SCHOOL OF FINANCE AND ECONOMICS

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1 SCHOOL OF FINANCE AND ECONOMICS UTS: BUSINESS WORKING PAPER NO. 48 May 006 Endognous Mony, Non-nuraliy and Inrssnsiiviy in h Thory of Long Priod Unmploymn Pr Dochry ISSN: hp://

2 Endognous Mony, Non-nuraliy and Inrs-snsiiviy in h Thory of Long Priod Unmploymn Pr Dochry School of Financ and Economics Univrsiy of Tchnology, Sydny Asrac This papr invsigas h rol playd y ndognous mony in modls wih inrs-snsiiv xpndiurs. In paricular, i xamins h impac of ndognous mony on a aslin noclassical modl arguing agains h frqunly assrd claim ha radiional noclassical macroconomics is compail wih ndognous mony. I dmonsras firsly ha ndognous mony is a sufficin condiion o rndr unsal a noclassical modl characrisd y inrssnsiiv xpndiurs, full mploymn and mony nuraliy. Scondly, i shows ha h inroducion of ihr mony illusion on h par of workrs or a Taylor rul govrning monary policy ar alrnaiv mhods of sailising modls wih inrs-snsiiv xpndiurs and ndognous mony, hough wih diffrn implicaions for h full mploymn and nuraliy characrisics of h sandard modl. Thirdly, i raiss qusions aou whhr modls which incorpora Taylor ruls can proprly characrisd as conaining ndognous mony and i provids an alrnaiv inrpraion of such modls. Th papr concluds y arguing ha mony supply ndogniy of h xrm or accommodaionis yp is of fundamnal significanc for h consrucion of a hory of long priod unmploymn u i idnifis a s of rmaining qusions which nd o addrssd in h advancmn of his proc. JEL Classificaion Numrs: E40, E5, E58. Kywords: Endognous mony, mony nuraliy, unmploymn, inrs-snsiiviy. Thanks o Tony Aspromourgos, Pr Flaschl, Gordon Mnzis, Graham Whi and paricipans a h 8 h Pah o Full Employmn Confrnc and h 3 h Naional Confrnc on Unmploymn, Univrsiy of Nwcasl, Ausralia, 7-8 Dcmr 006 for commns and suggsions. Any rmaining rrors ar h auhor s rsponsiiliy. Corrspondnc o Pr Dochry School of Financ and Economics, Univrsiy of Tchnology, Sydny. Ph ; Fax ; mail: pr.dochry@us.du.au

3 Inroducion Th inrs-snsiiviy of xpndiurs has n a cnral faur of noclassical macroconomics sinc a las h im of Wicksll (898. I lis a h har of h noclassical mchanism which salishs full mploymn as h cnr of graviaion for an conomic sysm, and i is ingral o h docrin of mony nuraliy. Bu hs faurs of noclassical hory wr sriously challngd in h scond half of h wnih cnury. In h 960s, h capial das crippld h ida ha invsmn, in paricular, could a monoonically invrs funcion of h ra of inrs (s Harcour 97; Gargnani 978a. An conomic sysm in a sa of prsisn unmploymn migh wll gnra nominal inrs ras low h naural ra a which full mploymn oains u sinc hs lowr ras would fail o lici any xpndiur rspons, h sysm would fail o mov closr o full mploymn and h prolm would prsis. From h 970s, h ndognous mony school challngd h ida of mony nuraliy. An imporan par of h noclassical mony nuraliy mchanism is h xognous naur of h mony supply. Variaions in mony dmand agains an xognously fixd mony supply caus movmns in h nominal inrs ra ha shif h ral inrs ra ack o h naural ra. If h mony supply is ndognous, lvrag for nominal inrs ra movmns is unavailal and ras rmain sal. According o Kaldor (970, 986, Moor (979, 988, Lavoi (996, Rochon (999 and Dochry (005 h mony supply is no only ndognous u i is h ra of inrs ha is xognous, fixd y h cnral ank o avoid dsailizing flucuaions ha may caus svr conomic downurns. Th rsul of his approach is ha inrs ras ar no fr o prform h funcion rquird of hm y mony nuraliy and ha ras of inrs chosn y h cnral ank aov h naural ra ar capal of gnraing prsisn unmploymn. Inrsingly, oh h rsuls of h capial das and h principl of ndognous mony appar compail wih crain inrpraions of Kyns Th Gnral Thory. According o hs inrpraions, mony is non-nural and unmploymn consius an ssnial characrisic of h quilirium o which an conomy gravias rahr han a shor run disquilirium phnomnon. Bu h spara mrgnc of h wo challngs o noclassical Milga (977, 307 commnd som im ago on h rlaionship wn h ngaiv nrpris of criicising noclassical hory and h posiiv nrpris of consrucing an alrnaiv hory. If h ngaiv nrpris is succssful, h qusion is ggd as o how a capialis sysm opras if no along h lins suggsd y noclassical hory. Hr horiss hav ndd o hrown ack on som paricular inrpraion of Kyns (.g. Pasini 974; Gargnani 978a,; 984; and Eawll 983. Thr ar, of cours, alrnaiv inrpraions of Th Gnral Thory. Thos offrd y h noclassical synhsis and h Nw Kynsian school find in h logic of Th Gnral Thory various impdimns o h fficin opraion of h mchanism which pushs an conomic sysm from an posiion of unmploymn owards full mploymn. Bu unmploymn in hs inrpraions is a disincly disquilirium phnomnon ha can allviad y fring up a mark conomy from sricurs prvning h fficin opraion of h full mploymn mchanism. Ohr inrpraions find in Th Gnral Thory an xplanaion of prsisn or long priod unmploymn.

4 conomics dscrid aov raiss a numr of qusions aou hir rlaionship wih ach ohr ha hav y o squarly addrssd. Firsly, dos ndognous mony consiu a sufficin condiion for long priod unmploymn? Whil h ndognous mony school idnifid aov suggss ha i dos, ohr horiss, including som non-marginalis wrirs (.g. Pivi 985; 99; and 00 hav xplicily rcd his proposiion arguing ha a rang of noclassical modls, including ha of Wicksll (898 himslf, conain ndognous mony and dmonsra a capaciy o dlivr hir radiional rsuls dspi is inclusion. A scond qusion rlas o h prcis naur of ndognous mony islf. Dochry (005, 9 ff xplors h impac of a simpl form of ndogniy associad wih a naïv cnral ank rul ha fixs h nominal inrs ra. Bu cnral anks adus inrs ras in rspons o h inracion of paricular conomic goals and circumsancs, and hir anion ulimaly focuss on ral inrs ras rahr han nominal ons. For xampl, h famous Taylor (993, 0 rul, rquirs adusmn of h ral ra in rlaion o dviaions of inflaion and oupu from arg valus. Th qusion is hus whhr h opraion of a Taylor rul has any marial impac on h rsuls of h ndognous mony argumn and how his affcs h answr o h firs qusion posd aov. A hird qusion ariss from h rspons of noclassical horiss hmslvs o h concp of mony non-nuraliy. Fridman (968, for xampl, was highly criical of radiional Phillips curv analysis, which was characrisd y non-nuraliy, caus i assumd mony illusion on h par of workrs. Th qusion hn is: wha is h prcis rol of mony illusion in gnraing non-nuraliy and wha rlaionship dos i hav wih ndognous mony? This papr offrs answrs o hs qusions using a s of simplifid macroconomic modls which variously mody h horical faurs idnifid aov. A aslin noclassical modl is firs salishd using a vrsion of Fridman s (968 analysis. Th characrisics of quilirium and h condiions for is sailiy ar xamind. Th modl is hn modifid o incorpora a simpl form of mony supply ndogniy and h impac of his chang on quilirium and sailiy is considrd. This allows h firs qusion posd aov on h sufficincy of ndognous mony for an unmploymn quilirium o answrd. Th modl is hn xamind whn a Taylor rul is usd in plac of a naïv inrs ra rul. This allows h scond qusion aov o answrd. Finally mony illusion is addd o h modl in wo diffrn forms and h rsuls compard wih rsuls from h prcding vrsions of h modl, allowing h hird qusion aov o answrd. Rsuls from all of h modls ar summarisd and som conclusions drawn in h final scion of h papr.

5 3 Th Baslin Modl: Fridman s (968 Approach Fridman (968 argus ha in a world whr workrs do no suffr from mony illusion in h formulaion of hir wag claims and whr dmand for mony has a ransacions componn, h conomy will gravia o full mploymn and inflaion will dpnd only on h ra of growh of h mony supply. Fridman s modl may rprsnd in rms of quaions ( o (6 low. Equaion ( is a sandard IS curv wih ral oupu, Y, dpnding on a mulipl,, of auonomous xpndiurs, A, and xpcd ral inrs ras, whr i, is h nominal inrs ra,, is h xpcd ra of inflaion and is h snsiiviy of xpndiurs (principally invsmn o h ral inrs Y A i ( UE UE γ ( Y Y ( W & p (3 W W& W w β UE (4 d d [ ] (5 di d dy m& k k k (6 d m ra. Unmploymn (UE is drmind in quaion ( as a rsul of som minimum lvl of unmploymn UE associad wih mark fricions and Okun s law, whr Y is ponial oupu and γ is a scaling paramr assumd o sricly posiiv. Th inflaionary procss is s ou in quaions (3 and (4. Equaion (3 drmins inflaion as h ra of chang in h mony wag, W, pr priod lss growh in laour produciviy, p. Equaion (4 oulins h wag drminaion procss in rms of a asic claim for incrasd wags w, which is assumd o consan, compnsaion for xpcd inflaion and an adusmn for h lvl of unmploymn which undrmins h argaining posiion of laour and rducs h siz of any succssful wag claim. β is a paramr assumd o sricly posiiv.

6 4 Th ra of chang of xpcd inflaion,, is drmind in (5 y a sandard adapiv procss which compars h acual ra of inflaion,, wih xpcd inflaion (whr is a paramr assumd again o sricly posiiv. Th nominal inrs ra is drmind in (6 as h rsul of a mark procss which incrass h inrs ra whn dmand for mony xcds supply and vic vrsa. Nominal dmand dpnds on oh nominal incom, P Y, and h inrs ra, so ha changs in dmand rsul from ral growh in incom, inflaion and monary growh. Th supply of mony is assumd o grow a an xognous ra, m & / m. Th adusmn paramrs k and k ar assumd o sricly posiiv. This sysm may rducd o h following s of wo diffrnial quaions in xpcd inflaion and unmploymn (his is shown in h Appndix: d due m& ( k k βk UE k [ ( w p] (7 d γ d m d d β UE ( w p (8 o which h soluion is: And his soluion is sal providd: m& / m ( w p UE β (9 k > (0 This, of cours, confirms h sandard rsul ha xpcd inflaion will, in quilirium, qual o acual inflaion which will in urn qual o h ra of monary growh. Unmploymn is givn y h xcss of h asic mony wag claim ovr laour produciviy growh adusd for h xn o which unmploymn affcs mony wag growh. This is h naural ra of unmploymn or h non-acclraing inflaion ra of unmploymn (NAIRU in h sandard monaris-noclassical modl. Long run mony nuraliy is vidn in his soluion To simplify h mahmaics, h im drivaiv of inrs ras is a funcion in quaion (6 of h im drivaiv of ral incom and h growh ras of prics and h nominal mony supply. To mak h scaling of varials consisn, h im drivaiv on h RHS is givn a diffrn paramr o h growh ras. Th ffc of his approach is ha infrncs aou sysm sailiy mus inrprd as ing local rahr han gloal.

7 5 oh from h fac ha mony has no impac on h NAIRU and ha mony is h sol drminan of long run inflaion. Th sailiy condiion rquirs inrs ras o rspond mor quickly o changs in inflaion han rvisions o inflaion xpcaions do o discrpancis wn acual and xpcd inflaion ras. Considr, for xampl, a posiiv shock o monary growh. This would gnra addiional inflaion y iniially rducing h nominal inrs ra and raising aggrga dmand aov ponial oupu. As prics gin o ris afr his shock, upward prssur is placd on h nominal inrs ra in quaion (6 which incrass h ral inrs ra in quaion ( and pulls aggrga dmand ack owards ponial oupu, hus sailising h conomy. A h sam im howvr, h incrasd inflaion incrass inflaion xpcaions in quaion (5 and rducs h ral inrs ra in quaion (, incrasing aggrga dmand and pushing i furhr away from ponial oupu, hus dsailising h conomy. Whn (0 is saisfid, h firs sailising ffc ouwighs h scond dsailising ffc and h conomy sls down o a nw quilirium wih all nominal varials incrasd. This xampl highlighs h imporanc of xpndiur inrs-snsiiviy for his sysm s vrsion of mony nuraliy. A scond xampl highlighs h imporanc of inrs-snsiiviy for h modl s full mploymn rsul. L h conomy iniially in a siuaion whr hr is insufficin aggrga dmand o warran h mploymn of all availal laour. In his cas, unmploymn will aov h NAIRU, nominal wag growh will low is quilirium growh ra and inflaion will lowr han monary growh. In quaion (6, nominal inrs ras will fall which will simula aggrga dmand in quaion ( and rduc h lvl of unmploymn. This will coninu unil unmploymn rachs h NAIRU. Ths wo xampls oghr indica h significanc of xpndiur inrs-snsiiviy for h ky faurs of h aslin modl. W urn now o xamin h impac of inroducing ndognous mony ino his framwork. Endognous Mony: Th Pur Crdi Cas Th naur of ndognously drmind mony as dscrid y horiss such as Kaldor (970, 986 is rlaivly complx. Th ssnial principl, howvr, is ha cnral anks canno xr sric monary conrol xcp ovr h mos narrow mony aggrgas. This oains caus failur o accommoda variaions in mony dmand lads o variaions in h quaniy of widr aggrgas via xnsions or rducions in ank crdi, and corrsponding variaions in h vlociy of narrowr aggrgas. Sinc variaions of his kind may gnra significan variaions in inrs ras, failur o accommoda has h ponial o caus financial insailiy.

8 6 Accommodaioniss hus argu ha rprsning ndognous mony in rms of an lasic mony supply curv a a fixd inrs ra is a rasonal rprsnaion of cnral ank haviour dsignd o avoid financial insailiy (s Dochry 005, Th horical consquncs of his approach hav n argud o ssnially ngaiv for h full mploymn and nuraliy characrisics of modls such as h aslin modl considrd in h prvious scion. Som hav challngd his argumn, howvr, claiming ha noclassical conomics has h capaciy o cop prfcly wll wih ndognous mony. Wicksll s (898 famous modl of pur crdi mony is frqunly cid as an xampl of his capaciy (s Pivi 00. Th ociv of his scion is o xplor hs conflicing proposiions y inroducing ndognous mony ino h aslin modl and xamining is impac. Th firs variaion of Fridman s aslin modl o considrd, hrfor, incorporas ndognous mony in h simpls way possil. Th inrs ra is s according o h rul shown in quaion ( which implis ha dmand for mony is prfcly accommodad a his inrs ra y appropria cnral ank mark opraions. i i ( Th full modl is hn mad up of quaions ( o (5 and (. Onc again, his modl may rducd o a sysm of wo diffrnial quaions in xpcd inflaion and unmploymn. Equaion ( low is h firs of hs quaions and diffrs from quaion (7 in h aslin modl caus of h rplacmn of quaion (6 wih h simpl inrs ra rul. Th drivaion of his quaion is shown in h Appndix. Th scond quaion is simply quaion (8 from h aslin modl rproducd low for h sak of xposiion and is oaind in h sam mannr as for. UE UE Y ( A i ( γ γ d β UE ( w p (8 d Th soluion o his sysm is: UE Y A ( i ( w p β (3

9 7 This is an imporan and a firs glanc surprising rsul. I indicas ha a nominal inrs arg has no impac on quilirium unmploymn which rains h sam NAIRU valu as for Fridman s aslin modl in (9 aov whil h ra of xpcd inflaion dpnds on aggrga dmand (which is affcd y h inrs ra rlaiv o ponial oupu. This rsul is surprising caus on migh hav xpcd unmploymn rahr han inflaion o hav dpndd on h nominal inrs arg. Som rflcion on his oucom is hus warrand. Th quilirium valu for unmploymn rflcs quaions (3 and (4 which oghr gnra h xpcaions augmnd Phillips curv (EAPC: ( w p β UE Sinc quaion (5 indicas ha acual and xpcd inflaion will idnical in quilirium, h rms for acual and xpcd inflaion cancl ou in h aov xprssion laving only h ra of unmploymn as an unknown which has h following valu: UE w p β This argumn also applis o h aslin modl and xplains why h rsuls for unmploymn ar idnical for hs wo modls. Th inflaion rsul in h aslin modl is drivn from quaions (, (, (5 and (6. Having drmind h quilirium unmploymn ra from h EAPC, quaion ( drmins ponial oupu. In quilirium, h im drivaiv of his oupu lvl will zro as will h im drivaiv of h nominal inrs ra. In addiion, quaion (5 implis ha acual and xpcd inflaion mus h sam in quilirium. All of his, oghr wih quaion (6, implis ha xpcd inflaion mus qual o h ra of monary growh. From quaion (, h quilirium valu of h nominal inrs ra is ha valu which rconcils ponial oupu wih aggrga dmand drivn y auonomous xpndiurs and h xpcd inflaion ra. Thus h sysm is drmina. If a dmand shock wr o incras auonomous xpndiurs from a posiion of quilirium, h nominal inrs ra rquird o rconcil aggrga dmand wih a givn lvl of ponial oupu would highr. Bu h dynamic procss rquird o dlivr his highr inrs ra would hav h highr aggrga dmand iniially incrasing oupu a h old lvl of h nominal inrs ra. This would rduc unmploymn and mporarily incras inflaion. Toghr h highr oupu and inflaion would rais dmand for mony and inrs ras would ris via

10 8 quaion (6. Th highr nominal inrs ra would dampn aggrga dmand via quaion ( which would pull h sysm ack owards quilirium whr oupu would rurn o is ponial lvl, unmploymn would rurn o h lvl spcifid in quaions (0 and (3, and inflaion would qual o h ra of monary growh. Bu h nominal inrs ra would prmannly highr. Equaion (6 in h aslin modl is cnral o his dynamic procss. In h prsn modl, whr quaion ( rplacs quaion (6, his mchanism is inopral. Any shock o aggrga dmand implis ha on of h componns of h ral inrs ra in quaion ( mus adus o rurn h ral inrs ra o is naural or full mploymn lvl. Bu h nominal inrs ra canno prform his funcion as i dos in h aslin modl. Any incras in mony dmand associad wih an iniial incras in oupu rsponding o h dmand shock will now implicily accommodad y h cnral ank according o quaion ( o lav h nominal inrs ra unaffcd. As a rsul, quaion ( no longr drmins h nominal inrs ra u h xpcd ra of inflaion, is funcion ing o rconcil ponial oupu wih aggrga dmand givn h componns of aggrga dmand alrady drmind y h fixd nominal inrs ra and auonomous spnding. This is h maning of h xpcd inflaion soluion in quaion (3. I lls us ha a highr lvl of auonomous aggrga dmand rquirs a highr xpcd inflaion ra o mak h inrs-snsiiv componns of aggrga dmand smallr, hus rconciling hm wih a fixd lvl of ponial oupu. Bu his valu of xpcd inflaion is, of cours, simply an quilirium rquirmn. Whhr his rquirmn is m and how i is m is a dynamic issu. Th analysis oulind in h Appndix indicas ha his quilirium is in fac unsal, dpnding on h soluions o h characrisic quaion of h sysm mad up of quaions (8 and (. Th Appndix shows ha hr is only on characrisic roo in his cas givn as follows: r γβ (4 This roo is unamiguously posiiv indicaing ha h sysm is unsal wihou cycls. I signals h fac ha if h nominal inrs arg is s aov h nominal ra drmind y quaion ( in h aslin modl (ohr hings qual, h ral ra will also highr han h naural (ral ra (givn iniial inflaion xpcaions. In his cas, aggrga dmand will low ponial oupu, oupu will fall and unmploymn will ris aov h NAIRU. In h Phillips curv quaion shown aov, highr unmploymn will rduc acual inflaion which will fall low xpcd inflaion causing a downwards rvision o xpcd inflaion. Thus whras a highr nominal inrs ra rquirs a highr ra of xpcd inflaion o salish

11 9 quilirium, h mchanics of h modl gnra a lowr ra of xpcd inflaion. This lowr ra of xpcd inflaion furhr incrass h ral ra of inrs, dprssing aggrga dmand and oupu furhr, raising unmploymn and rducing acual inflaion. Furhr rducions in acual inflaion caus furhr downward rvisions o xpcd inflaion and h sysm movs away from h quilirium spcifid in quaion (3 rahr han owards i. Prcisly h opposi ffc occurs if h nominal inrs arg is low h naural ra. Figur shows h rsul diagrammaically. Th quilirium givn in (3 is shown a poin A. Th dmarcaion curv (Chiang 984, 69 for xpcd inflaion is givn y quaion (8 which indicas h im drivaiv of xpcd inflaion in rms of unmploymn. This is zro whn unmploymn is a h NAIRU so ha h dmarcaion curv for xpcd inflaion is vrical a d d 0 A Y ( i A 0 w p β UE Figur : Phas Diagram for Endognous Mony Cas his lvl. For lvls of unmploymn low h NAIRU, xpcd inflaion is rising and for lvls of unmploymn aov h NAIRU, i is falling. Ths racoris ar shown y h phas pahs o h righ and h lf of h vrical dmarcaion curv for xpcd inflaion. Sricly, h dmarcaion curv for unmploymn is undfind in his cas. Equaion (A in h Appndix shows h im pah of unmploymn in rms of xpcd inflaion. Taking h im drivaiv

12 0 of unmploymn gnras an xprssion in h im drivaiv of xpcd inflaion alon. Howvr, quaion (A consius h xpcaions augmnd Phillips curv and indicas ha h im pah of unmploymn dpnds on h im pah of xpcd inflaion. This is drawn ino Figur. A any poin on h EAPC o h lf of A, unmploymn is low h NAIRU and h phas pahs for xpcd inflaion indica ha i should incras, moving us furhr o h lf along h EAPC and away from poin A. In fac wha happns whn inflaion incrass is ha xpcd inflaion is rvisd upwards y quaion (5 so ha h inrcp of h EAPC is incrasd and h curv islf shifs upwards. A any poin on h EAPC o h righ of A, xacly h opposi adusmn occurs. Poin A is hus inhrnly unsal and whil an inlligil quilirium xiss for Fridman s modl wih ndognous mony, h conomy will mov sysmaically away from his quilirium. Ths rsuls, oaind whn ndognous mony is incd ino h aslin modl, rprsn Wicksll s famous pur crdi modl. Som argu ha hy rflc h ailiy of noclassical conomics o cop wih ndognous mony and o xplain inflaionary and dflaionary phnomna. Bu his is a fundamnally misakn inrpraion. Th cumulaiv procss in Wicksll s pur crdi modl rprsns an indrmina pric lvl du o h asnc of an ffciv nominal anchor for h sysm (cf. McCallum 986. Tha is, h sysm fails o xplain h asic conomic phnomna a hand: h lvl of oupu, unmploymn and pric lvl. And Dochry (995 dmonsras ha Wicksll himslf dos no rgard his modl as an opraional ndpoin u as an xposiional ool dsignd o show h corrc opraion of h quaniy hory in a modrn financial sysm wih fracional rsrv anking. In h nd, Wicksll rinroducs an xognous mony as, and hus supply, o rndr h pric lvl drmina hus ffcivly rurning us o a modl similar in spiri o h aslin modl considrd aov. Thus if h simpl inrs ra rul in quaion ( is a rasonal rprsnaion of h ssnial principls of ndognous mony, h rsuls of his scion suggs ha ndognous mony, as a srucural faur of modrn financial sysms, is anihical o asic noclassical principls. Capialis conomic sysms do no hav a ndncy o auomaically gravia owards full mploymn whn h mony supply is ndognously drmind. An alrnaiv xplanaion of h opraion of his sysm mus hrfor sough. Rsolving Indrminacy: Th Rol of Mony Illusion W considr now h firs of wo possil insrumns y which h unsal noclassical modl xamind in h prvious scion may rndrd sal. This is h insrumn of mony

13 illusion. A scond insrumn, h Taylor rul for monary policy, will considrd in h nx scion. Insailiy in h noclassical modl wih pur ndognous mony ariss caus changs o h nominal inrs ra which push h sysm owards quilirium canno gnrad whn h sysm is away from quilirium. Mony illusion provids a complx alrnaiv sourc of sailiy firsly y rndring h Phillips curv sal in h fac of inflaion or dflaion, and scondly y allowing unmploymn o varial wih rspc o inflaion hrough h affc of ral inrs ras on xpndiurs rahr han ing fixd a h naural ra. Th rsul is an quilirium wih unmploymn diffrn from h NAIRU and inflaion dpndn on h ra of as mony wag growh rlaiv o produciviy growh and h lvl of unmploymn. Whn considring mony illusion w may mak on of wo assumpions. W may ihr assum ha workrs suffr from mony illusion y allowing h unmploymn ra o affc hir mony wag dmands rahr han hir ral wag dmands, or ha firms suffr from mony illusion y asing invsmn dcisions on h mony ra of inrs rahr han h ral ra of inrs. W ak ach of hs possiiliis in urn ginning wih workr illusion. This involvs a rformulaion of quaion (4 in h aslin modl o rmov xpcd inflaion: W& W w β UE (5 Th hird modl w considr hn is mad up of quaions (-(3, (5, (5 and (. This sysm may rducd o wo quaions y susiuing (5 ino (3 o gnra h radiional Phillips curv shown in (6 low, and y rcognizing from (5 ha xpcd and acual inflaion will h sam in quilirium. W hn susiu ( ino ( and h rsuling vrsion of ( ino ( o produc (7 afr som rarranging. ( w p β (6 UE UE [ Y ( A i ] γ UE γ (7 Ths wo quaions xprss h inrdpndnc of unmploymn and inflaion in his modl. Inflaion dpnds on unmploymn caus h formr is drivn y wag growh, and unmploymn invrsly drmins h siz of wag claims, whil unmploymn dpnds on h lvl of oupu via Okun s law which in urn is drivn y h lvl of aggrga dmand (islf

14 affcd y h inflaion ra hrough h ral ra of inrs. Equaions (6 and (7 may solvd simulanously o oain h following soluion vcor: βγ [( A i Y] βγ UE γ UE [ Y ( A i ] βγ (8 According o his soluion, quilirium unmploymn is mad up of wo componns. Th firs is som as lvl unmploymn which w hav so far inrprd in rms of h NAIRU. Th scond dpnds on h xcss of auonomous xpndiurs (including ha associad wih h fixd nominal inrs ra ovr ponial oupu (a kind of adusd oupu gap corrcd for h laour rquirmn in producion and h fac ha spnding dpnds on h ral rahr han nominal inrs ra. A clar and imporan aspc of his rsul is ha h quilirium valu for unmploymn is posiivly rlad o h nominal inrs ra, i. Equilirium inflaion is drivn y h siz of his adusd oupu gap corrcd for h laour rquirmn in producion and h impac of unmploymn on h asic wag claim. This follows from h asic concpion of h simpl Phillips Curv. Wihin his concpion, inflaion dpnds on h asic mony wag claim ovr growh in laour produciviy and h dgr of unmploymn which undrmins laour s argaining powr. Sinc unmploymn is mad up of h as and oupu rlad componns dscrid aov, hr ar ffcivly hr componns driving inflaion. Bu h firs wo xacly offs ach ohr whn w assum ha as unmploymn, UE, is h NAIRU, laving only oupu-rlad unmploymn having a dirc ffc on h lvl of quilirium inflaion. Th soluion o his modl rflcs h argumn advancd y som horiss ha ndognous mony rprsns a sufficin condiion for h gnraion of quilirium unmploymn in an ohrwis noclassical modl (s Lavoi 996; Dochry 005, 343ff. I may sn howvr, ha h naur of h condiion mus undrsood clarly. Endognous mony rndrs h pric lvl indrmina in h noclassical modl rquiring an alrnaiv hory of prics and inflaion. On such possiiliy is h radiional Phillips Curv in which prics implicily dpnd on mony wags rflcing in urn h coss of producion. In his sns h nominal anchor is h social convnion rgarding mony wags which dpnd on h rlaiv argaining srngh of laour wih appropria adusmn for h chnical characrisics of h producion procss in rms of produciviy. Unmploymn is characrisically Kynsian in his rsul dpnding on aggrga dmand and varying posiivly wih h nominal inrs ra.

15 3 Th soluion in quaion (8 is rprsnd in Figur low. Boh h Phillips curv, rprsning quaion (6, and h unmploymn curv, rprsning quaion (7, ar invrs rlaions wn inflaion and unmploymn. Thy inrsc a poin E in Figur which rprsns h quilirium of h sysm. An incras in h nominal inrs ra would shif h unmploymn rlaion upwards o h dashd rlaion, moving is poin of inrscion wih h Philips curv from E o E. Th nw quilirium would hus characrisd y a highr lvl of quilirium unmploymn u a lowr lvl of quilirium inflaion holding vryhing ls consan. Unmploymn Rlaions E E 0 UE UE UE UE Figur : Equilirium and Sailiy Faurs of h Modl wih Endognous Mony and Workr Mony Illusion Th quilirium, E, dpicd in Figur is sal providd ha h slop of h Phillips curv is smallr in asolu rms han h slop of h unmploymn rlaion. Considr a dmand shock which mporarily incrass h nominal ra of inrs and movs h unmploymn rlaion o h dashd lin. Unmploymn is now highr a UE han is quilirium valu UE. Th highr valu of unmploymn will, in urn, rduc h inflaion ra via h Phillips curv o. Sailiy of h original quilirium, E, hings on h valu of unmploymn ha corrsponds o his nw valu of inflaion. If his valu of unmploymn is lss han UE, (for xampl, UE a sailizing dynamic adusmn procss will nsu. Sinc unmploymn now

16 4 falls, inflaion incrass via h Phillips curv, highr inflaion rducs h ral ra of inrs, incrasing aggrga dmand and rducing unmploymn. Th sysm hus movs from E ack owards E as indicad y h arrowd adusmn pahs. Howvr if h lvl of unmploymn corrsponding o is aov UE, a dynamically unsal adusmn pah nsus, aking h conomy away from E. In his cas unmploymn would ris, inflaion would rducd via h Phillips curv, oupu would fall du o h incrasd ral ra of inrs ha h fall in inflaion rprsns, and unmploymn would ris furhr. Addiional incrass in unmploymn would lad o furhr incrass in inflaion in an unsal spiral. Th condiion for sailiy hn is ha h unmploymn ra corrsponding o mus o h lf of poin E. This in urn rquirs ha h slop of h Phillips curv smallr in asolu rms han h slop of h unmploymn rlaion. Exprssion (9 oulins his condiion: 3 β < (9 γ Mony illusion, hrfor, plays an imporan rol in h conx of an ohrwis noclassical modl wih ndognous mony. I dlivrs sailiy o an unsal modl y providing h nominal anchor funcion usually prsrvd for h xognous mony supply. I also nsurs ha h quilirium o which h modl gravias is characrisd y unmploymn diffrn o h NAIRU and snsiiv o h lvl of aggrga dmand. Whn firms suffr from mony illusion, h rsul is somwha diffrn. If firms mak spnding dcisions y aking ino accoun h nominal inrs ra rahr han h ral inrs ra w may rvis quaion ( o xclud h xpcd ra of inflaion. This is don in quaion (0 low: Y A (0 i Th fourh modl for considraion is hus mad up of quaions (0, ( o (5 from h original modl and ( rflcing ndognous mony. This modl may rducd o hr quaions y susiuing (4 ino (3 o oain quaion (8, h EAPC as prviously, ( ino (0 and h rsuling vrsion of (0 ino ( o oain (, and quaion (5: ( w p β UE (8 UE UE γ [ Y ( A i ] ( 3 Th Appndix confirms his rsul wih sailiy analysis idnical o ha usd for h modls prviously considrd.

17 5 d d [ ] (5 Equaion (5 indicas ha in quilirium xpcd and acual inflaion ar qual. This implis from quaion (8 ha unmploymn will a h NAIRU. Howvr quaion ( also spcifis h lvl of unmploymn. Givn ha: w p UE β h wo quaions ar consisn only if: Y A i ( Tha is, if aggrga dmand is qual o ponial oupu, h oupu gap will zro and unmploymn will a h naural ra. If h nominal inrs ra is s oo low so ha aggrga dmand xcds ponial oupu, unmploymn falls low h naural ra, inflaion riss aov xpcd inflaion and, y quaions (5 and (8, inflaion riss in a prmann upward spiral. Sinc inflaion has no way of fding ack ono h xpndiur quaion, which dpnds only on h nominal ra of inrs du o mony illusion on h par of firms, his spiral maks h sysm dynamically unsal. Exacly h opposi rsul occurs if h nominal inrs ra is s aov h lvl ha quas aggrga dmand wih oupu. This oucom is rflcd in h formal soluion for inflaion drivd in h Appndix and shown in quaion (3: { ( w p β UE βγ [ Y ( A i ]} C (3 According o his quaion, h quilirium valu of inflaion is im varying whr C is a consan drmind from som oundary condiion. If, for xampl, inflaion is osrvd o 0 a im 0, C 0. This quilirium valu for inflaion is sal only if h cofficin of in racs is zro, and h condiion for his is prcisly ( aov. In his cas h quilirium valu for inflaion is 0 and unmploymn is a h NAIRU. If his condiion is no m, unmploymn will diffr from h NAIRU and h sysm will coninuously infla or dfla wihou limi. Th sysm is hus dynamically unsal whn firms suffr from mony illusion. A Modl wih Endognous Mony and a Taylor Rul A scond approach o making h Fridman sysm wih ndognous mony sal is h imposiion of a Taylor rul for monary policy. Taylor ruls funcion o rplac h auomaic

18 6 inrs ra adusmn mchanism associad wih quaion (6 in h aslin modl wih a cnral ank-oprad mchanism wih ssnially h sam characrisics. A variy of forms could adopd for his rul u w xamin a form closly rlad o Taylor s (993, 0 original suggsion rprsnd in quaion (4: i r θ θ ( UE U (4 ( E According o (4, h cnral ank ss h nominal inrs ra in rms of som as ral ra, r, plus h currn inflaion ra plus an upwards adusmn of θ for ach prcnag poin ha h inflaion ra xcds h arg inflaion ra,, lss an adusmn of θ for ach prcnag poin ha h unmploymn ra xcds h arg unmploymn ra U E. 4 Idally h as ral inrs ra usd in his calculaion is h naural or full mploymn ra. This kind of sysm is argud o rprsn a form of ndognous mony sinc h cnral ank is arging h inrs ra and mus accommoda mony dmand o conduc monary policy in his fashion. Th qusion is whhr his mor sophisicad approach o policy has h sam horical impac on h noclassical sysm as h naïv policy rul associad wih ndognous mony hroughou his papr. Th fifh modl for considraion hus xamins his qusion and is mad up of quaions (- (5 of h original modl and (4. Th Appndix shows how his nw sysm can rducd o wo complx diffrnial quaions, again in xpcd inflaion and unmploymn: [ γθ γ( θ β ] UE [ γ γ( θ ] UE γ( θ ( w p γ [ Y ( A ar ] γ( θ θ U (5 E d d β UE ( w p (6 Th soluion o his sysm is: UE w p β (7 4 Taylor (993 uss GDP rahr han unmploymn and laggd inflaion and GDP rahr han currn valus for hs varials in his original xposiion.

19 7 Th Taylor rul hus givs us h sam unmploymn rsul as h aslin modl wih inflaion a h cnral ank s arg lvl providd w assum ha arg unmploymn is h NAIRU and qual wigh is givn o h wo args in h policy rul (h Appndix shows how h aov rsul dpnds on hs assumpions. Sailiy of his quilirium rquirs: βγθ < 0 γ [ θ ( θ β ] (8 which is shown in h Appndix o rasonal. Thus h noclassical sysm wih ndognous mony and a Taylor rul posssss an quilirium similar in naur o h quilirium of h aslin modl and is sal undr rasonal condiions. Som also inrpr his rsul as implying ha noclassical conomics has h capaciy o handl ndognous mony. Bu on mus vry carful of his inrpraion in h ligh of h analysis in h rs of h papr. Fridman s aslin modl rflcs h radiional cor claims of noclassical conomics ha capialis sysms nd o full mploymn auomaically, ha is, wihou h assisanc of govrnmn, and ha mony is nural in is ffcs on h sysm. Th rsuls aov indica ha ndognous mony rndrs h firs of hs proposiions invalid. A noclassical sysm wih ndognous mony dos no auomaically gravia o full mploymn and lacks h capaciy o drmin h asolu pric lvl. Th sysm is, howvr, rndrd sal and drmina if h cnral ank prforms h inrs ra adusmn funcion ha marks prform in h aslin modl. Bu h opraion of his funcion implis no fundamnal chang o h monary naur of h conomy compard wih h firs modl considrd aov. Alraions o h inrs ra simply com h mchanism y which h quaniy of mony is adusd in a mannr consisn wih h cnral ank s inflaion arg: whn inrs ras ar incrasd, h quaniy of mony availal in h mony mark is rducd and vic vrsa. I is ru ha h conomy rconcils is dmand for mony o h nw supply caus xpndiurs ar inrs-snsiiv, and in his sns mony is ndognous. Bu a mor accura dpicion of his mchanism is ha of an alrnaiv opraing procdur for dlivring a spcific quaniy of mony o h sysm rahr han a chang o h principl ha mony supply growh drmins inflaion. If h cnral ank dcids o rlax is aiud o inflaion and raiss h inflaion arg,, his will lad o a rducion in h policy-drmind inrs ra via quaion (4. If mony dmand is sal, his inrs ra chang will corrspond o a highr lvl of h mony supply. In fac, h lowr inrs ra will achivd y mans of a largr volum of mony mad availal o h sysm. Th quaniy of mony hus coninus o drmin h pric lvl in his kind of

20 8 modl or pu in dynamic rms, inflaion is drmind y h ra of monary growh as wih h aslin modl. Th monary characrisics of his mchanism can only dscrid as ndognous in a smanic sns and no in h sns ha aggrga dmand drmins h volum of mony wihou h ncssary consqunc of fdack o dmand which r-rvrss mony-incom causaliy, causing i o flow in h radiional dircion. In his sns, a Taylor rul dos no rprsn ndognous mony a all u a cnral ank mchanism for idnifying and dlivring h sock of mony ncssary for and consisn wih a paricular inflaion arg, laving h quaniy hory of mony firmly in plac. Th ida ha Taylor ruls incorpora ndognous mony and a h sam im nsur h sailiy and succssful opraion of h noclassical modl mus, hrfor rcd. Taylor ruls do nsur h sailiy of h noclassical sysm u hy achiv his oucom y rassring h quaniy hory of mony in an opraionally ffciv way, no y manipulaing a gnuinly ndognous mony supply. In addiion, Taylor ruls canno usd o assr h slfcorrcing naur of a mark conomy sinc hir vry naur rquirs h co-ordinaing hand of govrnmn. Conclusion Considraion of h fiv modls in his papr dmonsras a numr of hings. Firsly, ndognous mony is no a horical srucur ha h asic noclassical modl has h capaciy o handl. Th proposiion advancd in h liraur y such horiss as Pivi (99, 00 ha i dos, mus dismissd. Endognous mony in h sns of Kaldor (970, 986, Moor (979, 989, Lavoi (996, Rochon (999 and Dochry (005 complly undrmins h ailiy of h asic noclassical modl o auomaically adus o full mploymn and dlivr a drmina asolu pric lvl. If ndognous mony consius a phnomna ha should o incorporad ino macro modls, an alrnaiv modl mus sough o xplain h naural or auomaic ndncis of a macro sysm. Th rol of Taylor ruls in rndring h noclassical sysm drmina do no rvrs his conclusion. A fundamnal principl of noclassical conomics is ha conomic sysms auomaically gravia o full mploymn. Dlira policy acion may dlivr full mploymn in a rang of modls som of which may also xplain why an conomy will sl down o an quilirium characrisd y unmploymn in h asnc of such policy acion. Such modls would hav o rgardd as suprior o on in which a spcific form of policy acion is rquird no simply o dlivr h spcific ociv of full mploymn u o mak h modl islf inlligil.

21 9 On possiiliy for such an alrnaiv is h hird modl considrd in his papr which assums mony illusion on h par of workrs in framing hir wag claims. This modl was shown o sal u h quilirium o which i argus h conomy gravias is characrisd y unmploymn diffrn o h NAIRU and snsiiv o aggrga dmand and h lvl of inrs ras. I is hus characrisd y mony non-nuraliy. Inflaion in his modl is drmind no y mony supply growh u y mony wag growh in xcss of growh in laour produciviy corrcd for h lvl of unmploymn. This modl wih ndognous mony and mony illusion is no surprisingly, hrfor, Kynsian in naur. I suffrs, howvr, from wo prolms. Firsly, whil mony illusion is usful in rndring a Fridman-yp, aslin modl sal wih Kynsian rsuls, i surly dos no rprsn a snsil form of conomic haviour on h par of workrs. Fridman s ocion o mony illusion in his sns is corrc. Scondly, i incorporas inrs-snsiiv xpndiurs aou which h capial das rais imporan horical ocions. Addiional vidnc from sudis such as Fazzari, Prsn & Huard (988 ha cos of capial ffcs on invsmn spnding ar mpirically wak, suppor hs ocions. Rsolving hs wo prolms rquirs carful considraion givn h imporan rol playd y oh mony illusion and inrs-snsiiv xpndiurs in h unmploymn modl considrd in his papr. A modl conaining ndognous mony u wihou inrs-snsiiv invsmn spnding or mony illusion on h par of workrs raiss a furhr s of qusions. Th firs is whhr ndognous mony in a modl wih inrs-insnsiiv xpndiurs is ncssary o dlivr an quilirium unmploymn rsul. I has n argud in his papr ha ndognous mony is sufficin o dlivr his rsul whn xpndiurs ar inrs-snsiiv, u sinc inrs-insnsiiv xpndiurs ar usually argud o consiu an alrnaiv sufficin condiion for unmploymn (Corll 994, 59, h saus of ndognous mony in h prsnc of inrs-insnsiiv xpndiurs mus carfully considrd. A scond qusion is whhr quilirium in a modl wihou mony illusion will sal givn ha mony illusion nsurs sailiy in h Kynsian modl considrd in his papr. Ths qusions rprsn challngs for h dvlopmn of a cohrn alrnaiv o noclassical conomics u h ngaiv work of criicising an xising ody of idas is always asir han h posiiv work of craing nw and r horical srucurs. Boh, of cours, ar imporan for improving our ailiy o manag h conomy and improv human wlfar.

22 0 Rfrncs Chiang A. (984, Mony Fundamnal Mhods of Mahmaical Economics, Third Ediion, Nw York: McGraw-Hill. Corll A. (994, Pos-Kynsian monary conomics, Camridg Journal of Economics, 8, Dochry P. (995, Endogniy in Wicksll's monary hory, Hisory of Economics Rviw, 3, -. Dochry P. (005, Mony and Employmn: A Sudy of h Thorical Implicaions of Endognous Mony, Chlnham, UK and Norhampon, MA, USA: Edward Elgar. Eawll J. (983, Thoris of valu oupu and mploymn, in Eawll J. & Milga M. (ds., Kyns s Economics and h Thory of Valu and Disriuion, London: Duckworh, Eawll J. and M. Milga (983, Inroducion, in J. Eawll and M. Milga (ds., Kyns s Economics and h Thory of Valu and Disriuion, London: Duckworh, pp. 7. Fazzari S., R.G. Huard and B.C. Prsn (988, Financing consrains and corpora invsmn, Brookings Paprs on Economic Aciviy, no., Fridman M. (968, Th rol of monary policy, Amrican Economic Rviw, 58, -7. Gargnani P. (978a, Nos on consumpion, invsmn and ffciv dmand I, Camridg Journal of Economics,, Gargnani P. (978, Nos on consumpion, invsmn and ffciv dmand II, Camridg Journal of Economics, 3, Gargnani P. (984, Valu and disriuion in h classical conomiss and Marx, Oxford Economic Paprs, 36, Goodhar C.A.E. (988, Th Evoluion of Cnral Banking, Camridg, MA: MIT Prss. Harcour G.C. (97, Som Camridg Conrovrsis in h Thory of Capial, Camridg: Camridg Univrsiy Prss. Kaldor N. (970, Th nw monarism, Lloyds Bank Rviw, 97, -7. Kaldor N. (986, Th Scourg of Monarism, Oxford: Oxford Univrsiy Prss, scond diion. Kyns J.M. (936, Th Gnral Thory of Employmn, Inrs and Mony, rprind in Th Collcd Wriings of John Maynard Kyns, Volum 7, London: Macmillan (973 diion of Royal Economic Sociy. Lavoi M. (996, Horizonalism, srucuralism, liquidiy prfrnc and h principl of incrasing risk, Scoish Journal of Poliical Economy, 43, McCallum B.T. (986, Som issus concrning inrs ra pgging, pric lvl drminacy, and h ral ills docrin, Journal of Monary Economics, 7, Milga M. (977, Kyns on h classical Thory of Inrs, Camridg Journal of Economics,, 307,35. Moor B.J. (979, Th ndognous mony sock, Journal of Pos Kynsian Economics,, Moor B.J. (988, Horizonaliss and Vricaliss: Th Macroconomics of Crdi Mony, Camridg: Camridg Univrsiy Prss.

23 Pally T.I. (000, Th Cas for Posiiv Low Inflaion: Som financial Mark Considraions wih spcial Anion o h Prolms of Japan, Easrn Economic Journal, 6, (3, Pasini L.L. (974, Incom Disriuion and Growh, Camridg: Camridg Univrsiy Prss. Pivi M. (985, On h monary xplanaion of disriuion, Sudis in h Surplus Approach, (, Pivi M. (99, An Essay on Mony and Disriuion, Nw York: S. Marin s Prss. Pivi M. (00, Mony ndogniy and mony non-nuraliy: a Sraffian prspciv, in L.P. Rochon and M. Vrnngo (ds, Crdi, Inrs Ras and h Opn Economy, Chlnham, UK and Norhampon, MA, USA: Edward Elgar, pp Rochon L.P. (999, Crdi, Mony and Producion: An Alrnaiv Pos Kynsian Approach, Chlnham, UK and Norhampon, MA, USA: Edward Elgar. Taylor J.B. (993, Discrion vrsus policy ruls in pracic, Carngi-Rochsr Confrnc Sris on Pulic Policy, 39, Wicksll K. (898, Inrs and Prics: A Sudy of h Causs Rgulaing h Valu of Mony, ranslad y R.F. Kahn (936, rprind in 965, Nw York: Augusus M. Klly.

24 Appndix This appndix oulins h soluion and sailiy procdurs for ach of h modls considrd in h x. Modl : Fridman s (968 Baslin Approach Equaions ( o (6 in h x may simplifid considraly. Diffrniaing ( and ( wih rspc o im and susiuing h rsuling vrsion of ( ino h rsuling vrsion of ( and rarranging givs: ( due d m k & k k (A γ d d m Susiuion of (4 ino (3 yilds Fridman s xpcaions-augmnd (EAPC: ( w p β UE (A Equaion (A may susiud ino (A and (5 o rmov inflaion. This gnras h following sysm of wo firs ordr diffrnial quaions in xpcd inflaion and unmploymn: d due m& ( k k βk UE k [ ( w p] (A3 d γ d m d d β UE ( w p (A4 This sysm may xprssd in marix form as: ( k ' k γ ' 0 0 UE βk β UE k [ m& / m ( w p] ( w p or in mor compac noaion as: J μ M υ g (A5 Consan soluions o (A5 ar givn y: m& / m ( w p UE β (A6

25 3 No from h dfiniion of ponial oupu Y ha whn unmploymn is a is quilirium valu Y Y. Thus from quaion (: β p w UE Th sailiy of his long run quilirium is ascraind y inspcion of h roos of h characrisic quaion of (A5. W oain his characrisic quaion from h rducd quaion corrsponding o (A5: 0 υ μ M J A non-rivial soluion o his quaion of h form and rquirs h following vanishing drminan: r m r n UE 0 M J r (A7 which afr susiuion for J and M, rarranging and normalisaion gnras h characrisic quaion: 0 ( k k r k k r γβ γβ (A8 Th roos of his characrisic quaion ar: 4 ( ( k k k k k k r γβ γβ γβ (A9 4 ( ( k k k k k k r γβ γβ γβ Sailiy hings on h rm undr h radical signs on h LHS of (A9 and hr cass ar rlvan dpnding on h following condiion: 4 ( k k k k γβ γβ (A0 In Cas, (A0 is saisfid non-sricly. In his cas h rm undr h radical signs in (A9 is posiiv and w hav disinc ral roos. Sinc all of h paramrs ar sricly posiiv, h following is ru:

26 4 if γβ ( k k k > > 0 (A (A This condiion rquirs inrs ra adusmn in rspons o inflaion and monary growh o grar han h adusmn of incorrc inflaion xpcaions. Howvr if his condiion is m, h radical rm in ach roo will smallr han h firs xprssion on h RHS of (A9, oh roos will ngaiv and h sysm convrgs o is quilirium valus. In Cas, (A0 is m sricly and h radical rms vanish in oh roos. Givn (A oh roos ar idnically ngaiv and w hav sailiy. In Cas 3, (A0 is no m and w hav complx roos wih cyclical flucuaions. Sailiy hn hings on whhr h ral par of h roos is ngaiv. This ral componn is simply h firs rm on h RHS of (A9 and his is ngaiv givn (A. This in urn dpnds on (A as wih Cas. W may hus conclud ha a sufficin gnral condiion for sailiy of h Fridman sysm is givn y (A. Modl : Th Baslin Modl wih Endognous Mony Th scond modl in h x mad up of quaions ( o (5 and ( may simplifid y susiuing ( ino (, ( ino h rsuling quaion, and rarranging. This yilds quaion (A3 low. UE UE Y ( A i (A3 γ γ Susiuion of (4 ino (3 and h rsuling quaion ino (5 givs (A4 as for. Equaions (A3 and (A4 now consiu h modl s sysm which in marix form is givn y (A4: 0 ' 0 UE ' 0 Y γ β UE 0 UE / γ ( A i ( w p (A4 Th soluion o (A4 is: Y UE UE A w p ( i aγ βγ ( w p β (A5

27 5 Bu rcognising ha: β p w UE his coms: β ( ( p w i A Y UE (A6 Th sailiy of his quilirium dpnds on h soluion o h following characrisic quaion implid y h rlvan vrsion of (A7 for h prsn sysm: 0 γ β r (A7 Th soluion o (A7 is sraighforward: γβ r (A8 Th rm on h RHS of (A8 is unamiguously posiiv indicaing ha (A6 is unsal wihou cycls. Modl 3: Endognous Mony and Workr Mony Illusion Th modl wih mony illusion on h par of workrs is mad up of quaions (-(3, (5, (5 and (. Susiuing (5 ino (3 gnras h radiional vrsion of h Phillips curv which may susiud ino (5 o oain (A9 low. Rarranging ( and susiuing h rsuling xprssion along wih ( ino ( and normalising givs (A0. Equaions (A9 and (A0 hus consiu our wo quaion summary of h sysm. ( p w UE d d β (A9 ] ( [ i A Y UE UE γ γ (A0 In marix form his may wrin as: ] ( [ ( ' ' i A Y UE p w UE UE γ γ β (A

28 6 Th soluion o his sysm is: βγ [( A i Y] ( γβ UE γ UE [ Y ( A i ] ( γβ (A Th sailiy of his inrmporal quilirium dpnds on h roo of h characrisic quaion associad wih h following drminanal condiion: r γ Thr is only a singl roo for his quaion: β 0 (A3 r ( βγ (A4 which mus ngaiv for sailiy. Ngaiviy is nsurd undr h following condiion: β < (A5 γ Modl 4: Endognous Mony and Mony Illusion on h Par of Firms Th modl wih mony illusion on h par of firms is mad up of quaions (0, ( o (5 and (. Following h sam procdur as prviously, w may susiu ( ino (0 and h rsuling xprssion for oupu ino (. This givs h following xprssion for unmploymn afr rarranging: UE UE γ Y γa γi (A6 Th EAPC is also oaind h sam way as for y susiuing (4 ino (3 o oain (A. Whn (A is susiud ino (5 w oain (A4 onc again. Bu now w may susiu (A6 for unmploymn o oain h following firs ordr diffrnial quaion in xpcd inflaion: d d ( w p β UE βγ [ Y ( A i ] (A7

29 7 This dlivrs a much simplr xprssion han in h modls prviously considrd and h soluion for unmploymn is immdialy apparn. Th soluion is oaind y sraigh ingraion (Chiang 984, 473 and is givn y: { ( w p β UE βγ [ Y ( A i ]} C (A8 w p whr C is a consan ha dpnds on som oundary condiion. Givn ha UE h β rm in racs on h RHS of (A8 is zro whn aggrga dmand is qual o ponial oupu, ha is whn: Y A i (A9 In his cas xpcd inflaion is consan a h oundary condiion. Ohrwis h valu of xpcd inflaion riss wihou limi if Y < A i or falls wihou limi if Y > A i. Modl 5: Fridman s Modl wih a Taylor Rul Fridman s modl wih a Taylor rul is mad up of quaions ( o (5 and (4. W follow h now familiar procdur of susiuing (4 ino (3 o oain h EAPC. Susiuing h EAPC ino (5 givs h familiar diffrnial quaion in (A30 low. Thn susiuing (4 ino ( and h rsuling quaion along wih h EAPC ino ( givs (A3 low: d d β UE ( w p (A30 [ γθ γ( θ β ] UE [ γ γ( θ] UE γ( θ( w p γ [ Y ( A ar ] γ( θ θ UE (A3 Rvrsing h ordr of hs quaions and puing hm ino marix form givs: 0 ' γθ γ ( θ β ( θ 0 UE ' 0 β UE 0 UE γ [ Y ( A r] γ ( θ( w p γ ( θ θ UE ( w p (A3

30 8 Th soluion o his sysm of quaions is givn y: θ θ UE θ UE UE ( w p θ [ ] [ Y ( A r ] γ θ β θ γθ θ w p β (A33 Th Taylor rul gnras h sam unmploymn rsul as dos h original Fridman sysm alhough h inflaion rsul is complx and difficul o inrpr. This may, howvr, simplifid y making hr assumpions or osrvaions: Firsly w follow Taylor (993 y assuming θ θ θ ; scondly w no from ( ha Y A ( i. By dfiniion whn h rackd rm is qual o h naural ra of inrs, r, oupu is a is ponial lvl, hus ( A r 0 ; Thirdly, w assum ha h unmploymn arg, U E, is h Y NAIRU, which in our modl is givn y UE. Undr hs condiions, h quilirium inflaion is simply h cnral ank s policy arg: (A34 Th sailiy of hs rsuls dpnds on h roo of h characrisic quaion associad wih h following drminanal condiion: γθ r γ [ θ ( θ β ] 0 β (A35 Thr is only a singl roo for his quaion: βγθ r (A36 γ [ θ ( θ β ] Sinc all of h paramrs ar sricly non-ngaiv, his xprssion is sricly ngaiv and h inrmporal quilirium in (A33-34 is sal.