Woodford Fiscal Requirements of Price Stability

7/30/2019 Woodford Fiscal Requirements of Price Stability

1/61

Fiscal Requirements for Price Stability

Author(s): Michael WoodfordReviewed work(s):Source: Journal of Money, Credit and Banking, Vol. 33, No. 3 (Aug., 2001), pp. 669-728Published by: Ohio State University PressStable URL: http://www.jstor.org/stable/2673890 .

Accessed: 01/01/2012 17:02

Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at .http://www.jstor.org/page/info/about/policies/terms.jsp

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of

content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new formsof scholarship. For more information about JSTOR, please contact [email protected].

Ohio State University Press is collaborating with JSTOR to digitize, preserve and extend access toJournal of

Money, Credit and Banking.

http://www.jstor.org
http://www.jstor.org/action/showPublisher?publisherCode=ohiosuphttp://www.jstor.org/stable/2673890?origin=JSTOR-pdfhttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/stable/2673890?origin=JSTOR-pdfhttp://www.jstor.org/action/showPublisher?publisherCode=ohiosup


2/61

MICHAELWOODFORD

Fiscal Requirements or Price StabilityMaintainingprice stabilityrequiresnot only commitment o an ap-propriatemonetarypolicy rule, but an appropriateiscal policy ruleas well. Ricardianequivalence does not imply that fiscal policy isizaelevant, xcept in the case of a certainclass of policies ("Ricar-dian" policies). The role of fiscal developments n inflation deter-mination under a non-Ricardianregime is illustratedthrough ananalysis of the bond-price supportregime of the 1940s. A mone-tary-fiscalregime with attractivepropertieswould combine a "Tay-lor rule" for monetaly policy with nominal-deficittargeting as afiscal policy commitment.

"Proposals or a 7Y1071.etS77 rule requirea supplementary roposalof afiscalule?Karl Brunner 1986), p. 54RECENTYEARShave seen a worldwide movement towardgreateremphasis upon the achievementof inflationtargets as the plimaly clîtelîonfor judging the success of central banks' conduct of monetarypolicy. At the sametime, the independenceof centralbanks in thelr choice of the means with which topursuethis goal has also increased.An implicationwould seem to be that it is nowwidely acceptedthat the choice of monetarypolicy to achieve a tal^get ath for infla-tion is a problem hatcan be, and indeed ought to be, separated iôm thel^ spects ofgovernmentpolicy, such as the choice of fiscal policy.1But is this really so clear? Ordo the agencies lêsponsibleor inflationstabilizationproperlyneed to concernthem-selves with fiscal policy choices as well, while the agencies concerned with fiscalpolicy have a correspondingneed to coordinate heir actions with those of the mone-

tary authority?The argument for separation of decision making about these two aspects ofmacroeconomicpolicy necessarily relies upon two theses: first, that fiscal policy is

This Jollsnr71f Moszevy,7edits7Z?dalzlkislgecturewas presentedat Ohio State University on May 1,2000. The author thanks Michael Bordo, Matt Canzonezi, Steve Cecchetti, Larry Christiano, JohnCochrane, Paul Evans, EduardoLoyo, Bennett McCallu1n,Helene Rey, Stephanie Schmitt-Grohe,andChris Sims for helpful discussions, Gauti Eggertsson for researchassistance, and the National ScienceFoundation or researchSUppOlthrougha grant o the National Bureauof Economic Research.1. A particularly trikingexample of an attempt o separate he two types of policy decisions is the Eu-ropeanmonetaryunion, in which monetarypolicy is the responsibilityof a supranationalEuropeallCen-tral Bank, while fiscal policies continue to be the prerogativesof individual1lational overnments.

MICHAELWOODFORDs proJessor of eco7107nicls It P7 71ceto71U7ziversity.E-nlail:[email protected] Mo7ey, Credit,co7zdcl7zki7zg,ol. 33, No. 3 (August 2001)Copyright2001 by The Ohio State University


3/61

670 : MONEY,CREDIT,AND BANKING

of little consequence as far as inflationdetermination s concerned,and second, thatmonetarypolicy has little effect upon the governmentbudget.I shall arguehere thatneitherproposition s true,for reasons that are related.The fiscal effects of monetarypolicy are often thoughtto be an insignificantconsideration n the choice of mone-tary policy by the major ndustrialnations, because seigniorage revenues are such asmall fractionof total government evenues n these countries.But such a calculationneglects a more important hannel for fiscal effects of monetarypolicy, namely theeffects of monetary policy upon the real value of outstanding government debt,through ts effects upon the price level (given that much of the public debt is nomi-nal) and upon bond prices, and upon the real debt scrvice requiredby such debt (in-sofar as monetarypolicy can affect real as well as nominalinterestrates).2Fiscal policy is often thought to be unimportant or inflation determination atleast when, as in countries ike the United States and theUnited Kingdom, a desire toobtain seigniorage revenues plays no apparentrole in the choice of monetarypol-icy on two different, hough complementary, rounds.On one hand, it is often ar-gued that inflation s purely a monetaryphenomenon,andhence that only the choiceof monetary policy matters for what level of inflation one will have. And on theother, the celebrated "Ricardianequivalence" proposition implies that insofar asconsumers have rationalexpectations, fiscal policy shouldhave no effect upon ag-gregatedemand,and hence no effect upon inflation.

I shall argue that neither proposition s of such generalvalidity as is often sup-posed. As a considerable ecent iterature as stressed,3 iscalshocks affect aggregatedemand,and the specificationof fiscal policy matters or theconsequences of mone-tarypolicy as well, in rationalexpectationsequilibriaassociatedwith policy regimesof the kind that I shall call "non-Ricardian"Woodford1995, 1996), even when themonetarypolicy rule involves no explicit dependence upon fiscal variables of anysort.This happens,essentially, hrough he effects of fiscaldisturbances pon private-sector budget constraintsand hence upon aggregatedemand.Such effects are neu-tralized by the existence of rationalexpectations and frictionless financial marketsonly if it is understood hatthe governmentbudget tself will always be subsequentlyadjusted o neutralize he effects, in present value, of anycurrent iscal disturbance.A "non-Ricardian"iscal policy is one that does not have thisproperty;we show thatnon-Ricardianpolicies may easily be consistent with the existence of a rationalex-pectations equilibrium,which means that the expectationthat the governmentwillfollow such a rule need never be disconfirmed.

2. See King (1995) for discussion of this point, with some quantitative vidence.3. The discussion of price-level determination ndera non-Ricardian olicy regime n section 1 belowrecapitulates esults from Woodford 1994, 1995, 1996, 1998c), drawingalso upon the important ontri-butions of Leeper (1991), Sims (1994), and Cochrane(1999). Importantprecursorsof this literature n-clude Sargent (1982), Begg and Haque (1984), Shim (1984), d'Autume and Michel (1987), andAuernheimerand Contreras 1990, 1993). Other recent discussions andextensions of this work includeBassetto (2000), Benhabib, Schmitt-Grohe,and Uribe (2001a, 2001c), Benassy (2000), Bergin (1996),Buiter (1998, 1999), Canzoneriand Diba (1996), Canzoneri,Cumby, andDiba (1998, 1999), Carlstromand Fuerst (2000), Christianoand Fitzgerald (2000), Cochrane (1998, 2000), Cushing (1999), Daniel(1999), Dupor (2000), Gordonand Leeper (1999), Kenc, Perraudin, ndVitale (1997), Kocherlakota ndPhelan (1999), Leith and Wren-Lewis (1998), Loyo (1997, 1999, 2000), McCallum (1998, 1999),Schmitt-Grohe nd Uribe (2000), and Sims (1997, 1998, 1999).


4/61

MICHAELWOODFORD : 671

This possibility, however, means that a central bank charged with maintainingprice stabilitycannotbe indifferentas to how fiscal policy is determined.To be con-crete, I shall arguethatthe melee ommitmentof a centralbank to conductmonetarypolicy accordingto a rule such as the "Taylor ule" (Taylor1993) is insufficienttoensurea stable, low-equilibriumrate of inflation.On one hand, (non-Ricardian)is-cal expectationsinconsistentwith a stable price level may frustrate his outcome,even when monetarypolicy is itself consistentwith pricestability.Indeed,the com-binationof a Taylorrule with certainkinds of fiscal policy may result n an inflation-ary or deflationary spiral. And on the other hand, even when fiscal policy isconsistent ith stableprices, the policy regime(includingthe commitment o a Tay-lor rule) may not precludeotherequally possible l^ationalxpectationsequilibria,such as equilibria nvolvingself-fulfillingdeflationary pirals.4Alternative iscalpol-icy commitmentsmay instead exclude these undesireddeflationaryequilibria[asdiscussedby Woodford(1999a)], and thus in this way help to ensurestable prices.As a practicalproposal hat addleesses oth of these issues, I shall suggestthat a Tay-lor rule for monetarypolicy shouldbe accompaniedby targetsfor the size of gov-ernmentbudget deficits.1. PRICE-LEVELDETERMINATIONUNDER A BOND PRICE-SUPPORTREGIME

Beforeturning o a discussionof Taylorrules,it will be useful to takeup the moregeneralquestion of how fiscal policy can affectthe determination f the equilibriumplice level. The role of fiscal developmentsas a sourceof disturbanceso the plicelevel canbe seen mostclearly npolicy regimessometimessaid to involve"fiscaldom-inance."These are policyregimes,often associatedwith the special fiscalpressuresofwar finance, n whichothergoalsof centralbankpolicy aresubordinatedo the goal ofassisting n the financingof the governmentbudget. However, t is importanto notethatthisdoes notnecessarilymeanthat fiscaldevelopmentsaffect theprice level onlybecausethe centralbankadjustsmonetarypolicyin response o them.A familiartextbookaccountof fiscally dominantregimesruns as follows: fiscalexigencies determinethe size of a real governmentbudgetdeficit that must be fi-nanced; this budget shortfall is then assigned to the central bank as a level ofseignioragerevenue hat t mustgenerate hroughmoneycreation; he monetarybaseis increasedby whateveramountsuffices to generatethe requiredrevenues;andfi-nally, therate of moneygrowthdetermines he equilibrium ate of inflation,thleoughthe usualquantity-theoreticmechanism.Underthis account,fiscal developmentsaf-fect therateof inflation,butonlybecause theyaffect monetarypolicy,under hispar-ticular sort of monetary policy rule; inflation is still a "purely monetary"phenomenon.Such an accountis still perfectlyconsistentwith the view that com-mitment o an anti-inflationarymonetarypolicy is sufficientto ensureprice stability.

4. Benhabib, Schmitt-Grohe,and Uribe (2001b) criticize regimes involving a Taylor rule on thisground, hough t is importanto note thatthe problem hatthey identifyis in no way special to the Taylorrule.


5/61


Furthermore,he model just sketched Illightseem to applyonly to a few less-devel-oped economies, not to advancedeconomies such as the United States or the Euro-pean Union. For it would seem not to apply in the case of an independentcentralbank, thatneed not acceptseigniorage targetsdictatedby theTreasury;norwould itseem likely to apply to aneconomy with sophisticated inancialmarkets, n which itis difficultfor the government o raise largeseigniorage revenues,because of peo-ple's abilityto substituteawayfrom non-interest-earningssets.Thus the partof theworld in which such a regimewould even be a potential outcomemight seem to berapidlyshrinking.Instead, shall argue hatfiscal policy canaffect the pricelevel even whenthe cen-tralbankpursuesanautonon1.0lzsonetarypolicy, by whichI mean a rule for settingits instrument in practice,a nominal interestrate) that is iMdepeMdeMt offiscalvari-ables.Thusit will not be enough,to avoidprice-level instabilityresulting romfiscaldisturbances, o simply adoptan institutionalarrangementunder which the centralbank leeceivesno directivesfiom the Treasurydictatingchangesin policy;nor will itbe enoughthat the centralbank commits itself to an interestrate rule, like theTaylorrule, that nvolvesno directfeedbackfromvariablessuch as the the governmentbud-get. Furthermore,he potentialeffects of fiscaldisturbancesdescribedherewill con-tinue to exist even in what I shall the "cashless limit" (Woodford 1998a) thehypotheticallimiting case of an economy in which financial innovationhas pro-ceeded to the extent that availableseignioragerevenues are negligible. This is be-cause these effects in no way depend upon attempts to use monetary policy togenerate seignioragerevenues.Thus the possibility that fiscal policy may interferewith the achievementof price stability cannotbe so easily dismissed, even for ad-vanced economies.In fact, "fiscallydominant" egimes often do not involveany direct assignmentofa seignioragetargetto the centralbank, as in the textbookanalysis. Instead,"fiscaldominance''manifests itself throughpressureon the centralbank to use monetaleypolicy to maintain he market alueof governncentebt.A classic example is pro-vided by U.S. monetary policy from 1942 up until the Treasury-Fed"Accord"ofMarchl951.5Beginningin April 1942, the Fed and the Treasuryagreedto an interestrate con-trol program, he declaredaim of which was to maintain"relatively tableprices andyields for government securities."6The yield on ninety-day Treasurybills waspegged at 3/8 of a percent; his peg was maintained hroughJune 1947, andas shownin Figure la, until that point the price of bills was completelyfixed, as the Treasuryoffered both to buy and sell bills at that price.An intentionwas also announcedofsupportingone-year Treasurycertificatesat a price corresponding o a 7/8 percentannualyield; this policy continuedafter 1947, though at a slightly higheryield. Fi-nally, the pricesof twenty-five-yearTreasurybonds were supportedat a pricecorre-

5. See, forexample, riedmanndSchwartz1963,chap.10);EichengreenlldGarber1991);Tim-berlake1993,chap.20); andToma1997,chap.8).6. Eccles 1951,p. 350);quoted y Timberlake1993,p. 304).


6/61


7/61


this period s typically describedas thoroughlysubordinateo Tleasurypolicy,this isactually an example of an autonomousmonetalypolicy, in the sense definedabove.A policy of conductingopen-marketpurchasesand sales so as to stabilizethe plicesof Treasury ecurities s one thatrequiresno centralbankmonitoringof fiscal devel-opments for its implementation,nor any directivesfrom the Treasuryabouthow torespond o fiscal developments. t is in fact an especially simpleexample of an intel--est raterule,essentially equivalent o an interest at.e eg.Any effect of fiscal shocksupon the growthof the monetarybase underthis leegimewas purely a genel-al-equi-libriumphenomenon,andnot a consequenceof any directdependence of the Fed'sinterestratetargetsupon such shocks.Yet fiscal developmentsclearly have a major impact uponthe course of inflationundelOuch regimes. For example, in the case of the United States in the 1940s, theregime was inflationaley uringthe war period,though wage and price controlssup-pressed much of this inflationuntil their relaxation n several stages during 1946.(The burstof inflation n 1946-47 seen in Figure lb shouldnot be attributedo anysulege n aggregatedemandat thattime, butrather o the allowanceof pricesto finallyrise to theirequilibrium evel.) On the otherhand, the price-support egimeresultedin deghationver the period1948-50. This corresponds o a period n whichthe largewartimedeficitshad ended,and the U.S. governmentbudgetwas instead chronicallyin surplus.With the outbreakof the Koreanwar in June 1950, inflationsuddenlybegan again.It was only at this time that the bond price-support egime came to bedenouncedas "an engine of inflation," ndwas for that reasonsuspended.8How is one to explain theseeffects uponthe general evel of prices of variation nthe fiscal situation?It cannotbe throughany directeffect of fiscal developmentsupon monetalypolicy, understood o referto the Fed's rulefor setting interestrates.Rather, ucheffects indicatethatthe governmentbudgetcanplay a role in price-leveldeterminationn addition o the specificationof monetarypolicy.Might one still salvage a traditionalquantity-theoretic iew of inflationdetermi-nation by sayingthat in such a regime, themoney supplydepends upon the govern-ment budget,as well as the interest rate rule?In equilibrium,t is true thatit does;fiscal disturbancesaffect the equilibriumgrowth rate of the money supply.But thecausality is notfrom the governmentbudgetto the growthof the money supply,andthen only from the change in the money supply to prices. Rather, he governmentbudgetaffectsthe general evel of prices, andonl.y ecause riceschangedoes it alsoaffect the money supply (as higher prices lesult in highermoney demand,which theFed passively accommodatesunder such a regime). Thus one cannot explain thechange in theprice level as being due to the increase n the money supply.Upon first thought, one might suppose that under a bond price-support egime,thereis a directconnectionbetween the governmentbudgetand growth in the mon-etarybase.One might reasonthata commitmentby the Fedto act as the residualpur-chaser of governmentdebt will require the Fed to increase the monetarybase, in

8. See Brunnerand Meltzer (1966) for an importantdiscussion of this period, stressing thatthe infla-tionaryor deflationary haracterof the regime dependedupon fiscal policy.


8/61


order to increase its holdings of governmentdebt, whenever the Treasury ssuesmore debt, which is to say, whenever (and to the extentthat) the governmentruns abudgetdeficit. But this superficialanalysis implicitlyassumes thatthe public's de-mand for governmentbonds is fixed, so that (in the absence of a price change) theFed will haveto acquire he additional ssues, while it assumes at the same time thatthere is no obstacle to increasing the public's money holdings by an arbitraryamount,without anychange in therelativeyield on moneyandbonds.Instead,economic theoryimplies that if anything, the opposite elationsshouldobtain.Thereare good reasons why it may notbe possible for the Fedto increasethemonetarybase withouthaving to accept a change in theyields onTreasury ecurities.A money demandrelation of the conventional sort [for example, equation (16)below] implies that the public's desiredmoney balances will be a function of theprice level, of the quantityof real transactions,and of the interestdifferentialbe-tween money and bonds,butnotof fiscal variablessuch as the stock of publicdebt.Thus it is generallysupposedthatthe Fed cannot changethe monetarybase withoutaccepting a change in the level of interestrates,something that is precludedunderthe bondprice-supportegime.At the sametime, there areequallygood reasonswhyanincrease n governmentborrowingmightwell increasethe public'swillingness tohold governmentbonds,even in the absenceof any change in bond yields. Indeed,the doctrineof RicardianEquivalenceassertsthatgovernmentborrowingautomati-cally createsan increasein desiredprivatebond holdings of exactly the same size(due to an increase in expectedfuturetax obligations), so that bondyields need notchange at all to maintainequilibrium n thebond market.The analysis that I shall proposehere will not imply thatRicardianEquivalenceobtains (in thatcase, there would be no inflationary mpactof anexpectationof bud-get deficits,either).Butit will assume a conventionalmoney demandrelation,so thatthe quantityof moneythat must be supplied n order o maintainbondprices at theirtarget evels is a functionsolely of prices andreal activity.Thus thegovernmentbud-get will be able to affect the money supplyonlybecauseit is able to affectequilib-rium pricesthroughanotherchannel;priceswill not be affected only because of thechange in the moneysupply.1.1A SisnpleModel

Let us consider price-level determinationunder such a regime using a simplemonetaryframework,namely, a representative-householdmodel of the kind intro-duced by Sidrauski(1967) and Brock (1974, 1975). I shall suppose that the repre-sentativehouseholdseeks to maximize a discountedsum of utilitiesof the formr 00 1Eoj , |3tU(ct+ gt,MtIPt)J

t=0

where U(c, m) is an increasing,concave function of both arguments,and the dis-count factorsatisfies O< 13< 1. The second argumentof U indicates the liquidity


9/61


services providedby end-of-periodmoney balances Mt;these depend upon the realpurchasingpower of those balances, so thatMt is deflatedby the price level Pt. In thespecification 1), I assume that (real) governmentpurchasesgt are perfect substitutesfor (real) privateconsumptionexpenditurect. This simplificationallows us to focussolely upon the effects of fiscal policy upon privatebudget constraints;governmentpurchaseshave exactly the same effect on the economy as transfers o households offunds sufficientto finance privateconsumptionof exactly the same amount.(I shallassume thattaxes are lump sum for the same reason;a tax increase will then have thesame effect as a reduction n transfers hat reduces household budgets in the sameamount.)The representative ousehold is subject each period to a flow budget constraintofthe form

Mt + Et[Rtt+l(Wt+l-Mt)] ' Wt + Ptyt-Tt-Ptct, (2)stating that end-of-period inancialwealth (money balances Mt plus bonds) must beno greater n value than financialwealth Wtat the beginning of the period, plus in-come from the sale of period t production t' net of tax paymellts and consumptionexpenditure.The variableTtrepresents nominal) tax obligations net of any govern-ment transfers; he two componentsneed not be distinguished,as taxes are assumedto be lump sum. The difference Wt+ -Mt represents he (nominal) value in periodt + 1 of the household'sbond portfolio at the end of period t; as I assume completefinancialmarkets, his portfolio may include state-contingent laims of many sorts.The (nominal)marketvalue of such a bundleof state-contingent laims in period t isgiven by Et[Rtt+l(Wt+l-Mt)], where the randomvariableRtt+l is a stochastic dis-count factor for pricing arbitrary nonmonetary)financial claims.9 Note that thehousehold, as a price taker n financialmarkets as well as goods markets), akes theevolution of the stochastic discount factor as being independentof its own portfoliodecisions (indicatedby the evolution of Mt and Wt).

The nominal interest rate it on a one-period riskless claim purchased n period tmust satisfy1 + it = Et[Rt,t+l]

Using this, we may rewrite(2) in the form

Poct t Mo + Er[Rt+lWt+t] Wo [Ptyo-Tr], (4)

9. The existence of such a pricingkernel follows from the absence of arbitrage pportunities; he pric-ing relationapplies, of course, only to financialassets that (unlike money) do not yield additionalnonpe-cuniarybenefits.Under our assumptionof complete markets,R, +g is uniquely defined.


10/61


in which it/(l + it)appearsas the effectivecost of holdingwealthin rllonetaryorm.Let us also assume a borwowingimit each period,accordingto which the house-hold'sportfolio (includinganyshortpositions)mustsatisfy00

Wt+1 - E Et+1[Rt+1,T(PTYT TT)] (5)T=t+1in each possible statein periodt + 1; this states thatthe householdmust neverhavedebts greater hanthe presentvalue of all futureafter-taxncome.10The sequenceofflow budgetconstraints 4) combinedwith (5) is thellequivalent o the intertemporalbudgetconstraintll

00 1 00

E EtRt,TPTCT . MT C Wt + E ElRtvT[PTYT TT] (6)T=t 1 + tT _ T=tWe may thus statethe household'sproblem, ookingforward romany date t, as thechoice of a consumptionplan and plannedmoney holdingsto maximize (1) subjectto (6),given financialwealthWt.

Necessaryand sufficientconditionsforhouseholdoptimizationl2are thenthatthefirst-order onditionsl3Usal Ct + gt ' }}>t = ttUC (Ct + gt ' }}1't ) 1 + it

UC(ct + gt}nt) = D - (8)Uc(ct+l + gt+l,mt+l) Rt,t+l Pt+l

hold at all times, and that the householdexhaust ts intertemporal udgetconstraint,that is, that00 * 00

E EtRtT PTCT 1 . MT = Wt + E EtRt,T[PT)T TT] ( )T=t + tT _ T=tThis lastconditionstates boththat the left- and right-hand ides of (6)areequal, and

10. FIere he discountfactor R{+1,Tor discounting ncome in period Tback to period t + 1 is definedas tlle productof factorsRs + for s runninghom t + l tllroughT-l; it is equalto one when T = t + 1.1 . See Woodford l 999a) for details.12. For simplicity,we ignore thepossibility of cornersolutions.13. In writingthese, I use the notationm,-M,lP, for real moneybalances.


11/61


that both infinite sums converge.14This condition for optimality could equivalentlybe replacedby the stipulation hat the household's planned expenditurehas a finitepresentvalue,

T=t + tT _

togetherwith a transversality ondition on wealth accumulation,15lim Et[Rt TWT (11)

A rationalexpectationsequilibrium s then a collection of state-contingentpathsfor the various endogenous variables hat satisfy these conditions for household op-timization,togetherwith the market-clearing onditionsct + gt = Yt, (12)Mt= Mts, (13)Wt+1= Wt+1 (14)

at all dates and in all possible states.16Here the aggregate upply of goods Yt s an ex-ogenously specified stochasticprocess, whereas the money supply Mtsand the mar-ket value of total beginning-of-period government liabilities Wt+1 evolve inaccordancewith the specification f monetaryandfiscal policy (to be clarifiedbelow).Substituting 12)-(13) into (7), we obtain the equilibriumconditionu,7](yt,Mt IPt)= ir . (1.5)UC(yt,MtslEt) l+it

Under standardassumptions on preferences,17 his equation can be solved for aunique equilibrium evel of real money balances,

14. The latterstipulation s necessary,as both left- and right-hand ide being infinite wouldnot implythatthe householdcould not affordto consum more. Indeed, n such a case, (S) would impose no limit onborrowing,and "Ponzi schemes" would be possible, allowing unbounded onsumptionat all dates.15. Again, see Woodford 1999a) for details.16. Equilibrium rom some date t onwardrequires hat (12)-(14) be expected to hold at all dates t 'T. The fact that WT= WTwould follow from the specificationof the initial portfolio of the representativehousehold, rather hanbeing a market-clearing ondition.17. In addition o those noted earlier,we assume thatboth consumptionand liquidity services are nor-mal goods, and also assume boundary onditions guaranteeing n interior olution to (15).


12/61

MICHAELOODFORD679Ms' = L(yt, t) t (16)t

where the "liquiditypreference unction"L is increasing n its first argumentand de-creasing n the second.Thus our model incorporates n equilibrium ondition statingthat the price level is at all times such thatthe implied real value of the money sup-ply is equal to desiredreal balances;butas we shall see, this need not mean that theevolution of the pricelevel is best explainedy the evolutionof the money supply.A similar substitutionof (12)-(13) into (8) allows us to solve for the stochasticdiscount factor,obtaining

R = D Uc(Yt+lMt+l / Pt+l) pt (17)tt+1 Uc(yt,MtIPt) Pt+Substitutionof this into (3) then yields

1 + i, = 13-1E, Uc(Yt+lM,+l / P+l) Pt 4 (18)

This equilibrium elation s a sort of "Fisherequation," inkingnominal nterestratesto expected inflation,but also involving the real factors thatdeterminethe equilib-ium real rate of interest.In the familiartextbook case of a utility function U that isadditivelyseparablebetween consumptionand liquidity services (or in the "cashlesslimit" discussedbelow), (18) reduces to

l+i,=: IjE, ,('+) p' | , (19)

where u(ct + gt) is the palt of U thatdependsupon consumption or the value of U inthe "cashless imit").In this special case, the expected rate of inflation s the only en-dogenous variableon the right-hand ide of the equation.Under similarsubstitutions, he remainingrequirements or optimality,(10) and(1 1), become

00, ,B Et Uc YT,nT )CT + UE71 YT ZMTMT m (20)T=t

Tlim: Et Uc yT,Mt I PT WT PT = (21)


13/61


HereI havesubstituted 17) to eliminatethe stochasticdiscountfactors,andin (20)havealso substituted 15) for the factor l(1 + i). Let us supposefurthermorehattheshareof governmentpurchases n the totalnationalproduct s bounded,thatis, that ' gt ' Bt at all times, for some bound 0 < Y < 1. Thenwe musthaveCT YT (1 ny) CT

at all times, so that(20) is equivalent o the condition00

T=t

whereF(Y, m)-Uc(y, m)y + Us7Z(y, m)m .

Thusbothof the remainingequilibrium onditions,(21) and(22), placeboundsuponhow far the price level can divergeasymptotically rom proportionalityo the nomi-nal asset suppliesMtsandWts.The transversality onditionfor optimalwealthaccumulation an alternativelybeexpressedby the equalityin (9). A similarsubstitutionof conditions(12)-(14) andintothis equationyields

_ _

+ E D]T-tEUC(YTH7HT) TT (23)

as a substitute or (21). One notes that the presentvalue of theYT-gT terms on theleft-handside must be finite, as a consequenceof (22) and the assumedboundongovernmentpurchases.Subtractinghese termsfromboth sides andrearranging, neobtainsthe equilibrium ondition

WT= E [D] -tE UCYT T s + T TPt T=t Uc (Yt, , ) 1 + iT PT (24)wherest denotesthereal primarygovernmentbudgetsurplus

TS - t _ oPt


14/61


This condition states that the real value of net government iabilities must equal thepresentvalue of expected futureprimarybudget surpluses,corrected o take accountof the government's nterestsaved on the partof its liabilities that the public is will-ing to hold in monetary orm. Note, however, hatthis relationnecessarily obtains na rationalexpectations equilibrium,not because we have assumed it as a constraintupon the government's iscal policy, but ratherbecause it follows from privatesectoroptimization, ogether with marketclearing. (This point will be of considerable m-portance or the discussion below.)To sum up, a rational expectations equilibrium is a collection of stochasticprocesses {Pt, it, Mts, Wts} hat satisfy (16), (18), and (22), as well as either (21) or(24), along with the equations specifying monetary and fiscal policy. These equa-tions suffice to determineequilibrium ll the case that both the monetarypolicy ruleand the law of motion for government iabilities given the fiscal policy rule can bespecified without referenceto asset prices other than it. (An example of such a caseis presented n the next subsection.) Once an equilibrium that is, solution to theseequations) s found, the implied equilibriumprocesses for all other asset prices arethen given by (17). If instead monetaryand/or iscal policy cannotbe specified with-out reference o longer-termbond prices, the necessary bond pricing equationsmustbe adjoined o the system of equations isted above, and the bond prices in questionaddedto the list of endogenous variables hat arejointly determined.1.2 A Treasury-BillPegLet us now consider the equilibrium price level under a bond price-supportregime. As a first simple example, suppose that monetarypolicy pegs the price of aone-period Treasury bill; thus it is equivalent to specification of an exogenousprocess {it} for the short-termnominal nterestrate.We shall assume that it > 0 at alltimes.l8 Let us suppose furthermore hat fiscal policy is describedby an exogenousprimary-surplusprocess {st}. Since Yt is assumed to be exogenous, such a fiscalspecification might correspondto an exogenous process {gt} for real governmentpurchases, ogetherwith an exogenous process for a proportional ax rate {t}, withaggregatetax collections then evolving as Tt = ttPtyt.Such a specificationof fiscalexpectations s particularly ikely to apply in wartime,when governmentpurchasesvary for reasons largely independentof the state of the economy or the government'sbudget, and when the government'sability to further ncrease tax rates may also betightly constrained.Suppose also, for simplicity, hatthe public debt consists entirelyof (riskless nom-inal) one-periodTreasurybills. Then total government iabilities at the beginning ofany period t are equal to

Wts = Mts_l + (1 + it_l)Bts_l,

18. The theory extends directly to the case of a zero yield, as long as preferences nvolve satiation nmoney balances at some finite level. In that case, the equilibriumpath of the price level would still beuniquely defined, but the equilibriummoney supply would be indeterminate it could take any valuegreater hanor equal to the satiation evel) in all periods with i, = O.


15/61


whereBtsdenotes the supply of Treasurybills at the end of period t (measuredbytheir marketvalue at the time of issuance). The flow budget constraint or the gov-ernment mplies that the supply of bills must satisfyBts = Wt -P4t-Mt .

It follows that underthis fiscal regime, total government iabilities evolve accordingto the law of motion

Wt+l=(l+ir) Wts_P,st-1 ' Mts (25)

OUrproblem s now to solve for rationalexpectationsequilibriumpleocesses Pt, Mts,Wts atisfying (16), (18), (22), (24), and (25), given exogenous processes {Yt, t, st}and an initial quantityof nominal government iabilities.The equilibriumconditions may be solved sequentially,as follows. We first notethat (16) determines he equilibrium volution of real balances, given the exogenousprocesses {Yt, t}. Substituting his solution for real balances nto (24), we obtain

P, T=t ()),, i, ) 1 + iT _ (26)

wherek(, i)-Uc(J, L(,i))

Note that all terms on the right-hand ide are now functions of exogenous variables.Let us suppose that the fiscal expectationsrepresentedby the process {st} are suchthat the right-hand ide has a finite positive value. 9 We then also obselve that Wts sapredetersined uantity n periodt, undele he fiscal regime specified here. Thus ifWts 0, there is a unique equilibriumprice level Pt > 0 that satisfies (26).Once we have solved for Pt, (25) then implies a value for Wt+1, given by

19. If not, and if (as we assume) Wts 0, then no equilibrium s possible. This would representa mon-etary-fiscalpolicy mix that is inconsistent; n equilibrium,one policy or the other would have to be ex-pected to deviate from the proposed specification at some point. If one supposes that the the primarysurplusprocess is unchangeable, his would mean thatpeople would not be able to expect maintenanceofthe bill-ratepeg forever.If the "inflation ax"proceeds iL@,i)l(l + i) are increasing n i, and expected pri-marydeficits are too large to be consistent with the contemplated equence { ,}, an increase n the bill rateat some point might solve the problem.On the other hand, f projectedprimarydeficits are too larae, theremight be slo path of bill yields consistent with the {s,} process, which would then necessarily have to beadjusted.We do not take up such cases here, but insteadconsider the effects of fiscal news within the classof processes {s,} that are consistent with the postulatedbill-ratepeg.


16/61


Wts+l=(l+it) Wts-Ptst- ' PtL(yt,it) (27)1 + ttWemay thenapply the same reasoning n period t + 1, solving (26) forPt+1, and soon iteratively.We thus solve for uniqueequilibriumprocesses {Pt, WtS}, iven an ini-tial (positive) level of government iabilities and expectationsregarding he exoge-nous processes. The equilibrium process for the price level then implies anendogenousevolution for the money supply, given by (16), and for any other assetprices that maybe of interest,given by (17).It might be thoughtproblematic hatthe aboveconstructionof an equilibriumre-quires that Wt+lturn out to be positive in all periods. But in fact it suffices that theprocess {st} satisfy boundsthat mplythattheright-hand ide of (26) is positive at alldates. Underthisassumption,one canshow thatthelaw of motion (27) always yieldsa positive valuefor Wt+ , given a positive value for Wts.This allows continuationofthe construction orever.The constructed eries must also satisfy (22) in orderfor itto representanequilibrium.However,this simplyrequirescertainboundson the ex-ogenous processes {Yt, t}; in particular, t suffices that F(yt,L(yt, it)) be a boundedprocess.Itmay also be noted thatno reference o equilibrium ondition(18) hasbeen madein this construction. This might lead to a suspicion that equilibrium is actually"overdetermined" nder the kind of policy regime that has been postulated.But infact the equilibrium ust constructednecessarilysatisfies (18). Note that if (26), withall timesubscriptsadvancedby one, is expectedto determine he price level in periodt + 1, it follows that in period t the conditionalexpectationshould satisfy

Er[X(yo+l, it+l )P+1 ] = 5 E E Et(YT' iT) ST + l + i L(YT)T)

= Ws (X(Yt, t) p -(Yt, it) st + 1 + i L(Yt, t) )(Yt,it)

(1 + it )Pt

where the finalline uses (27) to substitute or Wts+l.Thus (18) holds as well.Note the effects of fiscal disturbancesupon the price level in this equilibrium.News thatreduces the conditionalexpectationat date t of cultent and/orfutureval-ues of the primarysurplusST, results(other thingsbeing equal) in a lower positivevalue for theright-hand ide of (26). As a result,since Wts s predetermined,he equi-librium price level Pt must rise. Thus fiscal disturbances esult in variations n therateof inflationundersuch a regime.Furthermore,he natureof the effect is consis-


17/61


tent with the observation hatthe outbreakof war in June 1950 (leading to expecta-tions of lowergovernment urpluses n the near future)resulted n an increase n theU.S. price level.This effect of fiscal developmentson inflationcannot really be explainedby thefact that the money supplyexpands when the governmentbudget deteriorates or isexpected to in the future).It is true that the quantityequation(16) is satisfiedat alltimes; but thereason for the increase n theprice level is suppliedby (26), while (16)simply indicateshow muchthe money supplymust expand iveM that the pricelevelrises. Furthermore,he factthatthe price level may rise (andthe money supplythere-fore expand)even the reducedsurplusesactually materialize,but simply becausethey areexpected,makes it clear that a mechanicalconnectionbetween the govern-ment budgetand the monetarybase is not at work.The principle that most directly explains inflation determinationunder such aregime is insteadthe following: the price level adjusts as necessary to maintain n-tertemporal overnmentbudgetbalance. Suchafiscalheor of theprice evelmakesthe connectionbetween fiscal developmentsand price-level instability straightfor-ward.The basiceconomicmechanism s thewealth effect of fiscal disturbancesuponprivateexpenditure.The anticipationof lowerprimarygovernment urplusesmakeshouseholds eel wealthier(ableto afforda greater um of privateand government x-penditure, iventheirexpectedafter-tax ncomeand given expectedgovernmentpur-chases on theirbehalf), andthus leads themto demandgoods and services in excessof those the economy can supply, except insofaras prices rise. A sufficientrise inprices can restoreequilibriumby reducingthe real value of the nominal assets heldby households(which, in aggregate,are simplythe nominalliabilities of the govern-ment). Equilibrium s restoredwhen prices rise to the point that the real value ofthose nominalassets no longerexceeds the presentvalue of expected futureprimarysurpluses,since at this point the (privateplus public) expenditure hat householdscan afford s exactly equal in value to whatthe economy can produce.Note thatin this analysis,the inflationary ffects of fiscal disturbancesdo not re-

late primarily o changes in expected seignioragerevenues.The fiscal effect of thechange in the real valuationof nominal government iabilities is also an importantconsequenceof inflation;and this effect may well be the more importantone forhigh-debteconomieswith sophisticated inancialmarkets.Indeed, theequilibrium ust describedremainswell defined n the limitingcase ofa "cashless"economy. By thisI mean an economyin whichthe transactionsrictionsresponsiblefor the demandfor cash balancesare negligible.20 n this limitingcase,seignioragebecomes negligible relative to the size of the governmentbudget,andvariations n real balances (in percentage erms)come to have a negligible effect onthe marginalutility of income.This means thatthe marginalutility of incomemay beexpressed simply as S(ct + gt), a decreasingfunction of total (private and public)purchases; hattotal nominal iabilities Wtcorrespond implyto tlle value of (interest-earning)publicdebt;and thatthe primarybudgetsu1plusneednot be corrected o in-

20. See Woodford 1998a) for a more formal analysis.


18/61


clude interestsavings on the monetarybase in theevolutionequation or governmentliabilities. Thusin this limitingcase, (26) and(27) reduce toWt = E DT tEt T STPt T=t S(YF (28)

andWts+ = (1 + it)[Wt -Ptst] (29)

respectively.This pair of equationscan be solved recursively o obtain uniqueequi-libriumsequences {Pt, Wts}, ust as in the discussion above.1.3 AnExtensionto Longer-TermGovernmentDebt

A similaranalysis is possible of price-support egimes with debt of longerdura-tion, at the price of greateralgebraiccomplexity.Here I considera single, relativelysimple case that llustrates hemain new elementintroducedby longel termdebt:thefact that Wts s in generalno longer completelypredetermined, s it will dependuponthe marketvalue at t of governmentdebt thathasnot yet matured. n this simplecase,I shall supposethat all govelalmentdebt consists of perpetuitieswith coupons thatdecay exponentially.Specifically, I suppose thata bond issued in period t pays pdollars + 1 periods later, for each j ' Oandsome decay factor0 c p < D 1.Theclassic "consol" s a securityof this kind, with p = 1. Moregenerally, n anenviron-ment with stable prices, the durationof such a bond is (1 _ p) 1.Thus oursimpleassumptionallows us to analyzebonds of arbitraryduration.At the same time, weneed considerthe equilibriumprice at each point in time of only one type of bondbecause a bondof this type thathas been issued k periods ago is equivalent o pk newbonds. Let Qt be the price in period t of a new bond. (Note thatthe bond'syield-to-maturity s a monotonic functionof this, givenby Qt 1-(1-p).)Now let us consider a price-supportpolicy underwhich the centralbank fixes theprice of thisbond each period.To simplify theanalysis, let us suppose that {Qt} is anexogenously specifieddeterministicpositive sequence.2l Then arbitrageconsidera-tions determinea uniquerational expectationsequilibriumsequence for the short-term nominal nterestrate it,given by

i = l+PQt+l -1Qt

21. Thisassumption till allows us to consider he effectsof a one-timesurprise hange n monetarypol-icy, afterwhichhouseholdsare assumed o have perfectforesightabouttheeconomy's path. In the case ofsmall enoughrandom luctuations n the bond-price argets, he effects of randomvariations n bondpricesare approximatelyhe same as in thisperfect-foresightnalysis,but the extension s not takenup here.


19/61


(I assume that the bond-price argetssatisfy Qt+l > P l(Qt-1) at all times, so thatthe implied short-term nterest rate sequence satisfies it > 0.) The policy is thusequivalent o a Treasury-billpeg corresponding o this particular equence, and wemay solve for the equilibriumprice level as above.If the public debt consists solely of this single type of bond, the value of total gov-ernment iabilities at the beginning of any period t is given by

WtS = Mts_ 1 + Bt - 1(1 + PQt),

where now Btsdenotes the quantityof the geometricallydecaying bonds outstandingat the end of period t. When p > 0, the dependence upon Qt means that Wts s nolonger a predetermined ariable.Nonetheless, Wtsdepends only upon the predeter-mined variablesMts_l,Bts_l and the exogenous variableQt. Given the specificationof monetaryand fiscal policy from date t onward, and the predetermined alues ofMts_ ,Bts_ ,there s a uniquely determinedvalue for Wts.There s also a uniquely de-termined value for the right-handside of (26), given the uniquely determinedse-quence { iT} just discussed. Thus (26) continues to uniquely determine theequilibriumprice level Pt.The money supply in period t is determinedby money demand given this pricelevel,Mts = PtL(yt it)

while the supply of bonds is then determinedby the government's low budget con-straint,Bts = Q t 1 Mts_+ B - 1 ( 1 + p Qt)-Ptst-PtL(yt, it)] (3 1

These equationsthen determinea value for Wts+ln the following period, given theexogenously specified value for Qt+ l.-One can then use (26) to solve for Pt+1, and soon, iterating on the system of equations comprised by (26), (30), and (31). Onceagain, we assume monetary/fiscal ommitmentssuch that the right-hand ide of (26)is positive and finite at all times. Then if we start rom initial conditions that mply apositive value for Wtsat some initial date, the implied price level and the impliedvalue of total government iabilities will also be positive at all later dates.Thus the basic logic of price-level determination emains the same in this case.The main difference that longer-termdebt makes is in the case of an unexpectedcha>ge in the sequence of bond-pricetargetsexpected to be maintained rom somedate t onward.In the case that all debt is shortterm, Wts s predetermined, nd is thusunaffected by an unexpected change in monetarypolicy (currentor future interestrate expectations)at date t. A change in monetarypolicy then cannot affect the pricelevel immediately,except insofar as it affects the presentvalue of futurebudget sur-pluses (including the government's interest savings on the monetary base). Thismeans that in the case of a high-debteconomy, in which means for economizing on


20/61


cash balancesarealso well developed,the main effect of an increasein nominalin-terest ratesby the centralbankwill be a fasterrate of growthof nominalgovernmentliabilities, resultingin faster inflation.(This can be clearly seen in the case of the"cashlesslimit'' discussed above.)Yet such a resultmakes it puzzling that in early1951, the Fed wished to suspend ts commitment o keep interestrates low, in orderto containthe increase n pricesunderwayat that time. (It would seem instead,underthe presentanalysis,that an increasein nominalinterestrates would only maketheprice level grow even fastel:)Allowing for longer-termgovernmentdebtchangesthis conclusion.A decisiontoincreasetargetbond yields lowers Qt, and so lowers the value of Wts or any givenpredetermined aluesMt_ l, Bt_l > 0. In the absenceof any changein the value ofthe right-hand ide of (26), the increase in bond yields would thereforerequirea de-cline in the equilibriumprice level Pt. In fact, the effects of interestrate changesonthe presentvalue of futuresurplusesare likely to be small;in the "cashless imit," heright-hand ide of (28) is completely independentof monetarypolicy. Thus in thecase of greatest nterest,an increase n bondyields will be associatedwith deflation,initially,though t will also lead to faster subsequentgrowthof nominalgovernmentliabilities,and consequently o a highereventual pricelevel. (It is this expectationofhighergoods pricesin the future hat ustifiesthe immediatedecline in bondprices.)The theoryjust expoundedhas severalappealingfeaturesas a model of the U.S.bond price-support egime of the 1940s. Firstof all, it can explainwhy a regimethatsoughtto fix nominal nterestrateswas consistentwithrelativelystable pricesfor somany years. Conventional heoriesof interestrate pegs generally imply that suchpolicies should lead to severeprice instability.Accordingto the familiar (Wicksel-lian) view summarizedby Friedman 1968), an attempt o peg nominalinterestratesshouldlead to eitheran inflationaryor a deflationary piral, requiring he peg to beabandonedbeforelong. Accordingto Sargentand Wallace(1975), instead, it shouldlead to indeterminacyof the rational expectationsequilibriumprice level, so thatfluctuationsn inflationmay occuras a pureresult of self-fulfillingexpectations.Therelativestability of prices in the 1940s is a puzzle fromeither pointof view. In par-ticular, t is striking hat people continuedto be willing to hold long-termU.S. Trea-sury securities at low nominal yields (below 2.5 percent per year) during thetemporaryhigh inflation(a 25 percentannualrate) of 1946-47; evidentlytherewaslittle fearthatthis indicated hatthe price-support egimewould generatechronic n-flation, et alone anexplosiveWicksellian"cumulativeprocess."Friedmanand Schwartz(1963, pp. 583-85) hypothesizethatpeople did not ex-pect inflationto continuebecausepreviouspostwar periods(such as that followingWorldWarI) had beenassociatedwith deflation.22 ut it is unclearwhy post-warpe-

22. However,they also discuss a mechanismclosely relatedto the one analyzedhere, when they dis-cuss the role of the government'sbudgetsurpluses."Had the federalgovernmentnot run a surplus,thepublic,with its accumulated iquid assets and pent-updemand,would have to spendmore in the postwarperiod thanit received, . . . [This] would have tendedto raise prices and incomes and so would have re-duced the level of liquidassets relativeto income by this inflationary oute.... As it was, the federalsur-plus enabledsome reductionof liquidassets relativeto income to be achieved withoutinflation" p. 583).However,FriedmanandSchwartzexpoundtheir deain terms of effects of the governmentbudgeton "the


21/61


riods shouldbe expected to bring aboutdeflation n the absence of a commitment oreturn o the gold standardat a prewarparity,which therewas no reasonto expectfollowingWorldWarII.EichengreenandGalsber 1991 insteadproposethatthe pol-icy regimeof the earlypost-warperiodwas actually an "implicit argetzone" for theprice level, with the price level maintainedwithin the zone by an expectationof in-tervention hould theboundaries ver be reached,eventhough ittle interventionwasobservedduring hese years.But such a hypothesis explainsthe behaviorof the pricelevel in termsof a purelyhypotheticalcommitment o interventions hatwere not ac-tuallyobserved; t is hardto see why the public should havehad confidencein sucha presumedcommitment.The explanationoffered here, instead, dependsonly uponcredibility of the commitment to interestrate targeting(which commitment wasbeing continuouslydemonstrated y the Fed's actions), andbeliefs aboutthe exoge-nous evolution of primarybudget surpluses(which againrequiredonly a simple ex-trapolationnto the futureof the policy thatcould alreadybe observed).The model can also explain the variationsovelstime in the degree to which theregime generated inflation, at least broadly speaking. During WorldWar II, theregime was inflationary,hough much of the inflationwas suppressedby a system ofpricecontrols, until theirremoval in 1946. This corresponded o a periodof time inwhich largegovernmentdeficits turnedout to be necessarythat would not initiallyhave beenexpected.Thetransitoryburstof inflation n 1946-47 representeddelayedpriceadjustment nce thewartimecontrolshad beenremoved,rather hana demand-driven nflation.Once this adjustmenthadoccurred, he regime was actuallymoder-ately deflationary in the early postwar period. The model predicts that peggingnominal nterestrates at a low rate, withexpectationsof primary urplusessufficientto makethese interestratesconsistent with equilibrium,should lead to steady milddeflationas the nominalliabilities of the governmentcontractover time. Finally, in-Hation ook off againsuddenly n the secondhalf of 1950, following the outbreakofwar in Korea.The modelexplains why sucha suddenchange in expectationsregard-ing the govelmmentbudgetshould be inflationary.Furthermore,t can explain whythe outbreakof war was able to cause inflationeven before ny large budgetdeficitsmaterialized.23 t is the present value of currentandexpecteduturesurpluses thatmatters n equation(26);because of thecrucial role of fiscalexpectations n this the-ory, it is completelyunderstandable hat the outbreakof war should affect inflationeven beforeit has significantlychanged the governmentbudget.The model also offers an explanationfor the abandonmentof the price-supportregime afterMarch 1951. As just explained, the model implies that such a regimeshould lead to inflation when previously unexpected deficits come to be antici-pated.24The Fed's complaint that the regime had become an "engine of inflation"market or loanable funds" rather han a general-equilibrium nalysis in ternasof its effect upon privatebudgetconstraints,of the kindpresentedhere.23. Note that the U.S. governmentbudgetcontinued to be in surplusduring the secondhalf of 1950(Timberlake1993, p. 313).24. In the flexible-pricemodelset out above, theprice-level increaseresulting iom anysingle changein fiscal expectations occurs immediately,as soon as informationchanges.However, in a mole realistic


22/61


was justified, given the return o wartimefiscal policy. Furthermore,he model (inthe version with long-termbonds) implies that an increase in bond yields shouldhave been able to mitigate the degree to whichpricesneeded to rise in the shortrun,following the revision of fiscal expectations.Hence the Fed's interestin allowingbond yields to rise above the 2.5 percentceiling, in order to containinflation.Themodel impliesthat, n the absenceof any changein fiscalexpectations, he changeinmonetarypolicy actually mpliedgreatereventual ncreases n theprice level, thoughthe suspensionof the bond price-supportpolicy allowedthem to be delayed in time.Given the inflationthat did in fact occur in the years subsequent o the "Accord,"twouldbe hardto call this an inaccurateprediction.25Finally,the model offers insight into why a policy regime of this kind would beappealingas an approach o warfinance.Firstof all, theregime is one which loosensthe constraintupon fiscal policy requiredfor consistency with stable prices. Notethatequilibrium ondition(26) must hold in the case of any monetaryand fiscalpoli-cies; the right-hand ide is simply not always a functionof purelyexogenous vari-ables.This impliesthatonly a certainspecificvalue for the expectedpresentvalueoffutureprimarygovernmentbudgetsurpluseswill be consistentwith maintainingaprice level Pt+j-Pt_1 for all j ' 0. The bond price-supportregime, as modeledhere, insteadallowsthatpresentvalue to varyarbitrarilyn responseto fiscal shocks,within certain bounds. Such flexibility would obviously be quite valuable duringwartime n particular.At the sametime, theregime is one underwhichinflationvari-ations areexpectedto be transitory; ven whennews of governmentbudgetshortfallsresultsin inflation,people canbe confident(insofaras they expectequilibrium o bedeterminedas describedhere)that inflationwill quicklyreturn o a stable (andquitelow, possibly negative) long-runlevel. Such stable long-runinflationexpectationswould be valuableto a governmentneeding to issue large quantitiesof long-termbonds exactlyat a timewhen (becauseit hasjust been learned hatthe government'sfiscal needs are more dire than previouslyanticipated)prices are currentlyrising.Fromthispoint of view, the Treasury'spressureupon theFed to cooperatewith sucha regimeduringWorldWarII would hardlybe surprising.2. RICARDIANAND NON-RICARDIANFISCALPOLICIES

Beforeturning o the policy implicationsof this view of the effects of fiscalpolicyon inflation, t is appropriateo addresssomequestionsthat may ariseaboutthelogicof the analysis just presented.One of the most obvious of these is, why shouldnotRicardianequivalenceimply thatfiscal disturbanceshave no effect upon aggregatedemand,and hence no effect uponthe pricelevel?sticky-priceextension of the model [expoundedby Woodford 1996)], the price increase s predicted o bemore gradual,and to be associatedwithhigh outputduring he periodof adjustment.25. Toma(1997, pp. 109-110) similarlyinterprets he Treasury-Fed"Accord"of March 1951 as a"default"on the government'sprevious"commitment o long-runmonetaryconstraint"under the bondprice-supportegime. See also Grossman 1990).


23/61


The answer is that the usual argumentfor Ricardianequivalenceassumes hatchanges in the governmentbudget must involve no change in thepresentvalueofcurrentand futurebudgets. (It is asserted, or example, that a current ax cut financedby governmentborrowing s necessarily accompaniedby the expectation of tax in-creases at some laterdate or dates, of equal presentvalue.) If this is so, then equation(26) is satisfiedby thesameprice level Pt as would have been the case in the absenceof the fiscal disturbance.We would then indeed find that there should be no effectupon the price level of any such event. We have reacheda differentconclusion abovebecause we have assumedthat when war breaksout unexpectedly, his news reducesthe present value of expected future budget sulpluses. We have thus considered atype of fiscal disturbance hat Ricardian heoryassunces annotoccu^Let us call a fiscal policy commitmentRicardianf it implies thatthe present-valuerelation (24), or equivalently he transversality ondition (21), necessarily holds forall possible goods-priceand asset-priceprocesses.26As an example of how this couldbe so, suppose thateach periodthe primary urplus s set according o the lmle

P,st = OlWoS-1 f MrS, (32)

for some coefficient O< oc ' 1. This rule states that the primarybudget surplus schosen to pay off a certainpositive fractionof existing government iabilitieseach pe-riod, but that the required urplus s adjusted o take accountof the government's n-terestsavings on the monetarybase. Using the government's low budgetconstraint,Mts+ Et[Rt+ l (Wt+ -Mt )] = Wt -Ptst, (33)

we observe that (32) implies thatEt[Rtt+l Wts+l] = (1-oc) Wt

each period, and hence thatEt[RtT WT = (1 - oc) Wt

26. This differs slightly from the definition of Ricardian policy originally proposed in Woodford(1995). There policy was defined to be Ricardian f it ensured hat the value of the interest-earning ublicdebt (as opposed to total government iabilities) satisfied a transversality ondition. My reason for theoriginalproposalwas thatI wantedto argue hatthe Ricardianpostulatewas implicit in standard uantity-theoretic analyses of price-level determination; he definition was thereforetailored to include a policyregime with an exogenous money supply and zero governmentdebt at all times as an example of "Ricar-dian"policy. Such a regime is not Ricardian n the sense used here, since for price-level paths involvingsufficientdeflation,real balances would grow rapidlyenough to violate the transversality ondition (21);and this fact can be used to exclude deflationarypaths that would otherwise satisfy all conditions for ra-tional expectationsequilibria(see, for example, Woodford, l999a, sec. 4.2). The definition of Ricardianpolicy used here, and in references such as Benhabib,Schmitt-Grohe,and Uribe (2001a), is conceptuallypreferable,as it defines the case in which the transversality ondition ceases to play any role in equilib-rium determination.


24/61


for all T > t. But this guarantees hatlim Et[Rt,TWT ] '

and hence that the transversality ondition (21) holds, regardlessof the paths of anyof the endogenous variables.This condition plus the fact that (33) holds at all timescan also be used to show that (24) necessarily holds.In such a case, neither(21) nor (24) places any additionalrestrictionsupon possi-ble equilibriumpaths for goods prices or asset prices. Rationalexpectationsequilib-rium is then defined simply by satisfactionof conditions (16), (18), and (22), alongwith the equation specifying monetarypolicy. None of the first three equations in-volves any fiscal variable (such as the governmentbudget or the size of the publicdebt).Then if the monetarypolicy rule is autonomous n the sense defined above, thefinal equation s independentof all such variablesas well, and the complete systemof equations available to determinethe equilibriumpath of the price level is inde-pendentof all fiscal variables.We thus obtain the RicardianEquivalence proposition: f monetarypolicy is au-tonomous, the set of possible rationalexpectationsequilibriumprocesses for goodsand asset prices is the same for all alternative iscal policy specificationswithin theRicardianclass. If monetary policy suffices to uniquely determine equilibrium nsuch a case, then a change in fiscal policy does not change the equilibriumpath ofprices. More typically,therewill be a set of possible equilibriumprice processes;butas the set is the same for each possible fiscal policy, one might suppose thatthe sameequilibrium hould be selected regardlessof fiscal policy.27We have obtaineda differentresult n the previoussection because we have insteadassumeda non-Ricardian iscal policy specification. n the case of an exogenous realprimary urplusprocess {St}, most paths for the price level and the nominal interestrate even most of the pathsthat are consistentwith the otherrequirements or ratio-nal expectationsequilibrium will not imply dynamics for total government iabili-ties that satisfy the transversality ondition (21). Unlike what is assumed in (32), inthe previous section we did not assume that the governmentbudget would be auto-maticallyadjusted n responseto changes in the level of total liabilities, so as to keepthe latter quantityfrom growing explosively. The consequence is that only certainprice-levelpathswill result n the transversality onditionnonethelessbeing satisfied;these are those that satisfy condition (26). Hence the latterbecomes a condition forequilibrium,makingfiscal expectationsrelevant o price-leveldetermination.2.1 Mustn'tFiscal Policy Satisfy an IntertemporalBudget Constraint?The explanation just offered raises questions of its own. It may be doubtedwhether t is in fact possible for fiscal policy to be anythingother than Ricardian; f

27. In fact, I shall arguebelow that there may insteadbe good reasons for fiscal variables o affect theequilibrium election in such a case. See section 3.2.


25/61


not, Ricardianequivalenceshould indeed hold (and the qualificationabout"Ricar-dian" iscalpolicies may be omitted).A common objection o the logical possibilityof a non-Ricardianiscalpolicy is toassel^thatcondition 24) is nothingbut the intertemporaludget onstraintf the gov-ernment;t is al^guedhatgovel^nmentolicynouste expected o satisfythisconstraint,regardlessof what pricesthe government aces, just as in the case of privatehouse-holds andfirms.It wouldthenfollow thatfiscal policy mustnecessarilybe Ricardian.It is truethat generalequilibriummodels always assumethat privatehouseholdsand firmsoptimize subjectto a set of budget constraints hatinsply n intel^temporalbudgetcollstraint, houghthey may be even more stringent(as it may not even bepossible to bolaow againstall of a household or firm'sexpected future ncome). Butit is not obvious thatgovernment iscalpolicy must be modeled as subjectto a simi-lar constraint, or the situation of a government s different from that of a privateagent in certain mportant espects.First of all, if plîvategents were allowedto borrow by issuing debt thatplômisesto pay a marketrate of retul^n) ithout any limit relatedto the amountthattheir ex-pectedfuture income should make it possible for them to eventually êpay,hen anequilibriumwould be impossible. For no plan involvingfinite amountsof bolaowingandconsumptionat each date will be optimal for such an agent; it would always bepreferred o borrowandconsume even more, simply rollingover the additionaldebtforever.And if demands areunboundedat any prices, there cannot be any market-clearingprices. But there is no similarproblemwith a general equilibriummodel inwhichgovernmentpolicy is assumedto be specified by a rule that does not satisfy acolaesponding ntertemporal udgetconstraint.As the example in the previous sec-tion shows, one may specify non-Ricardian olicy rulesthat arenonetheless consis-tent with the existence of a rationalexpectationsequilibrium.Indeed, it is not even necessary,at the level of generalprinciple, for an intertem-poral budgetconstraintof the form (24) to be satisfied i> equilibriun>.he famousoverlappinggenerationsmodel of Diamond (1965) describes a situationin which(because the equilibriumreal rate of returndoes not exceed the economy's growthrate) t is possible for a government o financetransfers o aninitial old generationbyissuing debtthat t then"rolls over"forever,without everraising taxes. Of course, inthe settingassumed above, condition (24) is a requirement or equilibrium,nd theDiamondresult that it is possible to violate this conditionin equilibriumdependsupon a numberof rather pecialassumptions even once one has granted hat peoplearefinite-lived),as explained in Santos andWoodford 1997).28But this is a conse-quence of optimal wealth accumulationby households, not of any constraintupongovernmentbol^rowing rograms other than the requirement that in equilibriumsomeone has to choose to hold he debt thatthe government ssues.

28. Note that the possibility of rolling overgovernmentdebt forever mplies the possibilityof an equi-librium nvolving an asset pricing"bubble"; he same people who hold the governmentdebt in the debtroll-overexample can hold the "bubbleasset" instead.Thus the Santos-Woodford esults on the fragilityof exampleswith "bubbles"also apply to thepossibility of rationalexpectationsequilibria n which (24)is violated.


26/61


Even if we wish to analyze the behaviorof an optimizinggovernment, he govern-ment should not optimize subject to given marketprices and a given budget con-straint,as privateagents a1êssumedto in the theoryof competitiveequilibrium.Forthe government is a laIge agent, whose actions can certainly change equilibriumprices, and an optimizing government urely should take accountof this in choosingits actions. Such a government hould also understand he advantagesof committingitself to a rule (given the way that expected futuregovernmentpolicy affects equilib-rium), and should consider which rule is most desirableby computing he equilibriathat should result undercommitment o one sort of policy rule or another.Advice tosuch a governmentwould then involve computingsuch equilibriaunderthe assump-tion of one rule or another,as an input to the government'sdeliberationsabout opti-mal policy. There would be no reason to exclude non-Ricardian egimes from therules that are considered in such an exercise, in those cases where they are in factconsistentwith an equilibrium.29Thus far I have addressedonly the question of whethera commitment o satisfy anintertemporal overnmentbudget constraint s a logical necessity, as suggested byauthors uch as Buiter (1998, 1999). A subtlerquestion is whether t makes sense tosuppose that actual market nstitutions do not actually impose a constraintof thiskind upon governments whether ogically necessary or not), given that we believethat they impose such borrowing imits upon households and firms.The best answerto this question, I believe, is to note that a government hat issues debt denominatedin its own currency s in a differentsituationthan from that of privateborrowers, nthat ts debt is a promise only to delivermore of its own lirlbilities. (A Treasurybondis simply a promiseto pay dollarsat variousfuturedates, but these dollarsare simplyadditional government iabilities that happen to be non-interest-earning.)There isthus no possible doubt aboutthe government's echnical ability to deliver what it haspromised; his is not an implausible1êasonor financialmarkets o treatgovernmentdebt issues in a differentway than the issuance of privatedebt obligations.Furthermore, o one would doubt the ability of a government o issue an arbitraryamountof currency,without any commitment o 1êtiringt from circulation for ex-ample, by runningbudget surpluses) at some later date. Marketparticipantsdo notconsider whether newly issued government liabilities of this kind exceed somebound on what it is consideredprudent or the government o issue before decidingwhetherto accept them as paymentfor real goods and services; instead, each agentmakes an individualdecision about the terms on which to accept such governmentpaper, hatdependupon the expected rate of returnon the asset in equilibrium.An is-suance of furthermonetary iabilities by the government,without any increase n the

29. Woodford 1998c, section 5) gives an example of a case in which a non-Ricardian olicy regime-one quite similarto our descriptionabove of a bond price-support egime, in fact provides a simple wayof implementing he Ramsey-optimalallocation of resources. [See also Sims (1999) and ChristianoandFitzgerald (2000).] I do not wish to dwell upon this case here, as I do not wish to suggest that such aregime is likely to be a desirablepolicy commitment n general. But the example illustrates he point thatthe mere wish to hypothesize that governmentpolicy is optimal, from the point of view of some coherentobjectivethat the governmenthappens o pursue, s not in itself a reason to exclude the possibility of noll-Ricardianpolicy.


27/61

694 : MONEY.CREDIT,AND BANKING

real money balancesthatthe private ector wishes to hold, requiresan increase n theprice level (reduction n the exchangevalue of the governmentpaper) n order or themarket o clear;but this is a conditionfor marketequilibriumgiven the government'spolicy, and not a precondition hat must happen o hold for otherreasons in order orthe government o be able to create additionalmoney. All this is a familiar way ofthinking about monetary financing of the governmentbudget. But what is funda-mentally differentabout the issuance of interest-earning ebt, when this is simply apromise of futuredelivery of money?A useful analogy is suggested by Cochrane 2000) and Sims (1999). Consider heequilibriumvaluationof the stock of a company that pays no dividends, and insteaddistributes ts earnings to its shareholders ntirely throughshare repurchases. Theexample may seem fanciful, but in fact share repurchaseshave become a more im-portant ource of distributions o shareholders n the case of some U.S. stocks, suchas Microsoft, and the tax code favors this development.)The correct (beginning-of-period) equilibriumshare price qt for such a stock would generally be agreed to begiven by the present-value elation

qtSt = E E Et eT T (34)T=t (Yt )

where St is the numberof shares outstandingat the beginning of period t, et is thetotal earningsof the companyused to finance sharerepurchases n period t, and(Yt)is again the marginalutility of (real) income in period t. (I here assume the "cashlesslimit,"as is standard n financialeconomics.)The argument or this valuation equation is simple. If the earnings stream {et}were insteadpaid out in the form of dividends,the valuation ormula(34) would fol-low from standard heory. But suppose instead that each period, the stock were to"split"at a rate given by

(7t= et (35)qtSt-et

meaning that duringperiod t, each owner of a share of the stock receives a distribu-tion of (Stadditionalunits, followed by a repurchase f ( 1 + cyt)etlqtharesof the out-standingstock. Under this alternativepolicy, the total payoutby the companyduringperiod t is again equal to et (because the price per share after the split is qt/l + (St),and the value of the distributionper share s againetlSt. The same prices and portfo-lio allocationsthen continueto describean equilibrium; t should not matterwhetherthe distribution s called a distributionof stock followed by a repurchaseof exactlythe numberof new shares ust issued, or a cash dividend.On the otherhand, the fact thatthe stock splits at exactly the rate (35) should be ir-relevant o its valuation.Whatever he process {(ST} describing the expected rate ofsplitting or dates T ' t, the equilibrium volutionof the total value of the company'sstock qtSt should be the same, as long as the process {eT} describing the total re-


28/61


sources used to finance repurchases emainsthe same. Thus (34) should continue toapply,regardlessof the splittingpolicy. Note that for any given process {eT} specify-ing the funds available for repurchases,and any given process {(5T}describing therate of splitting, the evolution of the numberof outstandingshares {ST} is given bythe accounting dentitySt+l = (1 + cyt)[St-etlqt] (36)

Equations 34) and (36) then ointly describe he evolutionof the endogenousvariables{qt, St} undera rationalexpectationsequilibrium.Note that the equilibrium aluationqt impliedby (34) is necessarilysuch that (36) implies a positive numberof outstand-ing sharesat the beginningof the following period,so thatthese two equationscan besolved recursively orever,yielding a positive equilibliumshareprice at all dates.One may now observe a formal analogy between equations (34) and (36) for thevaluationof the zero-dividend tock and equations(28) and (29) for the equilibriumvaluationof nominalgovernment iabilities (also in the "cashless imit").To the vari-able St in the stock exampletherecorrespondsWts the numberof dollarclaims on thegovernment utstanding t the beginningof periodt); o qt therecorresponds /Pt (theexchange value of each dollar'sworth of public debt); to et there corresponds t (thestreamof "earnings" sed to retirepublic debt);and to st therecorresponds t (the rateat which additionaldollarclaims are distributed o the holdersof existing claims).

The advantageof consideringthis analogy is that it is clear in the stock case that(34) is an equilibriumonditionhat determines he share price, given earnings ex-pectations(thatmay well be causally independentof the evolution of the company'sstock value), and not a constraint upon possible corporatepolicies. There is no re-quirement,enforced by the financial markets, that the company generate earningsthat validate whatevermarketvaluationof its stock may happen to exist. Indeed, ifthe company'searningswere o be determinedby such a requirement, ts equilibriumshareprice would come to be indeterminate,ust as the equilibriumprice level is in-determinateunder a bond-price supportregime, if the governmentbudget is deter-mined by a Ricardian ule such as (32).The analogy is also deeperthana mere similarityof algebraic orm. The economicmechanism hat ensures that (34) must hold in equilibrium s in fact the requirementthat households must exhaust their intertemporalbudget constraints f they are be-having optimally;a stock valuationqtSt in excess of the presentvalue of futurecor-porate earnings would imply that households should believe themselves wealthyenough to purchasea streamof goods with greatervalue thanthe economy's product(the source of corporateearnings), which (if households exhaust their budget con-straints)will be inconsistentwith goods marketclearing.30Finally,the stock analogy providesan answerto a common question aboutthe fis-cal theory of the price level: What is special about the government, hat itsbudget

30. Above, I have instead presenteda heuristic argument or (34) starting rom the standardpresent-value theory in the case that all distributions re cash dividends. But that lattertheory relies upon the re-quirement that households exhaust their intertemporal budget constraints in order to exclude thepossibility of an equilibriumpricing "bubble"; ee, for example, Santos and Woodford 1997).


29/61


shouldbe able to determine heequilibriumprice level (underpolicy regimeslike thebondprice-support egiIneanalyzed above), and not that of any other personor or-ganization?Tlle answer is not simply that nationalgovernmentsroutinelyissue lia-bilities that entitle the holdersonly to the receipt of furthersimilar liabilities in thefuture;as we have seen, a private organizationsuch as Microsoft could do this aswell, in principle. (It would call its liabilities "stock"rather han "debt" n such acase.) The other crucial special feature of a nationalgovernment s thatprices arecommonly quoted in units of its liabilities, that is, in terms of the nationalcurrency.If it happened that prices of goods and services were routinely quoted in units ofMicrosoft stock, say, then it would indeed be Microsoft's budget that would deter-mine the price level, and not that of the federalgovernment.2.2 Consequencesof a Govers>nent olfrowingLinitFinally, even if one supposesthat marketsdo impose a limit on how much a gov-ernmentcan borrow, t is notclear thatthis invalidates he analysis given aboveof theway in which fiscaldevelopmentsdetermine heequilibriumprice level undera bondprice-support egime. Supposethat there is a finitelevel of real public debt (the de-terminationof which we shall not model here) beyond which new debt issues willsimplynot be purchased.Thiswould mean that t is notpossible for a government orefuseto adjust ts budgetwhenits debts grow too large; hus a purelyexogenous pri-marysurplusprocess, as assumed n section 1, wouldbe precluded.Forthe sake of concreteness,suppose that there is anupperbound on thepossibleend-of-periodvalue of outstandinggovernment iabilities, so that governmentbor-rowingmust remainwithin thebound

Mts+ QtBts dPt

at all times, for some finite positive bound d. (Forsimplicity, I shall assume in thediscussion to follow thatgovernmentdebt consists entirely of single type of bondwith geometric coupons, the price of which is Qt.) This implies a lower boundst ' wt-d upon possible levels of the real primary urplus,where wt-WtslPt is therealvalue of beginning-of-periodgovernment iabilities. We may similarlyimaginethatthere should be a lower bound on the value of end-of-period iabilities as well(not so much because the private sector will not allow unlimited government end-ing, butbecause we may suppose that governmentswill never actually be so gener-ous); for simplicity, et us suppose thatthis is zero. Thiswould imply an upperbounduponfeasible primary urplusesas well, st ' wt, thevalue that would leave the gov-ernmentwith no net liabilitiesat the end of the period.3lThen the fact that totalgov-ernment iabilities must satisfy the bounds

31. As noted earliel; this boundwould already mply some government ending, but the governmentwoulddiscount privateobligations only in the a1nount hat the centralbank could hold as backingfor themonetarybase.


30/61


oc Mt +QtBt d (37)

implies that the primarysurplusprocess {st} would have at all times to satisfy theboundsWt-d C St C Wt * (38)

Condition 37) implies that in any equilibrium

-Et U171(YT,>T)nT Et A(YT, iT) 1 + i PC E T( i ) 1 MT + QTBT

< Et A(YTHiT) T QTBT

' i A(YT, iT )d

Furthermore,he third erm in this series is equal to

Et A(YT+ , iT+ 1) p ' (39)T+1so that expression (39) must be bounded above and below by the initial and finalterms in the previous series. But equilibriumcondition (22) implies that the initialterm must converge to zero as t is made unboundedly arge; and for all interestratepaths {iT} satisfying bounds sufficient to imply that {X(YT iT)} is uniformlybounded,32he final term must converge to zero as well. Thus (39) must convergetozero as Tbecomes large as well, and the transversality ondition (21) is necessarilysatisfied.It follows that any fiscal policy that satisfies the bounds (38) at all times isessentially Ricardian;33nd condition (24) places no restrictionsupon possible equi-libriumpaths of the price level.

32. This assumption s certainlynot problematic n the case of a bond price-support egime which im-plies bounds on interestrates that are independentof the evolution of goods prices.33. The qualification s that the transversality ondition has not been shown to hold for allpossibleprice-level and interestrate paths, but only those that satisfy certainbounds on interestrates and the equi-libriumcondition(22). But this near-Ricardian roperty uffices to imply that the transversality ondition,or alternatively ondition (24), places no additionalrestrictionsupon the possible equilibriu1n aths of theprice level, given a monetarypolicy that maintains nterestrates within the assumed bounds.


31/61


Nonetheless, fiscal disturbancesmightwell affect the price level. To see why, letus consider a modifiedversion of our previous analysis of the bond price-supportregime. Suppose that the government's"desired"real primarysurplusevolves ac-cording to some exogenous stochasticprocess {st} as assumed earlier,and that theactualbudgetsurplusequalsthis, exceptwhen one of thebounds n (38) would be vi-olated; in the lattercase, the real primarysurplus s equal to the bound.Thus underthis fiscalregime,

( wt if Wt < SFSt = S(Wt


32/61


equilibriumpath. The existence of debt limits such as (37), that eventuallyconstrainthe growth of the public debt in the case of paths far from the equilibrium n ques-tion, do nothingto interferewith this.Despite this conclusion, under fiscal policy of the type just described, RicardianEquivalenceholds, when properlyunderstood.The set of possible state-contingentequilibriumpaths is the same regardlessof the evolution of the desired primarysur-plus process {st}. But under this policy regime, the set of equilibrium priceprocesses is quite large;among the possibilities is a solution in which the price levelhappens to fluctuateat the same time as unexpected changes in the desired primarysurplus.In order to illustratethe multiplicity of possible equilibria, t is useful to furtherspecialize our example, and considerthe case in which s t = s > O orever,Qt = Q O orever.Let z > Obe the constantnominal nterestrate mplied by the bond-price arget,and m-L(y, z) be the implied stationary qui-librium evel of real money balances.We assume that

fl > 1 D S +-m > O, (40)

so thatan equilibriumof the kind describedearlierexists, and remains oreverwithinthe interiorof the bounds (38). To simplify, let us consider simply the set of perfectforesight (deterministic) quilibria p.f.e.) consistent with such a regime.Given an initial condition WOs-Ms l + QBs l > O,any path for {wt} satisfyingthe differenceequation

Wo+l = t Wt-S(Wf, S)-m ( 1 + ) (41)

for all t ' O,and the transversality onditionlim twt = O, (42)F4

representsa p.f.e. The equilibriumpath of the price level corresponding o any suchsolution is given by

Pt = [t(1 + z)]t .wO

A graph of the right-hand ide of (41) is shown in Figure 2. Under assumptions(40), there are three possible steady-statesolutions to (41), given by


33/61


Wt+ 1 A,

45

_ . .. . .. .. .. .. . .. .. .. . .. .. .. .. . .. .. . ,

* /e pv

/ ,''.! ; t ,

fS'/ 1/ . ' / ,/ /

/ / q * .

//f/ / ' . b 6 .

/ / s

/ / ' . 4 .

/ / . ./ / ' ' */ / * ;

:: : : :_ / ' , '

/ . q

.

/

/ . /

', ' I > WtWOW1W2 W3 W4FIG.2. Perfect ForesightDebt Dynamics

1 1 _w--- m O,< 1+1wt-- s+t-8m >O1- \1+1 J

w-- d-t-8m >w8.8 \1+1 JIn additionto these three solutions with a constant evel of real government iabili-ties, there exists a continuumof nonstationary olutions to the difference equation.In particular, or any choice of wO> O,the sequence can be continuedforever.(Anexample of a nonstationary olution with wX< wO< w is shown in the figure.) Be-cause the implied sequence {wt} is necessarilybounded,the transversality ondition(42) is necessarily satisfied,and as long as wO> O, he implied price sequence is for-ever positive. Thus this entire continuumof solutions representsalternativepossiblep.f.e. undersuch a regime.


34/61


One of these solutions, the one with WF = W I forever, s the fiscalist equilibriumdiscussed earlier.Previously,when we assumed that st = s at all times, this was theonly possible equilibrium; n that case, the correspondinggraphwould continue thesteep center segment off indefinitely n both directio1ls, nd all solutions to the dif-ference equationstarting rom w0 7&w* would be explosive, and would violate (42).With the assumedbounds on government iabilities, this is no longer true.For exam-ple, anotherequilibrium s the one shown in the figure, n which the price level is ini-tially (and foreverafter) ower than n the fiscalist equilibrium.This lower price levelis sustained as an equilibriumby people's (correct)expectationsthat the explodingpublic debt will eventually lead to a fiscal consolidation, following which primarysurplusesare increased.Anticipationof this leads to feel less wealthy, so that lowerprices are required or goods markets o clear.But the fiscalist equilibrium s still the only equilibrium n which neitherbound in(37) is ever binding; thus this equilibrium s locally isolated, as mentioned above.One may also observe that none of the otherp.f.e. are locally unique;correspondingto any equilibrium ike the one with an exploding public debt shown in Figure 2,there exist an infinite numberof other equilibriaarbitrarily lose to it (in the sensethat the price level and other variablesare nearly the same, but not exactly the same,at all times as in this equilibrium).Slightly differentexpectationsabout the size andtiming of the eventualfiscal consolidationare equally consistent with equilibriu1n.

Given the existence of a multiplicityof possible self-fulfillingexpectations,an ob-vious question s whether he fiscalist equilibrium emainsa plausible qleilibrium se-lection, undera regime of the kindjust described.This is presumablywhat McCallum(1998) means to challenge, in arguing hat the fiscalist equilibrium s a bubble equi-librium."Howeve1;what constitutesa "bubbleequilibrium"s often in the eye of thebeholder;one might at least as easily say that the equilibrium hown in Figure 2 is a"bubbleequilibrium," s the higher value of the public debt is sustainedby self-ful-filling expectationsof a future fiscal consolidation.Here I present an argume1ltorwhy expectationsmight naturally oordinateupon the fiscalist equilibrium.35

Essentially,I would argue that the fiscalist equilibrium s an especially plausiblefocal point for households' expectations,because it involves simple^ fiscal exp

Documents

Woodford Fiscal Requirements of Price Stability