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February 2024
Optimal Bailouts in Banking and Sovereign Crises†
Sewon Hur
Federal Reserve Bank of Dallas
sewonhur@gmail.com
C´esar Sosa-Padilla
University of Notre Dame and NBER
csosapad@nd.edu
Zeynep Yom
Villanova University
zeynep.yom@villanova.edu
Abstract
We study optimal bailout policies amidst banking and sovereign crises. Our model
features sovereign borrowing with limited commitment, where domestic banks hold
government debt and extend credit to the private sector. Bank capital shocks can
trigger banking crises, prompting the government to consider extending guarantees
over bank assets. This poses a trade-off: Larger bailouts relax financial frictions and
increase output, but increase fiscal needs and default risk (creating a ‘diabolic loop’).
Optimal bailouts exhibit clear properties. The fraction of banking losses the bailouts
cover is (i) decreasing in government debt; (ii) increasing in aggregate productivity;
and (iii) increasing in the severity of banking crises. Even though bailouts mitigate the
adverse effects of banking crises, the economy is ex ante better off without bailouts:
Having access to bailouts lowers the cost of defaults, which in turn increases the default
frequency, and reduces the levels of debt, output, and consumption.
Keywords: Bailouts, Sovereign Defaults, Banking Crises, Contingent Transfers, Sovereign-
bank diabolic loop.
JEL classification codes: E32, E62, F34, F41, G01, G15, G28 H63, H81.
†We thank Mark Aguiar, Manuel Amador, Javier Bianchi, Markus Brunnermeier, Pablo D’Erasmo, Alok
Johri, Illenin Kondo, Leonardo Martinez, Enrique Mendoza, Yun Pei, Fabrizio Perri, Linda Tesar, Jing
Zhang, and participants at numerous conference and seminar presentations for insightful discussions. This
research was supported in part through a grant from Villanova University and computational resources
provided by the Big-Tex High Performance Computing Group at the Federal Reserve Bank of Dallas. The
views expressed herein are those of the authors and not necessarily those of the Federal Reserve Bank of
Dallas or the Federal Reserve System. First draft: February 2020.
1 Introduction
Recent European debt crises highlighted the ‘diabolic loop’ between sovereign risk and bank
risk. On the one hand, the Irish bailout of 2008 illustrated how bailouts and asset guarantees
can shift financial risk to the government (Acharya et al.,2014). On the other hand, the
Greek debt crisis of 2012 showed how sovereign risk can weaken banks’ balance sheets due
to overexposure to government debt (Sosa-Padilla,2018). In the presence of this diabolic
loop, how much—if at all—should the government intervene to ‘save’ the domestic banking
sector during banking crises?
To answer this question, we build a quantitative model that features a rich interaction
between sovereign and banking risk. To mitigate the adverse effects of banking crises, which
reduce credit to the private sector and thereby decrease output, the government may find
it optimal to bail out banks. Bailouts come with a trade-off, allowing the government to
boost liquidity and output during banking crises while increasing sovereign debt and default
risk. Sovereign defaults weaken banks’ balance sheets, completing the ‘diabolic loop.’ In
this environment, we find it optimal—from an ex ante perspective—to ban bailouts. Absent
bailouts, the diabolic loop is severed, and this consideration dominates the ex post benefits
of bailing banks out.
We model bailouts as contingent guarantees over bank capital. This is guided by empirical
evidence from the recent European sovereign debt crisis. In Section 2, we document that the
issuance of sovereign guarantees is the most prevalent form of intervention during banking
crises. Among European countries, the average share of government guarantees relative to
GDP is three times larger than the average share of direct capital transfers during banking
crises—a relationship that does not hold during normal times.
Every period, the economy observes the realization of a productivity shock and a bank
capital shock, which represents the fraction of bank capital that could become lost if a
banking crisis materialized. In response, the government chooses the amount of potential
capital losses to guarantee. These guarantees (bailouts) are financed with a mix of new
borrowing and distortionary taxation. The government lacks commitment to repay, and if
it should default, it temporarily loses access to new borrowing and cannot extend bailouts.
We calibrate our model using data from European countries facing sovereign risk. Our
model matches salient moments in the data, both targeted and untargeted. We show that
the occurrence of a banking crisis increases the default probability (from 0.5 to 0.7 percent
annually), resulting in sovereign spreads that are higher (from 0.7 to 0.9 percent) and more
volatile (from 0.6 to 1.0 percent). From an ex post perspective, the government finds it
1
optimal to issue bailouts (i.e. contingent guarantees) that are on average 1.7 percent of
GDP during banking crises.
We further validate the model by comparing its dynamics around banking crises with
the data. We find that banking crises are associated with sharp output contractions and
sovereign yield spikes. Furthermore, governments that experience a banking crisis with high
debt levels face deeper and longer recessionary dynamics and higher spreads. These dynamics
are consistent with the data.
Using the calibrated model, we study the ex post optimal properties of bailouts. Other
things equal, the fraction of banking losses that the bailouts would cover: (i) increases with
the severity of the banking crisis, because the impact of bank capital shocks is nonlinear—
small shocks negligibly affect lending to the private sector, whereas large shocks can generate
a severe private credit crunch absent government intervention; (ii) decreases relative to the
level of government debt, since a more indebted government has less fiscal space to prop
up banking sector assets; and (iii) increases with aggregate productivity, since the better
the economy’s overall state, the more valuable credit is and the cheaper it is to borrow to
provide the guarantees.
Our model has implications for the design of institutions that govern bailouts. Is it
optimal from an ex ante perspective to allow governments to bail out the banking sector,
knowing that this may lead to higher default risk? We find that the costs of bailouts (higher
sovereign risk) outweigh the benefits (ability to increase liquidity during banking crises).
Even though the welfare gains of maintaining access to bailouts are state-contingent, we find
that for the empirically relevant cases (i.e., economies with moderate to high initial debt
levels), the country is better off banning bailouts altogether. This is because governments
without the ability to issue bailouts face better borrowing opportunities.
Why does ruling out bailouts improve bond prices? The answer is in the default costs: An
economy without bailouts endogenously features larger default costs, which in turn allows it
to have higher levels of debt, output, and consumption than an economy with bailouts, on
average. The endogenous default costs in our model are given by reduced liquidity (because
banks’ holdings of government debt become non-performing), which leads to reduced out-
put. This reduced liquidity continues once the government regains access to credit markets
(because it does so with zero debt). However, the severity of this reduced liquidity depends
on whether the government has access to bailouts: If bailouts are available, the government
can use them to prop up liquidity and increase output immediately after re-entering from a
default. This is why access to bailouts lowers the costs of default, reduces government debt
capacity and average consumption, and decreases welfare.
2
We show that our main findings are robust to alternative modeling assumptions and
parameter values. For example, we study an extension of the model in which the government
does not lose access to bailouts during default and exclusion periods. Allowing for bailouts
during default and exclusion reduces the cost of default even further, leading to larger welfare
losses for the bailout economy. In another extension, we assume that the government places
equal weight on households and banks (as opposed to placing full weight on households as
in the baseline). We also extend the model to allow for moral hazard, a feature that we
abstract from in the baseline model, which further reinforces the ex ante undesirability of
bailouts. Finally, we also investigate the possibility that the announcement of a bailout can
reduce the probability of banking crises. We find that the ex ante sub-optimality of bailouts
is robust to these and other alternative specifications.
Related literature. This paper belongs to the quantitative literature on sovereign debt
and default, following the contributions of Eaton and Gersovitz (1981), Aguiar and Gopinath
(2006) and Arellano (2008). Our work differs from these early papers, in that it presents a
model that entails a rich interaction between the government and the financial sector to study
the transmission of risks between these sectors and their implications on the real economy.
Our paper is at the intersection of two strands in the literature. The first uses dynamic
quantitative models of sovereign risk to examine how the banking channel amplifies the ef-
fects of sovereign risk. The closest paper to ours is Sosa-Padilla (2018), which studies how
a sovereign default affects banks’ balance sheets and creates a private sector credit crunch,
endogenizing output declines. Bocola (2016) studies the macroeconomic implications of in-
creased sovereign risk in a model, where banks are exposed to government debt. His frame-
work takes default risk as given and shows how anticipation of a default can be recessionary
on its own. Perez (2015) also studies the output costs of default when domestic banks hold
government debt. Public debt serves two roles in his framework: It facilitates international
borrowing, and it provides liquidity to domestic banks. In addition to the bank balance sheet
effects highlighted in these studies, our paper also incorporates the transmission of banking
crises to sovereign crises, which these papers do not consider.1
The second strand of the literature to which we are especially related is the one studying
1The theoretical work on sovereign risk and bank fragility is vast. A branch of the literature uses stylized
models of domestic and external sovereign debt in which domestic debt weakens the balance sheets of banks
(e.g., Bolton and Jeanne,2011,Gennaioli et al.,2014,Gaballo and Zetlin-Jones,2016, and Balloch,2016).
Other papers, more quantitative in nature, explicitly consider how banks are either affected by or amplify
default risk (e.g., Boz et al.,2014,Mallucci,2015,Thaler,2021,Abad,2019,Coimbra,2020, and Moretti,
2020). Without explicitly modeling banks, Arce (2022) studies how government bailouts of the private sector
can lead to increased sovereign risk.
3
the feedback loop between sovereign risk and bank risk, the so-called ‘doom loop.’ Acharya
et al. (2014) model a stylized economy where bank bailouts (financed via a combination of
increased taxation and increased debt issuance) can solve an underinvestment problem in
the financial sector, but exacerbate another underinvestment problem in the non-financial
sector. Higher debt needed to finance bailouts dilutes the value of previously issued debt,
increases sovereign risk, and creates a feedback loop between bank risk and sovereign risk
because banks hold government debt in their portfolios. Cooper and Nikolov (2018) and
Farhi and Tirole (2018) also study the dynamic interaction between sovereign debt and the
banking system and show the conditions (in their respective theoretical models) under which
a bailout-induced doom loop may arise.
We borrow insights from these papers and focus on the ex ante optimal properties of
bailouts using a quantitative model calibrated to recent GIIPS (Greece, Italy, Ireland, Por-
tugal and Spain) data. We also differ from these papers in that we model bailouts as
contingent guarantees over bank capital (motivated by the evidence in Section 2).
The existing literature is split on the desirability of bailouts. For example, Bianchi (2016)
and Keister (2016) study bailouts, abstracting from sovereign risk, and find that bailouts can
be desirable even when taking into account moral hazard consequences. Our main departure
from this literature is the consideration of sovereign risk, whereby bailouts can lead to a
‘doom loop.’ In this environment, we find that bailouts are ex ante suboptimal for the
empirically relevant states of initial debt, even in the absence of moral hazard concerns.
Farhi and Tirole (2018) and Cooper and Nikolov (2018), share our prescription: If at all
possible, a country is better off ruling out bank bailouts. These papers also have theories of
bailout-induced diabolic loops; we differ from them in that we provide a quantitative model
with a strategic default decision. Finally, there are papers that assume an exogenous level
of initial debt, and therefore focus on the ex post effects of bailouts.2
On the policy side, various proposals have aimed at lowering the fragility of the banking
sector and its exposure to sovereign risk. Examples include the implementation of eurobonds
(Favero and Missale,2012) or the creation of European Safe Bonds (Brunnermeier et al.,
2017). These proposals highlight how important it is to have reliable estimates of the dynamic
relationship between sovereign risk, bank fragility, and economic activity. We provide a
quantification of the role that government bailouts play in these dynamics.
Finally, our paper also relates to the large literature on country bailouts, either from a
central authority (such as the ECB or IMF) or from another individual country. Contribu-
2For instance, Capponi et al. (2022) find that governments should bailout banks that have a high ‘network
centrality’ and Acharya et al. (2014) derive conditions under which the ex post optimal bailout is non-zero.
4
tions inspired by the recent European debt crisis include Gourinchas et al. (2020), Azzimonti
and Quadrini (2023), Pancrazi et al. (2020), Roch and Uhlig (2018), and De Ferra and Mal-
lucci (2020), among others. These authors typically focus on moral hazard concerns and
(the lack of) policy coordination. We view our work as complementary to theirs since our
focus is on domestic governments bailing out their own banking sector, and we abstract from
moral hazard considerations.3
The rest of the paper is organized as follows: Section 2 summarizes the stylized facts
that motivate our theoretical model. Section 3 introduces the model. Section 4 explains
the calibration of the model, presents the quantitative results, and discusses the properties
of the optimal policies. Section 5 discusses the optimality of bailouts. Section 6 provides a
discussion of extensions and robustness. Finally, Section 7 concludes.
2 Motivating Facts
The nexus between sovereign and banking crises is not a new phenomenon, and various
aspects of it have been studied previously. In this section, we highlight three features of
banking and sovereign debt crises that motivate our study: (i) defaults and banking crises
tend to happen together, (ii) domestic banking sectors are highly exposed to government
debt and this exposure tends to be greater during crises, and (iii) the most prevalent form
of government intervention (during banking crises) is the issuance of asset guarantees.
•Default and Banking crises tend to happen together. This is a well-established fact.
Reinhart (2010) documents 82 banking crises, of which 70 are accompanied by sovereign
defaults. Focusing on more recent data, Balteanu et al. (2011) identify 121 sovereign
defaults and 131 banking crises for 117 emerging and developing countries from 1975
to 2007. Among these, they find 36 “twin crises” (defaults and banking crises). In 19
of them, a sovereign default preceded the banking crisis and in 17 the reverse occurred,
suggesting that both directions of causality are likely at play.4
•Banks are exposed to sovereign debt and this exposure is higher during crises. Gennaioli
et al. (2018) report an average bank exposure ratio (net credit to the government as a
3Naturally, this paper is also related to the body of work on government bailouts of banks that abstracts
from sovereign risk considerations. For recent examples, see Niepmann and Schmidt-Eisenlohr (2013) and
Keister (2016).
4Another empirical study documenting this fact is the one by Borensztein and Panizza (2009). They
construct an index of banking crises that includes 149 countries for the period 1975–2000. In this sample,
they identify 111 banking crises (implying an unconditional probability of having a crisis equal to 2.9 percent)
and 85 default episodes (unconditional default probability of 2.2 percent). When conditioned on a sovereign
default episode, the probability of a banking crisis increases by a factor of 5.
5
fraction of bank assets) of 9.3 percent using data from both advanced and developing
countries. When they focus only on defaulting countries, they find an exposure ratio
of roughly 15 percent. Similarly, Abad (2019) documents that the banking sectors in
Spain and Italy increased their exposure to domestic sovereign debt during the recent
European debt crisis (with exposure ratios increasing by 8 percentage points).
Our own empirical contribution is to document a third motivating fact regarding how
governments intervene during banking crises. Specifically,
•Issuance of sovereign guarantees is the most prevalent form of government intervention
to alleviate banking crises. European Union governments have largely intervened in
two ways—via asset guarantees and capital transfers. Using data from Eurostat, we
construct the average net annual change in government guarantees and average capital
transfers as a percentage of GDP in the 23 EU countries from 2007 to 2019.5Figure 1
shows that governments mostly rely on asset guarantees rather than capital transfers
as the way to intervene during banking crises (defined following Laeven and Valencia,
2013b). We find that the average change of government guarantees as a fraction of
GDP is close to 1.7 percent during banking crises, whereas it is close to zero in the
overall sample. We also find that the change in capital transfers is less different across
the two time periods, suggesting that transfers figure less prominently in government
banking crisis intervention. In Appendix A, we show that a similar pattern holds for
“contingent liabilities” (a broader definition of asset guarantees).6
3 Model
We extend the banking and sovereign default model of Sosa-Padilla (2018) in two dimen-
sions: banking crises that are driven by exogenous shocks to bank capital in addition to the
bank balance sheet effects triggered by sovereign defaults, and government bailouts that can
mitigate a banking crisis but may trigger sovereign default crises.
5See Appendix Bfor the details.
6Metrick and Schmelzing (2021) introduce a historical dataset of banking crisis interventions that covers
1257-2019. The authors show that high-income countries (with income per capita greater than 30,000 USD)
favor guarantees more than capital injections as an intervention policy. Specifically, guarantees constitute 33
percent of the interventions whereas capital injections make up 26 percent of the interventions in high-income
countries.
6
Figure 1: Government guarantees and capital transfers
Environment. We consider a closed economy populated by four agents: households, firms,
banks, and a government. Households supply labor to firms, but do not face any intertem-
poral decisions. Firms hire labor and obtain working capital loans from banks to produce
a consumption good. Banks lend to both firms and the government and are subject to a
lending constraint. Additionally, banks are subject to shocks to the value of their capital.
Finally, the government is a benevolent one (i.e., it maximizes households’ utility). It faces
an exogenous stream of spending that must be financed, and it can also provide contingent
guarantees to the banks. To meet its obligations, the government has three (endogenous and
potentially time-varying) instruments: labor income taxes, borrowing, and default.
Debt contracts are unenforceable, and the government may default on its debt. We
assume defaults are total: All debt is erased. If the government decides to default, it gets
excluded from the credit market for a random number of periods. During this time, the
government cannot conduct bailouts.7
There are four aggregate state variables in our model economy: one endogenous and
three exogenous. The level of government debt, B, is the endogenous state variable. The
first exogenous state variable is aggregate productivity, z, which follows a Markov process.
The second exogenous state variable, ε, captures the fraction of bank capital that could be
7In Section 6(and Appendix C.1), we relax this assumption and allow the government to issue bailouts
even during default/exclusion periods. Our main result, that bailouts are ex-ante welfare decreasing, is
robust to (and even strengthened by) this extension.
7
lost and follows an iid process. We denote s={z, ε}. The third exogenous state variable,
A, is the realized level of bank capital: With probability 1 −π, this level is unaffected (and
equal to a baseline value, A=A); with probability π, it is reduced to A= (1 −ε)A.
Timing of events. If the government enters the period in good credit standing, then the
sequence of events is as follows:
1. The exogenous aggregate state sis realized
2. Considering the aggregate state (B, s), the government decides whether to repay (d=
0) or to default (d= 1)
3. If d= 0, then:
(a) the government announces a bailout policy
(b) given the bailout policy, banks decide their loan supply
i. with probability π, the bank’s capital is reduced by ε, and the government
disburses the promised bailouts
ii. with probability 1 −π, the bank’s capital is unaffected, and the government
does not pay any bailouts
(c) all other private decisions occur
(d) the government chooses its borrowing policy B0(B, s, A)
4. If d= 1, then:
(a) the government cannot promise bailouts and is excluded from financial markets
(b) banks determine their loan supply
(c) with probability π, the bank’s capital is reduced by ε
(d) all other private decisions occur.
If the government enters the period in bad credit standing (i.e. it finished the previous period
excluded from financial markets), the government regains market access with probability θ.
If it regains market access, then the timing of events is as above, with an initial debt level of
zero. Otherwise, if the government remains excluded, the timing of events amounts to the
sequence of stages 1 and 4 above.
8
3.1 Decision problems given government policy
Households. Households’ only decisions involve labor supply and consumption levels.
Therefore, the problem faced by the households can be expressed as:
max
{c,n}U(c, n) (1)
s.t. c= (1 −τ)wn + ΠF,(2)
where U(c, n) is the period utility function, cstands for consumption, ndenotes labor supply,
wis the wage rate, τis the labor-income tax rate, and ΠFrepresents the firms’ profits. The
solution to the problem requires:
−Un
Uc
= (1 −τ)w, (3)
which is the usual intratemporal optimality condition equating the marginal rate of substi-
tution between leisure and consumption to the after-tax wage rate.
Firms. Firms demand labor to produce the consumption good. They face a working capital
constraint that requires them to pay upfront a certain fraction of the wage bill, which they
do with intra-period bank loans. Hence, the problem is:
max
{N,`d}ΠF=z F (N)−wN −r`d(4)
s.t. γwN ≤`d(5)
where zis aggregate productivity, F(N) is the production function, `dis the demand for
working capital loans, ris the interest rate charged for these loans, and γis the fraction of
the wage bill that must be paid upfront.
Equation (5) is the working capital constraint. This equation will always hold with
equality because firms do not need loans for anything other than paying γwN ; thus, any
borrowing over and above γwN would be sub-optimal. Taking this into account, we obtain
the following first-order condition:
zFN(N) = (1 + γr)w, (6)
which equates the marginal product of labor to the marginal cost of hiring labor once the
financing cost is factored in. Therefore, the optimality conditions from the firms’ problem
9
are represented by equation (5), evaluated with equality, and equation (6).
Banks. Banks play a vital role in the economy by providing loans to both the government
and the firms. They face a lending constraint requiring that loans to firms do not exceed the
value of their loanable resources. These resources amount to the sum of three components:
b,A, and T. The first component is the banks’ holdings of sovereign bonds, b. The second
component is banks’ capital, A, which is subject to aggregate shocks. The third component
is government guarantees, T(B, s, A) (i.e. the state-contingent bailouts that the government
may provide).
The dynamics of bank capital are as follows: Every period, bank capital has a reference
value of Athat is subject to shocks, ε, which represent the fraction of bank capital that
could be lost. The magnitude of the shock εis realized at the beginning of the period,
but uncertainty regarding whether the shock hits the banks is only resolved at the end of
the period. With probability π, the bank’s capital is reduced by a fraction ε, and with
probability 1 −π, the bank’s capital is unaffected. These dynamics can be summarized as
A=
Awith probability 1 −π
(1 −ε)Awith probability π.
(7)
Let A(ε) = (1 −ε)A. We refer to the event that A=A(ε) and ε > 0 as a banking crisis.8
The lending constraint faced by banks is such that it must be satisfied in every possible
state. This implies that in every period the supply of loans is limited by the worst-case
scenario (i.e., the minimum) of the banks’ loanable funds:
`s≤min
A{A+b+T(B, s, A)}.(8)
This constraint is intended to capture, in a stylized way, the idea that (a) increased uncer-
tainty about the state of the banking sector can spill over into the real economy, and (b)
the government can prevent banking sector shocks from causing contractions in output by
8While we describe shocks to Aas fluctuations in banks’ capital, they could more broadly be interpreted
to include: (a) domestic bank runs (as they will affect the funding side of the banks’ balance sheet), (b)
shocks to the valuation of holdings of foreign debt (as highlighted in Gunn and Johri,2018), and (c) global
shocks (e.g. ‘sudden stops’ that may be transmitted through cross-border banking networks). See Section 6
and Appendix C.5 for a discussion on the sensitivity of our results to different values of A.
10
issuing bailouts.9
When the government has access to credit, the value function of the representative bank
is given by
WR(b;B, s) = max
`s
EA
max
x,b0x+δEs0|s(1 −d0)WR(b0;B0, s0) + d0WD(s0)
s.t. x≤T(B, s, A) + b−q(B0, s)b0+r(B, s, A)`s
(9)
s.t. (8)
where xis consumption, δis the banks’ discount factor, r(B, s, A) is the interest rate on
private loans, q(B0, s) is the price of government bonds, and B0,T, and dare government
policies for debt, bailouts, and default, which the banks take as given. Wdis the value of
the representative bank when the government does not have access to credit, and is given by
WD(s) = max
`s,x x+δEs0|sθW R(0; 0, s0) + (1 −θ)WD(s0)(10)
s.t. x≤rdef(s)`s(11)
`s≤A(ε) (12)
where θis the probability that the government regains access to credit and rdef(s) is the
interest rate on private loans when the government does not have access to credit. In this
case, the bank can provide loans only up to the adverse realization of its loanable funds,
given by equation (12).
3.1.1 Characterization of equilibrium given government policies
Hereafter, we focus on bailout policies that take the following form:
T= 0 if A=A
0≤T≤ε A if A= (1 −ε)A.
(13)
In other words, the government cannot provide bailouts if the adverse bank capital shock
does not materialize, and it can only cover a sum not to exceed the amount of the bank’s
capital loss if the shock does materialize. In that sense, we also refer to the bailouts as
9Our modeling assumptions imply that transfers have a one-for-one effect on bank loans. There are
several papers that study how government interventions affect bank lending using micro-level data. For
example, focusing on the effect of the Troubled Assets Relief Program (TARP) on bank loans, Berrospide
and Edge (2010) show that a $1 increase in capital received resulted in an increase of between $0.4 and $1.5
in loans over the following year. See Berger et al. (2020) for a summary of this literature.
11
government guarantees.
Loan market. When the government does not have access to credit, banks supply
`s
def(s) = A(ε).(14)
When the government has access to credit, banks supply
`s(B, s) = B+A(ε) + T(B, s, A(ε)).(15)
Note that the loan supply does not depend on the realization of A. Instead, given our
restrictions on government bailout policies, the total loan supply is determined by the level
of government debt (B), the reduced bank capital A(ε), and government transfers T.
The demand for intra-period loans comes from the firms. Combining equations (6) and
(5) (with equality) we obtain the following loan demand function:
`d(B, s, A) = γznFn
1 + γr .(16)
Note that the loan demand depends on the realization of A. This is because during a banking
crisis (A=A(ε) with ε > 0), the government may need to raise distortionary labor income
taxes to pay for the bailouts, affecting equilibrium labor.
It is then straightforward to derive the equilibrium conditions for the loan rate under
repay and default:
r(B, s, A) = max (zn(B, s, A)Fn
B+A(ε) + T(B, s, A(ε)) −1
γ,0)(17)
and
rdef(s) = max (zndef(s)Fn
A(ε)−1
γ,0).(18)
As was the case in Sosa-Padilla (2018), there is the possibility that the interest rate that
clears the loan market in (17) or (18) is not strictly positive. In that case, the equilibrium
loan amount is demand determined. Notice that a default shrinks the supply of loanable
funds and, other things equal, increases the rate on the working capital loans. This loan
rate increase arises from two reasons: Bonds are not repaid, and the government is unable
to extend bailouts during defaults.
12
Government bond market. After the proceeds from private loans are received (recall
these are intra-period loans), the banks invest in government bonds before the end of the
period. These bonds are the only way to transfer resources across time, and they are priced
according to their inherent default risk. The bond pricing function satisfies
q(B0;s) = δEs0|s
1−d(B0, s0)
|{z }
default premium
EA0
1 + r(B0, s0, A0)
|{z }
lending discount
(19)
This expression shows that in the case of a default in the next period, d(B0, s0) = 1,
the lender loses not only the original sovereign bond investment but also future gains
that those bonds would have created had they been repaid. These gains are captured by
EA0[r(B0, s0, A0)].
3.2 Determination of government policies
The government’s optimization problem can be written recursively as:
V(B, s) = max
d∈{0,1}(1 −d)VR(B, s) + d V D(s)(20)
where VRand VDare the values of repaying and defaulting, respectively. Let κ≡(B, s, A)
denote the complete aggregate state and Φ ≡ {τ, T, B0}summarize the fiscal policies under
repay. The value of repaying is:
VR(B, s) = max
Φ
EAnUc(κ; Φ) , n (κ; Φ) +βEs0|sV(B0, s0)o(21)
subject to:
τ w(κ; Φ) n(κ; Φ) + B0q(B0, s) = g+B+T(gov’t b.c.)
c(κ; Φ) + x(κ; Φ) + g=zF (n(κ; Φ)) (resource constraint)
T= 0 if A=A
0≤T≤εA if A=A(1 −ε))(constraint on T)
and
13
q(B0, s) = δEs0|sn[1 −d(B0, s0)] EA01 + r(κ0; Φ0)o
r(κ; Φ) = max nzn(κ; Φ)Fn
B+A(ε)+T(A(ε)) −1
γ,0o
−Un
Uc= (1 −τ)w(κ; Φ)
zFn= (1 + γ r (κ; Φ)) w(κ; Φ)
`(κ; Φ) = γw(κ; Φ)n(κ; Φ)
x(κ; Φ) = T+B−q(B0, s)B0+r(κ; Φ)`(κ; Φ)
(comp. eq. conditions)
where c(κ; Φ), n(κ; Φ), x(κ; Φ), `(κ; Φ), w(κ; Φ), r(κ; Φ), and q(B0, s) represent the equilib-
rium quantities and prices for the private sector given public policy (under repayment).
The value of default is:
VD(s) = max
τUcdef (s;τ), ndef (s;τ)+βEs0|sθV (0, s0) + (1 −θ)VD(s0)(22)
subject to:
τ wdef(s;τ)ndef (s;τ) = g(gov’t b.c.)
cdef(s;τ) + xdef (s;τ) + g=zF (ndef (s;τ)) (resource constraint)
rdef(s;τ) = max nzndef (s;τ)Fn
A(ε)−1
γ,0o
−Un
Uc= (1 −τ)wdef (s;τ)
zFn= (1 + γ rdef (s;τ)) wdef (s;τ)
`def (s;τ) = γwdef (s;τ)ndef(s;τ)
xdef(s;τ) = rdef (s;τ)`def (s;τ)
(comp. eq. conditions)
where cdef(s;τ), ndef(s;τ), xdef(s;τ), `def (s;τ), wdef(s;τ), and rdef(s;τ) represent the equilib-
rium quantities and prices for the private sector given public policy (under default).
3.2.1 Equilibrium definition
A Markov-perfect equilibrium is then defined as follows:
Definition 3.1. AMarkov-perfect equilibrium for this economy is (i) a set of value functions
for the government {V(B, s), V R(B, s), V D(s)}; (ii) a set of government policy rules for bor-
rowing B0(κ), taxation τ(κ), bailouts T(κ), and default d(B, s); (iii) a set of decision rules and
prices from the private sector under repay {c(κ; Φ), n(κ; Φ), x(κ; Φ), `(κ; Φ), w(κ; Φ), r(κ; Φ)},
and under default {cdef(s;τ), ndef (s;τ), xdef(s;τ), `def (s;τ), wdef(s;τ), rdef(s;τ)}; and (iv) an
equilibrium pricing function for the sovereign bond q(B0, s), such that:
14
1. Given prices and private sector decision rules, the borrowing, tax, bailout, and default
rules solve the government’s maximization problem in (20)–(22).
2. Given the price q(B0, s) and government policies, the decision rules and prices of the
private sector are consistent with the competitive equilibrium.
3. The equilibrium price function satisfies equation (19).
4 Quantitative Analysis
In this section, we first describe how we set the parameters of the model. Second, we examine
the ability of our model to account for salient features of the data in GIIPS countries. Third,
we describe the properties of the optimal default and bailout policies.
4.1 Functional forms and stochastic processes
The period utility function of the households is given by
U(c, n) = c−nω
ω1−σ
1−σ(23)
where σand ωgovern risk aversion and the wage elasticity of labor supply, respectively.
The production function is given by
zF (n) with F(n) = nα.(24)
We assume that TFP shocks (z) follow an AR(1) process given by:
log (zt+1) = ρzlog (zt) + νz,t+1 (25)
where νz∼N(0, σz).
The potential bank capital shocks are assumed to take values that are between 0 and ε,
and have a cumulative distribution function
Fσε(ε) = 1−exp(ε)−σε
1−exp(¯ε)−σε,(26)
which is a transformation of the bounded Pareto distribution. The shape parameter, σε,
determines the variance of the εshocks.
15
4.2 Calibration
A period in the model is assumed to be a year. Table 1presents the parameter values.
Appendix Bhas details of the data we use to guide our calibration and Appendix Dprovides
details of the numerical solution. Whenever possible, we use data targets computed from
GIIPS. However, when appropriate, we also use an extended sample of countries that include
a mix of emerging and advanced economies to compute other moments such as default and
banking crisis frequencies, given that these are relatively rare occurrences.
Table 1: Parameters
Parameters Values Target/Source
Household discount factor, β0.81 Default probability: 0.5 percent
Risk aversion, σ2Sosa-Padilla (2018)
Frisch elasticity, 1
ω−10.67 Sosa-Padilla (2018)
Government spending, g0.15 Gov’t consumption (percent GDP): 19.1
Prob. of financial redemption, θ0.50 Expected exclusion: 2 years
Banks’ discount factor, δ0.96 Real interest rate: 4 percent
Baseline bank capital, ¯
A0.28 Bailouts in banking crises (percent GDP): 1.7
Bank capital shock shape, σε4.26 Standard deviation of output: 3.4 percent
Prob. of banking shock, π0.03 Banking crisis frequency: 1.8 percent
Labor share, α0.70 Sosa-Padilla (2018)
Working capital constraint, γ0.52 Sosa-Padilla (2018)
TFP shock persistence, ρz0.80 Standard value
TFP shock std, σz0.02 Standard value
The household and government’s discount factor is set to 0.81 to match a default proba-
bility of 0.5 percent. Since our analysis mainly focuses on the European periphery, our target
default probability of 0.5 percent is lower than that used for emerging economies (Aguiar
et al. 2016) and higher than that for advanced economies (Hur et al. 2018).10 Government
spending, g, is set to 0.15 to match the median government consumption share of GDP of
19.1 percent in GIIPS (1999–2019). The probability of financial redemption, θ, is set to 0.5,
which implies an average exclusion of 2 years.11
10The default frequency calculated for a panel of 38 advanced and emerging economies during 1970–2017
is 0.5 percent.
11This is a middle ground estimate given the long exclusion spells typically observed after defaults in
emerging economies and the relative quick resolution of recent sovereign crises in peripheral Europe. In
Appendix C, Table C.12 shows the sensitivity analysis for θ.
16
The bank’s discount factor is set to 0.96, to be consistent with a real interest rate of 4
percent. The level of the baseline bank capital, A, is set to 0.28 so that the model matches the
size of bailouts during banking crises, which is 1.7 percent of GDP as shown in the empirical
section. The shape parameter for shocks to bank capital, σε, is set to 4.26 to generate a
standard deviation of output that matches the median of 3.4 percent among GIIPS. The
parameter that governs the probability of shocks to banks’ capital, π, is set to 0.03 so that
the model matches the banking crisis frequency of 1.8 percent in a panel of 38 advanced and
emerging economies from 1970 to 2017.12
Six parameters are set externally. Following Sosa-Padilla (2018), we set risk aversion,
σ= 2, and set the value of ωto correspond to a Frisch elasticity of 0.67, both standard
values in the literature. Also as in Sosa-Padilla (2018), we set the labor income share α= 0.7
and the working capital constraint γ= 0.52. Finally, we set the persistence ρz= 0.8 and
standard deviation σz= 0.02, within the range of the typical values used in the literature.13
Appendix Cpresents a sensitivity analysis and shows that our main results are robust to
using alternative values for key model parameters.
4.3 External validity: simulated moments
In this subsection, we examine the fit of the model. Table 2shows the targeted and untar-
geted moments from our model simulations and their data counterparts. As is usual in this
literature, we report statistics for periods in which the government has access to financial
markets and no defaults are declared (the only exception is default frequency, for which we
use all simulation periods).
The model generates spreads that behave reasonably well. The mean and the volatility
of the spread are lower than in the data.14 This is not surprising, as the Global Financial
Crisis and the European Sovereign Debt crises occurred during the period (1999–2019). The
model also generates countercylical spreads, qualitatively consistent with the data, albeit
12In the data, we follow the classification in Laeven and Valencia (2013b), who use banking sector losses
and other indicators to identify banking crises. The list of 38 advanced and emerging economies is as in
Davis et al. (2016). In the model, we define a banking crisis as a non-zero reduction of bank’s capital. This
occurs with probability π(1 −Fσε(ε)) where εrefers to the lowest non-zero value in our discrete grid for ε.
13Previous works on sovereign default with production have parameterized the productivity process in a
similar way. For example, Boz et al. (2014) (in a calibration for Spain) estimate the TFP’s autocorrelation to
be 0.54 and impose a standard deviation of 2.6 percent; Hatchondo et al. (2022) (also calibrated to Spanish
data) find annualized persistence and standard deviation estimates of 0.89 and 2 percent, respectively. Our
parameterization of the TFP process (representative of GIIPS) is within these estimates.
14In the model, we compute sovereign spreads in our simulations as the difference between the bond’s
yield (1/q) and the real rate implied by the bank’s discount factor (1/δ). In the data, the spread is computed
as the nominal interest rate on government bonds in GIIPS minus that of Germany, from 1999 to 2019.
17
Table 2: Simulated moments: model and data
Model Data
Default frequency 0.5 0.5
Banking crisis frequency 1.8 1.8
Gov’t spending/GDP 19.1 19.1
Bailouts/GDP (banking crisis) 1.7 1.7
Sovereign spread
mean 0.7 1.2
standard deviation 0.6 1.8
corr(spread, output) –0.3 –0.6
Debt/GDP 15.5 25.8
corr(bailouts, debt) –0.3 –0.4
Bailout-output multiplier 1.5
Units: percent. Both the standard deviation and the cor-
relation are calculated based on HP-filtered residuals.
less so than in the data. The mean debt level in the model simulations is 15.5 percent of
GDP, below the median domestic government debt/GDP in EU countries, 25.8 percent.15
Accounting for more than 50 percent of this untargeted moment is a reasonably good fit,
given the well-known difficulty of sovereign default models with one-period debt in producing
sizeable debt ratios at the observed default frequencies.16
We find that the model produces a negative correlation between government guarantees
and debt. This correlation is −0.3, which is similar to the data.17 This negative correlation
highlights how higher indebtedness limits the ability of the government to issue guarantees.
We return to this issue in Section 4.5, where we describe the properties of the optimal
bailouts.
Our model generates a bailout-output multiplier of 1.5: a $1 increase in bailout transfers
leads to a $1.5 increase in output. While the empirical literature is not conclusive on the
magnitude (or the sign) of this multiplier, our number is very close to the multiplier of 1.6
15This median for domestic government debt is obtained using ECB data for the period 1999–2019 (in-
cluding debt at all original maturities). It includes all EU countries except for the UK, Greece, Ireland and
Latvia due to missing data.
16The literature has dealt with this shortcoming in different ways. One example is D’Erasmo and Men-
doza (2020) who study optimal domestic and external default using a one-period debt model calibrated to
European data. They create a maturity-adjusted debt-to-GDP ratio and report it to be 7.45 percent of GDP.
A different approach (e.g., Arellano,2008) is to target the debt service instead of debt stock. We focus on
domestic debt since we model a closed economy.
17Details regarding the estimation of this correlation are in Appendix B.
18
found in a recent quantitative study on bailouts (Bianchi,2016).18 Our number is also close
to those estimated by Faria-e Castro (2017), who finds a multiplier of 1.5 for equity injections
and 2 for credit guarantees.
Banking crises vs. normal times. Table 3shows that, conditional on experiencing a
banking crisis in the previous year, the default probability is 0.2 percentage points higher than
the unconditional default frequency of 0.5 percent. This increase in the default probability
is the ‘diabolic loop’ at work: Banking crises trigger payments of contingent bailouts, and
therefore, imply that governments need to borrow more. This higher level of indebtedness
pushes governments into the default risk zone, leading to more frequent defaults.
Table 3: Simulated moments: unconditional and banking crisis
Unconditional Banking crisis
Default frequency 0.5 0.7
Sovereign spread
mean 0.7 0.9
standard deviation 0.6 1.0
Debt/GDP 15.5 16.0
Bailout/GDP 0.9 1.7
Units: percent. The standard deviation is calculated based on HP-
filtered residuals of the spread.
These ‘diabolic loop’ dynamics naturally translate into sovereign spreads. The uncondi-
tional mean spread is 0.7 percent, but conditional on observing a banking crisis, the mean
spread increases by 0.2 percentage points. This increase reflects not only the higher likeli-
hood of default, but also a decline in the ‘lending discount’. If there is a banking crisis in
period t, then a default is more likely in period t+ 1 and, hence, the lender charges a higher
default premium. Additionally, if in t+ 1 the default is averted, then the interest rate on
loans is lower: There is higher debt and therefore greater loan market liquidity. Thus, the
sovereign bond becomes a less attractive investment for these two reasons: lower probability
of repayment and, in case of repayment, lower overall return. Our simulations also generate
higher spread volatility conditional on a banking crisis because default risk increases.
The last row of Table 3shows that, on average, the model features larger contingent
18For example, Barucci et al. (2019) and Laeven and Valencia (2013a) show positive effects of banking
sector interventions on economic outcomes, while Claessens et al. (2005) and Cecchetti et al. (2009) find that
bailout policies and liquidity support are associated with negative economic outcomes.
19
bailouts during banking crises than unconditionally.19 This is a distinctive feature of the
data, as we documented in Figure 1.
4.4 External validity: dynamics around banking crises
To further validate our model, we examine the behavior of output and sovereign yields around
banking crises. To compute the data counterparts, we construct an annual dataset of real
interest rates, GDP, government debt, and banking crisis indicators for 1950–2016, using the
Jord`a et al. (2017) Macrohistory database.20
Figure 2: Output around banking crises
Data Model
Note: The left and right panels show the dynamics of GDP around banking crises in the data and
in the model, respectively. The red dashed line conditions on high debt (above the 75th percentile).
All series in this figure are normalized to 100 in t=−1.
Absent government intervention, a banking crisis reduces loanable funds, increases firms’
borrowing costs and decreases output. At the same time, the government can issue contingent
guarantees to prop up the supply of loans and mitigate the negative effects of the shocks to
bank capital. Therefore, the equilibrium response of output depends on the initial debt level:
Governments with more debt (less fiscal space) face limits on the amount of bank capital
losses that can be guaranteed and will, therefore, experience a larger output contraction.
Figure 2shows that this model prediction also holds qualitatively in the data. Moreover,
19Consistent with the data, here we are reporting announced bailouts (as a percent of GDP), regardless
of whether a banking crisis materializes and bailout transfers are disbursed.
20See Appendix Bfor details regarding the construction of the dataset.
20
both model and data show that banking crises occurring at high debt levels are characterized
by protracted output declines. In the model, this happens for three interrelated reasons: (i)
mean reversion in productivity, (ii) worsening borrowing conditions and deleveraging, and
(iii) higher distortionary taxes. In this class of models, the samples identified as ‘high-debt’
samples are those where the economy experiences a series of good productivity realizations,
which allow it to take on higher debt. This eventually is followed by a mean reversion in TFP,
contributing to a decline in output. At the same time, deteriorating productivity worsens
borrowing terms, to which the government responds by deleveraging.
Figure 3: Debt and taxes around banking crises
Debt/GDP Tax rate
Note: The left panel shows the dynamics of Debt/GDP around banking crises and the right panel
shows the dynamics of the tax rate. Both panels are for model-generated data. The red dashed
line conditions on high debt (above the 75th percentile).
This deleveraging translates into lower liquidity in the domestic credit markets in subsequent
periods, further contributing to a decline in output. Finally, to finance this deleveraging, the
government raises distortionary taxes, which depresses equilibrium labor and output. These
model dynamics for debt and taxes are illustrated in Figure 3.
Furthermore, our theory predicts an increase in sovereign yields during banking crises.
Figure 4shows that this model prediction is qualitatively consistent with the data. We also
see that, both in the model and in the data, when the government suffers a banking crisis
with high debt levels, sovereign yields are higher. For the same reasons highlighted above, the
high-debt government faces worse borrowing terms, forcing the government to deleverage and
increase distortionary taxes. Because the government does not want to distort the economy
further, it chooses to accept higher equilibrium yields instead of deleveraging even more.
21
Figure 4: Sovereign yields around banking crises
Data Model
Note: The left and right panels show the dynamics of sovereign yields around banking crises in the
data and in the model, respectively. The red dashed line conditions on high debt (above the 75th
percentile).
4.5 Properties of optimal policies
Default incentives, bond prices, and debt dynamics. Our model features rich in-
teraction between debt levels, default incentives, banking crises, and bailout guarantees.
Consistent with the default literature, our model also generates default incentives that de-
crease with the aggregate level of productivity and increase with debt, which can be verified
in the left panel of Figure 5. In addition to this standard finding, we also see that the de-
fault set shrinks with higher values of the bank capital shock. This is because severe banking
crises can lead to sharp contractions in output absent government bailouts, thus increasing
the cost of default.
The price schedule (right-panel of Figure 5) reflects these default incentives. As usual,
higher realizations of productivity are associated with better prices (and higher debt capac-
ity). The price schedule demonstrates that borrowing is essentially risk-free for debt ratios
below 12 percent. Consequently, starting from zero debt, the economy’s debt-to-GDP ratio
quickly increases until it reaches 12 percent. It then ‘lives’ in the region where default risk
is small but positive, as in Figure 6, which plots the histograms of debt-to-GDP ratios both
unconditionally and conditional on banking crises. Since the left tails of these histograms
are very long, we choose to truncate them in our plots.
22
Figure 5: Default sets and bond prices
Note: The left panel shows the default sets with the shaded areas indicating default and the white
area indicating repayment. The right panel shows the equilibrium bond price schedule.
Figure 6also shows that the debt-to-GDP distribution conditional on a banking crisis is
more skewed to the left than the unconditional distribution. Thus, not only do banking crises
lead to a higher average debt-to-GDP ratio (Table 3), but they also increase the probability of
observing high debt-to-GDP realizations (greater than 20 percent), reinforcing the ‘diabolic
loop’ dynamics.
Figure 6: Conditional and unconditional debt distributions
23
Tradeoffs faced when choosing the bailouts. What are the trade-offs that the planner
is considering when choosing the promised bailout level? On the one hand, a higher T(·)
supports credit and output. On the other hand, higher transfers may require either higher
taxes (and therefore higher distortions) or higher debt (which increases default risk).
Figure 7: The effect of bailouts on output and taxes
Note: The left and right panels show output and the labor tax rate, respectively, as functions of
the proportional transfer (in percent of the potential loss). The markers denote the optimal choice
of bailouts, which is decided prior to the realization of the banking crisis. The graph assumes that
next-period debt is chosen optimally. The solid black line is for the case in which the banking crisis
does not occur and the dashed red line is for the case in which it does.
Figure 7illustrates this tradeoff. Output initially increases with the transfer, but it shows
a differential behavior depending on whether the banking crisis materializes. If there is no
banking crisis, then output is weakly increasing in the transfer: It increases monotonically
up to the point at which there is enough credit to make the borrowing cost for the firms
zero and after that point larger transfers have no further impact on output. On the other
hand, if the banking crisis occurs, then output is non-monotonic in the transfer: It initially
increases, but at around 40% (of the potential loss) it starts to decrease with the size of the
transfer. This is because when the banking crisis happens, larger bailout payments require
higher debt and/or higher taxes to finance them. For very large bailouts, the required higher
taxes are sufficiently distorting and lead to lower output.
As mentioned above, the behavior of taxes is important for this tradeoff. The right panel
in Figure 7shows the tax rate function for different candidate values of the bailout (assuming
that the debt is optimally chosen). If a banking crisis does not happen, then the promised
bailouts come “at no cost” – credit and output get propped up but since the impact on bank
capital doesn’t materialize the actual fiscal budget improves, allowing the government to
24
reduce taxes. However, if the banking crisis occurs, then the bailouts need to be disbursed
and these are financed partly with taxes.
Optimal bailout policies. The ability of the government to issue bailouts depends on
the state of the economy in terms of productivity (z) and potential losses to bank capital (ε),
in addition to the existing level of debt (B). Here we examine the bailout policy functions
generated by our model to highlight the role of each of these factors. Figure 8shows the
bailout policy functions expressed as the percent of the potential loss that the government
promises to guarantee. Inspecting both panels of this figure, we find the following properties
for the bailouts:
Figure 8: Bailout policy
Note: The panels show the bailout policy functions expressed as the percent of the potential loss
that the government promises to guarantee (i.e. 100 ×T(B, s, A)/¯
Aε).
1. Increasing in ε.As the potential loss to bank capital increases, the proportional
bailout the government chooses grows larger. This is because the impact of financial
shocks on the economy are non-linear. As can be seen in equation (17), absent gov-
ernment bailouts, higher values of εhave a disproportionately larger effect on rthan
lower values of ε(i.e., εaffects rin a convex manner). Thus, the government uses
bailout transfers to affect the supply side of the loan market, keeping the equilibrium
interest rate low, especially when the financial shocks are large.
2. Decreasing in B.While bailout guarantees play an essential role alleviating the
effects of banking crises on the real sector by boosting liquidity, increased default risk
25
makes it more difficult for government to provide transfers as the debt level rises. This
is because when the banking crisis occurs, the bailouts will need to be financed with
more borrowing. Therefore, the greater the stock of initial debt, the less fiscal space
the government has to extend asset guarantees.
3. Increasing in z.This intuitive property is due to two forces that move in the same
direction. First, with greater productivity, credit becomes more valuable. Therefore,
it makes sense for the government to extend larger guarantees in good times. Sec-
ond, the cost of borrowing necessary to finance a bailout is lower during periods of
high productivity. Given the persistence of productivity shocks, a high productivity
shock during this period increases the likelihood of a high productivity shock in the
subsequent period, leading to lower default risk, better prices for the government, and
greater borrowing capacity to finance the bailout transfers.
5 On the Optimality of Bailouts
As explained in the previous section, bailouts come with a trade-off. They allow the gov-
ernment to boost liquidity and output during banking crises but they also increase debt and
default risk (i.e., there is a ‘diabolic-loop’). Having described the properties of our model
and the equilibrium bailout policies, we proceed to ask: Are bailouts desirable?
To answer this normative question, we proceed in two steps. First, we solve a no-bailout
version of our model and compare its simulated moments to those in the baseline model. We
show that the baseline economy sustains less debt at higher borrowing costs. This suggests
that, from an ex ante perspective, allowing bailouts may not be optimal. Thus, as a second
step, we solve for alternative versions of the model in which bailouts are allowed but are
restricted in size, nesting both the baseline (with unrestricted bailouts) and the no-bailout
models. We find that when initial debt is very low, governments prefer unrestricted access to
bailouts. However, when governments begin with moderate to high levels of debt, banning
bailouts altogether is beneficial. We find these results remarkable since our analysis abstracts
from moral hazard concerns, a well-studied reason for which bailouts might be undesirable
from an ex-ante perspective. We show that the welfare consequences are large.
We first contrast the baseline economy with bailouts to the no-bailout economy. Table
4shows that the baseline economy exhibits higher default risk, higher and more volatile
spreads, and a lower debt-to-GDP ratio. These statistics reflect that the baseline economy
faces worse borrowing terms: It can sustain less debt at higher rates. The last row of Table
26
4reports the welfare effect of bailouts, evaluated at the simulated mean debt level.21 We
find that access to bailouts results in a welfare loss, equivalent to a 1.5 percent reduction in
permanent consumption, relative to the no-bailout economy.
Table 4: Simulated moments comparison
Baseline model Model without bailouts
Default frequency 0.5∗0.3
Sovereign spread
mean 0.7 0.5
standard deviation 0.6 0.5
corr(GDP, spread) –0.3 –0.3
Debt/GDP 15.5 26.8
Mean lending rate 0.0 0.2
Welfare gain of bailouts –1.5
Units: percent. ∗denotes targeted moments.
We next examine, from an ex ante perspective, what restrictions a country should opti-
mally impose on the size of the bailouts. To do so, we modify the constraint on T(B, s, A)
as follows:
T= 0 if A=A
0≤T≤min{εA, φεA}if A= (1 −ε)A)(new constraint on T)
where ε A corresponds to the largest possible financial shock and φ∈[0,1]. Setting φ= 0
corresponds to the model with no bailouts and φ= 1 corresponds to the baseline model.
With this modified framework, we compute the ex ante welfare-maximizing levels of φ
for different levels of initial debt, B0. First, we solve for Λ(B0;φ), the permanent increase in
consumption needed in the no-bailout economy to make households indifferent between this
economy and another with φ > 0. Formally, Λ(B0;φ) is implicitly defined by
EsVΛ(B0, s; 0) = EsV(B0, s;φ) (27)
21We calculate welfare using consumption equivalence. For each state (B, s), we compute the value,
1 + ∆(B, s), by which consumption of both households and banks—under no bailouts—would have to be
permanently increased in order to make the planner indifferent to gaining access to bailouts (bank con-
sumption only matters when the planner puts a positive weight on bank welfare, as explored in Appendix
C.2). Negative values of ∆(B, s) indicate a welfare loss from bailouts. We then integrate across the ergodic
distribution over s, and report the welfare loss evaluated at Bwhich corresponds to the simulated mean of
debt in the bailout economy.
27
Figure 9: Optimal bailout restrictions
where the expectation is taken over the ergodic distribution over s={z, ε}and VΛ(B0, s; 0)
is the value resulting from a permanent increase in consumption Λ in the economy without
bailouts. Second, for each initial debt level, we compute the welfare maximizing value of φ.
Figure 9shows three regions. For very low levels of initial debt, the economy is better
off with unrestricted bailouts (φ= 1)—that is, it is optimal to allow the government to
issue bailouts that can fully cover even the largest shocks to bank capital. For intermediate
debt levels, it is optimal to restrict considerably the governments’ ability to issue bailouts.
Finally, for debt levels exceeding 13 percent of mean output, it is welfare increasing to set
φ= 0—banning the government from issuing bailouts. What are the welfare consequences of
instituting the optimal restrictions on bailouts? As reported in Table 4, when a government’s
initial debt-to-GDP level is at 15.5 percent of GDP—the mean in the simulations—access
to unrestricted bailouts results in a 1.5 percent welfare loss relative to no bailouts, a large
welfare consequence.
Intuition. To gain more intuition of the forces behind our welfare result (that bailouts are
ex-ante undesirable), we study the debt-price menus faced by the economy with unrestricted
bailouts and by the no-bailout economy.
Figure 10 clearly shows that the no-bailout economy faces a more favorable price schedule.
As it is usual in this class of models, the optimal policies imply that the model lives most of
the time in the region where the price function is about to begin its steep decline. Therefore,
it follows that the no-bailout economy can sustain much higher debt (26.8% vs. 15.5%) at
28
Figure 10: Bond prices with and without bailouts
slightly lower spreads (0.5% vs. 0.7%).
Why does the no-bailout economy face better prices? The answer is in the default costs:
the no-bailout economy endogenously has larger default costs, which in turn allows it to have
higher levels of debt, output, and consumption than the bailout economy, on average. What
are the costs of defaults in our model? When the government defaults on its debt, it triggers
a credit contraction, an increase in the borrowing costs of firms, and a decrease in output.
We can think of the costs of defaults as made of two parts. The first part materializes in
the periods in which the government is excluded.22 In these periods, large realizations of ε
are particularly damaging: There is no debt, and therefore liquidity and output are low to
begin with—financial shocks make credit very scarce and output very low. This first part of
the cost is the same for the economies with and without bailouts.23
The second part comes once the government has reentered financial markets. Since debt
is totally repudiated in a default, the reentry to financial markets occurs with zero debt.
We can interpret the reduced output level (due to less liquidity stemming from low debt) in
the early periods after reentry as another component of the costs of defaults. In these early
22Recall that the exclusion periods include the period of the default plus subsequent periods until financial
redemption occurs (with probability θ).
23The assumption of no bailouts during exclusion is in part responsible for this feature. In Appendix C,
we relax this assumption and allow the government to issue bailouts even while excluded. In line with the
intuition presented here, we find that the two economies (with and without bailouts) are now even more
dissimilar. After recalibrating the model to match the same targeted moments as in Section 4.2, the welfare
result strengthens: Access to unrestricted bailouts results in a 2.3 percent welfare loss relative to no bailouts
(when evaluated at the mean debt level in the simulations).
29
periods after reentry, large εshocks are also particularly damaging, but there is a difference
between the bailout and no-bailout economies: The bailout economy suffers less because
it can prop up liquidity using bailouts. Therefore, having access to bailouts decreases the
second part of the endogenous costs of default. This means that from an ex-ante perspective,
the bailout economy can sustain less debt since it has a larger default region due to its lower
default costs.
Figure 11: Private Consumption
Note: The panels show the equilibrium consumption levels for the cases in which the banking crisis
does not occur (left panel) and in which it does (right panel). The plots are constructed assuming
average values for TFP and ε.
The flip side of this argument is that the no-bailout economy has higher default costs and
can sustain more debt. Having more debt on average, brings about higher liquidity and makes
the economy less vulnerable to large realizations of ε, in equilibrium. A higher and cheaper-
to-service debt level implies greater consumption, on average, and this holds for almost all
debt levels as can be seen in Figure 11. Therefore, even though the no-bailout economy
cannot issue asset guarantees, its higher liquidity reduces the need for those guarantees.
The argument developed in the previous paragraphs and the findings shown in Figure
9imply that living in an economy with unrestricted bailouts is ex-ante preferable only in
two extreme cases: either very low or very high initial debt. In the former, having access
to bailouts props up liquidity. In the latter case, both economies default and—as discussed
above—reentering financial markets is less painful with access to bailouts. For the empirically
relevant intermediate cases, restricting the availability to issue bailouts is welfare improving.
This is confirmed in Figure 12 where we plot the value functions for both economies.
30
Figure 12: Value functions with and without bailouts
Note: the graph shows the equilibrium value functions for the economies with (dashed line) and
without (solid line) bailouts. The lines are constructed assuming average values for TFP and ε.
The value of fiscal rules and the ex ante undesirability of bailouts. A recent paper
by Aguiar and Amador (2019) (see also Hatchondo et al.,2020) shows that the equilibrium
in the Eaton and Gersovitz (1981) model with one-period bonds is constrained efficient (once
one takes into account market incompleteness and the ability of the government to walk away
on its debt obligations). This implies that the ability to commit to a sequence of borrowing
policies (i.e. a fiscal rule) does not increase the government’s value over the Markov-perfect
equilibrium value.
One can think of our restrictions to bailouts, φ, as a type of fiscal rule, and therefore the
Aguiar and Amador (2019) result would seem to contradict our finding that it is optimal
to restrict the issuance of bailouts (that is to say, that we find that some fiscal rules are
ex-ante optimal). There is, however, a fundamental reason for which the result in Aguiar
and Amador (2019) does not apply in our setup: Government actions affect the production
choices of the firms (directly through taxes, indirectly through their effect on the loan rate)
and the lending constraint of the banks. These effects, in turn, change the value of repayment
and default in ways that are absent in Aguiar and Amador (2019), since they restrict their
attention to the canonical Eaton-Gersovitz environment with an endowment economy.24 The
intuition presented above builds on this insight—the economy without bailouts (which can be
understood as an economy with a very strict fiscal rule) has an endogenously lower default
24For example, Aguiar and Amador (2019) make it clear that their assumption on the value of default
being unaffected by the fiscal rule is important in obtaining the result that ‘fiscal rules add no value.’
31
value which allows it to face better prices (as seen in Figures 10 and 12).25 In this way,
restricting bailout policies (i.e. implementing a particular type of fiscal rule) can improve
welfare ex-ante.
Our ex ante result is also related to the work of Chari et al. (2020). They find that
financial repression (modeled as forcing banks to hold government debt in their balance
sheets) can be optimal in a model that is similar to ours. Ex post financial repression
weakens the banks’ balance sheets, and raises the cost of default, and this, in turn, reduces
the default incentives of the government ex ante, leading to higher welfare.26
Take-away. In summary, the results in this section indicate that for the mean debt level in
our simulations (15.5 percent of GDP), the economy will be better off if the government can-
not issue bailouts. This is a strong result considering that our framework has (i) a benevolent
government and (ii) a bailout policy that does not trigger moral hazard concerns. Overall,
our results highlight the negative effects of the sovereign-bank nexus (i.e., the ‘diabolic loop’).
6 Extensions and Sensitivity
In this section, we briefly discuss several extensions to the baseline model to show how our
main quantitative results can be generalized.
6.1 Bailouts during exclusion
We have studied the ex ante desirability of bailouts that followed a specific restriction:
Bailouts cannot be promised (or disbursed) during exclusion periods. We now relax this
restriction and allow the government to issue guarantees even if it is currently excluded from
borrowing (due to a current or previous default). The recursive formulation of this ‘relaxed’
problem is a straightforward extension of (20)–(22) and is presented in Appendix C.1.
As argued above, the welfare superiority of the no-bailouts economy comes from the fact
that it features larger default costs, and can therefore sustain more debt (which provides liq-
25There are, of course, other differences in setup (and assumptions) between our environment and the one
in Aguiar and Amador (2019). Apart from the one we highlighted above (of the value of default being affected
by the restrictions on the bailouts), the most important one is that the value under repayment is not weakly
decreasing in the level of debt: this can be seen clearly in Figure 12 for the no-bailout economy. This is a
natural feature of our model: for low enough debt levels, an additional unit of public debt increases liquidity
and output, and the benefits from this effect outweigh the costs that the higher debt imposes in terms of
distortionary taxation (and higher default probability)—this makes the value of repayment non-monotonic
on the debt level (a feature also present in Sosa-Padilla,2018)
26A similar intuition is present in Gennaioli et al. (2014).
32
uidity and increases output). Allowing for bailouts during exclusion increases the difference
between the default costs in the bailouts and no-bailouts economies. After recalibrating the
model to match the same targeted moments as in Section 4.2, the welfare results strengthen:
Access to unrestricted bailouts results in a 2.3 percent welfare loss relative to no bailouts
(when evaluated at the mean debt level in the simulations).27
6.2 Relative weights in the social welfare function
The baseline specification of our model makes the common assumption that the planner
only cares about the households’ utility. However, we can study the dynamics of the model
under different social welfare functions. In particular, one could study the default incentives
and the ex ante optimality of bailouts when the planner puts equal weight on the utility of
households and banks.
Appendix C.2 presents the results under this alternative assumption. As in the baseline
model, Table C.2 (the analogue of Table 4) shows that when we use equal weights in the
social welfare function, it remains the case that the no-bailout economy defaults less and
faces lower borrowing costs despite accumulating much higher levels of debt compared with
the bailout-economy. Importantly, the ex ante sub-optimality of bailouts is robust to this
alternative specification: Access to unrestricted bailouts results in a 1.4 percent welfare loss
relative to no bailouts (when evaluated at the mean debt level in the simulations).
6.3 Moral hazard
In the baseline model, we abstracted from moral hazard concerns. In an extension of the
model, we allow banks to choose the variance of bank capital shocks by paying a convex
utility cost that increases with the size of the variance reduction (Appendix C.4). In this
extended environment, bailouts give rise to moral hazard considerations as banks may choose
a higher variance (i.e. risk) in the anticipation that the government will issue bailouts for
large bank capital shocks. As can be expected, we find that the welfare loss from bailouts is
considerably larger when bailouts entail moral hazard considerations.
6.4 Bailout announcements affect bank crisis probability
We consider an extension of the model in which the size of the announced bailout policy
27 Table C.1 in the Appendix shows that the contrast between the bailout and the no-bailout economy is
now even stronger: the no-bailout economy defaults less, faces lower borrowing costs, despite accumulating
much higher levels of debt, compared with the bailout-economy.
33
can reduce the probability of a banking crisis. In Appendix C.4, we show that, in this
modified environment, the government optimally chooses to announce disproportionately
larger bailouts for more severe banking crises, leading to a different mix of equilibrium
banking crises: they are less frequent and less severe relative to the baseline model. We
find that allowing for announcement effects slightly reduces the ex ante welfare loss from
bailouts, but it remains the case that bailouts are suboptimal from an ex ante perspective.
6.5 Sensitivity
In this section, we discuss the sensitivity of our main results to changes in parameter values.
Overall, we find that our main findings are generally robust to these perturbations around
the baseline calibration, but we also discuss which parameters are particularly important for
the sub-optimality of bailouts result.
Parameters governing the process for bank capital. We call Abank capital, but a
broader interpretation is to think of it as “net assets excluding government debt.” In that
vein, the calibration of both its baseline level Aand its shocks εis crucial for the dynamics
of the model.28 This explains why both Aand the volatility of bank capital shocks, σε, are
part of the SMM procedure described in Section 4.2. In this section, we further explore how
the model reacts to small changes in the value of both of these parameters, and corroborate
that our main result is robust to this sensitivity analysis.
Table C.5 shows how the moments of interest react to changes in A, in both directions.
Larger values of Acorrespond to higher liquidity in the economy—this lowers the default
costs and reduces the debt capacity of the government, other things equal. For both larger
and smaller values of A, it remains true that the model without bailouts sustains higher
debt, has a lower volatility of spreads, and a lower default frequency for a given value of
¯
A. Therefore, our headline result regarding the welfare superiority of banning bailouts is
qualitatively robust to these alternative values of A.
Table C.6 illustrates the nonlinear effects of financial shocks on the real economy discussed
in Section 4.5—the larger the volatility of the potential loss to banking capital, the greater
the need for bailouts. Indeed, Table C.6 shows that a higher value of σεis associated with
a higher default frequency, and higher and more volatile spreads. Even though the welfare
loss from access to bailouts decreases slightly in this case, we still find that banning bailouts
altogether is optimal from an ex ante point of view.
28See discussion in footnote 8.
34
Importantly, it may be the case that the ex ante suboptimality bailout result would not
materialize for even higher values of Aor σεthan considered here. However, such higher
values would imply larger output volatility and larger bailouts than in the data (as these are
the data moments that we targeted to discipline these values), and thus we rule out these
alternative calibrations.
Parameters governing the probability of default. Many parameters in the model
affect the probability of default, but the two most direct determinants are the household
discount factor βand the reentry probability θ.
The reentry probability affects the welfare loss from bailouts in two opposing directions.
On the one hand, with a higher θ, the default costs faced by the government with access to
bailouts are smaller, leading to lower debt capacity and welfare (as explained in Section 5).
Therefore, for a given level of debt, a higher θis associated with a larger welfare loss from
bailouts. On the other hand, a higher θlowers the equilibrium debt level in the economy
with bailouts and since welfare losses from bailouts increase with debt (see Figure 9), this
leads to lower welfare losses. We show in Appendix C.5 that the latter effect dominates,
leading to higher values of θbeing associated with smaller welfare losses from bailouts.
When the household is more patient (i.e. has a higher discount factor β), the probability
of default decreases, with and without bailouts. By reducing the sovereign-bank diabolic
loop, a higher discount factor reduces the welfare loss from bailouts, though it remains the
case that bailouts are suboptimal from an ex ante perspective.
It is possible that even higher values of θor βcould reverse the suboptimality of bailouts
result. We rule out these alternative calibrations since even higher values of θwould imply
even lower levels of government debt and higher values of βwould imply default frequencies
that are too low for the set of economies we consider—the higher value of βconsidered in
Appendix C.5 features default frequencies of 0.3 and 0.2 percent, with and without bailouts,
implying 2–3 defaults every 1,000 years.
Frisch elasticity. Our baseline calibration sets the wage elasticity of labor supply, 1/(ω−
1), to an intermediate value from within the range of estimates in the literature. We have
argued that the diabolic loop that bailouts create is costly because bailouts are (partly)
financed with distortionary labor taxes. Therefore, one might expect that for a lower elas-
ticity, this distortion will be smaller and it could moderate or overturn the baseline welfare
results. While it is the case that, holding debt levels fixed, lower elasticity leads to a smaller
welfare loss, we show in Appendix C.5 that access to bailouts still results in a welfare loss.
35
Other parameters. Appendix C.5 also presents a thorough sensitivity analysis to other
parameters of interest. In a nutshell, perturbations around the benchmark values do not
affect our main conclusions, especially the result regarding the ex ante welfare inferiority of
having access to bailouts.29
7 Conclusion
We study the dynamic relationship between sovereign defaults, banking crises, and gov-
ernment bailouts. We first document that when governments intervene to help distressed
banking sectors, contingent guarantees are the most prevalent form of intervention.
We then construct a general equilibrium model of sovereign default in which there is
a benevolent government that maximizes households’ welfare by choosing debt, defaults,
distortionary taxes, and bank bailouts. The economy is subject to two types of aggregate
uncertainty—shocks to firm productivity and shocks to bank capital. In anticipation of
an adverse banking shock, banks reduce lending to the private sector. The sovereign may
choose to announce guarantees (i.e. conditional transfers) to compensate for the banks’
capital losses in the event of a crisis—a bailout. Sovereign defaults are costly because it
leads to a deterioration of bank balance sheets. Moreover, during default episodes, the
government temporarily loses access to debt financing and with it the ability to issue bailouts.
As a consequence, bank credit to the private sector declines, and eventually output and
consumption fall. The benefit of a default is that all existing debt is wiped out, relaxing
the government’s budget constraint, and allowing it to reduce distortionary taxes. Our
framework is flexible enough to feature defaults that lead to a decline in the health of the
banking sector and vice versa: a complete ‘doom loop.’
Using the calibrated model, we show that the occurrence of a banking crisis increases the
default probability by 0.2 percentage points (from 0.5 to 0.7 percent annually) and raises
the level and volatility of sovereign spreads (the latter increases from 0.6 to 1.0 percent). In
the model, the government issues contingent guarantees that exhibit clear properties. Other
things equal, they are: (i) decreasing in the level of government debt, since the more debt it
has, the less fiscal space the government has to prop up banking sector assets; (ii) increasing
in aggregate productivity, since the better the aggregate state of the economy, the greater the
value of credit and the cheaper it is to borrow to provide the guarantees; and (iii) increasing
with the severity of the banking crisis, because the effects of financial shocks are nonlinear.
Small shocks have negligible impacts on loans to the private sector, whereas large shocks can
29For brevity, we omit a fuller description of these exercises here and defer them to Appendix C.5.
36
lead to severe contractionary credit crunches in the absence of government interventions.
Even though bailouts are useful to mitigate the adverse effects of banking crises, we find
that from an ex ante perspective, the country is better off without bailouts: Having access
to bailouts lowers the cost of defaults, which in turn increases the default frequency, and
reduces the levels of debt, output, and consumption.
37
References
Abad, Jorge, “Breaking the sovereign-bank nexus,” CEMFI Working Paper, 2019.
Acharya, Viral, Itamar Drechsler, and Philipp Schnabl, “A pyrrhic victory? Bank
bailouts and sovereign credit risk,” The Journal of Finance, 2014, 69 (6), 2689–2739.
Aguiar, Mark and Gita Gopinath, “Defaultable debt, interest rates and the current
account,” Journal of International Economics, 2006, 69 (1), 64–83.
Aguiar, Mark and Manuel Amador, “A contraction for sovereign debt models,” Journal
of Economic Theory, 2019, 183, 842–875.
Aguiar, Mark, Satyajit Chatterjee, Harold Cole, and Zachary Stangebye, “Quanti-
tative models of sovereign debt crises,” in John B. Taylor and Harald Uhlig, eds., Handbook
of Macroeconomics, Vol. 2, Elsevier, 2016, pp. 1697–1755.
Arce, Fernando, “Private overborrowing under sovereign risk,” Working paper, Federal
Reserve Bank of Chicago 2022.
Arellano, Cristina, “Default risk and income fluctuations in emerging economies,” Amer-
ican Economic Review, 2008, pp. 690–712.
Azzimonti, Marina and Vincenzo Quadrini, “International spillovers and bailouts,”
Review of Economic Studies, 2023, p. 2674.
Balloch, Cynthia Mai, “Default, commitment, and domestic bank holdings of sovereign
debt,” Working paper, Columbia University 2016.
Balteanu, Irina, Aitor Erce, and Laura Fernandez, “Bank crises and sovereign de-
faults: Exploring the links,” Working paper, Bank of Spain 2011.
Barucci, Emilio, Tommaso Colozza, and Carlo Milani, “The effect of bank bail-outs
in the EU,” Journal of International Money and Finance, 2019, 95, 14–26.
Berger, Allen N, Phil Molyneux, and John OS Wilson, “Banks and the real economy:
An assessment of the research,” Journal of Corporate Finance, 2020, 62, 101513.
Berrospide, Jose M and Rochelle M Edge, “The effects of bank capital on lending:
what do we know, and what does it mean?,” International Journal of Central Banking,
2010, 6(34), 1–50.
Bianchi, Javier, “Efficient bailouts?,” American Economic Review, 2016, 106 (12), 3607–
59.
Bocola, Luigi, “The pass-through of sovereign risk,” Journal of Political Economy, 2016,
124 (4), 879–926.
Bolton, Patrick and Olivier Jeanne, “Sovereign default risk and bank fragility in finan-
cially integrated economies,” IMF Economic Review, 2011, 59 (2), 162–194.
38
Borensztein, Eduardo and Ugo Panizza, “The costs of sovereign default,” IMF Staff
Papers, 2009, 56 (4), 683–741.
Boz, Emine, Pablo D’Erasmo, and Bora Durdu, “Sovereign risk and bank balance
sheets: The role of macroprudential policies,” Technical Report 2014.
Brunnermeier, Markus K, Sam Langfield, Marco Pagano, Ricardo Reis, Stijn
Van Nieuwerburgh, and Dimitri Vayanos, “ESBies: Safety in the tranches,” Eco-
nomic Policy, 2017, 32 (90), 175–219.
Capponi, Agostino, Felix Corell, and Joseph E Stiglitz, “Optimal bailouts and the
doom loop with a financial network,” Journal of Monetary Economics, 2022, 128, 35–50.
Cecchetti, Stephen G, Marion Kohler, and Christian Upper, “Financial crises and
economic activity,” Working paper, National Bureau of Economic Research 2009.
Chari, Varadarajan Venkata, Alessandro Dovis, and Patrick J Kehoe, “On the
optimality of financial repression,” Journal of Political Economy, 2020, 128 (2), 710–739.
Claessens, Stijn, Daniela Klingebiel, and Luc Laeven, “Crisis resolution, policies,
and institutions: Empirical evidence,” in Patrick Honohan and Luc Laeven, eds., Systemic
financial crises: containment and resolution, Cambridge University Press, 2005.
Coimbra, Nuno, “Sovereigns at risk: a dynamic model of sovereign debt and banking
leverage,” Journal of International Economics, 2020, 124, 103298.
Cooper, Russell and Kalin Nikolov, “Government debt and banking fragility: The
spreading of strategic uncertainty,” International Economic Review, 2018, 59 (4), 1905–
1925.
Davis, J Scott, Adrienne Mack, Wesley Phoa, and Anne Vandenabeele, “Credit
booms, banking crises, and the current account,” Journal of International Money and
Finance, 2016, 60, 360–377.
De Ferra, Sergio and Enrico Mallucci, “Avoiding sovereign default contagion: a nor-
mative analysis,” Federal Reserve Board of Governors Working Paper, 2020.
D’Erasmo, Pablo and Enrique G Mendoza, “History remembered: Optimal sovereign
default on domestic and external debt,” Journal of Monetary Economics, 2020.
Eaton, Jonathan and Mark Gersovitz, “Debt with potential repudiation: Theoretical
and empirical analysis,” Review of Economic Studies, 1981, 48 (2), 289–309.
Farhi, Emmanuel and Jean Tirole, “Deadly embrace: Sovereign and financial balance
sheets doom loops,” Review of Economic Studies, 2018, 85 (3), 1781–1823.
Faria-e Castro, Miguel, “Fiscal multipliers and financial crises,” Review of Economics
and Statistics, 2017, pp. 1–45.
39
Favero, Carlo and Alessandro Missale, “Sovereign spreads in the eurozone: which
prospects for a Eurobond?,” Economic Policy, 2012, 27 (70), 231–273.
Gaballo, Gaetano and Ariel Zetlin-Jones, “Bailouts, moral hazard and banks’ home
bias for Sovereign debt,” Journal of Monetary Economics, 2016, 81, 70–85.
Gennaioli, Nicola, Alberto Martin, and Stefano Rossi, “Sovereign default, domestic
banks, and financial institutions,” Journal of Finance, 2014, 69 (2), 819–866.
Gennaioli, Nicola, Alberto Martin, and Stefano Rossi, “Banks, government bonds,
and default: What do the data say?,” Journal of Monetary Economics, 2018, 98, 98–113.
Gourinchas, Pierre-Olivier, Philippe Martin, and Todd Messer, “The economics of
sovereign debt, bailouts and the Eurozone crisis,” NBER Working Paper 27403, 2020.
Gunn, Christopher M. and Alok Johri, “Financial news, banks, and business cycles,”
Macroeconomic Dynamics, 03 2018, 22 (2), 173–198.
Hatchondo, Juan Carlos, Leonardo Martinez, and Francisco Roch, “Constrained
efficient borrowing with sovereign default risk,” Working paper, International Monetary
Fund 2020.
Hatchondo, Juan Carlos, Leonardo Martinez, and Francisco Roch, “Fiscal rules
and the sovereign default premium,” American Economic Journal: Macroeconomics, 2022,
14 (4), 244–273.
Hur, Sewon, Illenin Kondo, and Fabrizio Perri, “Real interest rates, inflation, and
default,” Federal Reserve Bank of Minneapolis Staff Report 574, 2018.
Jord`a, `
Oscar, Moritz Schularick, and Alan M Taylor, “Macrofinancial history and
the new business cycle facts,” NBER macroeconomics annual, 2017, 31 (1), 213–263.
Keister, Todd, “Bailouts and financial fragility,” Review of Economic Studies, 2016, 83
(2), 704–736.
Laeven, Luc and Fabian Valencia, “The real effects of financial sector interventions
during crises,” Journal of Money, Credit and Banking, 2013, 45 (1), 147–177.
Laeven, Luc and Fabian Valencia, “Systemic banking crises database,” IMF Economic
Review, 2013, 61 (2), 225–270.
Laeven, Luc and Fabian Valencia, “Systemic banking crises database II,” IMF Economic
Review, 2020, 68, 307–361.
Mallucci, Enrico, “Domestic debt and sovereign defaults,” International Finance Discus-
sion Paper no. 1153, Federal Reserve Board of Governors 2015.
Metrick, Andrew and Paul Schmelzing, “Banking-crisis interventions, 1257-2019,”
Working paper, National Bureau of Economic Research 2021.
40
Moretti, Matias, “The asymmetric pass-through of sovereign risk,” Working paper, Uni-
versity of Pennsylvania 2020.
Niepmann, Friederike and Tim Schmidt-Eisenlohr, “Bank bailouts, international link-
ages, and cooperation,” American Economic Journal: Economic Policy, 2013, 5(4), 270–
305.
Pancrazi, Roberto, Hern´an D Seoane, and Marija Vukoti´c, “Welfare gains of
bailouts in a sovereign default model,” Journal of Economic Dynamics and Control, 2020,
p. 103867.
Perez, Diego J., “Sovereign debt, domestic banks and the provision of public liquidity,”
Working paper, New York University 2015.
Reinhart, Carmen M, “This time is different chartbook: country histories on debt, default,
and financial crises,” NBER Working Paper 15815, 2010.
Roch, Francisco and Harald Uhlig, “The dynamics of sovereign debt crises and bailouts,”
Journal of International Economics, 2018, 114, 1–13.
Sosa-Padilla, C´esar, “Sovereign defaults and banking crises,” Journal of Monetary Eco-
nomics, 2018, 99, 88–105.
Thaler, Dominik, “Sovereign default, domestic banks and exclusion from international
capital markets,” Economic Journal, 2021, 131 (635), 1401–1427.
41
A Contingent Liabilities
In this section, we consider a broader notion of contingent government interventions by
looking at the changes in government contingent liabilities instead of government guaran-
tees. In addition to government asset guarantees, the concept ‘contingent liabilities’ includes
public–private partnerships (PPP) recorded off-balance sheet of the government and liabil-
ities of government controlled entities classified outside of general government operations.
For most countries, government guarantees make up the largest share in government contin-
gent liabilities. Because contingent liabilities are also stocks, we calculate the annual change
in contingent liabilities as a share of GDP, and take the average of that ratio across all
countries.
Figure A.1: Government contingent liabilities and capital transfers
Figure A.1 shows a side-by-side comparison of contingent liabilities and capital transfers
in the entire sample and conditional on banking crisis. We obtain a similar pattern as
before: Contingent liabilities exceed 2 percent during banking crises and they are close to
zero unconditionally.
42
B Data Appendix
Data description for Figures 1and A.1
We obtain the data for government guarantees, contingent liabilities, and capital transfers
from Eurostat. We obtain these series for 23 countries, which are Austria, Belgium, Bulgaria,
Croatia, Cyprus, Denmark, Finland, France, Germany, Greece, Hungary, Ireland, Italy,
Latvia, Lithuania, Luxembourg, Portugal, Slovenia, Spain, Sweden, the Czech Republic, the
Netherlands, and the United Kingdom. Our sample is limited by the data availability, and it
covers the years 2007–2019. For each country, we calculate the first difference of government
guarantees and contingent liabilities, and we divide them by the GDP series obtained from
the World Bank Database to generate the plots. Next, we calculate the share of capital
transfers in GDP for each country between 2007–2019. Using the banking crisis dates from
Laeven and Valencia (2020) we create the sample conditional on banking crises.
Data description for calibration and external validity
We calculate the unconditional default frequency and default frequency conditional on bank-
ing crises using the crises dates given in Laeven and Valencia (2020). This dataset covers the
years 1970–2017. The sample contains 21 advanced and 17 emerging market economies as
in Davis et al. (2016). The unconditional default frequency is calculated as the total count
of default events divided by the total number of country-year pairs.
The share of government spending in GDP is calculated using the data from OECD.
Our sample consists of GIIPS during 1999–2019. First, for each country we calculate the
average public consumption as a share of GDP and then compute the median across country
averages.
We calculate the domestic debt to GDP data from the ECB and OECD datasets. We
choose the period between 1999 and 2019. Our sample covers the same 23 countries above
plus Estonia, Malta, Poland, Romania, and Slovakia. For the majority of the countries in
our sample, domestic gross government debt series as a share of GDP are readily available.
For these countries, we calculate the average debt-to-GDP over 1999–2019. For Ireland and
the United Kingdom, ECB only provides total debt values. Therefore, first, we calculate the
average share of domestic debt in total debt from the OECD, which is the average share of
marketable debt held by domestic residents in the total marketable debt. Because of data
limitations for Ireland and the UK, we can construct the annual shares between 1999–2006
and between 1999–2010, respectively. We use these shares to calculate the domestic debt
levels for Ireland and the UK, and divide them by the corresponding GDP series. Finally,
the median domestic debt to GDP ratio for the whole sample between 1999–2019 is given
43
by 25.8 percent.
We calculate the output volatility for GIIPS using the GDP per capita series obtained
from OECD data between 1970–2019. First, for each country, we compute the standard
deviation of HP-filtered log output. Then we compute the median across countries to obtain
3.4 percent. For moments related to the spread, we obtain interest rates for GIIPS from
the OECD for 1999–2019. We calculate the spread as the difference between nominal yield
on 10-year government bonds of each country and that of Germany. For each country, we
compute the average and standard deviation of the spread and the correlation of spread and
the HP-filtered GDP. Finally, we compute the medians of average spread, standard deviation
of spread, and the correlation of spread with the GDP to obtain our moments.
The correlation between transfers and debt reported in Table 2is estimated using HP-
filtered government guarantees and HP-filtered short-term securities. Short-term securities
are defined as government consolidated gross debt at face value and obtained from Eurostat.
Data description for dynamics around banking crises
To compute the sovereign yields, we use Jord`a et al. (2017) Macrohistory database, which
covers 1950–2016 and 17 advanced economies including Italy, Portugal and Spain. The
sovereign yield is calculated as the nominal interest rate minus the inflation rate. Each
country’s output series is detrended using its own average growth rate. We define 7-year
windows centered around banking crises. We compute unconditional averages across win-
dows, as well as averages conditional on debt being above the country’s 75th percentile of
debt at the start of the banking crisis.
44
C Appendix to Section 6
C.1 Bailouts during exclusion
In the baseline model, we assume that the government is unable to issue bailouts during pe-
riods of default and exclusion. Here, we explore the implications of relaxing this assumption.
Given government policies, the value of the representative bank when the government does
not have access to credit is then given by:
WD(s) = max
`s
EA
max
xx+δEs0|sθW R(0; 0, s0) + (1 −θ)WD(s0)
s.t. x≤Tdef(s, A) + rdef(s, A)`s
(28)
s.t. `s≤min
A{A+Tdef(s, A)}.(29)
The value of default for the government is given by:
VD(s) = max
τ,T
EAnUc(s, A), n (s, A)+βEs0|sθV (0, s0) + (1 −θ)VD(s0)o(30)
subject to:
τ wdef(s, A)ndef (s, A) = g+T(gov’t b.c.)
cdef(s, A) + xdef(s, A) + g=zF (ndef (s, A)) (resource constraint)
T= 0 if A=A
0≤T≤εA if A=A(1 −ε))(constraint on T)
and
rdef(s, A) = max nzndef (s,A)Fn
A(ε)+T(A(ε)) −1
γ,0o
−Un
Uc= (1 −τ)wdef (s, A)
zFn= (1 + γ rdef(s, A)) wdef(s, A)
`def(s, A) = γwdef(s, A)ndef(s, A)
xdef(s, A) = T+rdef(s, A)`def(s, A)
(comp. eq. conditions)
where cdef(s;τ), ndef(s;τ), xdef(s;τ), `def (s;τ), wdef(s;τ), and rdef(s;τ) represent the equi-
librium quantities and prices for the private sector given public policy (under default) and
the dependence on government policies (τ, T ) has been omitted. The other equations that
govern the model remain the same as in the baseline.
In this robustness exercise, we recalibrate the model with the same strategy as described
in Section 4.2. The parameters affected by this recalibration are given by β= 0.90,¯
A=
45
0.21, σe= 4.94 (All other parameters remain the same as in the baseline). Notice that in
Table C.1 (the analogue of Table 4), the simulated moments from the extended model that
allows for bailouts in default are very similar to the baseline model. This is directly a result of
re-calibrating the model to feature the same frequency of defaults as in the baseline model.
Table C.1 also shows that the contrast between the bailout and the no-bailout economy
is now even stronger. The no-bailout economy defaults less, faces lower borrowing costs,
despite accumulating much higher levels of debt, compared with the bailout-economy. As a
result, the welfare cost of bailouts is even larger than in the baseline model.
Table C.1: Simulated moments
Bailouts during default No bailouts
Default frequency 0.5∗0.1
Sovereign spread
mean 0.7 0.3
standard deviation 0.8 0.2
corr(GDP, spread) –0.7 –0.6
Debt/GDP 18.1 57.0
Mean lending rate 0.2 0.1
Welfare gain of bailouts –2.3
Units: percent (except for corr. coeff.). ∗denotes targeted moments.
46
C.2 Relative weights in the social welfare function
In the baseline model, we assume that the government puts full weight on the welfare of
households. Here, we explore the implications of assuming, alternatively, that the govern-
ment puts equal weight on the welfare of the households and banks.
Formally, the planner’s value of repaying can be re-written as:
VR(B, s) = max
Φ
EAnµUc(κ; Φ) , n (κ; Φ) + (1 −µ)x(κ; Φ) + βEs0|sV(B0, s0)o(31)
subject to the resource constraint, government budget constraint, restriction on T, and
competitive equilibrium conditions found in problem (21).
Similarly, the planner’s value of defaulting can be formulated as:
VD(s) = max
τ(µUcdef (s;τ), ndef (s;τ)+ (1 −µ)xdef(s;τ)
+βEs0|sθV (0, s0) + (1 −θ)VD(s0))(32)
subject to the resource constraint, government budget constraint, and competitive equilib-
rium conditions found in problem (22).
In this robustness exercise, we recalibrate the model with µ= 0.5 and the same strategy
as described in Section 4.2. The parameters affected by this recalibration are given by β=
0.82,¯
A= 0.31, σe= 3.75 (All other parameters remain the same as in the baseline). As in
the baseline, Table C.2 (the analogue of Table 4) shows that the no-bailout economy defaults
less, faces lower borrowing costs, despite accumulating higher levels of debt, compared with
the bailout-economy. Importantly, sub-optimality of bailouts is robust to this alternative
specification.
Table C.2: Simulated moments (µ= 0.5)
With bailouts No bailouts
Default frequency 0.5∗0.4
Sovereign spread
mean 0.7 0.6
standard deviation 0.7 0.6
corr(GDP, spread) –0.3 –0.3
Debt/GDP 15.5 25.7
Mean lending rate 0.0 0.2
Welfare gain of bailouts –1.1
Units: percent (except for corr. coeff.). ∗denotes targeted moments.
47
C.3 Moral hazard
In this section, we consider an extension of the model so that bailouts can trigger moral
hazard considerations. Assume that banks can decide the variance of capital loss shocks ε
(i.e., σ2
ε) one period in advance, as a stand-in for risk-taking behavior by banks. Let the
utility cost—suffered by banks—of choosing ˆσεbe given by
X(ˆε) = Ψ(ˆσε−σε)2(33)
where σ2
εis the baseline level of volatility and Ψ >0. When Ψ → ∞, reducing the variance is
prohibitively costly and is equivalent to the baseline model (with no moral hazard consider-
ations). Conversely, when Ψ →0, reducing the variance is costless, leading banks to choose
zero risk—with or without bailouts—effectively eliminating banking crises and bailouts alto-
gether. For intermediate values of Ψ >0, banks may choose a higher variance (i.e., risk) in
anticipation of bailouts, thus triggering moral hazard considerations. We report the results
for Ψ = 0.05 in Table C.3. As in the baseline model, the economy without bailouts defaults
less frequently and faces lower borrowing costs, despite accumulating higher levels of debt,
relative to the economy with bailouts. We can also see that banks choose a larger variance
with bailouts, relative to the banks without bailouts. Finally, the welfare loss from bailouts
is even larger—a loss of 5.2 percent—compared with the baseline welfare loss of 1.5 percent.
Table C.3: Simulated moments (Ψ = 0.05)
With bailouts No bailouts
Default frequency 0.4 0.2
Sovereign spread
mean 0.6 0.4
standard deviation 0.6 0.3
corr(GDP, spread) –0.2 –0.5
Debt/GDP 19.8 61.9
Mean lending rate 0.0 0.3
Relative volatility bσε/σε1.0 0.8
Welfare gain of bailouts –5.2
Units: percent (except for correlation coeff. and relative
volatility).
48
C.4 Bailout announcements affect banking crisis probability
We consider the possibility that the proportional size of the announced bailout policy can
reduce the probability of a banking crisis. In particular, assume that π(·) takes the form:
πT/εA= ¯π×1−ηT /εA(34)
where η∈[0,1] governs the strength of the announcement effect. If η= 0, the announcement
has no effect on the probability of a banking crisis, as in the baseline economy. As ηincreases,
the probability of a banking crisis declines with relatively larger bailouts.
The rest of the model remains identical to the baseline model. As can be seen in Table
C.4, stronger announcement effects increase the size of the promised bailouts (first row),
reducing the probability of banking crises to 1.6 percent when η= 0.9, compared with 1.8
percent when η= 0.0 (second row). Because the government announces disproportionately
larger bailouts for more severe banking crises, the banking crises that do occur tend to be
milder. As a result, conditional on banking crises, actual bailout payments are smaller (third
row). Allowing for bailouts to have announcement effects slightly reduces the ex ante welfare
loss from bailouts (fourth row). Nevertheless, the ex ante suboptimality of bailout result is
robust to including announcement effects.
Table C.4: Simulated moments
Announcement effect (η)
0.0 0.5 0.9
Bailout/GDP (promised) 0.9 0.9 1.2
Banking crisis prob. 1.8 1.7 1.6
Bailout/GDP (conditional on BC) 1.7 1.5 1.2
Welfare gain of bailouts −1.48 −1.47 −1.46
Units: percent.
49
C.5 Sensitivity
We study the baseline model’s sensitivity to eight parameters, i.e. the bank’s baseline capital
(¯
A), the financial shock shape (σε), the Frisch elasticity (1/(ω−1)), the household discount
factor (β), the strength of the working capital constraint (γ), the probability of bank capital
shock (π), the labor share (α), and the probability of financial redemption (θ). We change
one parameter value at a time, keeping all others at their baseline values. We confirm that
our main results are robust to these alternative parameter values.
1. Bank’s baseline capital, ¯
A. During defaults, the government is unable to bailout
the banks and increase their liquidity. As a result, higher values of ¯
Areduce the costs
of default (since it implies higher loanable funds) and reduces the debt capacity of the
government. Nevertheless, the model without bailouts still sustains higher debt, has
a lower volatility of spreads, and a lower default frequency, for a given value of ¯
A.
We also find confirmation for our headline result regarding the welfare superiority of
banning bailouts.
Table C.5: Sensitivity to ¯
A
Baseline model Model without bailouts
Low ¯
A(¯
A= 0.26)
Default frequency 0.6 0.4
Sovereign spread
mean 0.8 0.5
standard deviation 0.7 0.5
corr(GDP, spread) –0.5 –0.4
Debt/GDP 22.9 33.4
Mean lending rate 0.1 0.3
Welfare gain of bailouts –1.9
High ¯
A(¯
A= 0.30)
Default frequency 0.6 0.4
Sovereign spread
mean 0.8 0.0
standard deviation 1.0 0.9
corr(GDP, spread) –0.2 0.0
Debt/GDP 10.5 19.8
Mean lending rate 0.0 0.8
Welfare gain of bailouts –0.8
Units: percent (except for corr. coeff.).
50
2. Financial shock shape, σε. Due to the nonlinear effects of financial shocks on the
real economy as discussed in Section 4.5, the larger the volatility of the potential loss to
banking capital, the higher the need for bailouts. Indeed, Table C.6 shows that higher
volatilities are associated with a higher default frequency, and higher and more volatile
spreads. This is because the model generates a stronger ‘diabolic loop.’ The increase
in the potential loss to banking capital creates higher incentives for the government to
borrow to finance the bailouts, which increases the risk of default. Even though the
welfare loss from access to bailouts is slightly smaller with higher values for σε, we still
find that banning bailouts altogether is optimal from an ex ante point of view.
Table C.6: Sensitivity to σε
Baseline model Model without bailouts
Low σε(σε= 3.76)
Default frequency 0.4 0.3
Sovereign spread
mean 0.6 0.4
standard deviation 0.5 0.4
corr(GDP, spread) –0.4 –0.4
Debt/GDP 22.3 34.0
Mean lending rate 0.0 0.2
Welfare gain of bailouts -1.8
High σε(σε= 4.76)
Default frequency 0.7 0.4
Sovereign spread
mean 1.0 0.5
standard deviation 1.0 0.7
corr(GDP, spread) –0.3 –0.3
Debt/GDP 12.2 22.2
Mean lending rate 0.0 0.3
Welfare gain of bailouts –1.3
Units: percent (except for corr. coeff.).
51
3. Frisch elasticity, 1/(ω−1). Our baseline calibration sets the wage elasticity of labor
supply to an intermediate value from within the range of estimates in the literature.
We have argued that the diabolic loop, which bailouts create, is costly (in part) because
distortionary labor taxes (and new debt) are used to finance those bailouts. Therefore,
one might expect that for a low elasticity, this distortion will be smaller and it could
moderate or even overturn the baseline welfare results. Figure C.2 shows that all else
equal, and, in particular holding fixed the level of debt, indeed the welfare loss from
bailouts is smaller when ωis higher (i.e. the Frisch elasticity is lower). Note that
access to bailouts still results in a welfare loss.
Figure C.2: Welfare gains with different ωvalues.
Note: the graph shows the welfare gain of having access to bailouts as a function
of the debt level, for different values of the Frisch elasticity parameter (ω). The
black dots denote the mean debt levels in the respective economies. The figure is
constructed assuming average values for TFP and ε.
Furthermore, as shown in Figure 12 and Figure C.2, the welfare gains of bailouts are
decreasing in the debt level. The solid dots in Figure C.2 show the total effect that
changes in ωhave on welfare: Holding debt levels fixed, a higher ω(i.e. lower elasticity)
reduces the welfare loss from bailouts, but at the same time, increases the debt capacity
of the economy with bailouts, thus increasing the welfare loss from bailouts. Table C.7
(and the solid dots in Figure C.2) shows that the second effect dominates.
52
Table C.7: Sensitivity to ω
Baseline model Model without bailouts
High Frisch Elasticity (ω= 2.3)
Default frequency 0.7 0.5
Sovereign spread
mean 0.9 0.6
standard deviation 1.1 0.8
corr(GDP, spread) –0.3 –0.3
Debt/GDP 12.6 22.8
Mean lending rate 0.0 3.0
Welfare gain of bailouts –1.4
Low Frisch Elasticity (ω= 2.7)
Default frequency 0.6 0.3
Sovereign spread
mean 0.8 0.5
standard deviation 0.6 0.5
corr(GDP, spread) –0.4 –0.3
Debt/GDP 19.9 30.5
Mean lending rate 0.0 0.2
Welfare gain of bailouts –1.8
Units: percent (except for corr. coeff.).
53
4. Household discount parameter, β. Since the government represents the preferences
of households, a lower discount parameter (corresponding to less patience) results in
an increase in default frequencies, as well as spreads (Table C.8). There is also a slight
increase in the amount of debt in the baseline model. The result that the no-bailout
economy features a lower likelihood of default, lower and less volatile spreads, and
higher welfare is robust to these alternative values.
Table C.8: Sensitivity to β
Baseline model Model without bailouts
Low β(β= 0.76)
Default frequency 0.9 0.5
Sovereign spread
mean 1.1 0.7
standard deviation 1.1 0.7
corr(GDP, spread) –0.3 –0.4
Debt/GDP 16.0 26.8
Mean lending rate 0.0 0.4
Welfare gain of bailouts –2.3
High β(β= 0.86)
Default frequency 0.3 0.2
Sovereign spread
mean 0.5 0.4
standard deviation 0.6 0.5
corr(GDP, spread) –0.3 –0.5
Debt/GDP 15.3 26.4
Mean lending rate 0.0 0.1
Welfare gain of bailouts –1.0
Units: percent (except for corr. coeff.).
54
5. Working capital constraint, γ. The working capital constraint parameter deter-
mines the amount of working capital loans that firms demand. Higher values increase
the demand for loans, which increases the loans’ interest rate. With higher values of
γ, we find that the government responds by injecting more liquidity into the finan-
cial system by increasing debt, as shown in Table C.9. The ex ante welfare loss from
bailouts is robust to alternative values of γ.
Table C.9: Sensitivity to γ
Baseline model Model without bailouts
Low γ(γ= 0.49)
Default frequency 0.7 0.4
Sovereign spread
mean 0.9 0.5
standard deviation 1.0 0.7
corr(GDP, spread) –0.1 –0.2
Debt/GDP 12.2 21.9
Mean lending rate 0.0 0.3
Welfare gain of bailouts –1.3
High γ(γ= 0.55)
Default frequency 0.6 0.4
Sovereign spread
mean 0.8 0.5
standard deviation 0.7 0.5
corr(GDP, spread) –0.5 –0.4
Debt/GDP 22.9 33.4
Mean lending rate 0.0 0.3
Welfare gain of bailouts –1.9
Units: percent (except for corr. coeff.).
55
6. Probability of bank capital shock, π. To examine the role of the bank capital shock
in our results, we set πto 1 percent and 10 percent. In our model, the government
promises bailout guarantees in the expectation of a banking crisis and thus, when the
probability of having a banking crisis increases, the government becomes more reluctant
to promise guarantees upfront knowing that the financing of that bailout will be costly
once the shock hits. As shown in Table C.10, we find larger welfare losses from access
to bailouts when πincreases.
Table C.10: Sensitivity to π
Baseline model Model without bailouts
Low π(π= 0.01)
Default frequency 0.5 0.3
Sovereign spread
mean 0.7 0.5
standard deviation 0.7 0.5
corr(GDP, spread) –0.3 –0.3
Debt/GDP 15.6 26.8
Mean lending rate 0.0 0.2
Welfare gain of bailouts –1.4
High π(π= 0.10)
Default frequency 0.6 0.3
Sovereign spread
mean 0.8 0.5
standard deviation 0.8 0.5
corr(GDP, spread) –0.3 –0.3
Debt/GDP 16.6 26.9
Mean lending rate 0.0 0.2
Welfare gain of bailouts –1.7
Units: percent (except for corr. coeff.).
56
7. Labor share, α. Similar to the working capital constraint parameter, γ, the labor
share parameter determines the amount of working capital loans demanded by firms.
As such, changes in αhave similar properties as changes in γ. As shown in Table C.11,
the ex ante welfare losses of bailouts increase with higher α.
Table C.11: Sensitivity to α
Baseline model Model without bailouts
Low α(α= 0.65)
Default frequency 0.6 0.5
Sovereign spread
mean 0.8 0.1
standard deviation 1.1 1.0
corr(GDP, spread) –0.3 –0.1
Debt/GDP 10.1 18.6
Mean lending rate 0.0 0.7
Welfare gain of bailouts –0.9
High α(α= 0.75)
Default frequency 0.6 0.4
Sovereign spread
mean 0.8 0.5
standard deviation 0.7 0.5
corr(GDP, spread) –0.6 –0.5
Debt/GDP 28.1 38.7
Mean lending rate 0.1 0.3
Welfare gain of bailouts –1.9
Units: percent (except for corr. coeff.).
57
8. Probability of financial redemption, θ. As we explained in Section 5, the ability
to issue bailouts affects the costs of defaults, and these are made of two parts. The first
part materializes in the periods in which the government is excluded, and is identical
for economies with and without bailouts. The second part comes once the government
has reentered financial markets: the reentry occurs with zero debt, which depresses
private credit and output. We can interpret the reduced output level upon reentry as
another component of the costs of defaults. This second part of the cost of default is
lower in the bailout economy because it can prop up liquidity using bailouts.
These two parts to the cost of default and how they are affected by the access to bailouts
interact with the reentry probability. The higher the reentry probability (θ), the more
relevant the second part of the default costs, and therefore the more important the
effect of bailouts on default costs. Under a higher θ, the relatively lower default costs
in the bailout economy are reduced even further, leading to lower debt capacity and
welfare. Therefore, other things equal (in particular, for a given level of debt), a higher
θis associated with a lower welfare gain of bailouts. Figure C.3 shows this result.30
Figure C.3: Welfare gains of bailout: the role of θ.
Note: the graph shows the welfare gain of having access to bailouts as a function
of the debt level, for different values of the reentry probability (θ). The black dots
denote the mean debt levels in the respective economies. The figure is constructed
assuming average values for TFP and ε.
As shown in Figure 12, the welfare gains of bailouts are decreasing in the debt level.
Figure C.3 also shows this, for different values of θ. The solid dots in Figure C.3 show
the total effect that changes in θhave on welfare: A higher θreduces the default costs
30Note that there is no recalibration involved in the construction of this figure.
58
of the bailout economy (lowering the welfare gain of bailouts, holding debt levels fixed),
which endogenously leads to a lower debt level (increasing the welfare gain of bailouts).
Table C.12 (as well as the dots in Figure C.3) shows that the second effect dominates.
Table C.12: Sensitivity to θ
Baseline model Model without bailouts
Low θ(θ= 0.40)
Default frequency 0.4 0.2
Sovereign spread
mean 0.6 0.4
standard deviation 0.5 0.4
corr(GDP, spread) –0.5 –0.4
Debt/GDP 24.5 34.6
Mean lending rate 0.0 0.2
Welfare gain of bailouts –1.7
High θ(θ= 0.60)
Default frequency 0.8 0.4
Sovereign spread
mean 1.0 0.3
standard deviation 1.3 0.8
corr(GDP, spread) –0.2 –0.1
Debt/GDP 10.2 21.8
Mean lending rate 0.0 0.6
Welfare gain of bailouts –1.1
Units: percent (except for corr. coeff.).
59
D Computational Appendix
The model is solved using value function iteration with a discrete state space. We solve for
the equilibrium of the finite-horizon version of our economy, increasing the number of periods
of the finite-horizon economy until value functions and bond prices for the first and second
periods of this economy are sufficiently close. Then, the first-period equilibrium objects are
used as the infinite-horizon-economy equilibrium objects.
Algorithm. First, we specify initial values of repayment (VR
0) and default (VD
0) as the
values at the last period of the finite-horizon version of the model. That is, for a point
(b, s, A) in the state space, we set
VR
(0)(b, s) = EA[u(c∗
LP, n∗
LP)]
VD
(0)(b, s) = EAu(c∗
def; LP, n∗
def; LP)
where (c∗
LP,n∗
LP) are the optimal consumption and labor decisions in the last-period of the
finite horizon economy (hence the LP subscript). A similar interpretation applies for (c∗
def; LP,
n∗
def; LP), but under default. From these initial guesses, we can derive an initial guess for the
default decision (being 1 if VD
(0) > V R
(0) and 0 otherwise). We also compute and retain the
equilibrium values of rLP, both under repayment and default: These values are needed to
compute the bond price.
Second, using these initial values, we solve for the problem stated in (20)–(22) for each
point in our discrete state space.
To solve the problem under default, we compute (c∗
def, n∗
def, r∗
def) following the equilibrium
conditions in the private sector. With these allocations and prices we can get the new guess
for the value of default, VD
(1).
To solve the problem under repayment we do the following for each combination (b, s):
1. Propose a candidate bailout, Tc.
2. Given (b, s, Tc) solve for the optimal borrowing level by searching over the debt grid
and selecting the level that maximizes VR(·;Tc). Denote this level, b0
c. Note that this
step involves solving the equilibrium of the private sector for each possible point in the
state space and each given candidate transfer Tc.
3. From all the candidate values of Tc(and associated b0
c), choose the one that maximizes
VR. This is done taking expectations over the possible realization of A:Awith
probability 1 −πor (1 −ε)Awith probability π.
60
4. Finally, update the guess for the value of repayment, VR
(1).
From the process above we also recover (among other quantities and prices) r∗, which is
the equilibrium loan rate. This rate needs to be saved in order to compute the bond price
(according to equation (19)) in subsequent iterations.
Third, we evaluate whether the maximum absolute deviation between the new and previ-
ous continuation values is below a give tolerance level. If it is, a solution has been found. If
it is not, we repeat the optimization exercise using the new continuation values VR
(1) and VD
(1)
to compute the expected value function at each grid point and to derive default probabilities
that affect the price faced by the borrower. We repeat the procedure until the maximum ab-
solute deviation between the new and previous continuation values is below a given tolerance
level.
Implementation. We use the Tauchen method to discretize the TFP shocks in 25 states.
We discretize the εshocks into four states in a one-sided application of the Tauchen method.
We use 50 evenly distributed grid points for debt. The debt grid is: b∈[0,0.80]. Recall
that GDP is endogenous in our model: In the benchmark calibration, mean annual GDP is
roughly 0.77 which implies our debt grid covers more than 100 percent of annual GDP.
The simulations presented in the main body of the paper come from the algorithm de-
scribed in this appendix and allowing for the bailout to take any of 50 evenly distributed
grid points ranging from zero to full coverage of the damage to the banking sector capital,
i.e. Tc∈[0, εA].
61
