Sovereign Default, Institutions and the External Cost of Capital
Eugenia Andreasen
January 15, 2012
Abstract
Recent empirical studies …nd a systematic tightening of external …nancial constraints for the private
sector after sovereign defaults. This paper develops a signaling model for a small open economy in which
the sovereign debt repayment decision of the government provides new information to international credit
markets regarding the institutional quality in the country. Credit markets care about institutional quality
because it a¤ects the expected repayment of loans. Therefore, if international investors receive negative
information on the institutional quality from the sovereign default they worsen the terms of credit they
o¤er to local …rms. The model can rationalize the restricted access to international credit observed after
default episodes as the result of the negative information revealed to credit markets.
Key words: Sovereign debt, Sovereign default, Reputation, Signaling, Institutions, Interest rate
JEL Codes: E62, F30, F34, G15
Department of Economics, European University Instittute, Via della Piazzuola 43, 50133 Florence, Italy. E-mail: [email protected]. Tel: (39) 331-304-5402. I am grateful for helpful suggestions from seminar participants at the annual
Latin American Economic Association meeting, the Berlin Sovereign Debt Conference, and at seminars at the European University Institute. I have received helpful comments from: Mark Aguiar, Luis Catao, Giancarlo Corsetti, Piero Gottardi, Ramón
Marimón, Nicola Pavoni, Guido Sandleris and Guido Ruta.
1
1
Introduction
Emerging market economies face recurrent and costly sovereign defaults that have pernicious e¤ects on
investment, consumption and growth. The ensuing tightening of private …rms’external …nancial constraints
presents one key channel through which sovereign default a¤ects economic activity. Since in emerging
economies about 25 percent of corporate bonds and bank credits are external, a worsening of international
credit conditions may have pervasive negative consequences in the economy. In e¤ect, recent empirical
studies …nd a signi…cant and economically relevant worsening of external …nancial conditions for the private
sector after sovereign defaults and a consequent reduction in private credit (Eichengreen and Moody (2000),
Arteta and Hale (2008), Trebesch (2010) and Trebesch et al. (2010)). In particular, after controlling for
fundamentals, banking crises and currency crises, Hale and Arteta (2008) …nd a decline in foreign private
credit of over 20 percent below the country-speci…c average that lasts until 3 years after the sovereign debt
restructuring.
What triggers the …rms’restricted access to foreign credit after sovereign defaults? I address this question
by developing a signaling model in which sovereign defaults reveal negative information to international
investors regarding the institutional quality in the country. The negative information on the institutional
quality provides the missing link to understand the restricted access to credit that follows sovereign defaults.1
Figure 1 illustrates this e¤ect by depicting the evolution of the average Investment Pro…le Index, published
by the International Country Risk Guide (ICRG), for the countries that defaulted between 1990 and the early
2000s for two years before and after the sovereign debt crises. The Investment Pro…le Index is a subjective
assessment of factors that depend on the institutional quality, and which a¤ect the risk to investing in the
country. Its possible values range from 0, maximum risk, to 10, minimum risk. The …gure shows that the
Investment Pro…le Index collapses with the sovereign debt crisis registering a total average reduction of 35%.
This reduction re‡ects the negative information that the crisis conveys to the market, and which triggers
the worsening of the …nancial conditions. The anticipation of the negative reaction to the e¤ective default
date is consistent with the signaling story and also with the results in Arteta and Hale (2008), which state
that the initial e¤ect on credit corresponds to the month when the debt renegotiations began.
1 The quality of institutions is widely recognized as one of the main determinants of the terms and quantity of credit available
for and within a country (La Porta et al. (1997), Djankov et al. (2007, 2008), and Alfaro et al. (2007, 2008)).
2
4
5
6
7
8
Investment Profile Index
-20
-10
0
10
Distance in months from sovereign debt crisis
20
Source: International Country Risk Guide.
Defaults Considered: Argentina, Ecuador, Pakistan, Russia, Ukraine and Uruguay.
Figure 1: Evolution of Investment Pro…le Index around the Period of the Sovereign Debt Crisis
The model developed in this paper considers a small open economy that lasts for three periods. The
economy is composed of a benevolent government and a continuum of identical entrepreneurs that have
access to foreign credit. In the initial period the government borrows from the foreign lenders to …nance an
optimal amount of public expenditure. In the second period, the government receives private information
regarding the institutional quality in the country; and, given this information, it decides whether to repay
or default on the sovereign debt. After the government repays or defaults, the entrepreneurs are allowed to
borrow in the international …nancial market. The interest rate of the entrepreneurs’borrowing depends on
the information revealed by the government’s action about the institutional quality. International investors
care about the institutional quality because it a¤ects the expected repayments of loans, therefore if they
receive negative information they worsen the credit conditions for the entrepreneurs. In the last period, the
entrepreneurs repay their loans and consume.
The key mechanism in the model is the negative relationship between institutional quality and sovereign
debt repayment costs, which provides the signaling value to the sovereign default and generates the single
crossing property in the model. Institutional quality tends to be homogeneous within an economy: countries
with good creditor rights also have, for example, low levels of corruption and e¢ cient tax systems.2 Then,
among other things, worse quality of institutions negatively a¤ects tax collection and government revenue in
general (Murphy et al. (1993) and Shleifer et al. (1993)). This means that countries with low institutional
quality face more di¢ culties raising the funds needed to repay sovereign debt and therefore default with
a higher probability. Figure 2 provides an example of how weaker institutions, in this case re‡ected by
higher corruption3 are negatively correlated with the ratio of revenue over GDP. It graphs the average for
2 In e¤ect, there is a very high correlation between the Investment Pro…le and Control of Corruption indexes both in time
series, 0.85; and in cross section, 0.74. Figure 9 in Appendix 7.1 con…rms the high correlation in average and illustrates a
prevalence of low values of both indexes among "defaulters".
3 The Corruption Index of the ICRG is an assessment of corruption within the political system that is a threat to investment
by distorting the economic and …nancial environment and reducing the e¢ ciency of government and business. It takes into
account excessive patronage, nepotism, job reservations, demands for special payments and bribes connected with import and
3
the last XX years of government revenues as a share of GDP (WDI) against the Corruption Index (ICRG)
for all countries with observations in both databases. The …gure also illustrates that defaulting countries are
characterized by relatively higher levels of corruption and lower ratios of revenue over GDP.
0
Government Revenues (%GDP)
10
20
30
40
50
Government Revenues and Corruption
0
.2
Non Defaulters
.4
Corruption
Defaulters
.6
.8
Fitted values
Sources: ICRG and WDI.
Defaults Considered: Argentina, Ecuador, Dominican Rep., Pakistan, Russia, Ukraine, Uruguay
Figure 2: Government Revenues and Corruption
Besides explaining the negative e¤ect of sovereign default over credit, this framework also provides incentives for sovereign debt repayment even in this …nite horizon setting. Governments have incentives to
repay to avoid the negative consequences of default over the credit conditions faced by the private sector.
Nevertheless, higher levels of sovereign debt and lower quality of institutions reduce these incentives thus
increasing the risk of sovereign default (Reinhart et al. (2003) and Kraay and Nehru (2006). In the model,
sovereign interest rates respond to the observable part of the higher default risk rising with the level of
indebtness (Arellano, 2008).
This paper contributes to the debate on the negative e¤ects of sovereign defaults on the domestic economy, speci…cally focusing on the private credit channel. Most of the literature that analyzes this channel
concentrates on the negative e¤ect that sovereign defaults have over the balance sheets of domestic agents
that hold sovereign debt (Broner and Ventura (2008), Gennaioli et al. (2010), and Guembel and Sussman
(2009)). In contrast, this paper assumes that domestic agents do not hold sovereign debt. Nevertheless, the
domestic economy is still harmed by the default due to the negative information that it reveals to …nancial
markets. This information story links the paper with the “reputational spillovers”of Cole and Kehoe (1997,
1998), the signaling model of Sandleris (2008, 2010) and with the “default traps” of Catao et al. (2009). In
particular, the signaling mechanism I adopt here is similar to the formulations in Sandleris (2008, 2010) but
with signi…cant di¤erences. The main point of distinction is given by the transmission channel of the e¤ects
of the sovereign default over the domestic economy. While in my paper the transmission goes from prices to
quantities, i.e. increased interest rates trigger reductions in investment and credit; in the work of Sandleris
the e¤ect is only through quantities, i.e. the tightening of collateral credit constraints. I …nd my approach
export licenses, exchange controls, tax assessments, police protection, or loans. Its possible values range from 0 (minimum) to
1 (maximum).
4
more appropriate since the transmission through quantitative constraints, besides being more mechanical,
only works as long as these constraints bind. This last feature limits the applicability of the model to credit
constrained developing economies and makes it irrelevant to explain the negative e¤ect over private credit
of the recent sovereign debt crises in the Euro zone.
Among the innovations of this paper is the possibility to make interesting predictions regarding thresholds
of sovereign debt sustainability. The analysis of past defaults shows that while some economies seem to be
able to manage very high debt-to-GDP ratios (Japan 160 percent in 2006), some other economies have
defaulted at ratios of external debt to GDP that would not be considered excessive for the typical advanced
economy: for example, Mexico’s 1982 debt crisis occurred at a ratio of debt to GDP of 47 percent, and
Argentina’s 2001 crisis at a ratio slightly above 50 percent. Furthermore, over half of the sovereign defaults
in the period 1970-2000 happened at debt-to-GDP ratios lower than 60 percent (Reinhart et al. (2003)).
Therefore it seems, as argued by Reinhart et al. (2003), that safe external debt-to-GDP thresholds vary
across countries and that there are clubs and regions of countries with di¤erent levels of vulnerability. The
di¤erences in vulnerability are also re‡ected in the "extreme duress many emerging markets experience at
debt levels that would seem manageable by advanced standards" a concept that Reinhart et al. (2003) call
"debt intolerance". In the current framework, I am able to provide a justi…cation for these phenomena by
considering two groups of countries that di¤er in their average quality of institutions. In this case, the results
show that countries that belong to "better clubs" are able to sustain higher levels of sovereign debt than
countries in the "not so good clubs".
The remainder of the paper is organized as follows: Section 2 presents the environment and describes the
model; Section 3 characterizes the possible equilibria and discusses the main results; Section 4 endogenizes the
quality of institutions, and explores the implications of the model in terms of sovereign debt sustainability;
and Section 5 concludes.
2
Environment
Consider a small open economy that lasts for three periods, t = 0; 1; 2. The economy is composed of a
government and a continuum of entrepreneurs. Both the government and the entrepreneurs have access to
the international …nancial market, which is composed of a continuum of identical foreign lenders.
The representative entrepreneur is risk neutral. He values public consumption in t = 1 and private
consumption in t = 2, and his preferences are given by:
U = v(G1 ) + C2 ;
(1)
where G1 and C2 are public and private consumption, respectively, with v 0 (G1 ) > 0, and v 00 (G1 ) < 0:
The representative entrepreneur owns a risky productive technology. The productive technology allows
the entrepreneur to get A(s)I1 units of consumption in t = 2 by investing I1 units of capital in t = 1. A(s);
with s = l; h; is an idiosyncratic shock realized at the beginning of t = 2 that takes the value A(h) = A > 0
with probability p(h) = p; and A(l) = 0, with probability p(l) = 1 p: Capital can be converted into
5
consumption goods at a one-to-one rate and it does not depreciate. ; p(s) and A(s) are public information.
At t = 1, the entrepreneur receives an endowment e1 ; which he can use to invest in the risky technology
or to pay taxes. Additionally, at t = 1 the entrepreneur gains access to the …nancial markets and can thus
borrow an amount D1 from the foreign lenders at the interest rate RE1 . The …nancial contract available to
the entrepreneur is collateralized by his assets, i.e. capital and the returns of his investment. Nevertheless,
the contract is subject to imperfect court enforcement: if the entrepreneur defaults, only a share i of his
assets can be seized by the foreign lenders and the rest is lost. The level of i with i = fG(Good); B(Bad)g
and G > B captures the quality of institutions within the country. The probability that i takes the
good value is given by ( G ) 2 (0; 1) and the probability that it takes the bad value is then (1
( G )):
( G ) is public information. Throughout the paper I refer to the quality of institutions in a broad sense.
In particular, in this framework the quality of institutions encompasses aspects such as: court enforcement,
creditor protection, investor pro…le, corruption, tax enforcement, etc.4
The problem of the representative entrepreneur can be generalized by allowing him to borrow, invest and
consume in both periods without a¤ecting the main results. Nevertheless, since these extensions obscure
the main mechanism without having any value added in terms of the question of interest, I abstain from
including them.
The government in this economy is benevolent and in‡uences the entrepreneurs’welfare through di¤erent
policy choices: public expenditure G1 ; sovereign debt S0 ; lump-sum taxes T1 ; and the repayment decision
over the sovereign debt z1 = f0 (def ault); 1 (repayment)g.
At t = 0, the government can contract sovereign debt S0 at the interest rate RS0 in order to …nance an
optimum amount of public good: In line with most of the sovereign debt literature, S0 is neither collateralized
nor subject to external enforcement. As a result, in the event of sovereign default, the foreign lenders do not
recover anything.
After contracting S0 , the government receives private information regarding the quality of institutions in
the country, i . There are several scenarios that can motivate both the fact that the government has private
information over i and that he only receives this information after S0 has been contracted. The simplest
scenario is to consider that when a new government comes to o¢ ce it needs more time to learn the quality
of institutions in the country than to decide on the policy of indebtedness. Another possible scenario is
that the new government inherits S0 from the previous government while i is a preference parameter of the
new government that re‡ects its willingness to enforce contracts. Finally, and probably the more plausible
scenario is that i is a choice of variable of the government. In Section 4.1, I thoroughly explore this last
alternative. In particular, I endogenize i by allowing the government to make (unobservable) investments
in the quality of institutions. The results from including this extension are completely analogous to the ones
from the simpler case where i is exogenous. Therefore, I consider the scenario with the exogenous i as the
benchmark case due to its higher tractability.
4 With respect to the speci…c aspect of creditor protection, Djankov, McLiesh, and Shleifer (2007) argue that in developing
countries, creditor protection is much poorer than in developed countries making it more di¢ cult for lenders to force repayment
or grab collateral. For example, while in the U.S. 70 percent of all commercial and industrial loans are collateralized (Berger
and Udell (1990)), in Argentina this …gure is reduced to only 10 percent (Fleisig (1996)).
6
At the beginning of t = 1, the sovereign debt matures and the government chooses whether to repay or
default. If the government chooses to repay, it can exercise its taxation power over the entrepreneurs’returns
and assets. Nevertheless, its taxation ability depends on the quality of institutions, i . In particular, one
can think that the the quality of institutions determines the level of corruption and the ine¢ ciencies in the
taxing technology that negatively a¤ect the ability to collect revenues of the government. This feature is
incorporated in the model by assuming that for each dollar of tax revenue, a proportion (1
i ) gets lost or
stolen. Then, for each dollar of …nancing needs, the government must collect 1i dollars in tax revenues from
the entrepreneurs. It is worth noting that even when considering the existence of corruption the government
is still benevolent, i.e. the corruption is performed by a third party like the bureaucrats, the tax payers, etc.
Foreign lenders maximize pro…ts from lending both to the government and to the entrepreneurs; they
face perfect competition and are risk-neutral. Therefore, the representative foreign lender is willing to lend
any amount of money to the local agents as long as he breaks even and recovers, in expected value, the
opportunity cost of his funds in the international market, which is equal to RW : The foreign lenders are
restricted by the information they observe and the set of …nancial contracts available. Their main restriction
in terms of information is that they do not observe the institutional quality in the country even though
they know the parameters that determine its probability distribution: f G ; B g and ( G ). Apart from this
exception, foreign lenders observe all the other relevant economic parameters: A(s); p, e1 ; and : The other
informational restriction regards the agents’actions: since the entrepreneurs operate in very atomistic and
anonymous markets, the foreign lenders cannot observe any of their actions. On the other hand, since the
government is a big player on the market, foreign lenders do observe the total amount of debt it contracts,
S0 ; and whether it repays it or not. In order to compensate for the informational restrictions, the foreign
lenders use all their knowledge about the economy and any kind of inference that they can make from the
behavior of the local agents to determine the interest rates, RS0 and RE1 , that maximize their pro…ts:
2.1
Timing
The timing of events in this economy is as follows. At t = 0 the foreign lenders set the sovereign interest rate,
RS0 . Given RS0 ; the government decides how much to borrow from the foreign lenders, S0 , in order to …nance
an optimum amount of public expenditure, G1 . The next period, t = 1; is divided into two subperiods. In
the …rst subperiod, the entrepreneurs receive their endowments, e1 ; and the government receives private
information regarding the institutional quality in the country, i . After learning i , the government decides
whether to repay or default on the sovereign debt, S0 ; and set the taxes, T . In the second subperiod, after
observing the repayment/default decision of the government, z1 ; the foreign lenders determine the interest
rate they charge to the entrepreneurs, RE1 : Given RE1 , the entrepreneurs decide how much they want to
invest, I1 ; and borrow, D1 : In the last period, t = 2; the entrepreneurs decide to repay or default on their
private loans and consume whatever resources they have left. Table 1 below shows the timing in a more
schematic way.
7
t=0
F L choose RS0
Gov borrows S0
t=1
E receive e1
Gov learns i
Gov repays or defaults: z1 ! T1
t=2
A(s) is realized
E repay D1
F L determine RE1
E borrow D1 and invest I1
Table 1: Timing of Main Events in the Economy
Where: Gov = Government
E = Entrepreneurs
F L = F oreign Lenders
3
Equilibrium
Given the timing of the events in the model, the equilibrium needs to be solved by backward induction. In
particular, I partition the problem in two subgames: one in which the agents taking as given the level of
sovereign debt solve for all the other decision variables; and the other one in which the government chooses
the level of sovereign debt taking as given the continuation implied for the other variables. In this section
I solve for the …rst subgame and leave the solution of the other subgame for Section 3.2. First, I solve the
problem of the representative entrepreneur since they are the last agents to make decisions in the economy:
given the interest rate, they choose how much to invest and borrow and whether to repay or default on their
debt: Second, I solve the problem of the foreign lenders that, after observing the government’s repayment
decision, decide on the interest rate at which they lend to the entrepreneurs. Third, I solve the problem of
the government that chooses whether to repay or default on the sovereign debt: Finally, I solve the second
problem of the foreign lenders that at t = 0 decide on the interest rate they lend to the government: After
solving all these maximizations, I de…ne the equilibrium for this economy and characterize it for all the
possible values of sovereign debt:
The entrepreneur maximizes his expected consumption by deciding how much to invest and borrow at
the second subperiod of t = 1 and whether to repay or default on his debt at t = 2. Then the entrepreneur’s
optimization problem for a given RE1 is:
max E1 [C2 (s)]
(2)
I1 ;D1
subject to
t = 1 : I1 = e1
T1 + D1
(3)
and
t = 2 : C2 (s) = max fA(s)I1 + I1
D1 RE1 ; 0g :
(4)
Since the representative entrepreneur cannot hide resources and all his assets are liquidated if he defaults,
8
the entrepreneur always prefers to repay his debt as long as it is feasible. Furthermore, the entrepreneur
would never choose a level of debt so high that it would force him to default in all states, s; since this would
imply zero consumption, an alternative that is inferior to just not contracting any debt at all. Nevertheless,
depending on the value of the parameters, the entrepreneur can prefer one of two possible situations:
i) fI1 ; D1 g are set such that the entrepreneur has enough resources to repay independently of s: In this
case the entrepreneur’s expected consumption is given by:
t = 2 : E1 [C2 (s)] = pAI1 (RE1 ) + I1 (RE1 )
RE1 (I1 (RE1 )
e1 + T1 )
(5)
and his optimum level of investment is:
I1 (RE1 ) = min
h
pA
RE1 1
i1 1
E1
(e1
; RR
E1 1
T1 ) ;
(6)
where the second element follows from the feasibility constraint when s = l.
ii) fI1 ; D1 g are set such that the entrepreneur can only repay if s = h. In this case, the entrepreneur’s
expected consumption is given by:
t = 2 : E1 [C2 (s)] = p [AI1 (RE1 ) + I1 (RE1 )
RE1 (I1 (RE1 )
e1 + T1 )]
(7)
and his optimum level of investment is:
I1 (RE1 ) =
h
A
RE1 1
i1 1
:
(8)
In order to focus only in the case where private lending is risky, from now on I assume that A >
1
(RW e1 )
: Intuitively, this assumption implies that the returns of the investment are so high that
the representative entrepreneur prefers to borrow a lot even if this implies the risk of having zero consumption
when the bad shock is realized.5
The next problem that needs to be analyzed is the decision of the foreign lenders, at the second subperiod
of t = 1; over the interest rate at which they are going to lend to the entrepreneurs, RE1 . Since foreign
lenders face perfect competition, in equilibrium, RE1 must be such that the foreign lenders break even by
recovering in expected value their opportunity cost RW .
In order to choose the interest rate that maximizes their pro…ts, the foreign lenders need to know the
recovery rate of their loans under each state of the world. Given the assumption over the productivity
parameter A; the foreign lenders know that entrepreneurs only repay their debts if they receive the good
(RW p)
p2
h
i 1
1
T1 ) is the solution to (6) since RpA 1
is not feasible, not
E1
1
h
i
h
i 1
1
1
even for the worst possible interest rate, i.e. RpW ; and for zero taxes: Then, since RA 1
> RpA 1
for all levels
E1
E1
i 1
h
1
of RE1 ; it follows that the entrepreneur maximizes his utility by choosing I1 (RE1 ) = RA 1
. This implies that the
E1
h
i 1
1
entrepreneur’s credit demand as a function of the interest rate is D1 (RE1 ) = RA 1
e1 + T1 :
5 Analytically,
the assumption implies that
RE1
RE1 1
(e1
E1
9
productivity shock and default otherwise. In this last case, the assets of the entrepreneur, which are equal
to the level of investment; are liquidated and distributed equally among his creditors. Then, from each
dollar lent to the entrepreneurs the foreign lenders recover a proportion D1 (Ri E1 ) : Nevertheless, since the
foreign lenders cannot observe neither I1 (RE1 ) nor D1 (Ri E1 ) ; they try to infer them indirectly. In the case of
I1 (RE1 ); since they know all the relevant parameters that determine investment they can calculate it from
(8) by anticipating the entrepreneurs’ behavior. On the other hand, further inspection of D1 (Ri E1 ) shows
that it depends on the unobservable i not only directly but also indirectly. The indirect dependence is a
result of T1 ; one of the determinants of D1 (RE1 ); being a function of the quality of institutions, as it will be
shown in the analysis of the government’s problem: From now on, I write D1 (RE1 ; i ) to make explicit the
dependence of the demand for credit on the institutional quality.
i
To make any inference about D1 (RE1
; i ) the foreign lenders need some beliefs regarding the unobservable
i : Their initial unconditional beliefs are given by the probability of the country of having the good quality
of institutions: ( G ): However, after observing z1 ; foreign lenders update these beliefs. In equilibrium, the
inference process is governed by a belief pattern, ( G =z1 ); that speci…es the updated probability that the
foreign lenders assign to the quality of institutions of being good for a given value of z1 observed. Using
( G =z1 ) foreign lenders calculate their conditional expectation on the recovery rate per dollar of observed
investment in the following way:
E1
h
i
D1 (RE1 ;
=z1
i)
i
= (
G =z1 ) D1 (RE1 ;
G
G)
+ (1
(
G =z1 )) D1 (RE1 ;
B
B)
:
(9)
Given this expectation, the interest rate, RE1 ; that allows the foreign lenders to break even in expected value
is such that:
i
h
i
=z
.
(10)
RW = pRE1 + (1 p)I1 (RE1 )E1 D1 (RE1
1
; i)
which cannot be solved for RE1 because investment depends non-linearly on the interest rate. Nevertheless,
by totally di¤erentiating (10), it becomes evident that a higher updated belief that the quality of institutions
is good, ( G =z1 ); reduces the interest rate the foreign lenders charge to the entrepreneurs. Then, it is possible
to see that the equilibrium private interest rate is a function of the updated beliefs: i.e. RE1 ( ( G =z1 )); which
implies that also the level of investment and the credit demand in equilibrium are a function of ( G =z1 );
i.e. I1 (RE1 ( ( G =z1 ))) = I1 ( ( G =z1 )) and D1 (RE1 ( ( G =z1 )); i ) = D1 ( ( G =z1 ); i ).
The next problem that needs to be analyzed is the government’s repayment decision at t = 1; which also
determines the level of taxes charged to the entrepreneurs: Since at this stage the government has already
learnt the quality of institutions in the country, the repayment decision can be contingent on this information,
i.e. z1 ( i ). At this point, it is worth noting the di¤erence between the government’s choice variable z1 ( i )
and the repayment decision observed by the foreign lenders z1 : The objective of the government is to choose
the optimum repayment decision in order to maximize the entrepreneurs’welfare:
z1 (
max
i );T1 ( i )
E1 [W ] = E1 [C2 (s; i )] ;
10
(11)
subject to
t = 1 : T1 ( i ) =
T1 ( i )
t = 2 : E1 [C2 (s; i )] = p [AI1 ( (
G =z1 ))
+ I1 ( (
z1 (
i )S0
;
(12)
e1 ; and
(13)
i
G =z1 ))(1
RE1 ( (
G =z1 )))
+ RE1 ( (
G =z1 )) (e1
T1 ( i ))] :
(14)
The optimum repayment decision, z1 ( i ); depends on the comparison of the costs and bene…ts of repaying
versus defaulting taking the belief pattern of the foreign lenders as given. Repayment is costly because it
absorbs resources that the entrepreneurs could use for investment. Besides, marginal repayment costs are
higher the lower the institutional quality since this implies that the tax burden on the entrepreneurs needs
to be higher for each dollar of sovereign debt. The di¤erences in marginal costs is what generates the single
crossing property in the model. Additionally, lower institutional quality implies that the feasibility constraint
implied by (12) and (13):
z1 S0 e1 i ;
(15)
binds for lower levels of sovereign debt, forcing the government to default at levels of indebtedness that
would be sustainable with better quality of institutions. In terms of the bene…ts, if in equilibrium the
observed repayment decision, z1 ; has an e¤ect over the welfare of the entrepreneurs, then the government
might have incentives to repay. The channel through which sovereign repayment can a¤ect the welfare of
the entrepreneurs is the belief of the foreign lenders about the quality of institutions. As previously argued
better beliefs imply a lower private interest rate, RE1 ( ( G =z1 ) and, consequently, higher investment and
consumption for the entrepreneurs. (The speci…c e¤ect of z1 on RE1 ( ( G =z1 )) in equilibrium is discussed
in the next section for each possible level of S0 .)
The trade-o¤ between the costs and bene…ts of sovereign repayment is re‡ected in the following incentive
compatibility constraint; the government prefers to repay as long as:
E1 [C2 (s; i )=z1 ( i ) = 0]
E1 [C2 (s; i )=z1 ( i ) = 1] :
(16)
While the feasibility constraint only depends on the parameters, the incentive compatibility constraint also
depends on the equilibrium levels of investment and interest rate under repayment and default. In particular,
replacing these values in (16), and rearranging we see that the incentive compatibility constraint holds for
levels of S0 such that:
S0
i
RE1 ( (
G =1))
[A(1
) [I1 ( (
G =1))
I1 ( (
G =0))]
+ e1 (RE1 ( (
G =1))
RE1 ( (
G =0)))] :
(17)
The expression between brackets in (17) represents the net bene…ts from sovereign repayment as a function
of the updated beliefs ( G =z1 ) : For future notational convenience I use 4 ( ( G =1) ; ( G =0)) in order to
refer to this expression. Combining (17) with the feasibility constraint, (15), gives us the following necessary
11
and su¢ cient condition for government repayment:
S0
n
min e1 i ; R
E1 (
i
(
4( (
G =1))
G =1) ;
(
o
G =0))
:
(18)
the government repays as long as the level of sovereign debt is below the two debt thresholds speci…ed.
From this condition it becomes evident that the government’s repayment decision changes with S0 as higher
levels of sovereign debt, by increasing the costs and reducing the bene…ts of repayment, make it harder for
this condition to hold. Additionally, since the two elements on the RHS of (18) depend on the institutional
quality, the decision of the government varies with i providing the signaling value to the sovereign default.
Finally, before moving to the characterization of equilibrium it is necessary to analyze the decision of the
foreign lenders over the interest rate at which they lend to the government, RS0 : Foreign lenders anticipate
that the repayment decision of the government depends on the level of sovereign debt and on the quality
of institutions. But since they do not observe i they can only set the interest rate as a function of S0 :
Since foreign lenders face perfect competition in equilibrium RS0 (S0 ) must be such that they break even by
recovering in expected terms their opportunity cost RW :
RW = RS0 (S0 )E[z1 =S0 ]:
(19)
Now that the problem for each of the agents has been analyzed, it is possible to de…ne the equilibrium
for this economy.
Given the level of sovereign debt, S0 ; a Weak Perfect Bayesian Equilibrium (WPBE) in pure strategies
for this economy is:
- a strategy pro…le: (z1 ( i ); T1 ( i )) ; (D1 ( ( G =z1 ); i ); I1 ( ( G =z1 ))) ; (RS0 (S0 ); RE1 ( ( G =z1 ))) ;
- and a belief pattern ( G =z1 ); such that:
i) (D1 ( ( G =z1 ); i ); I1 ( ( G =z1 ))) is a solution to the problem of the entrepreneurs given RE1 ( ( G =z1 )).
ii) (z1 ( i ); T1 ( i )) is a solution to the problem of the government given i and (RS0 (S0 ); RE1 ( ( G =z1 ))) .
iii) (RS0 (S0 ); RE1 ( ( G =z1 ))) satis…es in expected terms the zero pro…t condition of the foreign lenders
given ( G =z1 ); (z1 ( i ); T1 ( i )) and (D1 ( ( G =z1 ); i ); I1 ( ( G =z1 ))) :
iv) In equilibrium, beliefs, ( G =z1 ); are updated with Bayes rule, while out of equilibrium they may be
speci…ed arbitrarily.
3.1
Characterization of Equilibrium
The previous de…nition of WPBE allows for two types of equilibria depending on the information revealed
by the repayment decision of the government, z1 : pooling and separating. Within the pooling equilibria
the government always behaves in the same way independently of the institutional quality in the country.
Therefore the foreign lenders cannot make any inference on the quality of institutions, i ; from observing the
equilibrium repayment decision. There are two possible types of pooling equilibria in this setting, either the
government always repays or it always defaults. In contrast, within the separating equilibria, the repayment
decision of the government changes depending on its institutional quality allowing the foreign lenders to learn
12
the value of i from the observed z1 : There are also two possible types of separating equilibria in this setting,
either the government repays when the institutional quality in the country is good and defaults otherwise,
or vice versa. Only the …rst type constitutes an equilibrium in this economy.
For existence of equilibrium over the whole range of parameter values, I also need to allow for mixed
strategies over the repayment decision in the previous de…nition of WPBE. Within the mixed strategies
equilibria the government has di¤erent repayment probabilities, 0
( i ) 1; depending on the institutional
quality. This allows the foreign lenders to obtain partial or full information about i from the observed z1 : In
principle, there are many types of mixed strategies equilibria, but only one arises in this economy and only
arises for certain combinations of parameters. In this speci…c mixed strategies equilibrium the government
repays with certainty when the institutional quality is good while it only repays with a probability, ( B );
smaller than one when the institutional quality is bad.
In the next proposition, I characterize the type of equilibrium that arises for each possible value of
sovereign debt, S0 :
Proposition n1 Let’s de…ne:
n
o
n
o
o
P
S
4( ( G );0)
S
G 4(1;0)
B 4(1;0)
S = min e1 B ; B
S
=
min
e
;
;
S
=
min
e
;
;
and
:
1
G
1
B
RE1 ( ( G ))
RE1 (1)
RE1 (1)
Then, for
h values
i of S0 such that:
P
i) S0 2 0; S ; there exists a …rst type of pooling equilibrium in which the government always repays;
P
ii) S0 2 S ; S S ; there exists a mixed strategies equilibrium in which the government repays with
certainty when the institutional quality is high while it only repays with a probability ( B ) < 1 when the
A(1
)[I1 ( ( G =1)) I1 ( ( G =0))]
:
institutional quality is low. This interval exists for values of e1 > e1 =
RE1 ( ( G =0))
i
S
iii) S0 2 S S ; S ; there exists a separating equilibrium where the government only repays if the institutional quality is good and defaults otherwise;
S
iv) S0 > S ; there exists a second type of pooling equilibrium in which the government always defaults.
P
S
S S < S ; the pooling and the separating equilibria always exist and do not overlap while
Since 0 < S
the mixed strategies equilibrium only arises for speci…c combinations of parameters.
h
i
In these equilibria: RW = RS0 (S0 )E[z1 =S0 ] = pRE1 ( ( G =z1 ))+(1 p)I1 ( ( G =z1 ))E D ( ( Gi=z1 ); i ) =z1 :
1
Proof. See Appendix 7.2
3.1.1
Sovereign Repayment and Interest Rates
Information revelation within each equilibrium interval allows answering the central question posed in the
introduction: What triggers the …rms’ restricted access to foreign credit after sovereign defaults? In this
framework, the new negative information revealed through sovereign default triggers an increase in external private interest rates. Therefore, the signaling mechanism about the institutional quality provides an
explanation for the worsening of external credit terms to the private sector after default episodes. In particular, the level of information revelation increases with the level of sovereign debt in the interval 0; S S and
diminishes afterwards.
13
In this section, I illustrate the equilibrium properties of the government’s repayment decision, and the
private and sovereign interest rates that emerge from the equilibrium characterization. As stated in the
P
previous proposition, when e1 > e1 the interval in (ii) is non-empty and for values of S0 2 S ; S S there is
a mixed strategies equilibrium. Therefore, in the analysis of the equilibrium I consider both the case when
e1 > e1 and when e1 e1 ;
I begin by analyzing the government’s repayment decision as a function of S0 . Starting from very low
P
levels of S0 ; i.e. S0 S ; the government always prefers to repay its sovereign debt and has the necessary
resources to do it. Nevertheless, as S0 crosses some critical thresholds the repayment decision changes to
default. If the quality of institutions in the country is bad, the change happens at S S if e1
e1 ; or more
P
S
gradually throughout S ; S ; the mixed strategies’ interval, if e1 > e1 . If the quality of institutions is
S
good the change only happens at S ; the upper limit of the separating equilibrium. Figures 3 and 4 present
the behavior of the government as a function of S0 :
Good Institutions
Bad Institutions
Repayment
Decision
1
S
0
Pooling
1
Mixed
Strategies
Separating
Pooling
2
Figure 3: Repayment decision as a function of sovereign debt when e1 > e1
Good Institutions
Bad Institutions
Repayment
Decision
1
S
0
Pooling
Separating
1
Pooling
2
Figure 4: Repayment decision as a function of sovereign debt when e1
14
e1
The ex-post result of the repayment behavior of the government is an increasing level of information
revelation to foreign lenders in the interval 0; S S : Figures 5 and 6 show the private interest rate pattern
as a function of sovereign debt for each type of institutional quality. Within the pooling equilibrium there is
no information revelation from the sovereign repayment and RE1 ( ( G )) is the same independently of the
institutional quality. Additionally, RE1 ( ( G )) is increasing in S0 since the repayment of higher levels of
sovereign debt increases the leverage of the entrepreneurs reducing the recovery rate of the foreign lenders.
In contrast with the pooling equilibrium, in the separating equilibrium the quality of institutions is fully
revealed and the interest rate charged to the private sector di¤ers depending on the country’s institutional
quality as credit is perfectly priced. The interest rate in the repaying country increases with S0 throughout
the interval for the same reasons explained in …rst type of pooling. Finally, the case with mixed strategies
reveals partial information under repayment and full information under default. In terms of the interest
rates this means that the interest rate after default is the same as the default interest rate in the separating
equilibrium, while the interest rate after repayment decreases with the level of sovereign debt and lies between
the lowest interest rate of the separating case and the highest interest rate after repayment of the pooling
case. The decreasing pattern of the interest rate under the mixed strategies equilibrium is a consequence of
the assumption over the possible values of the quality of institutions since this makes the positive updating
e¤ect of repayment over ( G =1) stronger than the negative leverage e¤ect of the higher sovereign debt over
the foreign lenders recovery rate.
Good Institutions
Bad Institutions
S
Pooling
1
Mixed
Strategies
Separating
Pooling
2
Figure 5: Private interest rates as a function of sovereign debt when e1 > e1
15
Good Institutions
Bad Institutions
S
Pooling
Separating
Pooling
2
1
Figure 6: Private interest rates as a function of sovereign debt when e1
e1
As it is possible to observe from Figures 5 and 6, independently of the level of information revelation,
for all possible equilibria: RE1 ( ( G =1))
RE1 ( ( G =0)): Combining this result with the optimum levels
of investment and debt chosen by the entrepreneurs, it is possible to see that lower interest rates charged
@I1 (RE1 ( ( G =z1 )))
<0
by the foreign lenders imply higher investment and credit in the domestic economy: @R
( ( G =z1 ))
E1
@D (R
( (
=z ));
)
1
i
G
1i
E1
and
< 0 creating a link between the default/repayment decision of the government and
@RE1 ( ( G =z1 ))
the real economy: These e¤ects provide incentives for sovereign debt repayment even in this …nite horizon
setting.
While the ex-post repayment behavior of the government determines the pattern for private interest rate,
RE1 ( ( G =z1 )); the ex-ante result of this behavior is the pattern for the sovereign interest rate, RS0 (S0 ); as
a function of S0 : When lending to the government, the foreign lenders anticipate the expected repayment
probability for each level of sovereign debt and …x the sovereign interest rate accordingly. In particular, since
expected repayment probabilities decrease as S0 crosses each equilibrium threshold, the sovereign interest
rate, RS0 (S0 ); increases as a function of S0 : Figures 7 illustrates the pattern of RS0 (S0 ) for the cases when
e1 is larger than e1 ; I omit the other case since it is analogous to the one presented with the only di¤erence
that in this case the mixed strategies interval does not exist. The pattern of RS0 (S0 ) that results from the
model is consistent with the observed behavior of sovereign debt markets: as the level of sovereign debt
of a country increases, creditors ask for a higher interest rate to compensate for the increased default risk
(Arellano (2008)); however, above a certain critical debt level no premium can compensate investors for the
default risk, and credit rationing occurs (Eaton and Gersovitz (1981) and Zoli (2004)).
16
Infinity
S
Pooling
Mixed
Strategies
1
Separating
Pooling
2
Figure 7: Sovereign interest rate as a function of sovereign debt when e1 > e1
3.2
Optimum Level of Sovereign Debt
The solution for the previous subgame determines the equilibrium continuation values implied by each level of
sovereign debt: fz1 ( i ); T1 ( i ); RE1 ( ( G =z1 )); D1 ( ( G =z1 )),I1 ( ( G =z1 )); RS0 (S0 ); E1 [C2 (s; i )]g . Using
these values, it is now possible to analyze the other subgame, the optimization problem of the government
at t = 0 :
max E0 [W ] = v(G1 ) + E0 [C2 (s; i )] ;
(20)
S0
subject to
t = 0 : G1 =
S0
;
RS0 (S0 )
t = 1 : T1 ( i ) =
t = 2 : E0 [C2 (s; i )] = (
G )E1
[C2 (s;
z1 (
i )S0
i
G )]
+ (1
(21)
; and
(
(22)
G ))E1
[C2 (s;
B )] :
(23)
Since the government only receives information about the quality of institutions after choosing the level of
sovereign debt, there is no possible separation at this stage. Instead, as it is possible to see in (23), the
government must maximize the consumption of the entrepreneurs taking expectations over the institutional
quality (and also the productivity shock, s).
The optimum level of sovereign debt is determined by the trade-o¤ between higher public consumption
versus the higher costs of sovereign repayment or the potential negative e¤ects of default through the repayment signaling mechanism. Both the bene…ts and the costs associated with higher sovereign debt present
discontinuities iat speci…c values of sovereign debt. Public consumption grows continuously throughout the
S
S
interval 0; S at the rate R 1(S0 ) and collapses to zero at S + " as the sovereign interest rate becomes
S0
17
in…nity within the second type of pooling. Additionally, the growth rate of public consumption changes at
S S as the sovereign interest rate jumps from RW to R( WG ) :
The pattern of expected private consumption as a function of sovereign debt is illustrated in Figure 8,
for the case when e1
e1 . This pattern is determined by two e¤ects: the negative e¤ect of taxes and the
positive/negative expected e¤ect of the belief updating. Within the pooling equilibrium interval expected
private consumption decreases continuously with S0 as taxes grow and the updated beliefs of the foreign
lenders remain the same. But at S S expected private consumption can present a discontinuity and jump
up or down depending on whether the expectedie¤ect of the belief updating is positive or negative. Then,
S
throughout the separating equilibrium, S S ; S ; expected private consumption continues to decrease due
to the increasing taxes. Nevertheless, since now taxes are only paid if the quality of institutions is good,
S
the negative e¤ect over expected private consumption is smaller. Finally, from S onwards there is neither
belief updating nor sovereign repayment which means that expected private consumption is the same as
when there is no sovereign debt at all. Then, expected private consumption does not depend on the quality
of institutions and it is equal to:
E [C2 (s)] = p [AI1 ( (
G ))
+ I1 ( (
G ))
RE1 ( (
G ))(I1 (
(
G ))
e1 )] :
(24)
Without making further assumptions on the parameters and the entrepreneurs’valuation of public consumption it is not possible to determine the optimum value of S0 : Nevertheless, combining the analysis of
public consumption and expected private consumption under each level of sovereign debt allows to narrow
down the potential equilibrium values. In particular, it is necessary to analyze the points of discontinuity:
S S and S S : As previously mentioned, expected private consumption can fall or jump at S S :While the …rst
case does not rule out any level of sovereign debt in the interval (0; S S ), the second case allows to rule out
some values of S0 from the potential equilibrium values. Let’s de…ne:
d
H = E C (s; )=S S ; and
C
0
2
i
o
n
d
H ^ S 6= S S
Sb =
S0 : E0 [C2 (s; i )=S0 ] = C
0
(25)
(26)
b S S ) are never equilibrium values since both public and
then, the values of sovereign debt such that S0 2 (S;
d
H
expected private consumption within this interval are lower than at S S : In the speci…c case when C
E [C2 (s)] this implies that the …rst type of pooling never arises in equilibrium. Finally, private consumption
S
beyond S is again equal to E [C2 (s)] since there are neither taxes nor belief updating. Therefore, given the
S
concavity of v(:), welfare is higher for small enough levels of sovereign debt than for levels larger than S .
This means that the second type of pooling never arises in equilibrium.6
6 The analysis of the case with mixed strategies follows the same logic and the intervals excluded from the potential equilibrium
values are the same.
18
Expected
Consumption
S
Pooling
Separating
1
Pooling
2
Figure 8: Expected private consumption as a function of sovereign debt
4
Discussion
In this section, I discuss how to enrich the model by endogenizing the institutional quality and explore the
implication of the model in terms of sovereign debt sustainability for groups of countries that di¤er in the
parameters that determine the distribution of institutional quality.
4.1
Endogenous Institutional Quality
Allowing for the level of institutional quality to be a choice variable of the government is possibly the most
intuitive explanation for the government’s private information over i and also for the timing at which this
information is learnt in the model. In this section, I propose a reinterpretation and two minor modi…cations
of the environment in order to allow for this possibility. This approach is related to the recent work seeking to
explain the institutions that support …nancial markets and taxation by Rajan and Zingales (2003), Acemoglu
(2005) and Besley and Persson (2009). As in that work this section treats institutions as endogenous.7
In order to introduce these modi…cations, I …rst change the time preference parameter of the government, allowing it to di¤er from the one of the entrepreneurs and making it private information. Then, I
allow the government to make unobservable investments in order to improve the institutional quality in the
country. These modi…cations create an equilibrium where more patient governments prefer to invest more in
institutional quality since this brings bene…ts in the last period by reducing the costs of repaying sovereign
debt and increasing the chances that the entrepreneurs receive a lower interest rate. On the other hand,
7 The closest antecedents to this approach are Acemoglu (2005) and Besley and Persson (2009). In Acemoglu (2005) the
government raises taxes to spend on a mixture of transfers to the ruler and on productivity enhancing public goods that increase
future tax revenues. Weak states, where rulers have short time horizons, spend too little on productive public goods. Besley
and Persson (2009) extend this framework to allow for taxation institutions to be endogenous and for past investment in legal
and …scal capacity to constraint current policy decisions.
19
impatient governments prefer to invest less on institutional quality and instead use more resources for public
good consumption in period one.
Let’s consider a government that instead of being benevolent as before maximizes:
Wj =
j v(G1 )
2
j E0
+
[C2 (s;
1i ] ;
(27)
where j 1 is the government’s discount factor, not necessarily equal to the one of the entrepreneurs. At
t = 0, the government can contract sovereign debt S0 at interest rate RS0 (S0 ) in order to …nance an optimum
amount of public good and the investment in institutional quality: After contracting S0 but before deciding
on its uses, the government learns its discount rate j : In particular, j = f H ; L g where L < H and
( H ) is the probability of having the high discount rate:
The initial exogenous "stock" of institutional quality is given by 0 : Nevertheless, the government can
modify this stock by choosing how much to invest in institutional quality at t = 1. The level of investment is
given by 1i
0 where 1i ; the …nal "stock" of institutional quality, can take two possible values: 1B or 1G :
In order to simplify the analysis I set 1G > 1B = 0 : The cost of this investment is given by L( 1i
0 ),
0
where L(:) is an increasing convex function with L(0) = L (0) = 0. Since there is no depreciation of
institutional capacity 1i
0 is always non-negative. The amount invested in the quality of institutions is
unobserved and determines not only the strength of creditor protection but also the level of corruption and
ine¢ ciencies within the tax institutions.
Everything else in the model, decisions, timing and parameters, remains the same. Then, the solution of
the model including these modi…cations follows the same logic as before and it has to be solved by backward
induction.
Proposition 2 Let’s de…ne 1i ( j ) as the quality of institutions chosen when the discount rate is
i) 1i ( H ) = 1G is the dominant strategy when j = H ; as long as H is high enough;
ii) given that 1i ( H ) = 1G , 1i ( L ) = 1B is the dominant strategy when j = L ; as long as
enough.
More speci…cally, 1i ( H ) = 1G and 1i ( L ) = 1B as long as f L ; H g are such that:
v
S0
RS0 (S0 )
h
p 4( (
L
G =1);
v
(
S0
RS0 (S0 )
G =0))
L(
1G
z1 RE1 ( (
0)
1G =1))
S0
1B
i
H
min 1;
j,
L
then:
is low
h
i
S
p 4( ( 1G =1); ( 1G =0)) z1 RE1 ( ( 1G =1)) 0
1G
h
i
S
p 4( ( 1G =1); ( 1G =0)) z1 RE1 ( ( 1G =1)) 0
;
1B
(28)
iii) the equilibrium characterization is the same as in Proposition 1.
Proof. See Appendix 7.3.
4.2
Sovereign Debt Sustainability
The analysis of past defaults shows that while some economies seem to be able to manage very high debtto-GDP ratios (for instance, Japan’s ratio was 160 percent, in 2006, while Italy’s reached 120 percent in
2011) some other economies have defaulted at ratios of external debt to GDP that would not be considered
20
excessive for the typical advanced economy. For example, Mexico’s 1982 debt crisis occurred at a ratio of debt
to GDP of 47 percent, and Argentina’s 2001 crisis at a ratio slightly above 50 percent. Furthermore, over
50 percent of the sovereign defaults in the period 1970-2000 happened at debt-to-GDP ratios lower than 60
percent. Therefore it seems, as argued by Reinhart et al. (2003), that safe external debt-to-GDP thresholds
vary across countries and that there are clubs and regions of countries with di¤erent levels of vulnerability.
The di¤erences in vulnerability are also re‡ected in the "extreme duress many emerging markets experience
at debt levels that would seem manageable by advanced standards" a concept that Reinhart et al. (2003)
call "debt intolerance".
The simple structure of the model makes it easy to do interesting predictions regarding these phenomena.
Within the context of the model it is straightforward to interpret the sovereign debt boundaries of each
equilibria as thresholds that determine the sustainability or "safety" of sovereign debt: while within the
pooling equilibrium sovereign debt is fully sustainable and always repaid, as we move towards the mixed
strategies and separating equilibria, sovereign debt sustainability decreases as default probabilities increase.
In the present section, I analyze the consequences over these thresholds of assuming that countries belong
to separate groups that di¤er in their average quality of institutions. The objective of this modi…cation is to
capture the fact that foreign lenders are usually able to classify countries in some general frame as emerging
versus developed countries or whether the country belongs to Europe versus Latin America, but apart from
these major classi…cations it can be di¢ cult to compare Chile with Brazil or Greece with Portugal.
Let’s consider two countries x and y that belong to two di¤erent groups X and Y and assume, as in
the initial set up, that countries’institutional quality is exogenous and that i is private information: The
X
Y
groups of countries, X and Y; only di¤er in their average quality of institutions with
>
; but given
this average, the dispersion of the quality of institutions of the countries within each group is the same, i.e.:
Y
Y
X
X
G : As it was the case before, foreign lenders do not know whether x and y have good or bad
G = B
B
institutions but they know i distribution within each group and the group that each country belongs to.
Even though the results with this modi…cation are in many respects analogous to the ones obtained before,
there are signi…cant di¤erences in terms of the debt sustainability thresholds of each country.
Proposition 3 For all three types of equilibria (pooling, mixed strategies and separating):
i) the debt thresholds of country x are higher than the ones for country y; implying that countries that
belong or are believed to belong to better groups in terms of the quality of institutions are able to sustain
higher levels of sovereign debt; and
ii) the sovereign interest rates paid by country x are lower or equal than the ones paid by country y for
each level of S0 :
These results are mostly due to the stronger signaling e¤ect that the repayment/default decision has
for the country within the better group. To prove the …rst part of Proposition 4, I rewrite the quality
of institutions within group X as an improvement of size ! over the institutional quality of group Y; i.e.
X
Y
B = B + !; and evaluate the change over the limits of the equilibria as we increase this improvement.
From this rewriting it is straightforward to see that for the cases where the feasibility constraints determine
21
P
S
the limits of the equilibria, i.e. S = e1 B ; S S = e1 B and S = e1 G ; the sustainability limits are
always higher for the countries in the group with better average of institutions. For the cases when it is the
P
4( ( G );0)
incentive compatibility constraints the ones determining the limits of the equilibria, i.e. S = B
R ( ( G )) ;
E1
S
4(1;0)
G 4(1;0)
SS = B
RE1 (1) and S = RE1 (1) ; the derivatives of these limits with respect to ! also increase with the
average quality of institutions (the detailed steps to prove the positive sign of the derivatives are shown in
Appendix 7.4).8
@ B 4( ( G );0)
@ B 4(1;0)
@ G 4(1;0)
Since @!
RE1 ( ( G )) < @! RE1 (1) < @! RE1 (1) it is also possible to infer that the separating equilibrium interval is increasing proportionally more than the mixed strategies equilibrium interval, which is on its
own increasing proportionally more than the pooling equilibrium interval. The second part of Proposition 4
follows directly from the e¤ects of changing the limits of equilibria on the sovereign interest rate pattern.
5
Concluding Remarks
This paper represents a step towards a better understanding of the costs of sovereign debt crises. My model
is motivated by evidence from developing countries that sovereign defaults trigger a systematic tightening of
external …nancial constraints for the private sector. This paper provides a tractable framework to justify this
tightening through a signaling mechanism that o¤ers a new perspective on the links between institutional
quality, sovereign default, and the access to credit of private …rms in the country.
I argue that the repayment/default decision of the government provides new information to the foreign
lenders regarding the institutional quality in the country. Since the institutional quality a¤ects the recovery
rate of external private loans, foreign lenders change the debt contracts o¤ered to the private sector depending
on the information they receive from the repayment decision. Thus, the model can rationalize the reduced
access to international credit observed after default episodes as the result of the negative information revealed
to the foreign lenders. Furthermore, the connection between sovereign default and access to external private
credit provides a justi…cation for sovereign repayment even in this …nite horizon setting.
6
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24
7
7.1
Appendix
Correlation between di¤erent aspects of institutional quality
.2
Investor Protection
.4
.6
.8
1
Investor Protection and Control of Corruption
.2
.4
Non Defaulters
.6
Control of Corruption
Defaulters
.8
1
Fitted values
Sources: ICRG.
Defaults Considered: Argentina, Ecuador, Dominican Rep., Pakistan, Russia, Ukraine, Uruguay
Figure 9: Investor protection and control of corruption
7.2
Proof of Proposition 1
Let’s begin by assuming that the …rst type of pooling equilibrium, where the government always repays its
sovereign debt, does exist. Within this equilibrium, since the government always behaves in the same way
there is no information revelation and the foreign lenders’ updated beliefs after observing the repayment
decision just equals the unconditional beliefs, i.e. ( G =1) = ( G ). This implies that the after-repayment
private interest rate and investment of equilibrium are RE1 ( ( G )) and I1 (RE1 ( ( G ))); respectively: In
the o¤-equilibrium event of default, I assume that the foreign lenders believe that the government has bad
quality of institutions, that is ( G =0) = 0.
If this pooling equilibrium exists, the maximum level of sovereign debt that it can sustain is such that the
government is able and willing to repay even if thenquality of institutions
o is bad. According to (18), that means
P
B 4( ( G );0)
that S0 should be lower or equal than S = min e1 B ; R ( ( G )) : A su¢ cient condition for the interval
E1
i
h
P
to be non empty is to prove that 4( ( G ); 0) > 0: Recall that, for all S0 ; 4 ( ( G =1) ; ( G =0))
0; S
can be rewritten as the di¤erence between the expressions: AI1 (RE1 ( ( G =z1 ))) + I1 (RE1 ( ( G =z1 )))
RE1 ( ( G =z1 )) (I1 (RE1 ( ( G =z1 ))) e1 ) for z1 = 0, 1: The derivative of each of these expressions with
respect to the updated beliefs ( G =z1 ) is given by:
@[AI1 (RE1 ( (
G =z1 )))+I1 (RE1 (
( G =z1 ))) RE1 ( (
@RE1 ( ( G =z1 ))
25
G =z1 ))(I1 (RE1 (
(
G =z1 )))
e1 )] dRE1 ( ( G =z1 ))
;
d ( G =z1 )
(29)
which is positive since the …rst term equals
dRE1
=
d ( G =z1 )
p
(1 p)
+
1
1
I1 (RE1 )
RE1 1
h
I1 (RE1 ( (
I1 (RE1 )
(
G =z1 )
h
G =z1 )))
+ e1 < 0; and the last term is equal to:
G
D1 (T1 (
B
G ))
I1 (RE1 ) D1 (T1 (
G
D12 (T1 ( G ))
D1 (T1 (
G ))
B ))
+ (
i
B =z1 ) B
I1 (RE1 ) D1 (T1 (
D12 (T1 ( B ))
B ))
i <0
(30)
which is also negative. Since, ( G ) > 0; then 4( ( G ); 0) > 0 implying that this type of pooling equilibrium
always exist:
However, this is not the only possible type of pooling equilibria that can exist. There can also exist a
second type of pooling equilibria where the government always defaults independently of its institutional
quality. Therefore, there is no information revelation through the repayment decision z1 and after observing
the default, the foreign lender beliefs are again equal to the unconditional beliefs, what implies that the
equilibrium interest rate and investment are just equal to the ones in the previous pooling equilibrium: A
necessary and su¢ cient condition for the existence of this equilibrium is that the level of sovereign debt is
so high that government never has enough resources or incentives to repay even if the country has good
institutional quality.
Now, let’s assume the existence of a separating equilibrium where the government repays when the
institutional quality in the country is good and defaults otherwise. Then, in this equilibrium, foreign lenders
learn the exact value of i from the repayment decision of the government, that is ( G =1) = 1 and ( G =0) =
0. This implies that the equilibrium private interest rate and the equilibrium level of investment, are RE1 (1)
and I1 (RE1 (1)); respectively.
For this equilibrium to exist the level of sovereign debt has to be such that it makes it too costly for
the government with bad quality of institutions to repay S0 while the government with good quality of
institutions is still able and willing to repay. The fact that it must be too costly for the government with bad
quality of institutions to repay provides a lower bound on S0 : In particular, from combining the repayment
condition with the equilibrium
and interest rate under separating, we get that S0 must
n values for investment
o
4(1;0)
be higher than S S = min e1 B ; B
for
the
government
with bad quality of institutions to default.
RE1 (1)
On the other hand, the repayment condition
with the good quality of institutions provides
n of the government
o
S
S
G 4(1;0)
an upper bound on S0 equal to S = min e1 G ; R (1) : For values of S0 > S , the government always
E1
defaults independently of i ; which, as previously mentioned,
i cannot constitute an equilibrium. SVisual
S
S
inspection of the limits of the separating equilibrium S ; S shows that S S is always lower than S since
B < G . Then, this equilibrium always exists.
P
From the comparison of S and S S , it is possible to see that these limits coincide when the feasibility
constraint of the government with bad quality of institutions is tighter than the incentive compatibility
constraint. In particular this happens when the level of endowment of the entrepreneurs is lower or equal
P
A(1
)[I1 ( ( G =1)) I1 ( ( G =0))]
4( ( G );0)
B 4(1;0)
than
: In this case: S = S S = e1 B ; since B
RE1 ( ( G =0))
RE1 ( ( G )) < RE1 (1) : To
prove this inequality, …rst of all, it is possible to observe that RE1 ( ( G )) RE1 (1) since the expected loan
26
recovery in the event of a bad shock is lower under pooling:
E
h
i
D1 ( (
G );
i h
=1
= (
i)
<
G) D ( (
1
G
D1 (1;
+ (1
G ); G )
h
I
(1)
=
E
D
G) 1
(
G
i
1 (1;
G )) D ( (
i1
i)
B
=1
G ); B )
i
I1 ( (
G ))
:
(31)
Then a su¢ cient condition for the interval to exist is to prove that 4( ( G ); 0) 4(1; 0): Recalling (17) and
simplifying, the su¢ cient condition becomes 4(1; ( G )) 0; which is always true given the same argument
P
used to prove the existence of the pooling equilibrium. Then when S = e1 B ; the upper limit of the pooling
equilibrium coincides with the lower limit of the separating equilibrium.
However, when the incentive compatibility constraint of the government with bad quality of institutions is
P
4( ( G );0)
S
tighter than the feasibility constraint, then these limits do not coincide, i.e. S = B
R ( ( G )) 6= S : In this
E1
P
case, there exists a non-empty interval, S ; S S ; between the pooling and the separating equilibria. Within
this interval, the government is still able to repay but if the quality of institutions is bad it does not have
enough incentives to repay with certainty. Nevertheless, if the private interest rate after repayment is low
enough it can still make sense for the government in the country with bad quality of institutions to repay with
a positive probability lower than one giving rise to a mixed strategies equilibrium. A su¢ cient condition for
1
+ B . Intuitively this condition requires the possible values of institutional
this is that : G
h
i 1
1
A
RW
e1
1
quality to be su¢ ciently di¤erent. From now on I assume that the su¢ cient condition holds which guarantees
P
the existence of a mixed strategies equilibrium in thes interval S ; S S where the government repays with
certainty when the institutional quality is high while it only repays with a probability smaller than one ( B )
when the institutional quality is low. This implies that after observing a default, the foreign lenders are
certain that the country has bad institutional quality; whereas after observing repayment their information
is still incomplete, even though they are more informed than under the pooling equilibrium.
The fact that the incentive compatibility constraint of the government with bad quality of institutions
binds:
A(1
)I1
(
G)
+ RE1
(
G)
e1
S0
)I1 (0) + RE1 (0)e1 ;
(32)
implies that the incentive compatibility constraint of the government with good quality of institutions is
slack:
P
P
A(1
)I1 (1) + RE1
(1) e1 SG0 > A(1
)I1 (0) + RE1
(0)e1
(33)
(
G )+(1
(
G ))
(
B)
(
G )+(1
(
G ))
(
B)
B
= A(1
and that the respective repayment probabilities are 0 < ( B ) < 1 and ( G ) = 1: Given these probabilities the updated beliefs of the foreign lenders conditional on repayment and default become
( G =1) =
( G)
and
(
=0)
=
0;
which
implies
the
following
expected
recovery
rates
per
dollar of
G
( G )+(1
( G )) ( B )
observed investment:
h
i h
i
E D ( ( iG ); i ) =1 =
( G =1) D ( ( GG ); G ) + (1
( G =1)) D ( ( BG ); B ) I1 ( ( G ))
1
1
1
h
i
(34)
E D ( ( iG ); i ) =0 = D (1;B B ) I1 (0)
1
1
27
By totally di¤erentiating (32):
hh
@I1 ( ( G =1))
S0
A(1
) I1 1 ( ( G =1)) @R
( G =1)) + e1
E1 (
B
h
@I1 ( ( G =1))
+ A(1
) I1 1 ( ( G =1)) @R
+
e
1
( G =1))
E1 (
where it is possible to observe that (
d ( B)
=
dS0
hh
A(1
) I1
1
(
(
Which follows from: A(1
) I1
0 within the relevant interval; and
7.3
(
h
(
@RE1 (
S0
B
i
( G =1))
RE1 ( ( G =1))
@S0
i B
@RE1 ( ( G =1))
d ( B) =
@ ( B)
dS0
0
;
(35)
is always decreasing in S0 :
@I1 ( ( G =1))
G =1)) @RE1 ( ( G =1))
@RE1 ( ( G =1))
@ ( B)
1
B)
i
A(1
) I1
1
(
S0
+ e1
(
B
@RE1 (
(
@E D ( (
1
i
=
@RE1 (
(
@S0
G =1))
@I1 ( ( G =1))
G =1)) @RE1 ( ( G =1))
@I1 ( ( G =1))
G =1)) @RE1 ( ( G =1)) +e1
@RE1 ( ( G =1))
@ ( B)
i
S0
B
=
=1
S0
+ e1
(
@E D ( (
1
@ (
G =1))
G ); i )
D1 (
RE1 (
B
G =1))
i
G ); i )
B)
i
< 0;
(
G =1))
B
i
< 0:
(36)
@RE1 (
(
@S0
G =1))
=1
> 0:
Proof of Proposition 2
The proof of Proposition 2 involves two steps:
i) A proof that 1i ( H ) = 1G is always a dominant strategy; and
ii) A proof that 1i ( L ) = 1B is a dominant strategy given 1i ( L ) = 1G:
For both cases it is necessary to verify that this is the case at each relevant interval of S0 .
i) 1i ( H ) = 1G is always a dominant strategy as long as it is dominant 8 1i ( L ).
For the case when 1i ( L ) = 1B ;this requires that:
WH (
1G = 1i ( L )
=
1B )
WH (
1B = 1i ( L )
=
1B ):
(37)
This combination implies the following:
If 1i ( H ) = 1G the equilibrium characterization is the same as in Proposition 1
If 1i ( H ) = 1B ; 8S0 ; there is a pooling equilibrium where both governments always default and
( G =z1 ) = 0
Replacing the corresponding levels of public and private consumption into (37) for each of the intervals
implies that the necessary and su¢ cient condition for the patient government to choose 1G given 1i ( L ) =
1B is:
S
H
For the case when
1i ( L )
=
WH (
0
v
v R (S
)
h S0 0
p 4( ( G =1); (
1G ;this
S0
RS0 (S0 )
L(
1G
G =0)) z1 RE1 (1)
0)
S0
1G
i:
(38)
requires that:
1G = 1i ( L )
=
1G )
WH (
28
1B = 1i ( L )
=
1G ):
(39)
>
This combination implies the following:
If 1i ( H ) = 1B the equilibrium characterization is the same as in Proposition 1
If 1i ( H ) = 1G ; 8S0 ; there is a pooling equilibrium where both governments always default and
( G =z1 ) = 1:
Replacing the corresponding levels of public and private consumption into (39) for each of the intervals
implies that the necessary and su¢ cient condition for the patient government to choose 1G given 1i ( L ) =
1G is:
S
H
0
v R (S
v
)
h S0 0
p 4( ( G =1); (
S0
RS0 (S0 )
L(
1G
G =0)) z1 RE1 (1)
0)
S0
1B
i:
(40)
Combining (38) and (40):
S
max
H
0
v R (S
v
)
h S0 0
p 4( ( G =1); (
S0
RS0 (S0 )
G =0))
L(
0)
1G
z1 RE1 (1)
S0
1B
ii) The impatient government is better o¤ choosing
WL (
1B = 1i ( H )
=
1G )
S
0
v R (S
v
)
i ; h S0 0
p 4( ( G =1); (
S0
RS0 (S0 )
G =0))
L(
1G
z1 RE1 (1)
0)
S0
1G
given that the patient choose
1B
> WL (
1G = 1i ( H )
=
i
:
1G ;
(41)
as long as:
1G ):
(42)
This combination implies the following:
If 1i ( L ) = 1B the equilibrium characterization is the same as in Proposition 1.
If 1i ( L ) = 1G ; 8S0 ; there is a pooling equilibrium where both governments always default and
( G =z1 ) = 1:
Replacing the corresponding levels of public and private consumption into (42) for each of the intervals implies that the necessary and su¢ cient condition for the impatient government to choose 1B given
1i ( H ) = 1G is:
S
S
L
0
0
v R (S
v R (S
L( 1G
S0 0 )
S0 0 )
h
p 4( ( G =1); ( G =0)) z1 RE1 (1)
Combining (41) and (43) gives the …nal condition for the
S
L
7.4
S
0
0
v R (S
v R (S
L( 1G
S0 0 )
S0 0 )
h
p 4( ( G =1); ( G =0)) z1 RE1 (1)
0)
S0
1B
i
H
0)
S0
1B
i:
(43)
j s:
min 1;
h
i
S
p 4( ( G =1); ( G =0)) z1 RE1 (1) 0
1G
h
i
S
p 4( ( G =1); ( G =0)) z1 RE1 (1) 0
:
(44)
1B
Proof that sustainability thresholds increase with !
In order to be able to obtain closed form solutions of the derivatives I have simpli…ed the private loan
contract. Throughout this section I assume that if the entrepreneurs default on their private debt, the
foreign lenders can only seize a proportion i D1 from their assets. This way the private interest rate
e
becomes: RE1 ( ( G =z1 )) = RW (1p p) (z1 ) ; where e(z1 ) = ( G =z1 ) G + (1
( G =z1 )) B :
29
The derivatives of the limits of the equilibria with respect to ! lead to the following expressions:
P
@S
@!
=
@S S
@!
=
S
@S
@!
=
h
h
h
B (1
h
i
1
1
I
(1)
I
(0)
2
(A ) (R 1 (1) 1)2 p (R 1 (0) 1)2 p > 0; (45)
E1
E1
i
i
h
I1 1 (0)
I1 1 (1)
2
p)
B (1 p)
4(1; 0) + RE1 (1) (A ) (R (1) 1)2 p (R (0) 1)2 p > 0;
(46)
1)2 p
E1
E1
i
h
i
I1 1 (1)
I1 1 (0)
2
p)
(1 p)
4(1; 0) + RGE1
> 0:
(47)
(1) (A )
1)2 p
(R (1) 1)2 p
(R (0) 1)2 p
RE1 (1)
+
p)
(RE1 (1) 1)2 p
1
RE1 (1)
+
B (1
(RE1 (1)
1
RE1 (1)
+
G (1
(RE1 (1)
1
i
4( (
G ); 0)
+
B (1
p)
RE1 (1)
E1
E1
While the …rst term of the right hand side is trivially positive, the sign of the second term is not so clearly
determined and deserves further exploration. In particular, if the expression between brackets is positive,
then the whole expression is also positive. The condition for the expression between brackets to be positive
can be written as:
RW
(1
2
Y
p) e (0) + !
p
RW
RW
A p
Y
(1 p) e (1)+!
RW
Y
(1 p) e (0)+!
Y
(1 p) e (1)+!
p
p
>
p
Y
p) e (1) + !
(1
Which is equivalent to:
RW
1
2
>
RW
RW
Y
(1 p) e (0)+!
Y
(1 p) e (1)+!
where the inequality holds since the ratios are higher than one.
30
2
p
RW
p
p
A p
Y
(1 p) e (0)+!
1
p
:(48)
1
;
(49)