Journal of International Economics 69 (2006) 64 – 83
www.elsevier.com/locate/econbase
Defaultable debt, interest rates and
the current account
Mark Aguiar a, Gita Gopinath b,*
a Federal Reserve Bank of Boston, United States
b University of Chicago and NBER, United States
Received 20 August 2004; received in revised form 20 April 2005; accepted 17 May 2005
Abstract
World capital markets have experienced large scale sovereign defaults on a number of
occasions. In this paper we develop a quantitative model of debt and default in a small open
economy. We use this model to match four empirical regularities regarding emerging markets:
defaults occur in equilibrium, interest rates are countercyclical, net exports are countercyclical, and
interest rates and the current account are positively correlated. We highlight the role of the
stochastic trend in emerging markets, in an otherwise standard model with endogenous default, to
match these facts.
D 2005 Published by Elsevier B.V.
Keywords: Sovereign debt; Default; Current account; Interest rates; Stochastic trend
JEL classification: F3; F4
1. Introduction
World capital markets have experienced large scale sovereign defaults on a number of
occasions, the most recent being Argentina’s default in 2002. This latest crisis is the fifth
* Corresponding author. Department of Economics, Harvard University, 1805 Cambridge Street, Littauer
Center, Cambridge, MA 02138, United States. Tel.: +1 617 4958161.
E-mail addresses: mark.aguiar@bos.frb.org (M. Aguiar), gita.gopinath@gsb.uchicago.edu (G. Gopinath).
0022-1996/$ - see front matter D 2005 Published by Elsevier B.V.
doi:10.1016/j.jinteco.2005.05.005

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M. Aguiar, G. Gopinath / Journal of International Economics 69 (2006) 64–83
65
Argentine default or restructuring episode in the last 180 years.1 While Argentina may be
an extreme case, sovereign defaults occur with some frequency in emerging markets. A
second set of facts about emerging markets relates to the behavior of the interest rates at
which these economies borrow from the rest of the world and their current accounts.
Interest rates and the current account are strongly countercyclical and positively correlated
to each other. That is, emerging markets tend to borrow more in good times and at lower
interest rates as compared to slumps. These features contrast with those observed in
developed small open economies.
In this paper we develop a quantitative model of debt and default in a small open
economy, which we use to match the above facts. Our approach follows the classic
framework of Eaton and Gersovitz (1981) in which risk sharing is limited to one period
bonds and repayment is enforced by the threat of financial autarky. In all other respects the
model is a standard small open economy model where the only source of shocks are
endowment shocks. In this framework, we show that the model’s ability to match certain
features in the data improve substantially when the productivity process is characterized by
a volatile stochastic trend as opposed to transitory fluctuations around a stable trend. In a
previous paper (Aguiar and Gopinath, 2004b), we document empirically that emerging
markets are indeed more appropriately characterized as having a volatile trend. The
fraction of variance at business cycle frequencies explained by permanent shocks is shown
to be around 50% in a small developed economy (Canada) and more than 80% in an
emerging market (Mexico).
To isolate the importance of trend volatility in explaining default, we first consider a
standard business cycle model in which shocks represent transitory deviations around a
stable trend. We find that default is extremely rare, occurring roughly twice every 2500
years. The weakness of the standard model begins with the fact that autarky is not a severe
punishment, even adjusting for the relatively large income volatility observed in emerging
markets. The welfare gain of smoothing transitory shocks to consumption around a stable
trend is small. This in turn prevents lenders from extending debt, which we demonstrate
through a simple calculation a` la Lucas (1985). We can support a higher level of debt in
equilibrium by assuming an additional loss of output in autarky. However, in a model of
purely transitory shocks, this does not lead to default at a rate that resembles those
observed in many economies.
The intuition behind why default occurs so rarely in a model with transitory shocks and
a stable trend is described in Section 3. The decision to default rests on the difference
between the present value of utility (value function) in autarky versus that of financial
integration. Quantitatively, the level of default that arises in equilibrium depends on the
relative sensitivity of the two value functions to endowment shocks. When the endowment
process is close to a random walk there is limited need to save out of additional
endowment, leaving little difference between financial autarky and a good credit history,
regardless of the realization of income. At the other extreme, if the transitory shock is iid
over time, then there is an incentive to borrow and lend, making integration much more
valuable than autarky. However, an iid shock has limited impact on the entire present
1 See Reinhart et al. (2003).

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M. Aguiar, G. Gopinath / Journal of International Economics 69 (2006) 64–83
discounted value of utility, and so the difference between integration and autarky is not
sensitive to the particular realization of the iid shock. At either extreme, therefore, the
decision to default is not sensitive to the realization of the shock. Consequently, when
shocks are transitory, the level of outstanding debt–and not the realization of the stochastic
shock–is the primary determinant of default. This is reflected in financial markets by an
interest rate schedule that is extremely sensitive to quantity borrowed. Borrowers
internalize the steepness of the bloan supply curveQ and recognize that an additional unit of
debt at the margin will have a large effect on the cost of debt. Agents therefore typically do
not borrow to the point where default is probable.
On the other hand, a shock to trend growth has a large impact on the two value
functions (because of the shock’s persistence) and on the difference between the two value
functions. The latter effect arises because a positive shock to trend implies that income is
higher today, but even higher tomorrow, placing a premium on the ability to access capital
markets to bring forward anticipated income. In this context, the decision to default is
relatively more sensitive to the particular realization of the shock and less sensitive to the
amount of debt. Correspondingly, the interest rate is less sensitive to the amount of debt
held. Agents are consequently willing to borrow to the point that default is relatively
likely. This theme is developed in Section 4.
The next set of facts concerns the phenomenon of countercyclical current accounts and
interest rates. In the current framework where all interest rate movements are driven by
changes in the default rate, the steepness of the interest rate schedule makes it challenging
to even qualitatively match the positive correlation between interest rates and the current
account. This is because, on the one hand, an increase in borrowing in good states
(countercyclical current account) will, all else equal, imply a movement along the heuristic
bloan supply curveQ and a sharp rise in the interest rate. On the other hand, if the good state
is expected to persist, this lowers the expected probability of default and is associated with
a favorable shift in the interest rate schedule. To generate a positive correlation between
the current account and interest rates we need the effect of the shift of the curve to
dominate the movement along the curve. A stochastic trend is again useful in matching
this fact since the interest rate function tends to be less steeply sloped and trend shocks
have a significant effect on the probability of default. Accordingly, in our benchmark
simulations, a model with trend shocks matches the empirical feature of a positive
correlation between the interest rate and the current account. The model with transitory
shocks however fails to match this fact. The prediction for which both models perform
poorly is in matching the volatility of the interest rate process.2
The model with shocks to trend generates default roughly once every 125 years, which
is a 10-fold improvement over the standard model but still shy of the observed pattern for
chronic defaulters. We bring the default rate closer to that observed empirically for Latin
America by introducing third-party bailouts. Realistic bailouts raise the rate of default
dramatically—bailouts up to 18% of GDP lead to defaults once every 27 years. However,
the subsidy implied by bailouts breaks the tight linkage between default probability and
2 The additional observed volatility may be due to a volatile risk premium, as suggested by Broner et al. (2004).

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M. Aguiar, G. Gopinath / Journal of International Economics 69 (2006) 64–83
67
the interest rate. Interest rate volatility is therefore an order of magnitude below that
observed empirically.
The business cycle behavior of markets in which agents can choose to default has
received increasing attention in the literature. The approach we adopt here is a dynamic
stochastic general equilibrium version of Eaton and Gersovitz (1981) and is similar to the
formulations in Chatterjee et al. (2002) on household default and Arellano (2004) on
emerging market default. Our point of distinction from the previous literature is the
emphasis we place on the role of the stochastic trend in driving the income process in
emerging markets. We find that the presence of trend shocks substantially improves the
ability of the model to generate empirically relevant levels of default. Moreover, we obtain
the coincidence of countercyclical net exports, countercyclical interest rates and the
positive correlation between interest rates and current account observed in the data. This is
distinct from what is obtained in Arellano (2004) and Kehoe and Perri (2002).
In the next section we describe empirical facts for Argentina. Section 2 describes the
model environment, parameterization and solution method. Section 3 describes the model
with a stable trend and its predictions. Section 4 describes the model with a stochastic
trend and performs sensitivity analysis. Section 5 examines the effect of third party
bailouts on the default rate and Section 6 concludes.
1.1. Empirical facts
Reinhart et al. (2003) document that among emerging markets with at least one default
or restructuring episode between 1824 and 1999, the average country experienced roughly
3 crises every 100 years. The same study documents that the external debt to GDP ratio at
the time of default or restructuring averaged 71%. A goal of any quantitative model of
emerging market default is to generate a fairly high frequency of default coinciding with
an equilibrium that sustains a large debt to GDP ratio.
Table 1
Argentina business cycle statistics (1983.1–2000.2)
Data
HP
SE
r( Y)
4.08
(0.52)
r(Rs)
3.17
(0.54)
r(TB/Y)
1.36
(0.24)
r(C)/r( Y)
1.19
(0.04)
q( Y)
0.85
(0.08)
q(Rs, Y)
À0.59
(0.11)
q(TB/Y, Y)
À0.89
(0.10)
q(Rs, TB/Y)
0.68
(0.13)
q(C, Y)
0.96
(0.01)
The series were deseasonalized if a significant seasonal component was identified. We log the income,
consumption and investment series and compute the ratio of the trade balance (TB) to GDP ( Y) and the interest
rate spread (Rs). Rs refers to the difference between Argentina dollar interest rates and US 3-month treasury bond
rate (annualized numbers). All series were then HP filtered with a smoothing parameter of 1600. GMM estimated
standard errors are reported in parenthesis under column SE. The standard deviations ( Y, Rs, TB/Y) are reported
in percentage terms.

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M. Aguiar, G. Gopinath / Journal of International Economics 69 (2006) 64–83
Table 1 documents business cycle features for Argentina over the period 1983.1 to
2000.2 using an HP filter with a smoothing parameter of 1600 for quarterly frequencies. A
striking feature of the business cycle is the strong countercyclicality of net exports (À 0.89)
and interest rates spreads (À 0.59). Interest rates and the current account are also strongly
positively correlated (0.68). These features regarding interest rates, in addition to the high
level of volatility of these rates, have been documented by Neumeyer and Perri (2004) to
be true for several other emerging market economies and to contrast with the business
cycle features of Canada, a developed small open economy. Aguiar and Gopinath (2004b)
document evidence of the stronger countercyclicality of the current account for emerging
markets relative to developed small open economies. In the model we emphasize the
distinction between shocks to the stochastic trend and transitory shocks. This is motivated
by previous research (Aguiar and Gopinath (2004b)) that documents that emerging
markets are subject to more volatile shifts in stochastic trend as compared to a developed
small open economy.
2. Model environment
To model default we adopt the standard framework of Eaton and Gersovitz (1981).
Specifically, we assume that international assets are limited to one period bonds. If the
economy refuses to pay any part of the debt that comes due, we say the economy is in
default. Once in default, the economy is forced into financial autarky for a period of time
as punishment. This is similar to the framework adopted in Chatterjee et al. (2002) and
Arellano (2004).
We begin our analysis with a standard model of a small open economy that receives a
stochastic endowment stream, yt. (We discuss a production economy in Section 4.1.) The
economy trades a single good and single asset, a one period bond, with the rest of the
world. The representative agent has CRRA preferences over consumption of the good:
c1Àc
u ¼
:
ð1Þ
1 À c
The endowment yt is composed of a transitory component zt and a trend Ct:
yt ¼ ezt Ct:
ð2Þ
The transitory shock, zt, follows an AR(1) around a long run mean lz
zt ¼ lzð1 À qzÞ þ qzztÀ1 þ ez
ð3Þ
t
|q
z
2
z| b 1, et ~ N(0, rz ), and the trend follows
Ct ¼ gtCtÀ1
ð4Þ
À
ÁÀ À Á
Á
lnðgtÞ ¼ 1 À qg ln lg À c þ qglnðgtÀ1Þ þ egt
ð5Þ
r2
|q
g
2
g
g| b 1, et ~ N(0, rg ), and c ¼ 1
:
2 1Àq2g

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M. Aguiar, G. Gopinath / Journal of International Economics 69 (2006) 64–83
69
We denote the growth rate of trend income as gt, which has a long run mean lg. The
log growth rate follows an AR(1) process with AR coefficient |qg| b 1. Note that a positive
shock eg implies a permanently higher level of output, and to the extent that qg N 0, a
positive shock today implies that the growth of output will continue to be higher beyond
the current period. We assume that E{limt
b
Yl
t(Ct)1Àc} = 0 to ensure a well defined
problem, where 0 b b b 1 denotes the agent’s discount rate.
Let at denote the net foreign assets of the agent at time t. Each bond delivers one unit of
the good next period for a price of q this period. We will see below that in equilibrium q
depends on at and the state of the economy. We denote the value function of an economy
with assets at and access to international credit as V(at, zt, Ct). At the start of the period,
the agent decides whether to default or not. Let VB denote the value function of the agent
once it defaults. The superscript B refers to the fact that the economy has a bad credit
history and therefore cannot transact with international capital markets (i.e., reverts to
financial autarky). Let VG denote the value function given that the agent decides to
maintain a good credit history this period. The value function of being in good credit
standing at the start of period t with net assets can then be defined as V(at, zt,
C
G
B
t) = maxhVt , Vt i. At the start of period t, an economy in good credit standing and net
assets at will default only if VB(zt, Ct) N VG(at, zt, Ct).
An economy with a bad credit rating must consume its endowment. However, with
probability k it will be bredeemedQ and start the next period with a good credit rating and
renewed access to capital markets. If redeemed, all past debt is forgiven and the economy
starts off with zero net assets. We also add a parameter d that governs the additional loss of
output in autarky.3
In recursive form, we therefore have:
V Bðzt; CtÞ ¼ uðð1 À dÞytÞ þ kbEtV ð0; ztþ1; Ctþ1Þ þ 1
ð À kÞbEtV Bðztþ1; Ctþ1Þ
ð6Þ
where Et is expectation over next period’s endowment and we have used the fact that k is
independent of realizations of y. If the economy does not default, we have:
V Gðat; zt; CtÞ ¼ max fuðctÞ þ bEtV a
ð tþ1; ztþ1; Ctþ1Þg
ct
s:t: ct ¼ yt þ at À qtatþ1:
ð7Þ
The international capital market consists of risk neutral investors that are willing to
borrow or lend at an expected return of r*, the prevailing world risk free rate. The default
function D(at, zt,Ct) = 1 if VB(zt, Ct) N VG(at, zt, Ct) and zero otherwise. Then equilibrium
in the capital market implies
Etf 1
ð À Dtþ1Þg
qðatþ1; zt; CtÞ ¼
:
ð8Þ
1 þ r4
The higher the expected probability of default the lower the price of the bond.
3 Rose (2003) finds evidence of a significant and sizeable (8% a year) decline in bilateral trade flows following
the initiation of debt renegotiation by a country.

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M. Aguiar, G. Gopinath / Journal of International Economics 69 (2006) 64–83
Table 2A
Common benchmark parameter values
Risk aversion
c
2
World interest rate
r*
1%
Loss of output in autarky
d
2%
Probability of redemption
k
10%
Mean (log) transitory productivity
l
2
z
(À 1/2)dz
Mean growth rate
lg
1.006
To emphasize the distinction between the role of transitory and permanent shocks we
present two extreme cases of the model described above. Model I will correspond to the
case when the only shock is the transitory shock zt and Model II to the case when the only
shock has permanent effects, gt.4 Since few results can be analytically derived we discuss
at the outset the calibration and solution method employed.
2.1. Calibration and model solution
Benchmark parameters that are common to all models are reported in Table 2A. Each
period refers to a quarter with a quarterly risk free interest rate of 1%. The coefficient of
relative risk aversion of 2 is standard. The probability of redemption k = 0.1 implies an
average stay in autarky of 2.5 years, similar to the estimate by Gelos et al. (2004). The
additional loss of output in autarky is set at 2%. We will see in our sensitivity analysis
(Section 4.1) that high impatience is necessary for generating reasonable default in
equilibrium. Correspondingly, our benchmark calibration sets b = 0.8. Authors such as
Arellano (2004) and Chatterjee et al. (2002) also employ similarly low values of b to
generate default. The mean quarterly growth rate (lg) is calibrated to 0.6% to match the
number for Argentina.
The remaining parameters characterize the underlying income process and therefore
vary across models (Table 2B). To focus on the nature of the shocks, we ensure that the HP
filtered income volatility derived in simulations of both models approximately match the
same observed volatility in the data. In Model I, output follows an AR(1) process with
stable trend and an autocorrelation coefficient of qz = 0.9, which is similar to the values
used in many business cycle models and rz = 3.4%. We set the mean of log output equal to
À 1/2r2z so that average detrended output in levels is standardized to one. In Model
II,rz = 0, rg = 3% and qg = 0.17.
To solve the model numerically, we first recast the Bellman equations in detrended
form. To detrend, we normalize all variables by lgCtÀ1.5 This normalization implies that
the mean of the detrended endowment is one. A technical appendix available from the
authors’ websites derives some key properties of the value functions. In particular, the
appendix discusses the equivalence of the original and the detrended problem. We also
4 One of the reasons we consider the two extremes is to minimize the dimensionality of the problem, which we
solve employing discrete state space methods. Using insufficient grids of the state space can generate extremely
unreliable results in this set up.
5 Note that we have detrended using the cumulated trend through the previous period. Computationally, the
results do not differ with detrending by Ct.

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M. Aguiar, G. Gopinath / Journal of International Economics 69 (2006) 64–83
71
Table 2B
Model specific benchmark parameter values
Model I: transitory shocks
Model II: growth shocks
Model II with bailouts
rz
3.4%
0
0
qz
0.90
NA
NA
qg
0
3%
3%
qg
NA
0.17
0.17
b
0.8
0.8
0.95
Bailout limit
NA
NA
18%
demonstrate the homogeneity properties of the budget sets, value functions, and
equilibrium interest rate schedules that allow us to solve the problem in detrended form.
We will use the notation X
ˆ to represent the detrended counterpart for any variable or
function X. Specifically, aˆt = (at/(lgCtÀ1)) and cˆt = (ct/(lgCtÀ1)). The technical appendix
proves that the value functions are homogenous of degree 1 À c in a and C. Therefore,
(lgCtÀ1)À1V(at, zt, Ct) = V(aˆt, zt, ( gt/lg)) u Vˆ(aˆt, zt, gt).We define VˆG and VˆB in a similar
fashion. The interest rate schedule q is homogenous of degree zero in a and C.6 We
therefore define qˆ(aˆt+1, zt, gt) u q(aˆt+1, zt, ( gt/lg)) = q(at+1, zt, Ct). The detrended default
indicator function D
ˆ is defined in the same fashion.
To solve the detrended problem, we use the discrete state-space method. We
approximate the continuous AR(1) process for income with a discrete Markov chain
using 25 equally spaced grids7 of the original processes steady state distribution. We then
integrate the underlying normal density over each interval to compute the values of the
Markov transition matrix. The asset space is discretized into 400 possible values. We
ensured that the limits of our asset space never bind along the simulated equilibrium paths.
The solution algorithm involves the following:
(i) Assume an initial price function qˆ0(aˆ, z, g). Our initial guess is the risk free rate at
each point in the state space.
(ii) Use this qˆ0 and an initial guess for V
ˆ B,0 and VˆG,0 to iterate on the Bellman Eqs. (6)
and (7) to solve for the optimal value functions V
ˆ B, VˆG,Vˆ = maxhVˆG, VˆBi and the
optimal policy functions.
(iii) For the initial guess qˆ0, we now have an estimate of the default function D
ˆ 0(aˆ, z, g).
Next, we update the price function as qˆ1 = (Et{(1 À D
ˆ t+1)})/(1 + r*) and using this qˆ1
repeat steps (ii) and (iii) until |qˆi+1 À qˆi| b e,where i represents the number of the
iteration and e is a very small number.
6 Recall that the default function D is the indicator function that equals one if VB NVG. This plus the
homogeneity of the value functions implies that D is homogenous of degree zero in a and C. The interest rate
function inherits this property from the definition of q (Eq. (8)). See the technical appendix for a formal proof that
this holds in equilibrium.
7 It is important to span the stationary distribution sufficiently so as to include large negative deviations from
the average even if these are extremely rare events because default is more likely to occur in these states.

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M. Aguiar, G. Gopinath / Journal of International Economics 69 (2006) 64–83
3. Model I: stable trend
Model I assumes a deterministic trend (Ct = (lg)t) and the process for zt is given by Eq.
(3). In Fig. 1A, we plot the difference between the value function with a good credit rating
(V
ˆ G) and that of autarky (VˆA) as a function of z for our calibration. The agent defaults
when output is relatively low. The top panel of Fig. 2A plots the region of default in (z, aˆ)
space. The line that separates the darkly shaded from the lightly shaded region represents
combinations of z and aˆ along which the agent is indifferent between defaulting and not
defaulting. The darkly shaded region represents combinations of low productivity and
negative foreign assets for which it is optimal to default.
0.04
0.03
(V_
_G - V_
_B)
0.02
0.01
0
-0.184
-0.1091
-0.0342
0.0407
0.1156
-0.01
-0.02
-0.03
z state
0.04
0.03
0.02
0.01
V_
_G - V_
_B
0
0.881
0.932
0.983
1.0341
1.0851
-0.01
-0.02
-0.03
g state
Fig. 1. (A) Model I. (B) Model II. Note: V_G represents the (detrended) value function when the agent chooses to
repay and is in good credit standing and V_B is the (detrended) value function when the agent chooses to default.
We have plotted here the difference between the two value functions for a given level of assets, across different
productivity states. Fig. 2A corresponds to the case when z varies and Fig. 2B to the case when g varies. The
(V_G À V_B) line is more steeply sloped in the case of g shocks.

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M. Aguiar, G. Gopinath / Journal of International Economics 69 (2006) 64–83
73
0.15
0.1
0.05
z
0
-0.05
-0.1
-0.15
-0.4
-0.35
-0.3
-0.35
-0.2
-0.15
-0.1
-0.05
0
Assets
1.1
1.05
g
1
0.95
0.9
-0.4
-0.35
-0.3
-0.35
-0.2
-0.15
-0.1
-0.05
0
Assets
Fig. 2. Default region. Note: the darkly shaded region represents combinations of the productivity state and
(detrended) assets for which the economy will prefer default. The lightly shaded region accordingly is the
nondefault region. The vertical axis represents the realization of the productivity shock. The horizontal axis
represents assets normalized by trend income. In both pictures, the agent is more likely to default when holding
larger amounts of debt (negative assets) and when in worse productivity states. The line of indifference is less
steeply sloped in the case of g shocks.
For a given realization of z, clearly the agent is more likely to default at lower values of
aˆ. Since V
ˆ B refers to financial autarky, its value is invariant to aˆ. Conversely, VˆG is strictly
increasing in assets. This follows straightforwardly from the budget constraint and strict
monotonicity of utility. For each z, there is a unique point of intersection, say ˆa¯ðzÞ, and the
agent will default if foreign assets lie below ˆa¯.
The default decision as a function of z is less clear-cut. In the case when k = 0, it must
be the case that V
ˆ G should be at least as steep as VˆB at the indifference point, for a given aˆ.
To see this, consider the value of an additional unit of endowment at the indifference point.
Clearly, the continuation value for an agent in good credit standing is always (weakly)
greater than that of an agent with a bad credit standing (this is true given that k = 0). If an
agent is indifferent between defaulting or not, current consumption absent default must
therefore be (weakly) less than under default, implying an equal or higher marginal utility

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Document Outline

• Defaultable debt, interest rates and the current account
  • Introduction
    • Empirical facts
  • Model environment
    • Calibration and model solution
  • Model I: stable trend
    • Debt and default implications in Model I
    • Business cycles implications in Model I
  • Model II: stochastic trend
    • Sensitivity analysis
  • Third party bailouts
  • Conclusion
  • Acknowledgements
  • References

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