ï»¿ WPS5978
Policy Research Working Paper 5978
Using Pooled Information and Bootstrap
Methods to Assess Debt Sustainability
in Low Income Countries
Constantino Hevia
The World Bank
Development Research Group
Macroeconomics and Growth Team
February 2012
Policy Research Working Paper 5978
Abstract
Conventional assessments of debt sustainability in interdependence faced by a generic, low income country.
low income countries are hampered by poor data and The paper estimates a panel vector autoregression to
weaknesses in methodology. In particular, the standard trace the evolution of the determinants of debt, and
International Monetary Fund-World bank debt performs simulations to calculate statistics on external
sustainability framework relies on questionable empirical debt for individual countries. The methodology allows
assumptions: its baseline projections ignore statistical for the value of the determinants of debt to differ
uncertainty, and its stress tests, which are performed as across countries in the long run, and for additional
robustness checks, lack a clear economic interpretation heterogeneity through country-specific exogenous
and ignore the interdependence between the relevant variables. Results in this paper suggest that ignoring the
macroeconomic variables. This paper proposes to uncertainty and interdependence of macroeconomic
alleviate these problems by pooling data from many variables leads to biases in projected debt trajectories, and
countries and estimating the shocks and macroeconomic consequently, the assessment of debt sustainability.
This paper is a product of the Macroeconomics and Growth Team, Development Research Group. It is part of a larger
effort by the World Bank to provide open access to its research and make a contribution to development policy discussions
around the world. Policy Research Working Papers are also posted on the Web at http://econ.worldbank.org. The author
may be contacted at chevia@worldbank.org.
The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development
issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the
names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those
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its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent.
Produced by the Research Support Team
Using Pooled Information and Bootstrap Methods to
Assess Debt Sustainability in Low Income Countries
Constantino Heviaâˆ—
JEL codes: F34, F47, H63, H68
Keywords: Low income countries, debt sustainability, panel vector autoregression, bootstrap
Sector board: EPOL
âˆ—
The author is with the World Bank, DECMG. I am grateful to Aart Kray, Norman Loayza, Claudio
Raddatz, and Luis Serven for valuable comments and suggestions. I owe special thanks to Luca Bandiera,
Leonardo Hernandez, and Juan Pradelli for advice and endless discussions about the current IMF-World
Bank Debt Sustainability Framework, and to the World Bank's PREMED for support. I am also thankful
to Bledi Celiku for very able research assistance. The ndings, interpretations, and conclusions expressed
in this paper are entirely those of the author. They do not necessarily reect the view of the World Bank,
those of the Executive Directors, or the governments they represent.
1 Introduction
Assessing the sustainability of external debt requires making assumptions about the evolution
of its determinants. To make sensible predictions about future debt trajectories, projections
need to take into account the uncertainty, co-movement, and feedback eects between the
relevant macroeconomic variables. For example, crisis episodes with large increases of the
debt burden are typically associated with current account reversals, real exchange rate de-
preciations, and so forth. It is important to take into account these correlations to provide
reasonable projections and, therefore, to assess the sustainability of external debt.
The current joint International Monetary Fund (IMF)World Bank debt sustainability
1
framework (DSF) for low income countries is based on three pillars. The rst pillar is a set
of bounds on external debt as a fraction of gross domestic product (GDP) or exports that
vary according to the quality of the country's institutions and policies. The second pillar
is a set of projections of key macroeconomic variables coupled with a debt accumulation
equation to produce projections of external debt. Countries with current or projected debt
indicators above the proposed bounds are considered to have unsustainable levels of debt.
The third pillar is a set of stress tests designed to check the robustness of the baseline
projection. Even if the projected debt level is below the proposed bounds, it might become
unsustainable should the country suer suciently large negative shocks. The DSF considers
a number of negative shocks on the baseline projections to assess whether current levels of
debt are suciently safe.
2
The DSF for low income countries, however, has a number of drawbacks. The baseline
projection is based on experts' opinions or on the point estimates of the projections compiled
in the IMF's World Economic Outlook. The framework, however, ignores any uncertainty
associated with these forecasts. This is particularly important given the long projection
horizon (of 20 years) included in the current framework. Moreover, while the stress tests are
1 The current DSF is described in World Bank and IMF (2009) and Painchaud and StuÂ£ka (2011).
2 Some of these problems were already noted in IMF (2004) and Hostland (2011).
1
thought to be a way to cope with the uncertainty involved in the baseline projections, their
implementation is problematic for, at least, two reasons. First, the framework ignores the
co-movements between the macroeconomic variables that determine the evolution of external
debt. For example, a negative shock to GDP growth is assumed to have no impact on other
macroeconomic variables, like the real exchange rate, the current account, or the interest
rate. These variables are kept constant at their baseline projections. Moreover, shocks in
the current framework do not have a meaningful economic interpretation. Where do shocks
come from? What is their structural interpretation? Second, some argue that the stress
tests are too stringent because they consider highly unlikely and pessimistic scenarios. For
example, one of the stress tests in the current framework involves a simultaneous worsening
3
in four determinants of debt for two years. There is no rationale for the duration or the
size of the proposed shock.
This paper proposes to alleviate these problems by pooling data from many countries
and estimating the shocks and co-movements faced by a generic low income country. The
methodology is an extension to that proposed by Garcia and Rigobon (2005). I rst derive
a debt accumulation equation and identify key variables that determine the evolution of
4
foreign debt. Next, I estimate a panel vector autoregression with common slope coecients
and covariance matrix to model the evolution of the determinants of debt. Finally, I perform
simulations to generate a large number of future debt trajectories for a given country and
compute several statistics on external debtmedian forecasts, condence regions, the prob-
ability of debt crossing some threshold, and so forth. These statistics can be used to assess
whether external debt is, or is likely to be, too large relative to a predetermined criterion.
To perform the simulations, Garcia and Rigobon (2005) use a Monte Carlo method and
assume that shocks are drawn from a normal distribution with mean zero and covariance
matrix equal to that of the tted residuals. One contribution of this paper is to replace the
3 This is a combined negative shock to real GDP growth, exports growth, the GDP deator measured in
U.S. dollars, and private transfers and foreign direct investment.
4 The terms external debt and foreign debt are used interchangeably throughout the paper.
2
Monte Carlo step with a bootstrap approach. The bootstrap is a procedure to draw shocks
from the tted residuals and is robust to the tail risks inherent to probability distributions
with fat tails and skewness. One interesting result is that the condence bands of the debt
forecasts based on the bootstrap are tighter than those based on Monte Carlo. Relative to
the associated normal density, the histogram of tted residuals has more probability mass
around zero, more probability mass in few extreme values, and less probability mass in
medium-sized values. Thus, while it may occasionally draw extreme shocks, the bootstrap
most often draws small shocks relative to those of the normal distribution. This makes
condence bands tighter under the bootstrap approach.
The proposed methodology alleviates most of the aforementioned problems. Projections
are based on an econometric model that summarizes the co-movements between the key
variables and takes into account the uncertainty associated with them. The simulations
are computed by drawing shocks from the estimated residuals and, therefore, are based on
the typical shocks faced by low income countries. Moreover, the issue of identication of
structural shocks is irrelevant because we are interested in the usual bundle of shocks hitting
low income countries, not in identifying the debt response to some structural shock. In
addition, by averaging the behavior of many countries, the methodology is likely to reduce the
bias due to poor data quality in low income countries, like too few observations, measurement
errors, bad reporting, and so forth.
While aimed at capturing the behavior of a generic low income country, the methodology
allows for partial heterogeneity through the introduction of country-specic intercepts (or
xed eects) and exogenous variables. The xed eects allow the long run value of the
determinants of debt to dier across countries. The exogenous variables provide additional
heterogeneity. Admittedly, the degree of heterogeneity obtained with these mechanisms could
be limited. The methodology, however, is a compromise between the rigidity imposed by the
panel vector autoregression and the problems associated with the lack of adequate data in
low income countries. For example, the methodology allows performing debt sustainability
3
analysis even in countries with scarce or no data. The analyst could use external information
based, for example, on experts' opinions or from similar countries to propose a reasonable
guess of the long run values of the determinants of debt. Given the guess, the analyst can
recover the associated country-specic intercept. Moreover, the analyst can also study the
impact of reforms that aect the long run values of the determinants of debt. Such reforms
are manifested as changes in the country-specic intercept.
In performing these experiments, however, the analyst must be aware that there is a
feasibility constraint linking the long run values of the determinants of debt with the long
run level of external debt. While the dynamics of debt during the transition could take any
form, the choice of the xed eect determines the level to which foreign debt will converge
to in the long run. The link between the long run value of debt and its determinants is
not a characteristic of the methodology proposed in this paper but the result of a feasibility
constraint that holds independently of the approach used to compute the debt trajectories.
5
The literature that followed Garcia and Rigobon (2005) is vast. There are, however,
some studies that proposed interesting variations to the basic methodology. Celasum, De-
brun, and Ostry (2007) incorporate a policy reaction function aimed at capturing the en-
dogenous response of the scal surplus to the state of the economy. Frank and Ley (2009)
introduce structural breaks in the parameters of a vector autoregression and also use a boot-
strap procedure to analyze scal sustainability. Arizala et al. (2009) propose combining
vector autoregressions with external forecasts to arrive at an average forecast of the main
determinants of debt. Few papers have proposed applying Garcia and Rigobon's approach
to low income countries. IMF (2004) takes averages over twenty low income countries during
1985-1999 and performs univariate autoregressions for each determinant of debt to generate
projected debt trajectories. Hostland (2011) estimates univariate autoregressions for single
countries to generate predictions for future debt trajectories. To the best of my knowledge,
this is the rst paper that proposes to pool the observations of several countries to sum-
5 This methodology has received several names in the literature, including risk management approach to
debt sustainability, debt sustainability fan charts, and stochastic simulation methods.
4
marize the characteristics of a generic low income country but allowing simultaneously for
country-xed eects, country-specic exogenous variables, non-normal residuals, and exible
dynamics using a panel vector autoregression with exogenous variables.
The paper proceeds as follows. Section 2 discusses the basic framework for a single
country. Section 3 describes how to implement the methodology using a panel of time series
- cross section data. This section also provides a detailed analysis of a ctitious country to
illustrate the issues raised above. Section 4 considers Senegal as a case study and briey
compares the proposed methodology with the approach currently used by the IMF and the
World Bank. Section 5 provides robustness checks and Section 6 concludes.
2 The basic framework
This section describes the basic framework and identies key variables that aect the dy-
namics of external debt. To simplify the exposition, this section focuses on a single country.
Details of the implementation and how to cope with the data problems of low income coun-
tries are discussed in the next section.
The methodology is an extension of the approach proposed by Garcia and Rigobon (2005),
originally designed to study the sustainability of public debt, to the study of the sustain-
ability of external debt. The idea is to write a debt accumulation equation, measuring
and estimating a stochastic process for the variables that determine the evolution of debt,
and performing Monte Carlo simulations to compute a number of statistics on projected
debt trajectories. One contribution of this paper is to replace the Monte Carlo simulation
step with a bootstrap procedure based on re-sampling from the set of estimated residuals.
This modication makes the methodology robust to the tail risks inherent to probability
distributions with fat tails and skewness.
By denition, the international investment position of a country at time t, IIPt , equals
the position at time t âˆ’ 1, IIPtâˆ’1 , plus the current account balance, the amount of debt
relief, aid ows, grants, and valuation eects consisting in the change in the value of assets
5
hold abroad minus the change in the value of assets held by foreigners. Formally,
IIPt = IIPtâˆ’1 + CAt + Ï‰t ,
where CAt is the current account balance and Ï‰t is the contribution of the remaining items.
This equation implies that foreign debt evolves according to (Appendix A provides details)
1 + rt
dt = dtâˆ’1 âˆ’ mt âˆ’ ft + vt , (2.1)
(1 + gt ) (1 + Ï€t )
where dt is the ratio of external debt to GDP; rt is the implicit interest rate on external
debt; gt is the growth rate of real GDP; Ï€t is the growth rate of the GDP deator measured
in U.S. dollars; mt is the non-interest current account divided by GDP; ft denotes net FDI
ows as a fraction of GDP; and vt includes debt relief, aid ows, grants, and the change
in portfolio investment, nancial derivatives, and international reserves, all measured as a
6
fraction of GDP. From now on, vt will be referred to as a debt shock. Changes in any of
the variables Yt = {gt , Ï€t , rt , mt , ft , vt } lead to changes in the ratio of foreign debt to GDP.
The debt shock vt is dicult to measure, especially in low income countries. Thus, given
data on the variables {dt , gt , Ï€t , rt , mt , ft }, equation (2.1) can be used to recover the realized
value of vt as a residual,
1 + rt
vt = dt âˆ’ dtâˆ’1 + mt + ft .
(1 + gt ) (1 + Ï€t )
The idea of the methodology is to estimate a exible stochastic process for Yt , and then
using the estimated process to compute statistics on the evolution of the foreign debt-GDP
ratio derived from equation (2.1). For example, the average or median debt trajectory over
a number of years, condence intervals around these point estimates, the probability that
6 The implicit interest rate r is dened as total interest payments on external debt during period t divided
t
by the stock of external debt in period t âˆ’ 1. The non-interest current account mt is dened as the current
account plus interest payments on external debt.
6
debt-GDP ratio will cross certain threshold, and so forth. To that end, I assume that Yt is
a multivariate stochastic process that evolves according to
p q
Yt = Î± + Î˜j Ytâˆ’j + Î¦h Xtâˆ’h + Îµt (2.2)
j=1 h=0
where t = 1, ..., T is a time index, Î± is a (6 Ã— 1) vector, the Î˜j are xed (6 Ã— 6) matrices on
lagged endogenous values, Xt is a (k Ã— 1) vector of exogenous variables, the Î¦h are (6 Ã— k)
matrices on current and lagged exogenous variables, and Îµt is a (6 Ã— 1) vector of independent
and identically distributed (i.i.d.) random shocks with mean zero and covariance matrix â„¦.
Importantly, the shocks Îµt could come from any probability distribution.
Specication (2.2) allows for rich dynamics on the determinants of foreign debt, includ-
ing feedback eects between endogenous variables and interactions of endogenous variables
with current and lagged exogenous variables. To compute statistics on foreign debt, the
researcher estimates (2.2) and then performs a large number of simulations of length Â¯
T (the
relevant horizon) coupled with the debt accumulation equation (2.1) to generate many debt
trajectories. The statistics are then computed by taking sample averages on the simulated
t0 +TÂ¯
data. To implement each simulated path, the researcher draws histories of shocks {Îµt }t=t0 +1 ,
where t0 is the initial period. Next, given a path for the exogenous variables Xt (more on
Â¯
this below), equation (2.2) is used to compute
T
{Yt }t0 +0 +1 .
t=t Finally, given the simulated series,
Â¯
the researcher computes
T
{dt }t0 +0 +1
t=t based on equation (2.1).
The standard implementation of the methodology uses a Monte Carlo method. The
researcher takes a stand on the probability distribution of the shocks Îµt , usually the normal
distribution, and draws shocks from the proposed distribution. A drawback of this approach
is that the researcher could choose the wrong distribution. Indeed, in the case of low income
countries, the estimation of (2.2) lead to errors that are far from normally distributed:
estimated residuals have substantial excess kurtosis (fat tails) and skewness (see Subsection
3.2). To cope with this problem, I replace the Monte Carlo step with a bootstrap procedure.
7
The researcher estimates (2.2) and then computes the tted residuals {Îµt }T .
t=1 The required
shocks are then drawn with replacement from the set of tted residuals. This makes the
7
methodology robust to residuals with fat tails and skewness.
A second extension of the specication (2.2), relative to most of the literature, is the
inclusion of exogenous variables aecting the dynamics of the endogenous variables. This
extension could be important as several variables, arguably exogenous to low income coun-
tries (like world GDP growth, commodity prices, world interest rates, or even the terms of
trade), are likely to have a non-trivial impact on the endogenous variables. The presence of
exogenous variables requires proposing a stochastic process for Xt independent of that for
Yt . Thus, in implementing the methodology, I assume that Xt evolves according to
k
Xt = Î² + Î¨j Xtâˆ’j + Î¾t (2.3)
j=1
where Î² is a (kÃ—1) vector, Î¨j are matrices on lagged values, and Î¾t is a (kÃ—1) i.i.d. shock with
zero mean and covariance matrix Î£. To compute trajectories for the exogenous variables, I
draw samples assuming that Î¾t is normally distributed. While it could be possible to use a
bootstrap procedure analogous to that describe above, I follow a Monte Carlo procedure for
reasons explained below.
3 Implementing the methodology using pooled data
The simulation approach has been applied mostly to emerging market economies and ad-
vanced countries. In these countries, there is typically suciently long time series at a
quarterly frequency that makes feasible the estimation of (2.2). Unfortunately, it is virtu-
ally impossible to build the required quarterly data set for any low income country. Even
7 The bootstrap procedure helps with tail events as long as they are actually realized in sample. It
might happen that these events are never realized in the observed sample, in which case the bootstrapping
procedure will not be able to capture them. The sample used in this paper, however, is relatively large with
many country-year observations. Moreover, several extreme events that do not t a normal distribution
are actually observed in sample.
8
yearly data are scarce and of dubious quality. Although some low income countries have
annual data dating back to 1971, time series with less than 40 observations are insucient
to estimate the process (2.2) in a reliable way. For example, even with 40 observations per
equation, a vector autoregression with six endogenous variables, a constant, one lag on the
endogenous variables, and no exogenous variables has 63 parameters to estimate with 240
observations, less than 4 observations per parameter.
To cope with this problem, I pool data from several low income countries allowing for
partial heterogeneity in the form of country xed-eects and country-specic exogenous
variables, but assuming common slope coecients and covariance matrix across countries.
Thus, I replace the specication (2.2) with a vector autoregression applied to a panel of
cross-country and time series data (Panel VARX) represented by
p q
Yi,t = Î±i + Î˜j Yi,tâˆ’j + Î¦h Xi,tâˆ’h + Îµi,t . (3.1)
j=1 h=0
Here, countries are indexed by i = 1, 2, ..., N ; the time index is t = 1, 2, ..., Ti , where Ti
denotes the number of usable observations per country; and p and q denote the number
of lags on the endogenous and exogenous variables respectively. Thus, the total number
N
of observations is T = i=1 Ti . In addition, Î±i is a vector of country xed-eects and
the residuals Îµi,t are i.i.d. shocks satisfying E (Îµi,t ) = 0, E Îµi,t Îµi,t = â„¦ for all i and t,
E Îµi,t Îµi,s = 0 for all i and t = s, and E Îµi,t Îµj,s = 0 for any s, t and i = j. The slope
coecients Î˜j and Î¦k , and the covariance matrix â„¦ are common across countries. Thus, the
methodology computes the dynamic response on the endogenous variables of a generic low
income country. Note, however, that there are two sources of heterogeneity across countries.
The rst takes the form of a xed-eect aecting the intercept of the regression. The second
is that the realization and stochastic process followed by the exogenous variables Xi,t could
dier across countries.
9
The endogenous variables are represented by the (6 Ã— 1) vector
ï£® ï£¹
Real GDP growthi,t
ï£¯ ï£º
ï£¯ ï£º
Growth of GDP deator in US dollarsi,t
ï£¯ ï£º
ï£¯ ï£º
ï£¯ ï£º
ï£¯ ï£º
ï£¯ Implicit interest ratei,t ï£º
Yi,t =ï£¯
ï£¯
ï£º.
ï£º
ï£¯ Non-interest current account/GDPi,t ï£º
ï£¯ ï£º
ï£¯ ï£º
Net ow of FDI/GDPi,t
ï£¯ ï£º
ï£¯ ï£º
ï£° ï£»
Debt shocki,t
The set of exogenous variables is divided in two groups. The rst is a group of common
variables to all countries and includes (i) World GDP growth, (ii) a world interest rate proxied
by the U.S. one year constant maturity treasury rate, and (iii) the logarithm of the price of
oil. The second is a set of country-specic variables. Choosing a country specic exogenous
variable is problematic due to endogeneity concerns. The terms of trade is one variable
that is arguably exogenous to developing countries. This is a usual assumption made in the
literature and is based on the observation that developing countries, being small relative
to the rest of the world, have a negligible impact on the relative prices they face in world
markets (for example, Broda, 2004; Fomby, Ikeda, and Loayza, Forthcoming). Following this
8
literature, I include the logarithm of the terms of trade as an exogenous variable. In sum,
the vector of exogenous variables used in this paper is given by
ï£® ï£¹
Log of terms of tradei,t
ï£¯ ï£º
ï£¯ ï£º
ï£¯ World GDP growtht ï£º
Xi,t =ï£¯ ï£º.
ï£¯ ï£º
U.S. one year constant maturity treasury ratet
ï£¯ ï£º
ï£¯ ï£º
ï£° ï£»
Log price of oilt
Since the vector Xi,t includes a country-specic variable, the parameters of the process
8 I use the log-levels of the price of oil and the terms of trade because, as shown in Section 3.3 below, it
is possible to reject the null hypothesis of a unit root in both of these variables.
10
(2.3) must also be indexed by country i, or
k
Xi,t = Î²i + Î¨i,j Xi,tâˆ’j + Î¾i,t . (3.2)
j=1
It is well known that xed-eect least squares estimators of dynamic panel models (also
called least squares dummy variables estimator, or LSDV) lead to inconsistent estimates when
the time dimension Ti is short and xed, even if the cross-section dimension N increases to
innity (Nickell, 1981). As Ti grows large, however, the bias decreases and disappears as Ti
goes to innity. In practical terms, however, Ti of the order of 20-30 is usually enough to
make the bias small. The basic data set used in this paper includes 76 low income countries
with data going back to 1971. The panel, however, is unbalanced. Thus, whether the sample
is long enough is an empirical question. To cope with this issue, I implement a version
of the bootstrap bias correction algorithm originally proposed by Pesaran and Zhao (1999)
and recently extended by Tanizaki, Hamori, and Matsubayashi (2006), Everaert and Pozzi
(2007), and Fomby, Ikeda, and Loayza (Forthcoming). The interested reader is referred to
9
these papers for more details on the bias correction procedure.
3.1 Data
The data consist of an unbalanced panel of 76 low income countries over the period 1971-
2007 for which there is enough information to construct uninterrupted time series for the
endogenous variables Yit . Table 1 provides a list of the countries and the years for which there
are data for the entire vector of endogenous variables. Data are obtained from the World
Bank's World Development Indicators and the IMF's World Economic Outlook databases.
9 Fomby, Ikeda, and Loayza (Forthcoming) implement and extend a version of the bias correction method
proposed by Pesaran and Zhao (1999) to Panel VARs. In this paper, instead, I use an iterative procedure
similar to those proposed by Tanizaki, Hamori, and Matsubayashi (2006) and Everaert and Pozzi (2007). The
basic dierence between the two approaches is in the number of iterations in the bias correction algorithm:
while Pesaran and Zhao propose a single iteration on the procedure, Tanizaki, Hamori, and Matsubayashi and
Everaert and Pozzi propose iterating on an equation mapping regression coecients into updated regression
coecients. The bias corrected estimator is the xed point of that equation.
11
The variables and sources are presented in Table 2, and all growth rates are reported as
log-dierences.
Table 3 reports summary statistics of the raw data, including the debt shock constructed
using equation (2.1). The mean and median growth rates of GDP are 3.6 and 4.0 percent
respectively, but there is substantial heterogeneity across countries, as reected in a standard
deviation of 5.4 percentage points. Moreover, the minimum and maximum values observed
for the growth rate of real GDP are -70 and 30 percent, both corresponding to Rwanda
during 1994 and 1995 respectively. The average and median growth rates of the debt shock
are zero, but with a large volatility. The minimum debt shock corresponds to a large debt
relief episode occurred in Nicaragua, in 1996. Finally, the concessionality of the debt in low
income countries can be inferred by looking at the implicit interest rate. On average, low
income countries pay an interest of about 2.6 percentage points per year on their external
debt, with a relatively low standard deviation, of just 2 percentage points.
Table 4 reports the contemporaneous correlation of all endogenous and endogenous vari-
ables. Focusing on the rst column, one observes that GDP growth tends to be negatively
correlated with real exchange rate depreciations (as reected in its negative correlation with
the growth of the GDP deator in U.S. dollars), with net FDI inows, with world growth,
and with the price of oil. In addition, GDP growth is negatively correlated with both in-
terest rate measures, particularly so with the U.S. treasury rate. Moreover, there is a large
correlation between the implicit interest rate and the U.S. treasury rate, of about 46 percent.
This suggests that, although debt in low income countries contains a substantial concessional
component, it also responds to market forces. The table also shows a negative correlation
between the U.S. interest rate and FDI ows: periods with high interest rates are periods
with relatively low FDI ows, also consistent with the view that market forces do play sig-
nicant role in low income countries. Overall, two lessons can be learned from Table 4: rst,
it is important to take into account the co-movements between the variables that drive the
evolution of external debt, and second, it is important to incorporate exogenous variables
12
into the analysis.
3.2 Estimation of the Panel VARX
The lag structure of the panel VARX was chosen according to the Schwarz's Bayesian infor-
mation criterion (SBIC) and the Akaike information criterion (AIC). These are two standard
goodness of t criteria that select the lag length of dynamic models by adding a penalty term
to the likelihood value that increases with the number of parameters. The preferred model
is the one with lowest value of the information criterion. Table 5 reports the SBIC and AIC
values for dierent estimating models. In the table, p and q represent the number of lags in
the endogenous and exogenous variables respectively. The SBIC criterion selects the most
parsimonious model with one lag in the endogenous variables and no lags in the exogenous
variables. The AIC criterion selects a model with two lags in both the endogenous and
exogenous variables. To keep the model as parsimonious as possible, I use the lag struc-
ture selected by the SBIC criterion. (As a robustness check, Section 5 considers the model
selected by the AIC criterion.) The database is reduced to 72 countries with the required
information once we include the exogenous variables and proposed lag structure.
One contribution of this paper is to build a methodology consistent with fat tails and
skewness in the residuals of the equation (3.1). Figure 1 displays histograms of the esti-
mated residuals together with normal density functions with identical mean and variances.
If residuals are well approximated by a normal distribution, the histograms and the normal
densities should be close to each other. They are not. The histograms have fatter tails than
the normal density and, in some cases, one can observe some skewness as well. To com-
plement the graphical analysis, I performed six univariate and joint tests of (i) normality,
(ii) no excess kurtosis, and (iii) no skewness of the residuals based on the tests proposed
by Urzua (1997) (Table 6). In all cases, normality, no excess kurtosis, and no skewness are
rejected with extremely high condence in both the univariate and joint tests. Under the null
hypothesis of joint normality of residuals, the asymptotic distribution of the test statistic is
13
chi-square with 12 degrees of freedom. The estimated statistic is about 390000, leading to
rejection of the null hypothesis with enormous condence. Multivariate tests of no excess
kurtosis and no skewness are also rejected with great condence. Moreover, the kurtosis
statistic is two orders of magnitudes larger than the skewness statistic. This suggests that
the huge value of the joint normality test statistic is mostly due to fat tails in the distribution
of residuals. Regarding univariate tests, the data also reject normality, no excess kurtosis,
and no skewness for every residual. These results reinforce the need to use the bootstrap
procedure discussed above to perform the simulations.
Table 7 reports estimation results for the baseline specication. The upper panel reports
estimates based on the LSDV estimator; the lower panel, estimates based on the bias cor-
rected procedure. The rst two columns show the estimated coecients Î˜1 and Î¦0 . The
matrices on the third column report the estimated standard deviations of the residuals (on
the main diagonal) and the correlation coecients between estimated residuals (on the o-
diagonals). The two estimators deliver coecients of similar magnitude except for those in
the main diagonal of Î˜1 . The bias corrected estimator implies more persistence in the Yt
process than the LSDV estimator.
3.3 Country-specic information and implementation details
Additional pieces of information are still needed to apply the methodology in a particular
country: the country-specic intercept and the projections of the exogenous variables.
The Panel VARX provides estimates of country-specic intercepts Î±i . These estimates are
related to the mean values of the endogenous variables. In particular, taking unconditional
expectation in equations (2.3) and (3.1), and rearranging gives
ï£® âˆ’1
ï£¹
p âˆ’1 q k
Yi = I6 âˆ’ Î˜j ï£°Î±i + Î¦h I4 âˆ’ Î¨j Î²ï£» for all i, (3.3)
j=1 h=0 j=1
where Yi is the unconditional expectation of the endogenous variables in country i and Is
14
denotes an identity matrix of dimension s. This equation relates the parameters of (2.3) and
(3.1) to the long run averages of the endogenous variables Yi,t . Of course, because samples
are nite, the estimated country-specic intercept will be linked to historical averages instead
of population averages.
A baseline analysis proceeds as follows. If the proposed country is in the database, the
simulations are run using the estimated xed eect for that country. If the country is not
in the database or if the analyst distrusts the estimated historical averages, she could use
outside information (like experts' opinions or data from a similar country) to estimate or
guess a long run value for the endogenous variables, say Y. Then, she could use (3.3) to nd
the intercept as
p q k âˆ’1
Î±= I6 âˆ’ Î˜j Y âˆ’ Î¦h I4 âˆ’ Î¨j Î². (3.4)
j=1 h=0 j=1
Finally, simulations are based on the estimated parameters and the implied intercept Î±.
The analyst could also perform debt sustainability analyses under reform scenarios. For
example, suppose the analyst believes that some reform will increase the long run ow of
FDI to the country (and, perhaps indirectly, other endogenous variables as well). Then, she
could replace the vector of historical averages with a new vector Y reecting the long run
expectations of the reform. Equation (3.4) is then used to recover the intercept Î± to be used
in the debt sustainability analysis.
In such cases, however, the analyst must be aware that there is a feasibility constraint
relating the long run values of the endogenous variables with that of foreign debt. In eect,
taking unconditional expectations to both sides of equation (2.1) and rearranging leads to
Â¯ Â¯ Â¯
(1 + g ) (1 + Ï€ ) Â¯ Â¯
d= m+f âˆ’v
Â¯
(1 + r) âˆ’ (1 + g ) (1 + Ï€ )
Â¯ Â¯ Â¯
where a `bar' above a variable denotes its unconditional expectation. Thus, while the dy-
namics of external debt could vary during the transition to the steady state, the xed eect
15
determines the level to which foreign debt will converge to in the long run. This link between
the long run value of the endogenous variables and the long run value of debt is the result
of a feasibility constraint that holds independently of the methodology used to perform debt
sustainability analysis.
One could argue that it is strange to implicitly x the long run level of debt through
the choice of the country xed eect in an exercise whose objective is precisely to analyze
the sustainability of debt. The estimates obtained in the next section, however, imply that
external debt tends to converge to its long run value in 70 years or more. During the relevant
horizon (20 years or, preferably, less), the forecast levels of foreign debt are usually quite
dierent from those long run values.
The analyst also needs to estimate projections for the exogenous variables based on the
process (3.2). This specication could be dicult to estimate for each country of interest
due to data limitations. The following assumptions are imposed. First, I assume that the
(log) of the terms of trade follow a univariate autoregressive process independent of the other
exogenous variables. To perform the analysis for countries with minimal or no data on the
terms of trade, the analyst could use estimates from similar countries or simply assume a
process for it. Second, I assume that world GDP growth and the U.S. interest rate follow
a bivariate vector autoregression and that (log) oil prices follow a separate autoregressive
process. This is done for convenience and not necessarily for realism. In eect, oil prices
behave quite dierently before and after the mid 1970s. Thus, I use relatively long time
series (starting in 1962) to estimate a VAR for world GDP growth and the U.S. interest rate,
and a shorter time series to estimate the process for the price of oil and the terms of trade.
A standard augmented Dickey Fuller test rejects the null hypothesis of a unit root in
the logarithm of the price of oil over 1974-2010. According to the SIC and AIC information
criteria, an autoregressive process with one lag is enough to describe the dynamics of the
price of oil. The points estimates of the constant and coecient on lagged oil price are 0.33
and 0.91 respectively. The estimated standard deviation of the residuals is 0.27 and the
16
Durbin Watson statistic is 2.08, consistent with the absence of serial correlation in the tted
residuals. On the other hand, the two information criteria select a vector autoregression of
order 2 for the growth rate of world GDP and the U.S. interest rate.
Finally, to obtain projections for the exogenous variables, I draw samples assuming that
the residuals of the process (3.2) are normally distributed instead of following the bootstrap
approach. The reason for this choice is that many countries have short time series for their
country-specic exogenous variables (20 observations or less). It could be very misleading
to draw from such a small set of tted residuals.
3.4 A detailed example
This subsection implements the methodology using a ctitious country. First, I perform
a basic analysis of future debt trajectories and asses risks of debt distress, dened as the
probability that future debt trajectories cross certain thresholds. Second, I discuss how to
implement the analysis under a reform scenario that permanently increases the ow of FDI
in the long run. Finally, I use this example to illustrate that condence bands generated
with the bootstrap are tighter than those obtained under Monte Carlo.
To perform the experiment, I need to select a process for the logarithm of the terms of
trade, the initial values for Xt and Yt , and the country-specic intercept. I assume that the
logarithm of the terms of trade follows the process
log T oTt = 0.68 + 0.85 log T oTtâˆ’1 + ut ; ut âˆ¼ N (0, 0.152 ).
This process is roughly consistent with the observed evolution of terms of trade in low income
countries. The long run mean and standard deviation of the terms of trade implied by the
above process are 100 and 29.1 respectively.
The second and third columns of Table 8 display the initial conditions used in the exam-
ple. At time zero, the country has a level of foreign debt of 45 percentage points of GDP,
17
a growth rate of real GDP of 3 percent, a growth rate of the GDP deator measured in
U.S. dollars of 5 percent, and an implicit interest rate of 2 percent. The non-interest current
account and FDI are -7 and 3 percentage points of GDP respectively. These numbers imply
that the debt shocks is about -1.4 percentage points of GDP. The terms of trade is initialized
at log 100, and the price of oil is assumed to be 100 dollars per barrel. In addition, I assume
that at times t = âˆ’1, 0 world growth is 2 percent and the U.S. interest rate is 4 percent.
To set Î±, I use equation (3.4) and assume that the long run values of the six endogenous
variables are as displayed in the last column of Table 8. The remaining numbers in that
column are the implied long run values of the exogenous variables and of the debt-to-GDP
10
ratio as derived from equations (2.1) and (2.3).
The upper left panel of Figure 2 displays the projected histories of the debt-to-GDP
ratio over a 10 year horizon. These projections are based on 100000 simulations of length 10,
starting from the initial conditions in Table 8 and drawing shocks according to the bootstrap
procedure. The bold line is the median debt-to-GDP trajectory and the dashed lines are the
lower and upper quartiles of the implied distribution. The shaded areas denote percentiles
of the debt-to-GDP ratio at 5 percent increment. There are several things to note. Ignoring
uncertainty can be misleading in the debt sustainability analysis. In particular, one can
interpret the median evolution as the baseline projection of the debt-to-GDP ratio over the
proposed period. In this example, the median debt trajectory declines to 35 percentage
points of GDP over the proposed horizon, suggesting a low risk of debt distress. Results are
dierent, however, once we take into account the uncertainty involved in the projections.
Percentile bands are wide. One can nd many trajectories with suciently bad shocks that
drive the debt-to-GDP ratio to over 100 percent. Admittedly, the 95th percentile might be
an overly conservative bound to consider. Still, the upper quartile increases from the initial
45 percent to 62 percentage points over the simulation horizon, a non-trivial increase.
10 The long run average of the estimated process for the price of oil is 33.5. The joint process for world
growth and the U.S. interest rate delivers long run values of 3.5 and 6 percent respectively. Evaluating (2.1)
at the steady state gives a long run value of debt-to-GDP of 0.69.
18
A measure of risk of debt distress can be constructed by computing the probabilities,
conditional on information at time zero, that the debt-to-GDP ratio will cross some threshold
over the next years. The upper right panel of Figure 2 displays these probabilities for debt
thresholds of 60, 80, and 100 percentage points of GDP. I compute these probabilities at
each time horizon t = 1, 2, .., 10 by counting the number of debt histories that cross the
proposed bound at each horizon and dividing it by 100000. In this exercise, the probability
that foreign debt increases to 60 percent of GDP in ten years is 26 percent, to 80 percent of
GDP is 15 percent, and to 100 percent of GDP is 9 percent.
Figure 3 reports the evolution of the six determinants of debt. These projections give
an idea of the variables that explain the large condence bands of the debt trajectories.
The GDP deator in U.S. dollars is the most volatile variable, followed by the debt shock,
the non-interest current account, and GDP growth. The implicit interest rate and FDI are
less volatile. Moreover, these condence bands are consistent with the standard deviations
reported in Table 7. Note, however, that shocks tend to come in bundles. For example,
positive shocks to the non-interest current account tend to be associated with negative
shocks to FDI. This, of course, reects that estimated residuals are reduced form shocks of
some underlying structural shocks that remain unidentied by the proposed methodology.
The lower panel of Figure 2 shows results for a counterfactual reform that increases the
long run ow of FDI by one percentage point of GDP. The proposed reform has a large
impact on projected trajectories of debt. For example, the median forecast of foreign debt
decreases to 27 percentage points of GDP in 10 years, 8 percentage points smaller than before
the reform. The upper quartile increases only to 54 percentage points of GDP, 8 percentage
points lower than before the reform. Likewise, the probabilities that debt will cross any of
the proposed thresholds decline substantially after the reform.
Finally, Figure 4 compares statistics computed with the bootstrap procedure with those
based on Monte Carlo assuming normal shocks with a covariance matrix equal to that of
the tted residuals. Median debt trajectories are fairly similar under both methods. Sim-
19
ulations based on Monte Carlo, however, predict a somewhat lower debt-to-GDP ratio at
the end of the projection horizon. This might happen because the bootstrap distribution
is right-skewed. The remaining plots in Figure 4 show inter-percentile ranges of projected
debt-to-GDP ratios. For example, the lower left panel reports the inter-quartile range of
debt forecasts. The inter-quartile range is wider under the Monte Carlo approach. The same
is true for the 60th-40th inter-percentile range. The reason for this result is the following.
Relative to the associated normal density, the histogram of tted residuals has more proba-
bility mass around zero, more probability mass in few extreme values, and less probability
mass in medium-sized values. Thus, while it may occasionally draw extreme shocks, the
bootstrap most often draws small shocks relative to those of the normal distribution. This
makes condence bands tighter under the bootstrap approach. On the other hand, the 95th-
5th inter-percentile ranges are similar in both methods. This might be reecting that these
percentiles are capturing the extreme realizations occasionally drawn by the bootstrap.
4 A case study: Senegal
This section considers the case of Senegal to highlight some issues in implementing the
methodology. It is argued that following a mechanical approach could be misleading. To
obtain reasonable results, the analyst needs to consider carefully the choice of the country-
specic intercept. Failure to do so could lead to overly optimistic or overly pessimistic debt
scenarios. This section also compares the predictions obtained under the proposed method-
ology with those of the baseline IMFWorld Bank's debt sustainability analysis (DSA).
In 1996, the IMF and the World Bank launched the Heavily Indebted Poor Countries
(HIPC) initiative which consisted in providing debt relief to countries with unmanageable
debt burdens. In 2004, Senegal was granted 850 million U.S. dollars in debt service relief,
a large fraction of which was implemented immediately. Senegal's external debt declined
substantially, reinforcing a trend that started in 2000 (top panel of Figure 5). Foreign debt
20
declined from 82 to 34 percentage points of GDP between 2000 and 2006, with the bulk
of the drop between 2004 and 2006. Since 2006, however, the debt-to-GDP ratio begun to
11
increase, reaching slightly over 50 percentage points of GDP in 2010.
Panel B of Figure 5 displays the evolution of the six determinants of foreign debt, as
identied by equation (2.1). The average growth rate of real GDP between 2001 and 2010
was 4 percentage points, although with signicant volatility. The GDP deator in U.S.
dollars (that is, the reciprocal of the real exchange rate) was highly volatile, and the country
had a persistent current account decit net of interest payments. In addition, the large
negative values of the debt shock during 2005 and 2006 (-9 and -26 percent respectively)
reect the realization of the debt relief agreed under the HIPC initiative. FDI ows remained
roughly constant, at around 1.5 percentage points of GDP, and the implicit interest rate was
virtually constant at less than one percentage point.
The top panel of Figure 6 displays the evolution of foreign debt / GDP and the probabili-
ties that debt will cross the proposed thresholds during 2011-2020. Here, the country-specic
intercept is set at its estimated value based on historical data. The median foreign debt tra-
jectory decreases from 52 to just over 5 percentage points of GDP by 2020. Likewise, the
upper quartile of foreign debt decreases to 27 percentage points of GDP over the same hori-
zon. These trajectories imply that the probability of foreign debt increasing to 60 percentage
points of GDP during the next ten years is always smaller than 8 percentage points. Simi-
larly, the probabilities that debt will increase to more than 80 or 100 percent of GDP never
exceed 4 and 2 percentage points respectively. These predictions for foreign debt are, to a
large extent, driven by the proposed intercept. Evaluating equation (3.3) at the estimated
intercept implies very optimistic long run values of the endogenous variables: real GDP
growth is 4 percent, the growth rate of the GDP deator in U.S. dollars is 5 percent, the
ow of FDI is 3 percentage points of GDP, and the debt shock is -4.5 percentage points of
11 Throughout this section, the data for the debt-to-GDP ratio and the endogenous variables are taken
from the IMFWorld Bank May 2011 DSA (IDA and IMF, 2011).
21
12
GDP. These averages induce a strong decline in trajectories of foreign debt.
These estimated long run values, however, do not seem reasonable. For example, the
implied long run value for the debt shock is highly aected by the debt relief episode asso-
ciated with the HIPC initiative. In addition, it is dicult to believe that the yearly rate of
appreciation of the real exchange rate in Senegal will be, on average, 5 percentage points for
the indenite future. Therefore, it is important to be particularly careful with the long run
values of the determinants of debt implied by the proposed country-specic intercept. To
make this point more clear, the lower panel of Figure 6 displays results analogous to those in
the top panel, but setting the long run values of the endogenous variables in Senegal equal
13
to the pooled averages across time and countries. Results are quite dierent from those in
the top panel. For example, the median debt trajectory now decreases to only 29 percentage
points of GDP. Moreover, the probability that debt will increase to 60 percentage points
of GDP by 2020 is now over 20 percent, more than 12 percentage points larger than the
probability displayed in the top panel.
In sum, this exercise highlights the importance of having reasonable and accurate fore-
casts for the long run values of the main determinants of debt. Historical data is probably
not the best way to do that, given the changing environment in low income countries. Here,
the insight of experts knowledgeable of the country's idiosyncrasies could be extremely valu-
able. Alternatively, one could perform debt sustainability analysis under dierent long run
scenarios to assess the robustness of the results.
4.1 Comparison with the IMFWorld Bank DSA
This subsection explores the consequences of ignoring the co-movements between the deter-
minants of debt by comparing the predictions of the stress tests of a typical IMFWorld
Bank DSA (IDA and IMF, 2011) with those obtained using the methodology proposed in
12 The non-interest current account is -6 percentage points of GDP, inducing an increase in foreign debt.
This force, however, is not enough to neutralize the strong debt-reducing force of the other variables.
13 The implied country-specic intercept follows from equation (3.4).
22
this paper. Because the IMFWorld Bank framework ignores uncertainty, some changes are
needed to make the comparison possible.
The Senegal DSA includes baseline projections for external debt, real GDP growth, im-
plicit interest rate, growth rate of GDP deator in U.S. dollars, non-interest current account,
and FDI ows until 2030. Given these values, I recover the debt shock as explained in Section
2. Next, I obtain the residuals Îµt for t = 2011, 2012, ..., 2030 that make the predictions from
the IMFWorld Bank DSA consistent with the econometric model characterized by equa-
tions (3.1) and (3.2). While still ignoring uncertainty, this approach is equivalent to view the
projections from the DSA as being derived from a particular realization of the econometric
model (3.1)(3.2). Finally, I compute the standard deviation of the six determinants of debt
using their values over 2001-2010.
To compute the stress tests, I proceed as follows. The stress test according to the IMF
World Bank framework consists of adding a negative shock equal to one standard deviation
of the corresponding residual during 2011-2012. For example, in the case of GDP growth,
I subtract one standard deviation from the baseline projection only during the years 2011
and 2012. The remaining years and variables are set as in the baseline projection. A stress
test consistent with the methodology proposed in this paper is more involved. Consider the
case of GDP growth. On average, shocks to GDP growth are correlated with shocks to the
other variables. To take into account these correlations, I adjust the ve remaining residuals
in such a way that they are, on average, consistent with the covariance matrix of residuals.
Specically, let denote the proposed one standard deviation shock to GDP growth that
lasts for two periods and let Î¶t for t = 2011, 2012, ..., 2030 denote a new vector of residuals
for the proposed stress test. For t = 2013, 2014, ..., 2030, this vector satises Î¶t = Îµt . For
t = 2012 and 2013, the vector of residuals is given by Î¶i,t = Îµi,t + (â„¦1,i /â„¦1,1 ) where sub-
index i denotes the ith element of the corresponding vector and â„¦i,j is the (i, j) element of
14
the estimated covariance matrix of reduced form shocks. Finally, to compute the projected
14 Formally, I project the change in each reduced form shock into the change in the rst reduced form
shock. This is the same approach proposed by Pesaran and Shin (1998).
23
values for the determinants of debt, I use the dynamic equations (3.1)(3.2) evaluated at the
residuals Î¶t .
Figure 7 reports the baseline projection of foreign debt (solid line), stress tests ignoring
co-movements (dashed line), and stress tests taking into account the correlation between the
reduced form shocks and feedback eects between the determinants of debt (circled line).
Each panel represents a stress test equal to one standard deviation shock to the proposed
determinant of debt lasting for two years. The dierence between the dashed and circled
lines represents the bias induced by ignoring co-movements. In most cases, this dierence
is non-trivial and, typically, ignoring co-movements underestimates the increase in foreign
debt. For example, while a negative shock to FDI barely changes external debt according
to the IMFWorld Bank stress test, it does induce a sizable increase in foreign debt once
the co-movements are taken into account. In sum, this exercise suggests that ignoring co-
movements, as currently done in the IMFWorld Bank debt sustainability framework, could
lead to important biases in the projected trajectories of external debt.
5 Robustness checks
This section discusses three alternative specications to assess the robustness of the baseline
estimation. First, I consider the stability of the results to the sample of countries included
in the estimation. Second, I discuss results for the model chosen by the AIC criterion,
which includes two lags in the endogenous variables and two lags in the exogenous variables.
Finally, I re-estimate the model without exogenous variables. The robustness of the results
is assessed by comparing predicted debt trajectories and probabilities that debt crosses the
proposed bounds in the example economy under the baseline and alternative specications.
Consider rst the stability of the results to the sample of countries used in the estimation.
The top panel of Figure 8 displays results for a sub-sample of countries with 15 years of data
or more (the sample is reduced from 72 to 49 countries). The remaining panels of the gure
24
report results for sub-samples with twenty countries deleted at random independently of
their number of observations. In all cases, results are similar to those displayed in Panel A
of Figure 2, both in terms of projected debt trajectories and probabilities that foreign debt
/ GDP cross the proposed bounds. Thus, results do not seem sensitive to the particular
15
sample of countries used.
Consider next the predictions of the model selected by the AIC information criterion. This
is a model with two lags in the endogenous variables and two lags plus the contemporary
eect in the exogenous variables. Results are displayed in the top panel of Figure 9. Predicted
debt trajectories and probabilities of debt distress are very similar to those of the baseline
specication. Thus, it seems that there is not any signicant loss of information in choosing
the more parsimonious model selected by the SBIC information criterion.
Finally, results for the econometric specication with no exogenous variables are shown
in the lower panel of Figure 9. Here we observe some dierences relative to the baseline
model. In particular, the median, quartiles, and percentile bands of all debt trajectories
are higher than in the baseline specication. This implies that the probabilities of debt
crossing the proposed thresholds are also greater than those in the baseline specication.
I interpret these ndings as reecting the importance of including the proposed exogenous
variables when performing debt sustainability analyses. In this example, failing to do so
implies overly pessimistic statements about the projected evolution of foreign debt.
6 Concluding remarks
This paper presents an alternative to the current IMFWorld Bank debt sustainability frame-
work for low income countries. The proposed methodology alleviates several problems of the
current framework. Debt projections are based on a well dened econometric model that
takes into account the co-movements between the main determinants of debt and the un-
15 Results are still similar even when deleting thirty countries at random. There are, however, somewhat
larger dierences relative to the baseline model. This is to be expected as deleting thirty countries implies
dropping almost half of the original sample of countries.
25
certainty associated with them. Simulations are computed by drawing shocks from a set
of estimated residuals and, therefore, are based on the typical shocks faced by low income
countriestypically associated with a distribution with fat tails and skewness. In addition,
by averaging the behavior of many low income countries, the methodology is likely to reduce
the bias due to poor data quality in low income countries. As an example, the methodology
was applied to a ctitious country and to Senegal. Results in the paper suggest that ignoring
the co-movements between the main determinants of debt and the uncertainty associated
projected debt trajectories lead to signicant biases in these trajectories and, consequently,
in the assessment of whether external debt is sustainable or not.
The methodology has some limitations. First, it constraints the degree of cross-country
heterogeneity to a country-specic intercept and to country-specic exogenous variables.
The latter, however, could follow a dierent stochastic process for each country. In any
case, the methodology is a compromise between the rigidity imposed by the panel vector
autoregression and the problems associated with the lack of adequate data in low income
countries. Second, the set of reforms that can be analyzed by the methodology is limited.
The methodology considers reforms aecting only the long run values of the determinants of
debt. Reforms aecting short or medium term dynamics are not captured. This, however, is
a problem of any econometric approach analyzing policy evaluation, as Lucas (1976) pointed
out. Analyzing the impact of a reform on the entire data generating process requires writing
a fully specied structural model, something beyond the scope of this paper.
Finally, if other sources of country-specic forecasts are available, it could be possible to
combine these forecasts with those proposed by the current methodology. This could be done
by using Bayesian or other model averaging techniques to minimize prediction errors. The
combined model would lead to more precise forecasts and, therefore, to tighter condence
bands around median debt trajectories.
26
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28
A Appendix
This Appendix provides a detailed derivation of equation (2.1). Consider the evolution of
the international investment position
IIPt = IIPtâˆ’1 + CAt + Ï‰t . (A.1)
First, decompose the international investment position as IIPt = St âˆ’ Dt , where Dt is the
stock of foreign debt and St is the stock of equity-like positions (direct investment, portfolio
investment, nancial derivatives) and international reserves. Second, dene the non-interest
current account as N ICAt = CAt + IN Tt , where IN Tt is the country's interest payments
on its external debt. Introducing these denitions into the previous equation gives
St âˆ’ Dt = Stâˆ’1 âˆ’ Dtâˆ’1 + N ICAt âˆ’ IN Tt + Ï‰t ,
or, rearranging,
Dt = Dtâˆ’1 (1 + rt ) âˆ’ N ICAt + St âˆ’ Stâˆ’1 âˆ’ Ï‰t ,
where rt = IN Tt /Dtâˆ’1 is the implicit interest rate paid on external debt.
Furthermore, let St = Pt âˆ’DIt , where DIt is the (net) stock of direct investment owned by
foreigners, and Pt denotes the remaining items, consisting of the stocks of portfolio equity,
nancial derivatives, and international reserves. It then follows that St âˆ’ Stâˆ’1 = Pt âˆ’
Ptâˆ’1 âˆ’ F DIt , where F DIt is the net ow of foreign direct investment. In addition, letting
Vt = Pt âˆ’ Ptâˆ’1 âˆ’ Ï‰t , the last equation becomes
Dt = Dtâˆ’1 (1 + rt ) âˆ’ N ICAt âˆ’ F DIt + Vt . (A.2)
That is, the stock of foreign debt at time t equals the previous stock plus interest payments
minus the non-interest current account, minus the net ow of foreign direct investment plus
29
the term Vt which includes the changes in portfolio equity, nancial derivatives, international
reserves, valuation changes, and debt relief. The latter enters with a negative sign and is an
important item for low income countries.
Let Qt denote GDP measured in U.S. dollars and write (A.2) as
1 + rt
dt = dtâˆ’1 âˆ’ mt âˆ’ ft + vt . (A.3)
Qt /Qtâˆ’1
where dt = Dt /Qt , mt = N ICAt /Qt , ft = F DIt /Qt , and vt = Vt /Qt . Note that Qt /Qtâˆ’1
is the (gross) growth rate of GDP measured in U.S. dollars. The objective now is to write
Qt /Qtâˆ’1 in terms of the growth rate of real GDP (in constant local currency units) and
the growth rate of the GDP deator measured in U.S. dollars (a term proportional to the
reciprocal of the real exchange rate). Let Et denote the nominal exchange rate of local
currency per U.S. dollar, Pt the GDP deator in local currency, and qt real GDP measured
at constant local currency units. Then qt = Qt / (Pt /Et ) and thus,
Qt qt Pt /Et
=
Qtâˆ’1 qtâˆ’1 Ptâˆ’1 /Etâˆ’1
= (1 + gt )(1 + Ï€t ),
where gt is the growth rate of real GDP and Ï€t is the growth rate of the GDP deator
measured in U.S. dollars. Introducing this expression into (A.3) gives equation (2.1).
30
TABLE 1
Countries and number of observations
Country Years Country Years Country Years
Albania 1993-2007 Guinea 1988-2007 Paraguay 1971-1976
Angola 1990-2007 Guinea-Bissau 2000-2007 Rwanda 1971-2007
Armenia 1994-2007 Guyana 1971-2007 Samoa 2004-2007
Bangladesh 1984-2007 Haiti 1995-2007 Sao Tome and Principe 2002-2007
Benin 1988-2007 Honduras 1971-2007 Senegal 1971-2007
Bhutan 2002-2007 Jordan 1976-1977 Sierra Leone 1971-2007
Bolivia 1971-2007 Kenya 1975-2007 Solomon Islands 1991-2007
Burkina Faso 1973-2007 Kyrgyz Rep. 1995-2007 Sri Lanka 1977-2007
Burundi 1971-2007 Lao PDR 1988-2007 St. Kitts and Nevis 1985-1993
Cambodia 1994-2007 Lesotho 1980-2007 St. Lucia 1982-2007
Cameroon 1971-2007 Liberia 1979-1986 St. Vincent and the Gren. 1971-2007
Cape Verde 1987-2007 Macedonia, FYR 1995-2001 Sudan 1996-2007
Central African Rep. 1974-2007 Madagascar 1971-2007 Tajikistan 1993-2007
Chad 1971-2007 Malawi 1996-2007 Tanzania 1990-2007
Comoros 1987-2007 Maldives 1996-2007 Thailand 1971-1978
Congo, Dem. Rep. 1998-2007 Mali 1971-2007 Togo 1971-2007
Congo, Rep. 1971-2007 Mauritania 1977-2007 Tonga 2003-2007
Cote d'Ivoire 1971-2007 Moldova 1996-2007 Tunisia 1971-1976
Djibouti 1991-2007 Mongolia 1993-2007 Uganda 1991-2007
Dominica 1982-2007 Mozambique 1986-2007 Vanuatu 1982-2007
Egypt, Arab Rep. 1975-1998 Myanmar 1989-2004 Vietnam 1991-2007
Eritrea 1997-2007 Nepal 1996-2007 Yemen, Rep. 1991-2007
Ethiopia 1997-2007 Nicaragua 1995-2007 Zambia 1972-2007
Georgia 1997-2007 Niger 1971-2007 Zimbabwe 1971-2005
Ghana 1971-2007 Nigeria 1990-2007
Grenada 1982-2007 Papua New Guinea 1971-2007
This table reports the list low income countries included in the database and the years for which there is complete data for all of the endogenous variables.
TABLE 2
Variables and sources
Variable Definition Original Source
GDP growth Log difference of real GDP WDI 1/
Growth of GDP deflator in US dollars Log difference U.S. dollar value of the GDP deflator WDI
Implicit interest rate 3/ Interest on total external debt over total debt stock WDI
NICA/GDP 4/ Non-interest current account balance to GDP ratio WEO 2/
FDI/GDP Net Foreign Direct Investment to GDP ratio WEO
Debt shocks/GDP Derived from debt accumulation equation to GDP ratio WDI/WEO
Exports/GDP growth Log difference of Exports to GDP ratio WDI
Terms of trade Log terms of trade index (level = 100 in 2000) WDI
World Log GDP difference Log difference of World Real GDP WDI
US treasury rate Yield on U.S. Treasury securities at 1 year constant maturity U.S. Federal Reserve System
Log Oil Price Log Dubai crude oil price WDI
1/ World Development Indicators
2/ World Economic Outlook
3/ Current-year interest payments on external debt divided by previous period external debt stock.
4/ NICA is Current account balance plus interest payments on external debt
The data consist of 76 low income countries. If a country moves from low income to middle income, only the low income part of the sample is kept. Two
outliers were deleted from the sample: Liberia in 2007-2008 due to a huge drop in the current account balance, and Guinea in 1986, due to a unusual movement
in the GDP deflator in U.S. dollars. WDI data on non-interest current account and FDI had too many missing observations. For that reason, WEO data was used
instead. However, if several years of these variables are missing, data from WDI is used when available. If just one observation was missing, the observations
were interpolated using the two adjacent values.
TABLE 3
Summary statistics
Mean Median Std Dev Max Min
GDP growth 0.036 0.040 0.054 0.301 -0.697
Growth of GDP deflator in US dollars 0.038 0.041 0.149 1.136 -1.324
Implicit interest rate 0.026 0.020 0.022 0.243 0.000
NICA/GDP -0.049 -0.043 0.096 0.462 -0.942
FDI/GDP 0.028 0.012 0.057 0.487 -0.469
Debt shocks/GDP -0.004 0.001 0.136 0.804 -1.554
Log terms of trade 4.680 4.627 0.340 6.273 2.054
World GDP growth 0.031 0.033 0.011 0.063 0.003
US treasury rate 0.058 0.055 0.028 0.148 0.012
Log price of oil 3.000 2.920 0.676 4.225 0.525
This table reports summary statistics of data pooled across countries
TABLE 4
Pairwise correlations (percent)
GDP Deflator Int. rate NICA FDI Debt shock TOT World Treas. Oil
GDP growth 100
Growth of GDP deflator in US dollars -4.2 100
Implicit interest rate -1.9 4.0 100
NICA/GDP 2.0 5.5 11.9 100
FDI/GDP 9.6 1.8 -3.7 -45.2 100
Debt shock/GDP 1.1 10.8 17.6 45.9 2.0 100
Log terms of trade 0.2 3.9 17.9 17.6 -15.1 11.8 100
World GDP growth 8.7 8.7 -0.5 7.1 -2.0 -0.2 7.2 100
US treasury rate -9.8 -4.6 46.4 2.3 -17.4 0.3 22.4 1.1 100
Log price of oil 8.1 0.4 -10.5 -11.5 22.6 -9.0 -12.6 -16.6 -4.3 100
This table reports contemporaneous pairwise correlations in percentage points pooling observations across countries and time periods
TABLE 5
Lag structure selection
p 1 2
q SIC AIC SIC AIC
0 -18.75 -18.97 -18.73 -19.08
1 -18.72 -19.02 -18.69 -19.13
2 -18.67 -19.06 -18.65 -19.17
This table presents information criteria to choose the order of the
baseline Panel VARX. The letter "p" indicates the number of lags on
endogenous variables, the letter "q" indicats the number of lags on
exogenous variables. SIC stands for the Schwarz Information Criteria
and AIC, for the Akaike Information Criteria. Bold figures indicate the
minimum SIC/AIC.
TABLE 6
Normality, excess kurtosis, and skewness tests
Residuals Normality Kurtosis Skewness
GDP Growth 63646 *** 62728 *** 918 ***
Growth of GDP deflator in US dollars 12813 *** 12258 *** 556 ***
Implicit interest rate 240789 *** 235832 *** 4957 ***
NICA/GDP 11816 *** 11671 *** 146 ***
FDI/GDP 32144 *** 31659 *** 484 ***
Debt shock/GDP 21612 *** 20897 *** 715 ***
Joint Test 389841 *** 381945 *** 7897 ***
This table shows tests of normality, skewness, and kurtosis based on Urzua (1996). Individual residuals are tested
except in the last row which is a joint test. Univariate normality tests is distributed chi-square with 2 d.f. under the
null of normality. Joint normality test is distributed chi-square with 12 d.f. under the null of normality. Univariate
skewness and kurtosis tests are distributed chi-square with 1 d.f. under the null of zero skewness and zero kurtosis.
Joint test of skewness and kurtosis are distributed chi-square with 6 d.f. under the null of zero skewness and zero
kurtosis. Note: Asteriks (***) indicate rejection of the null at 1% significance level.
TABLE 7
Estimated coefficients and residuals
Coefficient on lagged values Coefficients on exogenous variables Residuals std. dev. (diagonal) and correlation
LSDV estimator
0.13 -0.01 -0.03 0.04 0.11 -0.01 0.01 0.41 -0.10 0.01 5.0 -7.1 5.5 3.4 -0.3 0.9
0.26 0.12 -0.16 -0.05 0.09 0.11 0.02 1.05 -0.26 0.00 -7.1 13.8 6.6 8.7 -3.9 9.7
0.02 0.00 0.52 0.01 0.01 -0.01 0.01 -0.04 0.16 0.00 5.5 6.6 1.2 1.9 1.3 15.0
ï?‘1 ï€½ -0.06 -0.03 0.10 0.54 -0.20 0.00 ï?™0 ï€½ 0.04 0.54 -0.14 0.00 3.4 8.7 1.9 6.0 -33.4 32.1
0.04 0.00 -0.04 -0.04 0.61 -0.01 0.00 0.09 -0.12 0.01 -0.3 -3.9 1.3 -33.4 3.5 8.1
-0.11 -0.03 0.43 0.30 0.16 0.05 0.07 -0.02 -0.24 -0.01 0.9 9.7 15.0 32.1 8.1 11.8
Bias corrected estimator
0.19 0.00 0.00 0.04 0.11 -0.01 0.01 0.41 -0.10 0.01 5.0 -7.1 5.6 3.4 -0.3 0.9
0.26 0.17 -0.15 -0.05 0.07 0.11 0.02 1.02 -0.26 0.00 -7.1 13.9 6.6 8.7 -3.9 9.7
0.02 0.00 0.59 0.01 0.01 -0.01 0.01 -0.03 0.14 0.00 5.6 6.6 1.2 1.9 1.3 14.9
ï?‘1 ï€½ -0.06 -0.03 0.11 0.61 -0.20 -0.01
ï?™0 ï€½ 0.03 0.54 -0.15 0.00 3.4 8.7 1.9 6.0 -33.5 32.1
0.04 0.00 -0.03 -0.04 0.68 -0.01 0.00 0.08 -0.10 0.01 -0.3 -3.9 1.3 -33.5 3.5 8.0
-0.11 -0.03 0.40 0.31 0.17 0.11 0.06 -0.03 -0.23 -0.01 0.9 9.7 14.9 32.1 8.0 11.8
This table report estimated coefficients using a least squares dummy variable estimator (top panel) and the bootstrap based bias corrected estimator (lower panel). The diagonals of the "Residual
std. dev." matrix display the standard deviation of estimated residuals in percentage points; the off-diagonals display the correlation coefficient between estimated residuals in percentage points.
TABLE 8
Initial conditions and long-run values for example economy
Variable/Period -1 0 Long run
Debt/GDP - 0.45 0.69
GDP Growth - 0.03 0.04
Growth of GDP deflator in US dollars - 0.05 0.01
Implicit interest rate - 0.02 0.02
NICA/GDP - -0.07 -0.04
FDI/GDP - 0.03 0.02
Debt shock/GDP - -0.01 0.00
(log) terms of trade - log(100) log(100)
World growth 0.02 0.02 0.035
U.S. interest rate 0.04 0.04 0.06
(log) price of oil - log(100) log(33.5)
This table reports initial conditions and long run values for baseline experiment of
debt sustainability analysis. The long run values are used to construct the country
specific intercept.
Figure 1
Estimated residuals and associated normal densitites
GDP Growth Growth GDP Deflator in US dollars Implicit Interest Rate
500 300 600
250 500
400
200 400
300
150 300
200
100 200
100
50 100
0 0 0
-1 -0.5 0 0.5 -1.5 -1 -0.5 0 0.5 1 -0.1 0 0.1 0.2 0.3
NICA/GDP FDI/GDP Debt Shock/GDP
400 700 400
350 600 350
300 300
500
250 250
400
200 200
300
150 150
200
100 100
50 100 50
0 0 0
-1 -0.5 0 0.5 -0.4 -0.2 0 0.2 0.4 -1.5 -1 -0.5 0 0.5 1
This figure shows estimated residuals from the Panel VARX estimation and the corresponding normal densities with the same mean and variance of the
estimated residuals.
Figure 2
Debt evolution and risk of debt distress in example economy
Panel A. Baseline economy
External Debt/GDP Risk of Debt Distress
1.50 0.30
Prob( Debt / GDP > 0.60)
1.25 Prob( Debt / GDP > 0.80)
0.25 Prob( Debt / GDP > 1.00)
1.00
0.20
0.75
0.50 0.15
0.25
0.10
0.00
0.05
-0.25
-0.50 0.00
0 2 4 6 8 10 0 2 4 6 8 10
Years Years
Panel B. Reform scenario: FDI flows increase 1 percentage point of GDP in the long run
External Debt/GDP Risk of Debt Distress
1.50 0.30
Prob( Debt / GDP > 0.60)
1.25 Prob( Debt / GDP > 0.80)
0.25 Prob( Debt / GDP > 1.00)
1.00
0.20
0.75
0.50 0.15
0.25
0.10
0.00
0.05
-0.25
0.00
-0.50
0 2 4 6 8 10 0 2 4 6 8 10
Years Years
This figure shows debt trajectories, percentiles, and probability of debt crossing predetermined thresholds in the example economy. The top panel corresponds to the baseline
experiment. The lower panel corresponds to a reform scenario where the flow of FDI as a fraction of GDP is increased by 1 percentage point in the long run. In the left figures the
solid line is the median trajectory of foreign debt / GDP. The dashed lines are the first and third quartiles of the distribution. Shaded areas represent percentiles in 5 percent
increment. The figures on the right display the probabilities, as of time zero, that the foreign debt-GDP ratio crosses a threshold of 60 (solid line), 80 (dashed line), and 100 (circled
line) percentage points of GDP.
Figure 3
Determinants of Foreign Debt / GDP in the example economy
GDP Growth Growth GDP Deflator Implicit Interest Rate
0.25 0.25 0.05
0.20 0.20
0.15 0.15
0.10 0.10 0.025
0.05 0.05
0.00 0.00
-0.05 -0.05 0.00
-0.10 -0.10
-0.15 -0.15
-0.20 -0.20 -0.025
0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10
Year Year Year
NICA / GDP FDI / GDP Debt Shock / GDP
0.25 0.25 0.25
0.20 0.20 0.20
0.15 0.15 0.15
0.10 0.10 0.10
0.05 0.05 0.05
0.00 0.00 0.00
-0.05 -0.05 -0.05
-0.10 -0.10 -0.10
-0.15 -0.15 -0.15
-0.20 -0.20 -0.20
0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10
Year Year Year
Figure 4
Forecast foreign debt / GDP with bootstrapped and Monte Carlo residuals
Median Forecasts 60th - 40th percentiles
0.25
0.44 Bootstrapped residuals
Monte Carlo residuals 0.20
0.42
0.40 0.15
0.38 0.10
0.36 0.05
0.34
0.00
0 2 4 6 8 10 0 2 4 6 8 10
Years Years
75th - 25th percentiles 95th - 5th percentiles
0.60 1.60
0.50
1.20
0.40
0.30 0.80
0.20
0.40
0.10
0.00 0.00
0 2 4 6 8 10 0 2 4 6 8 10
Years Years
The upper left panel shows median forecasts of foreign debt / GDP in the example economy for simulation using the bootstrap method (solid line) and a Monte
Carlo method (dashed line) based on sampling residuals from a normal distribution. The remaining panels show inter-percentile ranges of foreign debt/GDP
ratio when drawing residuals using the bootstrap (solid line) and Monte Carlo method (dashed line)
Figure 5
Panel A: Evolution of foreign debt in Senegal (percentage of GDP)
0.90
0.80
0.70
0.60
0.50
0.40
0.30
2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010
Panel B: Evolution of the determinants of debt in Senegal
0.20
0.10
0.00
-0.10
-0.20
-0.30
2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010
GDP growth GDP deflator growth Implicit interest rate
NICA / GDP FDI / GDP Debt shock / GDP
Figure 6
Debt evolution and risk of debt distress in Senegal
Panel A. Projections based on historical average in Senegal
External Debt/GDP Risk of Debt Distress
1.00 Prob( Debt / GDP > 0.60)
0.20
Prob( Debt / GDP > 0.80)
Prob( Debt / GDP > 1.00)
0.75
0.15
0.50
0.25
0.10
0.00
0.05
-0.25
-0.50 0.00
2008 2010 2012 2014 2016 2018 2020 2010 2012 2014 2016 2018 2020
Years
Panel B. Projections based on cross-country averages
External Debt/GDP Risk of Debt Distress
1.00 Prob( Debt / GDP > 0.60)
0.20
Prob( Debt / GDP > 0.80)
Prob( Debt / GDP > 1.00)
0.75
0.15
0.50
0.25 0.10
0.00
0.05
-0.25
-0.50 0.00
2008 2010 2012 2014 2016 2018 2020 2010 2012 2014 2016 2018 2020
Years
This figure shows debt trajectories, percentiles, and probability of debt crossing predetermined thresholds in the example economy. The top panel corresponds to the baseline
experiment. The lower panel corresponds to a reform scenario where the flow of FDI as a fraction of GDP is increased by 1 percentage point in the long run. In the left figures the
solid line is the median trajectory of foreign debt / GDP. The dashed lines are the first and third quartiles of the distribution. Shaded areas represent percentiles in 5 percent
increment. The figures on the right display the probabilities, as of time zero, that the foreign debt-GDP ratio crosses a threshold of 60 (solid line), 80 (dashed line), and 100 (circled
line) percentage points of GDP.
Figure 7
Shock to GDP growth Shock to growth of GDP deflator Shock to implicit interest rate
0.70 0.70 0.70
With endogenous dynamics
Ignoring comovements
DSA baseline
0.65 0.65 0.65
0.60 0.60 0.60
0.55 0.55 0.55
0.50 0.50 0.50
0.45 0.45 0.45
0.40 0.40 0.40
2010 2015 2020 2025 2030 2010 2015 2020 2025 2030 2010 2015 2020 2025 2030
Shock to NICA Shock to FDI Shock to "Debt Shock"
0.70 0.70 0.70
0.65 0.65 0.65
0.60 0.60 0.60
0.55 0.55 0.55
0.50 0.50 0.50
0.45 0.45 0.45
0.40 0.40 0.40
2010 2015 2020 2025 2030 2010 2015 2020 2025 2030 2010 2015 2020 2025 2030
This figure displays the evolution of foreign debt based on typical World Bank - IMF Debt sustainability analysis (IDA and IMF, 2010) and six "stress tests" that consist of adding a shock of one standard deviation to each determinant of debt.
The solid line is the baseline projection; the circled line is the prediction taking into account the comovements and feedback effects across determinants of debt; and the dashed line is the prediction ignoring all comovements in the determinants of
debt. The difference between the circled and dashed lines can be interpreted as the error induced by ignoring comovements.
Figure 8
Robustness to change in sample size
Debt/GDP - Subsample 1 Risk Debt Distress - Subsample 1
1.50 0.35
0.30
1.00
0.20
0.50
0.10
0.00
-0.50 0.00
0 2 4 6 8 10 0 2 4 6 8 10
Year Years
Debt/GDP Subsample 2 Risk Debt Distress - Subsample 2
1.50 0.35
0.30
1.00
0.20
0.50
0.10
0.00
-0.50 0.00
0 2 4 6 8 10 0 2 4 6 8 10
Year Years
Debt/GDP Subsample 3 Risk Debt Distress - Subsample 3
1.50 0.35
0.30
1.00
0.20
0.50
0.10
0.00
-0.50 0.00
0 2 4 6 8 10 0 2 4 6 8 10
Year Years
Debt/GDP Subsample 4 Risk Debt Distress - Subsample 4
1.50 0.35
0.30
1.00
0.20
0.50
0.10
0.00
-0.50 0.00
0 2 4 6 8 10 0 2 4 6 8 10
Year Years
Pr(Debt/GDP>0.60) Pr(Debt/GDP>0.80) Pr(Debt/GDP>1.00)
This figure displays the evolution of foreign debt and probabilities of debt reaching certain thresholds in four different subsamples of
countries. Each subsample randomly deletes 20 countries from the original sample and reestimates the model.
Figure 9
Predictions using different empirical models in example economy
A. Forecasts and distress probabilities using model selected by AIC criterion
External Debt/GDP Risk of Debt Distress
1.50 0.30
Prob( Debt / GDP > 0.60)
1.25 Prob( Debt / GDP > 0.80)
0.25 Prob( Debt / GDP > 1.00)
1.00
0.20
0.75
0.50 0.15
0.25
0.10
0.00
0.05
-0.25
-0.50 0.00
0 2 4 6 8 10 0 2 4 6 8 10
Years Years
B. Forecasts and distress probabilities using model without exogenous variables
External Debt/GDP Risk of Debt Distress
1.50 0.45
Prob( Debt / GDP > 0.60)
1.25 0.40 Prob( Debt / GDP > 0.80)
Prob( Debt / GDP > 1.00)
1.00 0.35
0.30
0.75
0.25
0.50
0.20
0.25
0.15
0.00
0.10
-0.25 0.05
-0.50 0.00
0 2 4 6 8 10 0 2 4 6 8 10
Years Years
This figure displays the forecast and confidence bands of the Debt/GDP ratio and the probability of reaching debt thresholds in two alternative specifications of the empirical
model. Panel A uses the model selected by the AIC criterion, with two lags in the endogenous variables and two lags in the exogenous variables. Panel B reports results for
the model without exogenous variables.