ON THE CONTINGENCY OF EQUILIBRIUM EXCHANGE RATES WITH TIME- CONSISTENT ECONOMIC POLICIES

ON THE CONTINGENCY OF EQUILIBRIUM EXCHANGE RATES WITH TIME- CONSISTENT ECONOMIC POLICIES N 27-8 March 27 Anoin BOUVERET OFCE Bruno DUCOUDRE OFCE

On h Coningncy of Equilibrium Exchang Ras wih Tim- Consisn Economic Policis * Anoin Bouvr and Bruno Ducoudré Absrac Equilibrium xchang ra horis (FEER, BEER and NATREX) mak h assumpion ha h Ral Equilibrium Exchang Ra (RER) is indpndn from inrnal quilibrium and conomic policis. W dvlop a modl in which conomic policis dpnd on h minimisaion of an inrmporal loss funcion, and w show ha in a Wag Sing-Pric Sing (WS-PS) framwork, h RER dpnds on h policymakrs objcivs, making h prvious assumpions highly qusionabl. W provid som rsuls for h impac of policymakrs prfrncs on h long run xchang ra and discuss h concp of inflaion illusion. In our modl, h long run (quilibrium) xchang ra is coningn on policymakrs prfrncs, implying ha quilibrium xchang ra simas mus b rad wih gra cauion. JEL Cods : F3, F32, F4, F42 Kywords: Equilibrium Exchang Ras, Tim-Consisn Policis, Long-Trm Inrs Ra Inroducion... 3 Par I: Economic Policis, Long-rm inrs ras and h RER... 3 I.. Economic Policis and h RER... 3 I.2. Long-rm ras in opn conomis... 6 Par II: RER, fiscal and monary policis: a modl... 8 II.. Main characrisics:... 8 II.2. Economic Policis:... 9 II.3. Th modl... II.4 Th long run... Par III Som simulaions... 2 III.. Th baslin scnario... 2 III.2. Som Varians... 6 III.3. Th wag-pric loop and inflaion illusion: A rappraisal... 6 Conclusion... 8 Annx I. Soluion of RE linar modls wih im consisn policy and wo auhoriis... 9 * W hank Hnri Srdyniak for providing us wih hlpful advic. Ph.D sudn a OFCE, anoin.bouvr@ofc.scincs-po.fr, 69 Quai d Orsay 757 Paris. Ph.D sudn a OFCE, bruno.ducoudr@ofc.scincs-po.fr. 2

Inroducion This papr aims a analyzing h rlaionship bwn h ral quilibrium xchang ra (RER), long-rm inrs ras and conomic policy. Equilibrium xchang ra horis (FEER, BEER and NATREX) do no ak conomic policis ino accoun. Th RER is assumd o b indpndn from h lar. Thus, in h FEER framwork, h inrnal quilibrium is achivd hrough conomic policis and is hrfor no affcd by h lvl of h ral xchang ra. Th indpndnc of RER and conomic policis is dbaabl and dpnds on qusionabl hypohss. Firs, agns ar risknural whn hy manag hir porfolio. Following a rad balanc dfici, h sock of financial asss adjuss wihou any spcific ffc on inrs ras. Y his assumpion dos no sm compaibl wih h xisnc of a hom bias oward domsic asss. Svral sudis hav also shown ha naional inrs ras do no convrg o a world lvl. Th Cnral Bank (CB) can hrfor influnc inrs ras ovr h long run, aking advanag of h rlaiv indpndnc of domsic and global financial marks. If hr is an inflaion/unmploymn rad-off, h CB can choos is RER (Bluz and Srdyniak (988); Capon and Villa (998)). In his framwork, for ach inflaion/unmploymn objciv pursud by h auhoriis hr is a corrsponding (and diffrn) RER. In addiion, h RER srongly dpnds on h goods mark quilibrium hrough h rad balanc, which is affcd by fiscal policy. Th govrnmn drmins fiscal dfici and public db lvls. Th fiscal auhoriy hn inracs wih h CB o achiv goods mark quilibrium, hnc h RER. W pu forward a modl in which conomic policis (fiscal and monary) rsul from h minimisaion of an inrmporal loss funcion, in conradicion wih h Taylor s rul. W us a modifid vrsion of h Södrlind (999) program ha compus consisn policis 2 for linar raional xpcaions modls wih wo auhoriis. Th modl is usd o analys h rlaionship bwn RER and conomic policis objcivs. W show ha h RER is coningn upon policymakrs prfrncs. Th papr is organizd as follows: par I provids a slciv rviw of h rlvan liraur, par II dscribs h modl and par III focuss on various spcificaions of conomic policis and hir impac on h RER. Par I: Economic Policis, Long-rm inrs ras and h RER I.. Economic Policis and h RER RER and inrnal quilibrium Equilibrium xchang ra horis (Williamson (985); Clark and MacDonald (998), Sin and Alln (995)) dfin h RER as h ral xchang ra ha achivs boh inrnal S Cumby and Obsfld (982), Mishkin (984), Kasman and Pigo (988), Frankl (99), Blundll-Wignall and Brown (99), Pigo (993), Throop (994). 2 Thr is no inconsisncy of opimal plans in h maning of Kydland and Prsco (977). S also Oudiz and Sachs (984).

and xrnal quilibriums. Inrnal quilibrium (oupu quals is ponial) is assumd o b rachd hrough conomic policis, whras xrnal quilibrium dpnds on h RER. Thos horis assum ha h RER has no impac on inrnal quilibrium. Howvr, in a Wag Sing-Pric Sing (WS-PS) framwork, h lvl of h RER affcs h inrnal quilibrium (Joly and al. (996); Bouvr and Srdyniak (25)). Assum ha consumr prics p dpnd on wags w and oupu y according o 3 : p = w + α y, and ha wags dpnd on consumr prics : w = l + n( p + s ) + ( n)p + β y. Th ral xchang ra ( q ) is fixd by wags and pric dynamics: q = s p + p = ( l + ( α + β) y ) / n () s is h nominal xchang ra, p is h forign consumr pric indx and l sums workrs dmands up. Th RER is hn a dcrasing funcion of oupu and workrs dmands. Th mdium run rad balanc is dfind by: bc = ny ny + nδ q (2) Combining () and (2) givs oupu and h RER: y = ( nq + l ) /( α + β ). Th inrnal quilibrium is a dcrasing funcion of h RER: a RER apprciaion raiss h oupu lvl. Inrnal quilibrium is no longr drmind by conomic policy bu by h quilibrium of goods and labour marks and h xrnal consrain. Th inrnal quilibrium dpnds on h RER. RER and xrnal quilibrium Concrning xrnal quilibrium, h RER mus sabilis h n forign asss posiion in h long run. W can dfin i (in % of GDP) as: f = ( + i π + ( s s ) ).f + bc whr f sands for N Forign Asss (NFA) and i is h forign inrs ra on xrnal db. Hnc NFA dpnds on rad balanc and h sock of pas xrnal db, including valuaion ffcs (s Branson (979) and Bluz and Srdyniak (988)). Th ral xchang ra mus sabilis h xrnal db in h long run. Th RER is affcd by h dynamics of h sock of n forign asss. Taking h dynamics of xrnal db ino accoun, Aris and Taylor (993) pu forward h concp of Dsird Equilibrium Exchang Ra (DEER). Th DEER improvs h FEER by aking dsird currn accoun and mploymn ino considraion. Bayoumi and al. (994) analys h DEER pah whn h n forign asss lvl is no qual o is dsird lvl. L us assum ha h counry is iniially indbd by d and i aims a paying off is db whil mainaining is oupu lvl; if r is h gap bwn h inrs ra on h db and is growh ra and q is h ral xchang ra, h db-dynamics ar: d = ( + r) d nδ q. In h long run, h ral xchang ra is q =.Th pah of h ral xchang ra mus vrify: d = nδ = q ( + r) Th DEER can b viwd as a consrain on xchang ra pahs o h quilibrium lvl. Th auhoriis can choos a rajcory undr his consrain. In his framwork, h RER is highly dpndn on policymakrs objcivs and is lvl dpnds on is pah. 3 All variabls xcp inrs ras ar in a logarihmic form. 4

RER and conomic policis Equilibrium xchang ra horis also assum ha inrnal quilibrium is rachd hrough conomic policis wihou spcifying h lar. Bouvr and Srdyniak (25) show ha monary policy spcificaion has an impac on h RER. In NPO modls (WS-PS and porfolio 4 modl) h monary policy dsign is crucial: if h LM quaion is usd, afr a dmand shock, h inrs ra will ris o sabilis prics. I rducs oupu and lads o an xchang ra apprciaion so as o achiv rad balanc quilibrium and sabilisaion of h n forign asss posiion. If h CB adops a Taylor s rul, h inflaion lvl is prmannly incrasd and oupu lvl is raisd du o h gap bwn prics and coss. Th prmann incras in oupu brings abou a dprciaion of h RER so as o rach h xrnal quilibrium. In boh cass h RER is coningn upon monary policy. W now dfin inflaion as 5 : ( n( s p ) ( n) p y ( i ) p ) π = λ + + + μ + ν π (3) wih i as h nominal shor rm inrs ra and π as h inflaion ra. W includ an ffc of h ral inrs ra on inflaion 6. Oupu is a dcrasing funcion of h ral inrs ra and an incrasing funcion of rad balanc: y = d σ ( i π) + nδq ny (d sands for a dmand shock). N forign asss sabilisaion implis rad balanc quilibrium in h long run: y q =. δ Hnc h RER quals: ( d σ ( Aν) i ) q = δ σan ( + μδ) λ A = λ + ν Th RER dpnds on h gap bwn h dmand shock and h long-run valu of h inrs ra. In h LM framwork h mony mark quilibrium implis: β =,m =, hn: ε y+ p m i =. W assum β d σ ( Aν) p q = = f(d,p) ( δ σan ( + μδ) + σ ( Aν) δε + ) Afr a dmand shock, h inrs ra riss o sabilis prics, incrasing h ral inrs ra and wakning oupu. Tha involvs a ral apprciaion of h RER (MNPO Modl). If h CB adops a Taylor s rul, hr is an inflaion/oupu rad-off: lads o : i = φ y+ ρπ, 4 W dfin h porfolio modl as a modl wih risk-advrs invsors on inrnaional financial marks. 5 W add h inrs ra in h pric quaion: p = w + α y + υ(i π ). Assuming ha firms adjus slowly hir prics o hir dsird prics w obain quaion (3). 6 I can b inrprd as h ffc of financial coss facd by firms on hir dsird pric. I implis a long-run ffc of inrs ras on oupu and unmploymn; s Chagny and al. (22). S also Carruh and al. (998), Nickll (998), Blanchard and Wolfrs (2) and Fioussi and al. (2) for mpirical rsuls on h inrs ra ffc on unmploymn. 5

q = d ( ( )) ( ) ( φδ + ρa(n + μδ ) δ σan+ μδ σ Aν ) ρυ Th inrs ra augmnaion will b wakr, allowing for an incras in oupu and hnc a dprciaion 7 of h RER o achiv rad balanc quilibrium. Th RER is dircly affcd by h monary policy spcificaion. Bouvr and al. (26) pu forward a modl for a dvloping counry in which h xchang ra is usd as a policy ool. Th auhoriis choos a low lvl of h xchang ra bcaus i raiss ponial dmand and consqunly invsmn. Th low lvl of h xchang ra booss ponial dmand, invsmn and allows a fall in unmploymn; in h long run domsic consumpion gos up and achivs h quilibrium. Y h modl dosn ak monary and fiscal policis ino accoun. Anohr flaw of quilibrium xchang ras horis is ha hy don ak hisory ino accoun. I may b fallacious o hink ha a counry ha has xprincd a long priod of xchang ra ovrvaluaion, a rducd growh ra, an incrasing public db, and a rducd capial sock, ha harmd boh h mployabiliy of is manpowr and is xporing scor and incrasd forign firms mark shar will rach h sam long-run quilibrium lvl as if hos vns had no occurrd. Anohr xnsion consiss of aking hysrsis ffcs ino accoun (Krugman and Baldwin (987); Bouvr and Srdyniak (25)) whr mporary shocks can hav long lasing ffcs (s Gock (22) for a discussion of hysrsis in conomics). This opic will no b analysd in his aricl. Th RER can hn b coningn on conomic policis. Howvr, shor-rm inrs ras ar s by Cnral Banks, whras hs ar long-rm ras ha mar for priva agns whn hy choos o invs and consum. In opn conomis, sudying bond marks linkags is hn crucial o undrsand h links bwn h inrnal and xrnal quilibriums. I.2. Long-rm ras in opn conomis Exchang ras ar inrwind wih inrs ras. Indd, in simpl modls, h xchang ra is gnrally dducd from uncovrd inrs ras pariy (UIP) applid o shor rm ras. Wha dos happn whn w ak ino accoun long-rm inrs ras? W should spcify how shor ras and long ons ar s, and how hy inrac wih h xchang ra. Monary policy, UIP, long-rm ras and RER Th shor-rm ra is s by h CB according o is macro-policy goals: inflaion and oupu sabilisaion. Th xchang ra dynamics is hn infrrd from UIP: i = i + Δs (4) W assum ha h Cnral Bank follows a Taylor rul, in which h shor rm ra dpnds ar ar on inflaion and oupu: i = π + λcb. ( π π ) + γcb.y. π is h CB s inflaion arg. ar i = π + λcb( π π ) + γcb.y is h forign shor-rm inrs ra and Δ s = s+ s is h xpcd dviaion of h xchang ra. Undr h UIP hypohsis, h xpcd dviaion of h xchang ra is qual o h sprad bwn domsic and forign shor-rm ras. I is condiional on h rspciv goals of h domsic and forign Cnral Banks: ar ar Δs = i i = π π + λ π λ π + λ π λ π + γ.y γ.y ( ) ( ) ( ) ( ) cb cb cb cb cb cb 7 For a broad rang of valus of h paramrs, h dnominaor is posiiv, h sabiliy condiions can b sn on dmand. 6

L I b h nominal inrs ra on a zro-coupon bond mauring in N priods. According o h xpcaions hypohsis of h rm srucur of inrs ras, and whn agns ar risk-nural, h long ra is an avrag of xpcd shor-rm inrs 8 : I i.( ).y N N N N ar = + j = π+ j + λcb π+ j π + γcb + j j= j= (5) Th long ra hn dpnds on h CB racion o xpcd inflaion and oupu. Combining (4) wih (5), w g: N = j + j = + N j= ( + Δ + ) ( + ) I i s I s s N N Th domsic long ra is qual o h forign on plus an xpcd man dviaion of h xchang ra bwn and +N-. In ha modl, i is quivaln o spcula bwn shorrm domsic and forign bills, or bwn long-rm domsic and forign bonds (Bnsock and Longboom (98)). Assum ha h long ra is a yar on. Also assum ha agns xpc ha h convrgnc o h long run quilibrium will las yars. s + N is h nominal quilibrium s = s N. I I. Long ras dpnd on monary policis goal, hn xchang ra s, and ( ) s s is coningn upon conomic policy. Th long run ral xchang ra is q = s + p+ N p+ N. L us brak up h long ra ino an xpcd ral long ra R and an xpcd man inflaion bwn and +N-. I follows: p+ N p p+ N p q = s + p+ N p+ N + N. R + R + N N hn: q q = N. ( R R ) (6) In porfolio quilibrium, h sprad bwn h RER and h ongoing ral xchang ra is inrwind wih h sprad bwn long-rm inrs ras. If q is no indpndn of conomic policy choics, h drminaion of h RER is inimaly linkd o h drminaion of long-run ral long ras in an opn conomy framwork. Risk avrsion, long ras and RER Unil now, w assumd ha h subsiuion bwn domsic and forign financial asss was prfc. Y, waching inrnaional porfolios composiion rvals ha agns hav a srong prfrnc for domsic asss. Tha mpirical assssmn is rfrrd o as hom bias (Tsar and Wrnr (994); Lwis (998)). Empirical ss hn rjc h hypohsis of prfc subsiuabiliy bwn shor-rm domsic and forign asss (Dankr and al. (987); Bnassy A and al. (992)). A possibl xplanaion is risk avrsion (Branson and Hndrson (985); Bluz and Srdyniak (988)). L us assum ha domsic and forign financial asss ar no subsiuabl. Equaion (4) is hn: f i = i + Δs (7) f n xrnal financial walh. Th highr k, h smallr risk avrsion is. I follows: k N N I = ( i j Δs j) I s N s f j N + + + = + + + j= N k (8) j= 8 S for xampl Shillr (979), Campbll and Shillr (99). 7

N + j j= and quaion (6) bcoms ( ) q q = N. R R + f. N.k Now h sprad bwn h currn ral xchang ra and h RER is inrwind wih h sprad bwn ral long ras and h xpcd dynamic for h n xrnal financial walh. According o (8), h long ra of a small counry can durably divrg from forign long-rm inrs ras. I hings upon xpcd xchang ra dviaion, bu also on a risk prmium if h financial asss subsiuabiliy is imprfc on h inrnaional scal. Now ha risk prmium can b vry imporan du o high variabiliy of xchang ras, and o h difficuly (or impossibiliy) o prdic hir long run dvlopmn. Thr is no rason for long-rm ras qualisaion in h long run, in opposiion o som works 9 according o which long-run ral long-rm ras ar drmind on h world financial mark and should hn b qual. Monary policy can affc long ras and h ral xchang ra o achiv is goals. Par II: RER, fiscal and monary policis: a modl This par focuss on h impac of conomic policis spcificaion on h RER. W analyz h impac of a prmann dmand shock on a small opn conomy. II.. Main characrisics: Th dscripion of h conomy is buil on hr modlling opions: h wag-pric loop, h xchang ra drminaion modl and h dsign of conomic policy. Givn ha hos poins hav bn prviously analyzd (s for insanc Bluz and Srdyniak (988); Bnassy and Srdyniak (992); Bouvr and Srdyniak (25)) w will brifly oulin h main characrisic of h modl. Th wag-pric loop is basd on h Wag Sing-Pric Sing modl (Layard and al. (25)). Th us of h WS-PS modl appars o b dcisiv: a prmann shock can hav a long-lasing ffc on oupu and h ral xchang ra, whil in a Phillips framwork is ffc is mporary. Rgarding xchang ra drminaion, if invsors ar unanimous, risk-nural and infinily rich, h uncovrd inrs pariy is vrifid. On h conrary, h porfolio modl dvlopd in h aricl assums risk-avrsion insofar as housholds dmand a risk prmium on forign asss. Afr a posiiv dmand shock, h domsic conomy is sabilizd hrough rad dficis and hir impac on h domsic inrs ra. In h modl, w mak a disincion bwn shor and long rm inrs ras. Turnovsky (986) analyzs h rm srucur of inrs ras in a small opn conomy. Turnovsky inroducs nihr financial asss dynamics, nor h govrnmn budg consrain, and assums prfc subsiuabiliy bwn financial asss. Sachs and Wyplosz (984) focus on fiscal policy ffcs on xchang ras, using h rm srucur of inrs ras. Howvr, hy don analyz h cas whn h CB follows a monary policy rul. Taking sock of hs issus, w xplicily inroduc financial asss dynamics, h govrnmn budg consrain, risk-avrsion and a monary policy rul. 9 S Blanchard and Summrs (984) and Barro and Sala-i-Marin (99). 8

II.2. Economic Policis: Th dsign of conomic policis appars o b crucial in our framwork. Thr ar wo auhoriis: h govrnmn and h CB. Economic policis ar conducd following h minimizaion of loss funcions which includ h policymakrs args and insrumns. Each policymakr has basically four main args: sabilizing h oupu a is ponial lvl (as in h baslin scnario); sabilizing inflaion, and ming h xrnal consrain so ha flucuaions in h xchang ra ar sabilizd, saisfying h inrmporal budg consrain of h govrnmn. In addiion, policymakrs conrol on insrumn and nd o minimiz is xpnsiv us. On h on hand, fiscal policy can b cosly bcaus of implmnaion dlay, and bcaus i may b irrvrsibl; on h ohr hand, monary policy affcs fuur growh hrough is impac on invsmn so ha using h inrs ra can b cosly. Morovr, larg flucuaions of h shor ra can induc undsirabl volailiy of ass prics on financial marks. Th shor rm inrs ra is s by h CB, whil h fiscal policy dpnds on h govrnmn. If w assum ha boh auhoriis follow a prdrmind rul (such as a Taylor rul for h CB, and a rul sabilizing oupu and db for h govrnmn), h modl is usually im-inconsisn (i machs h closd-loop modl cas of Oudiz and Sachs (984)). Policymakrs hav an incniv o modify hir rul ovr im. W will only considr imconsisn policis in our modl: hy rsul from h minimisaion of an inrmporal loss funcion. Policis ar im consisn in h sns ha h auhoriis hav no incniv o modify h rul. Policis driv from h loss funcion minimisaion, following Capon and al. (23); h sligh diffrnc is ha h auhors focus on non-coopraiv and coopraiv bhaviour in a hr-counry modl. This aricl aims a analyzing h ffcs of conomic policis on h ral xchang ra; w will hrfor only considr h non-coopraiv cas. Th quilibrium bwn boh auhoriis is hrfor a Nash quilibrium, as h quilibrium bwn auhoriis and h mark. Th loss funcions ar: 2 2 2 2 2 Min βcb ( απ,cb. π + αy,cb.y + αb,cb.b + αi,cb.i + αg,cb.g ) i 2 = for h CB, and 2 2 2 2 2 Min βg ( απ,g. π + α y,g.y + αi,g.i + α b,g.b + α g,g.g ) g 2 = for h govrnmn. Wighs pu on ach goal ar summarizd in Tabl. Th CB sks o sabiliz inflaion and oupu wihou larg swings in h inrs ra. Th govrnmn sabilizs oupu and o a lssr xn inflaion wihou larg swings in public spnding and public db. As a simplificaion, axs ar s in ordr o sabilis h db τ =,b. Th simulad modl is inrmporally consisn. Coopraion bwn h Govrnmn and h CB could b achivd by dfining a uniqu loss funcion (cnralisd conomic policy), or by a Nash-Bargaining procdur. S Capon and Villa (997); Capon and Villa (998). 9

Tabl. Wighs in h Loss funcion CB Govrnmn Inflaion 2.5 Oupu Public db Shor-rm inrs ra.5 Public xpndiurs.5 II.3. Th modl Th main quaions ar summarizd in Box. Oupu y is an incrasing funcion of laggd oupu, public spnding g, rad balanc, houshold walh w and a dmand shock d. I also ngaivly dpnds on axs τ and a long-rm ral inrs ra I π LT. Trad balanc dpnds on h diffrnc bwn domsic and world oupu and h ral xchang ra p + s p, whr s sands for h nominal xchang ra (an incras is dprciaion), p and p ar domsic and world prics. Th wag-pric loop is a WS-PS loop: h pric adjuss slowly o a dsird pric linkd wih oupu, ral xchang ra and h long-rm ra. Th porfolio modl of xchang ra drminaion implis h uncovrd inrs pariy wih a risk prmium dpnding on forign ass posiion. Th long-rm inrs ra is γ n s according o h xpcaions hory of h rm srucur of inrs ra: ΔI = ( I i), γ n n n wih γ n = γ.( γ ) /( γ ), and γ =, I is long run avrag of yild on an n-priod bond + I (Shillr (979)). Th long-rm xpcd inflaion ra π LT is a wighd avrag of fuur xpcd inflaion ras 2. Public db is h cumulad sum of pas fiscal dficis. In h sam mannr, h n forign asss posiion is h cumulad sum of pas rad dficis. Lasly h govrnmn and h CB minimis hir loss funcion according o inflaion, oupu, shor rm inrs ra, public db and public spnding. Th variabls ar xprssd as dviaions from baslin. Th modl volvs according o X = AX + + BU 3. I is solvd o drmin im consisn policis 4. d can b sn as a chock on w%, h housholds dsird walh: if dsird walh dpnds on h ral long w% = a + a. I π, a >, and if housholds slowly adjus hir walh o w% according o a paramr ra: ( LT ) b >, hn h par of housholds consumpion ha flucuas wih hir walh is cw = b( w w% ) = b( w a a. ( I π LT ) ). W g σ = a.b, θ = b and d = a.b. A posiiv prmann chock on d is quivaln o a prmann fall in housholds dsird walh. 2 Eijffingr and al. (2) Us h sam approach o compu a long-rm ral inrs ra. 3 To simplify, h modl is linarisd wih quilibrium valus s a zro. I implis ha inrs chargs on h public db and n xrnal walh ar no akn ino accoun in simulaions. 4 W us Malab 7 o simula h modl. Th rsoluion algorihm of raional xpcaion modls wih consisn policis is dscribd in Annx I. W hav adapd h algorihm of Södrlind (999) o h cas wih wo auhoriis. Programs ar availabl from h auhors.

Th govrnmn financs is dfici by issuing shor ( b s ) and long rm bonds ( b l ) in proporions α s and α l ( αs + αl = ). Public db is nirly hld by housholds: b = α s.b s; + αl.bl;. Housholds ar assumd o b risk-nural whn hy choos bwn shor and long rm bonds. Arbirag quilibrium implis ha h xpcd rurn on a domsic long-rm bond mus qual h shor rm inrs ra. W also assum his condiion o b fulfilld in h forign financial mark. I = γni + + ( γn).i I = γni ( γn).i + + whr I and i ar forign long and shor-rm inrs ras on forign bonds b s and b l. Arbirag bwn domsic and forign asss can b xplaind by quaion (9). f b = s; + b l; is h n forign asss sock hld in h housholds porfolio. Forign bonds ar convrd ino local currncy and sad as a % of GDP. Housholds choos o hold shor and long-rm asss in proporions α s and α l, wih αs + αl =. Exchang ra dynamics dpnd on h diffrnc bwn shor-rm inrs ras and h risk prmium. Equaion (9) is drivd from an opn conomy porfolio modl 5. Th accumulaion quaions for public db, forign ass and houshold walh ar: b = ( + αs.i + αl.i π).b + g τ f = ( + αs.i + αl.i π + ( s s ) ). f + bc w = b + f Rurn on public db dpnds on a man inrs ra, according o h financing srucur if h govrnmn. Th inrs ra on xrnal db dpnds on a man inrs ra according o h porfolio srucur in forign asss chosn by h housholds. II.4 Th long run In h long run, rad balanc mus b in quilibrium so as o sabiliz xrnal db. Th ral xchang ra hn achivs quilibrium. If h shock ffc is ransiory, h ral xchang ra rurns o is baslin valu. On h ohr hand, if h dmand shock has prmann posiiv (ngaiv) ffcs on oupu, h ral xchang mus dprcia (apprcia) o rsor h rad balanc. In porfolio modls wih WS-PS, h sabilisaion of h conomy hings upon monary policy: h rducion of h n forign asss posiion implis an incras in h shor-rm inrs ra so as o lad housholds o sll hir forign asss. Y his incras has a dirc impac on inflaion hrough is ffcs on coss. Th incras in h inrs ra nails a prmann incras of inflaion, which improvs oupu. Exrnal quilibrium implis a ral dprciaion of h xchang ra in ordr o offs h incras of impors du o oupu xpansion. 5 Proof is availabl from h auhors.

Box. Th Modl Goods mark quilibrium ( ) ( ) δ ( ) y = c.y + d + g ϖτ. σ I π + θ.w + bc c = σ = ϖ = 5, ; θ= 25. ; LT bc = n y y + n p + s p δ = 2; n =, 25 Wag pric loop ( ) ( ) π = λ n s p n p μ.y ν(i πlt ) p + + + + μ=,4; ν=,2; λ=,25 Financial mark quilibrium ( + ) f = k s s + i i k=4 (9) γ I = I i γ = 9, n + n γn γn γ π =. π. π n LT;+ LT; γn γn Walh and financial asss accumulaion ( π ) ( π ( )) b = + i.b + g τ f = + i + s s.f +.bc w = b + f CB loss funcion 2 2 2 2 2 Min βcb ( απ,cb. π + αy,cb.y + αi,cb.i + αf,cb.f + αg,cb.g ) βcb = 99, i 2 = Govrnmn loss funcion 2 2 2 2 2 Min βg ( απ,g. π + αy,g.y + αi,g.i + α f,g.f + αg,g.g ) βg = 99, g 2 = Par III Som simulaions III.. Th baslin scnario W analyz h impac of a %-of-gdp prmann priva dmand incras on h conomy. Rsuls ar dpicd on Figur. Dmand shock incrass oupu. Th nominal xchang ra ovrshoos in h shor run and apprcias. Th ris in oupu lads o a rad dfici and o a worsning of h 2

forign asss posiion. Th inrs ra augmns bcaus of growing inflaion and oupu. Thn h nominal xchang ra dprcias o rsor h rad balanc and o sabiliz h ral xchang ra. In h long run, hr is a prmann incras in oupu bcaus h ris in h inrs ra is no sufficin o wakn inflaion. Th rad balanc quilibrium is achivd hrough a ral dprciaion of h xchang ra. Th ris in h shor rm inrs ra is xpcd by h mark and lads o an incras in h long rm inrs ra. Th posiiv ffc on oupu allows for a dcras in public spnding and public db. In his framwork a prmann dmand shock has a prmann ffc on oupu and h RER, hs rsuls ar similar o Bouvr and Srdyniak (25), who focus on Taylor s rul (s Box 2). Long-run valus ar summarizd in Tabl 2. Figur. % priva dmand shock.7 Oupu Inflaion and xpcd inflaion.5 Trad balanc N xrnal walh and public db.6.5.4.3..5 -. -.2 -.3 -.5 - Exrnal walh Public db.2. 2 4 Inflaion Expcd inflaion -.5 2 4 -.4 -.5 2 4 -.5-2 2 4 Public spnding.4 Ral xchang ra.7 shor and long-rm ras 5 Nominal xchang ra -.2 -.4 -.6 -.8 -. 2 4.2 -.2 -.4 -.6 -.8-2 4.6.5.4.3.2. Long ra Shor ra 2 4 4 3 2-2 4 Sourc: Auhors calculaions. 3

Tabl 2.Long run valus Variabl Valu Oupu.56 Inflaion.3 N forign asss -.65 Shor-rm ra.54 Exchang ra + Exchang ra variaion.3 Ral xchang ra.28 Public db -.34 Public spnding -.3 Long-rm ra.54 Sourc: Auhors calculaions. 4

Box 2. Tim-consisn policy vs Taylor s rul W compar h baslin scnario o a varian in which h CB ss is shor-rm ra according o h following Taylor s rul:. r = ρ p + φy avc ρ =.5, φ =.5 Th govrnmn fixs axs and public spnding according o : τ =,. b g =,3. y Th rsuls ar oulind in Figur 2. As xpcd, h im consisn policy sabilizs h conomy mor fficinly: oupu is highr and flucuaions ar lowr whil in h Taylor s rul framwork variabls flucua mor. Figur 2. Comparison of Tim-consisn policy and a Taylor rul.7 Oupu.5 Inflaion.2 Trad balanc.5 N xrnal walh.6.5...4.3.5 -. -.2 -.5 -.2. -.3 -.4 -.5 2 4 -.5 2 4 -.5 2 4-2 2 4 Public spnding.4 Ral xchang ra.7 shor-rm ra 5 Nominal xchang ra -.5 -. -.5.2 -.2 -.4 -.6 -.8.6.5.4.3.2. 4 3 2 -.2 2 4 Sourc: Auhors calculaions. - 2 4 2 4 simpl rul consisn policy - 2 4 5

III.2. Som Varians Th modl can b usd in ordr o assss h impac of policymakrs objcivs on h RER. In varian, h CB pus a highr wigh on oupu sabilisaion: α y,cb = 2. Th CB incrass is inrs ra which in urn affcs h long-rm inrs ra, rducing h impac of h dmand shock on oupu and inflaion. Th ral xchang ra dprcias lss o sabilis h rad balanc and h n forign asss posiion (s Tabl 3). In varian 2, h govrnmn pus mor wigh on oupu s sabilisaion α y,g = 2. Public db dcrass, lading o a wakr ffc on oupu in h long run. Th CB can in urn incras is inrs ra by a smallr margin. W hn pu succssivly α q,cb =, α f,cb =, α q,g = α f,g =. In varian 3, h CB pus a posiiv wigh o h ral xchang ra. Thr is a rad-off bwn h ral xchang ra and h ohr objcivs. Afr a posiiv dmand shock, h RER is wakr in h long run compard o h baslin scnario, wih highr inrs ras and lowr inflaion and oupu. In varian 4, h CB pus a posiiv wigh on h n forign asss posiion; h RER dprcias mor in h long run bcaus of h wakr incras in h inrs ra. Th govrnmn lowrs is db o sabiliz oupu and inflaion. In varians 5 and 6 w modify h govrnmn s objcivs. In varian 5 i sabilizs h ral xchang ra and lowrs is db, rducing inflaion, lowring h inrs ra hik and h ral xchang ra. In varian 6 i sks o sabilis h n forign asss posiion. Thr is a largr lowring of public db, rducing h incras in oupu and inrs ra and inflaion. Th ral xchang ra dprcias lss in h long run Th RER hn srongly dpnds on CB and govrnmn objcivs. Th rsuls also show ha inrs ras and RER ar inrwind: highr RER (dprciad RER) in h long run ar coupld wih lowr ral inrs ras and a highr inflaion ra. Variabl Tabl 3. Long run valu and Policymakrs prfrncs Baslin scnario Varian α = 2 y,cb Varian 2 α = 2 y,g Varian 3 α = q,cb Varian 4 α = f,cb Varian 5 α = q,g Varian 6 α = RER.28.67.262.73.566.258.245 Long ra.537.66.482.66.352.533.489 Inflaion.25.93.6.95.28.8. Ral long-rm inrs ra Sourc: Auhors calculaions..42.53.366.52.44.45.378 f,g III.3. Th wag-pric loop and inflaion illusion: A rappraisal W assumd a WS-PS loop wih a slow adjusmn of prics o dsird prics. Y in h long run hr is a gap bwn ffciv and dsird prics, implying a prmann inflaion illusion (Dbonnuil and Srdyniak (984)). If w now assum h dsird pric will adjus according o xpcd inflaion: a p = p + π + λ n( s p ) ( n) p μ.y ν(i πlt ) p π + + + + () Expcd inflaion for h firms adjuss slowly o pas inflaion: 6

π = λ. π + ( λ) π λ =, 25 () Th highr h λ valu, h fasr h firms adjus hir inflaion xpcaion. In h long run hr is no inflaion illusion. Oupu, public spnding and n forign asss dcras, inflaion and inrs ras incras (Figur 3). Th lvl of h RER dosn dpnd on λ. W simula h prvious varians wih λ = 25. ; h RER appars o b lss dpndn on policymakrs prfrncs (Tabl 4). Th RER is srongly linkd wih h wighs on n forign asss. Whn h CB sks o sabilis NFA (varian 4), i lads o a fall in inflaion, a dcras of h inrs ra and a highr RER apprciaion. On h ohr hand whn h Govrnmn sabilizs NFA (varian 6) h RER apprciaion is lowr han in h baslin scnario. Figur 3. A dmand shock of % of GDP; λ = 25. Oupu Inflaion and xpcd inflaion.5 Trad balanc N xrnal walh and public db.5 -.5 -. -.5..5 -.2 -.4 -.5 - Exrnal walh Public db -.2 -.5 -.6 -.5 -.25 -.3 -. -.5 Inf laion Expcd inflaion -.8-2 -2.5 -.35 2 4 -.2 2 4-2 4-3 2 4. Public spnding Ral xchang ra shor and long-rm ras Nominal xchang ra.5 -.5.8 -.5 -.5 -. -.6.4 - -.5 -.2 -.25 2 4 -.5-2 2 4.2 Long ra Shor ra 2 4 -.5-2 2 4 Sourc: Auhors calculaions. 7

Tabl 4. Long run valus and Policymakrs prfrncs λ = 25. Variabl Baslin scnario Varian α = 2 y,bc Varian 2 α = 2 y,g Varian 3 α = q,bc Varian 4 α = f,bc Varian 5 α = q,g Varian 6 α = f,g Ral xchang ra -.44 -.44 -.44 -.45 -.58 -.44 -.55 Long ra.862.845.858.78.89.856.35 Inflaion.7.89.2.9 -.64..62 Sourc : Auhors calculaions. Conclusion In h quilibrium xchang ra horis framwork, conomic policy is givn, and assumd o b commid o an inrnal quilibrium which is indpndn of h RER. Th hypohss of indpndnc bwn h RER, h inrnal quilibrium and conomic policis ar highly dbaabl. This aricl shows ha rmoving hos hypohss can hav a srong impac on h RER. W pu forward a modl in which h RER ha sabiliss h NFA posiion and conomic policis ar im-consisn. W show ha in a porfolio modl and a WS-PS sing, h RER dpnds srongly on policymakrs prfrncs. If afr a posiiv dmand shock, h CB wans o sabilis h ral xchang ra, h dprciaion of h RER is lowr han in h baslin scnario. Whn h CB sks o sabilis h NFA posiion, inflaion and oupu ar highr in h long run. Th RER dircly hings on h dsign of conomic policis; i is no uniqu and coningn upon policymakrs prfrncs: for ach prfrnc s hr is a corrsponding quilibrium xchang ra. Wih rgard o quilibrium xchang ra horis, our rsuls wakn h lgiimacy of hos approachs o xchang ra drminaion: if h RER lvl is condiional on conomic policis, how can w us modls wihou spcificaion of conomic policis? W can rfr o Robinson (937) who claimd mor han fify yars ago: I is now obvious ha hr is no on ra of xchang which is h quilibrium ra corrsponding o a givn sa of world dmands and chniqus; in any givn siuaion hr is an quilibrium ra corrsponding o ach ra of inrs and lvl of ffciv dmand, and any ra of xchang, wihin vry wid limis, can b urnd ino h quilibrium ra by alring h ra of inrs approprialy. Morovr, any ra of xchang can b mad compaibl wih any ra of inrs providd ha mony wags can b sufficinly alrd. Th noion of h quilibrium xchang ra is a chimra. Th ra of xchang, h ra of inrs, h lvl of ffciv dmand and h lvl of mony wags rac upon ach ohr lik h balls in Marshall s bowl, and no on is drmind unlss all h rs ar givn. 8

Annx I. Soluion of RE linar modls wih im-consisn policy and wo auhoriis W prsn h mhod o solv RE linar modl wih im consisn conomic policy proposd by Backus and Driffill (986) and implmnd by Södrlind (999). Th mhod is modifid o ak ino accoun wo indpndn policymakrs, which can hav diffrn loss funcions, as in Oudiz and Sachs (984) and Capon and Villa (997). W us Södrlind s noaions. Assum an conomy volving according o: x+ x = A + Bu x x 2+ 2 (2) whr x is a n vcor of prdrmind variabls, and x 2 is a n 2 vcor of forward-looking variabls. u is a k vcor of insrumns of conomic policy. x is h x n= n+ n2 dimnsion vcor x. 2 Th govrnmn G and h Cnral Bank CB hav h following loss funcions: G, = βg G + G + G = ( 2 ) J E xq x xu u u R u CB, = βcb CB + CB + CB = ( 2 ) J E xq x xu u u R u (3) In priod, h wo auhoriis s hr insrumns so as o minimis hir rspciv loss funcions, aking ino accoun priva scor xpcaions for h fuur. Th priva scor prfcly xpcs fuur conomic policis. I nsurs ha h govrnmn and h Cnral Bank undrak im-consisn policis: policis announcd in for + will b implmnd in +, bcaus whn h auhoriis minimis hir loss funcions in +, h announcd policy in is h bs givn priva xpcaions for +2. Th linar quadraic form of h modl implis ha h soluion for + givs for ach auhoriy j a valu funcion ha is quadraic in h sa variabls x + V j, + x + + v j, +, and a linar rlaion bwn h forward-looking variabls and h backward-looking ons x2+ = C+ x+. Th auhoriis valu funcions in hn saisfy h following Bllman quaions: ( ) x Vj, x + vj, = min j, 2 j j u j, xq x + xu u + u R u + β E x + Vj, + x + + vj, + j = G,BC (4) wih consrains: Ex 2+ = C+ Ex + (5) quaion (2), and x givn. Combining (2) and (5), and injcing h rsul in (4), w g : x = Dx + Gu 2 9

( + + + + ) xv x + v = min xq x + 2xU u+ ur u+ β E x V x + v j, j, j, j, j, j, j, u j, s.c. x = A x + B u + (6) Thn w obain h following sysm of marics: ( 22 + 2 ) ( + 2 ) ( ) ( ) D = A C A C A A G = A22 C+ A2 C+ B B 2 A = A + A2D B = B + A2G Qj, Qj, Qj, 2D DQ j, 2 DQ = + + + j, 22D U j, = Qj, 2G + DQ j, 22G + U + D j,u 2 Rj, = Rj + GQ j, 22G + GU j, 2 + U j, 2G (7) Driving (6) succssivly in rspc o insrumns j conaind in vcor u, w g h following firs-ordr condiions: u = F x (8) ( β + ) ( β + ) = + + (9) F R B V B U B V A j, j, j, j, j, j, x C x avc C D G F = = (2) 2 Th firs lin of F includs h drivaivs wih rspc o h firs insrumn of auhoriy j, h scond on conains drivaivs wih rspc o h scond insrumn of auhoriy j and so on. Combining (8) and (2) in (6), w g : ( ) + ( ) V = Q U F FU + F R F + β A BF V A BF (2) j, j, j, j, j, j, Th sysm composd of quaions (7) o (2) is irad unil convrgnc is achivd (algorihm backward in im ). W hn obain h following sysm: ( ) x = A + A C BF.x 2 x u 2 = C.x = F.x (22) 2

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