Dellas Credibility for Sale

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Credibility For Sale

Harris Dellas Dirk Niepelt

January 21, 2013

Abstract

We develop a model with official and private creditors where the probability of

sovereign default depends on both the level and the composition of debt. Higherexposure to official lenders improves incentives to repay but also carries extra costssuch as reduced ex post flexibility. We characterize the equilibrium compositionof debt across creditor groups. Our model can account for important aspects ofsovereign debt crises: Namely, that official lending to sovereigns takes place only intimes of debt distress and carries a favorable rate. Our analysis also has two novelimplications: First, official lending tends to displace private funding. And second,with debt overhang the availability of official funding increases the probability ofdefault even if default does not trigger exclusion from credit markets.

JEL class: F34, H63

Keywords: Sovereign debt, official lending, default, enforcement

1 Introduction

The recent sovereign debt crisis in the EU, like many other crises before, has exhibitedtwo features: Sovereign borrowers with large borrowing requirements who face high in-terest rates on credit markets; and official lenders (such as the IMF and EU membergovernments) who step in to provide funds at a lower rate than private creditors. 1 The

For useful comments and conversations, we thank Marios Angeletos, Fernando Broner, Fabrice Col-lard, Behzad Diba, Martn Gonzalez-Eiras, Leo Martinez, Andreas Schabert, Jean Tirole as well asconference and seminar participants at the Federal Reserve Bank of Chicago/NBER Conference Macroe-conomics Within and Across Borders and EIEF Rome. greece721.tex

Department of Economics, University of Bern, CEPR. VWI, Schanzeneckstrasse 1, CH-3012 Bern,Switzerland. Phone: +41 (0)31-631-3989. [email protected], www.harrisdellas.net.

Study Center Gerzensee, University of Bern, IIES, Stockholm University, CEPR. P.O. Box 21, CH-3115 Gerzensee, Switzerland. [email protected], alum.mit.edu/www/niepelt.

1Another common feature, which our analysis will abstract from, is the implementation of adjustmentpolicies (fiscal adjustment, currency devaluation, structural reforms etc.) accompanying the provisionof official funds. We do not think that this is a distinguishing feature of official lending as often quitesimilar adjustment policies are undertaken in order to assure private investors about the safety of theirfresh funds. See, for instance, the recent experience of Italy and Spain.

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objective of this paper is to develop a model that can account for these features.We do so in the context of the standard sovereign debt model (Eaton and Gersovitz,

1981). The borrower lacks commitment and only repays its debt when the cost of default

is sufficiently large. This limits the amount the country can borrow ex ante. In order toprocure more funds, the sovereign may want to structure its debt in a way that increasesdefault sanctions.

The basic premise of this paper is that borrowing from certain groups of creditorscan indeed increase default sanctions.2 In particular, we claim that a borrower sufferslarger losses when it defaults against official lendershenceforth, the enforcerthanagainst private creditors. Borrowing from the enforcer therefore enhances credibility andimproves access to current funding. But it also carries extra costs. Not only does it reduceex post flexibility3 because of the higher cost of default but it may also carry a premiumthat compensates the official creditors for their higher cost of administering loans relative

to private creditors (such as IMF type surcharges or the cost of setting official lending-debt recovery mechanisms). The equilibrium debt ownership structure during normalperiods and periods of debt stress is a reflection of the relative size of such benefits andcosts.

Why would default sanctions depend on the identity of the borrowing countrys cred-itors? One possible reason could be that the credit relationship was one of several inter-connected relationships between the borrower and the lender, as it is typically the casefrom participation in the same club. Consider for instance the ongoing European debtcrisis with Greece (and other countries) drawing official funding from Germany (and otherEurozone countries). Greek default on German loans could conceivably trigger retaliation

and lower Greeces benefits from club membership in the European Union. Structuralfund payments and other transfers might be cut. Greece might even be forced to leavethe Euro area. Germany might be tempted to adopt policies that were less favorableto Greek interests than the policies that would have been adopted in the absence of adefault. EU support for certain Greek foreign policy positions might wither. And so on.

As the ongoing crisis constitutes the first instance in which certain members of theEurozone have borrowed large amounts from other members, and since no default againstofficial funds has occurred we cannot yet know whether Germany or other official lenderswould be in a position to inflict sanctions of the type described above. And if theywere, whether they would actually choose to do so.4 But what matters for the behavior ofagents in our modeland hence for the properties of equilibriumis the perception of the

existence and likely use of such sanctioning powers, rather than the powers themselves.5

2Unlike private loans to sovereigns, IMF loans are paid back. So the identityofficial vs. privateofthe creditor seems to make a difference. But the identity of the creditor also seems to matter in privateloan transactions. According to a widely shared presumption and also anecdotal evidence the incentiveto repay loans to Mafia is much stronger than the incentive to repay other creditors, due to Mafias moreextensive set of enforcement tools.

3See Zame (1993) for a discussion of the insurance benefits of implicitly state contingent debt.4Superior power certainly existed during the times when mighty countries would use military force to

enforce repayment (for instance, when the British navy bombarded Athens).5Naturally, in a model with asynchronous borrowing and default decisions of multiple borrowers,

default by one country could reveal the existence of such powers and affect perceptions in those countries

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In our view, the public debate in Europe and statements by policy makers provide ampleevidence for a widely shared belief that superior sanctioning powers do exist and officiallenders would be willing to use them.

In Germany, the statements of German politicians, the debates in parliament and thepublic reaction all conjure the impression that Germans perceive that their loans face alow probability of default. In fact, such a perception is sina qua non for large German loanprovision at low rates to have been politically feasible in the first place, given Germanvoters expressed antipathy to solidarity (transfers) towards Greece. This belief is alsofounded in the knowledge that a default by Greece on debt held by official creditorsamounts to violating EU treaties and breaking national laws, leaving Greece in unchartedand treacherous political territory regarding its future within the EU.6 Naturally, timeconsistency is an issue as it would also be costly for Germany to impose sanctions ex post.But the existence of a great deal of repeat business within the club (lending to Portugal,

Ireland and Spain is but one example) makes reputational considerations important. Notimposing sanctions following a Greek default could undermine Germanys credibility fortoughness.7 Note that in order to ensure broad political support for enforcement ex post,Germany has required club-wide participation in the official lending operations.

Similar perceptions about the additional, severe cost of Greek default on Eurozoneloans are also held in Greece. In particular, Greek voters have opted for parties thatstrongly oppose default and warn about the dire consequences of default for Greecesmembership in EMU and even EU. While the main opposition party advocates default onboth private and official loans this position may not reflect the view that official lenders arepowerless but rather an underlying desire to actually subject Greece to the enforcement

and get the country expelled from EMU.

8

In our view, the evidence thus points to awidely shared belief in both the existence of superior sanctioning powers on the part ofofficial lenders and their willingness to use such powers.

We characterize the conditions on the primitives (such as the rate of impatience, theoutput profile, the credibility gains induced by official lending etc.) under which ourmodel can account for the stylized facts mentioned above, namely, the shift away fromprivate towards official lending during periods of debt distress, combined with interestrates considerably below what the market rate would have been in the absence of officiallending. But our analysis also has some other, quite novel implications. First, we showthat even when official lenders try to avert the crowding out of private credit by officialloans, by accepting a pari passu clause, such crowding out is still likely to occur. In other

that have not made a default decision yet.6The German government spokesman Steffen Seibert argued that the countries of the Eurozone could

not accept a reduction in the value of their loans to Greece because this would contradict European Uniontreaties as well as national legislation in Germany and other countries that prohibits member countriesto assume the debts of other countries (Kathimerini, November 27, 2012).

7Steffen Seibert has argued that debt forgiveness would lead to a huge loss of credibility for Germanyand could encourage other countries with debt problems to ask for similar treatment (Kathimerini,November 27, 2012).

8The main opposition party is called the party of the drachma in the sense that special interestgroups that support itsuch as heavily indebted press barons, labor unions in the public sector, profes-sional guilds etc.are thought to profit from Greeces exit from European institutions.

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words, there is a strong tendency in the model towards corner equilibria with only onetype of creditor type. Second, we show that when there is long-term debt overhang, theprobability of default varies with the source of refinancing available to the borrowing coun-

try. In particular, the mere availability of official credit makes a sovereign more inclinedto default on outstanding debt in spite of the fact that in our modelby assumptiondefault does not trigger exclusion from private credit markets. The incentive to defaultis weaker when only private funds are available. At the same time, official creditors mayactually encourage the sovereign to default. This is because the profits of official lendersmay be increasing in the volume of official funds and the sovereigns demand for fundsmay be higher after a default than otherwise.

The literature on the composition of sovereign debt by type of creditor is scant. Boz(2011) reviews the literature on IMF lending, summarizes empirical evidence and presentsa quantitative model of a sovereign that may borrow from private lenders and the IMF.

She assumes that private lending is subject to default risk, IMF lending is default riskfree, and the cost of IMF funds exceeds the risk free rate by an exogenous surcharge. Shealso assumes that IMF lending triggers an increase in the sovereigns discount factor. Hermodel predicts modest, countercyclical and intermittent IMF lending.

In the model proposed here, official lending does not change the sovereigns discountfactor; the borrowers objective and the cost of official funding therefore are disconnected.Also in contrast to Boz (2011), we assume that the repayment rate on official and privatefunds is uniform.9 We believe that this assumption is reasonable for episodes like thecurrent European sovereign debt crisis where official lenders are anxious not to crowd outprivate funding. This view is supported by the conditions of the Greek debt exchange in

Spring 2012 and by the more recent discussions about financial support for Spain.

10

Bolton and Jeanne (2011) analyze the interaction between multiple sovereigns of dif-ferent credit quality and the banking system in a financially integrated area. They arguethat a country issuing safe haven government debt may derive rents from exploiting itsposition as monopolistic supplier of this safe asset. In the model proposed here, we alsoallow for non-competitive rents, but in contrast to Bolton and Jeanne (2011), we con-sider the possibility that (official) lenders rather than the borrower extract rents. Niepelt(2011) analyzes the composition of sovereign debt across maturities rather than lenders,as considered here, and Diamond and He (2012) analyze the implications of the maturitystructure of debt overhang on investment decisions. Finally, Tirole (2012) distinguishes

9

Boz (2011) rationalizes her assumption of default risk free official lending by the fact that historically,very few IMF loans went sour (p. 75).

10Zettelmeyer, Trebesch and Gulati (2012) report that the Greek debt exchange put private and of-ficial lenders (the EFSF) on an equal footing. Greece and the remaining signatories of the agreementcommitted to a payment schedule in which the EFSF and bondholders would be repaid pro-rata and onthe same day. In the event of a shortfall in payments by Greece, the common paying agent committedto distributing allocating this shortfall pro rata between the EFSF and the bondholders. Hence, the co-financing agreement makes it difficult for Greece to default on its bondholders without also defaulting onthe EFSF (p. 25). Regarding the financial support for Spain, The Wall Street Journal (June 29, 2012,Investors Cheer Europe Deal) writes that Merkels agreement to make ESM loans to Spain equal toSpanish bonds in creditors pecking order was largely a recognition by Germany that this was necessaryto protect Spains ability to sell bonds . . . .

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between ex-post bailouts that aim at avoiding collateral damage and ex-ante risk-sharing(for example joint-and-several liability) among sovereigns.

The rest of the paper is organized as follows. The model in set up section 2. The

equilibrium is characterized in section 3. Section 4 contains a series of tractable examplesthat help develop intuition and illustrate the main results. Section 5 concludes.

2 The Model

The economy lasts for two periods, t = 1, 2. It is inhabited by a representative taxpayer,a government and foreign investors. Taxpayers neither save nor borrow.11 They havetime- and state-additive preferences over consumption with strictly increasing and concavefelicity function u() and discount factor (0, 1). Welfare of taxpayers in period t = 1is given by

E

2

t=1

t1u(ypt t)|s1, 1

,

where ypt denotes exogenous, pre-tax income, t taxes, st the state (to be specified below)and t the policy choice in period t. We often write E1[] instead ofE[|s1, 1].

Foreign investors are risk neutral, require a risk free gross interest rate 1 > 1 andhold all government debt (since taxpayers do not save).12 To guarantee positive debtpositions, we assume as is standard in the sovereign debt literature.13 Foreigninvestors are composed of private and official lenders. Private lenders are competitive.Official lenderswe refer to them as the enforcermay coordinate amongst themselves

and behave non-competitively vis-a-vis the borrowing country. Either as a consequence ofthis, or due to differences in the cost of funds across lenders, the interest rate charged byofficial lenders may differ from that charged by private lenders. The central implicationsof the model are independent of this feature.

The government maximizes the welfare of taxpayers. In period t, it chooses the repay-ment rate on maturing debt, rt, issues zero-coupon, one-period debt, bt+1, of which b

et+1 is

held by the enforcer and bt+1bet+1 by private lenders, and (residually) levies taxes. With-

out loss of generality, public spending other than debt repayment is normalized to zero.Crucially, the government cannot commit its successors (or future selves). Short-sales areruled out.

Let b02 denote the stock of debt issued to private investors in the past that is due inperiod 2. Define b2 b021 + b2 to be the stock of maturing debt in period t = 2, where 1is a variable linked to the default decision in the first period: If default in the first periodapplies to debt maturing in that period and also to the outstanding long-term debt, then1 r1. If, instead, default in the first period does not affect the repayment rate onlong-term debt, then 1 1 and b2 = b02 + b2. While the latter specification is consistent

11Mankiw (2000) or Matsen, Sveen and Torvik (2005) analyze fiscal policy in economies with saversand spenders.

12The assumption that the sets of taxpayers and investors do not overlap simplifies the analysis anddoes not matter for the main results.

13For recent examples, see Aguiar and Gopinath (2006) or Arellano (2008).

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with a strict notion of lack of commitment, the former often seems plausible on the basisof legal and economic grounds and it also generates more closely intertwined default andrefinancing choices. We solve the model under either specification. Outstanding long-term

debt may be repurchased by the government in period t = 1. The short-sale constraints inthe first period therefore read b2b

e2 b021 and b

e2 0 or, more compactly, b2 b

e2 0.

Let B(b021) denote the set of debt ownership structures (b2, be2) that are consistent with

the two short-sale constraints.A sovereign defaulta situation where the repayment rate falls short of unitytriggers

income losses for taxpayers (cf. Eaton and Gersovitz, 1981; Cole and Kehoe, 2000; Aguiarand Gopinath, 2006; Arellano, 2008). More specifically, a default in period t triggersan income loss Lt 0 where Lt is the realization of an i.i.d. random variable withcumulative distribution function Ft() and associated density function ft(), ft(L) > 0 forall Lt 0. In the presence of official lending, default triggers additional income losses

for the borrowing country (see the discussion in the introduction). These losses are givenby L(be2) with L(0) = 0 and L

(be2) 0 for all be2 > 0. Default occurs uniformly across

privately and officially held debt (see the discussion on pari passu in the introduction).The sequence of events in each period is as follows. In the beginning of period t, Lt

and yt become known. The state is given by st = (yt, Lt, bt, bet). Conditional on st, the

government chooses policies, 1 = (r1, b2, be2) or 2 = r2, taking as given the equilibrium

relationship between these choices and bond prices.Let q1(s1, 1) and p1(s1, 1) denote the period t = 1 state s1 price of debt issued to

private and official lenders, respectively, if the government implements policy 1. Whenchoosing its policy, the government takes the price functions q1(s1, ) and p1(s1, ) as

given. Letting 1(s1, 1) q1(s1, 1) p1(s1, 1) denote the difference between the twoprice functions we define the borrowing countrys deficit in period t = 1 as

d1(s1, 1) b2q1(s1, 1) be21(s1, 1). (1)

The budget constraint of the government is 1 = b1r1 d1(s1, 1). The pre-tax incomeof taxpayers is yp1 = y1 1[r1


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maximized flow utility from consumption in period t = 2, as reflected by the second valuefunction. Importantly, the default rate in period t = 2 is chosen by the government inthat period alone, due to the lack of commitment.

An equilibrium conditional on the official-funds price function p1(st, ) then consists ofvalue and policy functions in periods t = 1 and t = 2 and a private-funds price functionq1(st, ) such that

i. conditional on s1 as well as the price functions, the policy choices are optimal forthe borrowing country,

t(st) solves Gt(st), t = 1, 2;

ii. the private-funds price function reflects rational expectations as well as the partic-ipation constraint of competitive private lenders (i.e., investors earn the expected,competitive rate of return),

q1(s1, 1) = E1 [r2(s2)] . (2)

Note that equilibrium is defined conditional on a price function for official funds,p1(, ). This allows us to study debt policy under alternative assumptions about theinstitutional environment in place and the enforcers cost of funds. Consider for examplethe case in which the enforcer has negligible bargaining power. In this case, the equilibriumprice p1(s1, 1) is set so that the enforcer attains no more than his outside option. Ifexposure to the borrowing country after a default generates some costs C(be2) (beyond

capital losses) to the enforcer then the enforcers binding participation constraint implies

be2p1(s1, 1) = be2 E1[r2(s2)] Prob[r2(s2) < 1] C(b

e2). (3)

As another example, consider the case where the enforcer has sufficient bargainingpower vis-a-vis the borrowing country to negotiate a fixed mark-down relative to theprice on private markets. The equilibrium price of official funds then equals

p1(s1, 1) = q1(s1, 1), 0 < < 1. (4)

In both examples, p1(s1, 1) q1(s1, 1).14

We proceed under the assumption that the governments program is well behaved andgives rise to smooth policy functions. In the examples considered below, we verify thatthis is indeed the case.

3 Analysis

The Choice of Repayment Rate in the Second Period Consider first the gov-ernments choice of repayment rate in the last period, r2. Since the marginal cost of

14It is also possible to think of situations where > 1, for example because official lenders subsidizeborrowing in order to account for externalities.

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lowering r2 is zero when r2 < 1, the optimal repayment rate equals either zero or unity.In particular,

r2(s2) = 1 if L2 b2 L(be2)

0 if L2 < b2 L(be2) . (5)

Condition (5) states that the government chooses to default when the resulting incomelosses, L2 + L(b

e2), are smaller than the amount of debt coming due.

15 Condition (5) isconsistent with the notion that governments tend to default when the political costsspecifically income losses of pivotal pressure groupsare low. Governments also tendto default when economic activity is depressed (Borensztein, Levy Yeyati and Panizza,2006; Tomz and Wright, 2007). The model is consistent with this fact as well when itis slightly extended to include direct default costs for the government in addition to theincome losses for taxpayers. Note that corner solutions for the optimal repayment ratefollow under more general assumptions about default costs than those made here.

Equation (5) pins down the expected repayment rate. From (2), the equilibrium priceof private funds equals

q1(s1, 1) = (1 F2(b2 L(be2))) (6)

and is decreasing in the quantity of debt issued, b2. Ifb02 > 0 and 1 = r1 then the choiceof repayment rate in the first period, r1, also affects the price because it determines b2.We return to this point later, when discussing the equilibrium choice of r1.

The Choice of Debt Issued to Private Lenders Issuing debt to private lendershas two effects on the deficit. On the one hand, it raises funds from the marginal unit

of debt, in proportion to its price. On the other hand, it reduces the funds raised frominframarginal units of private and official lending, by changing the price of these units.This latter effect is a direct consequence of the governments lack of commitment andreflects the endogeneity of subsequent repayment decisions. Formally, from (1) and (6),

d1(s1, 1)

b2= q1(s1, 1) + b2

q1(s1, 1)

b2 be2

1(s1, 1)

b2

= q1(s1, 1) b2f2(b2 L(be2)) b

e2

1(s1, 1)

b2.

Funding from private sources is maximized at the top of the debt-Laffer curve which

is reached when the above marginal effect equals zero. A completely myopic government15Letting bp2 denote privately held debt and r

p2 , r

e2 the repayment rates on b

p2 and b

e2, respectively, our

assumption in the main model corresponds to the case where

c2 = y2 be2r

e2 b

p2r

p2 1[re2r

p

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( = 0) maximizes the deficit and attains the maximum of the debt-Laffer curve. Anon-myopic government ( > 0), in contrast, does not maximize the deficit because eachadditional unit of debt strictly reduces the continuation value. In either case, the equilib-

rium value ofb2 is therefore (weakly) smaller than the value that attains the maximum ofthe debt-Laffer curve. Moreover, this equilibrium value (weakly) exceeds be2 b021, dueto the short-sale constraint vis-a-vis private investors (b2 b

e2 b021). In the following,

we refer to the range of b2 values defined by the lower bound of be2 b021 and the upper

bound of the maximizer of the debt-Laffer curve as the relevant range for b2.Let and denote the multipliers associated with the short-sale constraints be2 0

and b2 be2b021, respectively. The effect of a marginal increase in debt issued to private

lenders on the governments objective is given by

G1(s1; 1)

b2

= u(c1)d1(s1, 1)

b2

+ E1[G2(s2)]

b2

+

which can be expressed as16

(1 F2(b2 L(be2)))(u

(c1) E1[u(y2 b2)])

u(c1)

b2f2(b2 L(b

e2)) + b

e2

1(s1, 1)

b2

+ . (7)

The first part of this marginal effect represents the consumption smoothing benefitfrom the marginal unit of debt. It differs from the corresponding expression in the casewithout default risk because the price of debt equals (1 F2(b2 L(b

e2))) rather than

and because debt repayment occurs with probability (1 F2(b2 L(be

2))) rather thanalways.17 The marginal rate of substitution between current and future consumptionand thus, the profile of output, as well as the relative price between current and futureconsumption determine the strength of the consumption smoothing benefit.

The second part of the marginal effect arises because the repayment probability de-pends on the quantity issued: Each extra unit of debt issued lowers the price of allinframarginal units or, equivalently, raises the interest rate on them. This increase in theinterest ratewhich would be absent in a model with commitmentmakes first periodconsumption more expensive. As a consequence, the equilibrium amount of debt issued(conditional on be2) tends to be smaller than that under commitment. The second part alsoreflects the fact that issuance of b

2might affect the price difference

1(s

1,

1). The final

16We use the fact that

E1[G2(s2)]

b2=

b2

b2L(be2)0

E1[u(y2 L2 L(be2))|L2]dF2(L2) +

b2

b2L(be2)

E1[u(y2 b2)]dF2(L2)

= E1[u(y2 b2)]f2(b2 L(be2)) E1[u(y2 b2)]f2(b2 L(b

e2)) (1 F2(b2 L(b

e2)))E1[u

(y2 b2)].

17With risk free debt, the marginal effect would reduce to u(c1) E1[u(y2 b2)].

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part of the marginal effect, the multiplier , is strictly positive if the short-sale constraintb2 b

e2 b021 is binding, and equals zero otherwise.

It may seem surprising that the negative welfare effect associated with the reduction

of funds raised from inframarginal units of debt (the second part discussed above) is notbalanced by a positive welfare effect from the reduced repayment probability of theseinframarginal units in the future. In fact, this effect is present. However, it does notappear in (7) because it is equal in absolute value to a third welfare effect of oppositesign, reflecting the increased risk of future social losses in the wake of default.18 It is thesesocial losses that are the source of the reduced incentive (relative to the commitmentcase) for the government to issue debt. Niepelt (2011) contains a detailed discussion inthe context of a model with multiple maturities.

The Choice of Debt Issued to Official Lenders Issuing debt to official lenders

while holding total debt constant (that is, substituting official for private debt) affectsthe deficit threefold. First, by raising the output losses of the borrowing country in case offuture default, it reduces default risk and increases the price of debt. This has a positiveeffect on the deficit. Second, it reduces the deficit at the margin by the amount 1(s1, 1)if private creditors purchase debt at a higher price than official lenders. Finally, it maychange the price discount applied on the inframarginal units of debt issued to the enforcer.Formally, from (1) and (6),

d1(s1, 1)

be2= b2f2(b2 L(b

e2))L

(be2) 1(s1, 1) be2

1(s1, 1)

be2.

The effect of substituting official for private funds on the governments objective isgiven by

G1(s1; 1)

be2= u(c1)

d1(s1, 1)

be2+

E1[G2(s2)]

be2+

where the multipliers reflect the two short-sale constraints. This can be expressed as19

L(be2)

u(c1)f2(b2 L(b

e2))b2 E1

b2L(be2)0

u(y2 L2 L(be2))dF2(L2)

u(c1)1(s1, 1) + be21(s1, 1)b

e2

+ . (8)The first part of this marginal effect reflects the benefit of stronger credibility on the

one hand and the cost of reduced flexibility on the other. A larger share of official debtgenerates stronger repayment incentives and hence lower default risk; this raises q1(s1, 1)

18Higher debt issuance increases subsequent default risk and thus, the risk of future output losses inthe wake of default. The corresponding first-order welfare effects that operate through the continuationvalue are zero. This is a consequence of an envelope conditionthe subsequent government is indifferentat the margin between bearing the costs of debt repayment on the one hand or income losses in the wakeof default on the other (see footnote 16).

19Note that E1[G2(s2)]/be2 = L

(be2)E1 b2L(be

2)

0u(y2 L2 L(b

e2))dF2(L2) (see footnote 16).

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and the deficit, and it allows the country to consume more in the first period. But thelarger share of official debt also inflicts additional income losses in case default neverthelessoccurs subsequently (which happens for low realizations of L2). The second part of the

marginal effect reflects the price difference between the marginal units of private andofficial lending, and it also reflects the fact that changing the debt composition may affectthe price discount applied to inframarginal units of official funds.

The Choice of Repayment Rate in the First Period The trade-off governing thechoice ofr1 differs depending on whether 1 = 1 or 1 = r1. Consider first the latter case.When 1 = r1 (and b02 > 0), then the trade-off governing the choice or r1 is a dynamic onebecause default does not only wipe out maturing debt but also long-term debt overhang.This reduces the probability of default in the second period and raises the price q1(s1, 1).For r1 < 1, the net marginal benefit of reducing the repayment rate further is positive

and as a consequence, the optimal repayment rate equals either zero or unity. LettingG1(s1; r1 = ) denote the value of the governments program conditional on state s1 andrepayment rate r1 = , the equilibrium choice thus satisfies

r1(s1) =

1 if G1(s1; r1 = 1) G1(s1; r1 = 0)0 if G1(s1; r1 = 1) < G1(s1; r1 = 0)

. (9)

We discuss the interdependence between long-term debt overhang and the default decision(9) in more detail below.

If 1 = 1, in contrast, default wipes out maturing debt, b1, but not outstanding long-term debt, b02. The choice ofr1 therefore does not affect the price of debt paid by privatelenders, q

1(s

1,

1). If the same holds true for the price paid by official lenders, p

1(s

1,

1),

(and thus, the price difference 1(s1, 1)) then the deficit is independent ofr1 as well andthe repayment decision in the first period parallels the one in the second period, namely

r1(s1) =

1 if L1 b10 if L1 < b1

.

Independence of p1(s1, ) and r1 if 1 = 1 may be a reasonable assumption in someenvironments but not in others. The assumption is satisfied in the particular specificationsdiscussed above (see equations (3) and (4)) where the trade-offs present in the lendingrelationship between the enforcer and the borrowing country from period t = 1 onwardsare independent of the repayment rate r1. But it would not be satisfied if the enforcers

participation constraint held before r1 were chosen. Equation (3) then would be replacedby

be2p1(s1, 1) = be2 E1[r2(s2)] Prob[r2(s2) < 1] C(b

e2) + b

e1r1

and the equilibrium price of debt purchased by the enforcer would depend on the re-payment rate in the first period. In this case, the enforcer would be indifferent betweenlowering r1 by an amount and increasing p1 by the amount b

e1/b

e2. Such a combination of

changes in r1 and p1 could strictly increase the welfare of the borrowing country ifbe1 < b1,

that is, if there were another group of investors that could be burned.20 Consequently,

20Naturally, a proper specification of the problem would require that such incentives are recognizedand priced ex ante.

11


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a default in the first period could be in the joint interest of the borrowing country andthe enforcer.21 We do not pursue this variation of the model here.

Properties of Equilibrium The equilibrium conditions make clear that the quantityof debt issued, the ownership structure, and the default choices depend on factors suchas the intensity of the borrowing needs, as manifested in the ratio / and the steepnessof the output profile; the distribution function of output losses, F2(); preferences; theenforcement technology, L(); and the price discount, 1(). Since the general modelcannot be solved in closed form, the exact contribution of these factors is difficult to iden-tify. Nevertheless, the optimality conditions suggest two general properties of equilibriumwhich are confirmed in the examples analyzed later. The first general property concernsthe equilibrium debt ownership structure, and the second one the interaction between thisstructure and the default decision in the first period. We discuss the two properties in

turn.Regarding the debt ownership structure, note that four types of equilibria may emerge

(see (7) and (8)). Letting M(b2, be2) and M

e(b2, be2) denote the marginal effects without

multipliers in (7) and (8), respectively, these four types can be summarized as follows:

i. = = 0. b2, be2 interior with M(b2, b

e2) = M

e(b2, be2) = 0.

ii. = 0, > 0. b2 interior, be2 = 0 with M(b2, 0) = 0, M

e(b2, 0) < 0.

iii. > 0, = 0. b2 = be2 > 0 with M(b2, b2) + M

e(b2, b2) = 0.

iv. > 0, > 0. b2 = be2 = 0 with M(b2, b2) + M

e(b2, b2) < 0.

While all four types are theoretically possible, there exists a strong tendency towardsa corner solution. To see this, abstract from price differences between privately andofficially held debt (that is, let 1(s1, 1) 0) and, to simplify expressions, normalize (7)and (8) by the direct contribution of a marginal unit of debt to utility in the first period,u(c1)(1 F2(b2 L(b

e2))). This yields

M(b2, be2)

1

E1[u(cnd2 )]

u (c1)

b2H2(b2 L(b

e2)), (10)

Me

(b2, be

2) L

(be

2)

b2H2(b2 L(be

2))

E1 b2L(be

2)

0u(cd2)dF2(L2)

u (c1)(1 F2(b2 L(be2)))

. (11)

Here, H2() denotes the hazard function, H2() f2()/(1 F2()), and cd2 and c

nd2 denotes

consumption in default and non-default states, respectively. In (10), the first term (inparentheses) represents the consumption smoothing benefit from the marginal unit of debtand the second one the negative price effect due to higher debt issuance, weighted by the

21Broner, Martin and Ventura (2010) argue that secondary markets undermine the ability of a sovereignto discriminate between groups of lenders. The above argument suggests that the borrowing country maycollude with lenders rolling over its debt and discriminate against other holders of outstanding debt bychoosing r1 and p1 appropriately.

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quantity of debt. In (11), the first term represents the marginal benefit of credibility andthe second the cost of reduced flexibility.

Suppose that b2 is interior such that M(b2, be2) = 0. Substituting from (10) into (11)

then gives

Me(b2, be2) L

(be2)

1 E1[u(cnd2 )]

u(c1)

E1

b2L(be2)0

u(cd2)dF2(L2)

u (c1)(1 F2(b2 L(be2)))

.

Under risk neutrality, this expression reduces to L(be2) (1 / /) which genericallydiffers from zero; an interior solution for b2 therefore implies a corner solution for b

e2 (and

vice versa). With strictly concave preferences, this strong result does not hold in general.However, simulation results suggest that the forces that push lending into a corner in the

linear utility case operate strongly also in the general case.The source of this propensity for a single type of debt is the fact that debt issuanceto private and official lenders has very similar effects (of a different sign) on the fundsraised on inframarginal units of debt: Suitably normalized, the negative price effect dueto higher debt issuance and the positive price effect due to stronger credibility are ofequal absolute value.22 In an interior equilibrium with 1(s1, 1) = 0, this common valueshould correspond to two distinct expressions both of which are related to the marginalrate of substitution between first and second period consumption. For this to be possiblethe utility function must be sufficiently concave.

Note also that the negative price effect due to higher debt issuance and the positiveprice effect due to stronger credibility (suitably normalized) are of equal absolute value

precisely because of our assumption that the repayment rate is uniform. As discussedearlier, a uniform repayment rate is thought necessary if official lending is not to crowdout private funding. The model suggests, however, that even with a uniform repaymentrate crowding out may be hard to avoid.

Turning to the second general property of equilibrium, consider the role of long-termdebt overhang, b021 > 0. For given values of b2 and b

e2, long-term debt overhang has two

consequences for the marginal effects in (10) and (11). On the one hand, it lowers theprice of newly issued debt (and thus, the deficit) and changes the elasticity of the price,as is evident from the fact that the density functions F2() and f2() in (10) and (11)depend on b2. This affects the marginal benefit of both b2 and b

e2. On the other hand,

long-term debt overhang increases the marginal expected cost of enforcer funds, due toreduced flexibility in the future, as reflected by the term L(be2)

b2L(be2)0

u(cd2)dF2(L2) in(11). Long-term debt overhang therefore reduces the attractiveness of official relative toprivate funding. But precisely for this reason, outstanding long-term debt may encouragedefault when refinancing from official sources is desirable. We discuss this in more detailin one of the following examples.

22An additional unit of debt issued to private lenders reduces the funds raised on inframarginal unitsof debt by b2f2(b2 L(b

e2)) while a substitution of official for private lenders increases the funds by

L(be2)b2f2(b2 L(be2)).

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4 Examples

In order to characterize equilibrium in closed form and present solutions that shed light

on the first-order determinants of the debt ownership structure, we abstract from allnon-essential sources of non-linearity. In particular, we let u(c) = 1, L(be2) = L

with0 L < 1, and F2(L2) = f2 over the relevant range.

23 This implies (net of someconstants)

G1(s1) = maxr1[0,1], (b2,be2)B(b021)

b1r1 1[r1


15/24

The maximum of the debt-Laffer curve is obtained at the debt level (2 f2)1, the level

chosen by a myopic government with = 0, and is associated with a default probabilityof 1/2.

If instead all debt is funded from official sources then M(b2, b2) + Me(b2, b2) = 0 andthe equilibrium values (for ) are given by

bOF2 =1

f2

2 (1 L)

1

1 L, beOF2 = b

OF2 , G

OF1 =

1

2f2

( )2

2 (1 L)

1

1 L.

The maximum of the debt-Laffer curve is now obtained at the debt level (2f2(1 L))1

and is again associated with a default probability of 1/2. For L > 0, the debt levelattaining the maximum of the debt-Laffer curve is higher in the corner with official thanwith private debt.

Comparing the outcomes in the two cases, note that GOF1 > GPR1 whenever b

OF2 (

) > bPR2 ( ).26 Consequently, GOF1 > G

PR1 implies b

OF2 > b

PR2 and thus, countries that

borrow from official sources tend to be more heavily indebted than countries borrowingfrom private sources. This prediction of the model is consistent with the stylized fact thatofficial debt is more likely to be observed when debt levels are high.

To understand the countrys choice of debt instrument consider first the case of = 0.We found above that the debt level corresponding to the maximum of the debt-Laffercurve is higher in the corner with official debt. But this does not imply that a myopicgovernment that aims at maximizing the deficit necessarily chooses official over privatedebt since the former may be lower priced. In fact, comparing GPR1 with G

OF1 for = 0

reveals that the borrower will opt for official debt if and only if 1 < L that is, if the

positive effect of stronger credibility on prices outweighs the mark-down. In the following,we posit that this condition is met so that a myopic government would favor issuing debtto official creditors.

In the range 0 where both bPR2 and bOF2 are positive the criterion for the

choice of debt instrument is

GOF1 GPR1 =

1

2f2

( )2

2 (1 L)

1

1 L

( )2

2

.

For = 1, this expression is positive and official debt is preferred since it generates benefitsof credibility at no cost. For < 1, GOF1 G

PR1 is strictly positive for = 0, negative for

= and convex in in-between implying that there exists a unique threshold value such that for (high borrowing needs) official funding is preferred while for >

(low borrowing needs) private funding is preferred. The model thus predicts, in line withthe stylized facts sought to explain, that episodes of high borrowing needs (as captured bya low / ratio) are associated with borrowing from official rather than private sources.

Figure 1 presents a numerical example. It plots the difference GOF1 GPR1 against for

= 0.9 and f2 = 0.1. The solid curve corresponds to intermediate values of enforcementpower (L = 0.25) and price discount ( = 0.9). Holding fixed, the difference GOF1 GPR1 increases if L

is raised (dashed curve for L = 0.4) and decreases if is lowered

26This follows from the fact that GOF1 = bOF2 ( )/2 and G

PR1 = b

PR2 ( )/2.

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(dotted curve for = 0.8). Stronger enforcement power therefore raises and rendersofficial funding more likely while higher price discounts lower and increase the relativeadvantage of private funding. These intuitive comparative statics results hold for arbitrary

parameter combinations (under the maintained assumptions).

0.2 0.4 0.6 0.8 1.0

0.4

0.2

0.0

0.2

0.4

0.6

G1

OFG1

PR

Figure 1: GOF1 GPR1 as function of . Higher L

shifts the curve up (dashed line), lower shifts the curve down (dotted line).

Finally, consider the price of debt. A given amount of debt, b2, carries the price(1 f2 b2) when issued to private lenders and (1 f2 b2(1 L

)) when issued to

official lenders. A given amount of debt therefore is cheaper when financed from officialsources than from private sources if and only if

L 1 f2b2

f2b2

1

.

This inequality suggests that strong enforcement power, large levels of debt and a smallmark-down on official funds (a large value for ) all contribute to making official debtattractive relative to private debt.

Endogenous Price Discount, No Long-Term Debt Overhang Consider next the

case where the price discount is determined endogenously as the outcome of bargainingbetween the sovereign and the enforcer. In the simplest case, all bargaining power lieswith the sovereign and default generates a cost C(be2) to the enforcer (in addition to thecapital loss). The binding participation constraint of the enforcer (3) then reads

be2p1(s1, 1) = be2(1 F2) F2 C(b

e2),

where, as before, we let F2 f2 (b2 Lbe2). If the cost is linear, C

(be2) = C 0, then

this participation constraint simplifies to

p1(s1, 1) = q1(s1, 1) F2C = (1 F2)(1 + C

) C. (15)

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The properties of the equilibrium in this example are similar to those obtained previ-ously. The equilibrium is in a corner. If sovereign debt is exclusively funded from privatesources, the level of debt and the value of the governments program remain unchanged

relative to the previous example. But if all debt is funded from official sources then theequilibrium (for ) is characterized by

bOF2 =1

f2

2(1 + C) (1 L)

1

1 L, GOF1 =

1

2f2

( )2

2(1 + C) (1 L)

1

1 L.

The maximum of the debt-Laffer curve is now at the debt level (2f2(1 + C)(1 L))1,

the level chosen by a myopic government, and yields a default probability of 1/2(1 + C).Consequently, as long as (1 + C)(1 L) 1 and = 0, more debt is issued when thesource is official rather than private.

As far as the choice of the debt instrument in the range 0 is concerned, thedesirability of official relative to private funds is determined by

GOF1 GPR1 =

1

2f2( )2

1

2(1 + C) (1 L)

1

1 L

1

2

=

2(bOF2 b

PR2 )

and official funding is preferred if and only if bOF2 bPR2 .

The difference GOF1 GPR1 is positive at = 0 if (1 + C

)(1 L) 1, attains a zeroin the interval [0, ) if L(2C + L) < 2C, and always attains a zero at = . Hence, ifthe first two conditions are satisfied, there exists a unique threshold value such thatfor (high borrowing needs) official funding is preferred while the opposite holds for

>

. The threshold value increases with L

, as in the previous example, and falls withC. This is intuitive since a higher C increases the expected costs (beyond capital losses)that the enforcer bears in case of default; in order to compensate for these expected costs,the enforcer requires a premium relative to the rate charged by private debt buyers. Anincrease of C therefore has the same qualitative effect on as a decrease of in theprevious example.

As far as the price of funds is concerned, a fixed quantity of debt b2 carries a higherinterest rate when raised from private sources. The price for such debt equals (1 f2b2)while the price for the same quantity of debt issued to official creditors equals (1 f2b2(1 L

))(1 + C) C (from (15)) which is larger than (1 f2b2) under the first

condition described above.These findings are robust to changing the specification of the cost function C(). Sup-pose, for example, that costs are not proportional but contain a fixed component so thatC(be2) = c > 0 if b

e2 > 0 and C(b

e2) = 0 if b

e2 = 0. The enforcers participation constraint

(3) satisfied at equality then reads

p1(s1, 1) = q1(s1, 1) f2 (b2 Lbe2)c/b

e2

and equilibrium is again at a corner. Under conditions guaranteeing GOF1 GPR1 > 0 at

= 0, an increase in c reduces the threshold value at which GOF1 = GPR1 . That is, a

17


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higher fixed cost c has the same qualitative effect on as higher variable costs C or alower in the previous examples.27

Exogenous Price Discount, Long-Term Debt Overhang Finally, consider the con-sequences of long-term debt overhang, b021 > 0. The main objective of this exercise isto examine how debt overhang matters for the choice of the debt instrument as well asfor the decision to default in the first period. In parallel to the first example, we willassume an exogenous and constant mark-down, p1(s1, 1) = q1(s1, 1). The marginaleffects M(b2, b

e2) and M

e(b2, be2) are then unchanged relative to (13) and (14) except that

the probability of default, F2, is given by f2 (b2 Lbe2) rather than f2 (b2 L

be2). Wealso assume that f2b021 < 1 so that the probability of default is smaller than one andnew debt issuance depresses the price of debt.

If sovereign debt is exclusively funded from private sources then the equilibrium level

of debt (for ) is given by

bPR2 =1

f2

2 (1 f2b021).

In the first period, less debtby a factor of (1 f2b021)is issued relative to the casewithout long-term debt overhang. This is due to the fact that the existence of outstandinglong-term debt makes default more likely, making issuance of new debt more expensiveand thus less beneficial.

When all debt comes from official sources then the equilibrium debt level (for suffi-ciently low values for ) is given by

bOF2 =1

f2

2 (1 L)

1

1 L(1 f2b021)

1

f2

Lf2b0212 (1 L)

1

1 L.

As in the case with privately-held debt, outstanding long-term debt reduces the incentiveto issue debt because it pushes the borrowing country closer to the top of the debt-Laffercurve. This effect is reflected in the wedge (1 f2b021). But long-term debt overhangcarries an additional cost when accompanied by the issuance of official debt. As discussedpreviously in the context of the general model, this additional cost which only mattersfor the incentive to draw official funds derives from reduced future flexibility, F2L

.This has implications for the value of the governments program when refinancing is

provided from official sources relative to the value when refinancing is provided privately,GOF1 G

PR1 . It can be shown that this difference is decreasing in the debt overhang as

long as is sufficiently small.28 That is, while sufficiently high refinancing needs lead thegovernment to prefer funding from official over private sources this relative attractiveness

27We have (for (1 cf2(1 L)))

bOF2 =1

f2

(1 cf2(1 L))

2 (1 L)

1

1 L, GOF1 =

1

2f2

((1 cf2(1 L)) )2

2 (1 L)

1

1 L.

28Under the maintained assumption that 1 < L, we have (GOF1 GPR1 )/(b021) < 0 whenever

is in a neighborhood of zero.

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decreases with the stock of long-term debt overhang. Figure 2 plots the difference GOF1 GPR1 as a function of for different values of b021. The parameter values are as in theexample without long-term debt overhang. We also assume that b1 = L1 = 0. The solid

line corresponds to b021 = 0, the dashed line to b021 = 1 and the dotted line to b021 = 3.The figure shows that official debt becomes less desirable (the threshold value of forthe choice of official debt becomes smaller) as outstanding debt increases. Intuitively,long-term debt overhang places the economy closer to the top of the debt-Laffer curvewhere the benefits from higher credibility are necessarily outweighed by the higher costsassociated with the reduced flexibility in the future.

0.2 0.4 0.6 0.8 1.0

0.2

0.1

0.0

0.1

0.2

0.3

0.4

0.5

G1

OFG1

PR

Figure 2: GOF1 GPR1 as function of . Higher b021 reduces .

Let us no turn to the default decision in the first period. If the government can onlydefault on currently maturing debt (1 = 1) then the default decision is independent ofthe stock of long-term debt overhang and the threshold value L1 at which it becomesoptimal to default equals L1 = b1, as in the case without outstanding debt.

If default applies to both maturing and outstanding debt (1 = r1) then L1 exceeds b1whenever b02 > 0 (see (9)) and the sovereigns incentive to default increases with the stockof outstanding long-term debt.29 As discussed above, this incentive can be particularlystrong if refinancing is provided from official sources because in this case default moves

the country away from the top of the debt-Laffer curve and also reduces the marginalexpected cost of enforcer funds due to reduced flexibility in the future.

Figure 3 illustrates this (ignore the solid curve for the time being). It displays thethreshold values L1 as a function of for the two different sources of fresh funds. Thedefault threshold LPR1 applies when new debt is financed by private investors; and thethreshold LOF1 when it is provided by official lenders. Default occurs for realizations ofL1 below the relevant loci. For b02 = 0, the default thresholds are independent of

29In two different environments, one with 1 = r1 and the other with 1 = 1, the cost of defaultingmight differ. We disregard such differences as they are irrelevant for our analysis because we do notcompare outcomes across environments.

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and the two loci would coincide and be flat at level b1. For b02 > 0, as in the exampleillustrated in the figure (where b1 = 0, b02 = 3), the loci have a non-zero slope becausedefault reduces b02r1 to zero, and the effect of this change on the value of the governments

program depends on .30 More to the point, the figure shows that for low values of (lessthan 0.62), intermediate realizations of L1 (for instance, L1 = 1.3 for = 0) induce thesovereign to default if refinancing is provided by official but not if it is provided fromprivate sources.

0.2 0.4 0.6 0.8 1.0

1.4

1.6

1.8

2.0

2.2

2.4

2.6

L1

Figure 3: LPR1 (dotted), LOF1 (dashed), L1 (solid) as functions of .

The solid line in figure 3 represents the equilibrium default threshold L1 as a function of. It coincides with the default threshold conditional on official refinancing, LOF1 , wheneverthe government chooses to borrow from official sources independently of the realizationofL1. This is the case when is low. Intuitively, when funding needs are strong ( is low)official dominates private funding independently of whether the country chooses to defaultor not. With a low realization of L1, the country defaults, long-term debt overhang iswiped out and the benefits of credibility make it optimal to seek official funds. For highrealizations ofL1, in contrast, the country does not default and long-term debt overhangis not wiped out. Nonetheless, the country still prefers official funds because of the lowweight (due to the low value of ) it attaches to the reduced future flexibility associated

with official funding. Similarly, the refinancing decision is independent of the realizationof L1 for high values of and thus, the equilibrium default threshold coincides with thedefault threshold conditional on private refinancing, LPR1 .

For intermediate values of (roughly between 0.22 and 0.35), though, default andrefinancing decisions interact. This is evident from the fact that the equilibrium defaultthreshold in that region differs from both LOF1 and L

PR1 . When the source of funds

can be chosen along side the default decision, default occurs more often (with lower

30A reduction of b02r1 affects the price of new debt, the equilibrium quantity of debt issued as well asthe amount of long- and short-term debt to be serviced in the future. The price, the quantity, and theweight attached to the future all depend on .

20


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realizations ofL1) relative to the case where the government can only tap official creditorsbut less often than in the case where the government is forced to use private funds.Intuitively, low realizations of L1 and the ensuing default lead the government to seek

official funds because default wipes out long-term debt overhang and given this, thecredibility benefits render official funding attractive. But conditional on high realizationsofL1 and the ensuing non-default the presence of honored long-term debt overhang rendersofficial refinancing unattractive. As a consequence, the choices of repayment rate andrefinancing source are fully correlated in this intermediate range of values. Figure 4summarizes how the default decision and the debt ownership structure vary with andL1.

Figure 5 illustrates the equilibrium debt issuance in the first period, b2. New debtissuance is higher after a default (low realizations of L1) because it eliminates long-termdebt overhang and thereby improves access to new funding. Default therefore increases

consumption both directly and indirectly.

r1 1, b2e 0

r1 0, b2e 0

r1 1, b2e 0

r1 0, b2e 0

0.0 0.2 0.4 0.6 0.8 1.0

0.5

1.0

1.5

2.0

2.5

3.0

L1

Figure 4: Default and official lending regions.

In sum, the example shows that the availability of official funding may increase defaultrisk on outstanding debt when refinancing needs are high. Interestingly, it may not only

be the borrowing country that favors default in these circumstances, but also the officialcreditors. For they may profit from the debt they buy as long as < 1 and, as aconsequence, from a default because it increases the demand for official funds.

5 Concluding Remarks

In recent decades, the usual course of events following a sovereign debt crisis has beenfor an external official party (the IMF or a foreign government) to step in and providefundsoften in large amountsat a favorable rate to the affected country. This is alsothe course followed during the recent crisis in the Euro zone, with European countries

21


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Figure 5: Total borrowing as function of and L1.

together with the IMF providing funds to meet Greeces, Irelands and Portugals shortterm financing needs at below-market rates. While one can informally think of reasonsthat could justify these actions, the literature lacks compelling, coherent, formal theoriesthat could account for this.31

In this paper, we have rationalized foreign official lending during a debt crisis. Ourmain argument is that official foreign entities may possess superior enforcement powerrelative to private credit markets when lending to certain countries. To the extent thatthe superior enforcement carries costs to the lender when applied the model has thepotential to match the stylized fact that official lending only takes place during periods ofsovereign debt stress. If, in addition, the borrower has much bargaining power vis-a-visofficial creditors, then the model also predicts that the interest rate charged on officialloans is low relative to what private markets would charge for comparable amounts ofdebt.

Our analysis has two additional important implications. First, that official credit islikely to crowd out private credit even when official creditors accept a pari passu provision

in order to encourage private sector funding alongside official lending. And second thatin the presence of long-term debt overhang, default decisions are affected by the typeof refinancing available, private vs. official. In particular, the model predicts that acombination of strong borrowing needs and large outstanding long-term debt makes itmore likely that a sovereign will default on long-term debt obligations if official funds areavailablealongside private fundsfor debt refinancing.

Naturally, our analysis is quite general and applies equally well to credit relationshipsthat do not involve sovereign debt. What is important is the existence of different classes

31For a recent view related to the one proposed in this paper, see The eurozones journey to defaults,Financial Times, March 11, 2011.

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of creditors that differ both in terms of the punishment they can inflict on delinquentdebtors and the cost they themselves bear in the lending relationship.

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Diamond, D. W. and He, Z. (2012), A theory of debt maturity: The long and short ofdebt overhang, Working Paper 18160, NBER, Cambridge, Massachusetts.

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Matsen, E., Sveen, T. and Torvik, R. (2005), Savers, spenders and fiscal policy in a smallopen economy, Working Paper 1618, CESifo, Munich.

Niepelt, D. (2011), Debt maturity without commitment. Mimeo, Study Center Gerzensee.

Simon, C. P. and Blume, L. (1994), Mathematics for Economists, Norton & Company,New York.

Tirole, J. (2012), Country solidarity, private sector involvement and the contagion ofsovereign crises. Mimeo, Toulouse School of Economics.

Tomz, M. and Wright, M. L. J. (2007), Do countries default in bad times?, Journalof the European Economic Association 5(23), 352360.

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