The Problem that Wasn’t: Coordination Failuresin Sovereign Debt Restructurings

Ran BiInternational Monetary Fund

Marcos ChamonInternational Monetary Fund

Jeromin ZettelmeyerEuropean Bank for Reconstruction and Development

First Draft: April 2009Preliminary and Incomplete

Abstract

As bonds replaced bank loans as the main sovereign debt instrument, therewas a widespread expectation that debt renegotiation would become far morecomplicated following a default. Surprisingly, that has not been the case. In-stead, the distressed sovereign debts were restructured far more quickly thanin the 1980s. This paper links the surprising lack of collective action prob-lems to two legal innovations: minimum participation thresholds, and defen-sive exit consents, requiring participating creditors to consent to changes innon-payment terms of the defaulted bonds with the effect of compromise thelitigation prospects for hold-out creditors. After reviewing actual experienceswith these instruments, we develop a simple model which both rationalizes theinitial fears, and shows how the equilibria in the restructuring game are modi-fied by the legal innovations that tend to accompany modern debt exchanges,with the effect of making high acceptance the unique equilibrium of the re-structuring game. But since exit consents must be voted separately for eachbond series, a relatively small creditors can still acquire a majority stake in aparticular series and block them. Thus, if the country pursues too aggressive ahaircut, creditors will have incentives to pursue that litigation strategy.Keywords: Sovereign debt, sovereign debt restructuring, exit consents, cred-

itor coordination, Collective Action ClausesJEL classification: F33, F34, F53, K33

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1 Introduction

As bonds replaced bank loans as the main sovereign debt instrument, there was a

widespread expectation that debt renegotiation would become far more complicated

following a default. Surprisingly, that has not been the case. In most instances, the

distressed sovereign debt was restructured relatively quickly, using a debt exchange.

Creditor participation in these exchanges has typically been high (above 90 percent,

except for Argentina’s 2005 external debt exchange).

The purpose of this paper is two-fold. First, using a simple debt renegotiation

model, we give a formal interpretation to two types of collective actions problems

that have been extensively discussed in the literature, namely, the holdout problem

and what we call pure coordination failures. Pure coordination failures are cases in

which no participation (or low participation) in the exchange is an equilibrium, but an

equilibrium with high participation also exists. The problem is to coordinate on this

“good” equilibrium. The holdout problem, in contrast, is interpreted as a situation in

which there is a unique low participation equilibrium (or possibly multiple equilibria

that all involve low participation).

Second, we explore the extent to which collective action problems can be overcome

without requiring either new institutions or changes in bond contracts. In particular,

we study two mechanisms that have been observed in the recent exchanges: minimum

participation thresholds, which condition the exchange to a critical level of creditor

participation, and defensive exit consents. The latter refer to exiting creditors con-

senting to changes in the non-payment terms of the bonds, such as cross-default,

listing, and acceleration clauses, which can typically be changed by simple major-

ity. These changes destroy value by impairing the liquidity and litigation prospects

associated with a particular bond.

We show that minimum participation thresholds function as a coordination device,

removing the low participation equilibrium from the game in which both high partici-

pation and low participation equilibria exist. In contrast exit consents are interpreted

1

as changing the payoffs in ways that make litigation unattractive. As a result, partic-

ipation can become a unique equilibrium in the modified game even when the game

previously had a unique low participation equilibrium. These results are fairly robust,

and are not driven by particular assumptions of our stylized model. That is, in virtu-

ally any setting where the only reason for not participating is a coordination failure,

a minimum participation threshold will coordinate creditors in the good equilibrium.

Similarly, in virtually any setting where exit consents are sufficiently destructive of

litigation prospects, high participation will be achieved.

Based on these results, the positive experience with debt exchanges in the late

1990s and the present decade is interpreted as follows. First, our model suggests that

collective action problems, although a possibility, are not inevitable. In particular,

debt exchanges with atomistic bondholders could have a unique high participation

equilibrium if either litigation is unattractive ex ante (with the probability of success

too low relative to the cost) or if the haircut is small. Second, when the probability

of successful litigation relative to cost is not too high and/or the haircut is not too

high, collective action problems will take the form of multiple equilibria which include

the high participation outcome. This explains why the presence of a minimum par-

ticipation threshold alone may be enough to deal with the collective action problem.

Exit consents are needed only in response to “holdout problems” that arise when the

exchange offer is low and/or litigation success is high relative to cost.

The central prediction of the model is that debt exchange should be expected to

“fail”–meaning a decline of the exchange offer and litigation by a large group of

creditors”– only in situations where there are no participation thresholds, or when

the offer implies a high haircut and there are no exit consents, or both. The only

debt exchange offer during the 1998-2007 period to be rejected by many creditors,

Argentina (2005) arguably combined all of these features: no participation threshold;

no exit consents; and a haircut that was high compared to most other exchanges

during the period.

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It is important to stress that while exit consents do improve the countries bargain-

ing position, there are limits to how aggressively they can be pursued. If the country

uses them to seek too aggressive a haircut, it will give small creditors an incentive

to coordinate and bargain as a large creditor, since a 50% stake in any bond series

can block the exit consents. Moreover, to the extent that in practice a country’s debt

involves several bond series, even a relatively small creditor may be able to take a

controlling stake in a particular bond series. These issues are discussed in detail in

Section 3.3, which shows that this practical problems can revert the bargaining back

to the original setting where hold-outs are possible. Finally, an important result from

our analysis is that Collective Action Clauses (CACs) did not represent an improve-

ment over what could already be achieved using exit consents, if CACs are also voted

separately for each bond series. However, if CACs allow for aggregation across bond

series, then they would be a more powerful instrument than exit consents.

2 Experiences With Sovereign Bond Restructur-

ings, 1998-2007

As the new era of bond finance to emerging markets began to unfold in the early 1990s,

and particularly after the 1994-95 Mexican crisis, there were widespread fears that

collective action problems would make future debt crises more difficult to resolve,

even compared to the long and difficult crisis of the 1980s. Several developments

motivated and seemed to justify such fears.

First, collective action problems had been an issue even during the 1980s nego-

tiations, when creditors were relatively well organized and coordinated, as the debt

reschedulings that were agreed in the early 1980s typically required unanimity in

order to change their payment terms. This created problems in subsequent renegoti-

ations, as initial acceptance typically fell short of unanimity (Buchheit, 1991, 1998).

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In light of this experience, renegotiation of New York law bonds was expected to be

extremely difficult, since these bonds also required unanimity for changes in payment

terms but typically involved a much larger, more dispersed and less coordinated group

of creditors compared to the bank loans of the 1980s,

Second, a series of high profile litigation cases had demonstrated the potential

power of holdout creditors (see Sturzenegger and Zettelmeyer, 2007, Chapter II, for

details). While such cases were very rare in the 1980s, they became more common in

the 1990s, as defaulted debt began to be traded in secondary market, and "distressed

debt funds" began to buy such debt in order to litigate and ultimately settle with

the sovereign. In a famous 1996 case, CIBC Bank and Trust Co. v. Banco Central

do Brasil, a holdout creditor managed to extract almost full repayment on a fairly

large claim (about $1.3bn), a much better deal than the creditors that had negotiated

and agreed to the 1994 Brady agreement with Brazil’s. If holdouts could achieve such

deals, would not everyone want to be a holdout? Furthermore, even if holding out and

litigating required specific skills or a specific business model, and hence were not an

attractive to mainstream creditors—the presence of holdouts could weaken or interfere

with the debtor’s debt servicing capacity, and hence might complicate negotiations

between mainstream creditors and debtors.

Finally, the experience of the 1994-95 Mexican crisis seemed to demonstrate the

disruptive power of collective action problems associated with dispersed sovereign debt

first hand, even though these problems occurred not in the context of a restructuring

negotiation, but in the form of a run on short term debt that became the trigger

of a crisis. If lack of creditor coordination could bring a country to its knees, then

coordination could also be expected to be an issue in the aftermath of a crisis that

required a debt restructuring (as opposed to just liquidity that might be provided by

an official lender such as the IMF).

The consequence of these fears was a large number of policy proposals to reform

the "international financial architecture" in order to deal with creditor coordination

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problems in general, and specifically in the context of debt restructuring negotiations

(see Rogoff and Zettelmeyer, 2002, for a survey). Broadly speaking, they can be di-

vided into two sets. First, proposals to create a bankruptcy court-type institution at

the international level, either by changing the Articles of Agreement of the IMF, or

through a new international treaty, which would oversee debt restructuring negotia-

tions and declare agreements between the debtor and creditors to be legally binding

on all creditors, including holdouts (Sachs, 1995; IMF, 1995; Chun, 1996; Schwarcz,

2000; Krueger, 2001; IMF, 2002; Hagan, 2005). Second, proposals to change bond

contracts—and, possibly, national laws—to encourage collective representation of bond

holders, again, with the objective that changes in payment terms agreed to by a

qualified majority of creditors (or at least of the holders of a particular bond) would

become binding for all bondholders (Eichengreen and Portes, 1995; Macmillan, 1995;

G-10, 1996; Eichengreen, 2000; Taylor, 2002).

In the event, none of these proposals were realized in time for the next generation

(1998-2005) of large debt crises. The idea of creating an “International Bankruptcy

Agency” was discussed at the G-7 Halifax summit in June 1995, but not pursued fur-

ther until IMF First Deputy Managing Director revived it in a speech in 2001. This

led to a period of frantic paper-writing and discussions both within the IMF and in

the public, but the proposal was ultimately shelved after the 2003 IMF Spring Meet-

ings, when it became clear that the United States would not support it. The idea of

improving creditor representation through changes in bond contracts had a bit more

success, arguably because it was viewed by creditors and some debtor countries as a

more market-friendly and hence preferable alternative to an international bankruptcy

regime. After being mostly ignored by emerging market issuers for many years, the

idea of incorporating majority restructuring clauses in New York law bonds became

popular in the first half of 2003, beginning with a widely reported international Mex-

ican Bond issue, which was followed by similar issues by Brazil, South Africa, Korea,

and other countries (IMF, 2003c). Furthermore, majority restructuring clauses and

5

similar collective action clauses had traditionally been incorporated in bonds issued

under U.K. law. However, with only one exception (Ukraine’s 2002 restructuring)

these clauses played no role in the major 1998-2005 restructurings (Table 1).

Hence, as several large emerging market issuers began to default or experience

debt servicing problems in the late 1990s (Russia, Ukraine, Pakistan, Ecuador, and

eventually Argentina), debt market participants faced a series of potentially daunt-

ing restructuring challenges without the benefit of virtually any of the institutional

improvements that the literature and official policy community had been urging for

years. Amazingly, however, with only one exception (Argentina’s external debt re-

structuring, completed in 2005) all major bond restructurings in the last decade

occurred at record speed (less than 2 years, compared to 5-8 years in the 1980s;

see IADB, 2006; Benjamin and Wright, 2008; Trebesch, 2008), and achieved very

high levels of creditor participation (over 90 percent). Furthermore–and again with

Argentina’s external restructuring as the only exception–none of the major restruc-

turings since 1998 led to significant litigation (Panizza, Sturzenegger and Zettelmeyer,

2008).

What happened? We argue below that collective action problems were avoided

through what in effect became a new mechanism for the resolution of debt crises

with dispersed bondholders, namely, take-it-or-leave-it debt exchange offers (usu-

ally preceded by informal discussions with some creditors) accompanied by minimum

participation thresholds, which made the offer conditional on sufficiently high partic-

ipation of other creditors, as well as some additional legal innovations. As we show,

the combination of a take-it-or-leave it offer with a minimum participation threshold

is sufficient to avoid pure coordination failures: a reluctance to accept a restructur-

ing offer for fear that the share of participating creditors will be too low to restore

solvency, and hence to make the offer credible. It does not, however, remove the “hold-

out problem,” that is, the incentive to hold out even when all others have accepted.

We interpret “exit consents” (or “exit amendments,” a legal innovation undertaken

6

at the time of the Ecuador exchange), as addressing specifically this problem.

Exit consents consist in amendments to the non-payment terms of the bonds being

exchanged–which in standard bond contracts is possible with simple majority–based

on the consent of the bondholders tendering their instruments. Although they leave

payment obligation of the sovereign are unaffected, these amendments can be designed

to remove legal protections, hence making holdout litigation more difficult, and to

make it harder to trade the instruments (Bucheit, 2000; Bucheit and Gulati, 2000;

IMF, 2003b). Specifically, in the case of Ecuador, exit consents removed a prohibition

on the further restructuring of Brady bonds tendered at the exchange, cross-default

clauses (which define default on other instruments as an event triggering acceleration

on the present instrument), negative pledge clauses (which limits debt dilution by

prohibiting the issuance of collateralized debt without consent of incumbent debt

holders) and the requirement to list the bonds at a major stock exchange. In the

cases of Uruguay and the Dominican Republic, cross-default, cross-acceleration, and

listing requirements clauses were also removed, and the sovereign immunity waiver was

amended in a way that protected payments on new bonds issued by these countries

from attachment by holders of the old bonds.1 We argue below that these changes

can be interpreted as changing the payoffs of incumbent bond holders in a way that

increases the costs of litigation. This removes the incentive to hold out, and hence

any remaining collective action problem.

3 Model

We present a simple model for the debt renegotiation process. As emphasized in the

introduction, the main points of the paper will not depend on the particulars of the

model.

Consider the problem of a country that has defaulted or is about to default on

1For a detailed discussion of Uruguay’s debt exchange, please refer to IMF(2003c).

7

its debt, and is offering creditors new bonds in exchange for the defaulted ones. If

creditors act collectively as a single entity, then this problem can be solved as a

standard bargaining game, with the outcome depending on the particular bargaining

solution used (e.g. Nash or Rubinstein bargaining). However, if creditors do not

act collectively, the problem becomes far more complex, creating scope for hold-out

and coordination problems. We abstract from the bargaining game between creditors

and debtors in order to focus on the collective action problems among creditors. We

illustrate these problems in a simple static set-up in which creditors face the choice

of accepting a one time take-it-or-leave-it offer or rejecting it and litigating.

Each creditor holds a bond with face-value 1, but the country can repay them at

most 1− h, where h < 1 denotes the minimum haircut that needs to be imposed on

average given the country’s available resources. The country offers creditors 1 − h,

where h > h is the haircut. If creditors decide to litigate, they incur a cost c and

with probability p litigants get first pick at the "pie" and can potentially seize up to

1 − h.With probability 1 − p litigants get nothing. We assume that if litigants are

successful, what is left of 1−h is distributed to creditors participating in the exchange(which only get paid at most 1− h).

The assumption that with probability p litigants get first pick at a limited “pie” is

clearly extreme: taken literally, it means that with some probability, litigants will not

only obtain a favorable judgement but will also collect in full (if there are not too many

of them), thereby shrinking the resources available to service the restructured debt.

This has only rarely been the case in actual sovereign debt litigation (Sturzenegger and

Zettelmeyer, 2007, Chapter 3). However, the presence of successful litigants imposes

a cost on the sovereign through a variety of channels, including by limiting the ability

to borrow freshly in international markets, and through reputational effects. To put

a stop to these costs, sovereigns are likely to sooner or later settle with litigants.

In this sense, successful litigants do in fact hold a claim on the resources of the

sovereign that competes with that of participating creditors. It is this broad feature

8

that is captured by the simple setup above. Thus, the simplifying assumptions of

our static model capture features that would emerge from a dynamic setting where

the immediate repayment of hold-outs would increase the debt burden, decreasing

the likelihood that the country would repay the participants once their debt comes

due. But as long as successful litigation harms participating creditors, the qualitative

results would remain the same, and for simplicity we focus on the static setting.

Let s denote the share of creditors accepting the offer. This simple setting can

yield multiple equilibria:

* Everyone litigating ( s = 0). Litigants get pay-off of 1− h− c with probability

p, −c otherwise (the pay-off is lower than 1-c because total payments to litigants stillbound by the available resources 1 − h). A participant would get nothing left with

probability p, and get 1− h otherwise. So, everyone litigating an equilibrium if:

p(1− h)− c > (1− p)(1− h) (1)

or:

h > 1− p(1− h)− c

1− p

* Everyone accepting (s=1). A litigant would get pay-off of 1− c with probability

p, −c otherwise. Participants get 1− h. This is an equilibrium if:

p− c < 1− h (2)

or

h < 1− p + c

*Internal Solution (s>h/h). Litigants get repaid in full (after costs) with prob-

ability p, and there are enough resources to repay participants 1 − h. This is an

9

equilibrium if people are indifferent:

p− c = 1− h

Note that this only holds for a particular level of h and that the country could

ensure full acceptance by lowering h by an infinitesimal amount.

*Internal Solution (h<s<h/h). In this internal solution, participants still get

repaid in full, but their repayment affects that of participants.

p− c = p1− h− (1− s)

s+ (1− p)(1− h) (3)

This equilibrium is not trembling-hand-perfect, since if one creditor were to switch

from litigating to accepting, then all the other creditors would be better-off accepting.

*Internal Solution (0<s<h). This is an equilibrium where participation is so low

that there is not enough resources to repay hold-outs in full when they are successful.

For this to be an equilibrium we need:

p(1− h)

(1− s)− c = (1− p)(1− h) (4)

This equilibrium is trembling-hand-perfect (if one litigant were to switch and

accept it would still be optimal for the other litigants to continue litigating, and if

one participant were to switch and litigate it would still be optimal for the other

litigants to litigate). Let sinternal denote the solution to the equation above:

sinternal = 1− p(1− h)

(1− p)(1− h) + c(5)

Since sinternal ∈ (0, h), we must have:

1− p− c

1− p< h < 1− p(1− h)− c

(1− p)

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3.1 Equilibria in Baseline Set-up

In this setup, equilibria depend on 4 parameters: the litigations prospects p, the

haircut offered by the country h, the resources available h,and the litigation cost c:

(i) p ≤ c: Unique equilibrium with everyone accepting (s = 1)

The returns to litigation are negative, since its cost is higher than the expected

repayment if successful. Thus, a creditor is better-off accepting regardless of the

haircut.

(ii) p > c.The equilibrium will depend on the size of the haircut:

(ii.a) If:

h < h ≤ 1−µp− c

1− p

¶< 1−

µp(1− h)− c

1− p

¶(6)

The hair-cut is sufficiently small that every creditor is better-off accepting rather

than litigating, and s = 1.

(ii.b)If:

1−µp− c

1− p

¶< h ≤ 1− (p− c) (7)

There are two equilibria: If everyone else accepts, a creditor is better-off accepting

as well (s = 1), but the internal solution given sinternal is also an equilibrium.

(ii.c) If:

1− (p− c) < h ≤ 1−µp(1− h)− c

1− p

¶(8)

The internal solution is the unique equilibrium. Note that for sufficiently small h,

1 −³p(1−h)−c1−p

´≤ 1 − (p − c) and this equilibrium set will be empty (the resources

available are such that either the country offers a small haircut, or there will be full

litigation).

(ii.d) If:

1−µp(1− h)− c

1− p

¶< h ≤ 1− (p− c) (9)

Full acceptance (s=1) and full litigation (s=0) are both equilibria. Note that depend-

ing on parameter values, this equilibrium set will be empty.

11

(ii.e)If:

1− (p− c) < 1−µp(1− h)− c

1− p

¶< h ≤ 1 (10)

Full litigation (s=0) is the unique equilibrium. Note that for sufficiently large h,

1 −³p(1−h)−c1−p

´> 1 (so the resources available are so small that litigation is not

worthwhile even if no one else is litigating).

In this setting, the country has some margin to move between these ranges by

varying h. For example, while offering a very high h will lead to the widespread

litigation, the country can prevent that by offering a lower haircut, if that is feasible

(e.g. if h<1−2p+c1−p ). We assume that the country’s objective function values the

amount of resources it keeps after the restructuring, while seeking to minimize the

size of the haircut offered (for example, due to reputational reasons) and seeking to

avoid litigation:

UCountry = 1− h− repayments− l(h)− g(1− s) (11)

where l() is an increasing function of the haircut (which we interpret as a general

reputational loss), and g(s) captures the cost of an unorderly resolution (g(0) = 0

implying no additional loss under full participation, g0 > 0 implying increasing losses

as the number of litigants increases).

Solving for the haircut offered by the country involves simple constrained opti-

mization. Since that result is not central to the paper (which focuses on the selection

of equilibria), we characterize that solution in the appendix.

3.2 Equilibria with exit consents and minimum participation

threshold

If the unique equilibrium to the baseline renegotiation problem is full participation,

then there is no need to introduce the exit consents or participation thresholds into

the offer. That will be the case if the haircut is small.

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Proposition 1 Full participation is the unique equilibrium when the haircut is suffi-

ciently small

Proof. If p ≤ c, s = 1 is the unique equilibrium. If p > c, a sufficiently small h

satisfies (7), which implies s = 1.

If the haircut is small so that full participation is one of the equilibria, but not

sufficiently small for it to be the unique one, then the minimum participation threshold

is enough to move creditors into the good equilibrium.

Proposition 2 If both the internal solution and full participation are equilibria, then

a minimum participation threshold s>sinternal ensures that full participation emerges

as the unique equilibrium in the modified game.

Proof. If s=1 is not an equilibrium, then accepting the offer is a best response

for any participation level s > sinternal. Every creditor is willing to accept an offer

that is automatically canceled by the participation threshold if s ≤ sinternal, and full

participation becomes the unique equilibrium.

If full participation is not one of the original equilibrium, then exit consents are

needed to destroy the value of litigation to the point that full participation becomes

an equilibrium in the modified game. Suppose the exit consents lower the probability

of success of litigation to ep.Proposition 3 If exit consents lower the probability of success of litigation to ep < c,

then full participation emerges as the unique equilibrium in the modified game with

exit consents.

Proof. If ep < c, then a creditor whose bonds have been mutilated by the exit

consents is better-off accepting the offer. Since the exit consents must be approved by

a majority of bond holders, they implicitly set a minimum participation threshold of

1/2.Thus, either the bonds will be affected by the exit consents, or the offer will fail,

13

making its acceptance a weakly dominant strategy, and the unique trembling hand

perfect equilibrium.

Note that in the setting above, the country has the power to set a very high

haircut while using the exit consents to force that outcome on its creditors. For

example, maximization of (11) would yield a solution h∗ such that:

l0(h∗) = 1

As discussed in the background section, it is likely that creditors could challenge

too aggressive a haircut in court if the exit consents took an expropriatory nature.

But as shown in the next section, there is also a market solution, whereby creditors

can coordinate themselves to prevent the exit consents from being used. Finally, note

that in this setting the exit consents achieve the same result that CACs would.

3.3 Equilibria with large players

So far we have assumed that creditors are atomistic. But since the exit consents need

to be approved by a majority of creditors, if a large creditor, or a coordinated group

of small creditors, controlled over half of the bonds it could effectively block them. If

the offer is sufficiently benign, then there is not point in undergoing costly litigation.

Suppose that if creditors were represented by a single negotiator, they would bargain

with the country. For example, if creditors can credibly commit to a take-it-or-leave-

it offer, they could demand a haircut eh. They could set that demanded haircut atthe level at which the country would be indifferent between full acceptance and full

rejection (in the latter case, the country could counter-offer an infinitesimally lower

14

haircut so as to minimize the loss stemming from l(h)):

(1− h)− (1− eh)− l(eh)− g(0) = p(1− h)− l(eh−)− g(1), or:eh = 1− p(1− h) + g(0)− g(1)

More generally speaking, we can consider the situation where the country and

consolidated creditor bargain over the haircut. The outcome would depend on the

particular bargaining solution (the literature typically considers either Nash or Ru-

binstein bargaining). For the sake of simplicity, suppose we take that bargaining

outcome hbargaining as given. Then:

Proposition 4 If a settlement hbargaining < h∗ does not yield full acceptance in the

original game but can be sustained with exit consents when creditors do not coordinate

their actions, then they would have incentives to coordinate in order to block the exit

consents and force the country to offer at least hbargaining

Proof. Provided a mass greater than 1/2 of creditors coordinates, they can block

the exit consents so the offer can be rejected. If all creditors coordinate can then

bargain with the country to achieve hbargaining

The result above illustrates that the exit consents do not provide a free pass for the

country: if it behaves too opportunistically it will create sufficiently large incentives

for creditors to coordinate.

In practice, the exit consents must be voted bond series by bond series. That is, a

creditor need only take a majority stake in a particular bond series in order to block

exit consents from mutilating its bonds. To the extent that bond issues typically tend

to be relatively small vis-a-vis a country’s overall indebtness, a creditor can take such

majority stake in a series while still remaining relatively small vis-a-vis creditors as

a whole. This can put creditors in a position where they can hold-out and ask for

a full repayment. Suppose that there are several bond series, and that a measure m

of creditors consist of these hold-outs that are protected from the exit consents. For

15

simplicity, assume that they buy all bonds in their respective series (so other creditors

cannot free-ride on them). The remaining share 1−m of creditors are still vulnerable

to the exit consents (so accepting the offer is still their dominant strategy). There is

a bound on how large m can be (since at some point the country will not be able to

repay them in full, or would prefer not to given its objective function).

If the m exit consent-proof hold-outs are only known after h has been announced

by the country, then they will only be repaid in full if the value of the country’s

objective function given that full repayment is higher than under the situation where

an orderly settlement is not achieved. We assume the country will incur the reputa-

tional loss l(h) based on the offer made to the participating creditors. That is, the

additional repayment to the hold-outs does not improve on that reputational cost.

The feasibility constraint for enough resources to be available to repay these creditors

in full is:

m ≤ (1− h)− (1−m)(1− h) (12)

The incentive compatibility for the country to repay them in full is:

1− h−m− (1−m)(1− h)− l(h) ≥ 1− h− pm− (1−m)(1− h)− l(h)− g(m), or(13)

m ≤ g(m)/(1− p) (14)

where the left-hand-side is the pay-off to the country given the full repayment of

those creditors and the left hand side is the one where they are only repaid if their

litigation is successful (so pm in expectation), but the country also incurs a cost g(m).

The expressions above implies:

m ≤ min((1− h)− (1−m)(1− h), g(m)/(1− p)) (15)

As expected, it increases with the cost of an unorderly restructuring, and with

the prospects of litigation. If a larger mass than the one above holds-out, the country

would rather risk an unorderly exchange than repay them in full. As argued in Section

16

2, in the actual world, the successful hold-outs have typically been small vis-a-vis the

total debt of the country, a pattern consistent with our model.

Note that if a sharem0 > m were to hold-out, the hold-outs would have incentives

to coordinate among themselves. For example, provided:

m+ (m0 −m)h > pm

The m0 hold-outs would be collectively better-off by uniting and keeping their com-

bined litigation to m so they could be repaid in full. Of course, that does not mean

that they would do so as that involves a collective action problem (for example, a hold-

out among the hold-outs trying to be repaid in full at the other hold-outs expense).

These results imply:

Proposition 5 If there are several bond series, a share m < 1/2 of creditors may

be able to block exit consents on their bond holdings. Provided (15) holds, they will

be repaid in full. Otherwise, a litigious exchange will take place. Hold-outs may be

collective better-off capping m to (15), but standard collective action problems may

prevent them from doing so.

Finally, we can consider the case where the number of bond series is sufficiently

large, that a large number of groups of creditors can coordinate into owning majority

stakes in each series. As an extreme, suppose that every creditor groups with the

other creditors of its bond series, so that all debt holders can block exit consents. In

this case, we are back to square one, where multiple equilibria may arise:

Proposition 6 In the limit where there are several bond series and all creditors are

in groups that can block exit consent, if full participation is not an equilibrium in the

original setting, then it cannot be achieved with exit consents.

Thus, while exit consents are a powerful way of inducing creditors to participate,

their inability to operate across different bond series can lower the barriers to blocking

17

them to the point that we are back to the original setting. Note that if full participa-

tion is an equilibrium in the original setting it can still be achieved through minimum

participation thresholds. But if not, exit consents will no longer achieve it.

The same limitations on the use of exit consents apply to CACs, which also have

to be voted separately for each bond series. Thus:

Proposition 7 Collective Action Clauses that require a majority approval in each

bond series cannot induce full participation if groups of creditors control majority

stakes in bond series, and full participation is not an equilibrium in the original set-

ting.

4 Discussion

In a sense, the results in this paper have come full circle. We started in a typical

setting where collective action problems can lead to an inefficient break down in the

debt renegotiation process (to the detriment of both country and creditors as a whole).

We then showed that two innovative features: minimum participation thresholds and

exit consents can ensure the achievement of the good equilibrium. But that result

can break down in a realistic setting where the exit consents (or CACs) are voted for

each bond series separately, and as a result even a relatively small share of bonds can

block them, and we could potentially be back to the original setting.

One implication of our results is that major coordination gains could be achieved

through aggregation of the different bond classes. That is, if a majority of creditors as

a whole could amend a covenant against the will of a minority of creditors commanding

a controlling stake in a particular series. Such aggregation cannot be done through the

use of exit consents, but we could move into that direction if CACs began including

aggregation clauses. One argument against such move is that it may concentrate too

much power in the hands of the country. As shown in our model, the only constraint

on the country at that point could be the reputational cost of an overly aggressive

18

default. Depending on the size of that cost, creditors may be better-off dealing with

a messy renegotiation process than with a simple one where the country can de facto

make a take-it-or-leave-it offer. A balance must be achieved, where the country has

tools to impose a small haircut required to restore debt sustainability on creditors,

but has limited scope to use those tools to seek too favorable an exchange.

19

A Appendix

Solving for the country’s problem:

When choosing the haircut in the baseline model, the country will take into ac-

count the different equilibria the offer may imply. Below we characterize that choice

for the different parameter ranges described in Section X.

Let Vi denote the country’s problem in equilibrium (i) where p ≤ c and full

participation is the unique equilibrium:

Vi = maxh{(1− h)− (1− h)− l(h)}

s.t.h ≥ h, p ≤ c

If p > c, the solution to this problem is empty, otherwise, it is h∗i , where:

h∗i = max(h, hinti ), where l

0(hinti ) = 1

If p > c, the country’s problem depends on the range of parameters for h consid-

ered. For the next maximization problems we assume that to be the case (otherwise,

the solution would be empty).

In the first range, where full participation remains the unique outcome, it solves:

Viia = maxh{(1− h)− (1− h)− l(h)}

s.t.h < h ≤ 1−µp− c

1− p

¶, p > c

whose solution is:

h∗iia = minµmax(h, hintiia), 1−

µp− c

1− p

¶¶, wherel0(hintiia) = 1

The expression above indicates that the country will choose the internal solution

(if it lies within the bounds for h), and the upper (lower) corner if the internal solution

20

is higher (lower) than the bounds for h.

For the next parameter range (iib), both full participation and the internal solu-

tion are equilibria. Let π1 denote the country’s subjective probability that the full

participation equilibrium will be selected. Its problem is:

Viib = maxh{(π1 + (1− π1)(1− p))((1− h)− (1− h))− l(h)− (1− π1)g(1− s)}

s.t.1−µp− c

1− p

¶< h ≤ 1− (p− c), p > c

The solution, (still assuming p > c, so the solution is not empty) is given by:

h∗iib = minµmax

µ1−

µp− c

1− p

¶, hintiib

¶, 1− (p− c)

¶,

where l0(hintiib )− (1− π1)g0(1− s(hintiib ))s

0(hintiib ) = π1 + (1− π1)(1− p)

where s(h) is the internal solution (5).2 Again, the notation above implies that

the country chooses the internal solution if possible, and the upper (lower) corner if

the internal solution is higher (lower) than the bounds for h.

For the next parameter range the internal solution is the unique equilibrium:

Viic = maxh(1− p)((1− h)− (1− h))− l(h)− g(1− s)

s.t 1− (p− c) < h ≤ 1−µp(1− h)− c

1− p

¶, p > c

And the solution (if not empty) is given by:

h∗iic = minµmax

µ1−

µp− c

1− p

¶, hintiib

¶, 1− (p− c)

¶,

where l0(hintiic )− g0(1− s0(hintiic ))s0(hintiic ) = (1− p)

2Note that the internal solution is monotonic on h since both l0(h) and -g0(1 − s(h)) s0(h) arenegative (s∗ is monotonically decreasing on h).

21

For the parameter range where the two corner solutions are equilibria, and the

country’s subjective probability that s = 1 is selected is π1, we have:

Viid = maxh{(π1 + (1− π1)(1− p))((1− h)− (1− h))− l(h)− (1− π1)g(1)}

s.t.1−µp(1− h)− c

1− p

¶< h ≤ 1− (p− c), p > c

If the solution is not empty, it is given by:

h∗iid = minµmax

µ1−

µp(1− h)− c

1− p

¶, hintiib

¶, 1− (p− c)

¶,

where l0(hintiid ) = π1 + (1− π1)(1− p)

Finally, in the parameter range where full litigation is the unique equilibrium, the

problem is:

Viie = maxh(1− p)((1− h)− (1− h))− l(h)− g(1)

s.t 1−µp(1− h)− c

1− p

¶< h ≤ 1, p > c

the solution (if non-empty) is:

h∗iie = minµmax

µ1−

µp(1− h)− c

1− p

¶, hintiie

¶, 1

¶, where l0(hintiie ) = (1− p)

Note that since the constraints on the problems above span all possible values for

p and h, at least one of the problems has a non-empty solution set. The country’s

offer will be the one that maximizes its pay-off:

h = argmax(max(Vi, Viia, Viib, Viic, Viid, Viie))

22

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