3. The Rational Expectations Revolution

Transcription

1 Poliicas macroconomicas, handou, Migul Lbr d Frias (mlbrdfrias@gmail.com) 3. Th Raional Expcaions Rvoluion Indx: 3. Th Raional Expcaions Rvoluion Inroducion Th workr misprcpion modl Main assumpions Labour mark quilibrium Aggrga supply...5 Box 3.. Th Phillips curv Equilibrium of h modl Inflaion surpris Shor run and long run Th modl wih backward looking xpcaions Adapiv xpcaions Monary surpris Surprising and surprising again...3 Box 3.2. Adapiv xpcaions and h acclraionis hypohsis Summing up Raional xpcaions Prfc forsigh Raional xpcaions and forcasing rrors Th policy inffcivnss proposiion...8 Box 3.3: Only surpriss mar! Th call for a Ral Businss Cycls Thory Th slop of h supply curv...2 Box 3.3. Th Lucas criiqu Unprdicabl oucoms Ruls vrsus discrion Th cnral bankr objciv funcion Cnral bank opimum undr discrion Inconsisncy (undr discrion) Consisncy (undr discrion) /0/207 hp://sw.ua.p/afrias/aulas/noas%20apoio/noasmacro.hm

2 Poliicas macroconomicas, handou, Migul Lbr d Frias (mlbrdfrias@gmail.com) Ruls and ohr rmdis Th rol of policy Th nw Kynsian rspons Saggrd wags Anicipad changs do mar...3 Box 3.4. Th saggrd wags modl Policy implicaions Furhr rading...35 Rviw qusions and xrciss...36 Rviw qusions...36 Problms /0/207 hp://sw.ua.p/afrias/aulas/noas%20apoio/noasmacro.hm 2

3 Poliicas macroconomicas, handou, Migul Lbr d Frias (mlbrdfrias@gmail.com) 3. Inroducion Afr World War II, mos conomiss blivd ha policymakrs hav a rol in smoohing h businss cycls. In ligh of h rcnly popularisd Phillips curv, hr should b a rad-off bwn inflaion and unmploymn, ha policymakrs could xplor ihr using fiscal policy or monary policy. In fac of an advrs dmand shock, i should b possibl o driv back h conomy o full mploymn, a h cos of som modra inflaion. Sinc h dcads ha followd wr characrizd by rapid conomic xpansion across h world, nohing rally srious qusiond his wisdom. In 970s, howvr, h Wsrn conomis facd wo supply shocks, and a nw phnomnon of high inflaion and high unmploymn, which was coind as sagflaion. Th Kynsian docrin, by assuming pric sickinss and dmand drivn businss cycls could no xplain his phnomnon. In plus, policis o xpand aggrga dmand in som counris rsuld in vn highr inflaion, wihou dlivring lowr unmploymn. This was no in accordanc o h ida of a sabl inflaion-unmploymn rlaionship, as implid by h Phillips curv. Th failur of xpansionary policis in sabilizing h conomy pavd h way for h rsurrcion of h pr-kynsian viw ha mark conomis ar inhrnly sabl. Th firs wav of his movmn was h monaris school, lad by Milon Fridman and his collagus a h Univrsiy of Chicago. Fridman connd ha mos businss cycls ar accound for monary shocks. Ths shocks giv ris o inflaion uncrainy and undsirabl dparurs of oupu from is naural lvl. Advoca of fr marks, Fridman claimd ha policymakrs should absain from manipulaing h aggrga dmand, commiing insad wih simpl ruls, such as sady mony growh. Th scond wav in h nw classical movmn was h raional xpcaions rvoluion, launchd by Robr Lucas and Thomas Sargn in h arly 970s. Undr raional xpcaions, agns ar assumd o mak h bs possibl forcass abou h fuur, givn h informaion availabl a h im of h forcas. Undr raional xpcaions, Lucas claimd, mony is no good candida o xplain businss cycls. This conclusion s h agnda for h hird wav of h Nw Classical movmn, h Ral Businss Cycls School, ld by Finn Kydland and Edward Prsco. This school conndd ha ral disurbancs, rahr han monary disurbancs, ar h caus of businss cycls. In ligh of his modl, businss cycls ar associad o flucuaions in h naural oupu rahr han flucuaions of acual oupu around is naural lvl. Many of hir conribuions ar collcd in Lucas and Sargn (98) and Lucas (98) [Lucas, R. E Jr, Sargn, T. J., 98, Raional xpcaions and conomric pracic, Univrsiy of Minnsoa Prss, Minnapolis, MN; Lucas, R. E. Jr., 98, Sudis in Businss Cycls Thory. MIT Prss, Cambridg, MA]. 04/0/207 hp://sw.ua.p/afrias/aulas/noas%20apoio/noasmacro.hm 3

4 Poliicas macroconomicas, handou, Migul Lbr d Frias (mlbrdfrias@gmail.com) Th modlling innovaions inroducd by h Nw Classical School inspird a nw gnraion of conomiss alignd wih h Kynsian radiion. Ths conomiss dvlopd macroconomic modls groundd wih microconomic foundaions, bu wih diffrn yps of mark failurs, o argu ha h pric mchanism is oo slow, vn undr raional xpcaions. Sinc h mark mchanism fails in dlivring full mploymn, i is argud, hr is scop for h cnral bank o sabiliz h conomy. This no brifly rviws hs idas, focusing on h ky assumpion of Raional Expcaions. In Scion 2, w inroduc h workrs misprcpion modl, which will b usd o xplain how informaion failurs may giv ris o dparurs of oupu away from is naural lvl. In Scion 3, w dscrib h cas wih backward looking xpcaions. In Scion 4 w solv h sam modl assuming insad ha agns ar raional. In Scion 5, w illusra how raional xpcaions wighd on h dba ruls vrsus discrion. In Scion 6, w brifly xplain how arlir Nw Kynsian horis, by adding pric sickinss o h modl, r-sablishd h ffcivnss of monary policy, vn undr raional xpcaions. To kp hings simpl, h xplanaion is mor inuiiv han formal. Tchnical dails ar addrssd in boxs. 3.2 Th workr misprcpion modl 3.2. Main assumpions Considr a closd conomy wih prfc compiion whr prics and wags ar flxibl. In his conomy, producion aks plac using wo facors of producion, labour and capial. Th capial sock is pr-drmind and qual o. For simpliciy, l s considr a Cob-Douglass producion funcion: Q zn (3.) Firms ak produciviy (z), h oupu pric (P), and h nominal wag ra (W) as givn and choos h numbr of workrs so as o maximiz profis. Assuming prfc compiion, his problm dlivrs h wll known opimaliy condiion saing ha h dmand for labour is such ha h marginal produc of labour quals h ral wag. Solving for N, his givs: P N d z (3.2) W Th implid supply funcion is obaind rplacing (3.2) in (3.): P Q s z (3.3) W Th novly in his modl is ha workrs do no obsrv h pric lvl a h im hy mak hir dcisions: workrs s hir nominal wags aking ino accoun h ral wag hy aim o rciv, and h xpcd pric lvl, P. 04/0/207 hp://sw.ua.p/afrias/aulas/noas%20apoio/noasmacro.hm 4

5 Poliicas macroconomicas, handou, Migul Lbr d Frias (mlbrdfrias@gmail.com) For simpliciy, l s assum ha h supply of labour is infinily lasic a h dsird ral wag,. Formally, our labour supply funcion will b as follows: W P (3.4) In his modl, firms hav an informaion advanag ovr workrs: firms know h pric a which hy ar slling hir own oupu. Workrs, howvr, ar concrnd wih h consumr pric indx. Th consumr pric indx is an avrag of all consumr prics, and hnc no radily availabl. Thus, workrs will no immdialy noic whn h pric lvl changs. This is why nominal wags (in 3.4) ar s basd on an xpcaion of wha h pric lvl will b Labour mark quilibrium Givn (3.2) and (3.4), h quilibrium in h labour mark is givn by: P N N, wih z N P (3.5) Equaion (3.5) rvals ha h quilibrium mploymn in his conomy dpnds on h gap bwn xpcd prics and acual prics. In cas hr ar no informaion fricions ( P P ), h conomy will opra a is naural ra of mploymn, N, jus lik in a classical world. Whn prics ar highr han xpcd, workrs will sill supply labour a h agrd nominal wag, bcaus hy do no immdialy acknowldg h fall in ral wag. Firms, in urn, will dmand mor labour bcaus hy obsrv h ral wag dclining. As long as h xpcd pric dos no chang, quaion (3.5) implis a posiiv rlaionship bwn mploymn and prics, which basically accords o h Phillips curv (s Box 3.). Th novly in h modl wih xpcaions is ha changs in h lar dsabiliz h rlaionship bwn mploymn and prics Aggrga supply In his modl, h pric lvl only influncs oupu o h xn ha i is diffrn from xpcd. Rplacing (3.5) in (3.), h gnral xprssion of aggrga supply in his modl is: P Q Q P wih Whr Q rfrs o naural oupu. Q z (3.6) 04/0/207 hp://sw.ua.p/afrias/aulas/noas%20apoio/noasmacro.hm 5

6 Poliicas macroconomicas, handou, Migul Lbr d Frias (mlbrdfrias@gmail.com) Equaion (3.6) is known as h Fridman-Lucas supply funcion. I dscribs a family of aggrga supply curvs, ach on corrsponding o a givn xpcd pric, P. Along ach curv, whn h pric lvl incrass, firms produc mor oupu bcaus ral wags dclin 2. To illusra h modl wih a simpl numrical xampl, in wha follows w rfr o h following paramrizaion: z, 0. 5, and This dlivrs h convnin bnchmark: N Q, and h supply curv bcoms simply: P Q (3.6a) P In Figur, w dpic wo aggrga supply curvs (AS), corrsponding o his paramrisaion: on for P and ohr P 2. Th fricionlss cas corrspond o LS (for Long-rm Supply), whr oupu is a is naural lvl. 2 Th spli of h conomy ino firms and workrs is a mar of xposiional convninc. On could insad hink of diffrn agns rading wih ach ohr diffrn producs. This was h approach followd by Lucas [Lucas, R., 972. Expcaions and h nuraliy of mony. Journal of Economic Thory, 4, 03-24]. Whil h Fridman modl - skchd ou abov - mphasiss fooling workrs, h Lucas vrsion of h modl mphasizs an informaion barrir shard by workrs and firms alik: in h Lucas modl all agns ar lablld as firms, which sll diffrn producs in compiiv marks and hav no conrol ovr hir own pric. Firms obsrv changs in hir own prics, bu informaion barrirs prvn hm from corrcly assring how much of hs ar accound for by indusry-spcific shocks or insad by aggrga dmand shocks. Thus, dpnding on how firms xpc h gnral pric lvl o volv, hy will rspond o pric changs by producing mor or lss. Alhough h micro paradigm is diffrn from h on us by Fridman, h implid aggrga supply funcion is h sam. Th advanag of h Lucas formulaion is ha i dosn rly on a ngaiv corrlaion bwn oupu and ral wags, which is mpirically rfud. 04/0/207 hp://sw.ua.p/afrias/aulas/noas%20apoio/noasmacro.hm 6

7 Poliicas macroconomicas, handou, Migul Lbr d Frias (mlbrdfrias@gmail.com) Figur Aggrga supply wih and wihou informaion failur Box 3.. Th Phillips curv Th ida ha hr should b a posiiv rlaionship bwn oupu and inflaion is an old on, bu i was afr h work of A.W. Phillips ha h qusion rally nrd in h macroconomic dba. Phillips documnd an mpirical rgulariy in h cas of UK, consising in a ngaiv corrlaion bwn wag inflaion and unmploymn. Two yars lar, Paul Samulson and Robr Solow implmnd a similar invsigaion for h US, and confirmd a ngaiv rlaionship bwn inflaion and unmploymn, ha hy coind as h Phillips curv 3. In is iniial formulaion, h Phillips curv was as follows: u u. (3.7) Basd on ha mpirical rgulariy, hr was a priod in which policymakrs blivd hy could xploi h rad-off bwn inflaion and unmploymn, by rducing unmploymn a a small cos in rms of addiional inflaion. Th Phillips curv bcam par of h sandard Kynsian xbook modl of h 960s. 3 Phillips, A. W. (958). "Th Rlaionship bwn Unmploymn and h Ra of Chang of Mony Wags in h Unid Kingdom ". Economica 25 (00): Samulson, Paul A., and Robr M. Solow Analyical Aspcs of Ani Inflaion Policy, Amrican Economic Rviw Paprs and Procdings 50: May, no. 2, /0/207 hp://sw.ua.p/afrias/aulas/noas%20apoio/noasmacro.hm 7

8 Poliicas macroconomicas, handou, Migul Lbr d Frias (mlbrdfrias@gmail.com) This viw was srongly criicizd by Milon Fridman. In his 968 prsidnial addrss o h Amrican Economic Associaion, Fridman criicizd h Phillips curv on h grounds ha i nglcd h rol of xpcaions 4. Fridman hn proposd h xpcaions-augmnd Phillips curv, givn as follows: u u. (3.7a) In rms of h modl abov, h xpcaions-augmnd Phillips curv corrsponds o h supply funcion (3.6), bu in a log-linar vrsion of h modl. Formally, on mus firs subsiu (3.4) in (3.) and ak logs, obaining: q ln z ln p w (3.3a) whr lowrcas lrs dno h logarihms of h corrsponding upprcas variabls. Th linar quaion quivaln o (3.4) is: w p ln, (3.4a) Rplacing (3.4a) in (3.3a), w g: q q p p (3.6b) q ln. whr ln z ln Adding and subracing p o h rm in bracks in (3.6b) and dfining p p, and p p w g: q (3.7b) q Mdiaing (3.7b) and h Phillips curv (3.7a) hr is anohr sylizd fac, known as h Okun s Law. Th Okun s Law says ha h disanc bwn h acual and h naural ra of unmploymn is a ngaiv funcion of h disanc bwn acual and naural q q u u. Rplacing in h quaion abov, w g (3.7a). oupu. Formally, his is As w can infr from h modl, h iniial formulaion of h Phillips curv (3.7) would only b possibl in a world in which workrs wr concrnd wih nominal wags (insad of ral wags). In ha cas, i would b possibl for monary policy o chang rlaiv prics in a prmann mannr, giving ris o ral ffcs. In h mor ralisic cas in 4 Milon Fridman (968). Th Rol of Monary Policy. Amrican Economic Rviw, 58, /0/207 hp://sw.ua.p/afrias/aulas/noas%20apoio/noasmacro.hm 8

9 Poliicas macroconomicas, handou, Migul Lbr d Frias (mlbrdfrias@gmail.com) which agns ar concrnd wih ral wags, nominal variabls ar s according o xpcd changs in h consumr pric indx. Thus, h nir Phillips curv shifs upwards whn xpcd inflaion incrass (q. 3.7a) Equilibrium of h modl In lin wih h classical radiion, l s assum ha h quaniaiv hory of mony holds, and ha mony vlociy is qual o. Hnc, aggrga dmand is givn by h mony mark quilibrium: M PQ (3.8) Th wo main quaions of h modl ar aggrga supply (3.6) and aggrga dmand, (3.7). Solving hs wo quaions oghr, on obains h quilibrium lvls of oupu and of prics: P P M Q (3.9) M Q Q (3.0) P For insanc, whn M= and P, w hav P= and quilibrium is dscribd by poin 0 in Figur. Q Q. This paricular Inflaion surpris Rurning o Figur, suppos ha our conomy is iniially in a fricionlss quilibrium, wih M= and P P (poin 0). Thn, assum ha h mony supply unxpcdly shifs, onc-and-for-all, o M=4. Th incras in mony supply givs ris o an incras in h pric lvl, bu workrs ar sill xpcing h pric lvl o b qual o on. Th fac ha h pric lvl incrass ahad of xpcaions causs h ral wag ra o dclin, mploymn o incras, and oupu o xpand abov full mploymn. Th quilibrium in h oupu mark following h monary surpris is dscribd by poin in Figur 2. This poin corrsponds o h inrscion of h nw aggrga dmand, 4 PQ, wih h aggrga supply wih P, Q P, implying P Q 2. 04/0/207 hp://sw.ua.p/afrias/aulas/noas%20apoio/noasmacro.hm 9

10 Poliicas macroconomicas, handou, Migul Lbr d Frias (mlbrdfrias@gmail.com) Figur 2 Equilibrium in h oupu mark following an inflaion surpris Th rason undrlying h shif in oupu ahad of full mploymn is ha firms, obsrving h fall in ral wag, opimally dcid o hir mor labour. This is illusrad in Figur 3: bcaus h pric lvl doubld, ral wags halvd. Hnc, firms incrasd hir dmand for labour, hiring N=4 and hrfor xpanding producion o Q=2. Figur 3 Equilibrium in h labour mark following h inflaion surpris I is imporan o no ha in poin workrs ar ou of hir labour supply. Howvr, workrs will only prciv his in a lar sag, whn h informaion rgarding h pric lvl bcoms availabl. In his modl, h labour mark clars x an : wags ar s such ha h labour mark is xpcd o clar. Howvr, h labour mark dos no ncssarily clar x pos. Th labour mark clars in xpcaions only. Wih his rasoning, on can gnra dparurs from full mploymn, vn in a conx whr prics ar flxibl Shor run and long run Th main ida bhind his modl is ha agns may lack all h informaion hy nd o accuraly mak hir conomic dcisions. In paricular, popl may no prciv a chang in h pric lvl causd by a monary shock. Thus, vn if wags ar inhrnly flxibl, 04/0/207 hp://sw.ua.p/afrias/aulas/noas%20apoio/noasmacro.hm 0

11 Poliicas macroconomicas, handou, Migul Lbr d Frias (mlbrdfrias@gmail.com) agns may fail o adjus hir labour conracs, dparing from hir opimal pahs. In h aggrga, his rsuls in flucuaions of oupu around is naural ra. No ha h quilibrium dscribd in poin can only occur in h shor run. Soonr of lar, workrs will cach on o h fac ha hir purchasing powr has dclind. Th xpcd pric will b rvisd upwards and a highr nominal wag ra will b dmandd. Hnc, h aggrga supply curv shifs upwards. In h long run, informaion failurs vanish and h conomy rurns o is naural lvl (poin T in Figur 2, Poin 0 in Figur 3). This is why in his modl w hav a shor run aggrga supply (AS) and a long run aggrga supply (LS): in h long run, hr ar no informaion failurs and h implid aggrga supply is vrical, mimicking h classical cas. Th criical qusion is how long i will ak for workrs o corrcly guss h pric lvl: - If h adjusmn in xpcaions is slow, h businss cycl will b long-lasing. - If h adjusmn in xpcaions is fas, h businss cycl will b shor-livd. As w will s in a minu, hs wo cass mark h disincion bwn h iniial assumpion of backward looking xpcaions mad by Milon Fridman and ha of raional xpcaions, inroducd by Robr Lucas. 3.3 Th modl wih backward looking xpcaions In a sminal papr, dvlopd as par of is Prsidnial Addrss o h Amrican Economic Associaion in 967, Fridman offrd an xplanaion o h apparn rad-off bwn inflaion and unmploymn undrlying h Phillips curv. H conndd ha, bcaus of informaion failurs, monary xpansions caus oupu o xpand ahad of is naural lvl. In h long run, howvr, hr will b no rad-off bwn inflaion and unmploymn 5. Wih his hory, Fridman r-sad h ffcivnss of monary policy in h shor run and h classical proposiion of mony nuraliy in h long run Adapiv xpcaions Th assumpion of adapiv xpcaions prsums ha agns collc informaion on h pas valus of a givn variabl and us his informaion o guss h fuur valus of ha 5 Th sam conclusion was indpndnly discovrd by Fridman and h Kynsian conomis Edmund Phlps: Fridman, M., 968. Th rol of monary policy. Amrican Economic Rviw 58, -7. Phlps, Edmund S. Phillips Curvs, Expcaions of Inflaion and Opimal Employmn ovr Tim. Economica, n.s., 34, no. 3 (967): /0/207 hp://sw.ua.p/afrias/aulas/noas%20apoio/noasmacro.hm

12 Poliicas macroconomicas, handou, Migul Lbr d Frias (mlbrdfrias@gmail.com) variabl. In our cas, workrs ar assumd o guss fuur prics basd on h prics obsrvd in h pas. Th simplr modl in his cagory is as follows: P P (3.) Tha is, workrs xpc his priod prics o b qual o h lvl obsrvd in h las priod Monary surpris Considr again h monary surpris a im =, from M= o M=4. A =, workrs wr xpcing P, bcaus his was h pric lvl obsrvd a =0. Thus, h monary shock causs h conomy o mov o poin in Figur 4, jus lik in Figur 2. In momn =2 workrs xpc P 2 2, bcaus his is h pric obsrvd in =. In Figur 4, his is dscribd by h upward shif in h shor rm aggrga supply o Q P Th nw shor rm quilibrium (=2) occurs in poin 2, wih P 2 8, and Q 2 2 (s and 3.0). Thn, in priod =3, h workr will xpc P 3 8, implying a furhr upward mov in h aggrga supply, and so on. Thus, vn if mony supply shifd onc-and-for-all, h backward looking workr will b foold and foold again, unil h final poin T is rachd. 6 This cas is known as naïv, and is a paricular cas of adapiv xpcaions. Wih adapiv xpcaions, h xpcd pric ach yar is qual o h prvious yar xpcaion plus a parial-adjusmn rm, corrcing for h prvious yar forcasing rror: P P P P, wih 0. Whn adapiv xpcaions can quivalnly b wrin as a disribud lag of prvious yars prics, wih wighs j dclining xponnially a ra : P P j. Th lowr h valu of, h grar h inria j in xpcaions. Whn 0, xpcaions ar myopic and nvr rvisd (as implid by h original Phillips curv). Whn, w hav h naïv modl abov. 04/0/207 hp://sw.ua.p/afrias/aulas/noas%20apoio/noasmacro.hm 2

13 Poliicas macroconomicas, handou, Migul Lbr d Frias (mlbrdfrias@gmail.com) Figur 4 Adjusmn undr adapiv xpcaions In sum: h fac ha workrs gradually adap hir xpcaions implis ha following a onc-and-for-all shif in h mony supply, oupu will ak im o rurn o is naural lvl. Fridman conndd ha h procss hrough which workrs adjus hir xpcaions can b surprisingly long. Manwhil, a businss cycl was gnrad 7. In h long run, howvr, h Quaniaiv Thory will show up and oupu will b indpndn of h pric lvl: in h long run, hr is no rad off bwn inflaion and oupu, Fridman claimd. Th absnc of a long-rm rad-off bwn inflaion and unmploymn sms o accord br wih h vidnc during h inflaion yars of h 970s and h 980s. An implicaion of h modl wih adapiv xpcaions is ha i is difficul o rduc inflaion quickly wihou a significan incras in unmploymn. In rms of our modl, a sharp conracion in h mony supply would giv ris o an incras in ral wags and low mploymn. Bcaus workrs ar slow in adjusing xpcaions, oupu losss will prsis ovr im. Undr adapiv xpcaions, a gradualis policy, lik a slow dclin in h ra of mony growh, looks lik bing h bs sragy o rduc inflaion Surprising and surprising again Th prvious xrcis rlis on h assumpion ha h incras in mony was oncand-for all. If mony was allowd insad o xpand vry yar, would i b possibl o kp h conomy opraing abov is naural mploymn lvl on a prmann basis? 7 Toghr wih Anna Schwarz, Fridman wro A monary hisory of h Unid Sas, In his volum, h auhors conndd ha businss cycls in h US wr mosly accound for by changs in monary condiions. Thy also connd ha h Gra Dprssion was h rsul of a ragic policy misak : h dclin in h mony supply causd by bank failurs could hav bn avoidd by h Fdral Rsrv, and i wasn. 04/0/207 hp://sw.ua.p/afrias/aulas/noas%20apoio/noasmacro.hm 3

14 Poliicas macroconomicas, handou, Migul Lbr d Frias (mlbrdfrias@gmail.com) To answr his qusion, l s considr again h main quaions of our modl, aggrga supply (3.6) and aggrga dmand (3.8). Also considr h simpl cas in which N Q. Suppos ha h monary auhoriis wr arging h oupu lvl Q=2. How much should b h amoun of mony ach yar? Rplacing (3.8) in (3.8), and using h assumpion of adapiv xpcaions (3.7), on obains M Q M Q Q P M Q Sing Q=2 vry yar, his givs M M 2 Tha is, i would b possibl o mainain oupu sysmaically abov full mploymn, if mony supply doubld ach priod. Wih such rul, prics would b incrasing sysmaically ahad of wags, fooling h workr coninuously. Figur 5 illusras h succssiv quilibria undr h assumpion ha h monary auhoriis ar doubling mony vry priod, surprising workrs again and again. Figur 5 Dmand pull inflaion undr saic inflaion xpcaions No ha poins, 2, and 3 dfin a Phillips curv corrsponding o an xpcd inflaion qual o zro (agns xpc h pric lvl o b h sam as las yar). Along h quilibria, 2, 3, howvr, prics doubl ach yar, implying an inflaion ra of 00%. Sinc acual inflaion is highr han xpcd inflaion, oupu is abov full mploymn. In Box 3.2 w show ha h inflaionary impac of h policy is vn highr if workrs form xpcaions in rms of inflaion, rahr han in rms of h pric lvl. Box 3.2. Adapiv xpcaions and h acclraionis hypohsis In h xampls abov, w xamind h implicaions of changs in h quaniy of mony on h pric lvl. In h ral world, howvr, h mony supply xpands vry yar, and popl ar concrnd wih inflaion, no wih h pric lvl. Th righ ool o hink h inflaion-oupu rad off is h Phillips curv. 04/0/207 hp://sw.ua.p/afrias/aulas/noas%20apoio/noasmacro.hm 4

15 Poliicas macroconomicas, handou, Migul Lbr d Frias (mlbrdfrias@gmail.com) Fridman argud ha amps o kp unmploymn low a h xpns of highr inflaion would rsul in highr inflaion xpcaions. Fridman assumd ha inflaion xpcaions ar formd adapivly. Th naïv cas is: (3.a) Rplacing his in (3.7a), w g: u u This quaion suggss ha i is possibl o kp unmploymn sysmaically blow is naural ra, wih an vr incrasing inflaion ra. An incrasing inflaion ra would allow prics o oupac wags ach momn in im, fooling h workrs again and again. This implicaion of h modl is lablld h acclracionis hypohsis. To s h diffrnc rlaiv o h modl in lvls, no ha h naïv xpcaion in prics (3.) corrsponds o a myopic xpcaion in rms of inflaion: in Figur 5, along poins, 2 and 3 xpcd inflaion is always zro. Had popl guss inflaion in priod 2 o b qual o ha obsrvd in priod and h AS curv would hav shifd from Q=P in = o Q=P/4 in =2, drmining lowr oupu gap. Hnc, if h govrnmn wand oupu o rmain a Q=2, i would nd o accp an vr-incrasing inflaion ra. This is h acclraionis proposiion. Whn howvr h inflaion ra is consan, h modl dlivrs u u. Using his modl, Fridman inroducd h concp of h NAIRU h non-acclraing inflaion ra of unmploymn, u Summing up Kyns connd ha oupu may dvia from full mploymn bcaus of sicky prics. Focusing in h Gra Dprssion, Kyns advocad ha monary policy was inffciv and fiscal policy should hav bn usd. Fridman showd ha i is possibl o gnra businss cycls in a modl whr prics ar flxibl, bcaus of informaion failurs. In h scop of his modl, Fridman rsord h ffcivnss of monary policy, vu only in h shor run: in h long run, h classical dichoomy holds. As for h rol of policy, Fridman was rahr consrvaiv: alhough h cnral bank has h powr o xpand conomic aciviy, a qusion ariss as whhr such powr should b usd a all. Indd, in h absnc of monary surpriss, h conomy will opra a is naural lvl, wih workrs ging h ral wag hy wan. In conras, undr monary insabiliy, agns will dpar from hir supply curvs and hr will b undsirabl flucuaions of oupu around is naural lvl. This obsrvaion, oghr wih h claim ha 8 No howvr ha whn h unmploymn ra is blow h naural ra h inflaion ra is incrasing, no acclraing: wha is acclraing is h pric lvl. 04/0/207 hp://sw.ua.p/afrias/aulas/noas%20apoio/noasmacro.hm 5

16 Poliicas macroconomicas, handou, Migul Lbr d Frias (mlbrdfrias@gmail.com) policymakrs may lack h knowldg or h will o righly implmn sabilizaion policis 9 ld Fridman o dfnd ha cnral banks should follow simpl mony supply ruls, such as a sing h mony supply o grow a a consan ra ovr im (hnc, h labl monarism ). Wih ruls, surpriss would b minimizd and h conomy should opra clos o full mploymn. 3.4 Raional xpcaions Th assumpion of adapiv xpcaions proposd by Fridman is a srong on. Wih adapiv xpcaions, agns ar no givn h possibiliy of procssing opimally h informaion and larn wih pas misaks. Rfrring o h xampl in Figur 4, on may qusion whhr i would b rasonabl o bliv ha, following h onc-and-for-all shif in mony supply, workrs ngag in a squnc of sysmaic forcasing rrors all h way from o T. In alrnaiv, Robr Lucas and Thomas Sargn proposd ha agns should b raional 0. Undr raional xpcaions, popl ar forward-looking and mak h bs possibl forcas givn h all informaion hy hav. This is mor han jus using h pas informaion on h forcasing variabl. Undr raional xpcaions, forcass hav o ak ino accoun wha agns xpc o happn in h fuur (agns ar forward-looking), and hy hav o b formulad in consisncy wih h modl dscribing h conomy (raional xpcaions ar modl-consisn). In our modl, popl do no know xacly how much h cnral bank will xpand h mony supply (hr is uncrainy), bu hy ar awar of h mchanics hrough which changs in mony supply affc prics. Mor prcisly, popl ar assumd o undrsand Figur 4 and b awar of quaion (3.9). Thus, popl will know ha M= and P imply P= (poin 0); ha P and 0.5 M=4 imply P=2 (poin ); and ha P 2 and M=4 imply P 8 (poin 2). Wih his modl in mind, popl will raliz ha hr is no poin in gussing P 2 whn M=4, bcaus 9 Firs, govrnmns may lack rlvan informaion, such as h ru valu of muliplirs and h naural lvl of oupu. If, for insanc, h naural oupu is ovrsimad, hr is a risk of policymakrs o ngag in fuil xpansionary policis which only rsul is inflaion. This is likly o hav bn h cas in h arly 970s. Scond, policy acions ar ffcd by diffrn yps of lags, such as in h dcision-making procss, in implmnaion, and in h ransmission o h ral conomy. Hnc, h risk xis ha, onc h govrnmn sars o ac and h ffcs of h policy ar ransmid o h conomy, h lar is alrady on is way o full mploymn, risking mor insabiliy. Third, policy makrs ar influncd by lobbis, lcion calndars and ohr prssurs. Hnc, hir acions may dvia oo much from h public inrs. 0 Lucas, R., 972, op. ci. Forward looking xpcaions had alrady bn accound for in h work of Edmund Phlps, hough wihou raional xpcaions. Raional xpcaions wr firs proposd by John Muh, in 962 (Raional xpcaions and h hory of pric movmns, Economrica 29, 35-35). 04/0/207 hp://sw.ua.p/afrias/aulas/noas%20apoio/noasmacro.hm 6

17 Poliicas macroconomicas, handou, Migul Lbr d Frias (mlbrdfrias@gmail.com) such prdicion would imply frusrad xpcaions. If popl xpc h mony supply o b M 4, h only consisn xpcaion is P Prfc forsigh To br undrsand how h modl works undr raional xpcaions, l s considr firs h xrm cas wih no uncrainy: suppos ha popl know xacly whr h aggrga dmand curv ach momn in im is. This cas is lablld prfc forsigh. Rfrring o our prvious xrcis, if agns know ha M= a =0 and M=4 a =, popl will righly guss ha P 0 and P 4. Thus, h conomy will immdialy mov from poin 0 o poin T in Figur 6. Undr prfc forsigh hr ar no forcasing rrors, and h cnral bank is unabl o dvia h conomy from is naural ra. Sinc hr is no uncrainy, quilibrium rquirs ha h pric lvl and h xpcd pric lvl ar qual. Th prfc forsigh soluion of h modl (3.9) on for ach lvl of M - is obaind sing P P, which givs: M P (3.2) Q Raional xpcaions and forcasing rrors Ofn, h concp of raional xpcaions is confusd wih ha of prfc forsigh. Undr prfc forsigh hr is no informaion failur: popl always know h righ posiion of aggrga dmand. Undr flxibl prics, his implis ha h conomy will b always a full mploymn. Undr raional xpcaions, popl ar uncrain rgarding h marializaion of ky xognous variabls: in our modl, h mony supply is unknown. Thrfor, popl mak hir bs guss for h posiioning of h aggrga dmand curv, givn h informaion hy hav. This includs h srucur of h modl, h pas bhaviour of h cnral bank, or any ohr rlvan informaion availabl. Sinc hr is no full informaion, forcasing rrors ar possibl. Howvr, xpcaions will b consisn wih h modl and popl will larn wih pas misaks. Rurning o our prvious xampl, suppos ha popl xpcd h aggrga dmand curv o li a PQ= in priod =. Why should ha b? Assum, for insanc, ha in h rcn pas, h mony supply had bn consan a M=, bcaus ha was h nominal anchor h cnral bank lcd for is policy. In h absnc of any novly signalling a chang in h cnral bank bhaviour, ha will b h bs forcas for M, and accordingly h bs forcas for P will b P. This mans ha h shor-rm aggrga supply curv will b Q=P. Thn, any dviaion of h aggrga dmand from his prdicd lvl will giv ris o frusrad xpcaions and dviaions from full mploymn. Bu hr is nohing popl can do o limina such dviaion: wih h informaion hy had, h bs forcas had bn alrady mad. 04/0/207 hp://sw.ua.p/afrias/aulas/noas%20apoio/noasmacro.hm 7

18 Poliicas macroconomicas, handou, Migul Lbr d Frias (mlbrdfrias@gmail.com) Figur 6 Surpris vrsus prfc forsigh Th policy inffcivnss proposiion An imporan implicaion of raional xpcaions is ha anicipad changs in monary policy produc no ral ffcs. To s his, suppos ha, dparing from poin 0 in Figur 6, h cnral bank crdibly announcd ha h mony supply would xpand onc-andfor all o M=4. In ha cas, popl would acknowldg h nw posiion of aggrga dmand and would guss h pric lvl o b P=4. Thus, h shor rm aggrga supply would shif immdialy o Q=P/4, and h nw quilibrium would b poin T a =. Undr raional xpcaions and flxibl prics, an anicipad monary xpansion canno produc ral ffcs. This conrass o h cas in which agns ar caugh by surpris. If h cnral bank crdibly announcd M=, bu hn surprisd vrybody wih M=4, a shor rm quilibrium would b m a P=2, and oupu would hav xpandd o Q=2. Undr raional xpcaions, monary surpriss produc ral ffcs. By h sam okn, if h cnral bank crdibly announcd M=4 bu hn i missd h arg by som small diffrnc (say M=4.0804), hn hr would b a ral ffc (Q=.0), bu only in h proporion of h unprdicd componn of h monary xpansion: h par of h monary xpansion ha was anicipad impacd dircly on prics wihou dlivring ral ffcs. Wih his modl in mind, on can s why an quilibrium lik h on dscribd by poin 2 in Figur 4 canno occur undr raional xpcaions: agns caugh by surpris by h xpansion of mony a =, should ry o mak a consisn forcas for h pric lvl a =2 onc hy ralizd ha h mony supply had xpandd o M=4 a =. In cas popl xpcd h mony supply o rmain a M=4, h consisn forcas for h pric lvl a =2 formulad in momn = would b E P2 4. Th monary surpris would hav producd ffcs in =, bu afr h nw mony supply bcam known, hr would b no rason for workrs o b foold again: workrs should accuraly adjus hir xpcaions, moving h aggrga supply a onc o is final posiion. Th quilibrium dscribd by poin T would b 04/0/207 hp://sw.ua.p/afrias/aulas/noas%20apoio/noasmacro.hm 8

19 Poliicas macroconomicas, handou, Migul Lbr d Frias (mlbrdfrias@gmail.com) rachd in momn =2, and no afr many priods, during which workrs ar sysmaically foold by inconsisn gusss, as Fridman assrd. Th samn ha anicipad changs in mony hav no ffc on conomic aciviy is known and h policy inffcivnss proposiion. Th policy inffcivnss proposiion dos no rul ou oupu ffcs from unxpcd policy changs: monary surpriss will, in gnral, giv ris o ral ffcs. Ths ral ffcs will b howvr shorlivd, bcaus popl will rapidly adjus hir xpcaions. Ths conclusions hav implicaions for h dsign of a disinflaion programm. W saw ha undr adapiv xpcaions, a gradualis policy will in gnral com along wih lowr oupu coss han a policy ha ris o rduc vry sharply h inflaion ra in a small priod of im. Wih raional xpcaions, howvr, h sory is diffrn: wha mars for h coss of a disinflaion programm is h xn o which i is anicipad and popl bliv in i. This rasoning lad som auhors o argu h sociy would b br off if h cnral bank followd a shock hrapy ( cold urky ), han rying o b smooh. Th rason is ha his would b crdibiliy-nhancing, allowing agns o align fasr hir xpcaions wih h policymakr innions, dlivring fasr pric adjusmn and lowr oupu coss. Box 3.3: Only surpriss mar! To s how monary surpriss giv ris o ral ffcs in a modl wih inflaion, l s rurn o h linar vrsion of our modl, as dscribd by quaion (3.6b) plus a log vrsion of (3.8): q m p (3.8a) Using (3.6b) and (3.8a), h log-linar quivaln o (3.9) and (3.0) ar: E p m q p (3.9a) m E p q q (3.0a) In his formulaion, w rplacd p by E p o srss h fac ha h xpcaion was formulad basd on all h informaion availabl in h priod bfor. Taking xpcaions basd on h availabl informaion availabl a im -, w g: E E p E m p q Solving for p E p E m q, w obain h raional xpcaions forcas: E (3.2a) Sargn, Thomas & Wallac, Nil (975). "'Raional' Expcaions, h Opimal Monary Insrumn, and h Opimal Mony Supply Rul". Journal of Poliical Economy 83 (2): /0/207 hp://sw.ua.p/afrias/aulas/noas%20apoio/noasmacro.hm 9

20 Poliicas macroconomicas, handou, Migul Lbr d Frias (mlbrdfrias@gmail.com) You may compar his quaion o h soluion of h modl undr prfc forsigh (3.2): in h crainy cas, h pric lvl is proporional o mony; in h cas wih imprfc informaion, h forcas of h pric lvl has o b proporional o wha popl xpc h mony supply o b. Subsiuing his back in (3.0a), on obains: m E m q q (3.3) Dnoing for h forcasing rror, ha is, h diffrnc bwn h acual mony supply and h xpcd mony supply, w g: q q This quaion shows ha oupu only diffrs from is naural lvl o h xn ha agns ar surprisd by unxpcd incrass in h mony supply. Whn h mony supply is corrcly anicipad ( 0 ), hn oupu will b a is naural lvl. Undr raional xpcaions and flxibl prics, only surpriss produc ral ffcs Th call for a Ral Businss Cycls Thory In our days, informaion lags rgarding h consumr pric indx ar vry shor-livd. Hnc, any dparur of acual oupu from is naural ra bcaus of a monary disurbanc should b ncssarily shor-livd as wll. Wih raional xpcaions and flxibl prics, monary policy can no longr b a good candida o xplain businss cycls. Wih such a conclusion, Lucas conndd ha conomiss should urn o xplanaions for h businss cycls no rlying on informaion failurs and nominal shocks: If dviaions from full mploymn oupu ar so shor-livd, conomiss should urn o xplaining conomic flucuaions in h conx of flxibl prics. This was h agnda of h ral businss cycls hory 2. Proponns of h Ral Businss Cycls hory shifd h analysis away from informaion failurs and monary surpriss, o focus on produciviy shocks and ohr fricions ha caus flucuaions of h naural ra of oupu, rahr han flucuaions of acual oupu around is naural lvl. Th ral businss cycls hory absracs from informaion failurs, posulaing ha h conomy is always a full mploymn (h aggrga supply is vrical, vn in h shor run). Sinc produciviy shocks nd o b prsisn ovr im, h hory accouns for muliyar businss cycls, wihou h nd o rly on informaion lags. 2 Kydland, Finn; E. C. Prsco (982). "Tim o Build and Aggrga Flucuaions". Economrica 50 (6): King, R., Plossr, C., 984. "Mony, Crdi, and Prics in a Ral Businss Cycl," Amrican Economic Rviw, 74(3), /0/207 hp://sw.ua.p/afrias/aulas/noas%20apoio/noasmacro.hm 20

21 Poliicas macroconomicas, handou, Migul Lbr d Frias (mlbrdfrias@gmail.com) Th slop of h supply curv As w jus saw, onc agns raliz ha h mony supply shifd from a consan mony rul a M= o a novl M=4 a momn =, hy undrsand hy nd o rvis hir xpcaions. Th bs forcas implis, howvr, undrsanding h cnral bank innions. Agns should ask: why did h cnral bank chang h mony supply? Was his a onc-andfor-all mov? Or insad his was marking a chang in h monary rgim? Considr for a momn ha h announcmn ha h mony supply shifd oncand-for-all o M=4 was crdibl. If agns g convincd ha h cnral bank jus adopd a nw arg a M=4, hy will forcas E P2 4. In ha cas, h nw AS curv will b Q P 4. Thn, if h mony supply M=4 acually marializs, hr will b no mor ral ffcs. For h cnral bank, his could consiu a lsson: looking a h iniial AS curv, dscribd by Q=P, h cnral bank migh hav acknowldgd ha his curv implid a givn rad-off bwn inflaion and oupu. Th siz of his rad-off rlid howvr on a pas xprinc of monary sabiliy: i is bcaus mony supply was sabl unil =0 ha h slop of h AS curv was as i was. By unxpcdly xpanding h mony supply o M=4 a =, h cnral bank has xplord h rad-off implid by h slop of h AS curv, producing P=2 and Q=2. In ohr words, an oupu gap amouning o Q Q was achivd wih a pric incras of P (h rlaionship bwn Q Q and P can b inrprd as h slop of a Phillips curv). Howvr, h ral xpansion lasd for on priod only: onc popl ralizd ha h nw mony supply had incrasd o M=4, hy adjusd h xpcaions accordingly, roaing h AS curv upwards. This xampl illusras a ky rsul in modls wih raional xpcaions: onc policymakrs ry o xplor h rad-off bwn inflaion and unmploymn implid by h slop of h aggrga supply, h slop changs. Th iniial slop of h AS curv rflcd an arlir hisory of monary sabiliy. Afr h policy chang, h AS supply curv bcam much spr, implying ha a highr inflaion surpris will b ndd o gnra h sam oupu xpansion. In cas popl anicipa M o rmain a M=4, h nw AS curv will b Q 4 P. Thus, h pric lvl will nd o incras from P=2 o P=8 ( P 6 ) o gnra a similar oupu xpansion. Of cours, hings will g vn wors if popl bcom suspicious abou h innions of h cnral bank: afr all, i h cnral bank surprisd vrybody wih M=4 whn popl wr xpcing M=, why shouldn h cnral bank ry o surpris again (sing M=6) afr convincing vrybody ha M will rmain qual o 4? No in ha cas, in cas popl xpc M=6, h aggrga supply curv jumps o Q=P/6, bcoming vn spr: h lowr h crdibiliy of h cnral bank, h spr will b h aggrga supply, implying ha an vn highr inflaion will b ndd o gnra h sam oupu xpansion. In sum: iniially, h rus in monary sabiliy auhoriis crad h ponial for h cnral bank o xplor h posiiv rlaion bwn prics and oupu implid by h shor rm aggrga supply curv. Afr his rad-off was xplord, howvr, achiving h sam oupu gap will rquir much highr incras in prics: as popl larn wih pas misaks, par of h monary xpansion will b anicipad and will impac dircly on prics wihou 04/0/207 hp://sw.ua.p/afrias/aulas/noas%20apoio/noasmacro.hm 2

22 Poliicas macroconomicas, handou, Migul Lbr d Frias (mlbrdfrias@gmail.com) any ral ffc. Thus, a much highr inflaion ra will b ndd o achiv h sam oupu gap. In ohr words, h Phillips curv bcoms spr. Wih his rasoning, on may guss ha an inflaion surpris is likly o produc mor ral ffcs in h Euro Ara han in Vnzula: - In Vnzula, whr inflaion has bn xrmly volail and high, a monary xpansion will hardly surpris agns, implying ha h Phillips curv hr is almos vrical. - In conras, in h Euro Ara, whr h pas xprinc has bn of monary sabiliy, h slop of h Phillips curv is modra. This mans ha h ECB has h ponial o xpand oupu by craing an inflaion surpris. Th problm howvr is ha onc h monary auhoriis ry o xplor h rad-off, h rad-off will dissipa: h Phillips curv will bcom spr and spr, approaching h limiing cas of ha in Vnzula. All in all, alhough hr is a ponially ngaiv rad-off bwn inflaion and unmploymn, his rad-off rapidly disappars onc h monary auhoriis ry o xplor i. Box 3.3. Th Lucas criiqu Th changing slop of h Phillips curv is an illusraion of a ky implicaion of raional xpcaions: h saisical rlaionship bwn wo variabls may chang whn h policy changs, bcaus xpcaions also chang. This fac poss a srious limiaion o h us of conomric modls for policy formulaion and forcasing. This argumn is known as h Lucas Criiqu 3. To s his in rms of our modl, l s assum ha h mony supply has followd h sochasic procss: m m 0 (3.4) wih bing a whi nois. In ligh of (3.4), h mony supply has bn incrasing a h ra 0 (policy arg), bu hr ar unprdicabl shocks, rflcing h cnral bank inabiliy o xacly conrol h mony supply. In ha cas, h bs forcas for h mony supply a momn will b: E m m 0 3 Lucas, Robr (976). "Economric Policy Evaluaion: A Criiqu". In Brunnr, K.; Mlzr, A. Th Phillips Curv and Labor Marks. Carngi-Rochsr Confrnc Sris on Public Policy. Nw York: Amrican Elsvir. pp /0/207 hp://sw.ua.p/afrias/aulas/noas%20apoio/noasmacro.hm 22

23 Poliicas macroconomicas, handou, Migul Lbr d Frias (mlbrdfrias@gmail.com) Popl ar awar ha unprdicabl shocks will caus h aggrga dmand o vibra around h xpcd posiion, givn ris o ral ffcs, bu sinc hs shocks ar unprdicabl his is h bs forcas popl can mak. Subsiuing his in (3.3), givs h following quaion dscribing oupu: q q m m 0 (3.3a) No ha (3.3a) is no diffrn from (3.3): boh say ha only forcasing rrors (marializaions of ), produc dviaions of oupu from full mploymn. In (3.3a), howvr, h quaion for oupu is formulad in rms of h chang in mony supply, showing ha h mony rul oghr wih h supply curv giv ris o a saisical rgulariy involving h oupu gap, q q, and h acual ra of mony growh m m. If h cnral bank rid o sima an quaion for h oupu gap as a funcion of mony craion, i would probably obsrv ha changs in mony hav bn associad o dparurs of oupu away from full mploymn. Th simad quaion could b of h form: q q aˆ bˆ m Basd on h simaion rsuls, h cnral bank could ry o xplor h rlaionship bwn oupu and mony, changing h mony rul o: m m wih 0. Howvr, such a shif would only produc significan ral ffcs a h vry bginning. Afr popl raliz ha h mony rul has changd, hy will guss m, and only h unprdicabl rror will mar again. m Th imporan poin o mak is ha h policy chang alrd a cofficin in h rgrssion quaion, in his cas h inrcp. Wih h chang in xpcaions, h nw rlaionship bwn oupu and mony bcoms q q m m, implying ha h inrcp of h rgrssion quaion changs o a. Thus, onc h policymakr usd h conomric rlaionship for policy purposs, h conomric rlaionship has changd. In sum: conomric simas dscrib rlaionships bwn conomic variabls as hy hld in h pas, undr pas policis. Whnvr policy (h ruls of h gam) changs, h way popl form xpcaions will also chang. Hnc, h paramrs and lasiciis simad using pas daa will b a poor guid o wha will happn in rspons o a policy chang. This is h Lucas Criiqu Unprdicabl oucoms Undr raional xpcaions, popl larn wih pas misaks. Hnc, if h monary auhoriis insis in xpanding oupu ahad of is naural lvl, popl will bcom awar of h cnral bank innions, urning h cnral banks aim incrasingly difficul o b achivd: in ordr o surpris and kp surprising, h cnral bank would nd o b incrdibly imaginaiv. 04/0/207 hp://sw.ua.p/afrias/aulas/noas%20apoio/noasmacro.hm 23

24 Poliicas macroconomicas, handou, Migul Lbr d Frias (mlbrdfrias@gmail.com) To illusra his, w rfr o Figur 7: will i b possibl for a cnral bankr facing raional agns o kp h conomy opraing a Q=2? In h figur, poin 0 dscribs h iniial siuaion in which M M, and poin dscribs h quilibrium afr h monary auhoriis unxpcdly xpandd mony o M=4. Th inrsing qusion is wha happns nx priod. Will popl rus ha h mony xpansion was onc-and-for all? Of cours, w don know. Now, h quilibrium will dpnd on how popl inrpr h words and acions of h cnral bank, and on how h cnral bank xpcs popl o rac o is words and acions. Th rsul is uncrain. For a momn, assum ha h cnral bank, aiming o fool agns again, succssfully convincd h public ha h monary xpansion o M=4 was onc-and-for all. Assuming ha popl blivd and conjcurd M 4 - implying a nw AS curv wih h slop Q P 4 - h cnral bank could ry o surpris again, sing M=6. Th implid quilibrium is dscribd by poin 2 in Figur 7. Now pu yourslf in h workr shos a h im =3. Suppos h cnral bank promiss ha mony will sand a M=6. Of cours, you will no bliv. You would hav larnd wih h pas misaks. Evnually, you will conjcur ha h cnral bank wans you o xpc M=6, o fool you again, sing M=32, achiving Q=2 (his cas is dscribd by poin 2 in Figur 7). Bu if you anicipa M 32, h policy will no produc any ffc (poin 3). Of cours, h cnral bank can ry o surpris you wih M=64. Bu will ha work? Figur 7 Undr RE, popl larn abou h CB innions Undr raional xpcaions, h cnral bankr would nd o b incrdibly imaginaiv o kp surprising and surprising again. And mos probably, h rsul of such amp would b a highly dsabilizing monary policy. In alrnaiv, considr h cas in which h cnral bank, finally concrnd wih inflaion, dcidd o kp h mony supply consan a M=6, bu popl wr alrady gussing M=32. In ha cas, sicking wih h promis M=6 would imply a rcssion (poin 4). Would h cnral bank mainain h promis, sing M=6 dspi M 32 and accp a 04/0/207 hp://sw.ua.p/afrias/aulas/noas%20apoio/noasmacro.hm 24

25 Poliicas macroconomicas, handou, Migul Lbr d Frias (mlbrdfrias@gmail.com) rcssion? Or would i insad accommoda h rising inflaion xpcaions sing M=32, o avoid a rcssion bu validaing an ongoing inflaion? (poin 3). This discussion illusras how difficul i is o guss wha h quilibrium undr raional xpcaions will b. Expcaions dpnd on h cnral bank policy, and h lar dpnds on xpcaions. In ordr o solv his problm, w nd gam hory. 3.5 Ruls vrsus discrion Undr raional xpcaions, policymakrs canno prsum ha conomic agns ar passiv in rgard o policy changs. Changs in policy alr popl xpcaions and his in urn fds back on h ffcivnss of policy. Convnional macroconomic modls hardly accoun for hs inracions. Gam hory, in conras, provids a powrful ool o hink conomic policy undr raional xpcaions. Th conduc of policy can b viwd as a gam, in which h public ris o larn abou h policymakr innions and policymakrs ry o guss h public xpcaions. A famous applicaion of Gam Thory o Raional Expcaions is h iminconsisncy argumn, pu forward by Kydland and Prsco in This argumn is analysd blow Th cnral bankr objciv funcion Considr an conomy whr h Phillips curv is givn by (3.7b), wih q 0 and 2. In ha cas, h Phillips curv bcoms: q (3.7c) Similarly, assum and h aggrga dmand is dscribd by: q (3.8b) Whr m dnos for h ra of mony growh. This quaion implicily assums ha h conomy is dparing from is naural lvl. In his conomy, h cnral bankr ris o maximiz h social wlfar funcion, which w assum o b as follows: U a 2 2 bq a,b>0 (3.4) 4 Kydland, F, and E. Prsco, C. (977). "Ruls Rahr han Discrion: Th Inconsisncy of Opimal Plans". Journal of Poliical Economy: /0/207 hp://sw.ua.p/afrias/aulas/noas%20apoio/noasmacro.hm 25

26 Poliicas macroconomicas, handou, Migul Lbr d Frias (mlbrdfrias@gmail.com) Tha is, h sociy valus a posiiv oupu gap, bu disliks inflaion. Th cnral bankr objciv funcion is dscribd in Figur 8. A poin 0, oupu is a is naural lvl, and inflaion is zro, so h sociy wlfar is U=0. Poin implis a highr inflaion ra han poin 0, bu a highr lvl of oupu as wll ( q b a ). On balanc, givn h wlfar funcion (3.4), h sociy is br off in poin han in poin ( U bb a a 2b a b 2a 0 ). In h figur, w also dscrib h dmand sid, wih h ra of mony growh bing qual o zro.. Figur 8 Th cnral bankr objciv funcion Cnral bank opimum undr discrion Undr discrion, h cnral bank has h powr o choos h inflaion ra (by changing h ra of mony growh, ) so as o maximiz (3.4) aking popl xpcaions as givn. Subsiuing (3.7c) in h objciv funcion (3.4), on may solv h cnral bankr opimizaion problm: 2 a MaxU b (3.4a) Th soluion is: b (3.5) a No ha h opimal ra of mony craion dos dpnd on xpcaions. To s his, us (3.8b) and (3.7c) o find ou h quilibrium inflaion ra as a funcion of xpcd inflaion: Subsiuing his in (3.4a) and choosing h ra of mony growh ha maximizs h objciv funcion, you will g b a 2 (3.5a). 04/0/207 hp://sw.ua.p/afrias/aulas/noas%20apoio/noasmacro.hm 26

27 Poliicas macroconomicas, handou, Migul Lbr d Frias (mlbrdfrias@gmail.com) Thus, h opimal monary xpansion whn 0 b a. is 2b a, dlivring Inconsisncy (undr discrion) Assum ha h cnral bank, undr discrion, commis wih 0 o achiv 0. Will his announcmn b crdibl? Th answr is no. Th problm is ha, onc popl blivd in h mony arg, hr would b an incniv for h cnral bank o rnga is commimn, craing an inflaion surpris in an amp o achiv a highr social wlfar. Indd, from (3.5b), w s ha h cnral bank opimal policy whn 0 is o s 2b a, dlivring q b a. Figur 9: Inconsisncy undr discrion Th cnral bank problm undr discrion is illusrad in Figur 9: whn popl xpc 0, h cnral bank maximizs uiliy in poin I, whr h indiffrnc curv is angn o h shor-rm Phillips curv. This implis xpanding h ra of mony growh o 2b a. As w jus saw, his dlivrs a highr uiliy han poin 0, bu inflaion will b highr han h xpcd. In ohr words, undr discrion hr is an incniv for h cnral bank o b im inconsisn: im inconsisncy rfrs o h mpaion of policymakrs o dvia from a policy onc i is announcd and h priva scor hav racd o i. In rms of our modl, h monary auhoriis hav an incniv o rng on is announcmn and xpand h mony supply ahad of h implid by h xpcd inflaion. Th conclusion is ha h announcmn of a policy of low inflaion is by islf no crdibl undr discrion. Priva agns undrsand h incniv o rng and hrfor will no bliv h announcmn in h firs plac. Raional agns will nvr bliv in 0, 04/0/207 hp://sw.ua.p/afrias/aulas/noas%20apoio/noasmacro.hm 27

28 Poliicas macroconomicas, handou, Migul Lbr d Frias (mlbrdfrias@gmail.com) bcaus hy know ha h cnral bank could b mpd o surpris hm, sing onc xpcaions ar formd. 2b a Consisncy (undr discrion) Undr raional xpcaions, h public is awar of h cnral bankr prfrncs, and will form xpcaions accordingly. Th consisn quilibrium undr discrion is obaind whn popl formula hir xpcaions aking (3.5) ino accoun. In his modl, h only consisn xpcaion is: b a In his quilibrium, h inflaion ra is sufficinly high o dpriv h cnral bank from any incniv o spring an inflaion surpris. Undr consisncy, i is opimal for h b a. cnral bank o xacly valida h public blivs, sing Figur 0: Consisn quilibrium undr discrion Th consisn quilibrium is dscribd by poin C in Figur 0. Th problm wih h consisn quilibrium, is ha i dlivrs h sam lvl of oupu as in poin 0, bu wih highr inflaion. Th sociy pays h cos of inflaion wih no bnfi a all. No ha h 04/0/207 hp://sw.ua.p/afrias/aulas/noas%20apoio/noasmacro.hm 28