Gerhard Illing Script: Money - Theory and Practise

Transcription

1 Grhard Illing Scrip: Mony - hory and Pracis Spring 212 Par 2-2 Inracion bwn Monary and Fiscal Policy: Aciv and Passiv Monary Rgims Up o now, w lookd a a vry sylizd horical modl, rying o undrsand mchanisms bhind h drminaion of pric lvl and ra of inflaion. W lookd a h possibiliy of slf-fulfilling hypr-inflaionary (or dflaionary) quilibria vn whn cnral banks ry o implmn som sady sa arg ra of inflaion π*. In ral lif, howvr, priods of hyprinflaion usually aris during ims of disrss for public financ. h inuiion bhind his mchanism is fairly sraighforward and par of common sns: If govrnmn spnding (or public db) gs ou of conrol, hr is a nd o rsor o ohr mans for gnraing rvnus, and usually h prining prss sms o provid an asy way ou. Any analysis ignoring fiscal-monary inracions is likly o rach mislading conclusions abou how inflaion is drmind during hs pisods. Financing govrnmn spnding via mony prining is h sandard riggr for high and possibly hypr-inflaion. Obviously, hr is a link bwn public db and incnivs o prin mony, so w nd o sudy closr h link bwn fiscal and monary policy. Prining mony cras signorag rvnu for h govrnmn. I is on sourc of rvnu jus lik axaion. Usually, signiorag is jus a small par of govrnmn rvnu. Bu if public db is high, hr is a srong mpaion o as govrnmn budg consrain by acivaing h prining prss. High marginal ax ras caus allocaiv disorions. By issuing govrnmn bonds, h ax burdn is shifd ino h fuur insad, bu a h cos of imposing addiional burdn from inrs ra paymns. Prining mony allvias h inrs burdn, bu i riggrs disorions ou of highr inflaion. Whn anicipad, h incras in inflaion drivs inrs ras up a h sam im, corroding h dmand for mony. So, ffciv signorag in ral rms is likly o dclin dramaically. Can h nd o cra signorag incom for h govrnmn rally b a convincing xplanaion for monary policis nding in hypr-inflaion? Hav such policis bn moivad by h amp o imis som sady sa signorag rvnu or ar hy insad h rsul of a loss of conrol in govrnmn? Philip Cagan (1956) sudid hs qusions in his analysis of hyprinflaionary priods. If financing xcssiv govrnmn spnding via mony is likly o riggr hypr-inflaion, how can w dsign mchanisms o cu h link bwn govrnmn db and cnral bank financing? In Grmany, basd on h dvasaing xprinc wih hypr-inflaion during h Wimar rpublic, h nwly crad Dusch Bundsbank was xplicily prohibid o buy govrnmn bonds. Following ha rol modl, h ECB consiuion (as wrin in h Maasrich ray adopd in Maasrich on 1 Dcmbr 1991) ruls ou dirc lnding o Euro ara govrnmns on h primary mark. Fiscal ruls in h Maasrich ray ry o impos fiscal disciplin on govrnmn db (such as h limi of 6% for db o GDP raio and 3% for dfici o GDP raio). 38

2 Is hr a dirc link bwn h lvl of govrnmn db (or h db o GDP raio) and h ra of inflaion? No ncssarily. If w look a h daa, w g qui a divrs picur. h xprinc in UK and US shows ha vn whn db o GDP raios shoo up abov 12% or vn 2%, his xplosion nd no auomaically b followd by a dbasmn of currncy Insad, in many counris hy hav bn followd by a priod of rprssion for h financial scor imposing an ffciv ax on ass holdrs wih ral inrs ras bing blow h ra of ral growh: So for an xndd priod, nominal ras for govrnmn bonds hav bn lowr han nominal growh ras. Undr such condiions, high nominal growh ras allowd o grow ou of db (s Rinhar/ Sbrancia 212). On h ohr hand, in qui a fw counris hypr-inflaion sard alrady a much lowr db o GDP lvls. Obviously, hings ar much mor ricky. h ky issu is how boh monary and fiscal auhoriis ar xpcd o rac wih hir fuur policy acions o currn shocks in h conomy. Wha is h opimal policy dsign? Usually, w look a h opimal soluion of a social plannr. Bu for som issus, i is mor ralisic o analys assignmns of diffrn asks o diffrn agncis. So i may mak sns o dlga h ask of pric sabiliy o an indpndn cnral bank and assign fiscal policy (h ask o dcid abou h pah of govrnmn spnding and axaion) o h rasury. Obviously, sinc boh asks ar inrdpndn, a las som ims hr ar bound o b inhrn conflics. I is usful o disinguish bwn rgims wih ihr monary or fiscal auhoriy bing aciv or passiv. [Lpr/Walkr 212]. If, afr som incras in db, fiscal policy is xpcd o rspond wih ough masurs rducing h lvl of db ihr by raising axs or cuing govrnmn spnding, h rasury (h fiscal auhoriy) is calld passiv. I aks h inr-mporal govrnmn walh consrain srious and maks sur ha his consrain holds all h im (wihou forcing h cnral bank o ak acions). Such a rgim is calld Ricardian rgim. In ha cas, h cnral bank is calld h aciv par (i is commid o push is own agnda, such as implmning pric sabiliy), whras h rasury is acing passivly. No ha h rasury is no man o b passiv in dciding abou h opimal pah for govrnmn spnding. Qui h conrary. Bu whn adjusing h spnding pah afr shocks, i aks h inr-mporal walh consrain sriously for a givn pric lvl. So i dos no ry o inrfr wih pric lvl drminaion. In conras, if h cnral bank follows a passiv policy, i rsponds ndognously o movmns by h rasury, h lar bing commid o som prdrmind pah of axs and spnding, no adjusing ha pah passivly as a rspons o xognous shocks. Usually, sandard analysis simply assums ha h pah of fiscal policy auomaically adjuss such ha monary policy is allowd o conrol inflaion. In our rminology, fiscal policy is assumd o b passiv. Obviously, his is no always a corrc dscripion of hisory. Frqunly, h rasury ris o impos consrains on cnral bank opions, and hings may nd up pry bad. Exacly for ha rason, spcific insiuional arrangmns (lik indpndnc of cnral banks) hav bn sablishd o forc fiscal policy o b passiv. A good (or, as i urns ou, rahr badly dsignd) xampl is h ray of h ECB. I is basd on h ida ha a drmind cnral bank can always conrol inflaion by conrolling mony 39

3 growh. Bu a cnral bank can acivly (indpndnly) drmin h im pah of prics only if is policy acions riggr a validaing rspons from h fiscal auhoriis. hr is no auomaic mchanism by which fiscal disciplin can b complld by a cnral bank ha conrols mony growh. Hisorical xprinc augh ha fiscal-monary inracion ofn consiss of amps by h fiscal auhoriis o g h cnral bank o buy mor govrnmn db han is consisn wih sabl inflaion. If h rasury pursus is own inrs for poliical conomy rasons, his can rsul in a pry bad oucom and may jusify a dsign forcing h rasury o b passiv. An insiuional dsign in h Euro Ara wih a singl, larg cnral bank and fracurd fiscal auhoriis of many small naional rasuris was sn as lss likly o b subjc o his inflaionary prssur from h fiscal sid han in h usual singl-counry fiscal-monary pair of insiuions. For ha rason, i smd o b a gra ida o assign h ask of pric sabiliy as a clar manda o an indpndn cnral bank wihou a cnral fiscal counrpar. Unforunaly, h Euro crisis dmonsrad srious faul lins in his dsign: hr ar srious gaps in h insiuional srucur of h Euro Ara for h following rason: h inflxibl dsign ignors ha cnral banks conrolling fia mony may play a crucial wlfar improving rol as lndr of las rsor. For such cnral bank aciviis, hr is a crucial nd for fiscal backing, sinc by naur hs acions ar subjc o considrabl fiscal risks ha hav o b born by h rasury (or rahr, in h nd, by h ax payr). Wihou cnral fiscal counrpar, howvr, i is hardly fasibl such adjusmns. Finally, inflaion may ac as a wlfar improving cushion for som shocks (s Sims 212). As a rspons o svr shocks, movmns in h pric lvl may b h opimal scond bs oucom. In such cass, adjusing h pric lvl in an conomy wih nominal db can srv as a buffr, allowing implmnaion of sa coningn adjusmns. In ordr o undrsand hs issus br, w firs hav o g a clar undrsanding of h link bwn cnral bank s signorag and h govrnmn budg consrain. Signorag h govrnmn (h rasury) raiss axs and issus bonds in ordr o financ govrnmn spnding. Bu i is also h monopoly producr of bas mony. Evn hough cnral banks in many counris all ovr h world acquird saus of indpndnc for day o day opraions, ffcivly hy ar par of h govrnmn. Rvnu from signorag flows o h rasury. Cnral banks may hav h powr o dcid how much signorag incom is disribud o h rasury pr priod, bu in h nd h cnral bank s balanc sh is par of govrnmns asss. So in his scion, w will ra signorag as govrnmn rvnu. Sinc h cos for prining mony ar narly ngligibl, issuing addiional bas mony is on way for h govrnmn o gnra rvnus in ordr o g claims on ral rsourcs. his rvnu is calld signorag. In formr days, bfor h us of fia mony (banknos), signorag was vidn: i was h diffrnc bwn h rvnu gnrad by dnominaing coins wih som nominal valu and h cos of h mals lik gold and silvr usd as mdium of ransacion. Frqunly, coins wr gradually dbasd as currncy. ha is, h quaniy of gold, silvr, coppr or nickl conaind in a coin was rducd. h purpos was o cra mor coins ou of a givn amoun of spci and so o rais addiional rvnu for h sovrign a h xpns of his ciizns. his allowd building mor fancy palacs, bu of cours i rducd h purchasing powr of h coins (riggrd inflaion). Wih modrn fia mony, h mchanism o gnra rvnu is ssnially h sam, xcp ha producion coss for fia mony (colord pics9 of papr ar clos o zro. Wha ar h gains for h rasury? Effcivly, prining mony nabls h govrnmn o sav on inrs paymns for govrnmn bonds. h highr h sock of bas mony, h 4

4 lowr h sock of (inrs baring) govrnmn bonds ndd o financ a givn pah of spnding and axs. So ssnially, signorag pr priod from issuing som mony sock M is nohing ls bu h inrs paymns savd by bing abl o rduc n issuanc of bonds xacly by ha amoun M. Of cours, h nominal amoun is irrlvan; wha couns ar h ral rsourcs obaind. So w ar inrsd in ral mony balancs M/P. Frqunly, i is vn mor usful o masur M/P as shar of ral GDP Y. Wriing k=m/py for h raio of mony o nominal GDP w g: (.1) S = i k By issuing mony, govrnmn savs on inrs paymns for bonds. hs savings (rvnu from signorag) ar du o h fac ha priva agns ar willing o hold a las par of hir asss in h form of non-inrs baring mony insad of inrs baring govrnmn bonds. Nowadays, mos cnral banks pay som posiiv inrs i M i a las on rsrvs as par of bas mony. If inrs i M is paid on mony, signorag ariss only from h diffrnc bwn inrs on mony and inrs on bonds, ha is (.2a) S = ( i i ) M k. Frqunly, an alrnaiv concp is usd for masuring signorag, namly h addiional amoun of mony prind in ach priod. his dfiniion has srong inuiiv appal. Afr all, rvnu from prining mor mony is qual o h incras in h mony bas Δ M. o masur his rvnu as a shar of GDP, w again hav o divid Δ M by nominal GDP. his way, h ral rsourcs h govrnmn is abl o xrac as par of GDP from prining nw mony can b wrin as: Δ M Δ M M (.3) S M = = = μ k P Y M P Y S M capurs currn rvnu from prining nw mony as shar of GDP. As shown in h quaion, w can rformula ha rm using h dfiniion of mony growh ra μ = Δ M / M. S M is qual o h growh ra of mony ims h mony bas k. Wha is h diffrnc bwn S and S M ; how do hy fi oghr? W will s ha S M is jus on par of oal signorag. h corrc masur is S. Boh concps rla o ach ohr in h following way. Us h Fishr quaion i = r +π and assum raional xpcaions, so π = π. Now l us do sady sa analysis. In sady sa, k - h mony sock rlaiv o GDP will b consan across im. Wih a consan nominal inrs ra, mony dmand as shar of GDP will say consan. So in quilibrium, h mony sock has o grow proporional wih nominal GDP. ha is, h ra of mony growh is h sum of h ra of ral growh and inflaion: μ = y + π. For givn y, h highr μ, h highr h ra of inflaion π = μ y. Wih raional xpcaions, h nominal ra of inrs riss wih μ proporionally, giving h rlaion i = r + μ y. Using ha rlaion, h diffrnc bwn h wo concps can b sn as: S = i k = μ k + ( k = + ( k S M In sady sa usually r>y. So S M is lowr han S by h facor ( k. h diffrnc is ha S M capurs only h rvnu from prining nw mony. In ordr o driv h corrc masur, w hav o ak ino accoun ha ffciv oal n db of govrnmn is lowr h highr h asss hld by h cnral bank (h highr h sock of mony). In h cnral banks balanc sh, non-inrs baring liabiliis (h sock of mony) ar qual o h cnral bank s asss which arn posiiv inrs i. If priva agns ar willing o hold par of hir walh in h form of non-inrs baring asss calld mony, 41

5 h rasury dos no nd o issu inrs baring bonds by xacly ha amoun. Hr, w assum compl marks. If so, h risk-adjusd rurn on all asss hld will b qual hr is no diffrnc in rurn on govrnmn bonds, privaly issud bonds, forign rsrvs or vn gold. Arbirag aks car ha h risk-adjusd rurn will b h sam for all asss in quilibrium. ak h cas of gold as non-inrs baring ass, for xampl. According o h Holling rul, h ral pric of gold (rlaiv o ohr goods) is xpcd o ris such ha ral rurn on gold is qual o h rurn of ohr asss. No: If w ak risk ino accoun, h ffciv rurn may diffr across ass classs, bu hr w absrac from ha issu. In paricular, h risk olranc of h cnral bank (as par of govrnmn) may diffr from h willingnss o hold risk by hos priva agns abl o bar risk. By buying mor risky asss in unconvnional monary opraions (quaniaiv asing), h cnral bank may chang h risk-srucur of asss hld in h priva scor. W ignor his possibiliy. In a rprsnaiv agn conomy, hr would b no ffc if h cnral bank buys risky asss h priva scor is no willing o hold for h following rason: h rprsnaiv agn will ak ino accoun ha his ax obligaions ar ging mor risky by his opraion and so will ak off-sing acions. Afr all, h ovrall risk dos no disappar in h conomy. So obviously, unconvnional monary opraions can hav ral ffcs only if hr ar disorions in h mark (lik missing insuranc marks agains macro risks) which ar no capurd by a rprsnaiv agn modl. In an conomy wih disorions and hrognous agns, h cnral bank may b abl o rmov som of hs disorions by buying risky asss. Providing social insuranc mchanisms no offrd in priva marks may rduc ovrall risk in h priva scor of h conomy (s scion xx). Why is h ffciv ral rurn of h mony bas k qual o r-y? h nominal rurn of h asss hld by h cnral bank is i. If nominal GDP grows a h ra π + y, h asss mus arn his ra jus in ordr o kp h raio of asss o GDP consan: h rurn mus a las compnsa for inflaion and ral growh o kp mony as shar of GDP consan. So h ffciv ral rurn is jus i π y = r y. hus, h ral savings from issuing mony balancs compard o issuing nominal govrnmn bonds wih inrs paymns i is ( k. his rm has o b addd o h signorag from prining frsh mony o calcula oal signorag in sady sa. Maximum Signorag Up o now, whn masuring S = i k, w simply ook k as givn, indpndn of cnral bank policy. Bu of cours, whn h cnral bank incrass h growh ra of mony, his will caus a highr ra of inflaion and so a highr nominal ra of inrs. k will say consan only as long as mony dmand dos no rspond o inrs ras. Whn w analys priods of hyprinflaion, his is crainly no snsibl assumpion. Mony dmand dpnds ngaivly on inrs ras, so S = i k(i) wih k / i <. Whn w viw hyprinflaion as a phnomnon possibly arising from h nd o financ govrnmn spnding, w nd o ak ino accoun ha dmand for ral mony balancs dclins wih h ra of inflaion. Signorag is zro for i=. Bu hr will also b no rvnu from signorag whn agns ar no longr willing o hold mony bcaus h ra of inflaion is oo high. Obviously, hr is som imum lvl of sady sa rvnu. How can w drmin h imum sady sa govrnmn rvnu from mony craion? 42

6 h answr is sraighforward. If prining mony incurs no cos (a usful bnchmark), sady sa rvnu is simply S = i k(i). Maximising S givs h condiion S k k i = k( i) + i = 1+ η k = wih η k = as inrs lasiciy of mony dmand. i i i k h rvnu imising sragy is o choos mony growh ra (or inflaion) such ha lasiciy of mony dmand is qual o minus on. his is h sandard condiion for a k i monopoly producr imising rvnu: η k = =. i k S S k k i = i k(i) ; = k( i) + i = ; η k = = i i i k For i=, signorag rvnu S = i k(i) is zro. Wih i rising (as a rsul of incrasing inflaion, riggrd by mony growh), rvnu firs incrass vn hough dmand for ral mony balancs dclins. Bu abov som poin A (whn absolu valu of lasiciy of mony dmand gs smallr han 1), rvnu go down. h highr h ra of inflaion (and hus, in a raional xpcaion quilibrium, h inrs ra), h mor popl ry o mov ou of mony holding. Wih lasiciy of mony dmand bing highr han on, h dclin in dmand mor han offss h pric incras. So rvnu dclins abov som pric A as shown in figur xx. his curv is h familiar rvnu ffc for a monopolis slling his produc wih pric lasic dmand. I dos no pay o rais his pric furhr whn absolu lasiciy of dmand gs highr han 1. If so, addiional rvnu from h highr pric is mor han offs by rducd dmand. In public financ wih ax ra as pric, his ffc is frqunly calld Laffr curv: Philip Cagan sudid priods of hyprinflaion in hisory. Using a log-linar mony dmand funcion, h rid o sima h mony growh ra which imiss signorag in sady sa. As shown in figur xx, during hyprinflaionary priods h acual growh ra of mony is far abov h ra imising sady sa signorag. his indicas ha inflaion ras mus hav bn so high ha w mov o h wrong sid of h Laffr curv. Wih a lowr ra of mony growh (inflaion), rvnu would hav incrasd. his rsul is calld Cagan s paradox and suggss ha hyprinflaion canno b xplaind by som concrn for sady sa rvnu. i 43

7 Cagan did no us h concp of raional xpcaions, bu rahr assumd adapiv xpcaions. ha is, agns do no fully anicipa h fuur pah of h pric lvl, bu insad rly on pas xprinc for forming hir xpcaions. Wih adapiv xpcaions, h dclin in mony dmand is occurring a a slowr ra, allowing h rasury o capur highr rvnu a las for som inrmdia im priod. For som inrval, h ra of inflaion may hav hlpd o gnra highr rvnus. Hypr inflaions sar a low ras, bu hn nd o acclra pry fas. Avrag monhly daa may giv a mislading picur. Evn wors: Hyprinflaions ar shor-livd pisods lasing around 2 monhs. Du o lack of daa, mpirical analysis using monhly daa usually includs som priod prcding hyprinflaion (wih lowr ras), so monhly sudis of mony dmand may giv mislading rsuls. Mladnovic/Provic (21) usd daily daa for h las 6-7 monhs wih mos svr hyprinflaion in Srbia in (h priod wih h highs ras worldwid: h avrag monhly currncy dprciaion ra was 17% compard o 322% during Grman hyprinflaion). hy show ha h public adjuss mony dmand a daily frquncy in hs xrm condiions, bu h simas for dmand lasiciy ar far lowr han hos obaind wih monhly daa, so h conomy has bn on h corrc, incrasing sid of h Laffr curv mos of h im. Ovrall, hisorical xprinc is hard o rconcil wih som raional moivaion for craing signorag as a long rm, sady sa oucom. Obviously, during hs priods insiuional arrangmns rquird for gnraing susainabl ax rvnus hav brokn down, forcing auhoriis o rsor o ohr ways of financing. Alrnaivly, hyprinflaionary pisods may b sn as a way o adjus h pric lvl afr som srious shock, wiping ou a subsanial par of pas nominal db obligaions. his xplanaion is in lin wih h so-calld fiscal hory of h pric lvl. Wha is h opimal ra of mony growh or ra of inflaion? o provid a saisfacory answr, on has o hink abou adqua criria o apply. aking rvnu as cririon, w ask wha lvl of k is imising sady sa i k h ara D in figur xx. Bu gnraing rvnu is no a mans in islf. From a wlfar poin of viw, policy should b mor concrnd abou consumr surplus. h highr h inrs ra (h ra of sady sa inflaion), h lowr h consumr rn ou of holding ral mony balancs. In figur xx, consumr rn is masurd by h riangl C. 44

8 Incrasing i (as from i o i 1 in Figur xx) rducs consumr rn by A+B. A h sam im, i changs rvnu by A-E. Rvnu riss by A wih a highr pric for holding mony, bu sinc h highr pric rducs dmand k, hr is also a loss in rvnu quivaln o E. As long as η < 1, rvnu is rising wih highr i, whras whn dmand is lasic wih η > 1 k rvnu gos down wih highr i (h ara A bing smallr han E). If w ak h sum of consumr rn and producr rn (rvnu from signorag) as rlvan cririon, an incras in h inrs ra unambiguously rducs ovrall wlfar by h ara B+E. k b) Minimisaion of wlfar losss (Fridman rul): Opimum ra: i=. Edmond Phlps: dadwigh loss from axaion inflaion as on insrumn o ax: Opimal mix bwn axaion and inflaion ~ Fridman rul dos no hold. Bu: If mony as inrmdia inpu, i is opimal no o ax mony: s Corria/ls (1996) 45

9 h govrnmn s inr-mporal budg consrain L us now hav a closr look a h govrnmn s budg consrain and s how db volvs across im for som pah of spnding and ax rvnu. If B -1 is h lvl of (bond financd) nominal db incurrd a las priod -1, db changs according o: (xx) Δ B = B B 1 = D = G Δ M + i B Nominal db incrass Δ B > whn h govrnmn has a currn dfici D o b financd by issuing addiional db. h oal dfici D consiss of (1) h primary dfici PD G - h xcss of govrnmn spnding G ovr rvnu from axaion ; and (2) h inrs burdn arising from pas db i B. h highr (3) signorag from prining mony Δ M, h lowr h nd o issu nw inrs baring db. Evn wih a primary surplus and posiiv signiorag ( G + Δ M > ), h govrnmn is facing a oal dfici whnvr h inrs burdn from pas db xcds currn n rvnu. In gnral, Δ M is farily small and so i is usually ignord whn discussing db susainabiliy. Hr, w includ i as par of rvnu. Nominal valus ar rahr uninformaiv. Why should w car if nominal db incrass simply bcaus of inflaion, wih boh nominal rvnus and spnding incrasing a h sam ra? W ar inrsd in h ral dfici (imposing a ral burdn o h priva scor), so w nd o divid by h pric lvl P. Furhrmor, growing db will b of limid concrn whnvr ral GDP is growing a h sam ra or vn fasr han h ral inrs ra. o corrc for ral growh, w hav o adjus also by dividing by ral GDP Y. hus, h rlvan B issu is how dos h db o GDP raio b = volv across im? h ral burdn of db P Y as shar of GDP is h ral inrs (n of h ral growh ra) o paid on h db raio b. Wha drmins changs Δ b = b b in ha raio? o find ou, w simply rwri quaion xx as a raio of currn nominal GDP. As a firs sp, rformula xx as a diffrnc quaion bwn and : B B B = G Δ M + ( 1+ i ) B h db nx yar is h gross db (including inrs paymns) inhrid from las yar plus h primary dfici. Afr dividing all rms by currn nominal GDP, w g B G M B = + ( 1+ i ) 1 P Y P Y P Y P Y P Y Δ his looks pry ugly and uninformaiv, bu i can b rwrin as h following simpl and ky diffrnc quaion for h db o GDP raio: b τ μ or = g + k + ( 1+ r y ) b (Xx) b b μ = g τ + k + ( r y ) b o g o ha xprssion, w us h following dfiniions: b = B / P Y is h db o GDP raio a im g = G / P Y is govrnmn spnding rlaiv o GDP τ = / P Y is axs rlaiv o GDP 46

10 h incras in mony prind rlaiv o GDP (signorag from mony prining) can b xprssd as: Δ M Δ M M = = μ k wih μ as growh ra of mony and k as mony hld as shar P Y M P Y of GDP. Finally, w simplify h las rm as follows: B B 1+ i ( 1+ i ) = = b P Y P Y (1 + π ) (1 + y ) 1+ i (1 + π ) (1 + y ) ~ b (1 + r y ) Using h dfiniion P = ( 1+ π ) P 1 ; Y = (1 + y ) Y, h Fishr quaion i = r + π and h 1+ i approximaion 1+ i π y = 1+ r y (1 + π ) (1 + y ) (.4) b( ) = g( ) τ ( ) μ k + ( b( ) Frqunly, i is much asir o us coninuous im analysis. So l us rwri h voluion of h db raio across im as h diffrnial quaion: Again, h db raio dpnds on: (1) Primary dfici d () = g () τ () - h diffrnc bwn public spnding as shar of GDP and h ax ra (par of boh spnding and axs ar jus ransfrs across agns; for dynamic ffcs, h n bwn spnding and ax ra is crucial), (2) Signorag as shar of GDP μ k and (3) h ral db burdn ( r( ) y( )) b( ) - h inrs o b paid on db accumulad in h pas b(). o gain a br inuiion, l us again do sady sa analysis. So considr as simpls cas an conomy wih consan growh ra y and consan ral ra of inrs r (his simplifis calculaions and noaion, bu can asily b gnralisd). Again, w also assum a consan mony growh ra μ. Saring a som iniial lvl b(), h db raio volvs bwn = and = according o: ( ( ( ) (.5) b = b + [ g( ) τ ( ) μk d ] Calculad in prsn valu rms, viwd from im =: (.6) b = [ τ ( ) g( ) + μk] d + b Priva agns holding govrnmn db ar no willing o lav rsourcs unusd a h nd of h world, giving hm as gif o h govrnmn. So in a conomy wih som fini nd, h govrnmn is subjc o h quivaln of h No-Ponzi gam consrain such ha b. I is no allowd o nd h world wih posiiv db. For, wih no fini nd of h world, r y) h quivaln of ha consrain is lim b. Sinc govrnmn dos no accumula xcss walh, h consrain will b binding in quilibrium. Imposing h ransvrsaliy condiion lim b = givs (GW) (.7) b } = { ps( ) + μ k d = [ τ ( ) g( ) + μ k] d 47

11 Milon Fridman inroducd h concp of prmann incom. ha is a consan lvl of annual incom which givs xacly h sam prsn valu of walh as h xpcd acual, possibly flucuaing incom sram. In analogy o ha concp, l us dfin τ and g as h prmann (normal) ax and spnding ra which givs h sam prsn valu as h xpcd, possibly flucuaing sram of ax rvnus and govrnmn spnding. ha is dfind as: (.8) τ = ( τ d = ( τ ( ) d and (.8a) g = ( g d = ( g( ) Using h dfiniion of τ and g or ps = τ g as prmann primary surplus, w can rwri our condiion for h govrnmn walh consrain as: GW2 b B = P τ g + μ k = r y ps + μ k = r y his condiion has a sraighforward inuiiv inrpraion: h currn lvl of db /GDP is qual o h prsn valu (discound by h ffciv ral inrs ra r-y) of fuur prmann rvnu from primary surplus (as raio o GDP) and signiorag. Mahmaical xcursus: Unlss GW holds, h db raio will ihr xplod or implod. o s his, l us considr a pah wih a consan primary surplus and consan signorag: ps + μ k = τ g + μ k. h voluion of h db raio across im is characrizd by h following linar diffrnial quaion (h law of moion): b & ( ) = { ps + μ k} + ( b( ). How can w solv a linar diffrnial quaion b& ( ) = a b( ) c? W spli h soluion in wo pars. Firs, w c look a a paricular soluion. L us ak h sady sa valu b & ( ) = or b p =. a Scond, by ingraing b & a ( ) = a b( ) (sing c=), w g h homognous par h soluion: b ( ) = A for undrmind A. h gnral soluion is givn by h sum of homognous par and h paricular soluion. Sinc a b( ) = A + c / a has o hold also a h saring poin = wih h givn saring valu b (no ha a = 1 ), w mus hav b ( ) = A + c / a = b or A = b c / a. So h dfini soluion is: a b( ) = [ b c / a] + c / a ( r y) Using a=(r-y) and c= {ps+μk}, w g b( ) = [ b { ps + μ k}/( ] + { ps + μ k}/( r ) d y Obviously, for r>y h govrnmn db raio is unsabl unlss b = { ps + μ k}/( Bu of cours, mporary dviaions lik a smallr surplus or vn dfici ps ( ) < ps for som im priod - do no harm as long as h lowr valus will b offs lar by addiional surplus: ps + μ k b() = + r y [ ps( ) ps] ( ) d h ransvrsaliy condiion lim b = implis [ ps( ) ps] r y) d = 48

12 Rlaion bwn diffrn signorag concps and h govrnmn walh consrain: If w look a h govrnmn s balanc sh, l b b h bond-financd db pr GDP hld by h priva scor. So b is govrnmn db xcp for h asss hld by h cnral bank: b = b ~ k. As a hough xprimn, l us brifly spara h balanc shs of rasury and cnral bank. Wih oal db issud by h rasury bing b ~, rasury s ral inrs burdn ~ pr priod is ( b. Each yar, h cnral bank disribus som profis (which may b ~ ngaiv) o h rasury. L S ( ) b h rvnu paid o h rasury by a h nd of yar. If S ~ is qual o sady sa signorag as dfind in xx: S = S = μ k + ( k, hn w g xacly h law of moion for govrnmn db as drivd in xx: ~ ~ Δ b = g τ + ( i π y) b S = g τ + ( b μ k wih b = b ~ k. In GW, w lookd a h govrnmn walh consrain using h concp of n govrnmn ~ db b rahr han oal db hld by h priva scor is b = b + k. h fac ha h cnral bank issud h mony sock k rducs n obligaions for h govrnmn. ~ Susainabiliy of db Wha limis dos h govrnmn walh consrain impos for h db raio? Undr wha condiions will h govrnmn mov on h vrg o bankrupcy? W hav sn ha h db raio will ihr xplod or implod unlss currn db obligaions ar covrd by a fuur primary surplus which, in prsn valu rms, maks sur ha h walh consrain holds. Bu frqunly, govrnmns run prsisn dficis. Will a govrnmn wih a consan dfici ncssarily run ino solvncy problms? Dos i mak sns o impos som uppr limi o h dfici raio such as in h Maasrich criria or should w vn impos condiions rquiring a posiiv primary surplus? W hav o disinguish bwn primary dfici and oal dfici which also includs h inrs paymns on db issud in h pas. h Maasrich criria impos a limi for h nominal db raio b,6 and for h nominal oal budg dfici raio d,3. How will h db raio volv whn h oal budg dfici raio (including db srvic) says consan? Will h db raio xplod or convrg o som sady sa? B& L = g τ μ k + i b = d = consan p Y hn b & = d ( y + π ) b. Hr d is oal dfici including inrs paymns! For an iniial db o GDP lvl b, h soluion for his diffrnial quaion b = d ( π + y) b is: π + y) ( π + y) ( ) d π + y) d b( ) = b + [ d] d = b + y π + π + y So indpndn of b, w hav d d lim b( ) =, convrging o h sady sa: b* = π + y π + y A h im whn h Maasrich criria hav bn dsignd, h xpcd ral ra of growh for h Europan conomy was assumd o b y=,3 and h arg ra of inflaion π =. 2. By imposing h limi d=,3 for oal dfici, b was xpcd o convrg o b=,6 = 6% indpndn of h saring poin. Of cours, h lowr y and π, h highr will b h sady sa raio b*. 49

13 h highr h sady sa b*, h highr h ax burdn imposd on h conomy (for a givn ffciv ral inrs ra r-y). Can w calcula som imum lvl of db raio which should nvr b xcdd? Assum w iniially sard - long im ago - wih a low lvl. Bu manwhil, as h rsul ihr of bad shocks or lax spnding habis, h db raio ros sadily during h las dcads and has now (ha is, a =) rachd h lvl b. Equaion GW lls us ha such a pah is fasibl as long as h prsn valu from fuur primary surplus and/or rvnu from signorag ar sufficin o covr currn db obligaions. If no (if w xcd som criical hrshold lvl), hn govrnmn would b insolvn and would hav o dfaul. So ky for solvncy is o hink abou imum susainabl primary surplus and signorag. Obviously, hr is a minimum lvl of govrnmn spnding ndd o mak sur ha sociy survivs (lik nsuring propry righs by lgal auhoriis and polic, providing basic ducaion c.), and hr is a imum ax ra (crainly blow 1) which can b nforcd wihou dsroying incnivs for conomic aciviy. h govrnmn says solvn as long as ps ps = τ g min wih τ as h imum prmann susainabl ax ra and g > < 1 min as h minimum susainabl spnding ra rquird o nsur a funcioning sociy. Furhrmor, l μ b h mony growh ra giving imum fasibl sady sa signorag. hn db is susainabl as long as b b No ha τ = b gmin + μ r y k = ps + μ r y k is h absolu limi o susainabiliy. Givn ha ngaiv shocks (such as an incras in h ral ra r-y) may advrsly affc (lik a financial crisis) may rsul in a drasic suddn incras in o impos som prudn cushion for h sady sa lvl b b* << b. b and ha srious shocks o h conomy b b, i is, howvr, rasonabl Sinc h ras τ and g min ar somwha arbirary, as pragmaic approach, w can calcula as susainabl ax ra h avrag ax ra which would b ndd o financ annuiy valu of fuur xpcd spnding and ransfrs, plus h ral inrs ra burdn on currn db: ˆ τ = ( [ g( ) d + b ] If τ < ˆ τ, axs hav o b raisd or spnding has o b cu in ordr o mak db susainabl. h magniud ˆ τ τ givs a masur for h adjusmn ndd. Frqunly, policy makrs ar rlucan o nforc adjusmn hoping o pospon ough, unpopular masurs and bing ha som posiiv shock in h fuur may allvia h prssur. If so, h db raio will incras furhr, forcing a sricr adjusmn in h fuur. How will a dlay of adjusmn unil im affc h siz of ndd policy acion? h iming of adjusmn is givn by d ˆ τ ( diffrniaing h quaion abov: = ( ˆ τ τ ) d 5

14 Ky assumpions usd in his conx: 1) h ral inrs ra xcds growh ra: r>y (ohrwis, hr would b no nd o car abou walh consrains any db could b paid back in fini im if h ral growh ra xcds h ral ra of inrs. r y) 2) ransvrsaliy condiion holds: lim b = Adjusmn mchanisms: Monary vs. fiscal adjusmn Whn w ak a closr look a h govrnmn walh consrain, w s ha, hr is a nd o coordina fiscal and monary policy. (GW) b = B / P Y = [ τ ( ) g( ) + μ k] In GW; h iniial lvl of nominal db B is givn from promiss mad in h pas. Again, w also ak h ral lvl of GDP Y as givn. h currn pric lvl P is drmind as a forward looking variabl, drmind by h xpcd pah of monary policy. h link bwn public db and prssur on h cnral bank o chang is policy cours ariss from h fac ha hr ar diffrn opions o cop wih looming solvncy problms. Basically, hr ar 4 diffrn ways of adjusmn whn h db raio is oo high for a givn spnding pah: A) Fiscal adjusmn: h rasury could commi o rais fuur primary surplus by incrasing fuur axs and cuing fuur spnding. ps (r y ) { ( )} d = [ τ ( ) g( )] d. his sragy aks boh h cnral bank pah μ k and also h iniial ral db raio b = B / P d as givn. B) Monary adjusmn: h cnral bank could rais h ra of mony growh (inflaion), aking h pah [ τ ( ) g( )] d as givn. Of cours, raising μ, by incrasing inflaion and inrs ras, will ngaivly affc ral mony dmand k(i). Bu as long as h conomy is on h incrasing sid of h Laffr curv, a highr μ can gnra mor rvnu from signorag. In a famous papr calld Som unplasan monaris arihmic Sargn/Wallac (1975) showd ha if h rasury is no willing o mov (o consolida is budg, commiing o a highr fuur primary surplus) and h cnral bank ris o play ough as wll, h following paradox may aris: A mporary igh monary policy may lad o an incras vn in h currn pric lvl P whn priva agns raionally anicipa ha in h fuur, h ra of inflaion nds o b vn highr in ordr o saisfy GW bcaus of h dlay in policy adjusmn. Chickn gam: Who will blink firs fiscal or monary auhoriy? Who imposs disciplin on whom? Diffrn objcivs, no a uniqu wlfar imising govrnmn agncy. Sargn/Wallac (1975) argu ha h naural assumpion is ha h fiscal auhoriy movs firs (by commiing o som pah of primary surplus), and monary policy mus b drmind in a way consisn o ha pah. If so, h cnral bank can mak mony ighr now only by making i loosr in h fuur. hy suggs ha changs in mchanism dsign may hlp o bind monary auhoriy by commiing o an announcd fixd rul (a pah of mps o chang h ruls of h gam such ha h cnral bank can commi no o adjus. 51

15 Chickn Gam and h rol of commimn Sylizd gam bwn fiscal and monary auhoriy on h vrg of bankrupcy: Sragis for fiscal auhoriy: High dfici wih xcssiv spnding ( d = 1) or db consolidaion (fiscal rform) ( d = ). Sragis for monary auhoriy: Pric sabiliy ( π = ) or us prining prss o avoid bankrupcy, riggring high inflaion ( π = 1). Payoff marix: d= d=1 π = 1 (3,3) (2,4) π = (4,2) (,) h firs numbr in ach Payoff marix rprsns h cnral bank s payoff, h scond numbr h rasury s payoff. Boh auhoriis hav diffrn objcivs; so hir payoffs diffr wih h sragis implmnd. Bu ( d = 1, π = ) is no susainabl for long. I is bound o nd up in bankrupcy, giving boh auhoriis h wors payoff (which is normalizd o ). Fiscal consolidaion ( d = ) is prfrrd by h cnral bank (allowing hr o achiv pric sabiliy π = ). Wih his combinaion, h cnral bank achivs h highs payoff (4). For h rasury, howvr, implmning spnding cus and raising axs is unpopular, so is payoff is highr whn h cnral bank givs in and rsors o h prining prss. h combinaion ( π = 1, d=1) is h prfrrd oucom from h rasury s poin of viw, bu i givs a low payoff of 2 o h cnral bank. h ohr way round wih ( π =, d=). Whn boh auhoriis chang hir cours (d=; π=1), bankrupcy is avoidd and budg surplus achivd, giving boh a payoff normalizd o 3. Wih simulanous movs, hr ar wo Nash-qulibria in pur sragis: Boh (1) (d=1; π=1) and (2) (d=; π=) ar bs rspons quilibria. If rasury russ ha h cnral bank will giv in firs, i is bs no o blink bu rahr coninu wih xcssiv spnding. If h cnral bank xpcs h rasury no o blink, i is bs for hr o giv in, giving h oucom (1). Symmrically, (2) is also an quilibrium. Bu hr is a high risk ha nihr of hs quilibria will occur, bu insad rahr h quilibrium in randomizd sragis wih a high risk of ralizing h wors oucom. Wih squnial movs, h possibiliy of commimn is crucial. In h gam r blow, again boh (d=; π=) and (d=1; π=1) ar Nash quilibria. Bu if h rasury movs firs, (d=1; π=1) is no subgam prfc. (d=; π=) is h only subgam prfc oucom. If, in conras o h gam r shown blow, h cnral bank would hav h powr o commi o a no bailou sragy righ from h sar, h squncing of movs would rvrs, giving (d=1; π=1) as subgam prfc soluion. Crucial: Ways o mak commimns crdibl? Challng for mchanism dsign. Dynamic vrsion: War of ariion 52

16 C) Adjusmn of h pric lvl: Fiscal hory of h pric lvl Lpr/Walkr (s also Cochran, Sims, Woodford, h iniial pric lvl P adjuss such ha GW is saisfid (opimal sa dpndn coningn Ramsy policy: Nominal govrnmn db as buffr o dampn svr shocks). o b wrin. D) Dfaul on ral db Rfrncs: Cagan, Phillip (1956). "h Monary Dynamics of Hyprinflaion". In Fridman, Milon (d.). Sudis in h Quaniy hory of Mony. Chicago: Univrsiy of Chicago Prss. Corria, Isabl/ ls, Pdro (1996) Is h Fridmanrul opimal whn mony is an inrmdia good? Journal of Monary Economics Volum 38, Issu 2, Ocobr 1996, Pags Eric M. Lpr / odd B. Walkr (212) Prcpions and misprcpions of fiscal inflaion hp:// BIS Working Papr 364. Mladnovic, Zorica/ Provic, Pavl (21) Cagan s paradox and mony dmand in hyprinflaion: Rvisid a daily frquncy, Journal of Inrnaional Mony and Financ 29, Rinhar, Carmn / Sbrancia, Bln (211) h Liquidaion of Govrnmn Db. BIS Working Papr 363. Sargn, homas/wallac, Nill (1981), Som unplasan monaris arihmic, Fdral Rsrv Bank of Minnapolis, Quarrly Rviw