Policy Research Working Paper 9017
Eurobonds
A Quantitative Analysis of Joint-Liability Debt
Vasileios Tsiropoulos
Macroeconomics, Trade and Investment Global Practice
September 2019
Policy Research Working Paper 9017
Abstract
This paper assesses the consequences of implementing a only if no participating sovereign is willing to service the
joint liability debt system in a two-country small open econ- debt. The findings suggest that the welfare consequences
omy model. With joint liability a default of one country of this policy proposal hinge critically on the timing of its
makes the other participant liable for its debt. The results introduction: Introducing such instruments at the peak of
highlight a trade-off between the contagion risk, in the the Eurozone crisis would have helped the Periphery and
sense that this instrument may push some member states harm the Core member states, while its adoption during
to default even though they are individually solvent, and normal times has the potential to make all participants
cheaper access to credit on average, since lenders are at risk better-off.
This paper is a product of the Macroeconomics, Trade and Investment Global Practice. It is part of a larger effort by the
World Bank to provide open access to its research and make a contribution to development policy discussions around the
world. Policy Research Working Papers are also posted on the Web at http://www.worldbank.org/prwp. The author may
be contacted at vtsiropoulos@worldbank.org.
The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development
issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the
names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those
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Eurobonds: A Quantitative Analysis of Joint-Liability Debt
Vasilis Tsiropoulos∗
World Bank
1 Introduction
This paper introduces bonds with joint liability in a model where two small open economies
borrow from risk neutral international lenders. Under joint liability a default in one country
makes the other country liable for its debt. This feature introduces the potential for contagion
of default decisions, while introducing further repayment guarantees for lenders. Hence, the
introduction of this instrument generates contagion risk, in the sense that this instrument may
push some countries to default even though they are individually solvent. On the other hand, it
may generate cheaper credit, thereby helping enhance ﬁnancial stability. In this paper I quantify
the eﬀects and generate predictions about the welfare implications of introducing joint liability
bonds under diﬀerent underlying fundamental conditions.
The recent Eurozone crisis has highlighted the necessity for the development of ﬁnancial
instruments that mitigate the eﬀects of the ﬁnancial crisis and stabilize the yields of sovereign
bonds. One of the mechanisms that was proposed by the European Commission (2011) as
a potential shield of future ﬁnancial crises is the implementation of bonds with joint liability
(Eurobonds).1 On the one hand, some member states may increase their debt accumulation
with this mechanism, since they will have easier access to ﬁnancial markets. This would be
∗ Email: vtsiropoulos@worldbank.org
Acknowledgment: The views expressed in this article are mine and do not necessarily reﬂect the views of the
World Bank. I am greatly indebted to Juan Carlos Conesa and Eva Carceles-Poveda for their encouragment and
guidance. I would also like to thank Alexis Anagnostopoulos, Marina Azzimonti, Gabriel Mihalache, Pau Pujolas,
Pavlos Karadeloglou, Doerte Doemeland, Tito Cordella, and participants of Stony Brook University workshop,
The Economic Seminar of Central Bank of Ireland, Irish Economic Association Annual Conference, The 11th
Annual Economics Graduate Students Conference, The 69th Annual New York State Economics Association, The
27th International Conference on Game Theory, and the seminar of University of Piraeus.
1Not to be confused with Eurobond, which are bonds denominated in a currency other than the local currency
of the issuing country.
problematic since a failure of a country to repay may trigger a contagion eﬀect if the other
countries do not have enough resources to absorb the troubled debt.2 On the other hand,
the introduction of joint liability bonds like Eurobonds could provide better access to ﬁnancial
markets especially to those countries under stress. Moreover, it could decrease the incentives
for some member countries to abandon the Euro or default, by promoting stability and setting
the basis for a prospective ﬁscal integration, European Commission (2014).
I consider two economies with exogenous incomplete markets. In the benchmark case coun-
tries can issue only individual sovereign bonds, following Arellano (2008). Then, I study the
interactions between two countries that can issue bonds with full joint liability. Following the
literature, I study an endowment economy and I abstract from production and input decisions.
The endowments follow a stochastic process taken from data on the performance of Core and
Periphery countries in the Eurozone.3 For my measurement I use two groups of countries, the
ﬁrst group is wealthier with less income volatility than the other group and represents the Core
member states of the Eurozone (Germany, France, Netherlands), while the other group repre-
sent the Periphery member states of Eurozone (Portugal, Italy, Greece, Ireland, Spain). In the
analysis, the prices of the bonds are endogenously determined and depend on both countries
choices, generating a strategic interaction between the two countries. In particular, there exist
a two-stage Nash equilibrium. In the ﬁrst stage countries make their repayment decisions and,
conditional on this, they make their borrowing decisions on the second stage. I do not allow
for partial default, and the penalty of default is a permanent output loss and exclusion from
ﬁnancial markets.
This paper is related to the novel literature that studies the eﬀects of Eurobonds. Delpla
& von Weizsacker (2010) discusses the ‘blue and red bond’ proposal, in which they propose
pooling debt up to 60% of GDP (blue bonds) and using individual bonds issued by each country
separately (red bonds) beyond that threshold. Hellwig & Philippon (2011) foresees a mutualiza-
tion of 10% of GDP for the short term debt. Claessens et al. (2012) discusses in depth various
proposals of Eurobonds and analyze potential eﬀects in the Eurozone, and Beetsma & Mavro-
matis (2014) and Tirole (2015) analyze stylized ﬁnite-period models of the strategic interactions
between two countries that can issue joint liability bonds. They ﬁnd that Eurobonds might
be beneﬁcial under some circumstances. This paper complements that literature by providing
2 The European Commission (2011) has tried to asses the feasibility of common issuance of sovereign bonds
among Member States of the Eurozone, while it highlights the “moral hazard” as a potential problem. As a
solution to this problem, all the proposals suggest borrowing limits in order to mitigate this potential problem.
3 The distinction between Core and Periphery countries in Eurozone follows the description of the related
literature.
2
quantitative predictions in an inﬁnite horizon general equilibrium model of debt and default.
This paper also builds on the literature on the quantitative implications of debt dynamics
and default in incomplete asset markets models: Eaton & Gersovitz (1981), Aguiar & Amador
(2013), Aguiar & Gopinath (2006), Cuadra et al. (2010), Pouzo & Presno (2014), and Yue
(2010).4 In fact, the benchmark for comparison is Arellano (2008), which accounts for the
empirical regularities in emerging markets as an equilibrium outcome of the interaction between
risk-neutral creditors and a risk averse borrower that has the option to default.5 Hatchondo
et al. (2017) studies the eﬀects of introducing a limited non-defaultable ﬁnancing option in
a small-open economy. However, they abstract from the strategic interactions that might be
generated among the participating member states. Their results suggest that access to such
an asset for a given country could produce substantial welfare gains and lead to signiﬁcant
reductions in sovereign debt and spreads. Arellano & Bai (2014a), Arellano & Bai (2014b)
and Lizarazo (2009) examine the contagion across sovereign defaults through the existence of
common lenders. In this paper, I extend this idea and I develop a model that nests common
` am et al. (2015) develop a model of the Financial Stability Fund
lenders and borrowers. Abrah`
(FSF) across sovereigns as a long-term partnership with limited ex-post transfers. To the best
of my knowledge, none of the papers in the quantitative default literature addresses the impact
of the strategic interactions that joint liability bonds might generate.
The benchmark model is calibrated for the case of a single country issuing individual bonds.
Then, I compare this benchmark to a world where two countries can issue joint liability bonds
under two diﬀerent scenarios: (i) the two countries are subject to diﬀerent processes of id-
iosyncratic income risk (asymmetric case), and (ii) the two countries are subject to the same
process of idiosyncratic income risk (symmetric case). The ﬁndings show that countries have
cheaper access to ﬁnancial markets in both scenarios, even though the welfare implications diﬀer
drastically between both scenarios. In the symmetric case (two core countries issuing joint lia-
bility bonds), the model predicts welfare gains for both countries since the cheaper credit eﬀect
dominates to the contagion eﬀect. In contrast, in the asymmetric case Periphery countries ex-
periment welfare gains, while Core countries face welfare losses when both countries start with
large debt-to-output ratios. If the Periphery countries start with low debt-to-output ratios, then
the Core countries could also beneﬁt from the introduction of Eurobonds.
The paper is structured as follows: Section 2 presents the theoretical models for the bench-
4 See Aguiar & Amador (2014) or Tomz & Wright (2012) who explore more key issues in this literature.
5 Alternative models of default focus on rollover risk, such as Cole & Kehoe (2000) and Conesa & Kehoe
(2015), but I do not consider this issue in my analysis.
3
mark economy and the Eurobonds, Section 3 calibrates the model and assesses the quantitative
implications of the model, and Section 4 concludes.
2 The Model
I consider two cases of sovereign bonds markets: ﬁrst the benchmark economy, in which countries
issue only individual bonds to the international markets, i.e. no joint liability. Second, both
countries are allowed to issue only bonds with joint liability.
I assume that the countries are risk-averse and they cannot aﬀect the world risk free interest
rate. The period utility function u(.) : R+ → R and is assumed to be strictly increasing,
strictly concave and satisﬁes Inada conditions. The lifetime payoﬀ of each borrowing country
∞
i is E0 t=0 β t u(ci,t ), where β ∈ (0, 1) is the discount factor, i ∈ {1, 2} is the index for each
set of countries, ci,t denotes each country’s level of consumption at period t. Moreover, in each
period the countries receive a stochastic endowment of a single perishable consumption good
yi,t , which is drawn from a compact set Y = [y, y ]. These shocks follow a Markov process with
transition matrix πi (yi , yi ).
In both models, the risk averse countries trade one-period asset with the risk-neutral com-
petitive foreign lenders. The lenders have access to an international credit market where they
can trade as much as they need at a constant risk free interest rate r. I assume that the lenders
always commit to repay their debt. However, countries have no commitment and each period
decide whether to repay their debt or to default.
The lenders have perfect information about the history of endowments and they can observe
the demand for next period’s assets. Given these two variables they estimate the probability
that the countries will be insolvent and they oﬀer an interest rate that compensates for the risk
of default. Considering the risk-neutrality and the zero expected proﬁts, the equilibrium prices
q are given by,
1−φ
q= (1)
1+r
1
where φ is the endogenous derived default probability. The bond price q lies in [0, 1+ r ], since,
0 ≤ φ ≤ 1. The probability of default is zero for any positive savings and the sovereign bond
1
price indicates the price of a risk free bond 1+r . When countries have negative savings there
might be some positive probability φ for the government to default which has a negative eﬀect
4
on the price of the sovereign bond to compensate the international creditors.6 The sovereign’s
1
interest rate is deﬁned as the inverse of the bond price, rs = q − 1 and the country’s spread is
the diﬀerence between the interest rate and the risk free interest rate, s = rs − r.
Inﬂuenced by the default episodes in various emerging economies, the cost originated by
default episodes is two fold: (i) de facto prohibited access to the ﬁnancial markets because of
high interest rates and (ii) a direct output loss due to liquidity problems, outﬂow of capital,
banking problems. If a country chooses to default, I assume that it will remain in permanent
ﬁnancial autarky since the incidence of the insolvency has created bad reputation for the country
from the international creditors. The output cost is a function g (yi ) ≤ yi that country has when
defaults and is an increasing function respect to yi , as in Arellano (2008).
2.1 Benchmark
This section is the benchmark economy and follows Eaton & Gersovitz (1981) for the theoretical
part and Arellano (2008) and Aguiar & Gopinath (2006) for the quantitative part. Deﬁne V (b, y )
to be the life-time value function for a country that starts the current period with assets b and
endowment y . The country chooses to maximize the present value of its welfare by choosing to
repay its debt or to default. Therefore, V (b, y ) satisﬁes
V (b, y ) = max {W def (y ), W r (b, y )} (2)
where W def (y ) is the value that is associated with the default, while W r (b, y ) is the pay-oﬀ
function associated with repaying:
W r (b, y ) = max u(c) + βEy /y V (b , y ) (3)
c,b
s.t. c+q (b , y ) · b = y + b
b>b
If the country defaults, it faces permanent ﬁnancial autarky and its consumption equals the
endowment, which entails some direct output costs. The value of default, W def (y ) is given by
the following:
W def (y ) = u(g (y )) + βEy |y W def (y ) (4)
6 Arellano (2008) models the price function in similar method.
5
Let A(b) be the set of y ’s for which it is optimal for the country to default. The default set of
the country, given that it has good credit history is:
A(b) = {y ∈ Y : W r (b, y ) ≤ W def (y )} (5)
The country may have incentives to default because it had a bad shock in the output com-
bined with a massive debt that is unsustainable. However, the country loses its ability to have
an intertemporal consumption smoothing since it has no access to the ﬁnancial markets. If the
country has a bad credit history then the default set is A(b) = Y .
The default probability for the country is deﬁned by:
φ( b , y ) = dπ (y |y ) (6)
A(b )
When the default set is empty, A(b) = ∅, then the equilibrium default probability is zero,
since it is not optimal for the country to default. When A(b) = Y then the probability to default
is equal to one. In general, the probability changes in a positive manner as the assets shift (i.e.
if the government debt is high then the probability is higher).
To derive the equilibrium prices I use Eq. 1, and we get:
1 − φ(b , y )
q (b , y ) = (7)
1+r
The level of the asset’s price depends on the probability that the country will default next
period. In the extreme case that the probability is equal to one then the price is equal to zero
and the country can not borrow. As the probability decreases, the price gets closer to the price
of a risk free bond.
Deﬁnition 1: A Recursive Equilibrium for a single country consist of: (i) policy functions
for borrowing and consumption {b (b, y ), c (b, y )} and a value function {V (b, y )} (ii) the price
function for individual bonds q (b , y ) st:
1. Given the prices, the policy functions and the value functions of the country solve its
maximization problem 2 - 4.
2. Taking as given country’s policy functions and value function, the bond price function
satisﬁes the maximization problem of the foreign lenders 7.
6
2.2 Eurobonds
In this part, I lay out the economy in which both countries can issue bonds with joint liability.
The vector of endogenous aggregate states consists of the vector of countries’ debt holdings,
{bi }∀i . Therefore, the economy’s state space consists of the endogenous and exogenous states
and is denoted by S = {b1 , b2 , y1 , y2 }. The countries’ repayment strategy is denoted by, {hi }∀i .
The repayment strategy is a binary variable, where hi = 0 stands for good credit, while hi = 1
stands for bad credit.
In this economy countries interact strategically about their borrowing and repayment de-
cisions simultaneously in two stages as shown in ﬁgure 1. In the ﬁrst stage they chose their
repayment decision. Conditional on the decision of the ﬁrst stage, they issue assets on the
second stage. Hence, there are three possible scenarios.
Figure 1: Timing of Decision
Scenario I - If both countries choose to repay, the payoﬀ function Wirr (S ; bi− ) of country i,
given the arbitrary asset strategy bi− for country i− , solves:
7
Wirr (S ; bi− ) = max u(ci ) + βEyi ,y − |S ViE (S ) (8)
ci ,bi i
s.t. ci + qE (bi , bi− , yi , yi− ) · bi = yi + bi
bi > b
Let ViE (S ) be the associated value function for Eurobonds for each country i, given that
both countries have good credit history. It is vital to know the level of debt for country i− , since
it inﬂuences the Eurobonds’ price qE (bi , bi− , yi , yi− ). Next period, since both countries choose
to repay, they will be able to borrow again with Eurobonds.
Scenario II/III - If country i chooses to repay while country i− chooses to default, the payoﬀ
function Wird (S ) solves:
Wird (S ) = max u(ci ) + βEyi |yi Vi (bi , yi ) (9)
ci ,bi
s.t. ci + qi (bi , yi ) · bi = yi + (bi + bi− )
bi > b
where, Wird (S ) is the payoﬀ function when country i chooses to repay while country i−
chooses to default. In this scenario, country i has to pay the sum of all the Eurobonds, while
next period country i will land in the benchmark case from section 2.1. The next period Value
function Vi (bi , yi ) is the same as in the benchmark economy, since next period the country will
issue debt without any joint liability. The price qi (bi , yi ) that country i receives today is also
derived by the benchmark economy, since it reﬂects the probability that the country has to
default next period.
Scenario IV - if country i chooses to default, its payoﬀ is:
Widd (yi ) = Widef (yi ) (10)
which is identical to the one in section 2.1.
I develop an intra-period game to derive the optimal strategy of repayment and borrowing
for each country i, since it internalizes the eﬀects of its strategies and the other’s country
strategies. The structure of the subgame depends on the aggregate state space S , as well as the
8
repayment and borrowing decisions of both countries. The equilibrium strategies of repayment
and borrowing {bi (S ) = bBR
i (S, bBR BR BR
i− , hi− ) , hi (S ) = hi (S, hBR BR
i− , bi− )}∀i are computed
by solving a Nash Equilibrium, thus they reﬂect the best response of country i given the best
response of country i− .
The best response for the repayment strategy of country i, given the arbitrary current strate-
gies {hi− , bi− } is deﬁned:
rr dd
(1 − hi ) · Wi (S ; bi− ) + hi · Wi (yi ) ,if hi− = 0
hBR
i (S ; hi− , bi− ) = argmax (11)
hi ∈{0,1}
(1 − hi ) · Wird (S ) + hi · Widd (yi ) ,if hi− = 1
The best response for the debt strategy of country i, given the arbitrary current strategies
{hi− , bi− } is deﬁned:
Wirr (S ; bi− ) ,if hBR
i = 0 & hi− = 0
bBR
i (S ; bi− , hi− ) = argmax Wird (S ) ,if hBR
i = 0 & hi− = 1 (12)
bi ∈B
0 ,if hBR =1
i
˜ E (S ; {b , h }∀i ) is the payoﬀ function of country i, given the arbitrary current
Moreover, V i i i
strategies {bi , hi }∀i
Wirr (S ; bi− ) ,if hi = 0 & hi− = 0
˜iE (S ; {bi , hi }∀i ) =
V Wird (S ) ,if hi = 0 & hi− = 1 (13)
Widd (yi ) ,if hi = 1
Deﬁnition 2: Given the future value functions {ViE (S ), Vi (bi , yi ) , Videf (yi )} and the prices
{qi (bi , yi ), qE (b1 , b2 , y1 , y2 )}, the intra-period Nash Equilibrium consists of the best response
strategies for borrowing and repayment {bBR
i (S ; bBR BR BR
i− , hi− ), hi (S ; hBR BR
i− , bi− )}∀i s.t.:
1. The best response strategies for repayment and borrowing are the solutions to maximiza-
tion problem 12 and 11
2. The equilibrium pay-oﬀ value function ViE (S ) is derived by the equilibrium strategies
{bBR
i (S, bBR BR BR
i− , hi− ), hi (S, hBR BR
i− , bi− )}∀i and equation 13 s.t.:
9
˜ E (S ; {bBR , hBR }∀i )
ViE (S ) = V i i i
Given the outcome of the intra-period Nash Equilibrium, let D(b1 , b2 ) be the set, for which both
countries choose to default simultaneously:
D(b1 , b2 ) = {y1 ∈ Y & y2 ∈ Y : h1 (S ) · h2 (S ) = 1} (14)
To derive the equilibrium prices I use Eq. 1 as in the benchmark economy, which gives:
1− D (b1 ,b2 )
dµ1 (y1 |y1 )dµ2 (y2 |y2 )
qE (b1 , b2 , y1 , y2 ) = (15)
1+r
Note that this price reﬂects the probability that both countries will default simultaneously,
and the analysis is similar to the benchmark case.
Deﬁnition 3: Given the price function {qi (bi , yi )}∀i and the value function {Vi (bi , yi ), Widef (yi )}∀i
from deﬁnition 1, a Markov Perfect Equilibrium for this economy consists of: (i) policy functions
for repayment, borrowing, consumption {hi (S ), bi (S ) , ci (S )}∀i , value functions {ViE (S )}∀i and
(ii) a price function for bonds {qE (bi , bi− , yi , yi− )} st:
1. Given the prices {qi (bi , yi ), qE (bi , bi− , yi , yi− )} and the equilibrium value functions from
deﬁnition 1 and 2, the policy functions and the value functions are the solution to the
maximization problem 8 - 13 and satisfy deﬁnition 3.
2. Taking as given both countries’ policies functions and values functions, the bond price
function {qE (bi , bi− , yi , yi− )} satisﬁes the maximization problem of the foreign lenders 15.
3 Quantitative Analysis
3.1 Calibration
Most parameter values of the benchmark economy are set following the literature or exogenously
estimated from the data. First, I cluster the Core countries (Germany, France, Netherlands) and
the Periphery countries (Portugal, Greece, Italy, Spain, Ireland) of Eurozone. Then I estimate
the stochastic processes for the outputs of these groups from their time series. I assume that
the stochastic processes of these two groups are independent and follow a log-normal AR(1)
process log yt = ρ log yt−1 + t , where t ∼ N (0, σ 2 ).7 The stochastic process is discretized into
7 In
future work, I will examine the spill-over eﬀects that may be generated by introducing correlation in the
endowment processes of the two countries.
10
an independent Markov Chain by using Tauchen & Hussey (1991). Furthermore, the diﬀerences
between Core and Periphery are not only in their income process, but also the Core is richer
than the Periphery by 20% on average according to Eurostat data. A period in the model refers
to a quarter, and the risk free interest rate is set equal to 1.7% as in Arellano (2008). The utility
function displays a constant coeﬃcient of relative risk aversion form,
c1−σ
u(c) = , with σ = 1
1−σ
The risk aversion coeﬃcient σ is set to 2, which is a common value used in real business cycle
studies. All the Eurobonds proposal had some form of borrowing limit for the member states in
order to mitigate moral hazard concerns. For this reason, I set an exogenous borrowing limit,
of 66% debt-to-income ratio for the Core and of 83% for the Periphery.8 As in Arellano (2008),
I assume that default entails some direct output cost of the following form:
γE (y ) , if yi > E (yi )
i
g (yi ) = (16)
y i , if yi ≤ E (yi )
where γ is the exogenous output cost that I set equal to 0.96, as in Arellano (2008). Finally,
I calibrate the discount factors of the benchmark model to match the sovereign spreads of Core
and Periphery and I set them equal to 0.89 and 0.88, respectively.
Table 2 presents some results on the performance of the benchmark models in comparison
with the data. To derive the business cycle statistics, I run many simulations of the model over
time until a default occurs and I evaluate the mean statistics of these simulations.
The model matches relatively well the spread for both countries. It predicts that the mean
interest rate spread for the Core is 0.5%, while in the data is 0.6%. The model is less successful
for the Periphery, since it generates a mean interest rate spread of 1.9%, while in the data is
2.4%. Moreover, the model has an exogenous debt-to-output ratio to match the data.
The model predicts lower volatility than the data. The volatility of the interest rates for the
Core is 0.9 % and the Periphery is 2.16% in the data; the model under-predicts the volatility
for both countries, since for the Core is 0.019% and the Periphery is 0.042%.
8 I am in the process of relaxing this assumption. I am solving for the economy that has no exogenous
borrowing constraints.
11
Table 1: Calibration
Values Target
Risk aversion σ=2 Arellano (2008)
Output cost after default γ = 0.96 Arellano (2008)
Risk free interest rate 1.7 % Arellano (2008)
Core’s income process ρ = 0.96, σ = 0.003 Data
Periphery’s income process ρ = 0.92, σ = 0.004 Data
Output diﬀerence ¯c /y
y ¯p = 1.2 Data
Core’s borrowing limit 66% Treaty
Periphery’s borrowing limit 83% Treaty
Calibrated parameters
Core’s discount factor βc = 0.89 0.6% spread
Periphery’s discount factor βp = 0.88 2.4% spread
Table 2: Business Cycle Statistics: The Benchmark Model and the Data
Data Benchmark
mean(%) Core Periphery Core Periphery
Debt/Y 66 83 66 79
Spread 0.6 2.4 0.5 1.9
C/Y 77 80 98.8 98.6
std(%)
Debt/Y 8.10 19 0.16 0.36
Interest rate 0.9 2.16 0.019 0.042
C/Y 1.15 1.9 0.14 0.15
3.2 Results
This section ﬁrst analyzes the policy functions of the benchmark and the Eurobonds models
and then examines the quantitative performance of the Eurobonds model in comparison with
the benchmark model.
The introduction of joint-liability bonds generates two opposing forces. On the one hand,
this instrument generates a contagion eﬀect, in the sense that it may push some countries to
default even though they are individually solvent. On the other hand, joint-liability bonds may
create cheaper access to credit, since insuring other countries allows for lower rates.
Figure 2 shows the eﬀects of introducing Eurobonds and having cheaper access to the ﬁnancial
markets for the Core countries. It compares the spread that is generated by the benchmark and
12
the Eurobonds model. The Eurobonds’ price depends also on the Periphery’s debt, which is
ﬁxed to 55% debt-to-output ratio. When the Core has below 53% debt-to-output ratio, there
is no positive externality from the introduction of Eurobonds, since if the Core defaults the
Periphery would also be dragged to default with high probability. It would have been very
expensive for the Periphery to cover the Core’s inherited debt, thus there is no signiﬁcant eﬀect
on the spreads. However, in the region 53%-47%, the Periphery would be willing to cover the
inherited debt if the Core defaults, since the Periphery inherits a lower amount of debt. Hence,
the Periphery would not default and for this reason the spread decreases and the Core receives
a positive externality. In the region above 47%, the Core would not default neither in the
benchmark nor in the Eurobonds model, for this reason there is no diﬀerence between the two
models.
Figure 3 shows the eﬀect of introducing Eurobonds and having cheaper access to the ﬁnancial
markets for the Periphery countries. As in ﬁgure 2, the Eurobonds’ price depends also on
the Core’s debt, which is ﬁxed to 50%, and it compares the spread that is generated by the
benchmark and the Eurobonds model. When the Periphery has above 53% debt-to-output ratio,
there is no positive externality from the introduction of Eurobonds, since the Periphery would
not default neither in the benchmark nor in the Eurobonds model. However, below 53% the
Periphery receives lower spreads in the Eurobonds model, because of the insurance mechanism
of the Eurobonds. If the Periphery defaults, the Core will cover the inherited debt with high
probability, for this reason international lenders are willing to buy bonds at a relatively lower
interest rate. As the level of the Core’s inherited debt increases the probability, that Core has
to payoﬀ the debt, decreases and for this reason the spread increases. It is clear from ﬁgure 2
and 3 that the price eﬀects for the Periphery are bigger than the Core, nonetheless Core also
receives some positive externalities by issuing debt with joint-liability.
Figure 4 and 5 compare the changes on the repayment policy functions for both the Bench-
mark and the Eurobonds model, given a certain combination of income level of Core and Pe-
riphery. The x-axis and y-axis measure the level of asset holding over the average income level
for Core and Periphery, respectively. The red region represents the combination of the inher-
ited asset levels for which both countries decide to default simultaneously, as in Arellano &
Bai (2014a). In the dark green area both choose to repay, while in the light green area I come
across with multiple pure strategy Nash equilibrium on the repayment decision and countries
choose either to repay or default. In case of multiple equilibrium, I choose by assumption the
outcome that yields the highest aggregate welfare, which is the scheme that both economies
13
Figure 2: Core’s spread in the Benchmark and the Eurobonds model, for the same level of
debt-to-output ratio and income realization. Periphery’s debt-to-output ratio is ﬁxed to 55%.
Figure 3: Periphery’s spread in the Benchmark and the Eurobonds model, for the same level of
debt-to-output ratio and income realization. Core’s debt-to-output ratio is ﬁxed to 50%.
14
repay simultaneously. The dark blue region shows the synthesis of asset level for which Core
defaults while Periphery repays the sum of Eurobonds and then issues individual bonds. Fi-
nally, in the white area no pure strategy Nash Equilibrium exists. For this reason, I solve for
the unique mixed strategy Nash Equilibrium of the repayment strategy. The solid yellow lines
exhibit the threshold at which countries would default below that level of asset for a speciﬁc
income realization in the benchmark model.
The analysis of repayment policies explains which of these two opposing eﬀects dominates in
the Eurobonds model in comparison with the benchmark model. Figure 4 shows the repayment
policy functions when the Core and the Periphery face the lowest possible income realization,
4% below the trend of each country. In this ﬁgure, the contagion eﬀect dominates, since after
the introduction of Eurobonds the region that both countries default simultaneously is growing.
On the left panel is the repayment policy function for the benchmark economy, in which there is
no form of joint liability or any strategic interaction among the countries. Below the horizontal
yellow line the Core countries default while below the vertical yellow line the Periphery countries
default. Below the vertical and the horizontal yellow line both countries choose to default
simultaneously while the vertical and the horizontal yellow line above both countries are solvent.
On the right panel is the repayment functions for the Eurobonds economy, where countries issue
assets with joint liability and they interact strategically on their repayment and borrowing
decisions. In this particular case, the contagion eﬀect dominates, since there are regions in
which countries choose to default even though they would not in the benchmark economy. The
area above the vertical yellow line and below the horizontal yellow line turns from blue in the
benchmark to red in the Eurobonds. Here the result is driven by the fact that in this region
the Periphery prefers to be insolvent while the Core inherits the sum of Eurobonds. Hence,
the Core does not have the means to pay the whole sum of Eurobonds and it is dragged to the
default region.
Figure 5 presents the repayment policy functions for which the cheaper access to credit eﬀect
dominates. In this ﬁgure, the cheaper credit eﬀect dominates, since after the introduction of
Eurobonds the region that both countries repay simultaneously is growing. The Core faces an
income realization of 2% below its trend, while the Periphery has 4% below its trend (same as
ﬁgure 4). On the left panel is the repayment policy function for the benchmark economy and
the threshold for the Periphery is the same as in the previous ﬁgure although the Core now
does not default. Here, the lower interest rate eﬀect dominates since there is a region below
the horizontal yellow line that turns from blue in the Benchmark model to dark green in the
15
Figure 4: Policy function for repayment. Both countries have a deep recession, 4% below s
steady state. DD is when both countries default, RR both countries repay, RD is when Core
repays and Periphery defaults, DR is when Periphery repays and Core defaults.
Eurobonds model. This happens because the Periphery takes advantage of the relatively better
income realization of the Core economy and receives a better interest rate. Hence, the Periphery
has less incentives to default in this environment with joint liability.
Table 3 shows some quantitative predictions of the Eurobonds model. To derive the business
cycle statistics, I run many simulations over time and report the mean, until at least one of the
countries defaults in the Eurobonds. I use the same parameters as in the benchmark economy,
to examine the eﬀects after the introduction of joint liability bonds.
The Eurobonds model predicts that interest rates will decrease signiﬁcantly in the long
run, not only for the Periphery but also for the Core, because of the cheaper credit eﬀect. I
conduct two experiments for the Eurobonds model, (i) two asymmetric countries (i.e. Core and
Periphery) and (ii) two symmetric countries (i.e Core and Core). Both experiments predict lower
mean spread than the benchmark model. In particular, in both experiments the mean interest
rate spread drops to 0.1% for both countries, while in the benchmark economy it was 0.5% for the
Core and 1.9% for the Periphery.9 Moreover, the volatility of interest rates reduces signiﬁcantly
in the Eurobonds model. The volatility of interest rate drops to 0.002% and 0.001% for the
asymmetric and symmetric case respectively, while in the benchmark economy it is 0.019% for
the Core and 0.042% for the Periphery. It is important to mention that the debt-to-output ratio
9 Both countries receive the same interest rate, since they issue debt with joint liability. The interest rate in
the Eurobonds model reﬂects the probability that both countries will be insolvent simultaneously.
16
Figure 5: Policy function for repayment, Core has a mild recession and Periphery has a severe
recession, 2% and 4% below steady state, respectively. DD is when both countries default, RR
both countries repay, RD is when Core repays and Periphery defaults, DR is when Periphery
repays and Core defaults.
is the same in the benchmark and Eurobonds models due to the exogenous borrowing limit,
therefore there is no need for comparison. However, the goal of this paper is not only to forecast
the eﬀects on the spreads per se, but also the potential consequences of the Eurobonds on the
countries’ welfare, as it will be shown in the next section 3.3.
Table 3: Business Cycle Statistics: The Eurobonds Model
Asymmetric Symmetric
mean(%) Core Periphery Core
Debt/Y 66 79 66
Spread 0.1 0.1 0.1
std(%)
Debt/Y 0.035 0.034 0.029
Interest rate 0.002 0.002 0.001
3.3 Welfare Eﬀects of introducing Eurobonds
I ﬁrst solve for the benchmark economy in which there is no form of joint liability. Then, I
measure the welfare eﬀects of an unanticipated announcement explaining that from now on, Core
and Periphery will be forced to issue debt with joint liability and interact strategically on their
borrowing and repayment decisions. I measure the welfare eﬀects as the proportional changes
17
of consumption that would leave the consumer indiﬀerent between living in the benchmark
environment or in the Eurobonds environment, given the stationary ergodic distribution of
income. This consumption change is given by
1
ViE (S ) 1−σ
λi =
Vi (bi , yi )
where ViE and Vi denote the value functions with and without joint liability, respectively.
Figure 6 shows the unconditional expected welfare eﬀects for both countries in the asym-
metric environment. The Core’s debt-to-output is ﬁxed to 50% and countries have welfare gains
above the zero line, otherwise they have losses. The Core is getting better oﬀ as the Periphery’s
debt-to-output ratio decreases. This is happening for two reasons, ﬁrst the Core receives a
better price because the Periphery has a lower debt-to-output and therefore a lower probability
to be insolvent. Second, the contagion eﬀects decreases, thus the Core has smaller negative ex-
ternalities if the Periphery defaults. On the other hand, the Periphery is overall better oﬀ after
the introduction of Eurobonds. More speciﬁcally, when the Periphery’s debt-to-output ratio is
between 80% and 54%, the Periphery faces welfare improvements as the debt level decreases,
since the country inherits lower level of debt. However, when the Periphery has a debt-to-output
ratio below 55%, the expected welfare eﬀects are getting stagnant, because the Periphery faces
negative externalities from the fact that the Core has a relatively high debt-to-output ratio.
When the Periphery has a debt-to-output ratio below 38% there is a Pareto improvement, since
both countries have welfare gains. The model also predicts that Eurobonds should not have
been implemented when they were suggested at the peak of the Eurozone debt crisis. At that
time, most of the Eurozone member states, especially the Periphery members, had relatively
high debt-to-output ratios. Moreover, as the model predicts, the Periphery member states were
in favor of Eurobonds while the Core were not. Nonetheless, the model foresees that when the
Periphery has relatively low debt-to-output ratio, all the member states are better oﬀ with the
introduction of Eurobonds. Hence, if Eurobonds had been introduced before the ﬁnancial crisis,
when almost all the member states had low level of debt, then it would have been beneﬁcial for
all the member states.
Figure 7 presents the expected Pareto Eﬀects in the asymmetric environment. In contrast
with ﬁgure 6, where the Core has a ﬁxed level of debt, this ﬁgure examines the Pareto Eﬀects
for all the possible asset combinations. The green region shows all the asset combinations for
which there exist a Pareto Improvement. As it is explained in ﬁgure 6, in order to have Pareto
18
Figure 6: Above the zero line countries face welfare gains, while below welfare losses. Core’s
debt-to-output ratio is ﬁxed to 50%.
Improvement the Periphery countries should have a relatively low level of debt. Otherwise, there
is a Pareto loss, mostly because the Core countries have welfare losses.
Figure 8 shows the expected Pareto eﬀects in the symmetric environment for all the possi-
ble asset combinations. As in Tirole (2015), as the countries get more symmetric the welfare
improvements are bigger after the introduction of bonds with joint liability. In particular, the
Core member states would be better oﬀ if they had a Eurobonds agreement with symmetric
countries instead of the Periphery countries. For example, Germany would be better oﬀ if it had
a Eurobonds agreement with France instead of Spain. The main force for this result is the fact
that the contagion eﬀect is smaller in comparison with the asymmetric case. Moreover, table 3
shows that there is no signiﬁcant diﬀerence on the average spread between the asymmetric and
symmetric environment, thus the cheaper credit eﬀect is similar in both environments.
It is likely that this model may underestimate the welfare gains from lowering the sovereign
spreads mainly for two reasons. Firstly, lower sovereign spreads lead to better allocation of
factors of production and therefore could create signiﬁcant positive eﬀects as in Mendoza &
Yue (2012). Secondly, they decrease the probability of a credit crunch and/or a banking crisis
as in Sosa-Padilla (2015) and Bocola (2014). In light of these ﬁndings, gains from introducing
19
Figure 7: Expected Pareto Eﬀects in the Asymmetric environment, for all the possible asset
combinations.
Figure 8: Expected Pareto Eﬀects in the Symmetric environment, for all the possible asset
combinations
20
joint-liability bonds may be larger than the ones I compute.
4 Conclusion
Europe faces the dilemma of whether to step forward to a higher degree of uniﬁcation. This
paper develops and analyzes a Eurobonds model where two small open economies issue bonds
with full joint liability and interact strategically on their borrowing and repayment decisions.
I compare this to the benchmark economy, which builds on a standard default model as in
Arellano (2008), under two diﬀerent scenarios. In the ﬁrst scenario countries are asymmetric,
one country is wealthier and less volatile than the other (i.e Core and Periphery member states of
Eurozone), while in the second scenario there are two symmetric countries (i.e Core and Core).
The ﬁndings show that in both scenarios Eurobonds decrease the yields of sovereign debt for
all the member states in the long run. Nonetheless, the welfare consequences in the asymmetric
scenario hinge critically on the timing of its introduction. More speciﬁcally, introducing such an
instrument at the peak of the Eurozone crisis would have brought welfare gains for the Periphery
member states and losses for the Core member states. However, adopting Eurobonds in “normal
times”, when member states have relatively lower debt-to-output ratios, has the potential to
make all participants better-oﬀ. In the symmetric scenario, the implementation of Eurobonds
produces welfare gains for all participants.
A natural extension of the model with the asymmetric scenario would be the analysis of
whether or not member states would be willing to take austerity measures to reduce the current
high debt-to-output ratios. This would allow the member states to reach the debt-to-output
ratio levels at which all participants would be better oﬀ with the introduction of Eurobonds.
Moreover, it would be newsworthy to explore the option of a joint liability mechanism that
allows for bailing-out insolvent participants, as in Azzimonti & Quadrini (2016). In particular,
in this environment countries will make transfers in order to decrease the default incentives. This
mechanism has the potential to generate not only less default, but also reduce the contagion
eﬀect. Finally, it would be interesting to examine the case which countries are not forced to
permanent ﬁnancial autarky and they are permitted to issue debt after a few years of the default
incident. I leave these for future research.
21
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23
A Appendix
A.1 Additional Results for the Eﬀects of Introducing Eurobonds
Figure 9 presents next period’s expected inherited debt for Core and Periphery in the asymmetric
experiment, when Core’s debt-to-output ratio is ﬁxed to 50%. If the model does not allow for
default, Core’s expected inherited debt would have been an horizontal straight line and the
45 degree line for the Periphery. However, in this model countries are allowed to default and
inherit zero debt. For this reason, when Periphery has low debt-to-output ratio the expected
inherited debt for Periphery is the 45 degree line and for the Core the expected inherited debt
is the horizontal line. Nonetheless, Periphery defaults more frequently as the debt increases,
thus below -0.75 Periphery’s expected inherited debt line is getting ﬂatter and Core’s expected
inherited debt is getting larger. Hence, this ﬁgure shows the negative externalities that Core
countries receive from the fact that inherit higher level of debt.
Figure 9: The Expected Inherited Debt for Core and Periphery, while Core’s debt-to-output
ratio is ﬁxed to 50%.
Figure 10 shows the unconditional expected welfare eﬀects of introducing joint liability bonds
in the asymmetric environment. On the right graph is Periphery’s welfare eﬀects after the
introduction of Eurobonds. As I discussed previously there are two opposing forces, the eﬀect of
cheaper credit and the contagion eﬀect. The introduction of Eurobonds brings welfare gains for
Periphery mainly because the cheaper credit eﬀect dominates for all the combination of assets
between Core and Periphery.
The left panel of ﬁgure 10 presents Core’s welfare eﬀects after the introduction of Eurobonds.
24
The welfare eﬀects are mixed and they depend on the asset combination of the Core and Periph-
ery. When Core and Periphery have relatively high debt-to-output ratio, the contagion eﬀect
dominates and Core is worse oﬀ. However, when Periphery has relatively low debt-to-output
ratio then Core has welfare gains due to the cheaper credit eﬀect. At this point I would like
to mention that the combination of the left and right panel of ﬁgure 10 generates the Pareto
Eﬀects that are shown on ﬁgure 7.
Figure 10: Welfare eﬀects after the introduction of Eurobonds (Core & Periphery). Dark green
and Red represent the welfare gains and losses, respectively.
Figure 11 performs the same experiment as in ﬁgure 10 for the symmetric environment. In
this environment countries are better oﬀ because the contagion credit eﬀect is smaller than the
asymmetric case, thus countries will be more willing to issue debt with joint liability at any
combination of assets. As I explained in the section 3.3 the cheaper credit eﬀect is similar in the
symmetric and asymmetric environment. The combination of this ﬁgure for both participating
countries in the symmetric environment derives the Pareto Eﬀects of ﬁgure 8.
25
Figure 11: Welfare eﬀects after the introduction of Eurobonds (Core & Core).
A.2 Computational Algorithm
The following algorithm is used to solve the Benchmark and Eurobonds models:10
1. Discretize the state space for assets b = (b1 ; b2 ) consisting of a grid of 1600 points equally
spaced and the endowment space y = (y1 ; y2 ) into 25 pairs using Tauchen & Hussey (1991)
method.
2. Solving the Benchmark model for the two countries separately (following Arellano (2008))
(a) Start with some guess for the parameters to be calibrated: βi and γ .
0
(b) Start with a guess for the bond price schedule such that qi (bi , yi ) = 1/(1 + r) for all
bi and yi .
(c) Given the bond price schedule, solve the optimal policy functions ci (bi , yi ), asset
holdings b (bi , yi ), repayment sets and default sets Ai (bi ) via value function iteration.
0
I iterate on the value function until convergence for a given qi .
(d) Compute business cycles statistics from 3,000 simulations that each have 3,000 pe-
riods. If the model business cycles match the data we stop, otherwise we adjust
parameters, and go to step 2.a.
3. Solving the Eurobonds model, given the parameters and the equilibrium outcomes of the
Benchmark model:
10 Itis important to compute ﬁrst the Benchmark model separately and then use the equilibrium parameters
to compute the Eurobonds model.
26
(a) Given the price schedules {qi (bi , yi )}∀i and the value functions {Widef (yi ), Vi (bi , yi )}∀i
from the Benchmark models.
(b) Derive the pay-oﬀ functions Wird (S ) ∀i, this is the scenario that country i repays
while country i− defaults.11
0
(c) Start with a guess for the eurobonds price schedule such that qE (S ) = 1/(1 + r) for
all the possible combinations of bi and yi .
0
(d) Given the price schedules {qE (S ), qi (bi , yi )}∀i and the pay-oﬀ functions {Widef (yi ),
Vi (bi , yi ), Wird (S )}∀i . To solve for the value function and the intra-period Nash Equi-
librium, for a given price schedule, the following algorithm is being used:
i. Assuming that both countries choose to repay, I solve for the pay-oﬀ function
{Wirr (S ; bi− )}∀i , and the best response of debt policy function {bBR
i (S ; 0, bi− )}∀i ,
for all the arbitrary next period asset decisions of country i− , given that the
country i− is solvent.
ii. Given the best response debt policy function for all the arbitrary debt decisions of
the other country. I solve for the ﬁxed point that yields the optimal best response
of asset and repayment decisions {hBR
i (S ; hBR BR BR
i− , bi− ), bi (S ; hBR BR
i− , bi− )}∀i
˜ E (S ; {hBR , bBR }∀i )}∀i .
and update the value function for Eurobonds, {ViE (S ) = V i i i
I iterate on the the value function for Eurobonds until convergence for a given
0
qE (S ).
(e) Given the optimal best response for repayment of both countries I update the price
0
schedule of Eurobonds {qE (S )}, and go to step 3.d until convergence.
11 W rd (S ) is one shot problem since in the ﬁrst period country i has to pay the sum of Eurobonds and then
i
continues as in the Benchmark model, without issuing assets with joint liability.
27