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Improving Sovereign Debt Restructurings

WP 22-06

Maximiliano Dvorkin
Federal Reserve Bank of St. Louis
Juan M. Sánchez
Federal Reserve Bank of St. Louis
Horacio Sapriza
Federal Reserve Bank of Richmond
Emircan Yurdagul
U. Carlos III and CEPR

Improving Sovereign Debt Restructurings∗
Maximiliano Dvorkin Juan M. Sánchez Horacio Sapriza Emircan Yurdagul
FRB of St. Louis

FRB of St. Louis

FRB of Richmond

U. Carlos III and CEPR

April 6, 2022
Abstract
The wave of sovereign defaults in the early 1980s and the string of debt crises in subsequent decades have fostered proposals involving policy interventions in sovereign debt
restructurings. The global financial crisis and the recent global pandemic have further
reignited this discussion among academics and policymakers. A key question about these
policy proposals for debt restructurings that has proved hard to handle is how they influence the behavior of creditors and debtors. We address this challenge by evaluating policy
proposals in a quantitative sovereign default model that incorporates two essential features
of debt: maturity choice and debt renegotiation in default. We find, first, that a rule that
tilts the distribution of creditor losses during restructurings toward holders of long-maturity
bonds reduces short-term yield spreads, lowering the probability of a sovereign default by 25
percent. Second, issuing GDP-indexed bonds exclusively during restructurings also reduces
the probability of default, especially of defaults in the five years following a debt restructuring. The policies lead to welfare improvements and reductions in haircuts of similar
magnitude when implemented separately. When jointly implemented, they reinforce each
other’s welfare gains, suggesting good complementarity.
JEL Classification: F34, F41, G15
Keywords: Crises, GDP-indexed Debt, Distribution of Creditor Losses, Default, Sovereign
Debt, Maturity, Restructuring, Country Risk, International Monetary Fund

∗

The views expressed in this paper are those of the authors and do not necessarily reflect those of the Federal Reserve Bank

of St. Louis, the Federal Reserve Bank of Richmond, or the Federal Reserve System. Yurdagul gratefully acknowledges the grant
IJC2018-038229-I by MCIN, grant 2020/00369/001 by AEI, grants EPUC3M11 (V PRICIT) and H2019/HUM-589 by Comunidad de
Madrid.

Introduction

The sovereign debt crises of the last decades, including those in Latin America in the early 1980s,
Russia (1997-1998), Argentina (2001-2002), Greece (2011-2012), and Ukraine (2015), among others, have encouraged the development of policy frameworks aimed at improving both the structure
of sovereign debt and the resolution of sovereign debt crises. Most recently, the large increases
in sovereign debt after the COVID-19 pandemic resurfaced concerns about debt sustainability.
Thus, the international economic landscape has raised the need to think more about policies
that may affect the debt restructuring process and outcome, and that may therefore provide
tangible recommendations for dealing with debt default resolutions. The proposals (e.g., Alfaro
and Kanczuk, 2006; IMF, 2017, 2020) have included the development of practices and instruments that improve incentives for borrowers and creditors to agree on a prompt, orderly and
predictable restructuring of unsustainable debt, as well as lowering debt levels and lengthening
debt maturity, among other measures.
The large and growing literature on quantitative sovereign default models in the tradition
of Eaton and Gersovitz (1981) has advanced our understanding of the causes and consequences
of default, the dynamics of emerging-market bond yields, and the issuance of debt of different
maturities by developing countries. However, by and large, policy proposals to resolve sovereign
debt crises are grounded on empirical analysis of previous default and restructuring episodes, or
based on policymakers’ and analysts’ judgments, with a minimal contribution to this debate—if
at all—from quantitative models of sovereign default.1 This disconnect stems mainly from the
difficulties in solving and computing rich and sophisticated models that capture many characteristics of emerging countries’ default, maturity choice, and restructuring decisions. In this
paper, we bridge such disconnect using a debt renegotiation framework based on Dvorkin et al.
(2021) that rationalizes several stylized facts of sovereign debt restructurings and microfounds
the behavior of creditors and debtors. It thus serves as a laboratory to gain insights into the role
1

For example, the extensive discussions on sovereign debt restructurings in the recent works compiled in
Guzman et al. (2016) and Abbas et al. (2019) focus on important institutional details, review the results of
previous restructuring episodes, and analyze the merits of different restructuring proposals. However, none of
these discussions is rooted in quantitative models of default.

of frequently-mentioned policy interventions on the behavior of economic agents and how these
shape debt restructuring outcomes and sovereign debt dynamics in general.
The IMF (2002) states that, “A sovereign debt restructurings mechanism (SDR) should aim
to preserve asset values and protect creditors’ rights, while paving the way toward an agreement
that helps the debtor return to viability and growth.” We analyze two policies that are directly
linked to these main reasons for conducting restructurings. Our first policy relates to asset
values and creditors’ rights. We assess the impact of alternative distributions of losses across
lenders holding sovereign bonds of different maturities. One major source of uncertainty in
sovereign debt restructurings is how to resolve inter-creditor equity issues.2 One aspect of this
complex issue that has proven particularly difficult to address is the treatment of claims with
different residual maturities. Moreover, framing these discussions in quantitative equilibrium
default models poses unique challenges. Our model allows us to overcome these challenges. The
results of our analysis suggest that a rule that tilts the distribution of creditor losses during
restructurings toward holders of long-maturity bonds reduces short-term yield spreads in bad
times, reducing the default probability of the sovereign during periods of elevated credit market
stress.
Our second policy relates to debt instruments that may help the debtor return to viability
and growth. We evaluate the use of GDP-indexed bonds during sovereign debt restructurings. As
pointed out in 2012 by the United Nations Economic and Social Council (ECOSOC), borrowers
would benefit from some “breathing space” after debt restructurings. GDP-indexed debt is an
instrument that has been widely discussed in policy circles as a tool for debt management and
sovereign risk-reduction that could help improve the resilience of public finances to economic
downturns and thus strengthen public debt sustainability. There is also broad recognition that,
except for cases in which GDP-indexed bonds are introduced in the context of a debt restructuring, it would require several years of consistent issuance before the share of these bonds in total
government debt became large enough to significantly enhance the resilience of public debt to
adverse economic shocks (see Barbieri Hermitte, 2020). In light of these considerations, we study
a policy where the country can issue GDP-indexed bonds with choice of maturity in the context
2

See, for example, IMF (2013a).

of a debt restructuring. Our analysis suggests that using GDP-indexed bonds during distressed
debt restructurings can contribute to remedying the lack of market access experienced by troubled borrowers and significantly reduce the probability of repeated restructurings. Furthermore,
Consiglio and Zenios (2018) observe that the prevalent early form of GDP-contingent debt was
that of GDP warrants, also known as value recovery rights, whereby additional payments were
made when output growth exceeded a threshold or another favorable event occurred. Such instruments were used in several restructurings, including Mexico, Nigeria, Uruguay, Venezuela,
Argentina, Greece, and Ukraine. The authors also point out that the G20 meeting in Chengdu,
China, in July 2016, revived the idea of GDP-contingent debt, but focused instead on cash instruments that pay differentially both on the upside and downside, depending on growth, which
they refer to as GDP-linked bonds.3 Following this distinction in the literature, we provide a
comparative analysis of the pricing and hedging implications of these two types of GDP indexation, and we find that GDP-linked bonds have more substantial effects on the recurrence of
defaults than asymmetric adjustment schemes like GDP warrants.
We evaluate the welfare gains of the two central policies discussed above. To this end,
we complement the equivalent consumption measure commonly used in the literature with a
measure that takes into account the presence of disagreement between the rate of discount of the
government and that of the households, following Aguiar et al. (2020). The disagreement reflects
that generally, the government may be more impatient than individuals because of political
economy considerations. This assumption implies that individuals prefer policies that reduce the
amount of debt and the rate of default. Therefore, without disagreement, there is a potential bias
in the welfare results, as gains favor policies that increase debt just because the model requires
an impatient government to capture the debt dynamics of emerging markets. To the best of our
knowledge, this is the first paper in the quantitative sovereign default literature that considers
disagreement when evaluating policy welfare in the context of debt restructurings. Our results
indicate that welfare gains are noticeably smaller when considering this effect, which suggests
caution when reading into the welfare gains derived in this literature.
3

Paragraph 11 of Communiqué G20 Finance Ministers and Central Bank Governors Meeting, G20 Web Site, 28
July 2016, available at http://www.g20.utoronto.ca/2016/160724-finance.html, last accessed February 14, 2018.

We use our quantitative framework to show that policy rules for indexing debt to GDP growth
and distributing losses across investors holding bonds of different maturities yields welfare gains
for a wide range of policy specifications. While we consider simple parametric rules, our setup
is designed as a general platform to perform more exhaustive searches for rules that maximize
welfare gains.
Our study is the first to evaluate indexation and investor loss distribution policies in a model
with endogenous debt maturity and restructuring. Such model features capture well-documented
stylized facts of sovereign debt and are essential to correctly evaluate the policies we study. Our
findings of welfare gains via the redistribution of losses of investors of different maturities rely
on an analysis that would be unfeasible without a maturity choice framework like the one we
consider. Similarly, our findings of welfare gains due to debt indexation speak to the “too little,
too late” concern regarding restructurings raised by Guzman et al. (2016) and others. In this
regard, the high exit yields generally observed in the data are consistent with the notion that
countries tend to be quite vulnerable to a recurring default immediately after a restructuring.
Therefore, it is particularly valuable for the country to have access to a risk-sharing debt instrument during reentry to credit markets. Finally, while the quantitative default literature has
given more attention to GDP indexation policies than to investors’ loss redistribution policies,
our welfare results indicate that the gains of the two policies are of similar magnitude. In this
way, our findings suggest that more attention should be paid to creditor loss distribution policies.
Finally, the joint implementation of the policies delivers larger welfare gains that suggest some
amplification effects are present.
Our analysis builds on the literature of sovereign default models initiated by Eaton and
Gersovitz (1981) and mainly borrows from three branches of this literature. First, we relate
to studies on sovereign default and maturity choice. While a significant portion of the literature on quantitative models of sovereign debt default has used one-period debt (e.g., Aguiar
and Gopinath, 2006; Arellano, 2008) or exogenous long-maturity bonds following Hatchondo and
Martinez (2009), the endogenous maturity choice approach in our model is necessary for evaluating any policies involving the distribution of maturity holdings across investors. Our model
of debt maturity choice, following Sánchez et al. (2018), is simply the choice of a discrete num4

ber of periods for which the country promises to make constant payments. This approach has
proven computationally convenient for applying dynamic discrete choice methods. The alternative model of maturity choice, developed by Arellano and Ramanarayanan (2012), allows for the
choice of duration (not maturity) with a perpetual bond that promises payments decaying at a
fixed rate and a 1-period bond. Thus, payments are concentrated in the year after issuance, a
feature that is quite inconvenient to represent issuances after debt restructurings.
Second, our paper closely relates to recent models on sovereign default and restructurings.
The first model that combined the Eaton and Gersovitz (1981) framework with debt renegotiation
was the study by Yue (2010) that considered a Nash bargaining approach. Asonuma and Trebesch
(2016) and Asonuma and Joo (2020) study different aspects of sovereign debt restructurings in
the context of one-period bond models. Mihalache (2020) explores sovereign debt restructurings
and maturity extensions based on political economy considerations, and maturity choice as in
Arellano and Ramanarayanan (2012). Recent complementary work by Arellano et al. (2019)
focuses on the role of partial defaults on restructuring dynamics.4
We extend the model of sovereign debt default and renegotiation developed by Dvorkin et al.
(2021), which accounts for the most salient features of debt restructurings such as delays, haircuts,
and maturity extensions, by incorporating the policy dimensions mentioned earlier. The focus
in Dvorkin et al. (2021) is to understand the key determinants of face-value haircuts and debt
maturity extensions that are a prevalent feature of the resolution of sovereign debt crises observed
in the data. Our analysis here extends that framework to incorporate (i) a rule to redistribute
losses among holders of different maturity and (ii) a rule to adjust yearly debt payments as a
function of output growth. The main contribution is on studying the effects of these policy
proposals on the behavior of creditors and debtors away and around default.5 Specifically, here
4

There is also an analysis of debt restructuring in a simple two-periods model by Fernandez and Martin
(2014). They discuss the gains of policy interventions in restructuring using a two-period model with legacy debt
maturing in the first period (“short term debt”) and in the second period (“long-term debt”). They find that the
redistribution of losses across holders of different maturity does not matter. Having only two periods does not
allow for our maturity mechanism to work. With more than two periods there would be maturity choice also in
the intermediate period and the redistribution policy would help to prevent defaults, as we show.
5
As in Dvorkin et al. (2021), here we also build on the endogenous maturity framework developed in Sánchez
et al. (2018), in which the maturity of the debt portfolio is a discrete variable. However, the latter paper abstracts
from sovereign debt restructuring and policies affecting the resolution of sovereign debt crises.

we study how different restructuring policies affect the cost of borrowing at different horizons, the
unconditional probability of default, the chances that countries default shortly after restructuring,
and welfare.
Last, our paper relates to studies on sovereign default that analyze GDP-indexed bonds,
such as Sandleris et al. (2009), Hatchondo and Martinez (2012), Barr et al. (2014), and more
recently Roch and Roldán (2021). In contrast to our study, such papers do not consider issuing
these bonds exclusively after restructuring. An advantage of considering the issuance of GDPindexed bonds exclusively in restructuring is that they have a significant economic impact while
only modestly modifying the current regulatory framework. The driver of this finding is that
countries remain excluded from financial markets for several years following a debt restructuring
episodes, as shown by Cruces and Trebesch (2013). Having a policy that represents a small
change to the status quo should make it a more appealing to international investors, which
should help alleviate adoption and liquidity concerns of these instruments, a problem that is
generally associated with indexed bonds.
In addition, the literature considers indexed bonds in models that exclude endogenous restructuring, have short-term bonds or exogenous maturity, and that generally do not distinguish
GDP warrants from GDP-linked debt instruments. Our results highlight the importance of including these features. For example, the introduction of these bonds have a significant effect on
haircuts, something that previous literature failed to capture.6
The remainder of the paper is organized as follows. Section 2 presents the two policy interventions under study, section 3 introduces the modeling framework to evaluate the policies, section
4 describes the calibration of the model and its quantitative business cycle properties, section
5 extends the basic model to incorporate the policy interventions, while section 6 evaluates the
implications of each of the policy interventions in restructurings for debt price, maturity profile,
and quantity dynamics. Section 7 evaluates the welfare implications of each policy, and section
8 evaluates the robustness of the results to different economic characteristics of the sovereign.
Last, section 9 assesses the effects of the joint implementation of the two policies on key debt
6

Our work also relates to studies discussing other types of default resolution or prevention mechanisms (e.g.,
Bianchi, 2016; Roch and Uhlig, 2016).

and macroeconomic moments, and section 10 concludes.

Previous Proposals and International Experience

This section discusses proposals for sovereign debt restructuring arrangements and related international experiences that we analyze in the following sections using a quantitative model of
sovereign default with endogenous restructuring and debt maturity choice.

2.1

A Rule for Distributing Losses across Creditors

A key issue affecting coordination among bondholders in sovereign debt restructurings is that it
is unclear how to redistribute the losses across creditors holding bonds of different maturities. In
particular, as shown empirically by Asonuma et al. (2015), creditors with short maturity securities
tended to suffer significantly more losses than creditors with long maturity securities during
recent sovereign debt restructuring episodes. We evaluate the implementation of a mechanism
that determines how to redistribute losses.
Proposals for strengthening the arrangements for sovereign debt restructurings aim to restructure unsustainable debt more orderly, predictably, and rapidly. The IMF has recognized
that achieving these objectives requires addressing several weaknesses in the existing sovereign
debt restructuring system.7 One aspect of restructurings where these challenges are present involves the way different types of creditors can “vote” for a debt resolution mechanism, and how
to aggregate their choices. Notwithstanding the potential benefits of aggregation, on different
occasions the IMF has highlighted the fear that strong aggregation mechanisms could lead to
inter-creditor equity concerns where, for example, a majority of creditors holding a certain type
of claims impose an agreement on a minority of creditors that hold very different claims. Such
a problem could arise where the aggregation involves claims of different seniority or where the
claims being aggregated continue to have different maturities.8 Clearly, creditors with differing
residual maturities have differing economic interests. If all creditors holding non-defaulted claims
7
8

See IMF (2003a).
See IMF (2003b) and IMF (2013b)

were forced to accept the same long-term instrument in a restructuring, creditors holding claims
with relatively short residual maturities would bear a disproportionate burden compared to those
holding claims with relatively long residual maturities9 .
This “one size fits all” approach was implemented in the Greek sovereign debt restructuring
in 2011-2012. The symmetric treatment of bonds in Greece created much larger NPV haircuts
for holders of shorter-dated bonds. Zettelmeyer et al. (2013) consider alternative ways that could
have increased debt relief or reduced the large amount of EFSF10 -financed cash incentives. From
that perspective, the study argues that the “one size fits all” approach of offering the same bundle
of new bonds and cash to all investors, irrespective of the maturity of their old bonds, and with
no distinction between foreign law bonds and Greek law bonds, was the costliest mistake in the
design of the Greek debt restructuring. They show that imposing a 70 percent haircut on all
investors would have resulted in an additional debt relief of almost €30 billion in face value terms
and €23 billion in present value terms. A 70 percent haircut would have been lower than the
haircut that was deemed to be acceptable for short-term creditors (about 80 percent), and thus
surely feasible. The work by Zettelmeyer et al. (2013) also points out three reasons motivating
the one-size-fits all approach: First, the intention to keep things simple in order to get the deal
done before March 20, 2012 when the next very large bond was coming due (€14.4 billion);
second, that the members of the creditor committee were likely mostly invested in longer-dated
Greek instruments; and third, that the so-called Troika11 , Greece, and the creditor committee
may have been sympathetic to taking a tough approach against short-term creditors, many of
which had deliberately bought short-dated instruments at large discounts in the hope of still
being repaid in full.
The above discussion of the aggregation of creditor claims and the corresponding distribution of creditor losses during the Greek sovereign debt restructuring applies to other episodes.
The “one size fits all” resolution approach has been documented for other exchanges, including
9

Other contractual features equal, a longer relative maturity extension implies a larger reduction in the present
value of the claim
10
European Financial Stability Facility
11
Troika in the context of the Greek debt restructuring refers to the European Debt Commission, the European
Central Bank, and the International Monetary Fund

Pakistan in 1999, Moldova in 2002, and Cote D’Ivoire in 2010. While restructurings offering
the same menu of new instruments across creditors tilt losses toward short-term bondholders,
Asonuma et al. (2015) reports more generally a difference in haircuts associated with a difference
in the maturity of instruments, where haircuts on short-term debt are more extensive than those
on long-term debt. Over their sample of recent restructurings, the study documents an average
difference of 17.2 percent in haircuts on short-term versus long-term debt.
Therefore, the analysis of the distribution of losses across creditors holding instruments of
different maturities can help make the process of debt restructuring more predictable by improving creditor coordination and facilitating the resolution of inter-creditor equity concerns.
Such changes to creditors’ conditions during restructurings may directly affect bond pricing and
bondholding incentives across maturities, impacting a country’s default incentives and welfare.
Our analysis quantitatively evaluates these transmission channels.

2.2

GDP-Indexed Bonds Issued in Restructurings

Since the theoretical arguments in favor of contingent debt for sovereigns discussed by Krugman
(1988) and Froot et al. (1989), and the work by Shiller (1993) proposing the idea of GDP-indexed
bonds, it has been increasingly discussed in academic and policymaker circles. The idea behind
these instruments is straightforward: by improving risk-sharing between the borrowing country
and international creditors, GDP-indexed bonds may diminish the probability of debt crises and
increase welfare. The string of sovereign debt crises, especially since the 2000s, renewed the
interest in using GDP-indexed debt as part of the design of sovereign debt contracts. Drèze
(2000) suggested the use of GDP-indexed bonds as part of a strategy to restructure the debt of
the poorest countries.
In 2001, Argentina experienced one of the largest sovereign debt defaults in emerging markets.
In March 2005, Argentina concluded the restructuring of its debt. One distinctive element of the
restructured debt was that it included an instrument called GDP-warrant, whereby a sizeable
share of the debt payments was linked to the evolution of Argentina’s GDP.
A few years later, the European debt crisis led policymakers to ponder once again the pos-

sibility of issuing debt indexed to real variables (i.e., real-indexed debt contracts). Under the
Greek debt exchange terms in March 2012, Greek bondholders were offered three new securities
in exchange for existing Greek bonds: One and two-year EFSF bonds and new 30 year global
greek bonds (GGBs) with a step-up coupon and GDP warrants. The GDP warrants were a small
sweetener, equivalent to about 0.2 percent of the original notional, or around 400 million euros.
The GDP warrants were set to mature on October 15, 2042.
More recently, Ukraine issued GDP-linked securities, known as warrants, to creditors who
wrote down 20 percent of bonds’ original values as part of a 2015 debt restructuring. The
warrants pay out if Ukraine’s economic growth exceeds certain thresholds.12
The IMF (2017) acknowledges that, in spite of potential benefits for using GDP-indexed
bonds, the frequency of these instruments in the financial markets is rather low. Accordingly, the
report suggests a potential role for the IMF to facilitate the take-up of these assets. More recently,
and largely motivated by the macroeconomic uncertainty and debt sustainability concerns in
several emerging economies as a result of the COVID-19 pandemic, the IMF (2020) has strongly
emphasized the relevance and encouraged the exploration of state contingent debt instruments
in the specific context of sovereign debt restructurings.
Our paper analyzes both qualitatively and quantitatively how the introduction of GDPindexed sovereign debt contracts affects borrowing, default, and the outcome of debt restructurings.

A Laboratory for Policy Evaluation

We consider a small open endowment economy a la Eaton and Gersovitz (1981) with a government
and hand-to-mouth consumers. The government participates in international credit markets
where lenders are risk-neutral. It cannot commit to repaying its obligations, so it has two
actions to choose from, given an outstanding amount of assets, b (debt if b < 0). The first option
is to pay its obligations and hence keep its good credit status. Alternatively, the government
may decide not to make its debt payment, i.e., default. After default, the country faces some
12

See Borensztein and Mauro (2002) for an early analysis of GDP-indexed bonds.

periods of financial autarky and an output loss. In the following periods, the government may
restructure its debt and get back to international credit markets.
In times of good credit status, the country may face two regimes in international credit
markets. Normal times are represented by a = 0, and times of distress in international credit
markets are represented by a = 1. In times of distress, the government does not have access to
borrowing and is limited to making the promised payments or default.13
The default decision is also influenced by the current level of debt, b, and its maturity, m, by
the country’s income, y, which fluctuates exogenously over time, by the costs of default, and by
the expected terms of the restructuring.
The conditions of the debt restructuring are endogenously determined as in Dvorkin et al.
(2021). Each period in default, either the lender or the borrower has a chance to make a
restructuring offer to the other party. Once there is an agreement on the value of the new debt,
the country chooses the maturity of that debt conditional on delivering the agreed market value
of the new bonds.

3.1

The problem of the sovereign in good credit standing

The value for the country when in good standing is
n
o
V G (y, a, b, m) = max V D (y, b, m), V P (y, a, b, m) ,
where V D and V P are the values if the country chooses to default and pay its debt, respectively.
The policy function for default D(y, a, b, m) takes value 1 if default is chosen, and 0 otherwise.
The value in case of default is
V D (y, b, m) = u(y D ) + βEy0 |yD V R (y 0 , b, m),
where y D = min {y, π} captures the default cost on endowment. V R is the value of a country in
13

We relate these episodes of financial distress in international markets as sudden stops of capital flows which
affect a large number of emerging market economies at the same time and are not closely linked to changes in
fundamentals of individual countries.

restructuring that will be explained in the next subsection.
Countries may issue bonds with different maturities when they are in good credit standing. Since modeling a debt portfolio with many different types of bonds in terms of per-period
payments and maturity would make the problem computationally intractable, we impose a restriction on the structure of the debt portfolio following Sánchez et al. (2018). We assume that,
at any point in time, the debt portfolio is characterized by the promised level of per-period
payment, b, and by the number of periods that these payments will be made (debt maturity),
m. The government optimally chooses b and m when it borrows. The portfolio may consist of
any number of bonds, and whether it is composed of a single bond or several bonds is irrelevant
in this framework, as we show next with some examples. The key restriction is that the profile
of payments of the selected debt portfolio is constant, so the portfolio can be characterized with
just two state variables, (b, m), making the problem tractable.14
Thus, a country’s “bond portfolio” is described by a fixed payment, b, and its maturity, m,
and its value is b×q(y, a, b, m; m). As the portfolio may consist of any number of bonds, the value
of a portfolio that pays b̃ < b for m, given a country’s portfolio characterized by (b, m), is simply
b̃ × q(y, a, b, m; m). This pricing is possible because q is the price per unit of the yearly payment.
To interpret the “m” after the semicolon, note that, given a country’s portfolio characterized
by (b, m), the market value of a bond that pays b̃ < b for n < m periods is b̃ × q(y, a, b, m; n).
Similarly, we can obtain the market value of a (zero coupon) bond that pays b̃ < b in m years,
given a country’s portfolio characterized by (b, m), by just subtracting the value of two different
portfolios, b̃ × [q(y, a, b, m; m) − q(y, a, b, m; m − 1)].15
14

For simplicity we assume the same payment b each period until the bond fully matures. However, it is
possible to relax this assumption and have a bond portfolio with a different payment profile, either increasing
or decreasing over time. This would not add important computational costs to the extent that this profile is
exogenously parameterized.
15
To further illustrate our notation, consider the following example. Suppose that the country has a debt
portfolio with maturity of four periods and total per-period payment of b, that is, {b, b, b, b}. Assume that the
portfolio consists of three bonds with payment promises
{b, b, b, 0},

(bond 1)

{b − b, b − b, b − b, 0}, and

(bond 2)

{0, 0, 0, b}.

(bond 3)

With this notation at hand, the value if the country repays the debt is
V P (y, 0, b, m) = max
u(c) + βEy0 ,a0 |y,0 V G (y 0 , a0 , b0 , m0 ),
0
0
b ,m

subject to
c = y + b − q(y, 0, b0 , m0 ; m0 )b0 + q(y, 0, b0 , m0 ; m − 1)b .
|
{z
} |
{z
}
market value of new debt

market value of old debt

The country chooses an integer m0 ∈ {1, 2, ..., M } representing the number of periods that will
make payments of b0 .16 Reading the constraint suggests that the government sells a new bond
that promises to pay b0 for m0 periods and it buys the old debt (or a bond that pays b for
m − 1 periods) at market prices, q(y, 0, b0 , m0 ; m − 1)b. Here q depends on b0 , m0 because prices
are forward looking and these two values describe the state of the country in the next period.
Note also that this price is multiplied by the old size of payments, b, and is has m − 1 after
the semi-colon because the old payments of b were promised last period for m periods and one
payment has been made, resulting in m − 1 payments outstanding.17
Note that since the repurchase transaction in this representation happens at market prices,
this constraint can be rewritten such that the interpretation is that countries issue only the
difference between the old portfolio (after this period’s repayment) and the desired one, as
represented in Figure 1. Adding and subtracting bq(y, 0, b0 , m0 ; m0 ) + (b0 − b)q(y, 0, b0 , m0 ; m − 1)
The value of each bond is
b × q(y, a, b, 4; 3),

(bond 1)

(b − b) × q(y, a, b, 4; 3), and

(bond 2)

b × [q(y, a, b, 4; 4) − q(y, a, , b, 4; 3)] ,

(bond 3)

respectively. Adding the value of these three bonds we obtain the value of the portfolio, b × q(y, a, b, 4; 4). These
prices provide very useful notation for the country’s choice of maturity and highlight that a wide array of bonds
can conform the total borrowing portfolio of the country in our setup.
16
Since our calibration is yearly, choosing M = 20 is enough to guarantee that there is no instance in which
countries would like to choose m0 > M .
17
Note that in the special case of m = 1, the country’s legacy debt consisted of one-period bonds, thus the
constraint is c = y−b0 q(y, 0, b0 , m0 ; m0 )+b, as q(y, a, b0 , m0 ; 0) = 1, which highlights that after making the payment,
the resources available for consumption expand via the new borrowing. Similarly, in the case of m0 = m − 1 we
can write c = y − (b0 − b)q(y, 0, b0 , m − 1; m − 1), which highlights that the available resources for consumption
expand by the additional (net) borrowing.

Figure 1: Change in the country’s debt portfolio

debt
b0
#2

Old debt

m−1

maturity

Note: This figure represents a change in the country’s debt portfolio
from (b, m − 1) to (b0 , m0 ). The new issuances are represented by the
rectangles #1 and #2, and the square #3.

in the budget constraint and reorganizing terms we obtain,
c=

y − b[q(y, 0, b0 , m0 ; m0 ) − q(y, 0, b0 , m0 ; m − 1)] − (b0 − b)q(y, 0, b0 , m0 ; m − 1)
|
{z
}
{z
}
|
#1: value of changing only maturity

−

#2: value of changing only the yearly payment

(b − b)[q(y, 0, b , m ; m ) − q(y, 0, b0 , m0 ; m − 1)]
|
{z
}

#3: value of changing the yearly payment by (b0 − b) only for the extra maturity m0 − (m − 1)

where the first term, labeled as (#1), represents what the countries would obtain (at market
prices) by changing only the value of maturity from m − 1 to m0 . The second term, labeled
as (#2), corresponds to the resources the country would obtain changing only the size of the
yearly payment from b to b0 . Finally, the last term, labeled as (#3), correspond to the additional
resources (b0 − b) that are promised for an additional m0 − (m − 1) years after the old debt
matures.
Lastly, if there is a sudden stop event, the country’s value is
V P (y, 1, b, m) = u(y + b) + βEy0 ,a0 |y,1 V G (y 0 , a0 , b, m − 1).
The policy functions for the choice of the amount of debt and the choice of maturity are
B(y, a, b, m) and M (y, a, b, m), respectively.
14

3.2

The problem of the sovereign in restructuring

When the country’s debt is in restructuring, the opportunity to offer a restructured debt portfolio
with market value W alters stochastically between the borrower and the set of lenders: the
probability that the lender (L) makes the offer is λ, after which the sovereign (S) decides whether
to accept. The probability that the sovereign has the option to make the offer is (1 − λ).
On the one hand, if the lender decides to make an offer, she will offer a value of debt portfolio
equal or smaller than the face value of the defaulted debt, W < −b × m. We write this problem
as
W L (y, b, m) = arg max W × H(y, b, m, W ),
W ≤−b×m

where H(y, b, m, W ) is a function indicating the probability that the country accepts the offer.
If the decision of the country whether to accept the offer or not depends only on (y, b, m, W ),
then H is an indicator function and the lender will offer the maximum it can so that the country
will accept it. We write this problem in a more general way, using a probability, only because
the country’s decision to accept the offer may be affected by a random preference shock as in
Dvorkin et al. (2021) and in that case H ∈ (0, 1).18 Also, the lender makes this offer only if the
value she can obtain is larger than the value of debt continuing in default; i.e., W L (y, b, m) ≥
−bq D (y, b, m; m), where q D is the price of debt in default.
On the other hand, if the country makes the offer, it will offer a value W such that the lenders
are indifferent between accepting and rejecting the offer; i.e., W S (y, b, m) = −bq D (y, b, m; m).
Independently of how the value of W is determined, given a value W , the country chooses
the yearly payment and the maturity of the restructured debt, {bR , mR }, and a transfer of fresh
money from the lenders to the country, τ R ≥ 0, such that
τ R (y, b, m, W, bR , mR ) = q E (y, bR , mR ; mR ) × (−bR ) − W − κ max{|b × m| − |bR × mR |, 0},
|
{z
}
regulatory cost of book-value haircuts

where the price of the debt being restructured, q E , takes into account that the country will
be excluded from credit markets next period with probability δ. Note also that we add, as in
18

More information on these shocks is provided in Section 4.

Dvorkin et al. (2021), a cost to compensate the lender for their extra cost in case of face value
haircuts, which is determined by the parameter κ.
The country makes the choice of {bR , mR , τ R } given a restructured value W and old debt
(b, m) to maximize utility,
Ṽ A (y, b, m, W ) = max u(y R + τ (y, b, m, W, bR , mR ))
bR ,mR

+βEy0 |yR (1 − δ)V G (y 0 , 0, bR , mR ) + δV E (y 0 , bR , mR )
subject to τ R (y, b, m, W, bR , mR ) ≥ 0,

where y R = min y, π R represents the income net of the cost of being in restructuring, and the
value function V E represents the value of exclusion, which occurs after restructuring. This value
can be written as

V E (y, b, m) = max{u(y − b) + βEy0 |y (1 − δ)V G (y 0 , 0, b, m − 1) + δV E (y 0 , b, m − 1) , V D (y, b, m)}
where the country leaves exclusion in any period with probability (1 − δ). Note that, while
in exclusion, the country must either make debt payments using current income (there is no
possibility of debt rollover) or default.
We can express the value of a country in restructuring with a given offer as
n
o
Ṽ R (y, b, m, W ) = max V D (y, b, m); Ṽ A (y, b, m, W ) ,
and the value of a country in restructuring as
V R (y, b, m) = λṼ R (y, b, m, W L (y, b, m)) + (1 − λ)Ṽ R (y, b, m, W S (y, b, m)).

3.3

Equilibrium debt prices

The price of a non-defaulted bond promising to pay one unit of the consumption goods for the
next n periods is
q(y, a, b0 , m0 ; n) =

o
Ey0 ,a0 |y,a n
(1 − D(s0 )) (1 + q(y 0 , a0 , B(s0 ), M (s0 ); n − 1)) + D(s0 )q D (y 0 , b0 , m0 ; n) ,
(1 + r)

where we denote the relevant states for the policy functions in good times as s0 = (y 0 , a0 , b0 , m0 ).
The variable a affects the price of debt indirectly through changes in the policy functions. Similarly, the price of debt during exclusion after default is
Ey0 |y
×
(1 + r)
n

δ 1 − DE (s̃0 ) 1 + q E (y 0 , b0 , m0 − 1; n − 1) + DE (s̃0 )q D (y 0 , b0 , m0 ; n)

o
+(1 − δ) (1 − D(ŝ0 )) (1 + q(y 0 , 0, B(ŝ0 ), M (ŝ0 ); n − 1)) + D(ŝ0 )q D (y 0 , b0 , m0 ; n) .
q E (y, b0 , m0 ; n) =

Here the notation of the relevant states for the policy functions in default is s̃0 = (y 0 , b0 , m0 ),
and those after the end of the exclusion –where the country is surely not in a sudden stop– is
ŝ0 = (y 0 , 0, b0 , m0 ). The difference with the price in normal times is that with probability δ the
country will not have access to credit markets again next period, and as a consequence the policy
functions will be different.
Finally, the price per unit of debt in default is

L 0

D 0 0 0
Ey0 |y
W (s̃ ) n
L 0
L 0
q (y, b , m ; n) =
(1 − λ) + λ(1 − H (s̃ )) q (y , b , m ; n) + λH (s̃ )
.
(1 + r)
−b0 m0
D

This price has two terms. The first term reflects that if the country makes the offer (probability
1 − λ) or if the lender makes the offer and it is rejected (probability λ(1 − H L )), the value of the
debt would continue to be the value of debt in default but in a different state q D (y 0 , b0 , m0 ; n).
The second term has the total repayment made by the country in case of a successful restructuring, W L (y 0 , b0 , m0 ), which is divided by the total amount of debt (−b) because it is the price
per unit of yearly payment. This value is divided among the bondholders of different maturities
17

using the ratio n/m0 . For example, if a bond in default in the debt portfolio has maturity of one
period, n = 1, and the total maturity of the defaulted portfolio is four years, m0 = 4, we have
that

W L (y 0 ,b0 ,m0 )
−b0

is multiplied by 1/4, as the one-year bond is entitled to one payment out of the

four payments the country had committed to. In this case, bondholders of all maturities would
be treated identically in terms of the fraction of the restructured debt they receive, irrespective
of whether they originally hold short or long term debt.

Model Calibration and Evaluation

4.1

Calibration

To calibrate the model we take some parameters from the literature or previous estimations. For
the remaining parameters, we follow Dvorkin et al. (2021) as closely as possible.
Table 1: Calibrated parameters and fit of targeted statistics
Parameter
Discount factor, β
Output loss, entering default, π D
Output loss, staying in default, π R
Lender’s offer prob., λ
Portfolio adj. cost, α1
Portfolio adj. cost, α2

Value
0.935
0.90
0.945
0.55
0.00005
20

Basis

Data

Model

Debt/output
Default rate
Length of default, years
Mean SZ haircut
Average issuance costs
∆ Debt/GDP near default

31%
2.50%
2.30
32.8%
0.2%
22p.p.

36.3%
2.27%
2.40
34.1%
0.3%
20p.p.

Note: See data sources in Appendix A. SZ haircut refers to the haircut measure proposed by Sturzenegger
and Zettelmeyer (2006) and it is defined in Appendix B.

The risk aversion parameter, γ, is set at 2, a value widely used in the literature. The risk
free interest rate is set at 4.2% to match the long-run average of the real 10-year US Treasury
bond yield between 1980 and 2010. Income follows an AR(1) process in logs with persistence
parameter ρz = 0.86 and the volatility parameter σz = 0.019 to mimic the detrended annual per
capita real GDP process for Colombia as estimated in Sánchez et al. (2018).
We set the regulatory cost of lenders’ book value losses at 3%, so κ is set at 0.03. This is a
conservative value associated to institutional lenders’ cost of raising capital due to adjustments
18

in the face value of the portfolio in restructuring. The probability of remaining in exclusion
after restructuring a debt portfolio, δ, is set at 0.7 to match the 70% probability of such event
estimated from the data in Cruces and Trebesch (2013) for emerging markets. Sudden stops
are modelled as a Markov process with a probability of experiencing a sudden stop of 12% next
period if not in this state at present, and a probability of 42% of continuing in a sudden stop
state, based on the definition of sudden stop in Comelli (2015) and controlling for domestic credit
conditions.
We also introduce adjustment costs for changing the debt portfolio in order to capture issuance
costs. Both changes in maturity and changes in the size of yearly payments are assumed to be
costly.19 The portfolio adjustment cost function has two parameters, α1 and α2 , that are set
at 0.00005 and 20, respectively, to replicate the average issuance costs and the variation in
debt-to-GDP ratio prior to default.
We calibrate the remaining parameters targeting data for Colombia—an emerging market
economy with good data availability. The discount factor β is set at 0.935 targeting a 31%
debt-to-output ratio. The output loss parameter for the first period in default, π, is set at 0.90
targeting a 2.5% default rate, while the output loss for other periods in default, π R , is set at
0.945 targeting the length of a default episode of 2.3 years. The probability of the lenders making
the offer for restructuring, λ is set at 0.55 targeting a 33% haircut rate.
For the numerical solution of the model, we add taste shocks drawn from a Generalized
Extreme Value distribution for each possible choice of the government (maturity, borrowing,
repayment, and accepting a renegotiation deal). This dynamic discrete choice procedure method,
introduced to sovereign default by Dvorkin et al. (2021), facilitates convergence by smoothing out
the policy functions. We follow that paper in the values assigned to the parameters associated
with the distribution of these shocks.
19

0
We use the functional form χ(b, m, b0 , m0 ) = α1 exp α2 ( m+m
|b − b0 | −
2

b+b0
2 |m

− m0 |) − α1 , where −b and

m are the level and maturity of the debt portfolio, respectively, after making the current payment, and −b0 and
m0 are those of the newly issued debt.

4.2

Evaluation

In the previous sections we introduced and calibrated our model of debt maturity choice and
distressed debt restructuring. In this section we evaluate the quantitative performance of the
model comparing several of its non-targeted moments with the data from Brazil, Chile, Colombia,
and Mexico, a set of frequently studied emerging market economies. The model does remarkably
well in capturing the business cycle properties of sovereign debt along several dimensions. We
present all statistics in Table 2.
Table 2: Fit of key non-targeted moments
Statistics

Brazil

Chile

Colombia

Mexico

Model

σ(log(c))/σ(log(y))
ρ(log(c), log(y))
Duration (years)
Maturity (years)
ρ(mat, log(y))
ρ(dur, log(y))
1-year spread (%)
10-year spread (%)
10Y S − 1Y S(%)
ρ(1Y S, log(y))
ρ(10Y S, log(y))

1.30
0.40
3.65
6.47
0.03
0.06
1.93
4.52
2.59
-0.04
-0.21

1.47
0.84
4.44
5.53
-0.30
-0.32
0.48
0.86
0.22
-0.33
-0.12

1.15
0.82
5.23
9.62
0.19
0.34
0.82
2.11
1.30
-0.23
-0.68

1.59
0.67
5.76
11.43
0.24
0.02
1.32
3.41
2.08
-0.01
-0.09

1.16
0.83
3.67
6.75
0.43
0.33
0.83
0.90
0.07
-0.18
-0.49

Note: The first-order moments are country-specific means in the data and
in the model. See data sources in Appendix A.

The table shows that our model closely mimics several non-targeted standard business cycle moments for emerging market economies. Our framework closely captures the volatility of
consumption relative to output volatility above one and the high correlation of consumption
with output documented in the data. The model also reproduces the median sovereign debt
maturity and duration from the data and their business cycle dynamics. The average duration
is 3.67 years, and the average maturity in the model is 6.75 years. While these two statistics are
slightly below the averages of our data sample, the model generates the procyclical pattern for
debt maturity and duration found in the data. We also evaluate the model in terms of the level
and cyclicality of 1- and 10-year spreads, and the term premium. Our setup captures well the
20

countercyclical dynamics of yield spreads for different bond maturities over the business cycle.

Policy Interventions: Extending the Model

This section introduces two commonly discussed policy proposals in debt restructurings, that
could be implemented for instance in the context of an IMF-sponsored program. Distressed debt
restructurings already typically involve the participation of the IMF, and as discussed in the
IMF (2014), of the 17 arrangements reviewed in an IMF report for the period from 1998 to 2014,
11 included conditionalities related to the restructuring. The policy exercises we study here
focus on standardized procedures across debt restructurings instead of a discretionary rule. Erce
(2013) suggests a standardized role for IMF in its approach to restructurings can be beneficial
by reducing the uncertainty when countries enter into a sovereign default crisis.20
For the two policy proposals we analyze, i.e., a rule for distributing losses across creditors
and the use of GDP-indexed bonds, we study how they affect, among other things, sovereign
debt prices, maturity, and the frequency of defaults both shortly after a restructuring and over
the long term. The potential welfare gains are analyzed in the next section.

5.1

A Rule for Distributing Losses Across Creditors

In the model presented above, the proceedings of restructuring are distributed to holders of bonds
of different maturities proportionally to the number of yearly payments, n/m0 . In this section
we extend the model to distribute these proceedings according to
distribution rule =

q ∗ (n; rR )
,
q ∗ (m0 ; rR )

where n is the maturity of a bond, m0 is that of the entire portfolio, and q ∗ (k, r) =

1
l=1 (1+rR )l .

This representation allows for a different treatment of long maturity debt vis-a-vis short maturity
20

A roadmap developed and published by the United Nations Conference on Trade and Development calls for
a clear procedure for sovereign debt renegotiations, which can be established by standardized rules guiding these
procedures. (See UNCTAD (2015).)

debt in the defaulted portfolio. The price of the debt in default is now
D

q (y, b , m ; n) =

L 0 ∗
D 0 0 0
Ey0 |y
W (s̃ ) q (n; rR )
L 0
L 0
.
(1 − λ) + λ(1 − H (s̃ )) q (y , b , m ; n) + λH (s̃ )
(1 + r)
−b0 q ∗ (m0 ; rR )

Here, q ∗ (n; rR ) is the present value of n payments, discounted at rate rR , which in turn shapes the
relative returns for each maturity. Intuitively, consider a simple example of a debt restructuring
with two creditors. The first creditor holds a bond that matures in the current period (shorterterm bond) and has a face value of $60. The second creditor holds a bond that matures in
one year (longer-term bond) and also has a face value of $60. The country defaults on these
bonds and the lenders and the country agree to a restructuring, issuing new bonds with a total
market value of $100. If the discount rate rR used for determining the recovery payments to the
creditors is zero (i.e., rR = 0), both the creditor with the shorter-term bond and the creditor
with the longer-term bond receive $50 according to the distribution rule

q ∗ (n;rR )
q ∗ (m;rR )

n
m

= 21 . Thus,

rR = 0 is the case in which the extended model with a redistribution rule nests the benchmark
model. Higher discount rates will lower the present value received by the holder of long-term
debt relative to the present value received by the holder of short-term debt. Accordingly, our
discount rule determines the losses to creditors holding bonds of different maturities.
To further illustrate the direct implications of changing rR on the distribution of creditor losses
across maturity holdings, we construct the shares of the total value that the country repays in
default obtained by holders of zero-coupon bonds of maturities 1, 3, and 8 years. These values
can be represented as follows:
• share obtained by bondholders of 1-year maturity zero-coupon bonds =

q ∗ (1;rR )
,
q ∗ (10;rR )

• share obtained by bondholders of 3-year maturity zero-coupon bonds =

q ∗ (3;rR )
q ∗ (10;rR )

(2;r )
− qq∗ (10;r
R) ,

∗

• share obtained by bondholders of 8-year maturity zero-coupon bonds =

q ∗ (8;rR )
q ∗ (10;rR )

(7;r )
− qq∗ (10;r
R) .

∗

Figure 2 shows how these values change as a function of rR . If we set rR = 0, the creditors
holding bonds of different maturity will get the same share—if the total maturity is 10 years as in
this example, that share is 1/10, i.e., 10%. As rR increases along the x axis, the share obtained
by bondholders of 1-year maturity zero-coupon bonds (red line) increases, the share obtained by
22

bondholders of 8-year maturity zero-coupon bonds (dashed green line) decreases, and the share
obtained by bondholders of an instrument with intermediate maturity varies more moderately.
Notice that in the extreme case where rR = 80%, the share obtained by bondholders of 1-year
maturity zero-coupon bonds is close to 50 percent.

50
40
30
20
10
0

Share of Proceedings (%)

Figure 2: Share of Restructuring Proceedings Obtained
by Bondholders of Selected Maturities

r (%)
Holders of Zero-Coupon Bonds with Maturity 1
Holders of Zero-Coupon Bonds with Maturity 3
Holders of Zero-Coupon Bonds with Maturity 8

Note: The figure shows the shares obtained by the holders of a bond
of maturity n = {1, 3, 8} in a portfolio of maturity m = 10. We plot
these shares for different redistribution rules represented by rR .

5.2

GDP-indexed bonds

We introduce new notation to capture the fact that the country can now issue GDP-indexed
bonds during debt restructurings. Let Ψ(y 0 /y) be the factor by which the debt payment is
adjusted as a function of the change in income, y 0 /y. We use Ψ(y 0 /y) as an step function, where



1 + ∆H


Ψ(y 0 /y) =
1



 1−∆

if y 0 /y > 1.03
if 1 ≤ y 0 /y ≤ 1.03
if y 0 /y < 1.00.

The thresholds for indexation are set at 1 and 1.03 as, on average, upon exiting a restructuring,
economies recover at an annual real GDP growth rate between 1 and 2 percent (Dvorkin et al.,
23

2021). As we explained in the case of redistributing losses among maturities, the exercise aims
to show the effect of this simple rule and not look for the optimal rule.
With this notation at hand, we can modify the expression for the value function of the country
in restructuring accordingly. The new value is

V E (y, b, m) = u(y − b) + βEy0 |y (1 − δ)V G (y 0 , 0, bΨ(y 0 /y), m − 1)

+δV E (y 0 , bΨ(y 0 /y), m − 1) .
Note that, unlike previous literature on contingent debt, we introduce indexed bonds only at
the time of restructuring. Thus, during the years after the restructuring in which the country
is excluded from financial markets, if the country’s income increases above 3%, the outstanding
yearly payments of the restructured debt increase by the factor ∆H . In addition, in the case we
referred to as “symmetric”, yearly payments decrease by a factor of ∆L if income decreases. This
indexation rule lasts while the country is in exclusion. Since the country leaves exclusion in any
period with probability δ = 0.75, the expected duration of the period in which the changes may
take place is 3 years.
Similarly, we also have to modify the price of debt used during restructuring,
q E (y, b0 , m0 ; n) =
n h
i

Ey0 |y
Ψ(y 0 /y) δ 1 − DE (y 0 , b0 Ψ(y 0 /y), m0 ) 1 + qE + DE (y 0 , b0 Ψ(y 0 /y), m0 )qD
1+r
h
io
+(1 − δ) (1 − D(y 0 , 0, b0 Ψ(y 0 /y), m0 )) (1 + q) + D(y 0 , 0, b0 Ψ(y 0 /y), m0 )qD ,
where
qE = q E (y 0 , Ψ(y 0 /y)b0 , m0 − 1; n − 1),
qD = q D (y 0 , b0 Ψ(y 0 /y), m0 ; n),
q = q(y 0 , 0, B(y 0 , 0, b0 Ψ(y 0 /y), m0 ), M (y 0 , 0, b0 Ψ(y 0 /y), m0 ); n − 1).

Policy Interventions: Quantitative Results

This section quantitatively evaluates the two policy proposals introduced in the previous section,
and provides intuition regarding the main findings on debt dynamics, pricing, and other key
macro outcomes over the business cycle as well as during and after default and restructuring.

6.1

A Rule for Distributing Losses Across Creditors

We compare economies with different loss redistribution rules across creditors holding bonds of
different maturity, where each rule is associated to a value of rR . The panels in figure 3 show that
the effects on credit spreads are significant, and suggest that policies that tend to favor short-term
bondholders in restructurings lead to a decline in the average spread and term premium mainly
in bad times, largely due to lower short-term spreads. Panel (a) shows that as rR increases,
the average EMBI spread decreases monotonically, and mainly in years in which the country’s
income is below trend (bad times). This result suggests that increasing rR may be desirable.
Meanwhile, panel (b) shows that the term premium measured by the 10-1-year spread increases
by 1 percentage point overall (blue line): As rR increases, holders of long-term debt receive a
lower share of the restructured debt, so the spread for long-term debt is higher. The effect of the
policy on the term premium is mainly driven by its impact during bad times. As shown by the
green line in the plot, in bad times the term premium increases about 3 percentage points for the
higher rR values. Panel (c) shows that the lower EMBI spread and higher 10-1-year bond term
premium in bad times as rR increases are mainly driven by a decline in the spread for short-term
bonds (1-year bond yield spreads), not for long-term bonds (10-year bond yield spreads).

-1

Term premium (p.p.)

1.5
1
.5

EMBI (%)

Figure 3: Effects on Debt Pricing of A Rule for Distributing Losses Across Creditors of Different
Maturities

Overall

r (%)

Good times

Bad times

Overall

Bad times

(b) Term Premium, 10-1-year spreads

1
.5
0
-.5

1-year spread (%)

1.5

(a) EMBI

Good times

r (%)
Overall

Good times

Bad times

Consistent with the discussion of figure 3, we find that, as rR increases, maturity becomes
lower particularly in bad times to take advantage of the lower financing cost at short maturities
during those periods, as shown by the green dotted line in Figure 4, panel (a). This behavior
implies that maturity becomes more cyclical. Notably, as displayed in panel (b), countries can
avoid more defaults because of this lower cost of short-term debt in bad times. The default
rate falls monotonically from about 2.3 percent to 1.7 percent, a reduction of more than 25
percent. Leverage is non-monotonic in the redistribution policy, initially increasing with rR and
then decreasing. Finally, panel (c) suggests that as loss redistribution policies favor short-term
26

bond holders more, debt restructurings tend to rely more on debt maturity extensions and less
on face value haircuts, and the average SZ haircut edges lower on net. Changes in maturity
extensions and face value haircuts are noticeably nonlinear in the policy, with most variation
occurring for values of rR below 40 percent. Within this policy parameter range, the median
maturity extension increases about four-fold, from about 2.5 years to almost 10 years, while
face value haircuts more than halve, dropping from about 9 years to about 4 years. As the
policy tilts the debt maturity profile toward shorter term debt especially in bad times when
output tends to be low and the country is closer to default, and the country engages in a
restructuring when output recovers, a restructuring that relies more on maturity extensions and
less on face value haircuts takes the country closer to its preferred maturity profile, given the
procyclicality of debt maturity. The stronger reliance on maturity extensions vis-a-vis face value
haircuts that the policy incentivates, brings the restructuring more in line with the restructuring
approach advocated by recent IMF work that argues in favor of considering more reprofilings
when addressing distressed debt negotiations (IMF, 2017). Note that all these significant changes
are achieved with a simple parametric rule for redistributing creditor losses by debt maturity.
The goal here is not to look for the optimal rule, which may depend on the calibration, but to
show how a simple rule can significantly affect the outcome of debt restructurings.

2.4

Default rate (%)

2.2

36.8

36.6

1.8

36.4

1.6

36.2

7
6.5
6
5.5

Maturity (years)

7.5

Debt*Maturity / Income (%)

Figure 4: Effect of a on Debt, Default, and Restructuring

r (%)
Overall

r (%)

Good times

Bad times

Debt*Maturity / Income

Default rate

(b) Debt and default

Haircut (%)

(a) Maturity
Median extension, years

r (%)
Median extension, years (net of excl.)
Avg. haircut, face value
Avg. haircut, SZ

(c) Extension and haircuts
Note: In the model, bad times are years where log-income is below its mean. SZ haircut refers to the haircut
measure proposed by Sturzenegger and Zettelmeyer (2006) and it is defined in Appendix B.

6.2

GDP-indexed bonds

The main policy-relevant question about indexed or state-contingent debt instruments (SCDIs)
issued in a restructuring is whether they help reduce the incidence of default in the years following
the restructuring. The COVID-19 crisis has brought further attention toward the important role
of SCDIs in restructurings. IMF (2020) highlights that the pandemic led to substantial increases
in sovereign debt and economic uncertainty that may lead to costly and inefficient sovereign
debt restructurings involving protracted negotiations over recovery values, and potentially even
28

relapses into default post-restructuring. The IMF work further points out that SCDIs could play
an important role in improving the outcomes of these restructurings. We distinguish between two
forms of indexation based on how the adoption of this instrument has evolved (see for instance
Consiglio and Zenios (2018)). Specifically, we consider the implications of GDP warrants, the
most frequently used early form of indexation that adjusts debt payments upwards when output
growth exceeds a threshold, and we compare such indexation rule to the symmetric indexation
discussed by the G20 and others. In the symmetric indexation case, debt payments adjust
upwards if the economy recovers faster than expected and downwards if growth does not recover
(GDP-linked bonds).
Figure 5 shows different default rates for the two parameterizations of this policy. The red
dashed line represents the case in which bonds are adjusted upwards when income increases
more than 3 percent and downwards when income does not grow. We refer to this case as the
symmetric indexation (GDP-linked instrument) because ∆H = ∆L > 0. The solid blue line
represents the policy in which the payments are only adjusted upward if income increases more
than 3 percent. We refer to this case as upside-only indexation (GDP warrant) because ∆H > 0
and ∆L = 0. The size of the adjustment in payments is represented in the x-axis, where we
consider a maximum adjustment of 20 percent (∆H = ∆L = 0.2). Recall that the adjustment
occurs while the country is in exclusion after restructuring, so the payments are increasing exactly
by the rate shown in the x-axis.21
21

Remember that during the period of exclusion after restructuring, conditional on not defaulting, the country
can neither issue new debt, nor buy-back any debt. During that period, the country is limited to making the
payments, which are subject to the GDP indexation in the case of the policy analyzed here.

18
17
16
15

Default 2-5 years after restr. (%)

11
10.5
10
9.5
9

Default 2-3 years after restr. (%)

Figure 5: The Effects of GDP-Indexed Bonds on Debt, Default, and Restructuring Dynamics

Debt adjustment factor (%)
Symmetric

Upside only

40
39
38
37

Debt*Maturity / Income (%)

2.3
2.25
2.2

Default rate (%)

2.15

Debt adjustment factor (%)
Upside only

Symmetric

(b) Prob. of Def 2-5 Years After Restructuring

2.1

Debt adjustment factor (%)

(a) Prob. of Def 2-3 Years After Restructuring

Upside only

Debt adjustment factor (%)

Symmetric

Upside only

(d) Debt/Income

36
34
32
30

Avg. haircut, SZ (%)

Symmetric

Debt adjustment factor (%)
Upside only

Symmetric

(e) Haircut
Note: SZ haircut refers to the haircut measure proposed by Sturzenegger and Zettelmeyer (2006) and it is
defined in Appendix B.

In Figure 5, Panels (a) and (b) show the effect of both indexation schemes on default incentives
in the years after the restructuring, so they inform about the use of the policy to address the
highly-debated issues of restructurings doing too little to ensure debt sustainability and avoid
repeated defaults. The probability of default 2 to 3 years after the restructuring, shown in
panel (a), declines about 7 percent (from 10.7 to 10 percent) as the adjustment increases from
0 to 5 percent. The effects are more linear and only slightly smaller for the symmetric policy.
When considering a longer post-restructuring horizon, as shown in panel (b), we find that the
probability of default in the years 2 to 5 after the debt restructuring also decreases significantly
for both indexation specifications, and substantially more under the symmetric case. Panels (a)
and (b) also suggest that the effects of these policies are nonlinear, with the default rate declining
more sharply as the symmetric adjustment increases from 0 to 20 percent. The upside-only policy
shows a similar though more subtle pattern.
Panels (a) and (b) focused on the default rate for periods immediately after the restructuring.
To provide a wider view of the implications of this policy, panel (c) shows the effect of the policy
on the average default rate across all periods, which decreases as the debt adjustment rate
increases, particularly for the symmetric specification. For instance, the default rate declines
about 5 percent (from 2.27 to 2.17 percent) as the adjustment increases from 0 to 10 percent.
Consistent with the lower default probability patterns shown in panel (c), as the adjustment
factor increases, the sovereign is able to increase its debt-to-income ratio (panel (d)), particularly
for the symmetric indexation scheme. As shown in the panel, an increase from 0 to 10 percent
in the adjustment is associated to an increase in leverage of more than 6 percent (from 36.3 to
38.6 percent). Panel (e) illustrates the effect of the adjustment rate on the average SZ haircut.
There are two opposing effects of the policies on haircuts. On the one hand, as pointed out by
Dvorkin et al. (2021), countries that default with higher debt-to-income ratios will experience
higher haircuts in a restructuring. On the other hand, as debt becomes contingent, the country
is better off for any given level of haircut compared to the non-indexation scenario. The lower
default rates that we document point to this gain for the country, in particular for the symmetric
indexation rule. Thus, when renegotiating a debt restructuring, part of that gain is transferred
to the creditors in the way of lower debt haircuts, i.e., a higher W . As shown in the plot, haircuts
31

increase with the adjustment rate under an upside-only indexation rule, and decrease under a
symmetric rule. Thus, panel (e) suggests that the debt level effect dominates the welfare effect
for the upside-only indexation, so the haircut increases under such scheme, while the opposite
is true under the symmetric indexation case. This intuition is confirmed by our welfare results
showing that welfare gains under symmetric indexation are substantially larger than under an
upside-only rule. The next section discusses the welfare effects in depth.

Welfare analysis

In this section, we use our quantitative framework to assess the welfare implications of the rule
to distribute losses across lenders with bonds of different maturities and the use of GDP-indexed
bonds upon exiting sovereign debt restructurings. We first present the methodology we employed
to construct the welfare measures, and we then discuss the welfare results of the two policies.
Technically, different behavioral and market functioning assumptions in our model may justify
policy interventions. For instance, lack of commitment to repay on the part of borrowers and
incomplete markets with no state-contingent debt may lead to an equilibrium allocation that is
not optimal. Interestingly, we find that some of those policies may be ex-ante desirable as they
lead to increases in welfare (a Pareto improvement).22 We compare welfare across different policy
interventions using two alternative measures. First, we use the value function of a country with
no debt and median income. Thus, the analysis can be contextualized as a country choosing the
type of bond to issue from that period onward. As this hypothetical country has no debt, default
is an event that may occur only in the distant future, so welfare gains or losses of restructuring
may be small. Second, we compute the welfare gains of a policy change evaluated by an agent
with a different discount factor than the government in charge of choosing default and borrowing
decisions. This concept of welfare under disagreement was recently introduced by Aguiar et al.
(2020) to evaluate the potential gains of restricting countries’ access to credit markets.
As it is standard, welfare gains are measured in terms of consumption equivalent units (CE).
22

We do not characterize the fully optimal policy, but rather focus on whether our proposed interventions lead
to welfare improvements.

They represent the percent change in consumption—in every period—necessary to make an
agent in the original economy indifferent with being in the economy after the policy. If gains are
positive, the agent prefers to live in the economy with the policy.

7.1
7.1.1

Computing welfare gains from policy experiments
Ex-ante welfare gains with disagreement

For each alternative model, we simulate NI paths for NT periods starting from no debt, mean
income, an normal times in international credit markets (i.e., b = 0, y = 1, a = 0) and a good
credit record.23
For each path i we compute the present discounted value of the realized consumption stream
NT
P
β̂ t−1 u(cit ), and we take the average
from the perspective of the initial period as V̂i (β̂) =
t=1

of these present discounted values across observations of the Nid paths, within each model,
NI
P
¯
V̂ (β̂) = V̂i (β̂)/NI . Given our CRRA preferences, the welfare gain from a policy is
i=1

exante

gains

¯
¯
(β̂) = V̂ (β̂)POL /V̂ (β̂)BM

1
1−γ

− 1.

For the standard welfare gains, we set β̂ = β, where β̂ and β are the discounts for the households
and the government, respectively.24 For the case with disagreement as in Aguiar et al. (2020),
we set β̂ 6= β. In particular, we consider households that are more patient than the government,
consistent with the presence of political economy features that can be associated with a lower
government’s discount factor, i.e., β̂ > β.
7.1.2

Welfare gains including the transition from the current state

Computing welfare gains considering the transition path is more challenging. Since the economy starts with no policy, we capture the initial stochastic steady-state using the time series
simulations of our baseline economy described above. Recall that we have NI different paths or
23

We set NI = 1500 and NT = 400.
For β̂ = β we can perform this computation simply by using the value functions of the two economies, without
using the simulations. We check that for β̂ = β, these two methods provide the same results.
24

economies i simulated for NT periods. For each observation in good financial standing at the
end of period t > t̂,25 the value from staying in the baseline setup (no policy) is
WitBM =

(cit )1−γ
BM
+ βEy0 ,a0 |yit ,ait [VG (y 0 , a0 , bit+1 , mit+1 )],
1−γ

where the variables cit , bit+1 , mit+1 denote the consumption, asset and maturity choices of a
country i in the baseline simulation at period t. Similarly, the value for a country with good
credit standing from switching to an economy with an alternative restructuring rule at the end
of the current period is
WitPOL =

(cit − xit )1−γ
POL 0 0
+ βEy0 ,a0 |yit ,ait [VG
(y , a , bit+1 , mit+1 )],
1−γ

where xit denotes the transfers to cover the lenders’s losses from implementing the switch from
the baseline to the alternative policy. Thus, the gains computed here would be those that result
after compensating lenders for the unexpected change in policy. The value xit can be obtained
as
xit ≡ q POL (yit , ait , bit+1 , mit+1 ; mit+1 )bit+1 − q BM (yit , ait , bit+1 , mit+1 ; mit+1 )bit+1 .
Notice that if the price becomes higher after the switch, the lenders’ losses are negative, and we
give additional resources to the country to compute the compensated value measure. Finally,
we can compute the welfare gains considering the transition to the new policy starting in good
financial standing as
gainstrans
i,t

WitPOL
WitBM

1
1−γ

− 1.

To compute the gains considering transitions for the countries that defaulted and before restructuring, we follow a similar approach using the debt prices and expected values in default.
Finally, note that we derive the entire distribution of gains for countries with different states
at the reform’s onset. Following the median voter argument commonly used in the literature,
we present the median gains for the whole distribution and conditional on being in default just
25

We set the threshold t̂ at 200, in order to have the observations in the baseline simulations after this period
to follow the corresponding ergodic distribution.

before restructuring.

7.2

Welfare gains of the proposed restructuring policies

The effects of a rule for distributing losses across creditors on yield spreads and default rates
described in subsection 5.1 suggest that it may be desirable to increase rR , i.e., tilt the loss
distribution in favor of the asset preservation of bondholders of shorter maturity instruments.
Figure 6 displays the welfare changes for different values of rR , showing that the gains are positive
and monotonically increasing at decreasing marginal rates across the different economies and
welfare measures.
The figure also shows that, when looking at transition gains -i.e., starting from the distribution
of debt in emerging markets at the time of the policy implementation- as the value rR is higher
the welfare increases the most for a country in default that has not yet restructured its debt.
In such scenario, gains are about 0.08 percent of consumption for a value of rR = 0.8.26 The
median transition gains (solid blue line) are slightly lower but follow the same pattern. The green
dotted line shows the gains for a country with no debt and median income. In this case, default
is an event that may occur only in the distant future, so welfare gains or losses of restructuring
are smaller than the gains computed in transitions. Finally, disagreement in the discount factor
of households and government (dashed red line) is associated to lower, yet still positive and
increasing welfare gains.
26

Recall that these are gains after the country compensates lenders for losses implied by the reform.

.06
.04
.02
0

Welfare gains (%)

.08

Figure 6: The Effects of A Rule for Distributing Losses

r (%)
Overall in transition
Disagreement (β*1.02)

Bad record in transition
No debt, y=1, m=6

To obtain additional insight on how the welfare gains depend on the current economic conditions at the time of the policy implementation, Figure 7 illustrates the gains from implementing
a rR = 0.8 rule under different leverage and GDP-growth scenarios. The left panel suggests that
countries with higher debt-to-income ratios at the time of the policy implementation tend to
benefit more, where a 10 percentage point increase in the ratio is roughly associated to a 0.01
percentage point additional welfare gain. The right panel suggests that countries that implement
the policies when GDP growth is lower benefit more, especially when growth is below trend, as
the relationship seems to be nonlinear.

.1
.08
.06

Welfare gain (%)

.02

.04

.07
.06
.05
.04

Welfare gain (%)

.08

Figure 7: Welfare Gains of rR = 0.8 Distribution Rule for Different Leverage and Income

Value of debt / Income (%)

(a) Across debt value

.95

Income

1.05

1.1

(b) Across income

Note: The figures plot the gains from applying a change in the distribution rule to rR = 80% against various variables. We group the
x-axis variables into 25 equally-populated bins. The gains are computed immediately after the announcement of the policy change,
using the distributions of the baseline. Except in the first panel, the samples are restricted the countries in good record.

Our final analysis quantifies the welfare effects of allowing the borrowing country to issue
GDP-indexed bonds upon exiting a debt restructuring process. We find, first, that the welfare
gains —Figure 8—of this policy increase in the size of the debt adjustment associated to the
indexation. As shown in all panels of the figure, this result holds for both ex-ante and transition
welfare measures. Second, as also shown in all panels, the country would gain more with the symmetric adjustment (GDP-linker) than with the upside-only adjustment (GDP warrant). Third,
the gains in transition are about twice as large for a country implementing the indexation policy
after defaulting and prior to restructuring, i.e., with a bad record, relative to the median gains
in transition (panel a). For the symmetric case, a country in default would have a gain of almost
0.1 percent of permanent consumption even after compensating lenders (panel b). Fourth, the
gains in transition (panels a and b) exceed the ex-ante gains (panels c and d). Similar to the
welfare result for the loss redistribution policy, ex-ante gains from indexation are small because
restructuring is far into the future for a country starting with no debt and average income. Fifth,
the presence of disagreement between domestic households and the government reduces the level

of gains but not the shape with respect to the debt adjustment (panel c).27

.08
.06
.04
.02
0

Gains in transition, bad record (%)

.04
.03
.02
.01
0

Median gains in transition (%)

Figure 8: Welfare Effects of GDP-Indexed Bonds with Different Debt Adjustment

Debt adjustment factor (%)
Upside only

Symmetric

Debt adjustment factor (%)

Symmetric

.005 .01 .015 .02 .025

Debt adjustment factor (%)
Upside only

Gains, no debt, y=1, m=6 (%)

.015
.005

.01

Gains with β*1.02 (%)

(b) Bad record, transition

Upside only

(a) Overall, transition

Debt adjustment factor (%)

Upside only

Symmetric

(d) No debt, output= 1, maturity= 6

The monotonic welfare increase in the debt adjustment payment seemingly stands in contrast
to Durdu (2009) who finds a threshold for the degree of GDP-indexation beyond which the policy
reduces welfare because it induces a higher volatility in bond returns and thus on consumption.
However, Durdu (2009) studies permanently GDP-indexed bonds in a model with sudden stops,
precautionary savings and exogenous interest rates that abstracts from debt maturity, default,
and restructuring, and his indexation mechanism adjusts the debt payments as a given fraction of
the output shock, while our work considers a given debt payment adjustment as output growth
exceeds a threshold and applies for a limited amount of time after restructuring. Our result
suggests, first, that higher degrees of indexation do not necessarily lead to welfare losses, and
second, that the way to model the GDP-indexation may matter considerably for welfare.
Historically, policies considering GDP-indexed bonds have garnered more attention than poli27

As in the loss redistribution policy analysis, we consider a 2 percent larger discount factor for households.

cies addressing the redistribution of losses across investors holding bonds of different maturities.
However, our welfare results suggest that the gains from implementing these two policies provide
similar magnitude when considering a range of plausible policy parameter values and a model
calibrated to an emerging market economy. Thus, our findings suggest that it may be worth
lending relatively more attention to such types of redistribution policies.
Similar to the analysis for the loss distribution policy, we obtain additional insight on how the
welfare gains depend on the current economic conditions at the time of the policy implementation
by plotting the gains from implementing the symmetric indexation rule for different leverage and
GDP-growth values (Figure 9). The left panel of the figure suggests that countries with higher
debt-to-income ratios at the time of the policy announcement benefit more. The result is similar
to that for the loss distribution policy, though the welfare sensitivity to the ratio under this
policy is slightly lower (flatter slope). The right panel suggests that countries that announce
the indexation policy when GDP growth is lower benefit more, especially when growth is below
trend, as the relationship seems to be nonlinear. The welfare gain sensitivity to income for the
indexation policy is also slightly lower (flatter slope) than for the loss distribution policy.

.06
.02

.04

Welfare gain (%)

.08
.06
.04
.02

Welfare gain (%)

.08

Figure 9: Welfare Gains of ∆H = ∆L = 0.2 Bond Indexation for Different Leverage and Income

Value of debt / Income (%)

(a) Across debt value

.95

Income

1.05

1.1

(b) Across income

Note: The figures plot the gains from introducing GDP-indexed bonds with symmetric change of 20% against various variables. We
group the x-axis variables into 25 equally-populated bins. The gains are computed immediately after the announcement of the policy
change, using the distributions of the baseline. Except the first panel, the samples are restricted the countries in good record.

Robustness

This section evaluates the sensitivity of the policy results to variations in key model parameters.
We document that the benchmark findings for the maturity distribution policy and the bond
indexation policy are robust to different assumptions regarding the economic environment. Our
results for alternative values for risk aversion, the discount factor, and default costs, help validate
the insights from the baseline setup for a broader set of economies. We present the summary of
relevant moments for each policy in a separate table, where each column illustrates the differences
between the economy without policy interventions and an alternative economy with a policy
intervention and same calibration. The results for the loss redistribution policy are shown in
Table 3, where the first column presents the moments for the benchmark calibration, and the
second, third and fourth columns present, respectively, results for an economy with a higher
coefficient of risk aversion, a higher discount factor (more patience), and lower default costs.
Table 3: Effect of a rR = 0.8 Policy for Alternative Calibrations

∆
∆
∆
∆
∆
∆
∆
∆
∆
∆
∆

EMBI, p.p.
EMBI (bad times), p.p.
Default rate, p.p.
Value of debt / Income, p.p.
Avg maturity extension, years
Avg. SZ haircut, p.p.
Maturity, years
ρ(n, log(y))
10Y S − 1Y S, p.p.
Med welfare (transition), % CE
Welfare (no debt, y = 1), % CE

Benchmark
calibration
γ=2
β = 0.935
π = 0.90

Higher
risk aversion
γ = 2.5
β = 0.935
π = 0.90

Higher
patience
γ=2
β = 0.945
π = 0.90

Lower
default cost
γ=2
β = 0.935
π = 0.91

-0.49
-0.80
-0.57
0.82
3.25
-3.19
-0.49
0.13
1.41
0.06
0.03

-0.50
-0.80
-0.44
0.87
4.31
-3.34
-0.66
0.13
1.59
0.06
0.03

-0.35
-0.59
-0.50
-0.18
3.13
-2.18
-1.08
0.15
0.57
0.03
0.02

-0.44
-0.71
-0.44
0.31
3.32
-3.77
-0.45
0.11
1.63
0.03
0.02

Note: SZ haircut refers to the haircut measure proposed by Sturzenegger and Zettelmeyer (2006)
and it is defined in Appendix B.

The first column suggests, as discussed earlier, that under the benchmark calibration, tilting
40

the preservation of asset values in favor of short term creditors, i.e., rR = 0.8, credit spreads
decline particularly in bad times, the default rate decreases, and the country can thus support a
higher debt-to-income ratio. Meanwhile, restructurings involve longer maturity extensions and
lower SZ haircuts. The average maturity also falls, and the term spread increases as longerterm bonds become riskier under restructurings. Welfare gains represent about 6 basis points in
consumption equivalent terms. An economy with higher risk aversion, presented in the second
columns, experiences similar declines in borrowing costs but a somewhat higher average maturity
extension of 4.31 years. The third column presents the results on the effects of the policy in an
economy with a higher patience. In this calibration, the policy induces a more moderate decline
in credit spreads relative to the other two economies discussed above. At the same time, there
is a larger decline in the size of the SZ haircut and the term spread increases by less. Finally,
the lower default cost, presented in the fourth column, leads to similar statistics as those for the
benchmark calibration.
Table 4 provides additional robustness insights similar to Table 3 but focusing on the effects
of the symmetric bond indexation policy. Under the benchmark calibration, the bond indexation
allows for a noticeable increase in the debt-to-income ratio, while reducing the average maturity
extension and particularly the SZ haircut in restructurings. The policy also reduces the probability that the country defaults again immediately after restructuring, and leads to welfare gains
that are comparable to those of the other policy. The economy with higher risk aversion exhibits
similar change patterns, with a slightly more moderate increase in leverage, and a bit larger decline in maturity extensions and in the average SZ haircut during restructurings. Similarly, the
probability of defaulting immediately after the restructuring falls only slightly more compared
to the benchmark calibration. Welfare gains of the transition, as expected, are slightly larger
compared to the benchmark calibration, as the country values more the insurance provided by
the contingency of the bond payments. In an economy with more patience, the policy leads to
slightly larger declines in maturity extensions and SZ haircuts than the benchmark and high risk
aversion calibrations. The probability of default post-restructuring declines a bit more strongly
as well. Finally, the effects of the policy in an economy with a lower default cost are also similar
to those of the benchmark calibration. Overall, our results for different calibrations suggest that
41

our benchmark findings are applicable to the debt restructurings of a broad range of economies.
Table 4: Effect of a ∆H = ∆L = 0.2 Bond Indexation Policy for Alternative Calibrations

∆
∆
∆
∆
∆
∆
∆
∆
∆
∆

EMBI, p.p.
EMBI (bad times), p.p.
Default rate, p.p.
Value of debt / Income, p.p.
Avg maturity extension, years
Avg. SZ haircut, p.p.
Def pr. 2 or 3yr after restruct, p.p.
Def pr. 2,3,4 or 5yr after restruct, p.p.
Med welfare (transition), % CE
Welfare (no debt, y = 1), % CE

Benchmark
calibration
γ=2
β = 0.935
π = 0.90

Higher
risk aversion
γ = 2.5
β = 0.935
π = 0.90

Higher
patience
γ=2
β = 0.945
π = 0.90

Lower
default cost
γ=2
β = 0.935
π = 0.91

0.02
0.02
-0.18
2.52
-0.77
-4.04
-1.73
-2.68
0.04
0.03

0.04
0.01
-0.17
2.40
-0.94
-4.35
-1.88
-3.01
0.07
0.03

0.02
0.03
-0.11
2.53
-0.54
-4.87
-2.04
-3.43
0.04
0.02

0.04
0.08
-0.15
2.37
-0.53
-3.15
-2.07
-3.18
0.05
0.04

Note: SZ haircut refers to the haircut measure proposed by Sturzenegger and Zettelmeyer (2006) and it is
defined in Appendix B.

Impact of the joint implementation of the policies

This section compares the effects of separately implementing each of the policies discussed earlier
and implementing them jointly. Table 5 presents the impact on the common moments from the
prior result tables. The table shows that the policies exhibit complementarity for some of the
moments. As shown in the third column, the introduction of both policies leads to lower EMBI
spreads, which decline almost one percentage point in bad times. Consistent with the average
effect on spreads, the default rate also declines noticeably. Both the default rate and the EMBI
spread fall more compared to their decline under either of the policies implemented separately,
which are shown in the first columns. The large drop in the default rate occurs even sustaining
the level of borrowing. The change in leverage from the joint implementation of the policies,
while positive, is slightly lower compared to the case of the indexation-only case, suggesting some
42

minor crowding out between the two policies in this dimension. When looking at the effects of the
joint policy implementation on restructurings, they display “healthy” features: larger maturity
extensions (2 years) and significantly smaller haircuts (8 percentage points). Finally, all the
metrics for welfare suggest an improvement, especially for countries that have defaulted but
have not yet restructured their debt, where the gain is almost 20 basis points in equivalent
consumption. The welfare gains of the joint implementation with disagreement are positive, and
compared to the individual policies, the effect is between two and five times larger.
Table 5: Effect of both policies at rR = 0.8 and ∆H = ∆L = 0.2

∆
∆
∆
∆
∆
∆
∆
∆
∆
∆

Only
redistribution,
rR = 0.8

Only contingent debt,
∆H = ∆L = 0.2

Both redistribution & contingent debt

-0.49
-0.80
-0.57
0.82
3.25
-3.19
0.06
0.03
0.08
0.02

0.02
0.02
-0.18
2.52
-0.77
-4.04
0.04
0.03
0.09
0.01

-0.53
-0.87
-0.79
2.40
1.95
-7.90
0.10
0.07
0.18
0.05

EMBI, p.p.
EMBI (bad times), p.p.
Default rate, p.p.
Value of debt / Income, p.p.
Avg maturity extension, years
Avg. SZ haircut, p.p.
Med welfare (transition), % CE
Welfare (no debt, y = 1), % CE
Med welfare, (bad record, transition) % CE
Welfare with disagreement (β ∗ 1.012 ), % CE

Note: SZ haircut refers to the haircut measure proposed by Sturzenegger and Zettelmeyer (2006) and it is
defined in Appendix B.

Conclusion

Our work provides a micro-founded framework to discuss the implications of policy interventions
for sovereign debt restructuring outcomes.
We consider a policy addressing asset preservation across creditors holding bonds of different
maturities. We find that a rule that tilts the distribution of creditor losses during restructurings
toward holders of long-maturity bonds may be desirable for a wide set of economies. This policy
lowers short-term yield spreads and debt maturity especially in bad times, reducing overall
43

portfolio borrowing costs and the associated default probability of the sovereign during periods
of elevated credit market stress. As the policy leads countries to experience default holding
shorter-term maturities, the associated restructurings rely more heavily on maturity extensions
and less on face value haircuts.
We also consider the use of GDP-indexed bonds during restructurings. They help remedy the
lack of market access experienced by troubled borrowers and significantly reduce the probability
of repeated restructurings. Our results also suggest that symmetric GDP indexation rules deliver
larger welfare gains than upside-only rules. Moreover, the welfare effects are much larger for a
country about to restructure its debt and are reduced when controlling for debt accumulation
biases specific to models in the quantitative sovereign default literature.
While policies involving GDP indexation have received more attention than loss-redistribution
policies in restructuring discussions, we also find that the welfare gains of the two policies are of
similar magnitude, suggesting that it may be worth lending more attention to cross-creditor lossredistribution policies. Finally, we document that when implemented together, the two policies
complement and reinforce each other along most dimensions of debt, default, and welfare metrics
considered in the analysis, suggesting benefits from their joint implementation.

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Appendix A

Data details

Our data moments are taken from the Dvorkin et al. (2021), which also explains the computation
of these variables, including the sources and variable names. For the sake of completeness, we
also include here a brief data description.
• Output measure is the GDP per capita (constant 2010 US$) from World Development
Indicators (WDI).
• Consumption is the households’ final consumption expenditure per capita (constant 2010
US$), from the WDI. The second order moments of consumption and output are obtained
after H.P. filtering the data for the entire horizon with available data.
• The maturity data for Colombia and Brazil are from country-specific sources, “Ministerio
de Hacienda y Credito Publico” and “Secretaria de Tesouro Nacioal”, respectively. For
Chile and Mexico, the source for maturity is the OECD.
• Duration measures follow the Macaulay definition as is standard in the literature. For Chile
and Colombia, such measure is available in the same sources as the maturity. The measures
for Brazil and Mexico are our own computations using the aforementioned maturity data
and the average interest rate data from the International Debt Statistics.
• Spreads: The yield spreads are obtained by subtracting U.S. yields from U.S. dollar
sovereign yields for Brazil, Colombia, and Mexico. Monthly zero-coupon one- and tenyear U.S. dollar sovereign yields are obtained from the Bloomberg database. The yearly
yields are the medians over months each year. The spreads are then obtained by subtracting
one- and ten-year U.S. These latter variables are from the FRED database.

Appendix B
B.1

Computational Details

Basics

We solve the model numerically with value function iteration on a discretized grid for debt
and output. We use a different debt grid for each maturity m, evenly spaced between 0 and
0.7q ∗ (m; rR ), where q ∗ (m; rR ) is the risk-free price for a bond of maturity m. We use 121 points
for the debt grid and 51 points for the output. We solve the policy and value functions for all
points on these grids. The price function is solved for 41 equally-spaced points on this grid, and
the implied function is linearly interpolated in the other parts of the algorithm. Since the steeper
regions of the price function is where default usually happens, we have an uneven grid for income
that is finer below the median income. In particular, the income grid is spread evenly below the
median income over 45 points and evenly above the median income grid over 5 points. We use
the Tauchen (1986) method to discretize the income process.
In solving the model, we introduce taste shocks to the government’s value to facilitate the
model solution. In particular, the government draws a vector of taste shocks each period and
each component of this vector shifts the value obtained by a different discrete decision. (This
means a vector with J = M × N + 1 components, where N is the number of possible debt
choices, and M is the maximum maturity allowed. One additional component corresponds to
the default/restructuring decision.) We follow Dvorkin et al. (2021) in assuming that these shocks
follow Generalized Extreme Value Distribution, and also in setting the parameters governing the
distribution. This approach introduces sufficient randomness into the government’s decision to
convexify its problem, hence smooth out its value and price functions, and allows convergence of
the model solution.
We solve for the lenders’ offer, W L (y, b, m), through a discrete search over 501 points on
a state-specific evenly-spaced W -grid. The lowest point on the grid is 0 and the highest is
min[0.7, −b × m]. Since the borrowers’ offer W S (y, b, m) is equal to −b q D (y, b, m; m) it is not
necessary to follow the same discrete search as W L for W S .
For convergence, we use a measure of distance for the price function of debt in good standing

in a given iteration that considers the maximum absolute distance of the prices across two
iterations relative to the price level in a given state. We declare convergence when this error is
lower than 10−4 . We update the lenders’ offer only when this error is < 10−3 .
We first solve the model (value, policy and price functions). Then we simulate 1500 paths
for 400 years, and compute our moments after dropping the first 100 years in each path. In
computing the model moments, we first obtain the means, correlations and standard deviations
for each path, and then take averages over paths.

B.2

Computing spreads, duration and haircuts

Spreads. Consider a country with income y, debt rollover shock a, and a debt portfolio choice
with maturity m and level b. The yield for a bond with maturity n in our model is

Y T M (y, a, b, m; n) ≡

1
q(y, a, b, m; n) − q(y, a, b, m; n − 1)

n1
− 1.

We use this yield-to-maturity measure to compute the n−year spread for a country with a
portfolio of maturity m as Y T M (y, a, b, m; n) − r.
On the other hand, the EMBI+ in our model is computed as:
EMBI = r̃ − r
where r̃ is the uniform discount rate that would correspond to the unit price of the chosen
portfolio:
t
n
X
1
= q(y, a, b, m; n).
1 + r̃
t=1

(1)

Duration and maturity. We use the following definition for the duration of a bond as a
weighted sum of future promised payments, which is consistent with the definitions of the variables we use for the data:

m0
P

Duration =

t×

t=1
m
P
t=1

t
1
1+r̃
t
1
1+r̃

where r̃ is the discount rate for the new portfolio given in (1). For maturity, we simply use the
maturity of the new portfolio, m0 .
Haircuts. We use the haircut measure proposed by Sturzenegger and Zettelmeyer (2006), HSZ
together with a measure of face-value haircut. The face value haircut is simply equal to one minus
the ratio of the face value of the new debt relative to the face value of the old (defaulted) debt.
The SZ haircut is defined as,
HSZ = 1 −

Present Value of New Debt
,
Present Value of Old Debt

where the present value of the cash flows is discounted using a fixed interest rate of 10%.

Full text of Working Papers (Federal Reserve Bank of Richmond) : Improving Sovereign Debt Restructurings, Working Paper 22-06

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