The full text on this page is automatically extracted from the file linked above and may contain errors and inconsistencies.
Working Paper Series
Sudden Stops, Time Inconsistency, and
the Duration of Sovereign Debt
WP 13-08
Juan Carlos Hatchondo
Indiana University and Federal
Reserve Bank of Richmond
Leonardo Martinez
International Monetary Fund
This paper can be downloaded without charge from:
http://www.richmondfed.org/publications/
Sudden Stops, Time Inconsistency, and the Duration of
Sovereign Debt∗
Juan Carlos Hatchondo
Indiana U. and Richmond Fed
Leonardo Martinez
IMF
July 13, 2013
Working Paper No 13-08
Abstract
We study the sovereign debt duration chosen by the government in the context of
a standard model of sovereign default. The government balances increasing the
duration of its debt to mitigate rollover risk and lowering duration to mitigate the
debt dilution problem. We present two main results. First, when the government
decides the debt duration on a sequential basis, sudden stop risk increases the
average duration by 1 year. Second, we illustrate the time inconsistency problem
in the choice of sovereign debt duration: Governments would like to commit to
a duration that is 1.7 years shorter than the one they choose when decisions are
made sequentially.
Keywords: sovereign debt, default, sudden stops, debt dilution, time inconsistency, debt maturity
JEL Codes:
This is an author’s original manuscript of an article published in the International Economic Journal [copyright Taylor & Francis]; The International Economic Journal article is available online at
http://www.tandfonline.com/doi/full/10.1080/10168737.2013.796112. The views expressed herein are those
of the authors and should not be attributed to the IMF, its Executive Board, or its management, the Federal
Reserve Bank of Richmond, or the Federal Reserve System.
E-mails: juanc.hatchondo@gmail.com; leo14627@gmail.com.
∗
1
Introduction
We study the optimal duration of sovereign debt using a model of sovereign defaults à
la Eaton and Gersovitz (1981) augmented to allow for long-term debt. This model allows
us to capture a trade-off in sovereign debt management.1 On the one hand, governments
(particularly in emerging economies) are subject to significant rollover risk—i.e., governments
face significant variations in the cost at which they can borrow. This indicates that it would
be convenient for these governments to borrow using longer-term instruments. On the other
hand, longer-term debt instruments strengthen the debt dilution problem (see Hatchondo
et al., 2010b and the references therein). This problem arises because when the government
borrows it does not internalize as a cost the effect of current borrowing decisions on the value
of debt claims issued in prior periods. This induces the government to expand its borrowing
and pay higher interest rates on its debt. If, instead, the government could commit to a path
of borrowing levels, it would internalize how borrowing decisions undertaken t periods ahead
affect borrowing opportunities between the current period and period t-1.2 The debt dilution
problem can also be mitigated by issuing shorter-term debt (Hatchondo and Martinez, 2009).
In the extreme case in which the government only issues one-period bonds, current borrowing
decisions cannot dilute debt because the government has already repaid its debt before any
new debt is issued.
As Arellano and Ramanarayanan (2012), we study a model in which the government can
issue both one-period bonds and bonds promising an infinite stream of coupon payments that
decrease at the same constant rate. Thus, each period, by choosing the levels of one-period
and long-term debt, the government chooses the duration of its debt. We use the calibration
presented by Bianchi et al. (2012), which uses Mexico as a reference, and produce simulation results that replicate distinctive features of economies facing default risk: a high and
countercyclical spread, a high consumption volatility, and a countercyclical trade balance.
We first show that the presence of sudden stops significantly increases the government’s
debt duration. The debt composition chosen in the economy without sudden stops implies
1
For a discussion of the relevant tradeoffs for choosing the optimal maturity of sovereign debt see Niepelt
(2008) and Broner et al. (2013).
2
Hatchondo et al. (2011) discuss how governments could gain from committing to debt ceilings.
1
an average duration of 4.5 years. The debt composition chosen in the economy with sudden
stops implies an average duration of 5.4 years.3
We also investigate how the debt duration chosen by the government differs from the
ex-ante optimal duration. We find that sudden stops also play a critical role in shaping the
optimal ex-ante duration. The government prefers to commit to an average duration of 0.8
years in the economy without sudden stops and to an average duration of 3.7 years in the
economy with sudden stops.
Our results indicate that the government would like to commit to a duration significantly
shorter than the one it chooses sequentially. In the economy with sudden stops, the duration
chosen by the government is almost 2 years longer than the one the government would like
to commit to. Similarly, in the economy without sudden stops, the government chooses a
duration that is on average almost 4 years longer than the one the government would like to
commit to.
Why does the government choose a duration longer than the one to which it would like
to commit? This occurs because of a time inconsistency problem similar to the debt dilution
problem discussed above. The debt dilution problem increases the value of committing to
a shorter debt duration that allows the government to pay a lower spread. However, when
the government decides on a sequential basis, it does not internalize the effects that the debt
duration chosen in a given period has on the borrowing opportunities available in previous
periods. Therefore, the government typically chooses a duration longer than the optimal exante duration. Our results cast doubt on the convenience of policies to increase the duration
of sovereign debt for economies facing significant sovereign risk.
We add to the results presented by Arellano and Ramanarayanan (2012) and Hatchondo
and Martinez (2009) by comparing the optimal durations with and without sudden stops,
and comparing the durations the government chooses sequentially with the ex-ante optimal
ones. They only consider model economies without sudden stops and do not compare the
ex-ante optimal durations with the ones the government chooses when it makes decisions on
a sequential basis.
3
Durations are computed using the average spread in the simulations as a weighted average of the
durations of short and long bonds, where the weight for each duration is given by the weight of each bond
on the total debt level.
2
Chatterjee and Eyigungor (2012) and Hatchondo et al. (2010b) present robustness exercises to their main results, indicating that one-period bonds are better than long-duration
bonds in their benchmark economies because these economies do not have rollover crises.
For a parameterization based on Argentina, Chatterjee and Eyigungor (2012) show that the
government prefers bonds with a five-year maturity over bonds with a one-quarter maturity when the probability of a self-fulfilling rollover crisis is high enough. Hatchondo et al.
(2010b) show that the government prefers bonds with an average duration of 4.2 years over
one-quarter bonds when the probability of a sudden stop is high enough. The results in this
paper add to their insight by showing that even in economies where the government would
want to commit to short-term debt, when it decides on a sequential basis, it chooses a debt
composition with a significantly larger debt duration.
The rest of the article proceeds as follows. Sections 2 and 3 present the model and its
calibration. Section 4 discusses how we solve the model. Results are presented in section 5.
Section 6 concludes.
2
Model
This section presents a dynamic small-open-economy model in which the government
can issue non-state contingent defaultable debt of short and long maturity. The economy’s
endowment of the single tradable good is denoted by y ∈ Y ⊂ R++ . This endowment follows
a Markov process.
We consider a benevolent government that maximizes:
Et
∞
X
β j−tu (cj ) ,
j=t
where E denotes the expectation operator, β denotes the subjective discount factor, and
ct represents consumption of private agents. The utility function is strictly increasing and
concave.
The timing of events within each period is as follows. First, the income and sudden-stop
shocks (to be described below) are realized. After observing these shocks, the government
3
chooses whether to default on its debt and makes its portfolio decision subject to constraints
imposed by the sudden-stop shock and its default decision.
During a sudden stop, the government cannot issue new debt and suffers an income loss
of φs (y). The government can buy back debt while in a sudden stop. Sudden stops intend to
capture sharp reversals in capital flows that have been observed in emerging economies. A
default model without sudden stops still features rollover risk but for standard calibrations
cannot replicate the magnitude and frequency of the reversals in capital flows observed in
the data. As in Bianchi et al. (2012), the sudden-stop shock follows a Markov process so
that a sudden stop starts with probability π ∈ [0, 1] and ends with probability ψ s ∈ [0, 1].
As in Arellano and Ramanarayanan (2012), we assume that the government can issue
both one-period and long-duration bonds. A long-duration bond issued in period t promises
an infinite stream of coupons that decrease at a constant rate δ. In particular, a long bond
issued in period t promises to pay (1 − δ)j−1 units of the tradable good in period t + j, for
all j ≥ 1. Hence, long-bond dynamics can be represented as follows:
bLt+1 = (1 − δ)bLt + iLt ,
where bLt is the number of long-bond coupons due at the beginning of period t, and iLt is the
number of long bonds issued in period t.
Let bSt denote the number of short bonds at the beginning of period t. The budget
constraint conditional on the government having access to credit markets is represented as
follows:
ct = yt − bSt − bLt + bSt+1 qtS + iLt qtL ,
where qtM is the price of a bond of maturity M ∈ {S, L}, which in equilibrium depends on
the exogenous shocks and the policy pair (bSt+1 , bLt+1 ).
When the government defaults, it does so on all current and future debt obligations.
This is consistent with the observed behavior of defaulting governments and it is a standard
4
assumption in the literature.4 As in most previous studies, we also assume that the recovery
rate for debt in default (i.e., the fraction of the loan lenders recover after a default) is zero.5
A default event triggers exclusion from credit markets for a stochastic number of periods.
Income is given by y −φd (y) in every period in which the government is excluded from credit
markets because of a default. Thus, as in Bianchi et al. (2012), the income level of an economy
in default is independent of whether the economy is facing a sudden stop. This implies that
the income loss triggered by a default is effectively lower for an economy facing a sudden
stop (since the sudden-stop income would be y − φs (y) in case the government repays). This
assumption is justified because the income losses during both defaults and sudden stops
intend to capture local disturbances caused by the loss of access to international credit
markets. This assumption also allows the model to capture the fact that some but not all
sudden stops trigger defaults. The government does not have access to debt markets in the
default period and then regains access to debt markets with constant probability ψ d ∈ [0, 1].
Foreign investors are risk-neutral and discount future payoffs at the rate r. Bonds are
priced in a competitive market inhabited by a large number of identical lenders, which implies
that bond prices are pinned down by a zero-expected-profit condition.
The government cannot commit to future (default and borrowing) decisions. Thus, one
may interpret this environment as a game in which the government making decisions in
period t is a player who takes as given the (default and borrowing) strategies of other players
(governments) who will decide after t. We focus on Markov Perfect Equilibrium. That is,
we assume that in each period the government’s equilibrium default, borrowing, and saving
strategies depend only on payoff-relevant state variables.
4
Sovereign debt contracts often contain an acceleration clause and a cross-default clause. The first
clause allows creditors to call the debt they hold in case the government defaults on a debt payment. The
cross-default clause states that a default in any government obligation constitutes a default in the contract
containing that clause. These clauses imply that after a default event, future debt obligations become
current.
5
Yue (2010) and Benjamin and Wright (2008) present models with endogenous recovery rates.
5
2.1
Recursive Formulation
We now describe the recursive formulation of the government’s optimization problem.
The sudden-stop shock is denoted by s, with s = 1 (s = 0) indicating that the economy is
(is not) in a sudden-stop.
Let V denote the value function of a government that is not currently in default. For any
bond price function q, the function V satisfies the following functional equation:
V (bS , bL , y, s) = max V R (bS , bL , y, s), V D (y, s) ,
(1)
where the government’s value of repaying is given by
V R (bS , bL , y, s) =
max
bS′ ≥0,bL′ ≥0,c≥0
subject to
u (c) + βE(y′ ,s′ )|(y,s) V (bS′ , bL′ , y ′, s′ )
(2)
c = y − sφs (y) − bS − bL + q S (bS′ , bL′ , y, s)bS′ + q L (bS′ , bL′ , y, s) bL′ − (1 − δ)bL ,
and if s = 1, bL′ − (1 − δ)bL ≤ 0, and bS′ = 0.
The value of defaulting is given by:
V D (y, s) = u y − φd (y) + βE(y′ ,s′)|(y,s) (1 − ψ d )V D (y ′, s′ ) + ψ d V (0, 0, y ′, s′ ) .
(3)
ˆ one-period
The solution to the government’s problem yields decision rules for default d,
debt b̂S , long-term debt b̂L , and consumption ĉ. The default rule dˆ is equal to 1 if the
government defaults, and is equal to 0 otherwise.
In a rational expectations equilibrium (defined below), investors use these decision rules
to price debt contracts. Because investors are risk neutral, the bond-price functions solve
the following functional equations:
h
i
ˆ S′ , bL′ , y ′ , s′)
q S (bS′ , bL′ , y, s)(1 + r) = E(y′ ,s′)|(y,s) 1 − d(b
6
(4)
and
h
ih
i
ˆ S′ , bL′ , y ′, s′ ) 1 + (1 − δ)q(bS ′′ , bL ′′, y ′, s′ ) , (5)
q L (bS′ , bL′ , y, s)(1 + r) = E(y′ ,s′ )|(y,s) 1 − d(b
′′
′′
where bS = b̂S (bS′ , bL′ , y ′, s′ ) and bL = b̂L (bS′ , bL′ , y ′, s′ ).
Equations (4) and (5) indicate that in equilibrium, an investor has to be indifferent
between selling a government bond today and investing in a risk-free asset, and keeping the
bond and selling it next period. If the investor keeps a one-period bond and the government
does not default in the next period, he receives a payment of one unit. If the investor keeps
a long-term bond and the government does not default in the next period, he first receives a
one unit coupon payment and then sells the bond at market price, which is equal to (1 − δ)
times the price of a bond issued next period.
2.2
Recursive Equilibrium
A Markov Perfect Equilibrium is characterized by
1. A set of value functions V , V R and V D ,
ˆ borrowing b̂S and b̂L , and consumption ĉ,
2. Rules for default d,
3. And bond price functions q S and q L ,
such that:
ˆ b̂S , b̂L , ĉ, and the value
i. Given bond price functions q S and q L , the policy functions d,
functions V , V R , V D solve the Bellman equations (1), (2), and (3).
ˆ b̂S , and b̂L , the bond price functions q S and q L satisfy equations
ii. Given policy rules d,
(4) and (5).
7
3
Calibration
The utility function displays a constant coefficient of relative risk aversion, i.e.,
c1−γ − 1
, with γ 6= 1.
u (c) =
1−γ
The endowment process follows:
log(yt ) = (1 − ρ) µ + ρ log(yt−1 ) + εt ,
with |ρ| < 1, and εt ∼ N (0, σǫ2 ).
As in Arellano (2008), we assume an asymmetric cost of default φd (y), so that it is
proportionally more costly to default in good times. This is a property of the endogenous
default cost in Mendoza and Yue (2012). Chatterjee and Eyigungor (2012) shows that this
property allows the equilibrium default model to match the behavior of the spread in the
data. In particular, we assume a quadratic loss function for income during a default episode
φd (y) = d0 y + d1 y 2, as in Chatterjee and Eyigungor (2012). As in Bianchi et al. (2012), we
assume that the income loss during a sudden stop is a fraction of the income loss after a
default: φs (y) = λφd (y).
Table 1 presents the benchmark values given to all parameters in the model. A period in
the model refers to a quarter. The coefficient of relative risk aversion is set equal to 2, and
the risk-free interest rate is set equal to 1 percent. These are standard values in quantitative
business cycle and sovereign default studies.
The average duration of sovereign default events is three years (ψ d = 0.083), in line with
the duration estimated in Dias and Richmond (2007). We study economies with and without
sudden stops. In the economies with sudden stops, there is one sudden stop every 10 years,
in line with the frequency estimated by Bianchi et al. (2012) and Jeanne and Ranciere (2011).
We set ψ s to match the duration of sudden stops in the data. We assume ψ s = 0.25 to have
an average duration of sudden stops of one year, which is consistent with the estimations of
Bianchi et al. (2012) and Forbes and Warnock (2012).
8
Table 1: Benchmark parameter values.
Risk aversion
Risk-free rate
Probability default exclusion ends
Probability sudden-stop exclusion ends
Probability of reentry after sudden stop
Debt duration
Income autocorrelation coefficient
Standard deviation of innovations
Mean log income
Discount factor
Income cost of defaulting
Income cost of defaulting
Income cost of sudden stops
γ
r
ψd
π
ψs
δ
ρ
σǫ
µ
β
d0
d1
λ
2
1%
0.083
0.025
0.25
0.03
0.94
1.5%
(-1/2)σǫ2
0.9745
-1.01683
1.18961
0.5
We assume δ = 0.03%. We will show that this implies a debt duration comparable to
those observed in the data.6
The parameter values that govern the endowment process, the level of debt, and the mean
and standard deviation of the spread are taken from Bianchi et al. (2012), who calibrate these
values using Mexico as a reference. They calibrate the value of the discount factor β, the
parameters of the income cost of defaulting d0 and d1 , and the parameter determining the
relative income cost of a sudden stop compared with a default λ targeting an average debtto-GDP ratio of 43 percent, a mean spread of 3.4 percent, a spread standard deviation of 1.5
percent, and an average accumulated income cost of a sudden stop of 14 percent of annual
income. We obtain values similar to these targets with our benchmark model. Thus, these
parameter values are still reasonable for our purposes.
In order to compute the sovereign spread implicit in a bond price, we first compute the
yield i an investor would earn if it holds the bond to maturity (forever in the case of our
6
We use the Macaulay definition of duration that, with the coupon structure in this paper, is given by
∗
∗
D = 1+r
δ+r ∗ , where r denotes the constant per-period yield delivered by the bond. Note that the one-period
bond is equivalent to a long bond with δ = 1 and thus has a duration equal to 1 period.
9
long bonds) and no default is ever declared. This yield satisfies
∞
qtM
X (1 − δ)j
1
=
+
,
(1 + i) j=1 (1 + i)j+1
where δ = 1 for one-period bonds. The sovereign spread is the difference between the yield
i and the risk-free rate r. We report the annualized spread
rts
=
1+i
1+r
4
− 1.
Debt levels in the simulations are calculated as the present value of future payment obliga−1
tions discounted at the risk-free rate, i.e., bM
t (1 + r)(δ + r) , where δ = 1 for one-period
bonds. We report debt levels as a percentage of annualized income.
4
Computation
The recursive problem is solved using value function iteration. The approximated value
and bond price functions correspond to the ones in the first period of a finite-horizon economy
with a number of periods large enough to make the maximum deviation between the value
and bond price functions in the first and second period smaller than 10−6. We solve the
optimal portfolio allocation in each state by searching over a grid of debt levels and then
using the best portfolio on that grid as an initial guess in a nonlinear optimization routine.
The value functions V D and V R and the bond price functions q S and q L are approximated
using linear interpolation over y and cubic spline interpolation over debt levels.7 We use 20
grid points for one-period and long-term debt, and 25 grid points for income realizations.
Expectations are calculated using 50 quadrature points for the income shock.
7
Hatchondo et al. (2010a) discuss the advantages of using interpolation and solving for the equilibrium
of a finite-horizon economy.
10
5
Results
We first show that the simulations of the benchmark model match features of emerging
economies reasonably well. We then show how the presence of sudden stops increases the
debt duration chosen by the government. In addition, we calculate the optimal ex-ante debt
duration. We show how the optimal ex-ante duration is also influenced by the presence of
sudden stops. Furthermore, a government that chooses the debt composition in each period
ends up choosing debt durations that are longer than the ex-ante optimal duration.
5.1
The effect of sudden stops on debt duration
Table 2 reports moments in the simulations of the benchmark model (with sudden stops).
The table shows that the simulations match features of emerging economies reasonably well
(Durdu, 2013 surveys the literature on business cycles fluctuations in emerging economies).
For instance, the simulations produce a high and countercyclical spread, a consumption
process that is more volatile than the income process, and a countercyclical trade balance.
The countercyclicality of the trade balance reflects the government’s choice of reducing its
borrowing in periods with low income. When current income is low, lenders anticipate that
income realizations and, thus, the cost of defaulting are likely to be low in future periods.
Consequently, for any debt level, lenders ask for a higher interest rate. This leads the
government to choose less borrowing.
Table 2 also quantifies the role of sudden stops on the debt duration chosen by the
government. The table shows that the debt duration declines almost by one year in the
absence of sudden stops (π = 0). With a shorter duration, the debt dilution problem is
mitigated and, therefore, the average spread is lower than the one observed in the benchmark
economy (see, for instance, Hatchondo and Martinez, 2009). Notice also that the change in
duration does not significantly affect the level of nominal debt obligations.
11
Table 2: Simulation results
With sudden stops
Without sudden stops
Average duration (years)
5.4
4.5
Mean Long-Debt-to-GDP
39.7
29.7
Mean Short-Debt-to-GDP
0.0
9.7
Mean Long-Debt rs
3.0
1.6
Mean Short-Debt rs
na
1.5
Long-Debt σ (rs )
1.7
1.0
Short-Debt σ (rs )
na
5.7
σ(c)/σ(y)
1.5
1.4
σ(tb)
1.3
1.9
ρ(tb, y)
-0.9
-0.5
ρ (c, y)
0.99
0.93
Note: The standard deviation of x is denoted by σ (x). The coefficient of
correlation between x and z is denoted by ρ (x, z). Moments are computed
using detrended series. Trends are computed using the Hodrick-Prescott
filter with a smoothing parameter of 1, 600. Moments for the simulations
correspond to the mean value of each moment in 250 simulation samples,
with each sample including 120 periods (30 years) without a default episode.
Samples start at least five years after a default. Consumption and income
are expressed in logs.
5.2
The optimal ex-ante debt duration
The previous subsection presented results for the case in which the government decides
the debt duration on a sequential basis. In this subsection we study the preferred duration
when the government can commit to a given duration. As in Hatchondo and Martinez (2009),
we find the preferred ex-ante debt duration by solving the model for different values of δ. In
order to save on computational time, we assume in this subsection that the government can
only issue long-term bonds (i.e., we assume bS = 0). We then look for the optimal value of
δ in the initial period.
12
Figure 1 presents ex-ante welfare for different debt durations. We measure ex-ante welfare
as the continuation value that follows from a state with zero debt and an income level equal
to the unconditional mean. The optimal δ for the economy with sudden stops is 0.056
(implying a duration of 3.7 years) and the optimal δ for the economy without sudden stops
is 0.29 (implying a duration of 0.8 years).
With sudden stops
Without sudden stops
−39.325
−38.87
−39.33
−38.871
−38.872
−39.335
Welfare
Welfare
−38.873
−39.34
−39.345
−38.874
−38.875
−39.35
−38.876
−39.355
−39.36
0.04
−38.877
0.05
0.06
0.07
δ
0.08
0.09
−38.878
0.15
0.1
0.2
0.25
δ
0.3
0.35
0.4
Figure 1: Value function V evaluated at a state with no debt and with income equal to
the unconditional mean. The left panel corresponds to an economy with sudden stops. The
right panel corresponds to an economy without sudden stops.
Figure 2 illustrates the effects of debt duration on consumption volatility and the spread.
On the one hand, for a given debt level, a shorter debt duration implies larger debt obligations
and, thus, a larger drop in consumption when the borrowing cost increases (either because
aggregate income falls or a sudden stop shock hits the economy). On the other hand, a
shorter debt duration mitigates the debt dilution problem and helps reducing the interest
rate spread (see Hatchondo et al., 2010b).
Table 3 reports moments in the model simulations with and without sudden stops, assuming the optimal value of δ for each case. As in Table 2, since a shorter duration mitigates
the debt dilution problem, it implies significantly lower spreads even though the debt level
does not experience a significant decline.
More interestingly, comparing Tables 2 and 3 indicates that in the economies with and
without sudden stops the optimal ex-ante debt duration is shorter than the duration the
government chooses sequentially. This occurs because of a time inconsistency problem similar
13
Without sudden stops
1.8
1
Spread
σ(c) / σ(y)
0.9
Spread (in %)
1.6
σ(c) / σ(y)
Spread (in %)
2
1
1.4
0
0.04
0.06
0.08
0.1
δ
0.12
0.14
2.2
Spread
σ(c) / σ(y)
1.2
0.16
2.15
0.8
2.1
0.7
2.05
0.6
2
0.5
1.95
0.4
1.9
0.3
0.1
0.15
0.2
0.25
δ
0.3
0.35
0.4
σ(c) / σ(y)
With sudden stops
3
1.85
0.45
Figure 2: Spread and consumption volatility for different debt durations. The left panel
corresponds to an economy with sudden stops. The right panel corresponds to an economy
without sudden stops.
to the debt dilution problem. As discussed in the introduction, the debt dilution problem
increases the value of committing to a shorter debt duration as it allows the government to
pay a lower spread. However, when the government decides on a sequential basis, it does not
internalize the effect that the debt composition at the beginning of a given period has on
the borrowing terms faced in previous periods. Therefore, the government typically chooses
a duration longer than the one it would like to commit to in the initial state.
6
Conclusions
We present two main results in the paper. First, we quantify the role that sudden stops
have on the preferred duration of sovereign debt. Second, we illustrate the time inconsistency
problem in the choice of sovereign debt duration: Governments would like to commit to a
duration shorter than the one they choose when they make decisions sequentially. Our
results cast doubt on the convenience of policies to increase the duration of sovereign debt
for economies facing significant sovereign risk.
14
Table 3: Simulation Results when the government commits to a debt duration
With sudden stops
Without sudden stops
Average duration (years)
3.6
0.8
Mean Debt-to-GDP
34.4
34.8
Mean rs
1.7
0.5
σ (rs )
1.2
0.7
σ(c)/σ(y)
1.8
2.1
σ(tb)
2.2
2.2
ρ(tb, y)
-0.3
-0.7
ρ (c, y)
0.76
0.91
Note: The standard deviation of x is denoted by σ (x). The coefficient of
correlation between x and z is denoted by ρ (x, z). Moments are computed
using detrended series. Trends are computed using the Hodrick-Prescott
filter with a smoothing parameter of 1, 600. Moments for the simulations
correspond to the mean value of each moment in 250 simulation samples,
with each sample including 120 periods (30 years) without a default episode.
Samples start at least five years after a default. Consumption and income
are expressed in logs.
References
Arellano, C. (2008). ‘Default Risk and Income Fluctuations in Emerging Economies’. American Economic Review , volume 98(3), 690–712.
Arellano, C. and Ramanarayanan, A. (2012).
‘Default and the Maturity Structure in
Sovereign Bonds’. Journal of Political Economy, volume 120, no. 2, 187–232.
Benjamin, D. and Wright, M. L. J. (2008). ‘Recovery Before Redemption? A Theory of
Delays in Sovereign Debt Renegotiations’. Manuscript.
Bianchi, J., Hatchondo, J. C., and Martinez, L. (2012). ‘International Reserves and Rollover
Risk’. NBER Working Paper 18628.
Broner, F. A., Lorenzoni, G., and Schmukler, S. L. (2013). ‘Why do emerging economies
borrow short term?’ Journal of the European Economic Association, volume 11, 67–100.
15
Chatterjee, S. and Eyigungor, B. (2012). ‘Maturity, Indebtedness and Default Risk’. American Economic Review , volume 102(6), 2674–2699.
Cole, H. L. and Kehoe, T. J. (2000). ‘Self-Fulflling Debt Crises’. Review of Economic Studies,
volume 67(1), 91–116.
Dias, D. A. and Richmond, C. (2007). ‘Duration of Capital Market Exclusion: An Empirical
Investigation’. Working Paper, UCLA.
Durdu, B. (2013). ‘Emerging Market Business Cycles: Recent Advances’. International
Economic Journal . This issue.
Eaton, J. and Gersovitz, M. (1981). ‘Debt with potential repudiation: theoretical and
empirical analysis’. Review of Economic Studies, volume 48, 289–309.
Forbes, K. and Warnock, F. (2012). ‘Capital Flow Waves: Surges, Stops, Flight, and Retrenchment’. Journal of International Economics, volume 88(2), 235–251.
Hatchondo, J. C. and Martinez, L. (2009). ‘Long-duration bonds and sovereign defaults’.
Journal of International Economics, volume 79, 117 – 125.
Hatchondo, J. C., Martinez, L., and Roch, F. (2011). ‘Fiscal rules and the sovereign default
premium’. Mimeo.
Hatchondo, J. C., Martinez, L., and Sapriza, H. (2010a). ‘Quantitative properties of sovereign
default models: solution methods matter’. Review of Economic Dynamics, volume 13,
no. 4, 919–933.
Hatchondo, J. C., Martinez, L., and Sosa Padilla, C. (2010b). ‘Debt dilution and sovereign
default risk’. Federal Reserve Bank of Richmond Working Paper 10-08R.
Jeanne, O. and Ranciere, R. (2011). ‘The Optimal Level of Reserves for Emerging Market
Countries: a New Formula and Some Applications’. Economic Journal , volume 121(555),
905–930.
Mendoza, E. and Yue, V. (2012). ‘A General Equilibrium Model of Sovereign Default and
Business Cycles’. The Quarterly Journal of Economics, volume 127 (2), 889–946.
Niepelt, D. (2008). ‘Debt Maturity without Commitment’. Manuscript, Study Center
Gerzensee.
Yue, V. (2010). ‘Sovereign default and debt renegotiation’. Journal of International Economics, volume 80, no. 2, 176–187.
16
@FedFRASER