Fiscal Stimulus Under Sovereign Risk — International Finance Discussion Papers No. 1257 (September 2019)

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International Finance Discussion Papers Number 1257, dated September 2019, from the Board of Governors of the Federal Reserve System, is by Javier Bianchi, Pablo Ottonello, and Ignacio Presno. The abstract says the excess procyclicality of fiscal policy is commonly viewed as a central malaise in emerging economies, and that the authors document that procyclicality is more pervasive in countries with higher sovereign risk. They provide a model of optimal fiscal policy with nominal rigidities and endogenous sovereign default. The abstract says financing a fiscal stimulus is costly for risky countries, that imposing austerity can backfire by exacerbating the exposure to default, and that a well-designed fiscal forward guidance can help reduce the excess procyclicality.

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Fiscal Stimulus Under Sovereign Risk
Bianchi, Javier, Pablo Ottonello, and Ignacio Presno

Please cite paper as:
Bianchi, Javier, Pablo Ottonello, and Ignacio Presno (2019).
Fiscal Stimulus Under Sovereign Risk. International Finance
Discussion Papers 1257.

https://doi.org/10.17016/IFDP.2019.1257

International Finance Discussion Papers
Board of Governors of the Federal Reserve System

Number 1257
September 2019
Board of Governors of the Federal Reserve System

International Finance Discussion Papers

Number 1257

September 2019

Fiscal Stimulus Under Sovereign Risk
Javier Bianchi, Pablo Ottonello, and Ignacio Presno

NOTE: International Finance Discussion Papers are preliminary materials circulated to stimulate
discussion and critical comment. References to International Finance Discussion Papers (other
than an acknowledgment that the writer has had access to unpublished material) should be
cleared with the author or authors. Recent IFDPs are available on the Web at
www.federalreserve.gov/pubs/ifdp/. This paper can be downloaded without charge from the
Social Science Research Network electronic library at www.ssrn.com.
Fiscal Stimulus under Sovereign Risk ∗
Javier Bianchi† Pablo Ottonello‡ Ignacio Presno§

September 2019

Abstract

The excess procyclicality of fiscal policy is commonly viewed as a central malaise in
emerging economies. We document that procyclicality is more pervasive in coun-
tries with higher sovereign risk and provide a model of optimal fiscal policy with
nominal rigidities and endogenous sovereign default that can account for this em-
pirical pattern. Financing a fiscal stimulus is costly for risky countries and can
render countercyclical policies undesirable, even in the presence of large Keynesian
stabilization gains. We also show that imposing austerity can backfire by exacer-
bating the exposure to default, but a well-designed “fiscal forward guidance” can
help reduce the excess procyclicality.

Keywords: Fiscal Stabilization Policy, Sovereign Default, Procyclicality
JEL Codes: E62, F34, F41, F44, H50.

∗
We would like to thank Neele Balke, Hiuxin Bi, Satyajit Chatterjee, Axelle Ferriere, Jesús Fernández-
Villaverde, Sylvain Leduc, Franck Portier, Oreste Tristani, Juan Sánchez, Martı́n Uribe, and Vivian Yue for
excellent discussions, as well as participants at the 2018 AEA Meetings, ADEMU Workshop, Bank of Canada-
IGIER Bocconi Conference, Barcelona GSE Summer Forum, CEBRA, IM-TCN-ND Workshop, ITAM-PIER
Conference, 2015 Ridge December Forum, Federal Reserve Board, FRB San Francisco CPBS Conference, FRB
St. Louis STLAR Conference, Iowa State University, Rochester Mini-Conference, 2016 SED meetings, XX IEF
Workshop, Atlanta Workshop on International Economics, and Yale University. Marı́a Aristizabal-Ramirez
and Dawson Miller provided excellent research assistance. A previous version of this paper circulated with
the title “Fiscal Policy, Sovereign Risk, and Unemployment.” Disclaimer: The views expressed herein do not
necessarily reflect those of the Board of Governors, the Federal Reserve Bank of Minneapolis, or the Federal
Reserve System.
†
Federal Reserve Bank of Minneapolis and NBER.
‡
University of Michigan and NBER.
§
Federal Reserve Board.
1 Introduction
There is a long-standing view that fiscal policy should play a stabilizing role in business cycles,
especially when there are constraints on monetary policy. The textbook Keynesian argument
is that by spending more in a recession, the government can prop up aggregate demand and
help to mitigate the rise in unemployment. Yet, few governments in practice follow this pre-
scription.1 As shown in Figure 1, the recent Eurozone crisis provides another emblematic
example in this regard. While facing a severe recession and mounting unemployment, gov-
ernments in Southern European countries reduced spending significantly. This contraction in
spending occurred despite their inability to use monetary policy, which left fiscal policy as the
only instrument available for macroeconomic stabilization.

(A) Unemployment rate (B) Government spending (C) Sovereign spreads
110 25
20
105
20
15 100

95 15
10
90
10

5 85
5
80
0
75 0

2008 2010 2012 2014 2008 2010 2012 2014 2008 2010 2012 2014

Figure 1: Unemployment, Fiscal Policy, and Sovereign Spreads during the Eurozone Crisis
Notes: Unemployment rate and sovereign spreads expressed in percentage point deviations from their 2008.q1
values. Government spending is set to 2008.q1=100. “Average” denotes the simple average of Greece, Ireland,
Italy, Portugal, and Spain. Data source: Eurostat.

In this paper, we show that sovereign risk can reverse the traditional argument for ex-
pansionary fiscal policy during a recession, and therefore rationalize the empirical evidence
on the different patterns of cyclicality in fiscal policy observed around the world. Our theory
lies in a fundamental conundrum that governments encounter when facing a recessions under
sovereign risk: Should the government trigger a stimulus to mitigate the recession at the ex-
pense of higher sovereign spreads, or should it follow austerity to reduce the probability of
a debt crisis, even if this means a more severe recession?2 A key contribution of our paper
is to explicitly model this conundrum by presenting an analysis of optimal fiscal policy in
1
See, for example, Gavin and Perotti (1997), Talvi and Vegh (2005), Kaminsky, Reinhart and Végh (2004),
and Ilzetzki and Végh (2008).
2
Many policy discussions in the austerity-versus-stimulus debate center on this question. For views on the
austerity side, see Barro (2012), and, for views on the stimulus side, see Krugman (2015). A similar debate is
ongoing in Argentina.

1
a Keynesian framework under sovereign risk and characterizing the resulting trade-offs. Our
quantitative results show that financing fiscal stimulus is costly for risky countries and can ren-
der countercyclical policies undesirable, even in the presence of large Keynesian stabilization
gains.
The paper begins by presenting empirical evidence that sovereign default risk is a key
predictor of the cyclicality of fiscal policy. Using data for a sample of around 100 countries,
we document that countercyclical fiscal policies are rare in countries with high sovereign risk,
measured by either sovereign credit ratings or the frequency of default. Half of the countries
with low sovereign risk have a countercyclical government spending policy, but only 20% of
countries with high risk exhibit such a policy. Moreover, in countries with high sovereign
default risk, the correlation between government spending and GDP is between 30% and 50%
higher than countries with low sovereign risk. These differences are not driven by income
per capita or other macroeconomic or institutional factors identified in previous literature as
relevant drivers of fiscal procyclicality.
We build a theoretical framework to study the role of sovereign risk in determining op-
timal fiscal policy over the business cycle. We consider a small open economy in which the
government borrows externally. We first construct a benchmark environment under which
Keynesian policies would be optimal, absent the risk of sovereign default. To this end, we
incorporate two key elements that have been identified in theory as providing an important
scope for fiscal stabilization. First, we consider nominal rigidities, in the form of downward
nominal wage rigidity, and a fixed exchange rate regime. As in the classic Mundell-Fleming
argument, an increase in government spending entails only limited crowding-out effects and
is effective for reducing involuntary unemployment. Second, we consider households that are
hand-to-mouth and face an uninsurable idiosyncratic risk of unemployment. The environment
features potentially large fiscal multipliers and substantial welfare gains from fiscal stabiliza-
tion policy. Such gains emerge from the stimulus effect on output and from the reduction in
inequality.
A calibrated version of this model for the Spanish economy shows that when the govern-
ment can commit to repaying the debt, fiscal policy is essentially Keynesian: During recessions,
the government increases spending that is financed by external borrowing and stabilizes invol-
untary unemployment. In this setting, optimal government spending has a −0.8 correlation
with economic activity, and unemployment volatility is an order of magnitude smaller than
that observed in the data.
Incorporating default risk drastically changes the desirability of a Keynesian fiscal stimulus.
We study the role of default risk by relaxing the assumption that the government can commit
to repaying external debt, as in Eaton and Gersovitz (1981). A debt-financed stimulus raises
the probability of a sovereign default in the future and therefore increases sovereign spreads.

2
As a result, fiscal policy now faces a trade-off between the Keynesian benefits of fiscal stimulus
and the costs of higher sovereign spreads, which has been at the heart of the popular austerity-
versus-stimulus debate.
Quantitatively, despite the large Keynesian benefits from fiscal stimulus, default risk can
overturn the nature of optimal fiscal policy. In the economy calibrated to match debt and
spread levels in the data, we find that optimal policy is strongly procyclical, with a 0.7 cor-
relation with output. This value is close to the one observed in the data for Spain and most
economies with substantive default risk, and contrasts with the large negative correlation that
characterizes economies without default risk. Moreover, the observed volatility in unemploy-
ment increases by an order of magnitude relative to the economy without default risk and is
close to the one observed in the data.
Although the optimal fiscal policy is overall procyclical, the model displays strong state
dependence, by which the response of government spending is non monotonic with respect
to the level of sovereign debt. When the stock of debt is relatively low, government spend-
ing expands in recessions as the Keynesian benefits outweigh concerns about sovereign risk.
When the stock of debt is very high, it is optimal for the government to default and redirect
resources toward spending rather than repaying debt. For intermediate values of debt, the op-
timal response is characterized by austerity, since the government tends to reduce government
spending to mitigate the rise in borrowing costs and reduce the probability of a debt crisis.
An important implication of this state dependence is that recessions turn out to be more
severe when preceded by high levels of debt. These results help to rationalize the empirical
evidence provided by Romer and Romer (2019) that countries with more “fiscal space” suffer
less severe recessions.
Finally, we use the model to study the desirability of austerity programs. A common
premise is that austerity programs enforced, for example, by the IMF can help correct dis-
torted incentives and ensure debt sustainability. We argue, however, that the balance between
austerity and default incentives is delicate. We show that although cutting spending during
a recession tends to be optimal for the government, imposing a sudden austerity program
can backfire by precipitating the government to default. The intuition for these unintended
consequences is that additional fiscal constraints imposed on a government can make debt
repayment less attractive and push the government to default, even under circumstances in
which the government would find it optimal to repay absent any constraints.
On the other hand, we show that an austerity program that constrains future spending can
be beneficial. By promising less spending in the future, the government, in effect, promises
lower debt accumulation and reduces future incentives to default. The result is that current
borrowing costs are reduced for the government, which facilitates an expansionary fiscal pol-
icy during a recession. We refer to this policy as a form of “fiscal forward guidance,” which

3
is analogous to the classic forward guidance in monetary policy. The mechanism we high-
light, however, is different, as it operates through sovereign spreads and the trade-off between
stimulus and sovereign risk rather than through intertemporal substitution.3 Importantly, we
establish that the desirability of fiscal forward guidance does not hinge on a state-contingent
fiscal adjustment. In addition, we show that if a state-contingent spending rule is feasible,
it should specify more aggressive cuts in states tomorrow with intermediate income states.
Larger cuts when income is very low are not optimal because they can exacerbate higher
spreads today. Larger cuts when income is very high are also not optimal, because they
deliver modest reductions in spreads ex ante and larger distortions ex post.

Related Literature. Our paper is related to several strands of the literature. First, the
paper relates to the New Keynesian literature that studies the role of government spending
as a macroeconomic stabilization tool. In this literature, nominal rigidities create a scope
for fiscal policy to manage aggregate demand. This role becomes especially important in the
presence of constraints on monetary policy, which arise in particular from a fixed exchange rate
or a zero lower bound. Some recent influential examples in both open and closed economies
include Gali and Monacelli (2008), Eggertsson (2011), Christiano, Eichenbaum and Rebelo
(2011), Werning (2011), Woodford (2011), Nakamura and Steinsson (2014), Michaillat and
Saez (2018), and Farhi and Werning (2017).4 We contribute to this literature by incorporating
sovereign risk, a central argument in policy discussions on the merits of fiscal stimulus. In
addition to characterizing how sovereign risk shapes the optimal conduct of fiscal policy, we
show that accounting for sovereign risk is key to understand the observed procyclicality of
fiscal policy as well as the importance of fiscal space in determining the severity of recessions.
Second, our model of sovereign risk follows the literature on sovereign default in the tra-
dition of Eaton and Gersovitz (1981), Aguiar and Gopinath (2006), and Arellano (2008). A
particularly relevant paper is Cuadra, Sanchez and Sapriza (2010), which was the first to es-
tablish that fiscal policy is procyclical in a canonical sovereign debt model with flexible prices.
Other contributions in a similar vein are Arellano and Bai (2017), Aguiar and Amador (2011),
and Balke and Ravn (2016). These papers do not consider nominal rigidities and hence do
not incorporate the traditional stabilization benefits that underpin fiscal stimulus.5 An early
3
As shown by Farhi and Werning (2017), in the New Keynesian model, future spending can be more
powerful than current policy changes—a “fiscal forward guidance puzzle.” See Canzoneri, Cao, Cumby, Diba
and Luo (2018) for further work on this topic. The classic references on forward guidance in monetary policy
are Krugman (1998), Eggertsson and Woodford (2003), and Werning (2011).
4
Related to this literature, a vast body of work empirically studies the effect of changes in government
spending on the economy. See Ramey (2019) for a recent survey.
5
In Balke and Ravn (2016), there is unemployment due to search and matching frictions, but government
spending affects employment through wealth effects on search efforts, not through aggregate demand, as in our
setup. A common element we share with their work is that our model also features household heterogeneity
and an insurance channel from fiscal policy.

4
contribution that incorporates nominal rigidities in the canonical sovereign default model is
that of Na, Schmitt-Grohé, Uribe and Yue (2018). Focusing on the optimal exchange rate
policy, they show that the model can account for the “twin Ds” phenonomenon (i.e., the joint
occurrence of large devaluations and sovereign defaults). The focus of our paper, instead, is
on the optimal fiscal policy in the context of a fixed exchange rate. Our contribution is to
provide the first analysis of the trade-off between fiscal stimulus and sovereign risk, and show
how this shapes the conduct of fiscal policy over the business cycle.
Our results on the macroeconomic and welfare effects of fiscal rules are related to an active
ongoing literature. In our setup, the future path of government spending affects investors’
expectations of future deficit and alters current bond prices. From a normative point of
view, the potential benefits from rules arise because of the debt-dilution effects generated by
long-term debt, as emphasized in Chatterjee and Eyigungor (2015), Hatchondo, Martinez and
Sosa-Padilla (2016), and Aguiar, Amador, Hopenhayn and Werning, 2019.6 We advance this
literature by providing two results. First, we show that fiscal rules are particularly desirable
during times of distress. Second, rules that impose too aggressive spending cuts can backfire
by raising incentives to default and worsening spreads.
Our paper is also to a literature that studies how increases in sovereign spreads can trans-
late into higher borrowing costs for the private sector and negatively affect economic activity.
Important examples include Mendoza and Yue (2009), Broner, Erce, Martin and Ventura
(2014), Corsetti, Kuester, Meier and Muller (2013, 2014), Gourinchas, Philippon and Vayanos
(2017), and Bocola (2016). Our framework includes both the costs of endogenous sovereign
default risk and the potential Keynesian benefits of fiscal stimulus, and we characterize both
theoretically and quantitatively the policy trade-off that emerges in this setup. A common
element we share with Gourinchas et al. (2017) is the importance on the level of debt and
fiscal consolidation in determining the magnitude of downturns.
Finally, our paper is related to the literature that has studied the difference in the cycli-
cality of fiscal policy between emerging and advanced economies. Several studies have doc-
umented how fiscal policies are more procyclical in emerging economies than in developed
economies (see, for example, Gavin and Perotti, 1997; Talvi and Vegh, 2005; Kaminsky et
al., 2004; Ilzetzki and Végh, 2008, among others). We contribute to this literature, first by
6
In a similar vein, Hatchondo, Roch and Martinez (2017) compare the welfare performance of debt and
spread rules using an endowment economy model with long-term debt, while Anzoategui (2018) evaluates
the macroeconomic effects in a production economy, as we do, but using empirically estimated rules. A
different mechanism studied by Gonçalves and Guimaraes (2015) allows the government to choose spending
in all future states of nature and through this channel reduce future temptation to default. In Lorenzoni and
Werning (2019), instead, sufficiently responsive fiscal rules are shown to reduce the exposure to multiplicity.
Fiscal rules have also been shown to counteract political economy distortions (Alesina and Tabellini, 1990;
Azzimonti, Battaglini and Coate, 2016; Alfaro and Kanczuk, 2017). Halac and Yared (2017) and Dovis and
Kirpalani (2017) study reputation mechanisms under which the government cannot commit to enforcing fiscal
rules.

5
providing empirical evidence that sovereign risk is a key predictor of the cyclicality of fiscal
policy, and second by providing a theory with endogenous default risk that can explain the
empirical patterns. We view our explanation as complementary to other explanations based
on political economy or institutional elements.7
The paper is organized as follows. Section 2 presents empirical facts documenting the
relationship between sovereign risk and fiscal policy. Section 3 presents the model of optimal
fiscal policy in the presence of default risk and nominal rigidities. Section 4 presents the
main policy trade-off. Section 5 presents the quantitative analysis of the optimal fiscal policy.
Section 6 studies fiscal austerity programs. Section 7 concludes.

2 Empirical Facts
We provide descriptive evidence documenting that countries with higher sovereign default risk
tend to have a more procyclical government spending policy. This relationship is not driven by
income differences or other macroeconomic and institutional factors identified in the previous
literature as important drivers of fiscal procyclicality.

2.1 Data
We measure the cyclicality of government spending and sovereign default risk for a sample
of around 100 countries for the period 1990-2016. To measure the cyclicality of government
spending, we use data from World Development Indicators (WDI), a dataset compiled from
officially recognized international sources of data on government spending (variable “General
government final consumption expenditure”) and GDP for a large set of countries.8 Table 1
presents summary statistics of the cyclical behavior of government spending around the world.
We compute second moments using the cyclical component of per capita variables in constant
local currency, detrending variables with the HP filter and a smoothing parameter of 100.
The first two columns of Table 1 show that government spending tends to display large and
persistent business cycle fluctuations. Most countries display a larger volatility in government
spending than in economic activity. The third column of Table 1 shows summary statistics
7
For instance, Talvi and Vegh (2005), Alesina, Campante and Tabellini (2008), and Ilzetzki (2011) study
the role of political distortions in explaining fiscal procyclicality. Another related explanation has been the
“voracity effect,” (e.g. Tornell and Lane, 1999), the quality of institutions and fiscal rules (Galı́ and Perotti,
2003, Frankel, Vegh and Vuletin, 2013), financial development (Aghion and Marinescu, 2007) and inequality
and social polarization (Woo, 2009).
8
The original dataset contains information on government spending and GDP during the period 1990-
2016 for 167 countries. We dropped countries that were missing more than half of the values on government
expenditure for the period 1990-2016 or countries with discontinuous data, leading to a sample of 122 countries,
of which 98 have data available on credit ratings. The countries included in the sample are detailed in Appendix
Table 6.

6
for our variable of interest, the correlation between government spending and output. In most
countries, government spending is procyclical, with a median correlation of 0.28 between
government spending and output. The cyclicality of government spending displays fairly
large dispersion across countries, ranging from −0.3 in the 5th percentile to 0.78 in the 95th
percentile, which we exploit in our empirical analysis.

Table 1: Cyclicality of Government Spending: Summary Statistics
σG /σY corr(Gt , Gt−1 ) corr(G, Y )
Mean 2.04 0.48 0.26
Median 1.23 0.53 0.28
Standard deviation 2.21 0.23 0.33
95th percentile 5.84 0.78 0.78
5th percentile 0.52 0.07 -0.30

Notes: This table shows summary statistics of government spending for 122 countries around the world with
data available from the WDI for the period 1990-2016. The variables σG /σY , corr(Gt , Gt−1 ), and corr(G, Y )
denote, respectively, the ratio of the standard deviation of government spending to the standard deviation out-
put, the first-order autocorrelation of government spending, and the correlation between government spending
and output. We compute moments using the cyclical component of per capita variables in constant local cur-
rency, detrending variables with the HP filter and a smoothing parameter of 100. The countries included are
detailed in Appendix Table 6. For details on the data see Section 2.

To measure the degree of sovereign default risk faced by countries, we use data on credit
ratings from Standard & Poor’s. Eighty percent of the countries in our sample (98 countries)
have received a sovereign credit rating at some point during the period of study. Appendix
Table 7 shows that the cyclical patterns of government spending for the subsample with
available credit ratings are similar to those of the full sample. To measure the degree of
sovereign risk in a country, we focus on the lowest credit rating that a sovereign ever received
in the period of analysis. With this variable, we want to measure how close a country was
to experiencing a sovereign default. We later show similar results for a measure of default
risk based on the occurrence of default episodes or the number of default episodes that the
country experienced.
Panel (A) of Figure 2 shows the distribution of our measure of sovereign credit risk across
countries. This distribution is characterized by a large mass of countries (62% of the sample)
in a middle region of credit ratings, having received ratings no higher than A but always
maintaining ratings of at least B, and a smaller mass of countries either in a low default risk
region, always receiving a rating above A (20% of the countries), or in a high default risk
region, having received a rating below B (16% percent of the countries).

7
(A) Distribution of credit ratings (B) Credit ratings and fiscal procyclicality
0.3 0.8

0.25
0.6

0.2

Frequency
0.4
0.15
0.2
0.1

0
0.05

0 -0.2
SD CC CCC B BB BBB A AA AAA SD CC CCC B BB BBB A AA AAA
Minimum Rating Minimum Rating

Figure 2: Distribution of Credit Ratings and Fiscal Procyclicality
Notes: Panel (A) shows the distribution across countries of our baseline measure of default risk, defined as the
minimum credit rating experienced by the country in the period of analysis. Data source: Standard & Poor’s.
Panel (B) shows the average cyclicality of government spending in the countries within a given category
of default risk, measured by the correlation between the cyclical component of real per capita government
spending and GDP (detrended using the HP filter, and a smoothing parameter of 100). Data source: WDI.

2.2 Empirical Findings
Panel (B) of Figure 2 shows a positive relationship between the procyclicality of government
spending and sovereign default risk, using the data described in the previous subsection.
Countries with higher credit ratings tend to be more countercyclical. For instance, countries
that received ratings below CCC display an average correlation of more than 0.6 between
government spending and GDP, whereas countries that were always rated AAA tend to display
countercyclical government spending, with an average correlation of −0.1.
To measure the relationship between procyclicality and sovereign risk, we estimate the
regression

fiscal procyclicalityi = α + β 0 sovereign riski + γ 0 Xi + εi , (1)

where fiscal procyclicalityi is the correlation between government spending and output from
country i, sovereign riski is a vector measuring the sovereign risk of country i, Xi is a vector of
country-level controls (discussed in detail later) and εi is a random error term. In our baseline
specification, we include in the vector sovereign riski two dummy variables: medium risk,
defined as a dummy variable that takes the value of 1 if a country ever had a rating below
A but above B, and high risk, defined as a dummy variable that takes the value of 1 if a
country ever had a rating below B. The omitted group includes countries with low default
risk, measured by the fact that they always received sovereign ratings above or equal to
A. Our coefficients of interest, βmedium and βhigh , associated respectively with the variables
medium risk and high risk, measure how much larger the correlation is between government

8
spending and output for countries with medium and high default risk relative to those with
low default risk.
Table 2 shows the results from estimating regression (1) with different sets of controls Xi .
The first column shows the relationship with no controls, which indicates that countries with
high and medium default risk tend to have, respectively, 0.46 and 0.3 higher procyclicality than
countries with low default risk. To understand this result, Appendix Tables 8-10, which include
detailed data by country, show that the average correlations between government spending
and GDP for high- and medium-risk countries, are, respectively, 0.41 and 0.3, whereas low-
risk countries are acyclical on average. Moreover, countercyclical fiscal policies are rarely
observed in high- and medium-risk countries (the 25th percentile depicts an average positive
correlation between government spending and GDP), whereas half of low-risk countries depict
countercyclical policies, with prominent examples being the United States (−0.28 correlation
between government spending and GDP), France (−0.6), and Sweden (−0.23).
Although low-income countries tend to have higher default risk (see Appendix Table 12),
Table 2 shows that the relationship between fiscal procyclicality and default risk is not driven
by the well-documented relationship between per capita income levels and fiscal procyclicality
(also observed for our sample, as shown in Appendix Table 11). In particular, columns (1)-(3)
of Table 2 show that the relationship between sovereign default risk and fiscal procyclicality
is similar without controls than when we include log(GDP) per capita in PPP as a control
variable, or when we control for dummies measuring whether the country is rich, emerging or
poor.9
The last column of Table 2 shows that the relationship between sovereign default and
fiscal procyclicality is not driven by other macroeconomic and institutional controls that have
been identified in the literature as important drivers of fiscal procyclicality (see, for example,
Woo, 2009; Céspedes and Velasco, 2014; Guerguil, Mandon and Tapsoba, 2017). In particular,
in this specification we include the following variables in the vector of controls Xi : rule of
law, measured by the average ranking from the WDI for the period 1990-2016; education
inequality, measured by the standard deviation of the percentage of population enrolled by
school level (data source: Barro and Lee, 1996); fiscal rule measured by the number of years
with a fiscal rule from the International Monetary Fund; average fuel production and average
trade openness as a percentage of GDP (source: WDI), and output volatility, measured as the
9
We define the dummy variables of poor, emerging, and rich countries with the thresholds defined in Uribe
and Schmitt-Grohé (2017). According to their classification, a country is poor if the geometric average of its
GDP per capita in PPP during the period 1990-2009 is less than $3,000 USD, emerging if it is between $3,000
USD and $25,000 USD, and rich if it above $25,000 USD. Other income controls, such as a polynomial of
income, lead to similar results.

9
standard deviation of output for the period 1990-2016 (source: WDI).10 Appendix Table 13
shows the estimated coefficients associated with these additional variables.

Table 2: Fiscal Procyclicality and Sovereign Risk

(1) (2) (3) (4)
High Risk 0.46∗∗∗ 0.45∗∗∗ 0.43∗∗∗ 0.56∗∗∗
(0.11) (0.12) (0.16) (0.14)
Medium Risk 0.30∗∗∗ 0.29∗∗∗ 0.26∗ 0.31∗∗∗
(0.08) (0.10) (0.14) (0.10)
log(GDP ) -0.01
(0.04)
Rich -0.13 -0.15
(0.16) (0.16)
Emerging -0.11 -0.09
(0.09) (0.13)

Additional Controls No No No Yes
Observations 98 98 98 59
R2 0.19 0.19 0.21 0.52

Notes: Results from estimating the model

fiscal procyclicalityi = α + βmedium medium riski + βhigh high riski + γ 0 Xi + εi ,

where fiscal procyclicalityi denotes the correlation between government spending and output from country i,
medium riski is a dummy variable that takes the value of 1 if country i ever had a rating below A but above
B, high riski is a dummy variable that takes the value of 1 if country i ever had a rating below B, Xi is a
vector of country-level controls, and εi is a random error term. Standard errors are shown in parentheses.
Column (1) estimates the empirical model without controls. Column (2) includes as controls the log of the
average GDP per capita in PPP. Column (3) includes as controls dummies measuring whether the country
is rich or emerging, using the thresholds defined in Uribe and Schmitt-Grohé (2017). Column (4) includes
the following additional controls in the vector Xi : rule of law, measured by the average ranking from the
WDI for the period 1990-2016; education inequality, measured by the standard deviation of the percentage of
population enrolled by school level (data source: Barro and Lee, 1996); fiscal rule, measured by the number
of years with a fiscal rule (source: IMF); average fuel production and average trade openness, as a percentage
of GDP (source: WDI); and output volatility, measured as the standard deviation of output for the period
1990-2016 (source: WDI).

Finally, Appendix Tables 14 and 15 show that the relationship between fiscal procyclicality
and sovereign default is robust to using other measures of sovereign default risk. Table 14 uses
10
Catão and Sutton (2002) document that more volatile countries are more prone to sovereign default.
Controlling for the volatility of output is aimed at analyzing the relationship between fiscal procyclicality
and default risk beyond that induced by an additional volatility in economic activity driven by procyclical
government spending.

10
a dummy variable if the country ever defaulted during the period 1990–2014. The estimated
coefficient is positive and statistically significant, and indicates that countries that defaulted
during the period are characterized by a correlation between government spending and output
that is around 0.2 percentage points larger than those countries that did not default during
the period. Table 15 shows that similar results are obtained if we use the number of default
events experienced by each country.
It is worthwhile to highlight that the evidence presented in this section is descriptive and
not aimed at being causal. This descriptive evidence uncovers a strong relationship between
fiscal procyclicality and sovereign default risk that can guide theories that include both of
these elements. In the next section, we present a model of optimal fiscal policy that generates
a higher procyclicality of government spending for countries subject to default risk, in line
with the empirical patterns we documented.

3 Model
We study fiscal policy in a small open economy model with nominal rigidities and sovereign
default risk. Households are endowed with one indivisible unit of labor and a stochastic
stream of tradable goods. Firms have access to a technology to produce nontradable goods
using labor. The government spends toward a nontradable public good, which is financed with
a fixed income tax rate and external borrowing, in the form of non-state-contingent bonds.
The government is benevolent and lacks commitment to repay. On the nominal side, wages
are downwardly rigid, which gives rise to the possibility of involuntary unemployment and
income inequality. Monetary policy follows a fixed exchange rate regime, or equivalently, the
economy is a member of a currency union.

3.1 Households
There is a unit continuum of households indexed by j. Households’ preferences over private
and public consumption are given by
∞
X
β t U (cjt ) + v(gtN ) ,

E0 (2)
t=0

where cjt denotes private consumption of household j in period t, gtN denotes public spending in
nontradable goods, β ∈ (0, 1) is the subjective discount factor, and Et denotes the expectation
operator conditional on the information set available at time t.11 We assume constant relative
11
We abstract from government spending in tradables because this represents a small share of total public
spending and because only spending in non-tradables have a macroeconoomic stabilization role.

11
risk aversion utility functions for private and public consumption with the same risk aversion
1−σ 1−σ
coefficient U (c) = (1 − ψg ) c1−σ and v(g) = ψg g1−σ , with σ > 0, ψg ∈ (0, 1), and that the
consumption good is a composite of tradable (cT ) and nontradable (cN ) goods, with a constant
1
elasticity of substitution (CES) aggregation technology c = C(cT , cN ) = [ω(cT )1− ξ + (1 −
1 ξ
ω)(cN )1− ξ ] ξ−1 where ω ∈ (0, 1) and ξ > 0 is the elasticity of substitution between tradable
and nontradable goods.
Households are endowed with one indivisible unit of labor. Because of the presence of
downward wage rigidity and rationing (to be described below), each household’s actual hours
worked is given by hjt ∈ {0, 1}, which is taken as given by the individual household. Each
period households receive a tradable endowment ytT and profits from the ownership of firms
producing nontradable goods ΠN T
t . We assume that yt is stochastic and follows a stationary
first-order Markov process. In addition, households face a tax Tt (hjt ) (transfer if negative).
This tax is contingent on their idiosyncratic employment status hjt , reflecting the availability
of unemployment insurance. As is standard in the sovereign debt literature, we assume that
households do not have direct access to financial markets, and we focus on a government
that centralizes the choices of borrowing and repayment.12 Households’ sequential budget
constraint, expressed in domestic currency, is therefore given by

PtT cTjt + PtN cN T T N
jt = Pt yt + Πt + Wt hjt − Tt (hjt ) ≡ Yt (hjt ), (3)

where PtT , PtN denotes the price of tradables and nontradables in units of domestic currency,
Wt denotes the wage in domestic currency, and Yt (hjt ) denotes the household’s disposable
income, which depends on aggregate variables and the idiosyncratic employment status hjt .
The left-hand side of equation (3) includes total consumption expenditures, and the right-hand
side includes all sources of revenues net of taxes from the government.
The households’ problem consists of choosing cTt and cN t to maximize (2) given the se-
quence of state-contingent prices {Pt , Pt , Wt }t=0 , endowments {ytT }∞
T N ∞ N ∞
t=0 , profits {Πt }t=0 , id-
iosyncratic employment status {hjt }∞ ∞
t=0 , and taxes {Tt (hjt )}t=0 . The optimality conditions
of this problem yield the equilibrium price of nontradable goods as a function of the ratio
between tradable and nontradable consumption:
! 1ξ
PtN 1−ω cTjt
= (4)
PtT ω cN
jt

for all j ∈ [0, 1]. That is, the relative price of nontradables is equal to the marginal rate of
substitution between tradables and nontradables for all households. Because of homothetic
12
This assumption is due to tractability and is not critical for our analysis. This structure can also be
decentralized with taxes on borrowing (see Na et al., 2018).

12
preferences, the relative consumption of tradables to nontradables consumption depends only
on the relative price between these two goods.

3.2 Firms
Firms are competitive and have access to a decreasing returns to scale technology to produce
nontradable goods with labor:
ytN = F hdt ,

where ytN denotes output of nontradable goods in period t, hdt denotes labor input hired by
firms, and F (h) = (hd )α . Firms’ profits each period are then given by

N N d
ΠN
t = Pt yt − Wt ht . (5)

The optimal choice of labor hdt equates the value of the marginal product of labor and the
wage rate, all expressed in domestic currency:

PtN F 0 hdt = Wt .

3.3 Government
The government determines public spending, external borrowing, and default decisions, sub-
ject to a predetermined tax scheme. In terms of monetary policy, we assume that the govern-
ment follows a fixed exchange rate policy et = ē. Alternatively, one can think of the economy
as being part of a currency union.13

External borrowing and budget constraint. In terms of borrowing, the government has
access to long-term bonds with a deterministic decay rate (Hatchondo and Martinez, 2009,
Chatterjee and Eyigungor, 2012). In particular, a bond issued in period t promises to pay
δ(1 − δ)j−1 units of the tradable good in period t + j, for all j ≥ 1. Hence, debt dynamics is
given by
bt+1 = (1 − δ)bt + it , (6)

where bt is the stock of bonds due at the beginning of period t, and it is the stock of new
bonds issued in period t. The government trades these long-term bonds with competitive
international lenders, further explained below. Debt contracts cannot be enforced, and each
period, the government may decide to default.
13
It would also be straightforward to extend our analysis to allow for an arbitrary exchange rate policy,
implemented, for example, with a Taylor rule for nominal interest rates.

13
The government’s default entails two costs. The first cost is that the government is ex-
cluded from financial markets for a stochastic number of periods. Denote by ζt a variable that
takes the value of 1 if the government can issue bonds in period t, and zero otherwise. Its
evolution is given by
ζt = (1 − χt )ζt−1 + ϑt (1 − ζt−1 ), (7)

where χt = 0(1) if the government repays (defaults) in period t, and ϑt ∈ {0, 1} is a random
variable that takes the value of 1 in period t when the government reenters financial market,
which occurs with probability θ.14 The second cost is a utility loss for households ψχ (y T ),
which we assume to be increasing in tradable income. This utility loss can be seen as capturing
various default costs related to reputation, sanctions, or misallocation of resources.15
The government’s sequential budget constraint during each period in which it has access
to debt markets is given by
Z
PtN gtN = T (hjt ) dj + qt et it − δet bt , (8)
j∈[0,1]

where et is the nominal exchange rate and qt is the price of the bond in units of foreign
currency. In equilibrium the bond price will depend on the current shock, as well as on the
government debt choice. The budget constraint (8) indicates that tax revenues and new debt
issuance have to finance public spending and the repayment of outstanding debt obligations.
When the government is in financial autarky, its budget constraint collapses to
Z
PtN gtN = T (hjt ) dj. (9)
j∈[0,1]

Tax scheme. We assume that the government has a limited ability to raise tax revenues.
The tax scheme has three components: taxes, transfers, and unemployment insurance. Tax
revenues are a fixed proportion τ ∈ (0, 1) of households’ total income. The government
provides lump-sum transfers Tt ≥ T . In our quantitative analysis, we rule out lump-sum
taxes by setting T = 0.
Finally, in the unemployment insurance scheme the government taxes each employed house-
hold with τte units of domestic currency in period t and transfers τtu units of domestic currency
14
Equation (7) indicates that if at time t − 1, the government could issue bonds (ζt−1 = 1), the government
loses access to credit markets when it defaults at time t. If instead, the government was in financial autarky
(ζt−1 = 0), then the government recovers access to financial markets if the realization of the stochastic variable
ϑt takes the value of 1.
15
An alternative assumption used in the literature is the cost of default in terms of output. Under the
assumption that the utility function is log over the composite consumption, and output losses from default
are proportional to the composite consumption in default, the losses from default would be identical for the
output cost and utility cost specifications. If the fraction of output losses in the tradable and nontradable
sectors are the same, the cost in terms of consumption is indeed proportional.

14
to each unemployed household. Absent labor disutility and moral hazard associated with un-
employment insurance, an optimal insurance mechanism would equalize the disposable income
for employed and unemployed households. Effectively, this would lead to a representative-
agent economy with complete markets for idiosyncratic risk. To preserve meaningful hetero-
geneity, we assume an imperfect insurance scheme. For simplicity, we assume that this scheme
is such that the disposable income of employed and unemployed households is proportional to
each other,
Yt (0) = κYt (1) for all t, (10)

with κ ∈ [0, 1]. A value of κ = 1 represents the case with complete insurance. We require that
unemployment insurance is self-financed, which implies that

τtu (1 − ht ) = τte ht for all t, (11)
R
where ht ≡ j∈[0,1] hjt dj denote aggregate hours worked. Given that we are allowing for lump-
sum transfers, the assumption that unemployment insurance is self-financed is relevant only
insofar as it prevents the government from levying taxes on net with the insurance. Equations
(10) and (11) define the path of state-contingent taxes {τte , τtu }∞
t=0 for any period t under the
insurance scheme.
The assumed tax scheme implies that the government budget constraint in periods in
which it has access to debt markets can be expressed as

PtN gtN = τ (PtT ytT + ΠN
t + Wt ht ) + qt et it − δet bt − Tt .

Effectively, the tax scheme implies that the government can only raise revenues as a proportion
of income. Similarly, while excluded from credit markets, the government budget constraint
is
PtN gtN = τ (PtT ytT + ΠN
t + Wt ht ) + Tt .

3.4 Foreign Lenders
Sovereign bonds are traded with atomistic, risk-neutral foreign lenders. In addition to invest-
ing through the defaultable bonds, lenders have access to a one-period riskless security paying
a net interest rate r. By a no-arbitrage condition, equilibrium bond prices are then given by

1
qt = Et [(1 − χt+1 )(δ + (1 − δ)qt+1 )]. (12)
1+r

Equation (12) indicates that, in equilibrium, an investor has to be indifferent between selling
a government bond in period t at price qt and keeping the bond until next period bearing the

15
risk of default. In case of repayment next period, the payoff is given by the coupon δ plus the
market value qt+1 of the non-maturing fraction of the bonds. In case of default, the price qt+1
is equal to zero since we assume no recovery of defaulted bonds. Equation (12) will play a
critical role when we turn to the optimal fiscal policy. If lenders anticipate a fiscal policy in the
future that will make default more likely, they will demand lower bond prices, or equivalently
higher bond returns, to compensate for a higher default risk. Similarly, if the government
wants to run a debt-financed stimulus, this will increase the future default probability and
reduce the current bond price today. In turn, if a default in the future is relatively more likely
(e.g., because the economy is in a recession), the government will find it more costly to finance
an expansionary fiscal policy.

3.5 Wage Rigidity and Competitive Equilibrium
In equilibrium, the market for nontradable goods clears:

cN N d
t + gt = F (ht ), (13)
R
where cN N
t ≡ j∈[0,1] cjt dj. We assume that the law of one price for tradable goods holds, that
is, PtT = PtT,∗ et , where PtT,∗ denotes the price of the tradable good in foreign currency, assumed
to be constant and normalized to one. Using the households’ budget constraint (3) and the
definition of the firms’ profits and market clearing condition (13), the resource constraint of
the economy can be rewritten as

cTt = ytT + (1 − ζt )[qt it − δbt ], (14)
R
where cTt ≡ cT dj.
j∈[0,1] jt

For the labor markets, we assume there exists a minimum wage in nominal terms, W , such
that 16
Wt ≥ W . (15)

The existence of a minimum wage gives rise to a non-Walrasian labor market. We follow the
notion of equilibrium in models with rationing (e.g., Barro and Grossman, 1971; Drèze, 1975;
Benassy, 1975; Schmitt-Grohé and Uribe, 2016) to determine the labor market allocations and
prices. We assume that aggregate hours worked are the minimum between labor demand and
16
This assumption is similar to that in Schmitt-Grohé and Uribe (2016). In their case, W depends on
the previous period wage. To simplify numerical computations, we take W as an exogenous (constant) value.
Different from another strand of models with nominal rigidities, under this framework there is no price setting,
which keeps the model closer to a Walrasian setting and eliminates monopolistic rents. Moreover, there is
only rationing on one side of the market (in this case, when market clearing wages are below the minimum).

16
labor supply,
ht = min(1, hdt ). (16)

If ht < 1, it has to be that Wt = W . If Wt > W , the aggregate amount of hours worked equals
the aggregate endowment of labor. These conditions can be summarized as

Wt − W (1 − ht ) = 0. (17)

When wage rigidity is binding, we assume that there is a random allocation of hours across
households every period. This means that every household has a probability ht of being
employed every period. This lottery is realized at the beginning of each period after the
aggregate shock is realized.
A competitive equilibrium, for a given set of government policies, is then defined as follows.

Definition 1 (Competitive Equilibrium). Given initial debt b0 and ζ0 , and sequences of
∞
exogenous processes {ytT , ϑt }∞ N
t=0 , government policies {gt , bt+1 , χt , Tt , et }t=0 , and credit market
access {ζt }∞ T N d ∞
t=0 , a competitive equilibrium is a sequence of allocations {(cjt , cjt , hjt )j∈[0,1] , ht }t=0
and prices {PtN , PtT , Wt , qt }∞
t=0 such that:

∞ d ∞
1. Consumption {(cTjt , cN
jt )j∈[0,1] }t=0 solves the households’ problem, employment {ht }t=0
solves firm’s problem.

2. Government policies satisfy the government budget constraint and the law of motion for
ζt satisfies equation (7).

3. The bond pricing equation (12) holds.

4. The market for nontradable goods clears (13).

5. The law of one price for tradable goods holds.

6. The labor market allocations and wages satisfy conditions (15)-(17).

3.6 Optimal Fiscal Policy
We now study Markov equilibria in which the government chooses policies sequentially and
without commitment. We consider a benevolent and utilitarian government, which chooses
fiscal policies to maximize households’ welfare, subject to implementability conditions. As
mentioned above, we focus on a fixed exchange rate regime, which leaves fiscal policy as the
central instrument for macroeconomic stabilization.17
17
As established in Na et al. (2018), under the optimal exchange rate policy, the government would undo
the nominal rigidity and allocations would coincide with the flexible wages (see also Bianchi and Mondragon,
2018).

17
Welfare criterion. The objective of the government is to maximize the average expected
lifetime utility of households:
∞
X
N T
E0 β t [Ut ((cTj )j∈[0,1] , (cN
j )j∈[0,1] ) + v(gt ) − (1 − ζt )ψχ (yt )],
t=0

R
where Ut ((cTj )j∈[0,1] , (cN T T
j )j∈[0,1] ) ≡ j∈[0,1] u(cj , cj ) dj is the social period utility from private
consumption. Notice that here we are using u(·) to denote u(cT , cN ) = U (c(cT , cN )). The
following result establishes how, in our environment, the social period utility from private
consumption admits an aggregation result, in the sense that Ut (.) can be expressed as a
function of only aggregate variables.

Lemma 1. The social period utility from private consumption can be expressed as

Ut ((cTjt )j∈[0,1] , (cN T N
jt )j∈[0,1] ) = u(ct , ct ) ˙ Ω(ht ) ,
| {z } | {z }
Utility of Inequality
aggregate concerns
consumption

h+(1−h)κ 1−σ
where Ω(h) ≡ (h+(1−h)κ)1−σ .

Lemma 1 indicates that the expression for welfare that would prevail in a representative-agent
economy is modified to allow for inequality concerns, which can be summarized entirely in the
˙ This result is useful because it implies that welfare can be evaluated based on a
term Ω(.).
minimum but critical departure from a representative agent economy. For a given aggregate
consumption bundle {cTt , cN t }, welfare is decreasing in the unemployment rate and in the
dispersion of consumption between unemployed and employed agents, governed by the degree
)˙ ˙)
of unemployment insurance. These results follow since ∂Ω(. ∂ht
> 0 and ∂Ω(.
∂κ
> 0. Furthermore,
a reduction in the unemployment rate leads to higher welfare, the bigger this dispersion in
∂Ω(.)˙
consumption is ∂h t ∂κ
< 0.

Government problem. Every period in which the government enters with access to finan-
cial markets, it evaluates the lifetime utility of households if debt contracts are honored against
the lifetime utility of households if they are repudiated. Given the current states, (y T , b), the
government problem with access to financial markets can be formulated in recursive form as
follows:
V (y T , b) = max {(1 − χ)V R (y T , b) + χV D (y T )}, (18)
χ∈{0,1}

where V R (y T , b) and V D (y T ) denote, respectively, the value of repayment and the value of
default. The value of repayment consists of maximizing the utility flow, adjusted by inequality,
plus the expected continuation value. The constraints are given by the resource constraint, the

18
government budget constraint, and the wage rigidity that characterizes the labor market.'®
Ve(yt,b) = max — {u(e", F(h) — g®)Q(h) + v(g%) + BEV(y™,B) (19)
g b',T>0,h<1

subject to
ch =y" + q(y", |b — (1 — d)b] + 6b
Pry? ho g™)g™ + 6b+T = qly",b)[b — (1 —6)b]) +7 [Phyl + PX (y", h, g®)F(h)|

PN yh, gE" (h) > @,

We have used in this formulation that in any equilibrium with allocations (c/, h;, g/’), the rela-

tive price of nontradable to tradable goods can be expressed as P® (c}, ky, g’) = ie (mca) .
t

as obtained by combining households’ optimality condition (4) and market clearing condition

(13). In addition, we denote by w= Ww the wage rigidity parameter in terms of tradable goods

and by q(y7,b’) the bond price schedule, taken as given by the government.

The value of default, in turn, is given by

Vay") =, max {u(e™, F(h) — g®)Q(h) + v(g%) — vy(y") + BE { (1 — Vy") + V(y™,0) }}

gN ,hS1,TST

(20)
subject to

Pr(y hg” gy +T =7 [Pye +PX(y" hg) Fh)

Pry" hg’) F' (h) >.

Notice that in the problem under default, once the lump-sum transfers are set, this determines
the level of spending and employment via the government budget constraint and the labor

market conditions.

Equilibrium under optimal government policies. Let {é"(y7,b), g% (y",b),7(y7, b), by", b),
h(y™, b), x(y7,b)} be the optimal policy rules associated with the government problem. A

Markov-perfect equilibrium is then defined as follows.

Definition 2 (Markov-perfect Equilibrium). A Markov-perfect equilibrium is defined by value
functions {V(y7,b),V"(y7, b), V7(y7)}, policy functions

eT (y™, b), GN (y™, b), T(y", b), b(y™, b), h(y”, b), x(y™, b)}, and a bond price schedule q(y",b)
such that:

1. Given the bond price schedule, policy functions solve problems (18), (19), and (20).

‘8Tt can be shown that the complementary slackness condition (17) does not bind, and so we omit it from
the constraint.

19
2. The bond price schedule satisfies

1
q(y T , b0 ) = E[(1 − χ̂(y T 0 , b̂(y T , b0 )))(δ + (1 − δ)q(y T 0 , b̂(y T , b0 ))].
1+r

4 Fiscal Policy Trade-Offs
In this section, we articulate the trade-off between stimulus and austerity that the government
faces. We show how an increase in spending can to help reduce unemployment and expand
output in a recession, in line with the Keynesian channel, and how these benefits have to be
balanced with sovereign default risk concerns. This result will provide theoretical guidance to
interpret the empirical findings of Section 2 when we turn to the quantitative simulations.

4.1 Stimulus versus Austerity: An Analytical Decomposition
We begin by examining the first-order condition with respect to g N in the government problem
(19). Using µ and η to denote, respectively, the Lagrange multipliers associated with the wage
rigidity constraint and the government budget constraint, we obtain

∂P N ∂P N N

0 N T N 0 N
v (g ) − uN (c , c )Ω(h) + µF (h) N − η p + (g − F (h)τ ) = 0, (21)
| {z } ∂g ∂g N
Samuelson | {z } | {z }
Stimulus Austerity

where uN (cT , cN ) ≡ ∂u(cTt , cN
t )/∂c
N
and all variables correspond to time t. At the optimum,
the government equates the marginal benefits from spending to the marginal costs. We will
next analyze the three terms in this condition that we label “Samuelson”, “stimulus” and
“austerity”.
Let us first focus on a version of the model without frictions (i.e., there are no nominal fric-
tions or financing frictions). In this case, the net marginal benefits are given by the first term
in (21): the government would equate the marginal benefits of higher government spending,
v 0 (gtN ), to the marginal costs of less private consumption, uN (cTt , cNt ), or put differently, the
government equates the marginal rate of substitution between private and public consump-
tion to the marginal rate of transformation, which is equal to one in the model. This is the
classic Samuelson rule for the efficient provision of public goods (Samuelson, 1954). Assum-
ing that the utility from tradables and nontradables is separable, and given the assumption
of homothetic preferences, this would imply that government spending would be a constant
fraction of nontradable output. The logic behind this principle is that movements in output
get translated into absolute movements in government spending while keeping constant the
share of public consumption.

20
In the presence of nominal rigidities, a second term in (21) emerges because private con-
sumption is not completely crowded out by public consumption when there is slack in the
labor markets. In this case, an increase in one unit of government spending in nontradables
leads to a rise in the price of non-tradables that increases the value of the marginal product
of labor by (OPN /Og%)F'(h), which, in turn, relaxes the wage rigidity constraint that has
a marginal utility benefit y,. Essentially, the increase in government spending generates an
increase in nontradable output, and hence private consumption does not fall one to one with

government spending.!°

It is also worth highlighting that with nominal rigidities, the limited insurance against
unemployment at the idiosyncratic level implies a welfare adjustment in the Samuelson term
(i.e., the Q(h) factor). When spending rises, employed households end up paying higher taxes
than unemployed agents, and this implies that crowding out effect on nontradable consump-
tion falls disproportionately more for these households. On the other hand, the increase in
g™ applies to all households equally. Because Q(h) is increasing in h, this means that aa
higher unemployment entails a lower cost from the crowding out in nontradable consumption.
Effectively, when some unemployed households become employed as a result of the stimulus,
this reduces the gap in inequality across households, and this calls for a more expansionary

fiscal policy.

To shed light on the benefits from the stimulus term, we can turn to the first-order condition
with respect to h;, to obtain an expression for the Lagrange multipliers on the wage rigidity
constraint yp. Assuming h < 1, we have

1 (FP +P) = wl" QUEL) + UEC eg UH)

~ more cN less consumption inequality
Value of stimulus
OPN OPN
Ny N
+n | ——F(h) +p F'(h) )t— ng". (22)
Oh Oh
effect on tax revenues price effect on g%

Equation (22) shows that whenever there is slack in the labor market, the shadow benefit
from relaxing the wage rigidity constraint arises from the higher amount of output available
for consumption and the reduction in inequality. These two objects are captured by the first
two terms on the right-hand side of (22). In addition, two additional terms interact with
the government budget constraints: an adjustment in the tax base because tax revenues are
proportional to output, and a price effect that occurs because the increase in employment
modifies the relative price at which the government makes purchases. These are, respectively,
the third and fourth terms on the right-hand side of (22).

19Tt should be clear that under the optimal exchange rate policy, the stimulus term would not arise because
the government undoes the nominal rigidity by depreciating the exchange rate.

21
Let us now focus on the austerity term on equation (21). When the government faces
financing frictions, there are additional costs from spending that go beyond the potential
crowding-out effects of private consumption. The last term in equation (21) indicates the
marginal utility cost of how an increase in spending tightens the government budget constraint.
If the government spends one additional unit, it directly tightens the budget constraint by pN ,
which is the cost for the government to provide the extra unit of public goods. In addition,
two general equilibrium effects arise from the increase in pN that results from the increase in
spending. First, the increase in the price raises the inframarginal units of spending, and this
∂P N
tightens the budget constraint by ∂gNt gtN . At the same time, an offsetting general equilibrium
t
effect occurs because the increase in g N also raises the amount of tax revenues (due to revenues
representing a fraction of total income). The overall marginal utility cost of tightening the
government budget constraint is given by the product of the sum of these three terms and η,
the Lagrange multiplier on the government budget constraint.
We argue next that the austerity term depends critically on the degree of default risk. We
have the following Euler equation for borrowing

∂qt
(λt + ηt ) qt + i = βEt [(λt+1 + ηt+1 )(1 − χt+1 )(δ + qt+1 (1 − δ))], (23)
∂bt+1

where λt denotes the Lagrange multiplier with respect to the resource constraint of tradables
in period t. This condition says that the marginal benefit from borrowing today is equated to
the marginal cost of repaying the debt tomorrow. Borrowing one unit of resources today helps
to relax today’s government budget constraint and increase the amount of tradable resources,
which has an overall marginal utility benefit of λt + ηt . By the same token, repaying the
debt tomorrow has the opposite effects, as captured by the term λt+1 + ηt+1 on the right-
hand side. Importantly, the overall trade-off is guided by how the bond price changes in
response to higher debt ( ∂b∂qt+1
t
), which, in turn, depends on how much the government raises
the degree of default risk by increasing the amount of debt. Notice that while a lower bond
price reflects that the government will pay in fewer states of nature tomorrow, it still faces
higer default costs, which represent a deadweight loss for the economy. If the bond price falls
sharply when the government borrows more, this means that for the given expected marginal
utility costs from repayment and for a given λt , there is a larger shadow cost from tightening
the government budget constraint today, ηt . In turn, as indicated by equation (21) a higher
η makes the austerity term bigger. Put it simply, if the bond price falls significantly, the
government obtains fewer resources for the same amount of debt issuances, making stimulus
less desirable.

22
4.2 Simple example
Under some simplifying conditions, we can provide a sharp characterization of fiscal policy that
sheds further light on the different dimension of fiscal policy discussed above. In particular,
under lump-sum taxes and a linear production function, we show in the next proposition
that the government finds it optimal to adjust spending to implement an allocation with full
employment at all times.

Proposition 1 (Benefits of Fiscal Stimulus). If there is a linear production function (α = 1)
and the government has access to lump-sum taxes (T = −∞), then full employment is optimal:
ht = 1 for all t.

This proposition highlights the effectiveness of fiscal policy to stabilize the economy. With
a linear production function, for a given level of tradable consumption, the value of the fiscal
∆yt
multiplier ∆g N is one, meaning that whenever there is unemployment, an increase in spending
t
does not lead to a crowding out of private consumption. To see this, notice that when the
economy features unemployment, given the firms’ first-order condition for labor demand, it
must be that pN = w. Using market clearing conditions and households’ optimization, we
arrive at 1ξ
cT

1−ω
= w.
ω h − gN
For a given cT , an increase in spending needs to be accommodated by a one-to-one increase
in nontradable output. The linearity of the production function is key for this result. When
the production function features decreasing returns, firms require a higher price to increase
production, and hence this leads to a fall in private consumption of nontradables, which
implies a fiscal multiplier below one.
From a normative standpoint, this implies that, as stated in Proposition 1, thanks to the
unit multiplier, the government eliminates any unemployment as long as it is able to raise
funds frictionlessly. In effect, fiscal stimulus is a free lunch in this case, and the government
spends until there is no slack in labor markets. It is worth noting that the result holds even if
there is no value from public spending (i.e., if government spending is wasteful). Because the
reduction in the fraction of unemployed households reduce inequality and improve aggregate
welfare, increasing spending until implementing full employment is optimal, even if v(g N ) = 0.
A natural question that follows is, how should the government adjust spending through
the business cycle to ensure that the economy is at full employment. The next corollary shows
that if tradable consumption comoves positively with the endowment of tradables (as would
typically be the case in incomplete market models), the government follows a countercyclical
fiscal policy.

Corollary 1 (Countercyclical Fiscal Policy). Under the assumptions of Proposition 1, given

23
states {b, y T } and {b̃, ỹ T } such that cT (b, y T ) > cT (b̃, ỹ T ), it follows that g N (b̃, ỹ T ) > g N (b, y T ).

The intuition for this corollary is that a low tradable endowment generates a contraction
in aggregate demand and requires a higher amount of spending to reduce the slack in the
labor market.

4.3 Counterfactual Experiment
The previous section underscores the key trade-off the government faces in the model. Raising
spending when there is slack in the labor market leads to an increase in output, whereas
financing the spending with debt leaves the government more exposed to default risk. To
shed light on how the government chooses the actual optimal level of spending, we conduct a
perturbation exercise in which we allow the government to choose a level of spending that is
different from the optimal one. The idea is to trace how output and sovereign spreads would
differ if the government were to choose a different level of spending.
Let us describe the experiment in more detail. We study how a change in spending today,
taking as given all future policies and value functions as defined in the Markov equilibrium,
affects current allocations and prices. To balance the changes in spending, we assume the
government adjusts the debt level and transfers to satisfy the budget constraint. Formally,
in terms of the government problem (19), rather than maximizing with respect to the entire
set of allocations, we fix an arbitrary level of government spending and solve optimally for
the remaining allocations conditional on that level of spending. Our model simulations will
be based on the optimal level of spending chosen by the government, but it is instructive to
consider alternative values of spending to understand the optimal choice.20
The results of this experiment are shown in Figure 3, using the parameter values of the
calibrated economy that we will describe in Section 5. As initial values for the states, we
assume that tradable endowment income is at its unconditional mean and current debt is 10%
above its average (results are qualitatively similar for other states). In each panel, the solid
dot indicates the level of the variable of interest at the optimal level of government spending,
which, as panel (a) shows, achieves the maximum welfare (i.e., at the optimum, the utility
value coincides with V (b, y T )). The blue lines trace the values of all variables if the government
were to choose the alternative value of spending, which delivers strictly lower utility values.
As Figure 3 shows, an increase in government spending stimulates economic activity. The
increase in spending raises the price of nontradables (panel b) and lowers unemployment
(panel a). Essentially, the increase in demand for nontradable goods raises the relative price
and leads firms to produce more in equilibrium. This is part of the standard channel from fiscal
20
Another way to see this exercise, which is potentially useful for interpreting empirical findings, is that this
constitutes a pure “fiscal shock.”

24
(a) Welfare (b) Unemployment (c) cN
-14.65 0.75
20

-14.7 % 10 0.7

-14.75 0 0.65
0.19 0.2 0.21 0.22 0.19 0.2 0.21 0.22 0.19 0.2 0.21 0.22
gN gN gN
(d) pN (e) Spreads (f) Borrowing
4.1 6 1.3

% 3 1.2

3.9

3.8 0 1.1
0.19 0.2 0.21 0.22 0.19 0.2 0.21 0.22 0.19 0.2 0.21 0.22
gN gN gN

Figure 3: Welfare, Prices and Allocations with Alternative Spending.
Notes: In this figure, the blue lines indicate the current repayment levels in the default model of utility,
unemployment, nontradable consumption, relative price of nontradables, spreads, and debt, as a function
of current government spending, given that current tradable income is set to its unconditional mean and
current debt is 10% above its average level. From next period on, allocations and value functions are given by
the Markov equilibrium. Dots indicate the equilibrium levels associated with optimal government spending.

policy in open economies and is consistent with a large empirical literature (e.g. Monacelli
and Perotti, 2010, Ilzetzki, Mendoza and Végh, 2013, Miyamoto, Nguyen and Sheremirov,
2019).21 A more subtle effect that emerges here from the fact that wages are only downwardly
rigid is the asymmetry and the state dependency of the expansionary effect on output, as
will become more clear below (see Born, D’Ascanio, Müller and Pfeifer, 2019 for evidence on
this asymmetry). One can also see that since nontradable consumption increases together
with government consumption (panel c), the fiscal multiplier is larger than one. Relative to
Proposition 1, the fiscal multiplier is bigger than one because spending is debt financed (panel
h) rather than tax financed, in line with the results from Farhi and Werning (2017).
An important observation from panel (e) of Figure 3 is that the increase in government
spending leads to an increase in spreads. Such increase reflects the higher risk of future
default associated with higher debt levels. This increase in spreads is a key factor deterring
the government from providing sufficient stimulus to attain full employment.
21
The stimulative role of fiscal policy that we analyze in this paper shares the core of the mechanism to
the closed economy counterpart. A different form of monetary policy constraint emphasized in the closed
economy literature is the zero lower bound. For a very clear exposition on this comparison see Farhi and
Werning (2017).

25
Overall, we have shown in this section how the presence of nominal rigidities and sovereign
risk create an austerity-stimulus trade-off for the government. When there is slack in the
labor market, spending helps to stimulate the economy. Investors, however, anticipate that
the increase in spending and borrowing makes the government more prone to default. As a
result, they are only willing to purchase government bonds at lower prices, and this makes
stimulus less desirable. In the quantitative section that follows, we will show how the level
of debt and income shocks are key to shaping the conduct of fiscal policy over the business
cycle.

5 Quantitative Analysis

5.1 Calibration
To characterize the aggregate dynamics under the optimal fiscal policy, we calibrate the model
to match key moments of the Spanish economy and use a year as the model period. We
calibrate the model to Spain because, as mentioned in the introduction, the recent Eurozone
crisis provides a prototypical example of the main mechanisms featured in our model: a
sharp increase in unemployment and sovereign default risk, and a currency peg that leaves
fiscal policy as the only instrument for macroeconomic stabilization. The model is solved
numerically using value function iteration. For details on the solution method, see Appendix
C.1.

Functional Forms. As mentioned in Section 3, we assume constant relative risk aversion
utility functions for private and public consumption, a CES aggregator for tradable and non-
tradable goods, and an isoelastic production function. These functional forms imply four
relatively standard parameters on preferences and technology {σ, ψg , ξ, α}. For the cost of
default, we assume the following functional form:

ψχ (ytT ) = max{0, ψχ0 + ψχy log(ytT )}, (24)

with ψχy > 0, which has been used in related literature to match the bond spread dynamics
observed in the data (see Bianchi, Hatchondo and Martinez, 2016; Chatterjee and Eyigungor,
2012, for related functional forms on default costs).
The tradable endowment ytT follows a log-normal AR(1) process,

T
log yt+1 = ρ log ytT + σy εt+1 ,

with |ρ| < 1 with εyt+1 ∼ i.i.d. N (0, 1).

26
Parameter Values. All selected parameter values used in the baseline calibration are shown
in Table 3. We choose a subset of parameters according to predetermined values and then
choose the rest of the parameters to match key moments in the data. Data used for moments

targeted in the calibration are detailed in Appendix C.2.

In the group of predetermined parameters, we set the coefficient of relative risk aversion to
o = 2 and the elasticity of substitution between tradable and nontradable goods to € = 0.5,
which is in the range of values considered in the literature;?? the share of tradables in the
consumption aggregator to w = 0.3, which implies a ratio of tradable output to total output
of around 20%, in line with the data for Spain in the period of analysis; and the labor
share from the nontradable sector to a = 0.75, following the estimate in Uribe (1997). For
the unemployment insurance, we set the ratio of the consumption of unemployed households
to that of employed households to & = 0.7, which is in line with the average expenditure
on nondurable goods and services during unemployment estimated by Chodorow-Reich and
Karabarbounis (2016) for the United States.?° Finally, we estimate the parameters p and
o,. for the stochastic process of y/ using Spanish national accounts data for agriculture and
manufacturing sectors, log-quadratically detrended. This estimation yields p = 0.78 and
oy = 0.029.

For the parameters related to the debt market, we set the international risk-free rate r equal
to 2%, which is roughly the average annual gross yield on German 5-year government bonds;
the maturity parameter 6 = 0.184, to generate an average bond duration of five years, in
line with the OECD data for Spain over the period 2000-2010;74 and the reentry probability
? = 0.18, to generate an average autarky spell of six years, which is close to the average
resumption of financial access reported by Gelos, Sahay and Sandleris (2011) over the period
1980-2000 for 150 developing countries.

?2This parameterization implies that the intertemporal elasticity of substitution equals the intertemporal
elasticity of substitution, and hence the marginal utility of tradables and nontradables is separable. Another
useful implication is that the amount of public spending, according to the Samuelson rule, does not depend
on debt nor on y’.

?3In Spain, the monthly benefit amount is 70% of the monthly base over the first six months and 50%
thereafter until the unemployment spell reaches two years, as indicated by the Servicio Publico de Empleo
Estatal.

24The Macaulay duration of a bond with price q and our coupon structure is given by

S56 /1-6\' 14+%y
D= t- =

where the constant per-period yield i, is determined by g = )7°, 6 (tee)! The debt level in the model is

computed as the present value of future payment obligations discounted at the risk-free rate r. Given our
coupon structure, we thus have that the debt level is given by Toya:

27
Table 3: Calibration

Parameter Value Description Target statistic/Source
Predetermined parameters
σ 2 Coefficient of risk aversion Standard business cycle literature
ξ 0.5 Intratemporal elasticity of subst. Standard business cycle literature
ω 0.3 Share of tradables Share of tradable GDP (20%)
α 0.75 Labor share in nontradable sector Uribe and Schmitt-Grohé (2017)
r 0.02 Risk-free rate Average German 5-year bond return
δ 0.184 Coupon decaying rate Average bond duration (5 years)
θ 0.18 Reentry probability Average autarky spell (5.5 years)
κ 0.7 Relative consumption unemployed Chodorow-Reich and Karabarbounis (2016)
ρ 0.777 AR(1) coefficient of ytT Spanish tradable GDP process
σy 0.029 Standard deviation of εt Spanish tradable GDP process
Calibrated parameters
β 0.907 Discount factor External debt/GDP (22.8%)
ψχ0 0.3277 Utility loss from default (intercept) Average bond spread (1.05%)
ψχy 2.42 Utility loss from default (slope) Volatility of bond spreads (1.4%)
ψg 0.02 Weight of gov. good in utility Average govt. spending/GDP (18.1%)
τ 0.19 Income tax rate Volatility of govt. spending/GDP (2)
w 3.068 Minimum wage Unemployment increase crisis (2.5%)

The six remaining parameters are calibrated to match six moments from the data.25 Tar-
geted moments are detailed in Table 3 and are informative of the default risk in the economy,
unemployment, and government spending, which are the key components of the trade-off faced
by fiscal policy. The first three moments speak to the amount of default risk in the economy.
These moments are the average Spanish public external debt-to-GDP ratio of 22.8%, and the
average and volatility of Spanish bond spreads of 1.05% and 1.4%, respectively. Although all
parameters affect all moments in our calibration, these three moments are mostly governed
by the discount factor β and the parameters on the default cost function ψχ0 and ψχy . The
second group of moments is linked to government spending and taxes. We target the mean
25
The parameters and moments reported in this subsection correspond to those that result from calibrating
the model with optimal fiscal policy with default risk. To compute the business cycle statistics, we run 10,000
Monte Carlo simulations of the model with 10,000 periods each and construct 1,000 subsamples of 32 periods
of financial access. The number of periods for each subsample is chosen to roughly match the number of
years in our sample period 1980-2012. To avoid dependence on initial conditions, we disregard the first 1,000
periods from each simulation. Also, in our model the borrower regains access to credit with no liabilities
after defaulting, whereas in the data countries typically do so, carrying a positive amount of debt settled at
a restructuring stage. We therefore impose that our candidate subsamples cannot be preceded by reentry
episodes for less than four years. To analyze the economy with no default risk (in the next subsection) we
re-calibrate the discount factor and the tax rate so that this economy is comparable with the data in terms
of external debt and government spending. Also, given the high persistence in the debt dynamics, we run
longer simulations for 140,000 periods. After disregarding the initial 100,000 periods, we construct 100,000
subsamples, allowing for 2, 000 periods between consecutive subsample time intervals.

28
Spanish government spending over GDP of 18%, and the ratio of the volatility of government
spending to the volatility of output of 2. These moments are mostly influenced by the weight
of the government good in the utility function, ψg , and the income tax rate, τ . Finally, we cal-
ibrate w to be consistent with the surge in unemployment during the episode of high sovereign
spreads. In the data, the increase in unemployment in Spain in 2011 relative to 2009-2010
was about 2.5%. Accordingly, we set w so that the average increase in unemployment in the
two years before a default is 2.5%. This yields w = 3.068. Appendix Table 16 shows that our
calibrated model approximates the targeted moments fairly well.26

5.2 Fiscal Policies over the Business Cycle
In this section we study how default risk shapes optimal fiscal policy over the business cycle.
To do so, we first consider an economy in which we shut down default risk, and then show
how incorporating default risk changes the nature of the optimal fiscal policy response. We
calibrate the two economies to match the same data targets, with the exception of spreads,
whiich are, of course, zero for the risk-free economy.27

Countercyclical fiscal policy with no default risk. Table 4 reports key business cycle
moments of the economy with risk-free debt and compares them with their data counterparts.28
The main result is that in the absence of default risk, optimal fiscal policy is countercyclical,
with a correlation of −0.81 between government spending and GDP. This result stems from
the countercyclicality of the benefits of fiscal stabilization stressed in Section 4. This model
prediction is in sharp contrast to the procyclical behavior of government spending observed for
Spain (0.46 in our sample) and, more generally, contrasts with the behavior we documented
for economies with medium and high default risk. However, it is qualitatively consistent with
the countercyclicality of economies with the highest credit ratings, as shown in Figure 2. Table
4 also shows that, thanks to the effective stabilization role of fiscal policy, the fluctuations of
unemployment are small: one order of magnitude smaller that those observed in the data for
Spain.
The key takeaway from these simulations is that when the government can finance spending
with external risk-free borrowing, there are large gains from stabilization that lead to strong
26
An exception is the volatility of spreads, which the model falls short in replicating that observed in the
data. As discussed in Aguiar, Chatterjee, Cole and Stangebye (2016), this is a common challenge faced by the
canonical sovereign debt model.
27
Essentially, we choose the same parameter values as in our baseline economy (detailed in Table 3), except
for the discount factor and utility of government spending, which we set to match the same average debt-to-
GDP and government-spending-to-GDP ratios as in our baseline economy, and the parameters governing the
default costs, which are set to large enough values to ensure that the economy never defaults for the targeted
debt levels.
28
Time series for public and private consumption and GDP are log-quadratic detrended.

29
Table 4: Business Cycle Statistics: Data and Models

Model
Statistic Data Risk-free Default
Averages (in percent)
mean(spreads) 1.05 0.00 1.09
mean(debt/y) 22.8 22.4 22.6
mean(pN g N /y) 18.1 18.6 18.2

Correlations with GDP
corr(GDP,g N ) 0.46 −0.81 0.72
corr(GDP, c) 0.98 1.00 0.98
corr(GDP,spreads) −0.38 0.00 −0.95
corr(GDP,unemployment) −0.34 −0.97 −0.44

Volatilities (in percent)
σ(GDP) 3.5 1.2 4.3
σ(pN g N )/σ(GDP) 2.0 1.6 2.0
σ(c)/σ(GDP) 1.1 1.1 1.1
σ(spreads) 1.4 0.0 0.7
σ(unemployment) 4.1 0.6 5.6

Notes: This table reports business cycle statistics for the data and the models with risk-free and risky debt.
Bond spreads are computed as the differential between the annual sovereign bond return and the annual
risk-free rate. The variables GDP and y denote total output at constant and current prices, respectively.

countercyclical fiscal policies. These policies are inconsistent with the data for Spain and for
economies with sovereign risk, which tend to follow procyclical fiscal policies. We show next
that default risk can provide an explanation for the observed empirical patterns.

Procyclical fiscal policy with default risk. The last column of Table 4 shows the busi-
ness cycle statistics for our baseline economy with default risk. The main result is that
government spending is procyclical, with a correlation of 0.72 with output. This table shows
that the resulting fluctuations in unemployment are also more aligned with the data.
The sharp contrast between the conduct of fiscal policy in the risk-free economy and the
economy with default risk can be clearly seen in Figure 4. This figure displays the opti-
mal policy function for government spending for the two economies. As the figure shows,
optimal government spending with risk-free debt, depicted by the solid red line, is monoton-
ically decreasing with income. In contrast, optimal government spending with defaultable
debt, depicted by the dashed blue line, features lower spending for small levels of income the

30
0.25

gN 0.2

defaultable debt
risk-free debt
0.15
0.9 0.95 1 1.05 1.1
T
y

Figure 4: Government Spending as a Function of y T

Notes: This figure shows the optimal government spending in the risky and risk-free debt models, as a function
of y T . Debt is set to its average level. The solid red lines correspond to the risk-free debt model and the
dashed blue lines to the risky model. The dotted vertical lines in black correspond to the default threshold.

government chooses to repay.29
To understand the optimal procyclicality in the economy with risky debt, Figure 5 shows
two key objects we discuss in the context of the optimal policy tradeoffs in Section 4. Panel
(a) shows the fiscal multiplier, defined as the increase in output from a marginal increase
in government spending, as a function of tradable endowment. As the figure shows, the
fiscal multiplier is positive when income is low and becomes zero once the economy is at full
employment. Panel (b) shows the increase in spreads that result from the increase in external
debt to finance one unit of government spending. A key property illustrated in the figure
is that the marginal financial cost is larger when income is low. This property stems from
the fact that periods with low income are periods in which incentives to default are higher
(Arellano, 2008). Overall, this figure shows that although in bad times the fiscal multipliers
are larger, the fact that the financial cost is also larger implies that the government chooses
to cut spending and follow a procyclical fiscal policy.
It is important to highlight that departing from the optimal fiscal policy under default risk
can entail large welfare costs. To show this, we replace the optimal countercyclical spending
with a benchmark Samuelson rule that specifies a constant g N over the business cycle and
evaluate the welfare costs from following this rule as opposed to the optimal one. Our results
29
Notice also that the amount of spending increases to the left of the default threshold. The reason is that
when the government repays and is close to the default threshold, it runs a fiscal surplus.

31
(a) Fiscal Multiplier (b) Increase in Borrowing Costs
3 1

1 0.5

-1 0
0.95 1 1.05 1.1 1.15 0.95 1 1.05 1.1 1.15
yT yT

Figure 5: Fiscal Multipliers and Borrowing Costs as Function of y T .
Notes: This figure shows the fiscal multiplier (left panel) and a measure of the marginal variation in borrowing
costs when increasing debt (right panel), as a function of y T . Fiscal multipliers are computed using the
steady-state relative price pN . Current debt is set to 10% above its average level. The marginal increase in
∂q 0
borrowing costs is given by ∂b 0 (b − (1 − δ)b).

show that the average welfare cost is 3.5% of permanent consumption.30 Moreover, the welfare
costs are significantly larger for states with high debt and relatively low levels of income. This
is because in these states the sovereign default risk of the economy is higher, and by following
a constant spending rule the economy becomes over exposed to the risk of a default. Welfare
costs are also larger for lower y T in low-debt states, where the government spends more than
prescribed by the Samuelson rule so as to reduce unemployment and stabilize the economy. In
contrast to Lucas (1977), macroeconomic stabilization entails significant welfare consequences.
Overall, the quantitative analysis of the model shows that default risk can account for the
procyclicality observed in the data in economies with sovereign default risk. This is in spite of
the fact that we constructed an economy with large fiscal multipliers that create an important
scope for fiscal stabilization.31
30
This calculation is obtained by first computing conditional welfare gains (i.e., the increase in private
and public consumption across all states of nature that leave the household indifferent between living in the
economy with a Samuelson rule and switching to the economy with the optimal policy). The unconditional
welfare gain of moving from the Samuelson policy to the optimal policy is computed as the expected conditional
gain under the ergo dic distribution of the state in the former economy. For more details on the computation
of the welfare gains, see Appendix C.1.
31
In fact, fiscal multipliers in our model are above 2 in a large region of the state space, and this is in the
upper tail of empirical estimates in the literature of open economy multipliers (see, for example, Chodorow-
Reich, 2019; Nakamura and Steinsson, 2014; House, Proebsting and Tesar, 2019).

32
5.3 The Debt Dependence of Optimal Fiscal Policy
In this section we show that default risk considerations lead to an important state dependency
in the optimal fiscal policy. In particular, the government’s optimal response to shocks depends
crucially on the country’s level of debt. To illustrate this debt state dependence, we consider
a one-standard-deviation drop in tradable endowment and simulate the model forward under
the expected path of income, starting from two initial levels of debt, one that is 25% below the
steady-state level (“low debt”) and another that is 25% above the steady-state level (“high
debt”).32
Figure 6 shows the results of this exercise. The figure reports the differences in macroeco-
nomic variables and spreads under the negative shock compared to the economy without the
shock. The dotted black line corresponds to the economy that starts with low debt. In this
case, the government chooses an expansionary path for government spending and borrowing
(panels (b) and (c) respectively). Facing low default risk, the government resorts to a fiscal
stimulus that virtually prevents any increase in unemployment (panel (f)).
In sharp contrast, the solid red line in Figure 6 shows that when initial debt levels are high,
the government chooses to contract government spending and reduce debt levels. Because the
negative shock triggers an increase in sovereign risk, the government finds it too costly to
engage in an expansionary fiscal policy. The increase in spreads that would result from the
increase in borrowing makes the stimulus too costly. This scenario is characterized by a large
increase in unemployment (around 8 percentage points) resulting from the contraction in both
public and private consumption.
The state dependency of the optimal fiscal policy predicted by the model is consistent
with important empirical observations. As shown by Romer and Romer (2019) countries use
fiscal policy tools more aggressively during recessions when these episodes are preceded by
relatively low debt-to-GDP ratios. By the same token, countries that have higher “fiscal
space”are able to better mitigate the effects of recessionary shocks. Interestingly, the model is
also consistent with the dynamics of government spending for Spain in recent years. When the
Great Recession hit, government debt did not exceed 20% of GDP. In line with our model, the
Spanish government responded by a fairly aggressive fiscal stimulus. At that time, borrowing
costs remained quite modest and government spending kept rising (see Figure 1). In 2011-
2012, there was a new slump in economic activity, but the situation was quite different. Facing
mounting spreads, the Spanish government decided to cut spending following the austerity
32
For this quantitative exercise, we simulate from t = 2 onward 10, 000 tradable income paths. Naturally,
along some paths, default occurs during some periods. To compute the impulse responses, we consider all the
simulations in each period and calculate the cross-sectional median of the variables.

33
(a) y T (b) Government Spending g N
0 0.01

-0.02 -0.01

-0.02

-0.04 -0.03
1 5 10 15 1 5 10 15

0 % 0.5

-0.06 0

1 5 10 15 1 5 10 15

(e) cT (f) Unemployment
0 10 low debt
high debt

-0.04 % 5

-0.08 0
1 5 10 15 1 5 10 15

Figure 6: Impulse Responses to y T for Different Initial Debt Levels.
Notes: This figure shows the responses of tradable endowment, unemployment, government spending,
debt, spreads, and tradable consumption when y T drops one standard deviation from its unconditional
mean in period 1. The vertical axis units are deviations from the unshocked path. Solid red lines
correspond to initial debt set to 75% of the steady-state level; dashed blue lines correspond to initial debt
equal the to steady-state level. The vertical axis units are median deviations from the unshocked paths.

prescription of our model.33
33
The optimal policy from the model as well as the implications for output are also broadly consistent with
the behavior of Greece, which first contracted spending significantly around 2010, and then ultimately entered
into default. In line with these results, Gourinchas et al. (2017) find that the Greek crisis was particularly
severe because of the high level of debt that generated a contraction in government spending.
34
6 Fiscal Programs
In this section, we explore the effects of alternative fiscal programs imposed by a third party.
Our analysis is motivated by the fact that many governments are often asked to engage
in austerity programs, sometimes in exchange for some financial assistance.34 We examine
spending cuts imposed today and in the future, and argue that they can have very different
implications.

6.1 Current spending cuts
The first counterfactual experiment we consider is a simple cut in current government spending
imposed by a third party. If the government wishes to remain in good credit standing, it has
to follow an exogenously imposed amount of spending. The government can still choose to
default, in which case it can freely choose the amount of transfers and spending. We assume
that the intervention lasts for only one period. In the following period, the equilibrium reverts
to the Markov equilibrium, in which the government optimally chooses all policies.
Our main result regarding this experiment is that imposing current spending at least
weakly deteriorates the incentives to repay. Proposition 2 formalizes this result.

Proposition 2. Consider an initial level of debt b and a shock y T . If the government finds it
optimal to default under no fiscal program, it also finds it optimal to default when there is an
imposed cut on current government spending. Moreover, there exists a spending cut such that
the government defaults with an imposed spending cut but not without it.

The proof of this proposition follows from the fact that restricting current government
choices in good credit standing reduces the value of repaying for the government and therefore
makes default more attractive. An important implication is that imposing a spending cut can
trigger a default, even under circumstances in which the government would find it optimal to
repay absent any constraints.
When is forced austerity more likely to backfire? To address this question, we examine
the spending cut that would push the government to default. Specifically, we compute what
would be the amount of current government spending as a fraction of the Samuelson level
that would make the government indifferent between repaying and defaulting. The left panel
of Figure 7 shows that when income is low, a low level of austerity is sufficient to precipitate
default. For high income, the government does not find default very attractive, and would
therefore choose to remain in good credit standing even with substantial cuts imposed on
34
Greece is a prominent recent example. In exchange for a fiscal consolidation in the form of the privatization
of government assets, public-sector wage cuts, pension cuts, and higher taxes, the Greek government received
several bailout loans from 2010 onward (see Gourinchas, Martin and Messer, 2018).

35
spending. Similarly, as shown in the right panel, the lower the current debt, the less sensitive
the repayment decision is to imposed spending cuts.
These findings shed light on the design of fiscal rules we will be exploring in the next
section. If the government is close to default, imposing austerity (beyond the optimal amount
chosen by the government) can be harmful. Importantly, both the government and investors
are ultimatlely worse off. On the other hand, if the government is relatively further away from
defaulting, even a moderate spending cut would not trigger default. Moreover, the spending
cut reduces debt accumulation and future incentives to default. In this case, investors who hold
government bonds would benefit ex post as the market value of the outstanding government
debt rises.

Difference relative to Samuelson gN (%) Difference relative to Samuelson gN (%)
0 -50

-20 -60

-40 -70

-60 -80

-80 -90

-100 -100
0.875 1 1.125 -0.5 0 0.5 1 1.5
T
y debt

Figure 7: Effects of Austerity on the Incentives to Default.
Notes: This figure shows the percentage difference relative to the Samuelson level of current public
spending that would make the government indifferent between repaying its debt and defaulting, as a
function of current y T , given current debt equal to the average level (left panel), and as a function of
debt, given y T set to its unconditional mean (right panel). From next period on, allocations are assumed
to take the equilibrium levels.

6.2 Fiscal Forward Guidance
We now investigate an alternative form of fiscal consolidation based on future spending cuts.
We refer to this policy as “fiscal forward guidance.” Two questions we address. First, can
spending cuts imposed in the future improve welfare? And second, how should the spending
cuts be designed?
N
The experiment we consider imposes cuts on next-period government spending (gt+1 ). In
period t, the government continues to choose all available policies, while in the next period,
the government chooses borrowing and repayment subject to the restriction that the spending
cut is implemented. We also assume that lump-sum transfers remain fixed at their optimal
levels and that in the period after the consolidation (t+2), the economy reverts to the Markov

36
equilibrium.
We consider two forms of fiscal forward guidance depending on whether future cuts are
predetermined or allowed to be contingent on the state of nature tomorrow. Different from the
current spending cuts analyzed above, we will show that a reduction in next-period spending
can generate positive effects on the economy. Less spending in the future implies less debt
accumulation, which reduces incentives to default in the future and allows the government to
borrow more cheaply today—and, in turn, render stimulus less costly.
The non-state-contingent austerity program specifies a fixed percentage cut in spending
relative to the optimal level, regardless of the state of nature tomorrow. On the other hand, the
state-contingent austerity program allows for the possibility that spending cuts are contingent
on the level of economic activity. In particular, we consider a spending cut that is active only
when total income y, given by y T + pN y N , is within a subset of future income values. Both
the size of the constant spending cut within the subset and the subset itself are selected to
maximize welfare.
The advantage of the state-contingent austerity program that spending cuts can be tar-
geted to the “right” state tomorrow. As it turns out, we find that it is optimal to promise a
spending cut only for intermediate values of next-period income (see Appendix Figure 11). If
income is sufficiently low, a spending cut can push the government to default tomorrow (for the
reasons explained above), which would increase rather than decrease sovereign spreads today.
It is also not optimal to promise a spending cut if income is excessively high tomorrow. The
reason is that when income is very high, the interest rate at which the government borrows
is closer to the risk-free rate and becomes fairly insensitive to lower debt accumulation. As a
result, promising a cut in these states will generate a distortion in the allocation of resources
across private and public consumption, with modest gains in terms of lower spreads today.
For each case, we look for the optimal spending cut given the initial conditions considered.
We focus on an initial value of debt of 20% above the mean and an income equal to its
unconditional mean.35 For the non-state-contingent case, the optimal cut is 3%. For the
state-contingent cut, the optimal cut reaches 4%. Under a state-contingent cut, the promised
cut is larger because it is implemented only in states in which it is beneficial. Moreover, in line
with the mechanisms highlighted above, the income states in which it is optimal to promise
the spending cut are between 22% below the unconditional mean of output and 3% above the
unconditional mean of total income.
Figure 8 shows the welfare gains of implementing these austerity programs for a range
of spending cuts. (For the state-contingent cut, we keep the interval for total income at
[−0.22%, 0.03%] from its mean level.) Welfare gains are measured as the percentage increase in
current private consumption that households are willing to give up to implement the austerity
35
Appendix Figure 10 shows how welfare gains vary with the current state for non-state-contingent cuts.

37
0.1

0.08

0.06
%
0.04

0.02
non-state-contingent cuts
state-contingent cuts
0
0 1 2 3 4 5 6
size of spending cut (%)

Figure 8: Welfare Gains as Function of Size of Spending Cut.
Notes: This figure shows the welfare gains for non-state-contingent (dashed blue line) and state-contingent
(solid red line) spending cuts next period, as a function of the size of the spending cut. State-contingent
spending cuts are implemented if total income y ≡ y T + pN y N lies within the range [y, y], where y and
y are set to 22% below and 3% above average total income, respectively. Welfare gains are expressed as
(percentage) increases in current total consumption under the optimal policy regime to be indifferent to
the corresponding austerity measure. The current state features debt equal to 20% above its mean and
tradable income given by its unconditional mean.

program. The dashed blue line shows the welfare gain from non-state-contingent cuts, and
the solid red line shows the gain for state-contingent cuts. The maximum welfare gains are,
respectively, 0.075% and 0.088% for the non-state-contingent and state-contingent programs.
Notice that although both programs require commitment to execute the spending cut, these
results show that even a 1-year-ahead commitment can be very effective in providing more
scope for stimulus. To the extent that fiscal budgets, once approved, are difficult to change,
this assumption does not seem very strong.
To shed light on the sources of these welfare gains, in Table 5 we show the impact of these
future austerity programs on today’s key macro variables. The table shows that the non-
state-contingent spending cut allows the government to borrow more cheaply and facilitates
stimulus, which in turn helps to reduce unemployment. In particular, spreads drop by 0.1%
despite the increase in borrowing, and unemployment is reduced by almost 0.3 percentage
points relative to the no-austerity plan. Notably, relative to the baseline economy, the risk
of observing a default in the next period actually rises by 0.1% with the austerity program,
but then it drops 1.41% in the following period. Under a state-contingent austerity plan, the
government engages in even more stimulus, further reducing unemployment and achieving
higher welfare gains.
To sum up, we find that in the midst of a recession with high sovereign default risk,
there is a significant role for an austerity program that involves future spending cuts. An
important qualification is that the program cannot be too aggressive, as it risks increasing

38
Table 5: Current and Future Fiscal Austerity

Current Promised Promised
Variable spending cut non-state-contingent state-contingent
spending cut spending cut
pN (%) −0.527 0.111 0.121
debt (%) −6.014 0.796 0.787
cT (%) −1.433 0.304 0.333
unemp (%) 1.405 −0.298 −0.326
g N (%) −3.000 0.636 0.696
spreads (%) −0.178 −0.103 −0.137
welfare gain (%) −0.056 0.075 0.088

Notes: Initial response of key variables and welfare gains for different austerity measures. These
measures are a promised spending cut next period in all states (column 1) and a current spending cut
(column 2), both of 3%. Column 3 corresponds to a promised spending cut of 4% next period only if
total income y ≡ y T + pN y N lies within the range [y, y], where y and y are set to 22% below and 3%
above average total income, respectively. Welfare gains are expressed as the (percentage) increases
in current total consumption that would leave households indifferent between remaining under the
baseline policy and switching to the alternative. Variations in pN , debt, cT , and g N are reported
as percentages relative to optimal baseline levels without any austerity measure. The current state
features debt equal to 20% above its mean and tradable income y T given by its unconditional mean.

default incentives and worsening borrowing conditions today. Hence the program needs to
be carefully designed, given the projections of expected economic activity. In particular, the
more protracted the recession, the more delayed the spending cuts should be. Moreover, the
desirability of fiscal forward guidance can vary with the initial conditions. The general lesson
is that the more sensitive the borrowing costs are, the higher the potential benefits from fiscal
forward guidance.

7 Conclusion
We examine how sovereign risk matters for the conduct of fiscal policy. Empirically, we show
that high sovereign risk is associated with more procyclical fiscal policies. We develop a
theoretical framework that integrates Keynesian features and sovereign risk concerns that are
consistent with this pattern. Consistent with the findings of Romer and Romer (2019), we also
show that an economy with low government debt, is less likely to experience severe recessions.
On the normative front, we offer a framework that articulates the fundamental conundrum
faced by fiscal policy in a severe downturn: Should a government increase spending to ease
the recession at the expense of higher spreads, or should it cut spending to reduce exposure
to a debt crisis, even if that deepens the recession? Our quantitative findings show that for
relatively high levels of debt, austerity tends to be optimal, even in the presence of large fiscal

39
multipliers. At the same time, our framework also shows how imposed austerity programs
can backfire by increasing a country’s incentives to default. We instead argue that programs
of fiscal forward guidance—an alternative that combines current stimulus with future fiscal
austerity—can be desirable during recessions.

40
References
Aghion, Philippe and Ioana Marinescu, “Cyclical budgetary policy and economic growth:
What do we learn from OECD panel data?,” NBER Macroeconomics Annual, 2007, 22, 251–
297. ed. by D. Acemoglu, K. Rogoff, and M. Woodford.

Aguiar, Mark and Gita Gopinath, “Defaultable debt, interest rates and the current
account,” Journal of International Economics, 2006, 69(1), 64–83.

and Manuel Amador, “Growth in the shadow of expropriation,” Quarterly Journal of
Economics, 2011, 126(2), 651–697.

, , Hugo Hopenhayn, and Iván Werning, “Take the short route: Equilibrium default
and debt maturity,” Econometrica, 2019, 87 (2), 423–462.

, Satyajit Chatterjee, Harold Cole, and Zachary Stangebye, “Quantitative models
of sovereign debt crises,” in J. Taylor and H. Uhlig, eds., Handbook of Macroeconomics,
Vol. 2, Amsterdam Elsevier, 2016, pp. 1697–1755.

Alesina, Alberto and Guido Tabellini, “A positive theory of fiscal deficits and government
debt,” The Review of Economic Studies, 1990, 57 (3), 403–414.

, Filipe R Campante, and Guido Tabellini, “Why is fiscal policy often procyclical?,”
Journal of the European Economic Association, 2008, 6 (5), 1006–1036.

Alfaro, Laura and Fabio Kanczuk, “Fiscal rules and sovereign default,” 2017. NBER
Working Paper No. 23370.

Anzoategui, Diego, “Sovereign debt and the effects of fiscal austerity,” 2018. Mimeo,
Rutgers University.

Arellano, Cristina, “Default risk and income fluctuations in emerging economies,” American
Economic Review, 2008, 98(3), 690–712.

and Yan Bai, “Fiscal austerity during debt crises,” Economic Theory, 2017, 64 (4),
657–673.

Azzimonti, Marina, Marco Battaglini, and Stephen Coate, “The costs and benefits
of balanced budget rules: Lessons from a political economy model of fiscal policy,” Journal
of Public Economics, 2016, 136, 45–61.

Balke, Neele Lisabet and Morten O Ravn, “Time-consistent fiscal policy in a debt
crisis,” 2016. Mimeo, UCL.

41
Barro, Robert, “Stimulus Spending Keeps Failing,” 2012. The Wall Street Journal May 9.
http://www.wsj.com/articles/SB10001424052702304451104577390482019129156?mg=id-
wsj.

Barro, Robert J and Herschel I Grossman, “A general disequilibrium model of income
and employment,” American Economic Review, 1971, 61 (1), 82–93.

and Jong Wha Lee, “International measures of schooling years and schooling quality,”
American Economic Review, 1996, 86 (2), 218–223.

Benassy, Jean-Pascal, “Neo-Keynesian disequilibrium theory in a monetary economy,” Re-
view of Economic Studies, 1975, 42 (4), 503–523.

Bianchi, Javier and Jorge Mondragon, “Monetary Independence and Rollover Crises,”
2018. NBER Working Paper No. 25340.

, Juan Carlos Hatchondo, and Leonardo Martinez, “International reserves and
rollover risk,” 2016. NBER Working Paper 18628.

Bocola, Luigi, “The pass-through of sovereign risk,” Journal of Political Economy, 2016,
124 (4), 879–926.

Born, Benjamin, Francesco D’Ascanio, Gernot Müller, and Johannes Pfeifer, “Gov-
ernment spending, downward nominal wage rigidity, and exchange rate dynamics,” 2019.
manuscript, University of Cologne.

Broner, Fernando, Aitor Erce, Alberto Martin, and Jaume Ventura, “Sovereign debt
markets in turbulent times: Creditor discrimination and crowding-out effects,” Journal of
Monetary Economics, 2014, 61, 114–142.

Canzoneri, Matthew, Dan Cao, Robert Cumby, Behzad Diba, and Wenlan Luo,
“The forward fiscal guidance puzzle and a resolution,” Journal of Economic Dynamics and
Control, 2018, 89, 26–46.

Catão, Luis and Bennett Sutton, “Sovereign defaults: the role of volatility,” 2002, 2. IMF
Working Paper 02/149.

Céspedes, Luis Felipe and Andrés Velasco, “Was this time different?: Fiscal policy in
commodity republics,” Journal of Development Economics, 2014, 106, 92–106.

Chatterjee, S. and B. Eyigungor, “Maturity, indebtedness, and default risk,” American
Economic Review, 2012, 102(6), 2674–2699.

Chatterjee, Satyajit and Burcu Eyigungor, “A seniority arrangement for sovereign
debt,” American Economic Review, 2015, 105 (12), 3740–65.

42
Chodorow-Reich, Gabriel, “Geographic cross-sectional fiscal spending multipliers: What
have we learned?,” American Economic Journal: Economic Policy, 2019, 11 (2), 1–34.

and Loukas Karabarbounis, “The cyclicality of the opportunity cost of employment,”
Journal of Political Economy, 2016, 124 (6), 1563–1618.

Christiano, Lawrence, Martin Eichenbaum, and Sergio Rebelo, “When is the gov-
ernment spending multiplier large?,” Journal of Political Economy, 2011, 119 (1), 78–121.

Corsetti, Giancarlo, Keith Kuester, Andre Meier, and Gernot J. Muller, “Sovereign
risk, fiscal policy, and macroeconomic stability,” Economic Journal, 2013, 123 (566), F99–
F132.

, , , and , “Sovereign risk and belief-driven fluctuations in the euro area,” Journal
of Monetary Economics, 2014, 61, 53–73.

Cuadra, Gabriel, Juan M Sanchez, and Horacio Sapriza, “Fiscal policy and default
risk in emerging markets,” Review of Economic Dynamics, 2010, 13 (2), 452–469.

Dovis, Alessandro and Rishabh Kirpalani, “Fiscal rules, bailouts, and reputation in
federal governments,” 2017. NBER Working Paper 23942.

Drèze, Jacques H, “Existence of an exchange equilibrium under price rigidities,” Interna-
tional Economic Review, 1975, 16 (2), 301–320.

Eaton, Jonathan and Mark Gersovitz, “Debt with potential repudiation: theoretical and
empirical analysis,” Review of Economic Studies, 1981, 48(2), 289–309.

Eggertsson, Gauti and Michael Woodford, “The Zero Bound on Interest Rates and
Optimal Monetary Policy,” Brookings Papers on Economic Activity, 2003, 34 (1), 139–235.

Eggertsson, Gauti B, “What fiscal policy is effective at zero interest rates?,” in “NBER
Macroeconomics Annual 2010,” Vol. 25, Chicago: University of Chicago Press, 2011, pp. 59–
112.

Farhi, Emmanuel and Ivan Werning, “Fiscal multipliers: Liquidity traps and currency
unions,” in J. Taylor and H. Uhlig, eds., Handbook of Macroeconomics, Amsterdam: Else-
vier, 2017, pp. 2417–2492.

Frankel, Jeffrey A, Carlos A Vegh, and Guillermo Vuletin, “On graduation from fiscal
procyclicality,” Journal of Development Economics, 2013, 100 (1), 32–47.

Galı́, Jordi and Roberto Perotti, “Fiscal policy and monetary integration in Europe,”
Economic Policy, 2003, 18 (37), 533–572.

43
Gali, Jordi and Tommaso Monacelli, “Optimal monetary and fiscal policy in a currency
union,” Journal of International Economics, 2008, 76 (1), 116–132.

Gavin, Michael and Roberto Perotti, “Fiscal policy in latin america,” in NBER Macroe-
conomics Annual, 1997, 12, 11–61. ed. by B. S. Bernanke and J. J. Rotemberg.

Gelos, R. Gaston, Ratna Sahay, and Guido Sandleris, “Sovereign borrowing by de-
veloping countries: what determines market access?,” Journal of International Economics,
2011, 83(2), 243–254.

Gonçalves, Carlos Eduardo and Bernardo Guimaraes, “Sovereign default risk and
commitment for fiscal adjustment,” Journal of International Economics, 2015, 95 (1), 68–
82.

Gourinchas, Pierre Olivier, Philippe Martin, and Todd Messer, “The economics of
sovereign debt, bailouts and the Eurozone crisis,” 2018. Mimeo, Berkeley.

Gourinchas, Pierre-Olivier, Thomas Philippon, and Dimitri Vayanos, “The analytics
of the Greek crisis,” NBER macroeconomics Annual, 2017, 31 (1), 1–81.

Guerguil, Martine, Pierre Mandon, and René Tapsoba, “Flexible fiscal rules and
countercyclical fiscal policy,” Journal of Macroeconomics, 2017, 52, 189–220.

Halac, Marina and Pierre Yared, “Fiscal rules and discretion under self-enforcement,”
2017. NBER Working Paper 23919.

Hatchondo, Juan Carlos and Leonardo Martinez, “Long-Duration Bonds and Sovereign
Defaults,” Journal of International Economics, 2009, 79(1), 117–125.

, Francisco Roch, and Leonardo Martinez, “Fiscal rules and the sovereign default
premium,” 2017, pp. 12–30. IMF Working Paper.

, Leonardo Martinez, and César Sosa-Padilla, “Debt Dilution and Sovereign Default
Risk,” Journal of Political Economy, 2016, 124(5), 1383–1422.

House, Christopher L, Christian Proebsting, and Linda L Tesar, “Austerity in the
aftermath of the Great Recession,” Journal of Monetary Economics, 2019.

Ilzetzki, Ethan, “Rent-seeking distortions and fiscal procyclicality,” Journal of Development
Economics, 2011, 96 (1), 30–46.

and Carlos A Végh, “Procyclical fiscal policy in developing countries: Truth or fiction?,”
Technical Report, National Bureau of Economic Research 2008. NBER Working Paper
14191.

44
, Enrique G Mendoza, and Carlos A Végh, “How big (small?) are fiscal multipliers?,”
Journal of monetary economics, 2013, 60 (2), 239–254.

Kaminsky, Graciela L, Carmen M Reinhart, and Carlos A Végh, “When it rains, it
pours: Procyclical macropolicies and capital flows,” NBER Macroeconomics Annual, 2004,
19, 11–53. ed. by M. Gertler and K. Rogoff.

Krugman, Paul, “It’s Baaack: Japan’s Slump and the Return of the Liquidity Trap,” Brook-
ings Papers on Economic Activity, 1998, 1998 (2), 137–205.

, “Austerity Arithmetic,” 2015. The New York Times
http://krugman.blogs.nytimes.com/2015/07/05/austerity-arithmetic/.

Lorenzoni, Guido and Ivan Werning, “Slow moving debt crises,” American Economic
Review, 2019, 109 (9), 3229–63.

Lucas, Robert, “Understanding business cycles,” in “Carnegie-Rochester conference series
on public policy,” Vol. 5 North-Holland 1977, pp. 7–29.

Mendoza, Enrique G. and Vivian Z. Yue, “A General Equilibrium Model of Sovereign
Default and Business Cycles,” Quarterly Journal of Economics, 2009, 127(2), 889–946.

Michaillat, Pascal and Emmanuel Saez, “Optimal public expenditure with inefficient
unemployment,” The Review of Economic Studies, 2018, 86 (3), 1301–1331.

Miyamoto, Wataru, Thuy Lan Nguyen, and Viacheslav Sheremirov, “The effects of
government spending on real exchange rates: Evidence from military spending panel data,”
Journal of International Economics, 2019, 116 (1), 144–157.

Monacelli, Tommaso and Roberto Perotti, “Fiscal policy, the real exchange rate and
traded goods,” Economic Journal, 2010, 120 (544), 437–461.

Na, Seunghoon, Stephanie Schmitt-Grohé, Martı́n Uribe, and Vivian Yue, “The
twin ds: Optimal default and devaluation,” American Economic Review, 2018, 108 (7),
1773–1819.

Nakamura, Emi and Jon Steinsson, “Fiscal stimulus in a monetary union: Evidence from
US regions,” American Economic Review, 2014, 104 (3), 753–792.

Ramey, Valerie A, “Ten years after the financial crisis: What have we learned from the
renaissance in fiscal research?,” Journal of Economic Perspectives, 2019, 33 (2), 89–114.

Romer, Christina D and David H Romer, “Fiscal space and the aftermath of financial
crises: how it matters and why,” Brookings Papers on Economic Activity, forthcoming,
2019.

45
Samuelson, Paul A, “The pure theory of public expenditure,” Review of Economics and
Statistics, 1954, 36 (4), 387–389.

Schmitt-Grohé, Stephanie and Martın Uribe, “Downward nominal wage rigidity, cur-
rency pegs, and involuntary unemployment,” Journal of Political Economy, 2016, 124 (5),
1466–1514.

Talvi, Ernesto and Carlos A Vegh, “Tax base variability and procyclical fiscal policy in
developing countries,” Journal of Development Economics, 2005, 78 (1), 156–190.

Tornell, Aaron and Philip R Lane, “The voracity effect,” American Economic Review,
1999, 89 (1), 22–46.

Uribe, Martin, “Exchange-rate-based inflation stabilization: The initial real effects of cred-
ible plans,” Journal of Monetary Economics, 1997, 39 (2), 197–221.

and Stephanie Schmitt-Grohé, Open Economy Macroeconomics, Princeton, NJ: Prince-
ton University Press, 2017.

Werning, Ivan, “Managing a liquidity trap: Monetary and fiscal policy,” 2011. NBER
Working Paper 17344.

Woo, Jaejoon, “Why do more polarized countries run more procyclical fiscal policy?,” Review
of Economics and Statistics, 2009, 91 (4), 850–870.

Woodford, Michael, “Simple analytics of the government expenditure multiplier,” American
Economic Journal: Macroeconomics, 2011, 3 (1), 1–35.

46
Appendices

A Additional Tables and Figures

Table 6: Countries Included in the Sample
Albania Gambia, The Nicaragua
Algeria Germany Nigeria
Argentina Greece Norway
Armenia Guatemala Oman
Australia Honduras Pakistan
Austria Hong Kong SAR, China Panama
Azerbaijan Hungary Papua New Guinea
Bahamas, The Iceland Paraguay
Bangladesh India Peru
Belarus Indonesia Philippines
Belgium Iran, Islamic Rep. Poland
Belize Ireland Portugal
Benin Israel Romania
Bhutan Italy Russian Federation
Bolivia Japan Rwanda
Botswana Jordan Saudi Arabia
Brazil Kazakhstan Senegal
Brunei Darussalam Kenya Sierra Leone
Bulgaria Korea, Rep. Singapore
Burkina Faso Kyrgyz Republic South Africa
Burundi Lao PDR Spain
Cameroon Lebanon Sri Lanka
Canada Lesotho Sudan
Chile Liberia Swaziland
China Luxembourg Sweden
Colombia Macao SAR, China Switzerland
Congo, Dem. Rep. Macedonia, FYR Tajikistan
Congo, Rep. Madagascar Tanzania
Costa Rica Malawi Thailand
Cyprus Malaysia Togo
Czech Republic Mali Trinidad and Tobago
Denmark Malta Tunisia
Dominican Republic Mauritania Turkey
Ecuador Mauritius Uganda
Egypt, Arab Rep. Mexico Ukraine
El Salvador Morocco United Arab Emirates
Equatorial Guinea Mozambique United Kingdom
Finland Namibia United States
France Nepal Uruguay
Gabon Netherlands Venezuela, RB
New Zealand Vietnam

Notes: This table shows the set of countries used in Section 2 to document the cyclicality of government
spending. This set of countries includes those with available data on government spending and GDP from
the WDI for the period 1990-2016 and excludes countries that were missing more than half of the values for
the period 1990-2016 or countries with discontinuous data.

47
Table 7: Cyclicality of Government Spending around the World
Summary Statistics for Countries with Available Data on Credit Ratings.
σG /σY corr(Gt , Gt−1 ) corr(G, Y )
Mean 1.78 0.49 0.26
Median 1.13 0.54 0.29
Standard deviation 1.95 0.24 0.34
95th percentile 5.24 0.79 0.81
5th percentile 0.52 0.05 -0.34

Notes: This table shows summary statistics of government spending for the subset of countries in Table 6
with credit ratings data available during the period 1990-2016, and used in the regression of Section 2. The
variables σG /σY , corr(Gt , Gt−1 ), and corr(G, Y ) denote, respectively, the ratio of the standard deviation of
government spending to the standard deviation output, the first-order autocorrelation of government
spending, and the correlation between government spending and output. We compute moments using the
cyclical component of per capita variables in constant local currency, detrending variables with the HP filter
and a smoothing parameter of 100. For details on the data, see Section 2.

Table 8: Cyclicality of Government Spending for High-Risk Countries
Country corr(Gt , Yt ) Country corr(Gt , Yt )
Argentina 0.78 Indonesia 0.69
Belize 0.63 Lebanon -0.03
Cameroon 0.60 Mozambique -0.03
Cyprus 0.29 Pakistan 0.53
Dominican Republic 0.66 Paraguay 0.49
Ecuador 0.51 Russian Federation 0.72
Egypt, Arab Rep. -0.30 Ukraine 0.53
Greece 0.81 Venezuela 0.55
Mean 0.46
Median 0.54
Standard deviation 0.32

Notes: This table shows the correlation between government spending and output for countries in our
sample with “high risk,” defined as those that ever had a sovereign credit rating below B. We compute
moments using the cyclical component of per capita variables in constant local currency, detrending variables
with the HP filter and a smoothing parameter of 100. For details on the data, see Section 2.

48
Table 9: Cyclicality of Government Spending for Medium-Risk Countries
Country corr(Yt , Gt ) Country corr(Yt , Gt )
Albania 0.06 Korea, Rep. 0.17
Azerbaijan 0.57 Kyrgyz Republic 0.95
Bahamas, The 0.35 Macedonia, FYR 0.31
Bangladesh -0.02 Madagascar 0.39
Belarus 0.65 Malaysia 0.34
Benin 0.02 Mali 0.48
Bolivia 0.44 Malta 0.25
Brazil 0.64 Mexico 0.11
Bulgaria 0.25 Morocco 0.08
Burkina Faso -0.08 Nicaragua 0.44
Chile 0.48 Nigeria 0.84
China 0.10 Oman -0.22
Colombia 0.29 Panama -0.41
Congo, Dem. Rep. 0.37 Papua New Guinea 0.29
Congo, Rep. 0.20 Peru 0.63
Costa Rica 0.08 Philippines 0.43
Czech Republic 0.56 Poland -0.34
El Salvador -0.16 Portugal 0.63
Gabon 0.45 Romania 0.28
Guatemala 0.04 Rwanda 0.85
Honduras -0.03 Senegal 0.69
Hungary 0.50 South Africa 0.33
Iceland 0.60 Spain 0.20
India 0.44 Sri Lanka 0.30
Ireland 0.67 Thailand 0.24
Israel -0.12 Trinidad and Tobago 0.03
Italy 0.27 Tunisia -0.02
Jordan -0.04 Turkey 0.23
Kazakhstan 0.57 Uganda 0.28
Kenya -0.03 Uruguay 0.81
Vietnam 0.82
Mean 0.30
Median 0.29
Standard deviation 0.30

Notes: This table shows the correlation between government spending and output for countries in our
sample with “medium risk,” defined as those that ever had a sovereign credit rating below A but always had
a credit rating greater than or equal to B. We compute moments using the cyclical component of per capita
variables in constant local currency, detrending variables with the HP filter and a smoothing parameter of
100. For details on the data, see Section 2.

49
Table 10: Cyclicality of Government Spending for Low-Risk Countries
Country corr(Yt , Gt ) Country corr(Yt , Gt )
Australia 0.26 Japan 0.02
Austria 0.01 Luxembourg 0.39
Belgium 0.11 Netherlands 0.13
Botswana 0.07 New Zealand 0.27
Canada -0.13 Norway -0.51
Denmark -0.30 Saudi Arabia 0.43
Finland 0.67 Singapore -0.36
France -0.60 Sweden -0.23
Germany -0.09 Switzerland -0.24
Hong Kong SAR, China -0.01 United Kingdom 0.37
United States -0.28
Mean 0.00
Median 0.01
Standard deviation 0.33

Notes: This table shows the correlation between government spending and output for countries in our
sample with “low risk,” defined as those that never had a sovereign credit rating below A. We compute
moments using the cyclical component of per capita variables in constant local currency, detrending variables
with the HP filter and a smoothing parameter of 100. For details on the data, see Section 2.

Table 11: Fiscal Procyclicality and Income
(1) (2)
log(GDP ) -0.06∗∗
(0.02)

Rich -0.29∗∗∗
(0.09)

Emerging -0.04
(0.07)

Observations 122 122
R2 0.051 0.107

Notes: Results from estimating the model

fiscal procyclicalityi = α + βincome Incomei + εi ,

where fiscal procyclicalityi is the correlation between government spending and output from country i,
Incomei is a measure of country’s i income per capita, and εi is a random error term. Standard errors are
shown in parentheses. Column (1) measures Incomei as the log of the average GDP per capita in PPP in
constant 2005 dollars. Column (2) measures Incomei with dummies indicating whether the country is rich,
emerging, or poor, using the thresholds defined in Uribe and Schmitt-Grohé (2017). For details on the data,
see Section 2.

50
Table 12: Income and Risk Level

High Risk Medium Risk Low Risk
Iceland Australia
Ireland Austria
Italy Belgium
Oman Canada
Denmark
Finland
France
Germany
Hong Kong SAR, China
Rich Japan
Luxembourg
Netherlands
Norway
Saudi Arabia
Singapore
Sweden
Switzerland
United Kingdom
United States
Argentina Albania Korea, Rep. Botswana
Belize Azerbaijan Macedonia, FYR New Zealand
Cyprus Bahamas, The Malaysia
Dominican Republic Belarus Malta
Ecuador Bolivia Mexico
Egypt, Arab Rep. Brazil Morocco
Greece Bulgaria Panama
Indonesia Chile Peru
Lebanon China Philippines
Pakistan Colombia Poland
Emerging Paraguay Congo, Rep. Portugal
Russian Federation Costa Rica Romania
Ukraine Czech Republic South Africa
Venezuela, RB El Salvador Spain
Gabon Sri Lanka
Guatemala Thailand
Honduras Trinidad and Tobago
Hungary Tunisia
Israel Turkey
Jordan Uruguay
Kazakhstan
Cameroon Bangladesh
Mozambique Benin
Burkina Faso
Congo, Dem. Rep.
India
Kenya
Kyrgyz Republic
Madagascar
Poor
Mali
Nicaragua
Nigeria
Papua New Guinea
Rwanda
Senegal
Uganda
Vietnam

Notes: This table shows the set of countries used in Section 2, classified according to their sovereign risk and
income level. Low Risk, Medium Risk, and High Risk denote, respectively, countries are that always had a
rating equal to A or above in the period 1990-2016, countries that ever had a rating below A but above or
equal to B, and countries that ever had a rating below B. Rich, Emerging, and Poor countries denote groups
with high, medium, and low income using the thresholds defined in Uribe and Schmitt-Grohé (2017). For
details, see Section 2.

51
Table 13: Fiscal Procyclicality, Income, and Institutional Factors
(1) (2)
Rich -0.15 -0.23
(0.16) (0.17)

Emerging -0.09 -0.02
(0.13) (0.13)

Fiscal Rule 0.01 0.00
(0.01) (0.01)

Rule of Law 0.08 -0.01
(0.07) (0.06)

Education Inequality 0.01 -0.00
(0.01) (0.01)

Fuel Production 0.00 0.00
(0.01) (0.01)

Trade openness -0.00 -0.00
(0.00) (0.00)

Output volatility 9.50∗∗∗ 7.19∗∗∗
(1.94) (2.56)

Variables of sovereign risk included Yes No
Observations 59 66
R2 0.521 0.341

Notes: Column (1) shows results from estimating the model fiscal procyclicalityi = α + γ 0 Xi + εi , where
fiscal procyclicalityi is the correlation between government spending and output from country i, and Xi
contains the following variables: rule of law, measured by the average ranking from the WDI for the period
1990-2016; education inequality, measured by the standard deviation of the percentage of population enrolled
by school level (data source: Barro and Lee, 1996); fiscal rule measured by the number of years with a fiscal
rule (source: IMF); fuel production and trade openness, measured as a percentage of GDP, averaged over the
period of analysis (source: WDI), and output volatility, measured as the standard deviation of GDP for the
period 1990-2016 (source: WDI). Column (2) shows the coefficients of the same variables estimated but in an
empirical model that also includes the sovereign risk variables, that is,
fiscal procyclicalityi = α + βmedium medium riski + βhigh high riski + γ 0 Xi + εi . For details on the data, see
Section 2.

52
Table 14: Fiscal Procyclicality and Sovereign Risk (measured by default occurrence)
(1) (2) (3) (4)
Default 0.24∗∗∗ 0.22∗∗∗ 0.19∗∗∗ 0.20∗∗
(0.07) (0.07) (0.07) (0.09)

log(GDP ) -0.05∗∗
(0.02)

Rich -0.24∗∗∗ -0.19
(0.09) (0.16)

Emerging -0.05 0.00
(0.07) (0.13)

Additional controls No No No Yes
Observations 122 122 122 66
R2 0.094 0.125 0.159 0.381

Notes: Results from estimating the model

fiscal procyclicalityi = α + βdefault defaulti + γ 0 Xi + εi

where fiscal procyclicalityi is the correlation between government spending and output from country i,
defaulti is a dummy variable that takes the value of 1 if country i ever defaulted during the period 1990-2014
(data source: Uribe and Schmitt-Grohé, 2017), Xi is a vector of country-level controls, and εi is a random
error term. Standard errors are shown in parentheses. Column (1) estimates the empirical model without
controls. Column (2) includes as controls the log of the average GDP per capita in PPP. Column (3)
includes as controls dummies measuring whether the country is rich or emerging, using the thresholds
defined in Uribe and Schmitt-Grohé (2017). Column (4) includes the following additional controls in the
vector Xi : rule of law, measured by the average ranking from the WDI for the period 1990-2016; education
inequality, measured by the standard deviation of the percentage of population enrolled by school level, (data
source: Barro and Lee, 1996); fiscal rule measured by the number of years with a fiscal rule (source: IMF);
average fuel production and average trade openness as a percentage of GDP (source: WDI), and output
volatility, measured as the standard deviation of output for the period 1990-2016 (source: WDI). For details
on the data, see Section 2.

53
Table 15: Fiscal Procyclicality and Sovereign Risk (measured by number of default episodes)
(1) (2) (3) (4)
Number of default episodes 0.24∗∗∗ 0.22∗∗∗ 0.19∗∗∗ 0.20∗∗
(0.07) (0.07) (0.07) (0.09)

log(GDP ) -0.05∗∗
(0.02)

Rich -0.24∗∗∗ -0.19
(0.09) (0.16)

Emerging -0.05 0.00
(0.07) (0.13)

Additional controls No No No Yes
Observations 122 122 122 66
R2 0.094 0.125 0.159 0.381

Notes: Results from estimating the model

fiscal procyclicalityi = α + βdefault defaulti + γ 0 Xi + εi

where fiscal procyclicalityi is the correlation between government spending and output from country i,
defaulti denotes the number of default episodes experienced by country i during the period 1990-2014 (data
source Uribe and Schmitt-Grohé, 2017), Xi is a vector of country-level controls, and εi is a random error
term. Standard errors are shown in parentheses. Column (1) estimates the empirical model without controls.
Column (2) includes as controls the log of the average GDP per capita in PPP. Column (3) includes as
controls dummies measuring whether the country is rich or emerging, using the thresholds defined in Uribe
and Schmitt-Grohé (2017). Column (4) includes the following additional controls in the vector Xi : rule of
law, measured by the average ranking from the WDI for the period 1990-2016; education inequality,
measured by the standard deviation of the percentage of population enrolled by school level (Barro and Lee,
1996, data source:[); fiscal rule, measured by the number of years with a fiscal rule (source: IMF); average
fuel production and average trade openness as a percentage of GDP (source: WDI), and output volatility,
measured as the standard Deviation of output for the period 1990-2016 (source: WDI). For details on the
data, see Section 2.

54
Table 16: Targeted Moments in Calibration
Parameter Value Target statistic Data Model
Risky Debt
β 0.907 External debt/GDP 22.8% 22.6%
ψχ0 0.3277 Average bond spread 1.05% 1.09%
ψχy 2.42 Volatility of bond spreads 1.4% 0.7%
ψg 0.02 Average govt. spending/GDP 18.1% 18.2%
τ 0.19 Volatility of govt. spending/GDP 2.0 2.0
w̄ 3.068 Increase of unemployment 2.5% 2.5%

Risk-free Debt
β 0.998 External debt/GDP 22.8% 22.4%
ψg 0.02 Average govt. spending/GDP 18.1% 18.6%

Figure 9: Welfare Gains: Optimal Policy versus Samuelson Rule

0.9 0.95 1 1.05 1.1
yT

Notes: This figure shows the welfare gains in the default model of optimal policy relative to the Samuelson
rule. The solid blue line represents the average conditional welfare gains as a function of y T . For each
value of y T , we set the debt equal to the average level implied by the ergodic distribution for that y T .
The horizontal dashed black line is the unconditional gain. Welfare gains are expressed in terms of a
permanent increase in total consumption.

55
Figure 10: Welfare Gains from Promised Non-State-Contingent Spending Cuts
0.2 0.2

0
0
-0.2

% -0.2 % -0.4

-0.6
-0.4
-0.8

-0.6 -1
0.95 1 1.05 1.1 1.15 0 0.5 1 1.5
yT debt
Note: This figure shows the welfare gains from promising non-state-contingent spending cuts next period
of 3%, as a function of tradable income y T (left panel) and as function of debt (right panel). Debt is set
to 20% above its average on the left panel and y T is equal to its unconditional mean on the right panel.
Welfare gains are expressed as (percentage) increases in current total consumption under the optimal
policy regime to be indifferent with the promised spending cut.

Figure 11: Welfare Gains from Well-designed Promised Spending Cuts
0.88 0.9

0.86 0.8

% 0.84 % 0.7

0.82 0.6

0.8 0.5
-29 -25 -21 -17 -8 -4 0 4 8
y (% deviation from average y) y (% deviation from average y)

Note: This figure shows the welfare gains from promising spending cuts of 4% for next period whenever
total income y ≡ y T + pN y N lies within the range [y, y]. The left panel plots the welfare gains as function
of y with y set to 3% above the average total income. The right panel plots the welfare gains as function of
y with y set to 22% below the average total income. Welfare gains are expressed as (percentage) increases
in current total consumption under the optimal policy regime to be indifferent with the promised spending
cut. The current state features debt equal to 20% above its mean and tradable income y T given by its
unconditional mean.

56
B’ Proofs

Proof of Lemma 1 First note that given that agents are hand-to-mouth, the social pe-
riod utility from private consumption is the weighted average of the utility of employed and

unemployed households, weighted by their shares in the population, hy and 1 — hy:

Ui((CH ico (aero g) = huw (ee) + Iau (ee eh"), (25)

households, and a” and cy ™ denote that of unemployed households. From the households’

optimality condition (4), we can express tradable consumption for any individual 7 as CH =

ie with mY = +#(p)~§. From the household’s budget constraint, this implies that
u(l + pin) = Yi(hjt). This means that the government unemployment insurance scheme

implies a constant ratio between the tradable consumption of the unemployed and employed

et
workers £ on = =k. Under the assumed CRRA period utility function, we obtain the expression

for welfare expressed in the statement of Lemma 1.

Proof of Proposition 1 By contradiction, assume, contrary to the statement of the propo-
sition, that there exists an optimal allocation {g/*,b/,T;', ht, vi} (henceforth “initial al-
location” ) in which, for some period ¢, hj < 1. Given that the allocation features unemploy-
ment, the labor market slackness condition implies that wages are equal to the minimum wage

cl* é . . . . .
prt = te (aa) * — 7. Now consider an alternative allocation with period-@ employment

given by some hy € (hi, 1), government spending given by g = g/* + (he — h;), lamp-sum
transfers given by Ty = T 7 —p)*(ge—gh*), and the rest of the variables in the initial allocation.
Because of the linear technology, period-@ nontradable consumption is identical under the al-
ternative allocation than in the initial allocation (see equation (13)), implying that the social
period utility from private consumption is at least as good in the alternative allocation as it
is in the initial allocation; that is, u(ci,hy — Ge)Q(he) > uch, ht — gh*)Q(hks) (with equality
under perfect unemployment insurance, k = 1). Moreover, given that the utility from the
public good is higher under the alternative allocation than under the initial allocation (given
that g > g)’* and v(.) is increasing), welfare is unequivocally higher under the alternative
allocation than under the initial allocation. Finally, we show that the alternative allocation
is also feasible, contradicting that the initial allocation is optimal. To see that the alternative

allocation is feasible, real wages in this alternative allocation are still equal to the minimum

1
cl* € : : : . .
wage, that is, +“ (; f_ )' = W, implying that the optimal allocation satisfies the labor

w he—9e"
market slackness constraint. Given the proposed lump sum taxes, the alternative allocation
satisfies the government budget constraint with the borrowing policy of the initial allocation

b,*. Finally, given that in the alternative allocation c}* and b;‘ are the same as in the initial

allocation, the resource constraint is also satisfied.

57
Proof of Proposition 2
Proof. Denote by V R,Austerity (y T , b; ḡ N ) the value of repayment under a fiscal program program
that imposes ḡ N . By definition, we have V R,Austerity (y T , b; 0) = V R (y T , b). Consider (b, y T ) such
that the government finds optimal to default under no fiscal program. We have V R (y T , b) <
V D (y T ). We have
0
V R,Austerity (y T , b; ḡ N ) = 0 max {u(cT , F (h) − g N )Ω(h) + v(g N ) + βEV (y T , b0 ) (26)
b ,T ≥0,h≤1

subject to
cT = y T + q(y T , b0 )[b0 − (1 − δ)b] + δb
P N (y T , h, g N )ḡ N + δb + T = q(y T , b0 )[b0 − (1 − δ)b] + τ PtT ytT + P N (y T , h, ḡ N )F (h)

P N (y T , h, ḡ N )F 0 (h) ≥ w,

Comparing (26) with (19) in the main text, it follows that V R,Austerity (y T , b; ḡ N ) ≤ V R (y T , b).
Since the value of default under the spending cut is unaffected, we can use that V R (y T , b) <
V D (y T ), to show that V R,Austerity (y T , b; ḡ N ) < V D (y T ), which completes the first part of the
proof.
Now consider (b, y T ) such that the government repays under no fiscal program. We have
that V R (y T , b) > V D (y T ). Consider a spending cut such that ḡ N is arbitrarily close to zero. Us-
ing the Inada condition for the utility of public spending, we have that limḡN →0 V R,Austerity (y T , b; ḡ N ) =
−∞. By continuity, it follows that there exists ḡ N > 0 such that V R (y T , b) > V D (y T ) >
V R,Austerity (y T , b; ḡ N ), completing the proof.

58
C Quantitative Analysis
C.1 Solution Method
Model solution. The model is solved numerically using value function iteration with in-
terpolation. Linear interpolation is used for the endowment and cubic spline interpolation for
debt levels. We consider an equidistant grid for tradable endowment of 21 points between
3 standard deviations below and above the unconditional mean. We use 61 gridpoints for
debt for the baseline model and 101 for the risk-free debt economy. To compute expectations
for continuation values and prices, we use 15 and 11 quadrature points for the endowment
realizations, respectively. For each state, conditional on an arbitrary choice of debt, we em-
ploy a variant of Brent’s method algorithm included in the IMSL library to find the roots
of the implementability conditions in the government’s problem. To maximize over debt, we
then use the UVMIF routine that relies on a quadratic interpolation method. We solve for
the optimality conditions under four alternative regimes: with and without a binding wage
rigidity constraint, and with and without zero lump-sum government transfers. We then com-
pute welfare under the four regimes. Our solution is given by the allocations that deliver the
highest utility.

Welfare gains. For the conditional welfare gains in Subsection 5.2, even though the house-
holds’ preferences are homothetic, the presence of additive default costs prevents us from
applying the standard formula for welfare gains. For that reason, we turn to value function
iteration and proceed as follows. We are interested in welfare gains expressed as a permanent
increase in private and public consumption that would leave the household indifferent between
living in the economy with a Samuelson rule and switching to the economy with the optimal
policy. For a given initial state and an arbitrary value for the welfare gain, we iterate on the
value functions for the Samuelson rule, keeping policy functions and default strategies fixed.
Upon convergence, we calculate the sup norm to the difference between the newly computed
Samuelson value function and the value function under the optimal policy evaluated at the
selected initial state. If the norm is lower than 1e−5 in absolute value, we stop and report the
welfare gain. If instead it is positive and larger than 1e−5 , we reduce the value of the welfare
gain and iterate again on the value function. Otherwise, we increase the welfare gain and
iterate again. We repeat this procedure for all the initial states of interest. For unconditional
welfare gains, we proceed in a similar fashion integrating over all states by using an asymptotic
distribution of (y T , b) and ζ, constructed by taking the associated state from the 10, 000th
period in each of 10, 000 simulations.

C.2 Data Used in the Calibration
The following data were used in the model’s calibration for Spain:

59
1. Tradable endowment process: estimated using data on the value added in the agricul-
tural and manufacturing sector, at constant prices, log-quadratically detrended, period
1980-2011. Data source: National accounts in the National Statistics Office (INE).

2. Ratio of tradable output to total output: average ratio of the value added in the agricul-
tural and manufacturing sector over total value added, in current prices, period 1980-
2011. Data source: INE.

3. Ratio of debt to GDP: total gross debt of the general government held by external
creditors, period 1996-2015. Data source: OECD government.

4. Bond spreads: difference between Spanish and German 5-year sovereign bond yields,
period: 2000-2015. Data source: Bank of Spain and Deutsche Bundesbank.

5. Government spending: ratio of general government final consumption expenditure to
GDP, in current prices, period 1996-2015. Data source: WDI.

6. Unemployment: unemployment rate, period 1996-2015. Data source: INE.

In addition, we calibrated the risk-free rate to match the average annual gross yield on
5-year German government bonds over the period 2000-2015.

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