Calvo Deuda Publica

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American Economic Association

Servicing the Public Debt: The Role of ExpectationsAuthor(s): Guillermo A. CalvoSource: The American Economic Review, Vol. 78, No. 4 (Sep., 1988), pp. 647-661Published by: American Economic AssociationStable URL: http://www.jstor.org/stable/1811165 .

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648 THE AMERICAN ECONOMIC REVIEW SEPTEMBER 1988-reflecting,perhaps, he factthatthemod-els are not entirely orrect-ratherthan acharacteristicf empirically elevantmodels.The central topic of these notes is thediscussion of a set of empiricallymotivatedexamples wherenon-uniqueness f Phelps-Pollak equilibria is clearly exhibited.Thepossible empirical relevance of the non-uniqueness ssuebecomes pparentwhen x-aminingtherole of interest-bearingovern-ment debt. The events of the 1970s and1980s suggestvery trongly hat whengov-ernments ecome strapped for funds, heytend torelymoreheavily nbonds' ssuance.In fact,Barro (1979) suggests hat thismayeven be optimal if governments re facedwith temporaryncomefallora temporaryincrease in government xpenditures. ow-ever, the consequenttaxationpostponementis not freefrom credibility" roblems:Willthe additional debt be paid off n full,willthe government ind t optimalto resort ohigher nflation r currency evaluationtodiminish he burdenofthedebt,etc.? Whenthesequestionsare posed in terms f moreprecise language they translate into thefollowing: Is debt repudiation-directly,throughnterest atetaxes say),or indirect-ly through inflation-a characteristic fPhelps-Pollak quilibria? ome answers anbe found n StanleyFischer, 983; HenningBohn, 1987; Herschel Grossman and JohnVan Huyck, 987; and iteraturen sovereigncountries' debt (see the recentsurvey byJonathan aton,MarkGersovitz,ndJosephStiglitz, 986). In thispaperwe pursuethediscussion nquiring,pecifically,hether hemere existence of government bligationsmay not be responsible or the existence fmultiplePhelps-Pollak equilibria.This ap-pears likely to happen because expected(partial) debt repudiationwould tendto bereflectedn the interest ate on governmentbonds (increasing t), while the higher heburden of thedebt,thehigherwould be thetemptationorepudiatet.Thus, t shouldbepossible to generate n equilibrium ith owinterest nd low repudiation, oexistingwitha high-interest,igh-repudiationquilibrium.Our examplesgivea strong upport o theabove conjecture: Multiple solutions arepossible even whenour examplesassume a

finitehorizon,and theexistence f govern-mentbonds may be the triggeringactor ornon-uniqueness.The implications for policy could bestaggering; or, ur results uggest hatpost-poning taxes (i.e., falling nto debt) maygenerate he seeds ofindeterminacy;t may,in otherwords,generate situationn whichthe effects f policy are at the mercy ofpeople's expectations-gone would be thehopes of leading theeconomy long an "op-timal"path.For thesakeoftheexposition, ewillfirstdiscussthese ssues n terms f nonmonetarymodels with one representativendividual.In Section I we will examinea two-periodmodel,where the debt is contractedn thefirst eriod and repaid n the second; taxesare distorting nd, hence, the governmenthas an incentive o renegeon the debt. Inorder to get an equilibriumwithpositivepublic debt,we assumethatdebt repudiationis costly, nd thatthecost s proportionalothe amount being repudiated. n addition,we assume that individualsknow the rele-vant model; hence,sincethere s no uncer-tainty, heequilibrium etrateof nterestnpublicbonds (adjustedfordebtrepudiation)equals the rate of returnon capital (theopportunityost ofprivate unds).Themainresult f the section s that f an equilibriumwith a positive public debt exists, here rein generaltwo equilibrium oints:a "good"Pareto-efficientquilibriumn which here sno debt repudiation,nd a "bad" Pareto-in-efficientquilibriumwheredebt is partiallyrepudiated.In Section II we focus on a monetaryeconomy with non-indexed bonds. Obvi-ously, n thiscontext nflations equivalentto some form of repudiation, ut negativerepudiationhas to be allowedfor incepricedeflation annot be ruled out. In order tocast the example in termsof a standardmonetary model, we follow Barro andGordon (1983a,b) and modify hepreviousmodel by assumingthatprice changesarecostly.This is enough ogiveresults hat requalitatively imilar o the ones in thenon-monetarymodel. Typical of a monetaryeconomy,however,the two equilibria arePareto inefficient. t the (relatively) ood

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VOL. 78 NO. 4 CALVO: SERVICING THE PUBLIC DEBT 649equilibrium,nflation nd thenominal nter-est rate on governmentondsare lower hanat the bad equilibrium.n addition,we showthat f nsteadthenominal eturn n govern-ment bonds were fully ndexed to the pricelevel, then the first-bestolutionwith pre-commitmentan be attained,which uggeststhat, f inflation s the onlymeans of debtrepudiation, ndexationof the public debtcould lead the economy o a Pareto-superioroutcome.In Section III the analysis s extended oan open economywhereforeigners old apositive hareof totalpublic debt. The mainpurpose of this hort ection s to establishlink with he relatively ell-developed heoryofsovereign orrowing.We show thatmulti-ple equilibria still can occur in this newcontext, and that the effect n the bondinterestrate of increasingforeigners' ar-ticipationnthatmarket ependson whethertheeconomy ettlesdown to the good or tothebad equilibrium.Finally, Section IV summarizes ome ofthecentralfindings,nd discusses ome ex-tensions and suggestionsfor further e-search.

I. DebtRepudiationThere are twoperiods:period0 and period1, and two types of agents: dentical com-petitive onsumers or individuals) nd thegovernment.n period 0 the governmentborrowsb per capitaunitsofoutputwith(gross) interest actor'Rb, that s, in period1 consumerswill receiveRb unitsof outputper unitof bond they old and which as notbeingrepudiated. herefore,fconsumers x-

pect that a proportion of total bondswillbe repudiated, < 0 < 1,thenet nterest ac-torwould be2(1- O)Rb.

We assume consumerscan accumulatephysicalcapital with constantnetinterestfactor equal to R >1; hence, in a perfectforesight quilibriumwithpositive tocksofcapital and government onds, consumersshouldbe indifferentetween hese wotypesof assets, and, consequently(1) (1- 9)Rb= R.

The budgetconstraint f the governmentin period1 is(2) x= (1-O)bRb+g+a9bRb,whereb, x, and g arethepercapita stock fbonds, taxes, and governmentxpenditure,respectively,nd a standsfor he percapitacostperunit ofrepudiated ebt3 O< a < 1).Thus, in other words, axes are required ofinancedebtrepayment,1- O)bRb, govern-ment expenditure, , and thecosts of debtrepudiation, aObRb. Furthermore, e as-sume that g is exogenous.4By (2),

bRb?g9- X(3) ObRb= 1In period 1 individualsconsume all oftheirwealth; thus, assuming that govern-ment expendituredoes not directly ffectprivate onsumptionn period1, c, we have

(4) c=y-z(x)+kR?(1-O)bRb-xIwhere y is endowmentncome, z(x) is afunction epresentinghe"deadweight" ost

ILet r be an interest ate; we define hecorrespond-ing nterest actor s (1+ r).Repudiationis a catchall word in thispaper thatincludes anything rom pen repudiation o a tax oninterest.

3a could be thought f as transactions osts associ-atedwithdebtrepudiationlegalfees, tc.,whenrepudi-ation is open). In Section V othertypesof costs arediscussed. It shouldbe stressed, owever, hat n thispaper we are interestedn examining he "mechanics"associatedwith these typesof costs as a preludeto amore substantive nalysis where those costs will besubject to a closerscrutiny.'In a morerealisticmodel,the expectednet returnon capital will also be a functionf expectedgovern-ment policy through xpected apital evies,for xam-ple). The relationship etweenthe latter nd "capitalflight" as recently een explored y Eaton (1987).



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650 THE AMERICAN ECONOMIC REVIEW SEPTEMBER 1988of taxation,5 nd k is per capita physicalcapital.6We assume(5a) z(0) = z'(O) = 0,(5b) z"(x)>0 forallx,(5c) lim z'(x)=xo=- lim z'(x).x > x -XThe last Inada-type conditionwill simplifythepresentationfourresults.Employing3) in (4), we get(6) c=y-z(x)+kR+bRb

-(bRb+g-x)/(1-a)-x.Consequently,a "benevolent" governmentthat triesto maximizec in period1 subjectto its budget constraint,2), and takingRbas given recall that,by assumption, b isnegotiated t time0), will choose x so as tominimize(7) z(x)- x,- asubjectto (2), and 0 < < 1. In otherwords,theproblem s tominimize7) bychoosingxsuch that the associated 6 in budgetcon-straint 2) is in the nterval0,1].Thiscondi-tion is equivalent to restricting in thefollowingmanner,(8) g+abRb 0, unless otherwisestated; thus,by (5), ifRb> 0 (theonly rele-vant case for themodel of this ection), heminimization f 7) subject o (8) is attainedat some unique x > 0. Notice that, due to(8), the solutionwilldependon g, and, mostimportantly or our discussionhere, t willalso depend on Rb, the interest actoronbonds (which, as argued above, is a prede-termined ariable n period 1).The maximum problem for the govern-ment n period1 is depicted n Figure .7 Inthe figurewe portrayhe two functions sso-ciated with constraint 8). Given Rb, thegovernments thus constrained o choose xbetween hetwostraightines temmingromg on thevertical xis. If x* is located as inFigure 1, the governmentwill be able toattaintheunconstrainedmaximum *, ifRblies between R and R (see Figure1). On theotherhand, fRb < RI the maximumwillbeattainedon the upperbound where here sno repudiation,6= 0), while f Rb > R, themaximumlie on the lower bound (whererepudiation is total, 6 = 1). Consequently,the set of best responses r "reactionfunc-tion" forthegovernmentn period1, givenRb, is depicted by the heavy ine of brokensegmentsn Figure1. Notice that when Rb< R thegovernment illbe induced to re-pudiate none of its debt (i.e., set 6 = 0),whereas f R ? R repudiationwill be total(i.e., 6=1). In betweenR and R, repudia-tionwillbe partial, nd-by (2), and recal-lingthat n thisregionx = x*- therepudia-tionshare, 6, will ncreasewithRb; thus, notherwords,theoptimal epudiationhare nperiod1 is an increasingunctionfthe nter-estratecontractednperiod .We will be interestedn an equilibriumconcept in which ndividuals t time0 areable topredict heoptimal overnmentolicyin period 1 (i.e., the optimal government5Alternatively,ne could follow Barro (1979) andassume 7(x) measurestax collection osts; under thisinterpretation,(x) should be included n the RHS of(2).6There s no realneed tokeep track f thenonnega-tivity f c, because in thismodel one can always nsurethatby setting ndowmentncome,y,sufficientlyarge.

7I amverygrateful o ElhananHelpman for uggest-ing Figures 1 and 2, whichgreatly mproved he ntui-tive appeal of the presentation.



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VOL. 78 NO. 4 CAL VO: SER VICING THE PUBLIC DEBT 651x g+bR/( no repudiation

PARTIALREPUDIATION g9+abR bX full repudiation)9 jGOVERNMENT'SEACTIONI FUNCTIONN PERIOD1

R R RbFIGURE 1. DETERMINATIONOF GOVERNMENT'SREACTION FUNCTION INPERIOD 1

decision about x and 6 at time1 as dis-cussed above) withperfect ertainty. nderthesecircumstances1) holds and,hence,by(2),(9) x = g + (1-a)bR + abRb.The latter s a "consistency ondition" hatmustbe satisfied y thegovernment'sudgetconstraint t equilibrium,where,by defini-tion,the public can predict xactlythe re-pudiationshare, 6, and it is indifferente-tweenholdingbonds or capital (i.e., equa-tion 1) is satisfied). otice, ncidentally,hatsince 6 is nonnegative,1) implies hat qua-tion 9) is onlyrelevant vertherangewhereRb2 R, that is, where the interest ate onpublicbondsexceedsorequals that fphysi-cal capital.The consistencyondition nd thegovern-ment'sreactionfunctionredepicted n Fig-ure 2 for the case in which x* > g + bR.Equilibria are foundat pointsof intersec-tion; in the present ase these are E0 andE. At E? the nterest actor n bonds, Rb,is equal to thaton capital,R, meaning hatthe public expectsno repudiation;on theother hand, the government'sptimal re-sponse in period 1 is to set x = g + bR,which, s indicated n Figures1 and 2, lies

on the no-repudiationection f itsreactionfunction.Expectationsare, thus, fulfilled.Notice thatat thisequilibriumolutionthegovernment ouldwish to increasex aboveg + bR and towardx*, but that s impossi-ble because it would call for setting6 < 0(negativerepudiation),whichhas beenruledout byassumption.8In the other equilibrium, ', repudiationis partial and, thus,the associatedinterestfactor, enotedR' in Figure , is larger hanthaton capital, R. At thisequilibrium,hegovernment s able to attain the uncon-strained ptimum alueof x,x*.Our previousdiscussion overed the casein whichx* > g + bR. If,contrariwise,*


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652 THE AMERICAN ECONOMIC REVIEW SEPTEMBER 1988X g+bRb

A g+(1-a)bR+abRxg+bRF t- GOVERNMENT'S EACTION_ I\ FUNCTION N PERIOD 1

I I CONSISTENCYCONDITIONI _ _ _ I _ _ _ _ _ _R RRbFIGURE 2. DETERMINATIONOF EQUILIBRIUM

cross, ecausethe lopeof theconsistency-conditionurve s equalto that f theright-most ection fthe eactionunction.onse-quently, here s no equilibrium ith apositivetock fbonds.Finally,ntheborderlineasewhere *g + bR, equilibrium s unique and R' = R =R.Thefollowingropositionummarizesurfindings:

PROPOSITION 1: If x* > g + bR, thenthere xist twoequilibriumolutions; ne ofthe olutions xhibits o repudiation, hile ntheother hepublic debt s partially epudia-ted. On theother and, fx* < g + bR, thereis no equilibrium,nd in theborderlineasethat x* = g + bR, equilibriums uniqueandthere s no repudiation.Ourmodelhasseveralnterestingmplica-tions. n thefirst lace,notice hat, y 7),x* is an increasingunctionf thecost ofrepudiation,; hence, ivenhe nitialtockofdebt, heres some ritical aluefor hecost of repudiationelowwhichno equi-libriumwith a positive mount f bondswould xist. hepossibilityfnonexistenceofequilibriumsintuitivelylear or he asea = 0; for, benevolentovernmentouldrepudiate00 percentf thedebtgiven hat

there re no direct epudiationosts, ndthat etting =1 eliminateshedeadweightcost of taxesrequiredo service hedebt.But, f course, his annot e an equilibriumwith positivetock fbonds.naddition oconfirminghisbasic ntuition,ur exampleshows hat henonexistenceroblemouldarisewith positive , and that he riticalvaluefor he atter epends ositivelyn thevalueof theoutstandingebt.The most importantmplicationf theanalysis, owever,s thatproblems o notnecessarilyo awaywhen epudiationostsare setabovethe riticalevel; or,nsuchcase theeconomy illnormallyxhibit woequilibria: nonrepudiationquilibriumnwhich axes qual g+ bR (recallFigure ),and another quilibriumnwhichhedebt spartially epudiatednd taxes reset at x*> g+ bR. Notice that, y (1) and (4), inequilibriume have(10) c=y-z(x)+(k+b)R-x.Therefore, hese two solutions can bePareto-ranked,nd thenonrepudiationolu-tion is the dominant ne. Unfortunately,however,without urther estrictionsheeconomy ould end up at any one of these



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VOL. 78 NO. 4 CALVO: SERVICING THE PUBLIC DEBT 653equilibria.The interest actor n the "good"equilibrium s always R; however, hevalueof R,, and 0 at the "bad" equilibrium E1in Figure 2) are sensitive o changes n b.Somewhatparadoxically, s it can easily beestablishedemploying igure2, at the badequilibrium hebond nterestactor s smallerthe arger s the totaloutstandingovernmentdebt. It should be noted,however, hat theconsumption ost of beingat the bad equi-librium s independent f total debt9 (be-cause x = x*, and the atter oes notdependon b). But,on theotherhand, x* dependspositively n a; therefore,ur analysisre-veals that while repudiation osts are im-portantforensuring he existence f equi-libria with positive tockofbonds,by (5),(7), and (10), the larger re therepudiationcosts,the argerwillalso be theconsumptioncost associated with the bad equilibrium.Thus, although ncreasinghe ostsofrepudi-ationenhances he credibility" fthegovern-ment nthecapitalmarkets,he attermaybebought t thecostof ower onsumptionftheeconomyndsupat thebadequilibrium.The way the above "game" has beenstructured s consistentwith situations nwhich the governmentt time0 auctions ffb, and lets themarket ree o determine heassociated interestfactor,Rb An alterna-tive10would be for hegovernmentt timeto refuseto sell bonds at interest actorswhich are equal to or exceed R',, (recallFigure 2). Thus, underour assumptions tfollows that the only possible equilibriumwould be Rh, R, the first est. This is animportant bservationwhich suggeststhatfree auctioningof the public debt may bedominatedbya systemn which hegovern-ment stops sellingbonds afterthe impliedinterest atesgo beyond ertain ounds.Thisobservationwill take up further elevancewhenwe discuss t in thecontext f thenextsection.

II. Money ndNon-IndexedebtThe concept of partialrepudiation akes amore familiar ormnthecontext f a mone-tary model, because whenvariables are ex-pressed n real terms, hanges n the rate ofinflation mply changes n the real value ofassets which are not indexed to the pricelevel. Two important ssetsof this kind are(high-powered)money nd nominalgovern-ment debt. The literature as paid a greatdeal of attention o the formerfor xample,Barro and Gordon, 1983a, ); Lucas andStokey, 1983; Calvo (1978a,b), but there sgrowing wareness about the mportance f

understandinghe roleofnominaldebt forexample,HenningBohn 1987; Grossman ndVan Huyck, 1987; Persson, Persson, andSvensson,1987). As faras I know,however,none of the available papers addresses theissue of non-uniqueness f equilibria,whichis the main focusofthefollowing iscussion.To minimize he use of new notation,weredefine b as the nominal nterest actor nnominalnon-indexed onds i.e., Rb =- + i,where i is the nominal interest ate fromperiods0 to 1). Thus, f we let Pf standforthe price level in period t= 0,1, then thereal interest actor n period-O onds wouldbe(11) RbPO/Pl.We can, therefore,hink f the ratioPO/Pias the shareofthedebtwhich s notrepudia-ted in period 1; hence,usingthenotation fprevious ection,we will write

(12) Po/Pi= (1- O).We define the rate of inflation etweenperiods 0 and 1, T,as follows,

p1 - PO(13) X = POThus, by (12) and (13)(14) 0=1+

9This invariancedoes not hold in the model dis-cussed in Section V.1(This fine point was suggestedto me by AssafRazin.



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654 THE A MERICA N ECONOMIC RE VIE W SEPTEMBER 1988Consequently, ach rate of inflation, , -1< , is associated with a unique rate ofrepudiation, . We are thus ntitled o carryout our discussion n terms f 0 insteadofr. Notice,however, hat ontraryo thepre-vious section,0 could be negative ecause itis onlyconstrained o satisfy(15) - Do O


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VOL. 78 NO. 4 CALVO: SER VICING THE PUBLIC DEBT 655subject to (1), (18), and (19).12 The latter sequivalent o(21) Min [z(g + bR-KO)+ 9(O)],

0 < Iwhich, y 5) and (20) has a uniquesolution,denoted 6 B (for "firstbest"). Since thefunctionn (21) is strictlyonvex,one canreadilyprove the following sefulproposi-tion:PROPOSITION 2: Assume that 1) holds,and let c' be theeffectiveonsumptionssoci-ated with9', i=1,2; then, fFB


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656 THE A MERICAN ECONOMIC REVIEW SEPTEMBER 1988In orderto completethenon-uniquenessargument, he next stepwill be to show asimple xampleof non-uniqueness henb >0. Considerthe case in which

(25) 3(O)= 9022Therefore, y (1) and (23), we have

6(26) Z (x) =bRI(I- )+Kand, by (1) and (18), we get(27) x=bR+g-KO.Equilibriumrelationships26) and (27) aredepicted in Figure 3 for the limit case inwhichthe demandformoneys zero,that s,X = 0. By continuity,t is quite clear thatmultiplicityf solutionswould continuetohold forK in some neighborhoodf 0. It is,however, ery nterestingo note that n thepresent xampleuniquenesswouldprevail fK is sufficientlyarge.'5This s perfectlyon-sistentwith our previousobservation hatthe existence fhigh-powered oney s con-ducivetouniqueness. heresult s alsohighlysuggestive; ince the value of K mayhave alot to do with the inflationary istory f acountry,he above resultndicates hatmul-tiplesolutionsmaybe a bigger roblem orcountrieswhichhave recentlyufferedromhigh nflation.'6

By (21), the first-orderonditionfor afirst-bestptimums(28) - z'(g + bR KO)K + 9V(O) = 0.Thus, recalling hat n Section I weassumedg>0 and b>0, we have 0FB>0. On theother hand, recalling 18), the first-orderconditionfor a second-best ptimum s atequilibrium-that is,when 1) holds-(29) -Z'(g + bR- K6)(bR+ K)

+?N'(6) =0.Notice that,by (5), (20), (28), and (29), thefirst-and econd-best ptima satisfyK06FBIn otherwords,we haveshownthatoptimalinflationwithprecommitments lower thanin any of the equilibriumolutions btainedunderno precommitment.onsequently, e-calling Proposition2, we deduce thatequi-libriawithout recommitmentan be rankedaccordingto their ssociated nflation ates:given any two of these equilibria, he oneexhibiting helargest ateof inflation ieldsthe smallest social welfare as measuredbyeffectiveonsumption,ee (19)). In terms ftheexampleassociatedwithFigure3, there-fore,we are entitled o call O0 the"good,"and 0' the "bad" equilibrium.'7Price indexationof governmentebt hasimportant ffects n this economysince itremovesthe inflationncentives ssociatedwith he debt burden.Withfull-pricendexa-if the elasticity f z'(x) withrespect o x is less thanunity,and the inflation ax does not exceed regulartaxes,thenormal ase. Ourproof, owever, elies n theexistence fmore thantwo periods, nd will, herefore,not be presented ere.For an infinite-horizonodel ofnon-uniquenessalong the present ines, but withoutgovernmentonds, see MauriceObsfeld 1988).'5The exact condition s K > bR+ g, that is, realmonetarybalances mustexceed totalgovernmentx-penditure, ncludingthe inflation-adjustederviceonthe publicdebt.6This point emergedduring usefulconversationwithSwedervan Wijnbergen.

17 Multiple equilibria is by no means a necessaryfeatureof these models. Uniquenesswould, in fact,prevail f,forexample, 9t0) = v2; the atter s relatedto the workof Barroand Gordon 1983a,b) and Bohn(1987). For a somewhatdetailed discussionof theseissues,see Calvo (1987).



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VOL. 78 NO. 4 CAL VO: SER VICING THE PUBLIC DEBT 657xZ'(x)=fl 0 bR-)

g+bR / T bFI I,I I

FIGURE 3. MONETARYEXAMPLE

tion and an interest-insensitiveemand formoney (i.e., constantK, as in the presentmodel), t is easy to see that he no precom-mitmentquilibrium oincideswiththe firstbest.'8An alternative o indexation-which wasdiscussed at the endof Section -is to putbounds on interest ates; this could ensurethat the solution settles t 60 in Figure 3rather han at 01. However, ne can easilyshow that uch a solution s inferior o bondindexation, ecause the atter esults n lowerinflation'9recall Proposition and (30)).2?

As the xampledepicted nFigure shows,an increase n the cost of inflationi.e., anincrease in /3,recall (25)), has ambiguousresultson welfare.A rise in /3causes thecurve in Figure 3 to shiftupward, raisinginflationn the bad equilibrium, nd lower-ing t in the good one.Clearly, etconsump-tion, c, will decrease n thebad equilibrium(because /3 nd inflation o up). In thegoodequilibriumi.e., 60), on the otherhand,thepicture s less clear,because inflation oesdown, which tends to be welfaremproving.However, if K = 0, a simple manipulationusing (26) and (27) shows that welfare n-creases with /3.Thus, as in Section I, theeffects f ncreasing hecostsof nflation/re-pudiation are ambiguous: they could bewelfare-improvingn the good equilibrium,but theydefinitelyowerwelfaren the badequilibrium.Our example sheds some ight n the ssuestudied by BennettMcCallum (1984) ofwhethermonetary olicycould be separatedfrom iscal onsiderations. is discussion asto do withthelong-run literallywhent --x) feasibility f policies thatkeep moneysupply at a constant evel whilerunningfiscaldeficit. n our model therelationshipbetween herateof nflationnd fiscal olicyis very direct for the case of non-indexedbonds (still the dominantkind of govern-

18Indexation wouldnotsuffice or ttaining hefirst-bestsolution f thedemandformoney s sensitive o therate of interest. conjecture, owever, hat there arerelevant xampleswhere ne could still how thatdebtindexation ncreases ocial welfare.19This is not intended o be a thoroughnalysisofthewelfare conomicsof bond indexation ince thereare some importantspectsof the ssuewhichhave notbeen taken ntoaccount.Forexample, s pointed ut tome by Nissan Liviatan, t has been argued that ndexa-tion may reduce thebase of the nflationax because nsuch a case bonds become better ubstitutes ordomes-ticmoney.This aspect s notcoveredbyourdiscussionbecause K was assumedtobe independent f thedegreeof indexation.

20 Bounds on interest atesmaybe particularlyif-ficult o implementwhenthere xists n activeprivatecapital market. ee Calvo (1987) for omediscussion nthis ssue.



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658 THE AMERICAN ECONOMIC RE VIEW SEPTEMBER 1988mentbonds in the United States and severalothercountries), nd confirms nd comple-ments McCallum's insight hat there re nogrounds forexpecting iscalpolicy to haveno monetarymplications ven though, orinstance, hemonetary uthority romises okeep a constant price level (or a constantmoneysupply n a setup where he atter sexplicitlymodeled). In our model thishap-pens because thegovernment aynot com-mit itselfcredibly o zero inflation n thepresence f non-indexed ebt, ince the evelof the latter determines he set of equi-librium inflationrates that could be sus-tamnedx post. This relationship etweenthe stockofgovernmentondsand inflation,incidentally,will hold true even when theequilibrium s unique see Bohn,1987).Our results dd a pessimistic ote to theview that price controlsmighthelp leadingthe economy o the good" solution,22 hichappears to have played some role in thedesign of the recent heterodox" stabiliza-tion plans in Argentina, razil,and Israel.This is so, because in our example thegovernment as directcontrolon thepricelevel, but, once again, non-uniquenessrisesdue to the fact that ts ex post behavior snot immune to ex ante expectations.As amatter f fact,our previousdiscussion ug-geststhat nterest-rateegging f some sortmay be as much a crucial ingredient f acredible stabilization fforts pricecontrolsare, and that interest atepegging ould insome occasions be all that is needed forcredibility.

III. Internationalebt.AShort etourBorrowing nd lending among sovereignstates has recently eceived onsiderable t-tention see, for nstance, he recent urveyby Eaton,Gersovitz, nd Stiglitz, 986),so a

few words establishing he connectionbe-tween the present paper and that type ofliteraturemay be in order.A common characteristicf our examplesis thatthe "size of thepenalty" i.e., the costof repudiation) s a function f thedegree frepudiation; n the example f Section II thecost was proportional o the value of thedebt,whereas n thatof Section II the costwas simply a function f the fraction hatwas repudiated. In the international ebtliterature, n the otherhand, it is typicallyassumed that the cost of repudiation earsno relationship o thesize of the debt.Thisexplains why t was relativelyo easy forusto generatemultiple quilibriawhile n thatliterature quilibriums typically nique.23The presence of foreign ebt adds an in-teresting wist o our previousmodels.Thus,for example,we could assume thatonly aproportiony, 0 < y


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VOL. 78 NO. 4 CALVO: SERVICING THE PUBLIC DEBT 659bondsmarket, nd thedegree frepudiationor inflation.

IV. Concluding emarksThe centralmessage hat omesacross thispaperis thatexpectationsmayplaya crucialrole nthedeterminationfequilibrium henthegovernmentebt is auctionedoff o thepublic, and there s no attempt o manageexpectations r to peg interest ates on thegovernment ebt. In our examples,we sawthatthenominal nterestate s notsimplypassive reflection fpeople's nflationaryx-pectations, utrather hat henominal nter-est rate s actuallyone of the maindetermi-nants of inflation. onsequently, credibleanti-inflationaryolicywould haveto imple-mentrules to prevent ominal nterest atesto become unduly high. The two simplemechanisms hatweresuggestedn our dis-cussion were: (a) price indexationof thepublic debt,and (b) refrainingromssuingnew government onds whentheir nterestrate exceeds some well-definedounds. Inmoregeneral erms, owever, urdiscussionpointed out to the advisability f govern-

mentstaking more active tance on nomi-nal interest ates. n myopinion, his mpli-cation of the formal nalysis s likely o beparticularly elevant n situationswherethestabilization programis launched in themidstofveryhigh nflation.The analysishas beenconducted n termsof modelswithone representativeonsumerbecause so muchof therelated iteratureasbeen couched in this form (prominentlyBarro, 1979; and Lucas and Stokey 1983).However, suspect hat ne of the mportantreasons for debt repudiation o be costly(otherthandue to "reputation" osts) s thefact thatnot all individuals re alike and,therefore,he ncidence frepudiations notuniform.24 onsider,forexample, a modelof the type discussedby Thomas Sargentand Neil Wallace (1982) whereonlya sub-set of total population holds non-interest

bearingpublic debt cash, say),while herestof society holds high-denominationon-indexed bonds. For the sake of the argu-ment, suppose, in addition, hat everybodypays the same amount of taxes. Clearly, ftheplanner adheres to utilitarian rinciples,for xample,debtrepudiation ould be costly(or beneficial), ecause the latterwould bean instrument f wealthredistribution.nthat context,the planner may end up re-pudiating ess than 100 percent f the debt(held by the "rich,"say) because of the ossit would cause cash-holdersthe "poor"). Ithink the analysis of thesetypesof modelsshouldprovideus with deeperunderstand-ing of these ssues. t ismy feeling, owever,that the central nsights f thispaper willcarry ver to thosemodels.Another nterestingxtensionwould be tointroduceuncertainty. otice, first,hat theabove two-period xampleswould not ex-hibit random equilibria, because once theinterest ate s determinednperiod 0, thereexists only one optimumresponse for thegovernmentn period1. An easy extension,however,would be to make the repudiationcost, a, random.Thus, f ndividuals re riskneutral, or example,Rb times he expectedrepayment harewould n equilibriumqualthe nterest actor n capital R; therepudia-tion shares for each state of nature, n theotherhand,woulddependon Rb (as in ourprevious analysis). Therefore, he equilib-riumvalues of Rb willbe deeply ntertwinedwiththeprobability istributionf a. Clear-ly, since Rb is just one number,we willobservesituationswhere ex post the actualnet return n bonds exceeds or falls shortof) that of physical capital. Consequently,these models could help explain phenomenalike the highex post real interest atesob-served at the beginning f anti-inflationaryprograms see, for nstance,Rudiger Dorn-busch, 1985,and Jeffreyachs, 1986).Finally, an important xtension of theanalysis would be to allow formore thantwo periods,25 and the simultaneous ex-istence of explicitrepudiationfor example,interest atetaxes)and inflation.

24See Carol Rogers 1986) and Calvo and Obstfeld(1988) formodelswhichhighlighthe inkbetween imeinconsistencynd wealthdistribution. 25Forsome progress n thisfront, ee Calvo (1987).



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VOL. 78 NO. 4 CALVO: SERVICING THE PUBLIC DEBT 661National Saving and Game-EquilibriumGrowth," Review of Economic Studies,April1968, 35, 185-99.Rogers, arol Ann, The Effectf DistributiveGoals on theTime Inconsistencyf Opti-mal Taxes," Journalof MonetaryEco-nomics, 986, 17,251-69.Rogoff,Kenenth,Reputation,Coordinationand MonetaryPolicy,"The Hoover In-stitution,Working Paper in Economics

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