss and unmploymn problm so h rgim may only coninu if h oupu shock is small. (Th canonical vrsion of h scond-gnraion modl is du o Obsfld, s Obsfld (1994) (1996) and Obsfld and Rogoff (1996)). Thr ar basic faurs of h criss which do no fi his scond gnraion modl howvr. W will argu ha h siuaion in h arly 1990s was on whr counris wr xprincing a rcssion ha had gon on for som im wih andan high unmploymn, and compiivnss problms, boh of which wr long lasing. Th UK provids a paricularly clar xampl. Economic condiions in h UK had driorad subsanially for som im bfor h Spmbr 199 crisis. Thus, growh had slowd sharply in 1990 falling from.1 o 0.6 prcn (Q1 on Q1 annualisd ras for GDP. Sourc; LBS/OEF Economic Oulook (000)). In 1991 GDP growh was subsanially ngaiv (-1.5) and only jus abou achivd a posiiv ra in 199 (0.1). Unmploymn ros sharply alhough lagging bhind hs changs in oupu, and by 1993 had risn abov 10 prcn boh on h claiman coun and on h inrnaional (ILO) masur, as compard wih a ra of jus ovr 6 prcn (claiman coun) and 7.3 prcn (on h ILO dfiniion) in Again, a similar judgmn Esudios d Economía Aplicada, 004: Vol. -

4 EXPECTATIONS FORMATION AND THE 1990S ERM CRISIS 163 may b mad abou h ohr ky ral indicaor- compiivnss- which many argud was sriously affcd by a oo high nry ra in 1989 (Wrn-Lwis a ( ) calculad ha h ra was som 0% abov is opimal valu ). This worsnd furhr as UK inflaion incrasd sharply in 1990 whn i rachd almos 10 prcn compard wih jus undr 5 prcn in 1988, alhough i nds o b nod inflaion fll sharply hrafr. Wha hs vns undrscor is ha h drioraion in h aggrga UK conomy was no jus h rsul of a on-off shock, bu a progrssiv worsning which prsisd ovr 3-4 yars. Th conomis of ERM counris coming undr aack a his im xprincd similar long lasing drioraion. Swdn's unmploymn ra for xampl, was ovr 5 prcn in 1993, having avragd undr half ha ra ovr h priod And h drioraion in is govrnmn financs wr qually profound, moving from an avrag surplus of.5 prcn in , o a dfici of ovr 7 prcn in 199 (Obsfld (1994). Ths faurs do no sm o fi h prdicions of h scond-gnraion modl, whr a singl larg oupu shock shifs h xchang ra from on rgim (fixd) o h ohr (floaing). Insad, modls ar ndd which imply boh prsisn oupu falls and ral xchang ra drioraion. According o scond-gnraion modls oupu shocks which prcipia currncy criss hav i.i.d characrisics; bing a singl larg shock which brings h govrnmn's willingnss o adhr o h currncy pg ino qusion. As w hav argud, h oupu shocks affcing all h counris undr hra in h ERM wr in fac highly prsisn. Morovr, whr h moiv for abandoning h currncy pg is on of worsning compiivnss, hn h scond-gnraion modl suggss his worsning is also likly o occur ovr a shor im. Again, h vidnc shows ha compiivnss worris wr long lasing in h 1990s. W argu ha i is possibl o xplain hs criss wihou rcours o h REH, using an alrnaiv o raional xpcaions, ha of bounddly raional larning. Mor significanly w suggs ha is implicaions fi h sylisd daa jus rviwd, whras h implicaions from h mulipl- quilibrium/ REH modls of h scond-gnraion modls do no. This papr xnds h approach usd in Marc and Nicolini (1997) in analysing h phnomnon of rcurrn hyprinflaion in Souh Amrica. Assuming h auhoriis financd spnding by signorag, unlss inflaion xcdd a prs arg whn h govrnmn usd an xchang ra rgim, hir papr showd h rlaiv as wih which h faur of rcurrnc could b inroducd in a modl whr boundly raional xpcaions formaion ( hncforh larning ) was assumd rahr han raional xpcaions. In implmning larning, Marc and Nicoloini assum ha h updaing quaions govrning agn's larning wr of wo yps; h firs is las- squars larning whr inflaion is high, bu h scond occurs whn big shocks hi h inflaion procss, and hn agns rsor o a racking rul. Par of h modl's rsuling non-linariy ariss as swichs occur bwn hs wo larning Esudios d Economía Aplicada, 004: Vol. -

5 164 Bby M, Hall S., Hnry S. G.B. and Marc, A. mchanisms. Th applicaion of larning o h ERM crisis w giv blow, xnds on hs Marc and Nicolini insighs.. MODELS OF CURRENCY CRISIS (a) Firs and Scond Gnraion Modls Thr ar wo srands o h currncy criss liraur. Th firs, bgun by Krugman (1979) and known as h spculaiv aack modl, mphasiss h inconsisncy bwn (assumd xognous) govrnmn policis, usually akn o b oo high a ra of monary growh, wih h currn valu of h fixd nominal xchang ra. Krugman's moivaion was o xplain h wav of dvaluaions across Lain Amrica in h 1970s as raional vns, and no as signs of mark failur, and in his modl currncy criss ar runs on h cnral banks' holdings of forign rsrvs. Any rbalancing of porfolios by invsors rquirs h slling of domsic asss and rsuls in an incras in domsic crdi, lading h cnral bank o inrvn o mainain h currncy pg. An xpansiv monary/fiscal policy will no b consisn wih his pg and will mchanically rsul in a spculaiv aack. Thrfor, spculaiv aacks nd o b sn as raional vns - if hr was no run on rsrvs hn h spculaors would b abl o fors h xac da of dvaluaion and mak crain profis. Prhaps a waknss of h modl is ha govrnmn policy is modlld as bing xognous. Spculaiv aacks occur bcaus h policy making auhoriis pursu policis ha ar, by assumpion, inconsisn wih h xchang ra. Bad fundamnals ar hn simply hos policis ha lad o a dvaluaion. I should b nod howvr ha Krugman was no rying o xplain why govrnmns pursu incorrc policis; rahr h was inrsd in sudying h consquncs of poor policis. And h modl dos sm o fi vns in 1970/80 Lain Amrica whr counris lik Argnina, Chil and Brazil wr amping o sabilis hir high inflaion and larg public scor dfici conomis. Wih h ERM crisis of 199 and 1993, h limiaions of assuming an xognous govrnmn policy bcam clar. I is ru ha xpansionis monary policy may hav bn an issu in h dvaluaions by Ialy and Spain, bu in counris such as Franc and h UK problms aros bcaus of h conracionary naur of h monary policy pursud. Grman runificaion ld o inflaionary prssur in Grmany ha h Bundsbank counrd wih a igh monary policy. This forcd upon h ohr ERM mmbr counris inrs ras highr han hy would hav prfrrd givn h sa of hir domsic conomis which wr xprincing incrasing lvls of unmploymn. This in urn incrasd h mpaion o dvalu sinc h lvl of inrs ras ndd o dfnd h xchang ra was inconsisn wih h domsic nds of monary policy. Th firs-gnraion modl providd only a limid Esudios d Economía Aplicada, 004: Vol. -

6 EXPECTATIONS FORMATION AND THE 1990S ERM CRISIS 165 framwork for analysing hs issus, paricularly givn is narrow dfiniion of xchang ra crdibiliy. Furhr, h ERM crisis showd ha broadning h s of conomic fundamnals in ha modl was no sufficin. Unmploymn had bn high and incrasing in Grmany yars prior o h crisis, so why was i ha h crisis occurrd a ha spcific im? Wha appard o b ndd was a modl ha xplaind spculaiv aacks no simply as a rspons o a givn lvl of h conomic fundamnals, bu also allowd a rol for slf-fulfilling spculaion. This ld o h dvlopmn of h scond-gnraion modl, lablld h scap claus modl. Th scond-gnraion modl was formalisd by Obsfld (s spcially, Obsfld (1994)). In his modl, counris xid h fixd xchang ra rgim no bcaus govrnmn policis wr inappropria, bu bcaus govrnmn's ar viwd as rading-off h coss and bnfis of adhring o h currncy pg on h on hand and raligning on h ohr. Undr RE h priva scor ralis his and givn a sufficinly advrs shock, will anicipa corrcly ha h govrnmn will abandon h pg. Thus, in his modl, govrnmns commi o a fixd xchang ra rgim only condiionally in h xpcaion of gaining ani-inflaion crdibiliy, bu any commimn mus b limid. If conomic fundamnals driora sufficinly hn h govrnmn has an scap claus allowing i o chang is xchang ra (.g. floa or dvalu), which h priva scor knows. Govrnmns (and consqunly spculaors) ar hn in a coninual procss of valuaing h coss and bnfis of mainaining a currncy pg, in h ligh of xognous shocks. Thr ar wo major conribuions of his modl. Firs, h noion of conomic fundamnals usd is a broad on, i can b any variabl ha h policymakr dcids is rlvan for h dcision on whhr o xrcis is scap claus. Scond, and prhaps mor imporanly, i provids a nw hory of slf-fulfilling spculaion and mulipl quilibria. Causaliy can flow no only from narrow conomic variabls o mark xpcaions bu also in h opposi dircion. Mulipl quilibria can hn aris from such circulariy. For insanc, in hs modls, any incras in h blif of priva agns ha h govrnmn may dvalu can lad o an incras in inrs ras o srnghn h currncy, which in urn raiss h probabiliy ha dvaluaion acually occurs. Whhr and whn xchang ra criss rsul is now dpndn upon h slf-fulfilling mood of h paricipans in h mark. Incorporaing mulipl quilibria ino xchang ra modls is appaling for a numbr of rasons. Firs, many conomiss (and mark paricipans such as Gorg Soros) bliv ha spculaion is moivad by mor han jus narrow conomic fundamnals. Scond, h sprad of conomic criss (i.. conagion) and hir iming can b mor asily xplaind in modls wih his faur. Third, mulipl quilibria is a compromis bwn hos who bliv ha criss ar a rsul of mark failur and hos ha bliv hy ar a rspons o bad govrnmn policis. To suggs ha criss ar purly a rsul of spculaion appars o absolv govrnmns of all h Esudios d Economía Aplicada, 004: Vol. -

7 166 Bby M, Hall S., Hnry S. G.B. and Marc, A. blam; bfor a currncy bcoms a ponial arg by spculaors hr has o b som conomic fragiliy. (b) Th Escap Claus Modl Obsfld's scap claus modl (1991, 1994 and 1996) is an opn conomy vrsion of Barro and Gordon (1983), and applis o a govrnmn wih an xchang ra objciv. I yilds h possibiliy of mulipl qulibria in xpcd inflaion ras in h modl. Th xnsion is basd on hr bing fixd coss o currncy changs, which h auhoriis will only counnanc if hr is a sufficinly larg shock o oupu. Whn hr is such a shock, h auhoriis dvalu and us monary policy o sabilis oupu. Th suprficial rsmblanc of his squnc o h ERM crisis sms clar. Th vrsion of h modl usd hr is Obsfld (1994) as his focusss on h dvaluaion cas, and links h xchang ra o oupu innovaions in a way which is convnin for our prsn purpos. L oupu b givn by (variabls in logs) y = α ( w ) + u (1) whr y is h log of oupu, w h log of nominal wags and is h log of h nominal xchang ra, which is qual o h domsic pric lvl undr PPP, and whr h forign pric is normalisd a uniy. Hnc, (1) givs an invrs rlaion bwn oupu and h ral wag, which is shifd by an oupu shock u (assumd o b i.i.d). Wags in priod ar s in priod (-1) basd on informaion a ha da, so dos no includ u i. Th govrnmn can rspond o dmand shocks in priod via changs in h currn xchang ra. Undr floaing h govrnmn minimiss whr β<1, and whr s L = Σ β l () s 1 s s = ( θ / )(s s 1 ) + ( 1/ )(ys y*) (3) l whr y* is h arg oupu lvl, assumd o b non-zro which cras a dynamic inconsisncy problm. I also suggss why a govrnmn migh choos o i is hands; h govrnmn ss h xchang ra afr obsrving u (unlik priva agns), so any dvaluaion lads o coss. (s blow) Subsiuing (3) and (1) ino () and minimising w.r., assuming ha is givn, givs h govrnmn's racion funcion, whr λ = α /( θ + α ). 1 = λ ( u / α ) + λ( w 1 ) + λ( y* / α ) (4) Esudios d Economía Aplicada, 004: Vol. -

8 EXPECTATIONS FORMATION AND THE 1990S ERM CRISIS 167 Equaion (4) is crucial, as i capurs h main ingrdins of h problm. Firsly, h quaion shows ha h govrnmn uss h xchang ra o offs oupu shocks, and scondly ha i can amp surpris dprciaions if wag inflaion affcs compiivnss. Lasly, according o h las rm in h quaion, h govrnmn may amp o push oupu abov is naural ra. As is sandard in hs scap-claus modls, h problm of mainaining a currncy pg is sn as on of h crdibiliy of h commimn o h pg. This nails adding a cos of ralignmn o h objciv funcion (3) abov, i.. l = l + cz (5) / whr Z is an indicaor funcion wih valu=1, if 0, and is 0 ohrwis. Using (5) i can b shown ha h loss undr a fixd xchang ra rgim is / F = ( 1 / )( απ + u + y*) (6) l as =0, and π = w 1, assuming, as w do, ha wags ar indxd o prics (qual in his modl o h xchang ra). Undr ralignmn, from (4) h loss is l / F = ( 1 λ )l c, (7) / R + from which i follows ha a ralignmn will occur whn ( > λ / )( απ + u + y*) c (8) Traing (8) as an qualiy, i is alrady vidn ha hr ar wo soluions o his for u; u > u, whr h govrnmn dvalus, and u < u whr i rvalus. Th roubl wih his drivaion so far is ha hs riggr poins for uppr and lowr valus of u dpnd on h mark xpcaions of dprciaion ((in his modl givn by π ), whil a h sam im hs xpcaions dpnd on whr h mark hinks hs riggr poins ar. To procd o analys his furhr, w limi h modl o h dvaluaion opion as anicipad arlir. Thn, (a) Th mark xpcaion of dprciaion, givn u, is π = = P{ u u }. 0 + P{ u > u }.E{ u u } (9) > whr P(.) rfrs o Probabiliy. Assuming ha u has a uniform disribuion bwn { µ, µ }, hn P{ u > u } = ( µ u )/ µ, and E{ u u > u } = ( µ u ) /. + Esudios d Economía Aplicada, 004: Vol. -

9 168 Bby M, Hall S., Hnry S. G.B. and Marc, A. Using hs in (4) w g, E{ u > u } = λ(( µ + u ) /( α )) + πλ + λ( y* / α ) (10) which is h mark's (raional) xpcaion of dvaluaion givn h hrshold u. From (9) and (10) i follows ha π = λ(( µ u ) / µ )[{( µ + u ) / α } + ( y* / α )] /[ 1 λ(( µ u ) / µ )] (11) = δ ( u ) (b) Calculaing h Thrshold Th govrnmn aks h xpcaion in (11) as givn whn minimising is loss funcion. Puing his ino (8), h valu of h largs shock consisn wih mainaining h pg is u ~ ( λ / )[ αδ (u ) + + y*] = c. (1) Sinc u ~ u = in quilibrium, (1) is a quadraic in u wih gnrally wo soluions. For calibrad valus of h paramrs{α,θ,µ,) and y*, Obsfld (1994) shows hr ar wo valus for h hrshold, and associad wih hs an xpcd dprciaion (or inflaion) ra. Th scond, highr, xpcd dprciaion ra will normally riggr an acual dvaluaion, unlss oupu shocks ar vry favourabl. 3. BOUNDEDLY RATIONAL LEARNING 3.1. Th Soluion undr RE Th raional xpcaions vrsion of h crisis modl s forward by Obsfld (op.ci) is an xnsion of h Barro-Gordon s up; namly ha wag bargainrs know h govrnmn racion funcion givn by (4) abov, and s wags according o i. Assum ha wag bargainrs (firms and unions) agr o wags which nsur a consan ral wag, hn w = E ( ) (13) 1 so h nominal wag is s condiional only on informaion dad a -1, and dos no includ h ralisaion of u, so h x-pos ral wag in priod will b affcd by his. Howvr, h RE bargain nsurs ha h wag is s in h full knowldg of how h govrnmn will rac o ralisaions of u as givn by (4). Thus in h RE quilibrium, from (13) and (4) h wag is Esudios d Economía Aplicada, 004: Vol. -

10 EXPECTATIONS FORMATION AND THE 1990S ERM CRISIS 169 w 1 + ( λ /( 1 λ ))[ E 1( u / α ) + ( y* / α )] (14) = which, as h xpcaion of u is zro, is w = 1 + ( λ /( 1 λ ))( y* / α ) (15) This, oghr wih h govrnmn racion funcion (4) implis h xchang ra is givn by (16). = λ( u / α ) + ( λ /( 1 λ ))( y* / α ) (16) Equaions (14) and (16) consiu h sysm of dynamic quaions w will us. 3.. Larning Mchanisms To implmn h alrnaiv Bounddly Raional soluion, w opra wih h sam basic modl of oupu, wag sing, and racion funcion as w hav abov. In conras o h REH cas w rplac h assumpion ha xpcd xchang ras and wags ar formd raionally wih h following wo assumpions. Undr larning, h xpcd xchang ra is akn o b qual o h laggd ra wih a consan and slop paramr ha ar im varying and which ar updad using a Kalman Filr. Thus, ϕ (17) = 0 + ϕ1 1 whil wag xpcaions ar formd by h rul w = ϕ + ϕ * ( y y ) (18) Equaions (17) is a simpl bounddly raional larning rul which says ha xpcaions of h xchang ra ar a funcion of pas acual valus, This rul has bn shown o work rmarkably wll in Bby, Hall and Hnry (00). Equaion (18) is of cours a bounddly raional vrsion of a sandard Phillips curv rlaionship which simply sas ha h xpcd chang in wag inflaion is a funcion of h obsrvd oupu gap. 4. MODEL SIMULATIONS In h simulaion h govrnmn is assumd o minimis h loss funcion givn by () and (3) abov, and h wo paramrs (β,θ) ar s qual o (0.95, 0.15) following Obsfld (1994). Thn, as in h accoun givn abov, h govrnmn considrs h advanags of mainaining h pariy vrsus a dprciaion, whr h dprciaion producs compiivnss gains, bu incurs a fixd (poliical) cos C which w s a in h simulaions. Esudios d Economía Aplicada, 004: Vol. -

11 170 Bby M, Hall S., Hnry S. G.B. and Marc, A. As in h horical modl arlir, opimising (3) abov w.r.. h xchang ra, h loss undr h fixd rgim is L 0. * ( y y ) F * = 5 (19) and undr h floaing rgim, L 0. * ( y y ) C / ( ) R S * S = θ (0) 1 S Th rms ( y S, ) ar h lvl of oupu and h xchang ra which would com abou if h govrnmn chos o dvalu, dfind blow. W hn obain a dynamic quaion for h xchang ra in rms of h disurbanc (µ ) as follows, whr F R * = ( diff /( L L ))( β( ) + ( γ / θ )( y y ) (1) diff = Max( 0,L F L R ) Th simulaion is gnrad by dfining valus for oupu and h xchang ra condiiond upon h floaing ra, i.. wha happns if h govrnmn chooss o go for h dprciaion opion. Thus, S y = γ + µ, and () S S S ( p ) S * S = 1 + β( ) + ( γ / θ )( y y ) (3) Simulaions ak arificial daa for a priod of 40 obsrvaion o cra a bas soluion. Thn h disurbanc is shockd by a rang of valus. Undr Raional xpcaions h rsul should b fairly sraigh forward. A shock blow h ky hrshold should lav h xchang ra unchangd and so no dvaluaion occurs. Bcaus xpcaions ar fully raional, h pas insanly bcoms a bygon, and as furhr shocks of a similar magniud occur hy also hav no ffc. So h simpl rsul is ha ihr a shock is largr han h hrshold, in which cas dvaluaion occurs, or i is no and dvaluaion rmains qually unlikly in h fuur. Howvr, undr larning h sory bcoms rahr diffrn and mor complx. If a shock occurs which is blow h ky hrshold o oupu, his bgins o chang wag xpcaions (as oupu will b diffrn from h naural ra). This ffc will hn hav an impac on fuur oupu lvls. Of cours if hr wr no furhr shocks his ffc would almos crainly di away and, again, no dvaluaion would occur. Bu if a furhr similar shock should occur in h scond priod, hn h combinaion Esudios d Economía Aplicada, 004: Vol. -

12 EXPECTATIONS FORMATION AND THE 1990S ERM CRISIS 171 of h wo ffcs migh riggr a dvaluaion vn if ach singl shock dos no rach h RE hrshold. So wha w would xpc o find would b a combinaion of prsisnc and sizs of shocks, which riggr dvaluaion. On larg shock would b nough, wo smallr shocks migh also b nough, vn hr small shocks in a row migh b nough and so on. W ar agnosic as o h disribuion of h shocks. Evn if w assum h shocks ar acually i.i.d., hn in any givn simulaion hr is a chanc ha a sris of similar sign shocks will occur, and hs will riggr dvaluaion undr larning. In h ral world, as w argud in h inroducion, i sms clar ha shocks ar ofn highly corrlad Th Soluion undr REH Givn h chosn paramrs h RE soluion is xacly as xpcd and w find ha a shock of approximaly 1% of y is rquird o riggr dvaluaion. 4.. Th Soluion undr Larning In his cas, o illusra h propris of h modl, w prform a rang of simulaions whr w apply a shock for a numbr of priods (40 priods in all), w hn rcord how many priods laps bfor dvaluaion occurs. W find a rad-off bwn h siz of shock and h numbr of priods which laps bfor dvaluaion. This rad-off is illusrad in figur 1. I shows ha for a vry small shock of 1% applid in vry priod, dvaluaion will vnually b riggrd afr 1 priods whil for a vry larg shock i will occur in h firs priod Figur 1: Th rad off bwn h shock siz and h numbr of priods bfor dvaluaion Esudios d Economía Aplicada, 004: Vol. -

13 17 Bby M, Hall S., Hnry S. G.B. and Marc, A. 5. CONCLUSIONS W hav argud ha a vry clar sylisd fac of h ERM criss is ha h conomy was hi by a sris of ngaiv shocks bfor h criss occurrd, bu ha hr is no clar singl shock which could hav riggrd h crisis a h im of h crisis islf. This sylisd fac dos no conform o h sandard scond gnraion currncy criss modl. Howvr by rlaxing h assumpion of raional xpcaions w find ha h modl gnras a coninuum of combinaions bwn h siz of h shock and is prsisnc, any of which will riggr dvaluaion. Many show ha a squnc of vn rlaivly small shocks will riggr dvaluaion if hr is a sufficinly long squnc of hm. I is his faur- of a squnc of similar signd shocks prcding h crisis, rahr han a singl larg on - which w argu conforms vry closly wih h UK xprinc during his priod. APPENDIX. THE GENERAL CASE Th modl sars from h govrnmn loss funcion which, in his cas is, L = ( y y*) + βε + C( ε ) (1) whr all lowr-cas lrs dno naural logs, and y is oupu, y* h arg lvl of oupu, and ε 1 is h chang in h xchang ra, dfind as h pric of forign currncy. This is qual o h inflaion ra undr PPP. Th las rm in (1), C(.) capurs h faur ha h govrnmn has adopd an xchang ra objciv and hnc hr ar coss in dviaing from i, as w dscrib blow. Oupu is drmind by an xpcaions augmnd Phillips curv, y = y + α ( ε ε ) u () whr y is h naural oupu lvl, ε is h domsic pric srs' xpcaion of ε basd on laggd informaion (assumd im invarian), and u is an i.i.d. man-zro supply shock. Th assumpion ha y* > y cras a dynamic inconsisncy problm and is ndd o obain mulipl quilibria. I also suggss why a govrnmn migh choos o i is hands. Th govrnmn ss h xchang ra afr obsrving u (unlik priva agns), whr any dvaluaion lads o coss of C ( ε ) = c in () and a rvaluaion lads o coss of C ( ε ) = c. Esudios d Economía Aplicada, 004: Vol. -

14 EXPECTATIONS FORMATION AND THE 1990S ERM CRISIS 173 If h rm C(ε) in (1) is iniially ignord, so h xchang ra can b frly alrd, from (1) and (), h govrnmn chooss ε α( y* y + u ) + α ε a + β = (3) and subsiuing his ino () givs, and a policy loss of L y flx α ( y* y ) βu αβε y + a + β = β = α + β ( y* y + u + αε ) In h cas whr h govrnmn canno chang h xchang ra, hn h loss is insad, L fix = ( y* y + u +αε Rinroducing h fixd coss rm C(ε) mans ha h govrnmn only changs flx fix h xchang ra whn h supply shock u is sufficinly larg ha L + c < L or flx fix so small ha L + c < L. Dvaluaion hn occurs for u > u, and rvaluaion for u < u, whr 1 u = α c( α 1 + β ) y* + y αε,u = α ) c( α + β ) y* + y αε So wha happns is ha h auhoriis dfnd h xchang ra agains all bu vry larg shocks, bu whr hs occur, hy dvalu incurring h fixd cos of so doing, and onc h fixd cos is paid, hy us monary policy o sabilis oupu. Nx, mulipl quilibria for quilibrium xpcd inflaion ras can aris bcaus h raional xpcaion of nx priod's ε, givn pric srs' xpcaion ε, is E ( ε ) = E( ε u < u )Pr( u < u ) + E( ε u < u )Pr( u < u ), which shows ha h rlaion bwn x-pos inflaion and xpcd inflaion is a complicad on, and i is his propry which suggss h possibiliy of mulipl quilibrium xpcd inflaion ras. (i.. whr E( ε ) = ε ). Esudios d Economía Aplicada, 004: Vol. -

15 174 Bby M, Hall S., Hnry S. G.B. and Marc, A. Obsfld (1994) provids a calibrad vrsion for h cas of a dprciaion, and w us ha hr. Thus assuming ha ha h supply shock (u) is uniformly disribud on h inrval [-µ,µ], hn α u u u u E( ε ) = [( 1 )( y* y + αε ) ] (4) α + β µ 4µ Assuming raional xpcaions by wag srs givs, E(ε) = ε, and usually his producs on soluion. I is diffrn in his cas. To s his considr h slop of (4) shown blow. α α + β de( ε ) α α α = + ( y* y + αε ) dε α + β µ α α + β for u for u > µ = µ for u = µ This implis ha hr ar hr quilibria possibl in his modl which ar givn by h hr diffrn dvaluaion probabiliis and h consqun siz of h xchang ra chang. Th hr quilibrium xpcd dprciaion ras ar ε 1, ε, and ε 3 ach corrsponding o hr diffrn dvaluaion probabiliis (s Obsfld (1996) for dails). REFERENCES BEEBY M, HALL S and HENRY S (000). KRUGMAN. P. (1979) A Modl of Balanc of Paymns Criss, Journal of Mony, Crdi and Banking, 11 Augus, p MARCET. A and NICOLINI J. P. (1997) Rcurrn Hyprinflaions and Larning mimo, Univrsia Pomu Fabra. OBSTFELD. M. (1994) Th Logic of Currncy Criss Banqu D Franc- Cahirs Economiqus monairs, No 43. OBSTFELD. M. and ROGOFF K (1996) Foundaions of Inrnaional Macroconomics Th MIT Prss. Esudios d Economía Aplicada, 004: Vol. -