TIGHT MONEY PARADOX ON THE LOOSE: A FISCALIST HYPERINFLATION

Transcription

1 TIGHT MONEY PARADOX ON THE LOOSE: A FISCALIST HYPERINFLATION Eduardo Loyo John F. Kennedy School of Governmen Harvard Universiy June, 999 ABSTRACT: Hyperinflaion is usually inerpreed as a resul of he moneary financing of serious fiscal imbalances. Here, a fiscalis alernaive is explored, in which inflaion explodes because of he fiscal effecs of moneary policy. Higher ineres raes cause he ouside financial wealh of privae agens o grow faser in nominal erms, which in fiscalis models calls for higher inflaion. If he moneary auhoriy responds o higher inflaion wih sufficienly higher nominal ineres raes, a vicious circle is formed. The model is paricularly advanageous for hyperinflaions in which mos of he fiscal acion concenraes in he ineres bill on public deb and deb rollover, raher han seigniorage or primary budge deficis. Brazil in he lae 97s and early 98s serves as a moivaing case. (JEL E3, E5) Inflaion so goes he monearis dicum is always and everywhere a moneary phenomenon. Of course, here is no conflic beween ha claim and moneary expansion ulimaely originaing in he need o finance fiscal deficis. Nowhere is ha as disinc as in sudies of hyperinflaion in he radiion of Phillip Cagan (956). Adoping he fiscalis approach o price deerminaion advocaed by Eric M. Leeper (99), Chrisopher A. Sims (994) and Michael Woodford (994, 995), one can urn ha monearis sory righ on is head. In a fiscalis world, prices are driven no by liquidiy, bu by he ouside wealh of privae agens. Budge deficis, under a fiscal policy regime ha causes a eduardo_loyo@harvard.edu. I wish o hank, wihou implicaing: Marcelo de Paiva Abreu, Ben Bernanke, Alan Blinder, Jean Boivin, Marco Anonio Bonomo, Dionísio Dias Carneiro, Suzanne Cooper, Luiz Robero Cunha, Rudiger Dornbusch, Roger Farmer, Márcio Garcia, Marc Giannoni, Mario Mesquia, Kenneh Rogoff, Julio Roemberg, Jeffrey Sachs, Argia Sbordone, Chrisopher Sims, Harald Uhlig, Carlos Végh, Michael Woodford, and Richard Zeckhauser.

2 breakdown of Ricardian equivalence, add o ha wealh sock. Inflaion is none oher han a sympom of oo much nominal wealh chasing oo few goods : i serves o corrode he real value of financial wealh, hus bringing demand back in line wih supply. Inflaion becomes essenially a fiscal phenomenon. Jus as inflaion may have deep fiscal roos even in a monearis accoun, so can moneary facors be blamed for inflaion in a fiscalis accoun. Tha is because moneary policy, changing boh he share of governmen liabiliies ha bears ineres and he ineres rae iself, affecs he nominal growh of privae ne worh. Bu hen a igh money paradox arises: given he primary budge deficis, igher money leads o faser growh of ouside wealh, and o more raher han less inflaion. The reversion comes full circle wih regard o explosive inflaion, he subjec of his paper. A foohold on moneary policy may be especially imporan in explaining cerain hyperinflaions along fiscalis lines as much as fiscal pressures for moneary expansion are paricularly prominen in Cagan models. Under a moneary policy regime ha conrols nominal ineres raes, susained acceleraion of inflaion can only be generaed by persisen moneary ighening. Meanwhile, he rajecory of primary governmen budges can have no sysemaic effec on inflaion raes. Such hyperinflaions can be well modeled as a vicious circle of ever higher ineres raes and ever higher inflaion. Empirical moivaion for such heoreical exercise can be found in he Brazilian experience in he lae 97s and early 98s. Brazil boased a hriving marke for domesically denominaed governmen deb, an ingredien ha enhances he fiscalis deparure from convenional resuls. In 98, he counry underwen a noorious change in moneary policy regime, upon which a fiscalis model would have prediced exacly wha came o pass: a swich from sabiliy of inflaion raes o persisen inflaion acceleraion. Convenional explanaions for 2

3 he episode are unsaisfacory, and signs of a igh money paradox have no been los on a number of observers. 2 Secion I briefly reviews he Brazilian evidence. In secion II, he cenral resuls of he paper are derived from a general equilibrium model buil on microfoundaions. Secion III addresses a few recurren quesions, exending he baseline model as needed. Secion IV concludes. I. BRAZIL, Afer a period of reasonable sabiliy beween he oil shocks of he 97s, inflaion in Brazil swiched o a rajecory of persisen acceleraion (figure ). The mos convenional explanaion for such an episode, along he lines of a Cagan model, would rely on movemens in real seigniorage arges. Persisen increases in seigniorage would cause inflaion o accelerae commensuraely. Under cerain assumpions, even a discree upward sep in seigniorage requiremens can se off an explosive rajecory along which seigniorage need no increase any furher. Bu here is a nagging (and well known) piece of evidence in he case of Brazil: real seigniorage collecion remained remarkably sable all along (figure 2). 3 Long and seady inflaionary rends as seen in Brazil clamor for raional expecaions raher han backward looking mechanisms implying ha economic agens are sysemaically 2 Thomas J. Sargen (986) hined a he possibiliy of a igh money paradox explained by he unpleasan monearis arihmeic of Sargen and Neil Wallace (98). High ineres raes were mos frequenly menioned as a cos-push inflaionary facor, couning ineres on working capial among he coss of producion (as in Alber Fishlow, 97, or in Domingo Felipe Cavallo, 977). As far as physical invenories are concerned, only movemens in he real ineres rae should maer; bu he nominal ineres rae remains he relevan opporuniy cos of ransacions balances held by firms. Varians of he cos-push argumen based on credi raioning, eiher due o direc governmen inervenion or o marke imperfecions (as in Alan S. Blinder, 987) were also very frequen in he srucuralis lieraure (see Samuel A. Morley, 97). Ohers sill echoed Fishlow (97) wih he claim ha igh money fueled inflaion because i depressed oupu and increased uni coss of producion. Finally, he liquidiy services of governmen deb soon became a prominen heme: if he relevan moneary aggregae is as broad as o include public deb, money grows faser wih higher ineres raes. Tha channel was explored by Carlos Ivan Simonsen Leal and Sérgio Ribeiro da Cosa Werlang (99, 995), and reviewed in Deepak Lal (99). 3 Inflaion is he CPI compued by FIPE, Universidade de São Paulo. Ineres is he average overnigh rae from he ARIES daabase compiled by Fundação Geúlio Vargas, Rio de Janeiro. Ineres and inflaion are gross monhly raes (+ne rae/), as in he ex. Raw daa on he moneary base and governmen deb 3

4 fooled. Then, boh sable and exploding inflaion migh be equally consisen wih he same consan seigniorage arge, in a manifesaion of he equilibrium indeerminacy problems plaguing raional expecaions models of moneary economies. Typically, equilibrium is seleced by discarding speculaive inflaionary explosions namely, hose unjusified by seigniorage movemens. Tha sraegy produces a good explanaion for he early sabiliy seen in Brazil, bu urns a blind eye o he laer explosion. I also begs he quesion of why explosive rajecories could legiimaely be ruled ou before bu no laer. In he absence of addiional crieria o selec a paricular explosive rajecory, he observed explosion can only be inerpreed as a self-fulfilling prophecy. If he convenional selecion crierion is jeisoned, even he period of sabiliy reduces o a chance even. Given such shorcomings, i is no surprise ha a popular explanaion for he Brazilian episode focuses insead on a cerain paern of moneary accommodaion ha made permanen he oherwise emporary effecs of adverse supply shocks on inflaion raes. Favorable supply shocks are seldom menioned, which may be fair enough if policy did no make heir disinflaionary effec persisen. Such asymmery in policy responses could accoun for he upward drif in he rae of inflaion wihou any paricularly bad luck in he draw of supply shocks. Unlike in Cagan models, however, no inrinsic rai of he macroeconomic policy regime would be pulling inflaion up in he absence of exogenous shocks. The economy migh well have swiched from sabiliy o inflaionary explosion simply because he adverse shocks inensified, even wihou any change in policy regime. Bu here was a major change in macroeconomic policy regime in 98, virually conemporaneous wih he rend break in he inflaion series. I was he salien macroeconomic policy urnaround in Brazil beween he lae 96s and he Cruzado Plan of February used o generae he monhly fiscal series in figure 2 are from Boleim do Banco Cenral do Brasil, several issues. The fiscal series are deflaed by he price index. All plos show hree-monh moving averages. 4 Tha seems o be a fairly consensual opinion: for insance, see Fishlow (989), and Paulo Rabello de Casro and Marcio Ronci (99). 4

5 Nominal ineres raes had been kep fairly sable unil hen, displaying for several monhs no response o he inflaionary impac of he second oil shock. By mid-year, he swich o a new regime was clearly under way (figure ). High officials evenually wen on record o announce heir inen o raise ineres raes so ha hose wih money had beer hink wice before spending i. 5 The change in regime is aribued o foreign crediors having finally prevailed upon domesic policymakers o mend heir heerodox ways which had been ofen raionalized, wih regard o moneary policy and inflaion, wih allusions o he cos-push effecs of igh money. 6 In spie of all he lip service officially paid o quaniaive arges, moneary aggregaes were no ruly exogenous under eiher policy regime. Mos frequenly, moneary policy is described as passive for failing o exercise direc conrol over moneary aggregaes and for accommodaing compleely he inflaionary impulse from adverse supply shocks. However, he inensiy of moneary policy reacion o burss of inflaion and he choice of policy insrumen are wo poenially separae quesions. I is well known ha moneary policy can be very acive in spie of conrolling ineres raes raher han moneary aggregaes, as long as feedback from inflaion ino nominal ineres raes is srong enough. A nominal ineres rule wih feedback from inflaion can be described by: () R = θ + θ where R denoes he gross nominal ineres rae on asses carried from o +, while denoes he gross rae of inflaion beween daes - and (variables are daed according o when hey are deermined). Abundan evidence on he conduc of moneary policy in Brazil bears winess o ineres raes being he acual policy insrumen, wih moneary aggregaes urned endogenous as a consequence (see, for insance, Armínio Fraga Neo, 988). However, he evidence is no in he leas supporive of he idea ha moneary policy remained impervious o inflaion all along. 5 Miniser Anonio Delfim Neo, quoed by O Esado de São Paulo, /5/98, p.. 5

6 Moneary policy was indeed passive or accommodaive unil 98, when real ineres raes were allowed o drop whenever inflaion happened o pick up. In erms of equaion, ha would be capured by a very low value of θ, which is confirmed by he scaer plo and he linear regression line of figure 3, panel (a). The new regime, on he oher hand, srove o raise real ineres raes in reacion o higher observed inflaion, by making nominal ineres raes increase even more han inflaion already had. In erms of equaion, ha would require a relaively high value of θ, as revealed by panel (b) of figure 3. 7 The only problem is ha such a change in regime is normally supposed o curb inflaion as i presumably did in he US since he early 98s and no o make he problem worse. The vicious inflaion acceleraion ha followed he policy swich sounds even more bizarre when conrased wih he Brazilian experience afer he firs oil shock: moneary policy was much more accommodaive hen, and ye inflaion merely climbed o a permanenly higher plaeau insead of exploding. In he following secion, I presen a simple fiscalis model ha reconciles he sabiliy of inflaion in he lae 97s wih he explosion in he early 98s, and each oucome wih he moneary policy regime in place a he ime. II. INFLATION WITHOUT MONEY I consider here a closed economy inhabied by an infiniely-lived represenaive household. The household subsiss on a single good supplied exogenously. There is a governmen whose only business is o collec axes and make ransfers, all lumpsum. The only financial asses are one-period, riskless nominal bonds. I absrac from he exisence of an asse wih superior liquidiy services and poenially dominaed in rae of reurn hereby sressing ha inflaion 6 Poliical circumsances surrounding economic policymaking, he personaliies involved and heir economic hinking are described in deail by Fishlow (97, 989) and Thomas E. Skidmore (97, 989). 7 These simple esimaes do no purpor o serve as he basis for formal saisical inference abou a change in moneary policy regime, especially given he non-saionariy of he laer half of he sample. The daa alone canno deermine wheher he regressions are ruly srucural, or if hey are insead reduced form relaions capuring a srucural break ha occurred elsewhere in he economy, creaing he spurious appearance of a change in moneary policy regime. Bu he idenificaion of he esimaed parameers as 6

7 arises independenly of liquidiy effecs of any kind. Bu he economy is sill moneary, for prices and financial conracs are denominaed in a convenional uni of accoun. Moneary policy can be described in erms of direc conrol of he nominal ineres rae. 8 The represenaive household maximizes lifeime uiliy: = (2) β u( c ) where < β <. Is financial wealh evolves according o he series of flow budge consrains: b + c = y + g + b R Here, c and y respecively denoe consumpion and he exogenous endowmens, while g denoes he primary fiscal defici in real erms. By b - I denoe he real value a - of bonds carried from - o. Those bonds promise o pay he gross nominal ineres rae R -, deermined a -, and he gross rae of inflaion during he same period is. A well posed ineremporal maximizaion problem requires some limiaion on borrowing by he represenaive household. Prohibiing he household from ever borrowing more han he presen discouned value of fuure disposable income, is flow budge consrains can be urned ino he following series of ineremporal budge consrains ( ): b R + s (3) s s= c y+ s g R + k k= + k + s srucural is corroboraed by he narraive evidence on he conduc of moneary policy, which lends credence o he hypohesis of a deliberae regime change. 8 Moneary models wihou explici menion of money balances have been used ouside he fiscalis lieraure, as in Julio J. Roemberg and Woodford (997), Richard Clarida, Jordi Galí and Mark Gerler (999), and Woodford (999). A sandard liquidiy demand may exis in he background, bu cerain ineres rae rules for moneary policy reduce he model o a se of equaions ha fully deermine inflaion and oupu and make no reference o moneary aggregaes. In a fiscalis model, ha operaion is complicaed by wha he governmen saves in ineres by issuing money raher han bonds. Tha conribuion o he budges can be safely disregarded if i is largely unresponsive o endogenous variables (as in par D of secion III below). For he sake of exposiional clariy and in order o avoid discussing paricular assumpions abou he money demand funcion, much of he fiscalis lieraure ops for eliminaing money from he model ourigh, as I do here. Good examples are John H. Cochrane (996, 7

8 Maximizaion of objecive funcion 2 subjec o consrains 3, wih b - and R - given as iniial condiions, resuls in he following perfec foresigh equilibrium condiions ( ): (4) u ( y ) = β u ( y ) b R + + R = (5) s s= g+ s R + k k = + k Equaion 4 is he consumpion Euler equaion combined wih he marke clearing condiion c = y. Equaion 5 is he household s ineremporal budge consrain (HIBC) holding wih equaliy, as necessary for lifeime uiliy maximizaion, also combined wih marke clearing. The laer is readily recognized as he governmen s ineremporal budge consrain (GIBC). The model is closed by specificaion of fiscal and moneary policies. Given he moivaing Brazilian evidence, moneary policy is assumed o se nominal ineres raes wih feedback from inflaion, as described by equaion. As for fiscal policy, I assume hroughou ha primary deficis are se exogenously. Tha is jus he simples example of a fiscal regime wih he propery ha a unique iniial inflaion rae is consisen wih equaion 5 a each dae he cenral ene of a fiscalis approach o price level deerminaion. 9 I depars from he implici convenional assumpion ha, because primary deficis adjus endogenously o macroeconomic condiions so as o uphold he GIBC, equaion 5 is idenically saisfied for every iniial inflaion rae. If ha were he case, he household would no regard public deb as ne worh, since i would be simply idenical o he presen discouned value of fuure ne axes which accouns for Woodford (995) erming ha ype of fiscal regime Ricardian. Under he assumed fiscal regime, a perfec foresigh equilibrium saring from = is fully deermined by equaions, 4 and 5. From equaion 4 one obains a each dae he enire pah 998) and Sims (997). Bu he absence of moneary fricions is no an inheren feaure of he fiscal heory of price deerminaion, a poin carefully argued by Woodford (998c). 9 The only resricion on he exogenous choice of primary budges is ha he righ-hand side of equaion 5 mus have he same sign as he numeraor on he lef-hand side. 8

9 of fuure real ineres raes. Given ha, and exogenous and predeermined variables, a each dae equaion 5 deermines he curren inflaion rae (he one appearing on he lef-hand side). Given he pas inflaion rae, nex period s nominal ineres rae is se a each dae according o equaion. The semi-differenced form of 5: (6) b = g + b R finally deermines he pah of governmen deb. A rajecory compued in ha fashion is indeed a perfec foresigh equilibrium saring a = : i is easy o verify ha he resuling real ineres raes R / + saisfy he Euler equaion 4 for all. Inflaion driven by equaion 5 can be aribued o wealh effecs. Afer all, he equilibrium inflaion rae is deermined by he join requiremens of exhausion of HIBCs (given he nominal financial wealh he household brings from he pas and he expeced fuure pah of fiscal policy) and marke clearing. Faser growh of nominal financial wealh, as implied by higher nominal ineres raes, or higher expeced fiscal ransfers, boh require higher inflaion or oherwise he HIBCs would expand in real erms, and he household would wan o consume more relaively o endowmens. The same perfec foresigh equilibrium pah of inflaion can be more direcly compued by combining equaion 4 wih equaion ( ): (7) u βu ( y ) θ + = ( y ) + + θ Given an exogenous sequence of endowmens, his equaion reduces o a firs-order difference equaion for he inflaion rae. Complee deerminaion of he inflaionary rajecory sill requires an iniial condiion for, which can be obained from equaion 5 for =. A graphical descripion of he resuling dynamics is easies in he paricular case of consan equilibrium real ineres raes r. Two possible cases of ineres are depiced in figure 4. In panel (a), where θ < r, he inflaionary dynamics is sable. Wherever he economy sars, as 9

10 dicaed by he iniial GIBC, i mus converge o he seady sae. If moneary policy ighens, in he sense of responding o each given rae of inflaion wih a higher ineres rae (ha is, θ or θ increase, bu sill keeping θ < r ), hen seady sae inflaion goes up, and ha is where he economy mus converge o. The moneary policy esimaed for pre-98 Brazil is consisen wih his case. In panel (b), on he oher hand, where θ > r, he dynamics is unsable. If he economy happens o sar a he seady sae, i will remain here. Bu only by coincidence will he saring poin deermined by he GIBC be exacly he seady sae. Oherwise, he inflaionary dynamics will be explosive. In paricular, if he iniial inflaion rae is higher han he seady sae, he resul will be ever acceleraing inflaion. The pos-98 evidence abou he Brazilian moneary policy regime is consisen wih his case. Wih he esimaed regression coefficiens, and assuming an equilibrium real ineres rae of 6% per year, seady sae inflaion would be 2.4% per monh lower han he inflaion raes a he ime of he change in regime. Thus inflaionary explosion is raced back o an explosion of nominal ineres raes. The ineres bill on public deb is he fiscal variable pinpoined as responsible for he explosion of he nominal growh rae of governmen liabiliies. In fac, nohing was specified abou he emporal rajecory of primary budge deficis in order o obain he hyperinflaionary equilibrium. Focusing on paymens of ineres by he governmen raher han on movemens in primary deficis may seem warraned in he case of Brazil, in he ligh of he evidence in figure 2. Ye, i is naural o ask wha imporance primary deficis could ever have in producing ha kind of dynamics. The mere realizaion ha one can fully describe he perfec foresigh equilibrium pah of inflaion wihou much informaion on he emporal rajecory of primary budges indicaes ha he laer mus play a raher limied role. In he perfec foresigh equilibrium compued above, depended on fuure primary budges only hrough heir discouned sum (as in he GIBC for = ).

11 Since all laer inflaion raes had o urn ou as prediced, and a he same ime had o saisfy equaion 4, hey were fully deermined by he nominal ineres rae a each dae. Iniial inflaion had an impac on laer inflaion raes, bu only hrough he difference equaion 7 i.e., hanks o is impac on he laer pah of nominal ineres. Wheher he discouned sums on he righ-hand side of equaions 5 increased or decreased over ime provided ha hey did so exacly as foreseen would have no furher bearing on subsequen inflaion raes. Saisfacion of equaion 5 a every dae would be guaraneed by he implied evoluion of governmen deb (he numeraor on he lef-hand side). Tha sark disincion beween and laer inflaion raes along he equilibrium pah is jus an idiosyncrasy of perfec foresigh. I can be properly inerpreed as aesing ha, under nominal ineres rae conrol, only surprises abou he fuure pah of primary budges maer for inflaion: he arrival of news calls for a recompuaion of he perfec foresigh equilibrium, wih he iniial inflaion rae again resriced only by he iniial GIBC. Surprises regarding fiscal deficis and inflaion, however, should no be sysemaic, or agens would learn o expec hem. Once hey learn wha inflaion o expec, equilibrium canno keep violaing he Euler equaions 4. Therefore, in he absence of jusificaion from moneary policy, repeaed fiscal expansion is no a good reason for persisenly acceleraing inflaion if expecaions are raional. On he oher hand, unsysemaic fiscal surprises would cause inflaion o deviae from he previously foreseen pah also in an unsysemaic manner, excep insofar as jusified by persisen changes in he pah of ineres raes. Barring changes in ineres raes, a large one-ime fiscal surprise (abou he whole sequence of fuure primary deficis) could sill be blamed for a large blip in inflaion. Such blip could even urn ino a more proraced inflaionary burs in he presence of nominal rigidiies (as shown in Woodford, 998a). Bu inflaion would evenually run ou of seam as he pressure of real wealh on demand was alleviaed. Tha is hardly a good descripion of inflaion ha keeps acceleraing for years wihou any sign of apering off. Therefore, under moneary regimes ha

12 conrol he nominal ineres rae, he fiscalis diagnosic regarding persisen inflaion acceleraion mus poin he finger a he fiscal consequences of moneary policy ighening. I is also easy o verify ha he explosive inflaionary pah jus described is perfecly consisen wih he real value of governmen deb remaining bounded in equilibrium perhaps no even increasing a all. In he case of Brazil, real governmen deb did increase considerably, which can be accommodaed by movemens in real ineres raes or in primary deficis. Bu wha inflaion follows is he nominal rae of growh of governmen deb, exacly in order o preven deb from growing excessively in real erms. In his sense he fiscalis approach differs from argumens like he unpleasan monearis arihmeic of Sargen and Wallace (98), which aribue a similar igh money paradox o anicipaion of higher moneary financing of budge deficis as real deb approaches some hard ceiling. Tha observaion bears direcly upon an issue of fiscal policy ha has been debaed in connecion wih episodes of high inflaion: wheher one should worry abou he oal budge defici or only abou he narrower concep of operaional defici (primary defici plus real ineres on public deb). A case was frequenly made for racking he laer, downplaying he imporance of price level adjusmens of he nominal value of governmen deb. One argumen was ha such price level adjusmens would no pu pressure on curren or fuure seigniorage needs, since hey would no conribue o increasing he real value of governmen deb. Tha is consisen wih he Sargen-Wallace bu no wih he fiscalis view of he igh money paradox. According o he laer, he price level adjusmen of governmen deb does maer, exacly because i calls for inflaion in order o preven he real value of governmen deb from growing oo much and causing demand for goods o exceed supply. Anoher popular argumen for racking operaional deficis does focus on he evoluion of ouside financial wealh: he price level adjusmens of governmen deb should presumably have no effec on real aggregae demand, since hey do no expand real ouside wealh, bu only preven i from shrinking. No having any impac on real aggregae demand, he argumen goes, hey should have no impac on inflaion. Bu ha reasoning is analogous o looking a a simple quaniy equaion M/P = Y and making he absurd claim ha moneary expansion only causes inflaion if i increases real money balances. 2

13 The explosion of inflaion resuls from he moneary auhoriy repeaedly seing nominal ineres raes such ha, if inflaion remained he same as in he period before, he real ineres rae would be oo high for equilibrium. I may sound naive of policymakers o insis on seing nominal ineres raes higher and higher if ha simply calls for higher and higher inflaion. Bu here are many sources of inflaionary shocks in he real world, and he igh money paradox may no be so easy o deec especially wih convenional wisdom poining in he opposie direcion. Sicky prices would blur he whole picure even more: as shown in Loyo (998), in spie of he igh money paradox, moneary ighening would sill raise real ineres raes and depress oupu in he shor run, jus as convenionally expeced. Even if real raes fail o respond o he exen desired, and inflaion is repeaedly observed o accelerae in response o igher money, all ha may be raionalized wihou ever admiing ha moneary ighening is self-defeaing for some fundamenal reason. In Brazil, he moneary auhoriy ofen expressed is frusraion a he fac ha increases in nominal ineres raes were perceived no as an aemp o raise real raes, bu as incorporaing an upward revision in inflaion forecass. Bu hose were no idenified as he only raional expecaions agens could hold in a world where higher nominal ineres calls for higher inflaion. Insead, he problem was explained much like he price puzzle in he US: inflaion acceleraed because price seers revised heir forecass according o wha hey saw as a signal revealing he moneary auhoriy s superior informaion abou inflaion. Disabusing privae agens of such informaion asymmery would presumably cure he problem. The naure of he moneary policy regime is acually no paricular o my sory. Indeed, moneary regimes yielding a unique unsable seady sae inflaion rae are exacly wha convenional accouns rely on o deermine inflaion period by period, in models wih he same Tha inerpreaion became less persuasive as a massive privae effor of inflaion forecasing (and even price sampling) developed. Resuls by Márcio G.P. Garcia (995) for a laer period indicae ha nominal ineres raes on governmen bonds did no conain superior informaion abou inflaion. 3

14 basic srucure as he one presened here. 2 Wha disinguishes hose models from a fiscalis approach is only he role assigned o he GIBCs in equilibrium deerminaion. Implicily assuming ha he GIBC is idenically saisfied, heir sraegy o pin inflaion down is o rule ou perfec foresigh pahs in which inflaion is expeced o explode or implode. This naurally requires inflaion o remain always a he seady sae. Among moneary policy rules described by equaion and yielding a unique unsable seady sae, increases in inercep or slope reduce he seady sae inflaion rae. Inflaion hen displays he sandard response o moneary policy ighening, bu only because i is ied o he seady sae by assumpion. Along any explosive pah, i would sill be rue ha higher nominal ineres raes call for higher inflaion o saisfy he Euler equaion ha is exacly wha makes hese pahs explosive in he firs place. Bu ha becomes irrelevan once one assumes ha hese pahs are never followed. One migh conend ha moneary policy regimes wih a unique unsable seady sae sound more reasonable in combinaion wih he convenional approach o equilibrium selecion: an obdurae behavior is prescribed o he moneary auhoriy only ou of equilibrium, a siuaion ha is acually never supposed o arise. Bu equilibrium selecion based on he unsavory offequilibrium consequences of a policy regime is hardly persuasive if he regime is only deemed credible as long as he moneary auhoriy is never called upon o deliver on is off-equilibrium obduracy. Quie o he conrary, i migh even be argued ha convenional equilibrium selecion requires worse moneary obduracy han he fiscalis approach suggesed here. Convenional equilibrium selecion relies on i being believable ha he moneary regime would be mainained forever if he economy ever hiched on he explosive pah, producing equilibria ha are ruled ou on he grounds of inflaion growing wihou bound. In he fiscalis approach, he curren inflaion rae depends only on he conemporaneous and no on fuure nominal ineres raes. In paricular, 2 Tha argumen was applied o ineres rae feedback rules by Benne T. McCallum (98). See caveas in Jess Benhabib, Sephanie Schmi-Grohé and Marín Uribe (998). 4

15 i is never assumed ha he explosive moneary regime will remain in force forever; while i does, however, inflaion acceleraes. The righful bone of conenion wih regard o he fiscalis hyperinflaion suggesed here is really wheher he fiscal regime I assume is reasonable or no. I is no essenial ha he fiscal regime be exacly he one I use for clariy s sake, wih exogenous primary budges. Similar resuls obain even if primary budges do respond o endogenous variables, as long as i remains rue ha a unique iniial inflaion rae solves he GIBC, given he quasi-exogenous pah of fuure equilibrium real ineres raes and he predeermined financial wealh. The diamerically opposie assumpion of a Ricardian fiscal regime seems o proceed from he noion ha governmens ough o be subjec o borrowing consrains jus like households. However, while he household s borrowing consrains are necessary for he exisence of a soluion o is uiliy maximizaion problem, and hus for he exisence of equilibrium, he same is no rue of governmen s borrowing consrains. Tha does no preclude he governmen from being a maximizer in is own righ. Unlike he price-aking represenaive household, i should only recognize ha is acions have an impac on he aggregae equilibrium condiions. The policy problem would hen amoun o choosing among he aggregae equilibria ha differen policy regimes implemen. Resricing he choice space by imposing borrowing consrains on he governmen is no a all necessary o make ha a well posed problem, and opimal choices migh in fac be found ouside hose bounds. 3 Ricardian fiscal regimes, once he logical possibiliy of alernaive assumpions is seriously conemplaed, sar o look like quie special cases. There are in fac reasonable enough feedback rules for primary budges ha make he fiscal regime Ricardian (Woodford, 995), and one should no make he exaggeraed claim ha Ricardian regimes are non-generic excepional cases. There is also evidence ha fiscal regimes in cerain siuaions mus be Ricardian, or else 3 Woodford (998b), for insance, shows ha a regime yielding a fiscalis deerminaion of he price level may be he soluion o a Ramsey problem of opimal axaion. 5

16 he moneary policy rules esimaed in hese cases would resul in inflaionary explosion jus like in Brazil and hey do no. 4 Ye, Ricardian regimes do require a degree of fiscal reciude ha is hard o square wih Brazil s hisorical record. III. FAQ In his secion I address some of he mos frequenly asked quesions abou he above resuls. Variaions of he baseline model are made as required in each case. A. Indexed bonds High inflaion economies end o develop an exensive sysem of indexed conracs and here is hardly a beer example of ha han Brazil. If public deb is indexed, he model s assumpion ha all bonds are nominal could be challenged on wo couns. Firs, a feedback rule for conrolling he yield on nominal bonds migh be a poor descripion of moneary policy. Second, inflaion is deermined by he GIBCs assuming ha he real value of governmen deb can be corroded by inflaion. Those objecions lose much of heir force once i is recalled ha bonds linked o price indices are no anamoun o real bonds. Because of he ime involved in sampling and compuing price indices, he nominal value of indexed bonds is ypically adjused according o lagged inflaion raes. If he price index is made public wih a one-period lag, hen he nominal yield on one-period indexed bonds will depend only on heir conracual real yield and on an inflaion rae already realized a he dae of issue (alhough no ye officially compued). Tha is no far from Brazilian realiy, for insance, if a period represens a monh. Governmen deb appearing in he GIBCs would have a predeermined nominal value, and inflaion deerminaion would work jus as described above. Despie Brazil s already esablished fame as a highly indexed economy, i is no hard o make he case for a nominal ineres rae rule o describe pre-98 moneary policy. Firs of all, 4 The US since Volcker is a case in poin, according o he esimaes of Clarida, Galí and Gerler (997). See noneheless Cochrane s (998) fiscalis inerpreaion of US inflaion. 6

17 he proporion of indexed bonds in oal public deb was sill relaively low: around 4% beween 977 and 98 (Dionísio Dias Carneiro Neo, 987). On op of ha, an aemp o break inflaionary ineria wihou dismanling he legal indexaion srucure gave rise o as blaan an oxymoron as pre-fixed indexaion (announced monhs in advance). Under such circumsances, governmen bonds were nominal for all inens and purposes, and moneary policy could be described as argeing heir nominal yield. As inflaion exploded afer 98, honesly indexed bonds did become more prevalen in he sock of governmen deb: upwards of 8% beween , and even more aferwards (Carneiro Neo, 987). The nominal yields on indexed bonds can be wrien as R = ˆ r, where ˆ + rˆ denoes he conracual real yield on a bond carried from o + and earning ˆ + from is indexaion clause. The bes descripion of moneary policy migh hen be as argeing rˆ insead of he nominal ineres rae, bu sill doing so according o a feedback rule from inflaion: i would ighen in response o higher inflaion by raising he conracual real yield. Tha migh be represened by: θ rˆ = θ + Wih he coefficiens (θ, θ ) esimaed in panel (b) of figure 3, rˆ would reac posiively o a good forecas of he nex inflaion release, converging o a value ha exceeds he equilibrium real ineres rae as inflaion explodes. If he index applied o financial conracs is inflaion lagged once ( ˆ = ), ha paricular rule leads righ back o equaion. The more general message is + ha, if indexaion is iself lagged, hen a feedback rule for he nominal ineres rae may properly represen a regime based on a feedback rule for conracual real yields on indexed bonds. Bu even if rue real bonds were added o he model, heir presence side by side wih nominal bonds would no affec he above predicions abou he effecs of moneary ighening. 7

18 The equilibrium pah of inflaion would sill be deermined by equaion 7, excep ha now he iniial condiion would be provided by he modified GIBC: b R ~ + b ~ r = (8) = g s= ~ r s where b ~ is he sock of real bonds carried from o +, which earn a predeermined real rae of ineres r~. Suppose ha = brings news of a change in he parameers of he moneary policy rule, equaion. Tha canno affec he predeermined R - or ~ r, nor does i affec fuure real ineres raes, which mus sill conform wih exogenous endowmens according o equaion 4. So, equaion 8 deermines he same as in he absence of news, regardless of he proporion of real bonds in he iniial financial porfolios. Saring from ha unchanged iniial condiion, laer inflaion raes will be deermined by equaion 7 wih he new policy parameers, bu ha is again independen from he iniial porfolio composiion or from is subsequen evoluion. 5 Inuiively, he exisence of rue inflaion-proeced bonds is irrelevan for he inflaionary effecs of moneary policy because hese effecs were never inended o cause a surprise corrosion of he real value of accumulaed financial asses. 6 In fac, hey do no cause ha sor of surprise since hey affec inflaion only wih a leas one period s noice, and one period is exacly he mauriy of all bonds in his model. Inflaion ha is fully anicipaed mus be refleced in an equaliy beween he ex pos yields of nominal and real bonds, and so he porfolio composiion does no affec he rae a which he nominal value of he oal porfolio grows, or he subsequen raes of inflaion required o keep demand in line wih supply. 5 Nominal rigidiies would complicae he picure, because moneary ighening would hen cause a emporary increase in real ineres raes, and call for some surprise inflaionary corrosion of iniial nominal wealh in order o compensae for more inense discouning of fuure primary surpluses. 6 This is unlike he consequences of news abou fuure primary deficis, which mus be compensaed by he effecs of an inflaionary surprise on real iniial wealh. A higher proporion of indexed deb would magnify he inflaionary impac of fiscal shocks: a larger surprise jump in inflaion is necessary o bring lifeime wealh back o equilibrium when a larger proporion of financial wealh is inflaion-proof. 8

19 B. Open economy The main reason for curiosiy abou an open economy exension seems o be he possibiliy of foreign shocks o he household s lifeime wealh. If inflaion is driven by ouside wealh, ha migh be imporan. Also, he effecs of moneary or fiscal policy migh be differen wih he exra degrees of freedom afforded by he open economy. As i urns ou, opening he economy does no significanly aler he resuls already obained. This claim can be verified in a simple model of a small open economy, sill wih a single good and subjec o PPP. The real ineres rae is no longer deermined by he domesic endowmens, bu impored from he res of he world hrough ineres rae pariy. Even so, he consumpion Euler equaions mus sill be saisfied: consumpion will differ from domesic endowmens as needed, which can happen now hanks o inernaional rade. I assume ha here are one-period bonds denominaed in domesic currency, and also real bonds (he laer may sand for bonds denominaed in foreign currency, since foreign inflaion is exogenous). The HIBCs will read: + s y+ s g+ s + s= s ~ rk k = a R (9) + ~ ~ c a r = x + s Here, a denoes he household s holding of bonds, while b will be reserved for he governmen s liabiliies he wo need no coincide once foreign deb is allowed. Now, g denoes he ne ransfers made by he governmen, boh o he domesic households and abroad. The erm x denoes ne ransfers made abroad, boh by he governmen and by he household. Assumed o be lumpsum and exogenous, he laer are mean as a very sylized represenaion of foreign shocks o lifeime wealh ha do no simulaneously affec he real ineres rae (for insance, war reparaions, foreign deb forgiveness, or erms of rade shocks). Now ha auarkic marke clearing is no longer required, he model mus be closed by some limiaion on how much real resources he economy can absorb. A fairly sandard closure is 9

20 o impose foreign borrowing consrains on he counry as a whole he consolidaion of governmen and household. Tha resuls in naional ineremporal budge consrains (NIBCs): () ( a b ) R + + ( ~ ~ ) ~ c s y a b r = s s= + s + k = ~ r k x + s Jus as auarkic marke clearing reduced he HIBCs o GIBCs, so does he sequence of NIBCs (subrac equaion from equaion 9). As a resul, he equilibrium rajecory of inflaion is sill deermined by he difference equaion: () ~ θ + θ r = + wih iniial condiion given by equaion 8 above. Excep for he source of deerminaion of equilibrium real ineres raes, opening he economy makes no difference for how he equilibrium pah of inflaion is compued. Indeed, changes in moneary policy regime affec he pah of inflaion jus as in a closed economy wih he same equilibrium real ineres raes. The pure foreign wealh shocks x, wih primary deficis g unchanged, have no bearing on inflaion. The household becomes poorer if x increases given g, bu ha requires no compensaing increase in he real value of iniial wealh because wha he counry can absorb which here plays he role of supply decreases by exacly he same amoun. Realisically, foreign shocks migh simulaneously affec x and g, bu ha would have he same impac on inflaion as an equal change in g in a closed economy. Larger governmen ransfers abroad would call for as much inflaion as if hey were ransfers o he domesic household unlike domesic ransfers, hey do no make households feel any richer, bu insead consumpion mus be made o conform wih he ighened exernal consrain. 7 Shocks o equilibrium real ineres raes also have exacly he same impac on inflaion as hey would if he economy were closed. In paricular, ha impac depends on he liabiliy posiion 2

21 of he governmen, bu no on wheher he counry is a ne borrower or a ne lender abroad. If he moneary policy regime were ha of panel (a) of figure 4, a permanen increase in inernaional real ineres raes would even be helpful on he inflaion fron: he immediae impac would be inflaionary, as dicaed by equaion 8 (wih posiive governmen deb), bu in he long run he economy would sele a a lower seady sae inflaion. This should be conrased wih he lasing inflaionary impac prediced according o convenional equilibrium selecion, based on a Ricardian fiscal regime and on a moneary policy as in panel (b). C. Quasi-money An alernaive raionale for inflaion fueled by he nominal growh of governmen deb relies on governmen bonds being very liquid, hus qualifying as near money. The inflaionary explosion happens no because of he wealh effecs sressed by he fiscalis approach, bu o saisfy some liquidiy preference relaion where governmen deb appears as par of a broad moneary aggregae. Exposiions of his view for he case of Brazil can be found in Lal (995) and in Leal and Werlang (99, 995). Since governmen deb is ofen believed o provide imporan liquidiy services in chronic inflaion economies, specifying he model accordingly emerges as a key elemen even in a fiscalis sory aspiring o realism. Tha ingredien may be added by replacing he household s objecive funcion (equaion 2) wih: = β [ u( c ) + v( b )] for some increasing, concave uiliy funcion v. The resuling equilibrium condiions would hen be equaion 5 ogeher wih ( ): (2) u ( y ) v ( b ) = β u ( y ) R An exension wih nonradeable goods would indicae ha fiscal and foreign shocks may have an effec on he equilibrium real exchange rae, which is deermined joinly wih domesic inflaion. Bu i would remain rue ha changes in moneary policy only affec domesic inflaion, and jus as prediced here. 2

22 One recognizes in equaion 2 a well defined equilibrium demand for governmen deb a each poin along he perfec foresigh equilibrium pah. 8 Bu ha is no analogous o a convenional liquidiy preference relaion, whereby he ransacions demand for real liquidiy is associaed wih curren income and he nominal ineres rae. Here, he decision abou how much liquidiy o hold is indiscernible from he ineremporal allocaion of consumpion, since all wealh is in liquid bu ineres bearing form. Tha is differen from he convenional problem of balancing he convenience of holding cash wih is opporuniy cos in erms of foregone nominal ineres, when here is also an illiquid bu higher yielding sore of value. The compuaion of he perfec foresigh equilibrium is rendered more complicaed, because he equilibrium real ineres raes are no longer quasi-exogenous. In fac, i is ineresing o noe ha, if v is sricly concave, equilibrium real ineres raes naurally increase as he real value of governmen deb explodes, for any given pah of oupu a phenomenon disinc from real ineres flucuaions associaed wih flucuaions in oupu. Each passing day he governmen finds i harder o refinance is growing deb, facing a marke ha demands higher and higher real yields. Tha happens simply because he marginal uiliy of he addiional real deb is falling, and no for he ofen suggesed reason of growing fears of repudiaion of a snowballing deb. Bu he fundamenal logic of he model remains he same in erms of he fiscalis deerminaion of he price level. Equaions 6 and 2 form a difference sysem in (b, R / + ), wih he propery ha, as long as deb remains posiive, all fuure equilibrium real ineres raes are coninuous, decreasing funcions of iniial inflaion. Inuiively, he higher iniial inflaion he lower he iniial deb, allowing laer deb and hus also laer real ineres raes o be uniformly lower. Wih exogenous, posiive primary surpluses, he righ-hand side of equaion 5 (for = ) is a coninuous, posiive, and increasing funcion of. Since he lef-hand side is a coninuous, 8 Exisence of equilibrium requires he lef-hand side of 2 o remain posiive a all imes. Wih posiive deb and concave uiliy funcions, i is enough o have v () < u (y max ), where y max is some upper bound on 22

23 decreasing funcion of spanning R ++, here mus be exacly one solving ha equaion. Tha unique and iniial condiions deermine b. Then he difference sysem in (b, R / + ) deermines he enire perfec foresigh equilibrium pah of real deb and real ineres raes. As before, all laer inflaion raes are deermined by he sequence of nominal ineres raes generaed according o equaion, given he equilibrium real ineres raes. Governmen deb displaying inordinae liquidiy ofen invies proposals of insiuional reforms mean o reinsae he saluary disincion beween money and ineres-bearing asses. The moivaion for such reforms is o enile he governmen o non-inflaionary (i.e., nonmoneary) means of defici finance. One may wonder if hey would sill be warraned in a fiscalis world where a leas heir avowed purpose makes lile sense, since deb is inflaionary even wihou liquidiy effecs. Equaion 2 indicaes ha he verdic hinges on how he insiuional reforms would affec he firs derivaive v. Tha would deermine he effec on equilibrium real ineres raes, and by consequence he effec on inflaion raes resuling from a given policy for nominal ineres. If v is no a consan funcion, real ineres raes are deermined joinly wih he pah of real governmen deb, and his general equilibrium effec mus also be aken ino accoun. The verdic also hinges on he moneary policy regime. For a simple illusraion, I assume ha v is a consan funcion and ha endowmens are also consan over ime. Reform is assumed o raise he consan: u ( y) v η β u ( y) by reducing v. Figure 5 depics ha change under he same assumpions abou he parameers of equaion as explored in figure 4. Insiuional reform raising η makes good sense in he case of panel (a): seady sae inflaion, a which he economy will sele no maer where i sars, is indeed reduced. Bu he he exogenous sequence of y. 23

24 very same resul could be obained by changing he moneary policy rule parameers (θ, θ ) and leaving η alone. In he unsable case of panel (b), reform would insead raise he seady sae inflaion rae. Unless squarely hi by he iniial inflaion rae deermined by he GIBC, he posiion of ha unsable seady sae would be of limied imporance. 9 Even if he objecive were o make he seady sae coincide wih he iniial inflaion, o avoid seing off he inflaionary explosion wihou abandoning he acive moneary policy, ha would again be more easily achieved by manipulaing he policy parameers (θ, θ ). Bu i is hard o believe ha policy or insiuional parameers could be fine uned o ha exen even once, le alone o keep recifying repeaed perurbaion o he unsable equilibrium. In a fiscalis inerpreaion of he inflaionary explosion, eliminaion of liquid governmen deb would be of no avail. D. A classic hyperinflaion Hyperinflaion has so far been blamed on he nominal growh of public deb as caused by he accrual of ever higher nominal ineres, wih primary budge deficis relegaed o a lesser role. Tha sory, moivaed by he Brazilian evidence, makes he mos ou of he fiscalis igh money paradox. In conras, classic episodes of hyperinflaion are associaed wih he explosion of primary deficis financed by seigniorage, and public deb is seldom menioned. Fiscalis models can easily accoun for classic hyperinflaions as well, hough no making as big a splash in such cases. How hey can do so is described here as an elucidaive counerpoin o he diagnosic offered above. In order o discuss seigniorage finance, he model needs money balances. Wihou elaboraing on is microfoundaions, I direcly posi he liquidiy preference relaion: (3) ( R ) m = ψ ( y ) 9 Ineresingly, convenional equilibrium selecion under Ricardian fiscal regimes ruling ou explosive pahs, hence ying inflaion o he unsable seady sae would jusify opposing such reducion in deb liquidiy. 24

25 where ψ is a posiive funcion and m denoes he real money balances carried from o +. The lef-hand side is he ren on money paid by he household (he ineres foregone by holding money raher han bonds). The liquidiy preference relaion is chosen o have a uni ineres elasiciy, so ha oal ren on money depends only on exogenous endowmens. Tha is convenien because ren on money will now appear in he ineremporal budge consrains. The GIBCs become: (4) m + b = R ( R ) + s s s= m R + s + k k = + k g + s As for he moneary policy regime, insead of conrol of nominal ineres raes, I assume now ha he governmen conrols he composiion of is liabiliy porfolio so as o keep money and mauring deb in a consan proporion: R b = γm. As a resul, real seigniorage will be: (5) m g + γψ m = + γ ( y ) The case mos ofen associaed wih a classic hyperinflaion is ha of γ =, when oal deficis coincide wih primary deficis and are enirely financed by seigniorage. There is lile moneary policy o speak of apar from he mechanical financing of governmen budges. To simplify he exposiion, le endowmens be consan. In his case, for all, he Euler equaions 4 imply R / / β, and he GIBCs 4 simplify o: = (6) + γ = β s= s g β ψ + s ( y) If g is increasing along he perfec foresigh pah, equaion 6 makes clear ha inflaion mus be acceleraing oo. According o equaion 5, increasing primary deficis mus be accompanied by increasing seigniorage. There could hardly be a more classic hyperinflaion especially if γ =. Bu a each dae he price level is fully deermined according o fiscalis principles, and inflaion is driven by wealh effecs jus as in secion II. There is no conflic wih he asserion ha fiscalis price level 25