Download Download (PDF)

Determinants and Output Growth
Effects of Debt Distress
Michael Binder, Sebastian Kripfganz and Tihomir
Stucka
Determinants and Output Growth
Effects of Debt Distress∗
Michael Binder†
Sebastian Kripfganz‡
Tihomir Stučka§
December 2014
Preliminary
Abstract
While the potential perils of debt distress are well understood, considerable uncertainty remains as to the empirical magnitude of the costs of debt distress, particularly
with respect to output growth losses induced by debt distress. In this paper, we propose a data-driven yet structured empirical model to characterize the cross-country
output growth implications of a country being in debt distress. Our dynamic panel
model with debt regime switching and endogenous sample selection in particular allows us to both consider the direct effect of indebtedness on output growth as well as
its indirect effect through changes in the distress probability. Our empirical evidence
suggests that the debt distress vs. output growth nexus is nonlinear: The direct effect
of increases in the debt burden on output growth is either relatively small or insignificant even in episodes of debt distress; an overall significant effect arises through the
indirect effect of increases in the debt burden increasing the probability of debt distress. Also importantly, the probability of debt distress is in any case state dependent,
varying strongly with a country’s institutional and policy track record.
Keywords: Debt distress; Output growth; Dynamic panel model; Regime switching;
Sample selection; Bias correction; State dependence
JEL Classification: C23; H63; O40
∗
We thank Orcun Kaya, participants of the GSEFM Summer Institute and the 19th International Panel
Data Conference, as well as seminar participants at Xiamen University, ETH Zürich and Goethe University
Frankfurt for helpful comments.
†
Goethe University Frankfurt, [email protected]
‡
Goethe University Frankfurt, [email protected]
§
The World Bank, [email protected]. The views expressed herein are those of the authors and
should not be attributed to the World Bank, its Executive Board, or its management.
1
1
Introduction
The recent acceleration in U.S. federal debt and sovereign debt crises in the Eurozone
renewed interest in the relationship between public debt levels, sovereign default, and domestic output growth. This interest goes back to identifying levels of debt that are likely
to either start impeding output growth, result in default, or both. The source of sovereign
debt default can be idiosyncratic or systemic in nature (Kaminsky and Vega-Garcı́a, 2014),
and in conjunction with a wide range of country-specific transmission mechanisms will
determine the cost with respect to lost domestic output growth. Country-specific circumstances include, among others, the size of the fiscal deficit, contingent liabilities, overvalued exchange rates, and trade regimes limiting exports. When combined with external
shocks such as, for instance, high interest rates, these adverse circumstances can be greatly
exacerbated.
Public debt default can carry a high cost characterized by many facets of damaged
sovereign reputation. Emerging markets hit by a debt crisis experience a drop in the
sovereign rating and, thus, a rise in interest spreads (Dell’Ariccia et al, 2004). In the
1980s, the first significant post-World War II wave of sovereign debt crises occurred in the
emerging markets of Latin America driven by high interest rates and a world recession.
Gelos, Sahay, and Sandleris (2011) estimate the loss in market access to have lasted for an
average of four years, unable to borrow on normal market terms. During the recent EU
crisis, Greece needed four years to regain access to international financial markets after
defaulting in 2010, while Ireland and Portugal tapped capital markets after two years.
Default or near-default on public debt is likely to extend beyond the sovereign. Debt
difficulties of the sovereign often spill over to state owned enterprises and private companies
deepening the adverse impact on domestic output growth. Moreover, political reputation
can also be damaged beyond repair. The latter occurs with governments forced to undertake politically costly structural reforms, say under IMF programs, often resulting in
a change in government (Borensztein and Panizza, 2009). International trade between
the debtor and creditor country can also be affected by default dampening positive trade
spillovers (Rose, 2005), while Borensztein and Panizza (2010) demonstrate that sovereign
defaults hurt disproportionally more export-oriented industries, therefore affecting adversely the source of important positive externalities in an economy. Finally, if spillovers
from difficulties with external public debt to the domestic financial system are pronounced,
then output growth losses are exacerbated by domestic credit rationing, among others, as
demonstrated by the recent crisis in European countries. The aforementioned transmission
channels are likely to cause a drop in domestic capital formation, stifling further future
2
output growth.
After the sovereign defaults in Latin America, the focus of debt problems shifted to
Africa. The debt crisis in low income countries arose from a combination of policy actions
in debtor countries, macroeconomic shocks in the world economy, and an acceleration of
bank lending during 1979–1981.1 More precisely, tightened monetary policy in industrial
countries aimed at combating inflationary pressures led to a world-wide recession. The
latter caused a drop in export prices and terms of trade in developing countries, which led
to the reversal of the interest rate-export growth relationship in the 1980s. The resulting
rise in debt burden indicators dried up private lending (Cline, 1990). Official lenders
responded to this debt overhang with debt relief efforts in the late 1990s and in 2005.
When analyzing debt crises, it becomes critical to differentiate the composition of
public debt in middle and low income countries. Debt portfolios in middle income countries
are associated with predominantly held private debt and limited recourse to official lending.
Debt portfolios in low income countries, in contrast, rely predominantly on official debt,
which exhibits a much higher grant element compared to commercial debt as reflected
in a below-market interest rate, long grace period and long maturities, all best captured
through debt levels expressed in present value terms. However, after receiving debt relief
from creditors in the late 1990s and in 2005 in exchange for good policies, some low income
countries have accessed international capital markets, benefitting from the search for yield
in an environment of quantitative easing. Others drew on new commercial credit lines,
available largely from China. Furthermore, capacity constraints in low income countries
imply differences in managing the debt portfolio when compared to emerging markets.
Under such circumstances, debt incidents can be the result of maturity concentrations, for
instance, and thus a feature of portfolio composition rather than public debt level.
Intuitively, liquidity-driven crises do not occur during normal times, but are rather
generated by shocks, at which point the sovereign’s borrowing constraint becomes binding
(Mendoza, 2002). Such shocks, if they affect international liquidity reminiscent of
the recent financial crisis, can affect non-defaulters by preventing their access to capital
markets. Such defaults, driven by systemic shocks, in principle have different consequences
compared to idiosyncratic shocks. The latter corresponds better to solvency crises, which
are typically self-fulfilling in nature as debt stocks reach levels that would be difficult to
service even during normal times. This debt overhang problem lies at the core of most
debt crises (Kaminsky and Vega-Garcı́a, 2014).
The global financial crisis and the ensuing “great contraction” featuring critical public
debt levels for advanced and developing economies alike, pose new questions for debt sus1
See the contributions in Sachs (1989).
3
tainability analysis. What are the quantitatively important robust factors driving “debt
intolerance” (Reinhart, Rogoff, and Savastano, 2003)? How do various categories of debt,
such as external public debt, domestic public debt, and private debt, interact in driving probabilities of sovereign debt distress? Are there threshold levels of public debt
that are critical for a country’s output growth performance (Reinhart and Rogoff, 2010;
Caner, Grennes, and Köhler-Geib, 2011), and, if so, are these threshold levels in turn dependent on a country’s institutional development, public policy record, and/or its financial
development?
In this paper, we first set out to model empirically the dynamics of debt accumulation
to quantitatively characterize the determinants of debt distress. This should be useful
in helping to enhance early warning systems for debt distress. To this end, we model in
the first stage of our approach the determinants of debt distress using a state-dependent
dynamic panel Probit model. We use the latter to quantify the impact of factors reflecting debt burden indicators, macroeconomic fundamentals as well as the institutional and
policy track record on the probability that a country is facing an episode of debt distress.
Following the methodology of Kraay and Nehru (2006) and Cohen and Valadier (2011),
we initially define external public debt distress as default and near-default events related
to the stock of arrears on public and publicly guaranteed external debt, the level of IMF
financing, and debt restructuring.
Our analysis also accounts for sample selection issues when modeling the short- and
long-run output growth implications of a country in debt distress. In the second stage of
our empirical analysis, the first-stage dynamic panel Probit model is used as a selection
equation for the analysis of the output growth implications of a country in debt distress. In
other words, the first-stage selection equation is complemented by a dynamic panel model
with state-dependent parameters that captures short- and long-run output growth under
the various debt regimes. The first- and second-stage equations together form a dynamic
panel output growth model with debt regime switching and endogenous sample selection.
With the switching regression setup, we consider both the direct effect of indebtedness on
output growth and its indirect effect through changes in the probability of debt distress. In
addition, our model allows for a rich set of transmission channels that may help explain how
country-specific characteristics affect probabilities of debt distress as well as the output
growth implications of debt distress. Our estimation methodology corrects for sample
selection and incidental parameter biases and is based on Fernández-Val and Vella (2011).
We estimate our model using a relatively large cross-country data set involving public debt
records for 122 countries.
As opposed to the previous literature, our dynamic switching regression model al4
lows in a structural way for nonlinearity of the output growth effects of the debt burden
indicator. The previous literature usually incorporates these nonlinear effects by estimating single-equation models with polynomial, spline, or threshold specifications. Using
a sample of 44 countries over a span of two centuries, Reinhart and Rogoff (2010) suggest that at public debt levels of 90 percent of GDP and above output growth drops
sharply from between an average of 3 to 4 percent to 0 percent, on average. Moreover, for emerging markets, external public debt at 60 percent is associated with adverse output growth effects. Herndon, Ash, and Pollin (2013), however, identified estimation errors, omission of available data, and random weighting of data resulting in biased outcomes of the Reinhart and Rogoff (2010) paper. They further demonstrate that
once advanced countries hit the 90 percent of GDP debt level, output growth rates deteriorate only modestly. Other recent investigations of the debt-growth nexus include
Baum, Checherita-Westphal, and Rother (2013), who employ a dynamic threshold panel
model on data for 12 euro area countries. They find a positive short run impact of public
debt on economic growth below a debt-to-GDP threshold of 67 percent, and a negative effect above a second threshold of 95 percent. Similarly, Cecchetti, Mohanty, and Zampolli
(2011) find a threshold for government debt of 85 percent of GDP after which the output
growth effect turns bad in their sample of 18 OECD countries. At this level, a further 10 percentage point increase in the ratio of public debt to GDP is associated with
a 17–18 basis point reduction in subsequent average annual growth. They discriminate
between different debt components by considering also corporate and household debt.
Pattillo, Poirson, and Ricci (2011) estimate growth models with quadratic debt terms or
spline expressions for 93 developing countries and find a negative marginal effect of external debt on GDP growth already from about 20 percent of GDP onwards. A similar debt
overhang threshold is found by Cordella, Ricci, and Ruiz-Arranz (2010) who in addition
estimate a debt irrelevance threshold around 70 to 80 percent of GDP for their sample of
79 developing countries. The authors find also an insignificant debt-growth relationship
at very low and very high levels of debt.
Our estimation results confirm some findings previously reported in the literature,
but also add new insights. We confirm previous results that inertia is the single, most
important characteristic of debt distress, while the institutional and policy track record
also seems to contribute significantly to explaining cross-country differences in debt distress
probabilities. Countries featuring a relatively poor institutional and policy track record
experience notably higher probabilities of entering into debt distress for given debt levels.
In the context of the interaction between debt regimes and output growth, we also find
empirical support that higher values of debt are associated with lower output growth and
5
that this relationship is nonlinear. In contrast to the previous literature, we establish that
the direct effect of increases in the debt burden on output growth is relatively small or
insignificant even in episodes of debt distress. An overall significant impact arises primarily
through the indirect effect of increases in the debt burden increasing the probability of debt
distress. Also, these effects are state dependent, varying in strength across the complete
spectrum of institutional and policy track records. Even under a poor record, the effects
are much smaller than suggested by Reinhart and Rogoff (2010), with implications for the
current policy debate.
The paper proceeds as follows. In the next section, we define debt distress events. In
Section 3, we set out the econometric framework for our empirical analysis. We describe in
detail the dynamic switching regression panel data model, the necessary bias corrections,
and the calculation of the conditional marginal effects of the debt-to-GDP ratio on output
growth. Thereafter, in Section 4, we describe the data that we use in the empirical part
of this paper, and we discuss the estimation results. In Section 5, we conclude.
2
Debt Distress Events
Building on the methodology of McFadden, Eckaus, Feder, Hajivassiliou, and O’Connell
(1985) and Manasse, Roubini, and Schimmelpfennig (2003),2 Kraay and Nehru (2006) define episodes of debt distress as default and “near default” events. More precisely, debt
distress occurs when: (i) countries accumulate a stock of arrears on public and publicly guaranteed (PPG) medium and long term external debt exceeding 5 percent of total
medium and long term external debt outstanding, (ii) countries use IMF financing (in the
form of commitments rather than disbursements) in excess of 50 percent of their quota, or
(iii) receive Paris Club rescheduling or debt reduction without adjusting for HIPC Completion Point. Kraay and Nehru (2006) consider only prolonged distress episodes of at least
three years that are, in addition, not preceded by another distress period in the previous
three years. This aims at the identification of distinct episodes that are not just results
of sporadic fluctuations in the above indicators. As a control group, Kraay and Nehru
(2006) define normal times as periods of five consecutive years without any debt distress
incidence. This definition treats distress and non-distress periods in an asymmetric way,
and many country-year observations cannot be used in the empirical analysis because they
2
McFadden et al. (1985) consider repayment problems in the form of arrears, higher-tranche IMF support, or rescheduling requests. Manasse et al. (2003) define a country “to be in a debt crisis if it is classified
as being in default by Standard & Poor’s or if it receives a large nonconcessional IMF loan defined as access
in excess of 100 percent of quota.” The same definition is used by Bandiera, Cuaresma, and Vincelette
(2011).
6
are neither classified as one nor as the other.
Cohen and Valadier (2011) refine the Kraay and Nehru (2006) definition. With respect
to IMF financing, they consider disbursements rather than commitments in excess of 50
percent of a country’s quota. With this definition, the exceptional IMF financial support
can be interpreted as a substitute for falling into arrears. Furthermore, Paris Club debt
relief for countries that reach the completion point of the Heavily Indebted Poor Countries
(HIPC) initiative is not considered as a distress event. To treat distress and normal times
symmetrically, they define the latter as non-crisis years preceded by three more years
without crisis.
We follow the definition of Cohen and Valadier (2011) for single year debt distress
events, but do not explicitly try to identify prolonged distress episodes.3 Our strategy
rather is to control within our econometric modeling framework (as described in Section
3) for ongoing distress episodes and allow for different impacts of the distress determinants
on the probabilities of entering into and exiting from a crisis. Moreover, the leeway of a
government might still be narrowed when the above debt distress criteria are already back
to normal levels. Therefore, for our empirical analysis we consider a country to be in
debt distress if it faces a distress event according to the above definition in the current or
previous year. This definition also captures cases where a distress event occurs just at the
end of a calender year and thus distorts the economy primarily in the subsequent year.
Figure 1 illustrates the construction of the debt distress index for the case of Kenya. In
the mid-1970s, Kenya received balance of payments support in the form of IMF commitments exceeding 50% of its quota.4 However, actual disbursements still remained below
this threshold. They reached the threshold triggering a debt distress event for the first
time in 1980, remaining significant for four years. After falling back to zero in 1984, Kenya
had to rely on IMF assistance again just one year later. Due to the one-year inertia in
the construction of our index, we therefore classify the whole time span from 1980 to
1886 as a period of continuous debt distress. The next four years were characterized by
a gradual rise in the total arrears on public and publicly guaranteed external debt that
finally exceeded the threshold value of 5% in 1991. The arrears rose further until 1993
before Paris Club reschedulings came into effect. This second period of prolongued debt
distress lasted until 1997. The debt renegotiations did not have a long-lasting effect such
that additional Paris Club debt relief became necessary in 2000 and 2004, definining the
third debt distress episode that was still about to continue at the end of our sample.
3
4
McFadden et al. (1985) and Bandiera et al. (2011) also use single year observations in their analysis.
Compare Kraay and Nehru (2006).
7
3
Econometric Methodology
3.1
Dynamic Switching Regression Panel Data Model
We consider the following dynamic panel data model with fixed effects and sample separation. Cross-sectional units are indexed by i = 1, 2, . . . , N , and time periods by t =
1, 2, . . . , T . The sample separation is determined by the debt distress selection equation:
dit = I{d∗it + ǫit ≥ 0},
(1)
where I is an indicator function returning 1 if the condition is satisfied and 0 otherwise,
and
d∗it = θdi,t−1 + z′it β + α1i .
(2)
This specification is dynamic as in McFadden et al. (1985) and Celasun and Harms (2011).
The regressors in zit are allowed to have a different impact on the entry and exit probabilities of a crisis, respectively, because their marginal effects depend on the realization of
di,t−1 .5 We additionally include country-specific fixed effects α1i . The debt distress effects
equation is characterized by two regimes, being in distress (dit = 1) or not (dit = 0):
yit =

ρ(1) y
ρ(2) y
i,t−1
i,t−1
(1)
+ x′it γ (1) + α2i + u1it ,
+ x′it γ (2) +
(2)
α2i
+ u2it ,
dit = 1
.
(3)
dit = 0
We assume that (ǫit , u1it , u2it )′ are independent and identically trivariate normally
distributed with zero mean and variance-covariance matrix


1
ζ1
ζ2

Σ = ζ1
σ12

σ12  .
ζ2 σ12
σ22
Equations (3) and (1) form a switching regression model with known sample separation and
yit observed in both regimes. Sample separation is endogenous if the covariance between
the disturbance term of the selection equation and the errors of the effects equations are
nonzero, ζ1 6= 0 or ζ2 6= 0.6 The regressors xit and zit are predetermined with respect
(1)
(2)
to the disturbances, and the unobserved unit-specific effects α1 , α2 , and α2
are fixed
without any distributional assumption. The initial observations yi0 and the initial states
5
Manasse et al. (2003) include interaction terms di,t−1 z′it as part of d∗it . However, this is not necessary
to obtain state-dependent marginal effects because of the nonlinearity of the Probit model.
6
See Maddala (1986).
8
di0 are observed.
We apply the two-stage estimation procedure developed by Heckman (1976, 1979). Let
(t)
di = (di1 , di2 , . . . , diT )′ , Zi = (zi1 , zi2 , . . . , ziT )′ , and di = (di0 , di1 , . . . , dit )′ . The partial
likelihood function of unit i for the first stage, the selection equation (1), conditional on
Zi and the initial state di0 is given by:
Ldi (θ, β, α1i |di , Zi , di0 ) =
T
Y
(t−1)
f dit |di
, zit ; θ, β, α1i ,
(4)
t=1
with the density function of the Probit model
f
(t−1)
dit |di
, zit ; θ, β, α1i
= Φditit (1 − Φit )1−dit ,
(5)
where Φit is the cumulative distribution function of the standard normal distribution
evaluated at d∗it . The maximum likelihood estimates are obtained as
T
N X
X
[dit ln Φit + (1 − dit ) ln(1 − Φit )] .
θ̂, β̂, {α̂1i }N
=
arg
max
i=1
θ,β,
i=1 t=1
{α1i }N
i=1
(6)
The endogenous sample separation would lead to an omitted variable bias in the least
squares estimation of the debt distress effects equation (3). The properties of the multivariate normal distribution imply
E[ujit |dit , di,t−1 , zit , α1i ] = ζj λit ,
where
λit =
j = 1, 2,
(dit − Φit )φit
Φit (1 − Φit )
(7)
is the inverse Mills ratio, and φit is the probability density function of a standard normal
random variable evaluated at d∗it . Consequently, we can account for the endogenous regime
selection by introducing λit as an additional control variable in equation (3):7
yit =

ρ(1) y
ρ(2) y
i,t−1
i,t−1
(1)
+ x′it γ (1) + ζ1 λit + α2i + e1it ,
+ x′it γ (2) + ζ2 λit +
(2)
α2i
+ e2it ,
dit = 1
,
(8)
dit = 0
(j)
such that E[ejit |yi,t−1 , xit , λit , dit , α2i ] = 0, j = 1, 2. The lagged distress indicator di,t−1
7
In our estimations we substract yi,t−1 from both sides of equation (8) to obtain a model in the change
of yit . This transformation does not affect any of the arguments in this section.
9
and the interaction terms di,t−1 z′it in the debt distress selection equation provide valid
exclusion restrictions if their coefficients are significantly different from zero.
Let yi = (yi1 , yi2 , . . . , yiT )′ , Xi = (xi1 , xi2 , . . . , xiT )′ , Λi = (λi1 , λi2 , . . . , λiT )′ , and
′
′
(t)
(1)
(2)
yi = (yi0 , yi1 , . . . , yit )′ . Also stack α2i = (α2i , α2i )′ , and ψ = (ψ (1) , ψ (2) )′ with ψ (j) =
′
(ρ(j) , γ (j) , ζj , σj )′ , j = 1, 2. Then, the partial likelihood function of unit i conditional on
Xi , Λi , the observed states di , and the initial observation yi0 is given by:
Lyi (ψ, α2i |yi , Xi , Λi , di , yi0 ) =
=
T
Y
(t−1)
g yit |yi
, xit , λit , dit ; ψ, α2i
t=1
T h
Y
t=1
idit
(t−1)
(1)
, xit , λit ; ψ (1) , α2i
g1 yit |yi
h i1−dit
(t−1)
(2)
,
, xit , λit ; ψ (2) , α2i
× g2 yit |yi
(9)
where g is the density for yit , and subscripts 1 and 2 denote densities given the two regimes.
Consequently, we can identify the parameters for both regimes separately as long as there
are no cross-regime restrictions:
ψ̂
(1)
ψ̂
(2)
(1)
, {α̂2i }N
i=1
(2)
, {α̂2i }N
i=1
=
=
max
T
N X
X
(t−1)
(1)
, xit , λit ; ψ (1) , α2i ,
dit ln g1 yit |yi
(10)
max
T
N X
X
(t−1)
(2)
, xit , λit ; ψ (2) , α2i ,
(1 − dit ) ln g2 yit |yi
(11)
ψ (1) , i=1 t=1
(1)
{α2i }N
i=1
ψ (2) , i=1 t=1
(2)
{α2i }N
i=1
with
ln gj
(t−1)
yit |yi
, xit , λit ; ψ (j)
1
1
= − ln(2πσj ) − 2 e2jit ,
2
2σj
j = 1, 2,
(12)
and ejit defined in equation (8). Furthermore, σ12 is not identified in the model because
we observe only either of the two regimes at a time.8
3.2
Incidental Parameters Problem and Bias Correction
When the estimation of the parameters of interest cannot be separated from the fixed
effects, the presence of the latter leads to inconsistent estimates if the time dimension
T is held fixed while the number of units N increases. This is the familiar incidental
parameters problem discussed first by Neyman and Scott (1948). It is particularly relevant
8
See also Maddala (1986), Section 2.
10
in nonlinear models because there usually exists no transformation that removes the fixed
effects. Hahn and Newey (2004) show that the resulting bias also does not vanish when N
and T grow at the same rate towards infinity, and discuss panel jackknife and analytical
bias correction. Fernández-Val (2009) provides a large-T expansion of the bias for index
coefficients and marginal effects in panel binary choice models. We apply his procedure
to our maximum likelihood estimates of the debt distress selection equation.
The incidental parameters problem also arises in the estimation of the second stage,
the debt distress effects equation. One source of bias is again the presence of the fixed
(1)
(2)
effects, α2i and α2i . In linear models, one possibility to deal with unobserved unitspecific heterogeneity is to transform the model such that the fixed effects are wiped out,
for example by first differencing. However, in our switching regimes model first differencing
will only remove the fixed effects when they are restricted to be the same in both regimes
or when regime shifts do not occur within units over time. A second source of bias is
due to the inclusion of the inverse Mills ratio as a control variable for the endogenous
sample separation. As can be seen from expression (7) this control variable is a function
of the first-stage incidental parameters α1i and needs to be replaced by an estimate λ̂it =
λ(dit , di,t−1 , zit ; θ̂, β̂, α̂1i ). Therefore, the estimation error in the first-stage fixed effects
transmits to an error in the estimation of λit . We apply the analytical bias correction for
such two-stage fixed effects panel data estimators developed by Fernández-Val and Vella
(2011).
3.3
Marginal Effects of Debt on Output Growth
In our empirical analysis, the dependent variable yit of the debt distress effects equation
is the natural logarithm of real GDP per capita. We can easily obtain a representation of
equation (8) with the growth rate of real GDP per capita as the dependent variable by
subtracting yi,t−1 on both sides:
∆yit =

(ρ(1) − 1)y
(ρ(2) − 1)y
i,t−1
i,t−1
(1)
+ x′it γ (1) + ζ1 λit + α2i + u1it ,
+ x′it γ (2) + ζ2 λit +
(2)
α2i
+ u2it ,
dit = 1
.
(13)
dit = 0
Our key explanatory variable is the debt-to-GDP ratio that enters both the selection and
the effects equation. Without loss of generality, let x1it = z1it be the debt-to-GDP ratio.
11
We are interested in the marginal effect
1 X
∂E[∆yit |Iit ]
∂E[∆yit (dit )|Iit ]
∂f (dit )
=
f (dit ) + E[∆yit (dit )|Iit ]
∂x1it
∂x1it
∂z1it
dit =0
(1)
(2)
= γ1 Φit + γ1 (1 − Φit ) + E [∆yit (dit = 1) − ∆yit (dit = 0)|Iit ] β1 φit , (14)
where Iit = {yi,t−1 , xit , zit , di,t−1 }, and β1 φit is the marginal effect of debt on the distress
probability. We divide the total marginal effect into a direct and an indirect marginal
(1)
(2)
effect. The direct effect, γ1 Φit + γ1 (1 − Φit ), is the probability weighted marginal effect
for the two debt regimes. The indirect effect, E [∆yit (dit = 1) − ∆yit (dit = 0)|Iit ] β1 φit , is
the growth differential between the two regimes multiplied by the marginal effect on the
distress probability.
Due to the presence of Φit and φit the marginal effects are nonlinear in the regressor
variables xit and zit . That allows us to analyze the shape of the marginal effect over a grid
of values for our variables of major interest. For instance, we can calculate conditional
average marginal effects for given values of the debt-to-GDP ratio and the debt distress
indicator in the previous period by evaluating the marginal effect at these values and
averaging over the actual observations of the remaining variables in the sample.
State-dependent long-run effects of an increase in the debt-to-GDP ratio on the GDP
per capita level can be obtained as
∂E[yi∗ |d∗i , Ii∗ ]
∂x∗1i
=

γ (1) /(1 − ρ(1) ),
1
γ (2) /(1
1
− ρ(2) ),
d∗i = 1
d∗i = 0
,
(15)
where an asterisk denotes long-run equilibrium values. An overall direct long-run effect
results from weighting the two state-dependent effects with the respective long-run probabilities. The long-run probability for the distress regime is given by
Φ∗i =
Φi (d∗i,−1 = 1)
.
1 + Φi (d∗i,−1 = 1) − Φi (d∗i,−1 = 0)
(16)
The denominator results from ruling out regime switches in the long-run. An indirect
∗ , where
long-run effect can be computed as E [yi∗ (d∗i = 1) − yi∗ (d∗i = 0)|Ii∗ ] ∂Φ∗i /∂z1i
[1 − Φi (d∗i,−1 = 0)]φi (d∗i,−1 = 1) + Φi (d∗i,−1 = 1)φi (d∗i,−1 = 0)
∂Φ∗i
.
∗ = β1
∂z1i
[1 + Φi (d∗i,−1 = 1) − Φi (d∗i,−1 = 0)]2
A total long-run effect is again the sum of both.
12
(17)
4
Empirical Analysis
4.1
Data Description
Data on arrears, the external public and publicly guaranteed (PPG) debt stock, the external private non-guaranteed (PNG) debt stock, current debt service, and the Country
Policy and Institutional Assessment (CPIA) index are from the World Bank’s (WB) World
Development Indicators (WDI) database. The present value calculations of external PPG
debt using currency-specific commercial interest reference rates (CIRRs) taken from the
OECD database were provided by the Debtor Reporting System database and follow the
methodology outlined in Dikhanov (2005). External PPG debt in present value terms captures the financing terms in low income countries which have access to lending with a large
grant element. It can therefore be argued that this represents a superior debt burden measure when compared to nominal PPG debt, at least in the context of low income countries.
Data on Paris Club negotiations are from the Paris Club website and complemented with
data provided by the IMF. Data on IMF financing commitments and disbursements are
from the International Financial Statistics (IFS) database. We incorporate an extended
set of the domestic public debt data compiled by Abbas and Christensen (2010). Data on
GDP per capita, the investment share, and the population growth rate are taken from the
Penn World Table 7.0.
The dependent variable, ∆yit , in the distress effects model (3) is the growth rate of
real GDP per capita, measured as the difference in the natural logarithm of real GDP per
capita from period t − 1 to t. The explanatory variables, xit , are the ratio of the present
value of external PPG debt to GDP, the CPIA index, the investment-to-GDP ratio, and
the population growth rate. We further include a deterministic time trend. In additional
specifications, we add external PNG debt and domestic public debt as a ratio of GDP to
the list of regressors, as well as interaction terms to account for potential nonlinearities in
the direct marginal effects. The debt variables are measured in period t − 1 to accomodate
for potential endogeneity issues. This issue does not arise for the CPIA index which is
constructed as an assessment of the outcomes in the previous year. Thus, together with
the one-period lagged natural logarithm of real GDP per capita, yi,t−1 , these variables
represent the state of the economy at the beginning of a year. The investment share and
the population growth rate are standard variables in the empirical growth literature that
capture the contemporaneous change in the productive input factors capital and labor.
The explanatory variables zit in the distress selection model (1) and (2) contain the
whole set of explanatory variables from the output growth model.9 The measurement
9
Interaction terms are not included in the selection equation because interaction effects between the
13
of is the same as in the effects equation.10 Furthermore, the one-period lagged output
growth rate enters as a covariate to allow for dynamic feedbacks from the effects equation.
Together with the lagged distress indicator this variable serves as an exclusion restriction.
We restrict the analysis to developing and emerging market economies. In the main
part of the analysis we consider countries for which we have data available on all variables for at least 37 consecutive periods within the time span from 1970 to 2007. With
this restriction we obtain a slightly unbalanced panel data set for 72 countries. The sample shrinks to 53 countries when we add domestic public debt as a regressor variable.11
Without this restriction we have data available for 122 countries. Tables 3 and 4 provide
summary statistics for the variables used in the analysis for these samples which confirm
that the reduced samples have similar properties compared to the corresponding full sample. We also analyze subsamples for low and middle income countries according to their
classification by the World Bank.12
Table 3 reveals that the low income countries have a higher unconditional distress
probability (51 percent) compared to middle income countries (37 percent), and a smaller
real output growth averaging almost an entire percentage point annually. Both the higher
distress probability and smaller real output growth rates are also associated with much
smaller CPIA ratings, on average, in low income compared to middle income countries.
Low income countries accumulated a higher amount of external public debt relative to
GDP in present value as well as nominal terms. However, the difference in the nominal
and present value of external debt is 12 percentage points in low income countries, half the
size compared to the difference for middle income countries equivalent to 22 percentage
points. This reflects the more benign repayment profile in low income countries resulting
from more favorable financing terms obtained from official creditors.
Debt distress is related to lower output growth rates and higher debt-to-GDP ratios
(Table 5). The mean growth rate is seven times smaller in distress, and amounts to 0.3
percent only. Meanwhile, the median growth rate is three times smaller in distress (0.9
percent), emphasizing the sizeable variance in the data. Depending on the measure taken,
external PPG debt-to-GDP ratios are between 30 and 40 percentage points higher in the
variables arise already from the nonlinearity of the Probit model.
10
One-period lags of the explanatory variables to circumvent potential endogeneity problems are also used
by McFadden et al. (1985), Manasse et al. (2003), Kraay and Nehru (2006), and Bandiera et al. (2011).
Cohen and Valadier (2011) use two-year lags.
11
Table 1 lists the countries and available years. Note that the dynamic nature of our model reduces
the number of effectively available observations by one period per country. The limitation to countries
with many consecutive observations helps to reduce dynamic panel data biases that arise in small samples.
Also, the efficiency of the bias corrections is limited in strongly unbalanced panels.
12
A country is included in the low or middle income subsample over the whole time span if it was
classified as a respective country in at least one the years. Therefore, the two subsamples slightly overlap.
14
distress regime. When output growth rates are compared across four different debt groups,
along the lines of Reinhart and Rogoff (2010), we find a negative growth impact after the
first debt-to-GDP theshold set at 30 percent (Table 6). The average and median GDP
growth rates decline steadily with higher debt groups, in contrast to Reinhart and Rogoff
(2010), with the biggest drop in the median output growth rate occuring beyond 90 percent
of GDP in nominal terms, and 60 percent in present value terms. Interestingly, in nominal
terms the average GDP growth rate remains broadly constant between the second (30, 60)
and third (60, 90) debt group, and falls strongly thereafter. Furthermore, in line with our
working hypothesis, the unconditional distress probability increases steadily with higher
debt groups no matter how we measure debt. The unconditional probability of distress
doubles from 25 to 51 percent after countries reach a nominal debt level of 30 percent of
GDP. Above the last threshold of 90 percent of GDP in present value terms only three
observations in our sample are not distress events.
According to the taxonomy applied in the joint IMF-WB debt sustainability framework, we group the CPIA data into “weak performers” (CPIA ≤ 3.25), “medium performers” (3.25 < CPIA < 3.75), and “strong performers” (CPIA ≥ 3.75). The correlation
between output growth and policy performance is highlighted in Table 7, and is distinctly
different for each group. Weak policy performance is associated with much lower output
growth rates that are on average below 1 percent per annum. The difference in growth
performance seems to be somewhat asymmetric between the different CPIA groups, with
the increase in the average growth performance moderating as we move from medium to
high performers. For external PPG debt, the same relationship does not hold, in line with
our expectations. Better policy performers should be able to carry more debt, which we
can see for the median debt levels when we shift from weak to medium performers. A
shift from medium to high performers does not, however, translate into an increase in
the debt level. Together with the output growth description, this seems to suggest that
the difference between weak and medium performers is more critical when it comes to
economic performance, compared to the value of moving from medium to high performer.
This said, when measured against the unconditional probability of distress, it matters
whether a country is a weak, medium, or high performer. The distress probability drops
sizably between the last two groups.
In the following we report the estimation results based on the present value calculations.
Using nominal debt instead does not qualitatively alter the results. Quantitatively, the
effects become slightly smaller.
15
4.2
Debt Distress Determinants
The estimation results are presented in Appendix A. Table 8 shows the average marginal
effects on the debt distress probability for the samples with many consecutive observations,
and Table 9 for the extended samples that also include countries with shorter time series.
External PPG debt relative to GDP in present value terms is a significant predictor of
debt distress. An increase in the debt-to-GDP ratio of 10 percentage points adds on
average 2 percentage points to the probability of experiencing debt distress in low income
countries and 3 percentage points in middle income countries. Domestic public debt is
also significant in explaining debt distress. For the sample as a whole, the magnitude of
both external and domestic debt is close to 2 percentage points. In contrast to the findings
of Celasun and Harms (2011), adding external private debt to the model does not help to
explain the observed debt distress events among the low and middle income countries in
our sample.
Whether in the context of a low or middle income country, better quality of policymaking and of institutions matters. A higher CPIA index reduces significantly the distress
probability. More precisely, increasing the CPIA rating by one notch reduces the distress
probability by an average of 3 percentage points in low income countries, but has much
less significance in the context of middle income countries. The latter possibly goes back
to the notion mentioned above that shifts from weak to medium performers matter much
more than from medium to high performers, two groups in which middle income countries
are most likely to reside. The magnitude of the CPIA effect is robust in the presence of
other explanatory variables such as private external or domestic public debt. At the same
time, the initial level of GDP per capita does not have a significant effect suggesting that
it is the institutional development rather than the aggregate economic development that
matters for the distress probability. However, a drop in output growth by one percentage
point as a proxy of negative macroeconomic shocks significantly increases the debt distress
probability by about 2 percentage points in low income countries and 3 percentage points
in middle income countries.
The investment-to-GDP ratio can be seen as a measure of productive spending of the
available resources. Not surprisingly, a larger investment share significantly reduces the
probability of facing a debt distress event as it enhances the repayment capacity. Depending on the sample, the magnitude of this effect is almost as large as that of an increase in
external PPG debt with opposite sign, or even exceeds it. One possible argumentation is
that additional debt does not raise the distress probability if borrowed funds are invested
in productive capital projects.
16
State dependence matters for the determination of debt distress. The positive and
significant average marginal effect of the lagged distress indicator accounts for the inertia
of debt distress, although this effect captures in part the construction of our indicator.13
In this respect, we are able to distinguish between the entry and exit probabilities of debt
distress. On average, the probability of staying in distress is about 50 to 55 percentage
points higher than the probability of entering into debt distress. An important explanation
is that IMF program assistance and debt rescheduling plans typically last longer than a
single year. In addition, actual default or the perception of an increased default risk limits
the access to credit markets and further tightens the refinancing problems, in particualar
in middle income countries with larger private debt exposure.
The distress probability over the entire range of external PPG debt, conditional on
being already in distress or not is depicted in Figure 2, and the slope of the curve describes
the marginal effect.14 Countries that are not in distress in period t − 1 face a probability
of entering into distress of about 9 percent for very low debt levels. In the debt-to-GDP
range between 60 and 90 percent the probability of debt distress increases from 31 to 49
percent. At the upper limit, a debt level of 120 percent of GDP, our model predicts an
average distress probability of 65 percent. The distress probability of countries which are
already in distress does not decline below 63 percent even if their debt-to-GDP ratio is
close to zero. The level of debt still matters for these countries as the predicted probability
rises further to 76 percent at the first threshold of a debt-to-GDP ratio of 30 percent, and
to 89 percent for high-debt countries.
The average distress probability is clearly state dependent, varying along the whole
spectrum of a country’s institutional quality and policy track record (Figure 3). Comparing
countries with the highest and the lowest policy and institutional quality rating, we observe
significantly different entry probabilities into distress over the whole range of the debt
ratios under consideration. At 30 percent, countries with good institutions face an average
distress probability of only 7 percent as opposed to 31 percent in the case of weak policies
and institutions. The gap widens further when the second debt threshold is approached at
60 percent of GDP. At this point, the probabilities are 14 and 49 percent, respectively. If a
country is already in distress, good governance improves considerably the odds of returning
to normal times. At the lower end of the debt ratio range, the difference between the
highest and lowest CPIA category is 35 percentage points (42 versus 77 percent). However,
13
This effect is still strongly positive and significant if we consider only current period distress events
for the dependent variable. In the calculation of the marginal effects we take into account that the lagged
distress indicator is not a continuous but a binary variable.
14
The bootstrap confidence intervals are obtained by resampling the observations with country clusters.
We perform 2000 replications.
17
accumulating debt is more costly for good governance countries in this case because the
distress probability immediately starts rising while it remains virtually constant, though
on an already high level, for countries with weak policies. The difference between the two
groups remains significant up to a debt ratio of 45 percent of GDP.
4.3
Output Growth Effects of Debt Distress
In situations of debt distress output growth is on average two percentage points lower and
external PPG debt two to three times larger than in normal times (Table 5). Between
external debt and output growth we observe a negative relationship not only unconditionally (Table 6) but also conditional on the debt distress regime and additional covariates.
In the baseline case, adding 10 percentage points of external PPG debt relative to GDP
reduces annual output growth by 0.1 percentage points in the distress regime and by
0.3 percentage points in normal times, significant at the 10 percent level (Table 10). As
long as higher external PPG debt does not lead to a regime change, it may still increase
the perceived risk of future debt distress which in turn deteriorates the investment and
consumption climate. This effect remains unchanged when we add external private debt
and an interaction term of the two debt categories as additional regressors (Table 11).
However, while an increase in the external private debt-to-GDP ratio does not affect the
probability of debt distress, it enhances output growth. An explanation consistent with
both observations is that private debt is associated with direct capital investment, while
additional public debt is not uncommonly used for populist spending, in particular in the
run-up to elections. The effect of external private debt is more pronounced in the distress
regime for low income countries which reflects the mechanism that private activity can
step in as a growth driver when the government is not in a position to stimulate the economy. In middle income countries, the output growth effect of private debt is of a similar
magnitude in both regimes but significant at the 10 percent level in normal times only
(Table 12). The third debt component, domestic public debt, does not help to explain the
output growth differences among the two regimes (Table 13).
Among the other regressors, the effect of the quality of policy and institutions is significantly positive and slightly larger in the debt distress regime. While strong governance
generally help to boost economic growth it seems to be even more important when a
country faces a debt crisis. An improvement in the CPIA rating by one notch adds 1.5
percentage points to output growth in the distress regime, and 1 percentage point otherwise. The initial GDP level has a significantly negative effect on output growth which is
consistent with the conditional convergence hypothesis in the economic growth literature.
18
The coefficient of the investment share is significant and positive, as expected, while the
coefficient of the population growth rate is insignificant in most specifications. Only in low
income countries, a significantly negative link between the output and population growth
rates is observed.
The literature on the debt-growth nexus emphasizes that this relationship is nonlinear.
Conditional on not being in debt distress, we find evidence that the direct marginal effect
of external PPG debt accumulation is significantly negative for initially low debt-to-GDP
ratios but vanishes with higher initial debt ratios (second specification in Table 10). When
starting at zero debt, the first ten percentage points of accumulated debt are associated
with a cost of 1.7 percentage points in annual output growth.15 However, allowing for such
a polynomial specification increases the estimation uncertainty, and the output growth
effect of external PPG debt turns insignificant in the debt distress regime.
The direct effect of an increase in the debt-to-GDP ratio on output growth conditional
on the regime reveals only part of the picture. More external PPG debt also increases the
chance of falling into the debt distress regime that comes along with lower output growth.
This indirect effect adds up with the direct effect to the total effect of rising debt-to-GDP
ratios on output growth. Figure 4 shows these three effects for our baseline specification
with external PPG debt as the only debt component.16 The direct effect is given by
the probability-weighted average of the debt coefficient estimates for the two regimes in
the output growth regression. At the 95 percent confidence level it is insignificant over
the whole range of external PPG debt. Turning to the indirect effect, we can observe a
significant expected loss in output growth as a consequence of a higher debt distress risk
when additional external PPG debt is accumulated. The different shape of the output
growth effects conditional on being in debt distress in the previous period or not is due to
the strong state dependence of the debt distress probability. When a country is initially
not in debt distress, the indirect effect is significant for debt-to-GDP ratios below the
second threshold of 60 percent. If a country already faces a distress episode, additional
debt still triggers a significant loss in output growth until the first threshold of 30 percent
because it reduces the probability of exiting the distress regime.
In both situations, the total effect remains significant beyond the respective thresholds
even though both the direct and indirect effect turn individually insignificant. In this upper
range, only the combination of the direct and the indirect effect yields an overall significant
15
In further estimations not shown here we also add interaction terms between external public debt
and the additional regressors, in particular the CPIA index, but the respective coefficients turn out to be
insignificant.
16
As before, the bootstrap confidence intervals are obtained by resampling the observations with country
clusters 2000 times.
19
output growth response to changes in the debt-to-GDP ratio. If there is no distress in the
previous period, the accumulation of external PPG debt has an overall significant effect
until it reaches 107 percent of GDP. On average, an increase of the debt-to-GDP ratio
from 30 to 60 percent reduces the annual GDP growth rate about 1 percentage point.
When a country already is in distress the total effect becomes insignificant beyond a debtto-GDP ratio of 64 percent. The marginal effect is smaller than in normal times but a
debt accumulation from zero up to 30 percent of GDP still costs 0.75 percentage points
of output growth.
Figure 5 further differentiates these output growth effects of increases in the external
PPG debt-to-GDP ratio among the assessment of policies and institutions. Although the
marginal effect of external public debt on the debt distress probability depends significantly
on the policy and institutional quality, there is no evidence for significant interaction effects
with respect to output growth.
5
Conclusions
This article unifies two strands of the literature on the implications of rising public debtto-GDP ratios. On the one hand side, researchers and policy makers are interested in
quantifying a country’s capacity of debt absorption to avoid debt crises that impede a
sustainable development. On the other hand side, a lot of emphasis is recently put on analyzing the output growth consequences of debt accumulation. We argue that both issues
go hand in hand, and we provide a methodological framework to quantify simultaneously
the impact of increasing debt-to-GDP ratios on the probability of falling into debt distress
as well as their effect on output growth.
With regard to the first question, we go beyond the previous literature by allowing
for state dependence and unobserved country-specific heterogeneity in the determination
of debt distress probabilities by specifying a dynamic fixed effects Probit model. To
address the incidental parameters bias that results from the non-separability of the fixed
effects parameters, we employ the bias correction procedure of Fernández-Val (2009). A
novel contribution of our paper is that we use this first-stage regression in a second stage
to account for regime selection in a dynamic panel growth regression. Together, both
equations form a dynamic switching regression model that allows in a structural way for a
nonlinear relationship between debt-to-GDP ratios and output growth. Furthermore, we
are able to distinguish the direct effect of increases in the debt burden on output growth
and the indirect effect via the impact of rising debt on the debt distress probability. We
find that the direct effect is relatively small or insignificant even when a country is in debt
20
distress, while a significant impact on output growth results through the indirect effect.
This finding highlights that it is not the debt burden per se that hampers output
growth but the increased risk of experiencing a period of debt distress which is associated
with lower output growth. The probability of falling into debt distress is by all means state
dependent, varying across the complete spectrum of institutional and policy track record.
Countries with strong policies and institutions display a significantly larger debt tolerance.
This has important implications for the current policy debate, as it demonstrates that
there are no common fixed debt thresholds across countries after which a country’s output
growth performance deteriorates. Instead, the likelihood of falling into debt distress, and
consequently also economic distress, depends on country-specific characteristics which asks
for a differentiated analysis to determine sustainable trajectories for (external) public debt.
This conclusion is in line with the findings of Eberhardt and Presbitero (2013) who also
emphasize the importance of country-specific heterogeneity in the nonlinear relationship
between debt and growth.
While allowing for a rich set of transmission channels in the joint explanation of how
country-specific characteristics affect probabilities and output growth consequences of debt
distress, our model remains parsimonious by differentiating between two regimes only.
Different types of debt distress could hae a different impact on output growth in the
short and the long run. While we subsume default on sovereign debt, near-default events
as represented by IMF programs with exceptional quotas, and debt relief in low income
countries all under one debt distress definition, a more detailed analysis could potentially
provide further insight. While we do not find noteworthy differences for the output growth
effects of increasing debt-to-GDP ratios under variations of our debt distress definition,
allowing for additional heterogeneity in the form of a larger diversity of debt distress
regimes can still be a promising task on the future research agenda. Different forms of
debt distress might be associated with a different macroeconomic performance in terms of
output growth. However, on average this does not necessarily affect the marginal effects
of changes in the debt burden on output growth. Nevertheless, it may shed additional
light on the transmission mechanisms that are at play.
Moreover, a relevant research question is to see if the introduction of the multilateral
debt relief initiative (MDRI) in 2005 changes the picture. A debt relief event under
this initiative should carry a positive impact on output growth in the short and medium
run as low income countries gain more fiscal space for capital spending due to smaller
interest payments. Much smaller public debt levels should also remove the debt overhang
problem which is likely to increase investor interest eithr through more FDI inflows or
through additional financing my new bilateral lenders, for example China, and also may
21
even provide access to international bond markets. With our sample, the time span until
2007 is too short to provide a reliable answer to this question. However, restricting the
sample to end before 2005 tends to amplify the output growth effects suggesting that the
introduction of the MDRI might have led to a structural change in this relationship.
22
References
Abbas, S. M. A. and J. E. Christensen (2010). The Role of Domestic Debt Markets in
Economic Growth: An Empirical Investigation for Low-Income Countries and Emerging
Markets. IMF Staff Papers 57 (1), 209–255.
Bandiera, L., J. C. Cuaresma, and G. A. Vincelette (2011). Unpleasant Surprises: Determinants and Risks of Sovereign Default. In C. A. P. Braga and G. A. Vincelette (Eds.),
Sovereign Debt and the Financial Crisis, Chapter 2, pp. 45–62. Washington, D.C.: The
World Bank.
Baum, A., C. Checherita-Westphal, and P. Rother (2013). Debt and growth: New evidence
for the euro area. Journal of International Money and Finance 32, 809–821.
Borensztein, E. and U. Panizza (2009). The Cost of Sovereign Default. IMF Staff Papers 56 (4), 683–741.
Borensztein, E. and U. Panizza (2010). Do Sovereign Defaults Hurt Exporters? Open
Economies Review 21 (3), 393–412.
Caner, M., T. Grennes, and F. Köhler-Geib (2011). Finding the Tipping Point: When
Sovereign Debt Turns Bad. In C. A. P. Braga and G. A. Vincelette (Eds.), Sovereign
Debt and the Financial Crisis, Chapter 3, pp. 63–75. Washington, D.C.: The World
Bank.
Cecchetti, S. G., M. S. Mohanty, and F. Zampolli (2011). The real effects of debt. BIS
Working Paper 352, Bank for International Settlements.
Celasun, O. and P. Harms (2011). Boon or Burden? The Effect of Private Sector Debt on
the Risk of Sovereign Default in Developing Countries. Economic Inquiry 49 (1), 70–88.
Cohen, D. and C. Valadier (2011). The Sovereign Debt Crisis That Was Not. In C. A. P.
Braga and G. A. Vincelette (Eds.), Sovereign Debt and the Financial Crisis, Chapter 1,
pp. 15–44. Washington, D.C.: The World Bank.
Cordella, T., L. A. Ricci, and M. Ruiz-Arranz (2010). Debt Overhang or Debt Irrelevance?
IMF Staff Papers 57 (1), 1–24.
Dikhanov, Y. (2005). Historical PV of Debt in Developing Countries, 1980–2002. Mimeo,
The World Bank.
23
Eberhardt, M. and A. F. Presbitero (2013). This Time They Are Different: Heterogeneity
and Nonlinearity in the Relationship Between Debt and Growth. IMF Working Paper
13/248, International Monetary Fund.
Fernández-Val, I. (2009). Fixed effects estimation of structural parameters and marginal
effects in panel probit models. Journal of Econometrics 150 (1), 71–85.
Fernández-Val, I. and F. Vella (2011). Bias corrections for two-step fixed effects panel
data estimators. Journal of Econometrics 163 (2), 144–162.
Gelos, R. G., R. Sahay, and G. Sandleris (2011). Sovereign borrowing by developing
countries: What determines market access? Journal of International Economics 83 (2),
243–254.
Hahn, J. and W. K. Newey (2004). Jackknife and Analytical Bias Reduction for Nonlinear
Panel Models. Econometrica 72 (4), 1295–1319.
Heckman, J. J. (1976). The Common Structure of Statistical Models of Truncation, Sample
Selection and Limited Dependent Variables and a Simple Estimator for Such Models.
Annals of Economic and Social Measurement 5 (4), 120–137.
Heckman, J. J. (1979). Sample Selection Bias as a Specification Error. Econometrica 47 (1),
153–161.
Herndon, T., M. Ash, and R. Pollin (2013). Does High Public Debt Consistently Stifle
Economic Growth? A Critique of Reinhart and Rogoff. Working Paper 322, Political
Economy Research Institute.
Heston, A., R. Summers, and B. Aten (2011). Penn World Table Version 7.0. Center
for International Comparisons of Production, Income and Prices at the University of
Pennsylvania.
Kaminsky, G. L. and P. Vega-Garcı́a (2014). Varieties of Sovereign Crises: Latin America
1820–1931. NBER Working Paper 20042, National Bureau of Economic Research.
Kraay, A. and V. Nehru (2006). When is External Debt Sustainable? The World Bank
Economic Review 20 (3), 341–365.
Maddala, G. S. (1986).
Disequilibrium, Self-selection, and Switching Models.
In
Z. Griliches and M. D. Intriligator (Eds.), Handbook of Econometrics, Volume 3, Chapter 28, pp. 1633–1688. Amsterdam: North-Holland.
24
Manasse, P., N. Roubini, and A. Schimmelpfennig (2003). Predicting Sovereign Debt
Crises. IMF Working Paper 03/221, International Monetary Fund.
McFadden, D., R. Eckaus, G. Feder, V. Hajivassiliou, and S. O’Connell (1985). Is There
Life after Debt? An Econometric Analysis of the Creditworthiness of Developing Countries. In G. W. Smith and J. T. Cuddington (Eds.), International Debt and the Developing Countries, Chapter 7, pp. 179–209. Washington, D.C.: The World Bank.
Neyman, J. and E. L. Scott (1948). Consistent Estimates Based on Partially Consistent
Observations. Econometrica 16 (1), 1–32.
Pattillo, C., H. Poirson, and L. A. Ricci (2011). External Debt and Growth. Review of
Economics and Institutions 2 (3), Article 2.
Reinhart, C. M. and K. S. Rogoff (2010). Growth in a Time of Debt. American Economic
Review: Papers and Proceedings 100 (2), 573–578.
Reinhart, C. M., K. S. Rogoff, and M. A. Savastano (2003). Debt Intolerance. Brookings
Papers on Economic Activity 2003 (1), 1–74.
Rose, A. K. (2005). One reason countries pay their debts: renegotiation and international
trade. Journal of Development Economics 77 (1), 189–206.
Sachs, J. D. (1989). Developing Country Debt and Economic Performance, Volume 1:
The International Financial System. Chicago: University of Chicago Press.
25
A
Tables and Figures
Table 1: Estimation Sample, Countries with Long Time Series
Country
Sample 1
Sample 2
Country
Sample 1
Algeria
1970 – 2007
M
1971 – 2007 Laos
1971 – 2007
1971 – 2007
Argentina
1970 – 2007
M
1971 – 2007 Lebanon
Benin
1970 – 2007
L
1971 – 2007 Lesotho
1970 – 2007
1970 – 2007
Bolivia
1970 – 2007
L
1971 – 2007 Madagascar
Malawi
1970 – 2007
Botswana
1970 – 2007 LM
Brazil
1970 – 2007
M
Malaysia
1970 – 2007
Mali
1970 – 2007
Burkina Faso
1970 – 2007
L
1970 – 2007
Burundi
1970 – 2007
L
1971 – 2007 Mauritania
Cameroon
1970 – 2007
L
1971 – 2007 Mauritius
1971 – 2007
1970 – 2007
Central Af. Rep. 1970 – 2007
L
1971 – 2007 Mexico
1970 – 2007
Chad
1970 – 2007
L
1971 – 2007 Morocco
1970 – 2007
Chile
1970 – 2007
M
1971 – 2007 Nepal
Colombia
1970 – 2007
M
1971 – 2007 Nicaragua
1970 – 2007
1970 – 2007
Congo, D. Rep.
1970 – 2007
L
1971 – 2007 Niger
1970 – 2007
Congo, Rep. of
1970 – 2007 LM 1971 – 2007 Nigeria
Costa Rica
1970 – 2007
M
1971 – 2007 Pakistan
1970 – 2007
Panama
1970 – 2007
Cote d’Ivoire
1970 – 2007 LM
1970 – 2007
Dominican Rep.
1970 – 2007 LM 1971 – 2007 Paraguay
1970 – 2007
Ecuador
1970 – 2007 LM 1971 – 2007 Peru
Egypt
1970 – 2007 LM 1971 – 2007 Philippines
1970 – 2007
1970 – 2007
El Salvador
1970 – 2007 LM 1971 – 2007 Rwanda
1971 – 2007
Ethiopia
1971 – 2007
L
1971 – 2007 Samoa
Fiji
1971 – 2007
M
1971 – 2007 Senegal
1970 – 2007
Gabon
1970 – 2007
M
1971 – 2007 Sierra Leone 1970 – 2007
Sri Lanka
1970 – 2007
Gambia, The
1970 – 2007
M
Ghana
1970 – 2007
L
1971 – 2007 Sudan
1971 – 2007
1971 – 2007
Guatemala
1970 – 2007
M
1971 – 2007 Swaziland
Tanzania
1971 – 2007
Guinea
1971 – 2007
L
1970 – 2007
Guyana
1971 – 2007
L
1971 – 2007 Thailand
Haiti
1970 – 2007
L
1971 – 2007 Togo
1970 – 2007
1970 – 2007
Honduras
1970 – 2007 LM 1971 – 2007 Tunisia
1970 – 2007
India
1970 – 2007
M
1971 – 2007 Turkey
Indonesia
1970 – 2007
M
Uganda
1971 – 2007
1970 – 2007
Jamaica
1970 – 2007
M
1971 – 2007 Uruguay
1970 – 2007
Jordan
1971 – 2007 LM 1971 – 2007 Venezuela
1970 – 2007
Kenya
1970 – 2007
L
1971 – 2007 Zambia
Note: A country in sample 1 falls into the subsample “L” if it was classified as a low
and subsample “M” if it was classified as a middle income country in at least one of
26
Sample 2
L
M
1971 – 2007
L
L
L
1971 – 2007
M
1971 – 2007
L
1971 – 2007
L
LM 1971 – 2007
M
1971 – 2007
LM
L
1971 – 2007
LM 1971 – 2007
L
1971 – 2007
LM 1971 – 2007
M
1971 – 2007
M
1971 – 2007
LM 1971 – 2007
M
1971 – 2007
LM 1971 – 2007
L
L
L
1971 – 2007
L
1971 – 2007
L
1971 – 2007
L
LM
L
1971 – 2007
LM 1971 – 2007
L
LM 1971 – 2007
LM 1971 – 2007
L
M
1971 – 2007
M
L
1971 – 2007
income country
the years.
Table 2: Estimation Sample, Additional Countries with Shorter Time Series
Country
Sample 1
Sample 2
Country
Sample 1
Sample 2
Albania
1991 – 2007 L 1994 – 2007 Macedonia
1993 – 2007 LM
1993 – 2007
1974 – 2007
Armenia
1994 – 2007 L 1994 – 2007 Madagascar
1978 – 2007
L
1978 – 2007
Azerbaijan
1994 – 2007 M 1994 – 2007 Maldives
Bangladesh
1972 – 2007 L 1974 – 2007 Mauritania
1977 – 2004
1993 – 2007
L
1993 – 2007
Belarus
1995 – 2007 M 1995 – 2007 Moldova
1992 – 2007
L
1992 – 2007
Belize
1982 – 2007 M 1982 – 2007 Mongolia
Bhutan
1981 – 2007 L 1994 – 2007 Mozambique
1984 – 2007
L
Papua N. Guinea 1975 – 2007 LM
1975 – 2007
Bosnia a. Her. 1999 – 2007 M
1986 – 2007
M
1986 – 2007
Botswana
1972 – 2007 Poland
Brazil
1978 – 2007 Romania
1972 – 2007
M
1990 – 2007
1992 – 2007
M
1993 – 2007
Bulgaria
1990 – 2007 M 1991 – 2007 Russia
1971 – 2006
Burkina Faso
1976 – 2007 Rwanda
1971 – 2007∗
Cambodia
1989 – 2007 L 1993 – 2007 Samoa
Cape Verde
1981 – 2007 L 1981 – 2007 Sao Tome a. Pri. 1977 – 2007
L
1995 – 2007
1980 – 2007
M
1980 – 2007
China
1981 – 2007 M 1985 – 2007 Seychelles
1978 – 2007
L
1980 – 2007
Comoros
1976 – 2007 L 1982 – 2007 Solomon Islands
Cote d’Ivoire
1979 – 2007 Somalia
1971 – 2000
L
1994 – 2007
M
1994 – 2007
Djibouti
1978 – 2007 L 1993 – 2007 South Africa
1984 – 2007 LM
1984 – 2007
Dominica
1981 – 2007 L 1981 – 2007 St. Kitts a. N.
Eritrea
1994 – 2007 L 1995 – 2007 St. Lucia
1981 – 2007
L
1981 – 2007
1979 – 2007
L
1979 – 2007
Gambia, The
1976 – 2007 St. Vinc. a. Gr.
1971 – 2007∗
Georgia
1994 – 2007 L 1995 – 2007 Swaziland
1994 – 2007
L
1998 – 2007
Grenada
1975 – 2007 L 1975 – 2007 Tajikistan
Guinea
1991 – 2006 Togo
1975 – 2007
1985 – 2007
L
1985 – 2007
Guinea-Bissau 1977 – 2007 L 1986 – 2007 Tonga
1994 – 2007
M
Indonesia
1980 – 2007 Turkmenistan
Iran
1980 – 2007 M 1980 – 2007 Uganda
1971 – 2007∗
1994 – 2007
M
1994 – 2007
Kazakhstan
1994 – 2007 M 1994 – 2007 Ukraine
1992 – 2007
M
Kyrgyzstan
1994 – 2007 L 1995 – 2007 Uzbekistan
1981 – 2007
L
1982 – 2007
Laos
1989 – 2007 Vanuatu
Latvia
1994 – 2007 M 1994 – 2007 Venezuela
1971 – 2004
1981 – 2007
L
1992 – 2007
Lesotho
1973 – 2007 Vietnam
Zimbabwe
1980 – 2007 LM
1980 – 2007
Liberia
1971 – 2000 L
Lithuania
1994 – 2006 M 1994 – 2006
Note: A country in sample 1 falls into the subsample “L” if it was classified as a low income country
and subsample “M” if it was classified as a middle income country in at least one of the years.
∗
In sample 2, domestic debt data for Samoa is missing in the year 1998, for Swaziland in the years
1991 to 1993, and for Uganda in the years 1988 to 1993.
27
Table 3: Summary Statistics
Sample
1
(all)
Variable
Obs. Mean Std. Dev.
Min.
Max.
Distress
3731 0.464
0.499
0
1
GDP Growth
3731 0.017
0.078 -1.059
0.635
NPV of External PPG Debt / GDP
3731 0.404
0.572
0.000
10.596
Nominal External PPG Debt / GDP 3731 0.510
0.597
0.002
8.637
External Private NG Debt / GDP
3731 0.031
0.068
0.000
0.787
CPIA
3731 3.288
0.780
1.000
6.000
ln(GDP per Capita)
3731 7.724
0.958
4.764
10.169
Investment / GDP
3731 0.226
0.117 -0.331
0.852
Population Growth
3731 0.020
0.019 -0.376
0.450
1
Distress
2657 0.488
0.500
0
1
GDP Growth
2657 0.013
0.073 -1.059
0.619
(long)
NPV of External PPG Debt / GDP
2657 0.393
0.460
0.002
8.921
Nominal External PPG Debt / GDP 2657 0.496
0.490
0.003
8.241
External Private NG Debt / GDP
2657 0.030
0.058
0.000
0.585
CPIA
2657 3.309
0.769
1.000
6.000
ln(GDP per Capita)
2657 7.669
0.934
4.764
10.169
Investment / GDP
2657 0.218
0.116 -0.331
0.852
Population Growth
2657 0.023
0.013 -0.188
0.176
1
Distress
2638 0.510
0.500
0
1
GDP Growth
2638 0.014
0.078 -0.971
0.635
(all/L)
NPV of External PPG Debt / GDP
2638 0.462
0.656
0.000
10.596
Nominal External PPG Debt / GDP 2638 0.598
0.673
0.002
8.637
External Private NG Debt / GDP
2638 0.022
0.059
0.000
0.787
CPIA
2638 3.197
0.758
1.000
6.000
ln(GDP per Capita)
2638 7.381
0.829
4.764
9.488
Investment / GDP
2638 0.224
0.128 -0.331
0.852
Population Growth
2638 0.022
0.021 -0.376
0.450
1
Distress
1891 0.370
0.483
0
1
1891 0.022
0.073 -1.059
0.619
(all/M) GDP Growth
NPV of External PPG Debt / GDP
1891 0.337
0.464
0.010
8.921
Nominal External PPG Debt / GDP 1891 0.376
0.456
0.003
8.241
External Private NG Debt / GDP
1891 0.048
0.079
0.000
0.734
CPIA
1891 3.469
0.777
1.000
6.000
ln(GDP per Capita)
1891 8.314
0.744
5.130
10.169
Investment / GDP
1891 0.240
0.107 -0.108
0.722
Population Growth
1891 0.019
0.013 -0.107
0.108
Note: The sample classification is according to Tables 1 and 2. The subsample labeled “long”
only includes countries from Table 1. The debt-to-GDP ratios of external public and publicly
guaranteed (PPG) debt, external private non-guaranteed (NG) debt, and the natural logarithm
of GDP per capita are measured in period t − 1. GDP growth is constructed as the difference
in ln(GDP per Capita) from one period to the next.
28
Table 4: Summary Statistics
Sample
2
(all)
Variable
Obs. Mean Std. Dev.
Min.
Max.
Distress
3257 0.469
0.499
0
1
GDP Growth
3257 0.017
0.074 -1.059
0.622
NPV of External PPG Debt / GDP
3257 0.391
0.469
0.003
8.921
Nominal External PPG Debt / GDP 3257 0.498
0.532
0.006
8.241
External Private NG Debt / GDP
3257 0.031
0.066
0.000
0.734
Domestic Public Debt / GDP
3257 0.166
0.247
0.000
4.270
CPIA
3257 3.347
0.752
1.000
6.000
ln(GDP per Capita)
3257 7.795
0.959
4.764
10.169
Investment / GDP
3257 0.229
0.116 -0.331
0.852
Population Growth
3257 0.020
0.018 -0.376
0.450
2
Distress
1908 0.508
0.500
0
1
(long)
GDP Growth
1908 0.012
0.074 -1.059
0.619
NPV of External PPG Debt / GDP
1908 0.406
0.501
0.003
8.921
Nominal External PPG Debt / GDP 1908 0.494
0.517
0.009
8.241
External Private NG Debt / GDP
1908 0.031
0.056
0.000
0.536
Domestic Public Debt / GDP
1908 0.191
0.290
0.000
4.270
CPIA
1908 3.317
0.807
1.000
6.000
ln(GDP per Capita)
1908 7.778
0.952
4.764
10.169
Investment / GDP
1908 0.223
0.116 -0.331
0.852
Population Growth
1908 0.022
0.012 -0.107
0.108
Note: The sample classification is according to Tables 1 and 2. The subsample labeled “long”
only includes countries from Table 1. The debt-to-GDP ratios of external public and publicly
guaranteed (PPG) debt, external private non-guaranteed (NG) debt, domestic public debt, and
the natural logarithm of GDP per capita are measured in period t−1. GDP growth is constructed
as the difference in ln(GDP per Capita) from one period to the next.
Table 5: GDP Growth and Debt among Distress Regimes
Variable
GDP Growth (%)
No Distress
Distress
2.2
0.3
2.5
0.9
6.9
7.6
NPV of External PPG Debt (% of GDP)
21.4
58.1
17.1
46.6
17.0
57.8
Nominal External PPG Debt (% of GDP)
30.7
69.4
23.6
58.3
26.5
58.5
Observations
1356
1295
Note: These statistics are based on sample 1 (long). The distress indicator and the
GDP growth rate are measured in period t, while the ratio of external public and
publicly guaranteed (PPG) debt to GDP is measured in period t − 1.
Average
Median
Std. Dev.
Average
Median
Std. Dev.
Average
Median
Std. Dev.
29
Table 6: GDP Growth and Distress Probabilities among Debt Groups
NPV of External PPG Debt (% of GDP)
[0, 30)
[30, 60)
[60, 90)
[90, ∞)
GDP Growth (%)
Average
1.6
1.2
0.7
0.3
Median
2.1
1.7
0.9
0.6
7.7
6.1
7.0
8.5
Std. Dev.
Distress Events (%)
28.0
59.4
87.1
98.6
Observations
1430
717
295
215
Nominal External PPG Debt (% of GDP)
[0, 30)
[30, 60)
[60, 90)
[90, ∞)
GDP Growth (%)
Average
1.6
1.3
1.2
0.4
2.1
1.9
1.4
0.7
Median
7.7
6.4
6.3
8.5
Std. Dev.
Distress Events (%)
25.0
51.1
77.6
86.8
Observations
1138
756
407
356
Note: These statistics are based on sample 1 (long). The distress indicator and the
GDP growth rate are measured in period t, while the ratio of external public and
publicly guaranteed (PPG) debt to GDP is measured in period t − 1.
Table 7: GDP Growth, Debt, and Distress Probabilities among CPIA Groups
CPIA
[1, 3.25] (3.25, 3.75) [3.75, 6]
Average
0.2
1.8
2.6
Median
0.8
2.0
2.9
8.8
6.0
4.8
Std. Dev.
NPV of External PPG Debt (% of GDP) Average
41.5
39.0
35.6
Median
25.7
29.5
26.3
52.6
38.5
39.8
Std. Dev.
Distress Events (%)
56.2
49.8
34.7
Observations
1244
705
708
Note: These statistics are based on sample 1 (long). The distress indicator and the
GDP growth rate are measured in period t, while the ratio of external public and
publicly guaranteed (PPG) debt to GDP is measured in period t − 1.
Variable
GDP Growth (%)
30
200
20
150
15
% 100
10 %
50
5
0
0
1971
1977
1983
1989
1995
2001
2007
Debt Distress
Paris Club Rescheduling
IMF Commitments (SBA & EFF), Disbursed (% of quota)
PPG External Debt, Total Arrears (% of total PPG external debt)
Average Distress Probability (Percent)
20
40
60
80
100
0
0
Average Distress Probability (Percent)
20
40
60
80
100
Figure 1: Construction of the Debt Distress Indicator: Kenya
0
30
60
90
Net Present Value of External PPG Debt (Percent of GDP)
estimated probability
120
0
95% confidence interval
30
60
90
Net Present Value of External PPG Debt (Percent of GDP)
estimated probability
(a) No Distress in t − 1
95% confidence interval
(b) Distress in t − 1
Figure 2: Distress Probability
31
120
Table 8: Probit Results for the Debt Distress Selection Equation
Distresst
Distresst−1
(NPV of External PPG Debt / GDP)t−1
(External Private NG Debt / GDP)t−1
Sample 1 (long)
0.538
0.538
(0.041)***
(0.042)***
0.232
0.232
(0.062)***
(0.062)***
-0.021
(0.115)
(Domestic Public Debt / GDP)t−1
CPIAt
(GDP Growth)t−1
ln(GDP per Capita)t−1
(Investment / GDP)t
(Population Growth)t
-0.031
(0.011)***
-0.174
(0.078)**
0.010
(0.028)
-0.245
(0.087)***
0.248
(0.408)
-0.031
(0.011)***
-0.175
(0.078)**
0.011
(0.029)
-0.246
(0.088)***
0.247
(0.408)
Sample 2 (long)
0.553
0.549
(0.049)***
(0.050)***
0.211
0.207
(0.057)***
(0.058)***
-0.183
(0.152)
0.165
0.168
(0.069)**
(0.070)**
-0.030
-0.030
(0.012)**
(0.012)**
-0.190
-0.198
(0.090)**
(0.091)**
0.011
0.016
(0.034)
(0.036)
-0.282
-0.287
(0.103)***
(0.104)***
1.401
1.395
(0.768)*
(0.771)*
1908
970
53
36/36/36
Observations
2657
Distress Events
1296
Countries
72
Years (min./avg./max.)
36/36.9/37
* p < 0.1; ** p < 0.05; *** p < 0.01
Note: Bias corrected average marginal effects are obtained by applying the method of Fernández-Val
(2009) with the bandwidth parameter set to unity. The regressions include country-specific fixed effects
and a linear time trend. Standard errors are in parentheses.
32
Average Distress Probability (Percent)
0
20
40
60
80
100
Average Distress Probability (Percent)
0
20
40
60
80
100
0
30
60
90
Net Present Value of External PPG Debt (Percent of GDP)
CPIA = 1
CPIA = 3
CPIA = 5
120
0
CPIA = 2
CPIA = 4
CPIA = 6
30
60
90
Net Present Value of External PPG Debt (Percent of GDP)
CPIA = 1
CPIA = 3
CPIA = 5
CPIA = 2
CPIA = 4
CPIA = 6
0
0
Average Distress Probability (Percent)
20
40
60
80
100
(b) Distress in t − 1
Average Distress Probability (Percent)
20
40
60
80
100
(a) No Distress in t − 1
120
0
30
60
90
Net Present Value of External PPG Debt (Percent of GDP)
CPIA = 1
95% confidence interval
120
0
CPIA = 6
30
60
90
Net Present Value of External PPG Debt (Percent of GDP)
CPIA = 1
95% confidence interval
(c) No Distress in t − 1
(d) Distress in t − 1
Figure 3: Distress Probability, Conditional on CPIA
33
CPIA = 6
120
Table 9: Probit Results for the Debt Distress Selection Equation
Distresst
Distresst−1
(NPV of External PPG Debt / GDP)t−1
(External Private NG Debt / GDP)t−1
(all)
0.503
(0.024)***
0.232
(0.043)***
-0.124
(0.092)
Sample 1
(all/L)
0.476
(0.069)***
0.204
(0.039)***
0.039
(0.130)
(all/M)
0.530
(0.104)***
0.322
(0.148)**
-0.216
(0.156)
-0.026
(0.008)***
-0.238
(0.063)***
0.004
(0.022)
-0.152
(0.065)**
0.157
(0.211)
3731
1732
122
8/30.6/37
-0.028
(0.010)***
-0.198
(0.074)***
-0.015
(0.024)
-0.124
(0.070)**
0.092
(0.213)
2638
1346
83
13/31.8/37
-0.024
(0.013)*
-0.287
(0.152)*
0.046
(0.052)
-0.245
(0.137)*
0.323
(0.840)
1891
699
62
8/30.5/37
(Domestic Public Debt / GDP)t−1
CPIAt
(GDP Growth)t−1
ln(GDP per Capita)t−1
(Investment / GDP)t
(Population Growth)t
Sample 2
(all)
0.486
(0.031)***
0.171
(0.037)***
-0.129
(0.102)
0.181
(0.051)***
-0.028
(0.008)***
-0.256
(0.067)***
0.013
(0.026)
-0.226
(0.076)***
0.565
(0.399)
3257
1526
114
9/28.6/36
Observations
Distress Events
Countries
Years (min./avg./max.)
* p < 0.1; ** p < 0.05; *** p < 0.01
Note: Bias corrected average marginal effects are obtained by applying the method of Fernández-Val
(2009) with the bandwidth parameter set to unity. The regressions include country-specific fixed effects
and a linear time trend. Standard errors are in parentheses.
34
Table 10: Switching Regression Results for the Debt Distress Effects Equation
(GDP Growth)t
(NPV of External PPG Debt / GDP)t−1
Distress
-0.009
(0.005)*
(NPV of External PPG Debt / GDP)2t−1
(NPV of External PPG Debt / GDP)3t−1
CPIAt
ln(GDP per Capita)t−1
(Investment / GDP)t
(Population Growth)t
λ
0.015
(0.004)***
-0.077
(0.011)***
0.146
(0.035)***
0.019
(0.156)
-0.006
(0.006)
Sample 1 (long)
No Distress
Distress
-0.031
-0.018
(0.017)*
(0.016)
0.001
(0.007)
-0.000
(0.001)
0.010
0.015
(0.004)**
(0.004)***
-0.094
-0.079
(0.010)***
(0.011)***
0.174
0.148
(0.027)***
(0.035)***
-0.047
0.016
(0.227)
(0.156)
-0.004
-0.007
(0.006)
(0.006)
2657
1296
72
36/36.9/37
No Distress
-0.212
(0.063)***
0.408
(0.143)***
-0.214
(0.086)**
0.011
(0.004)***
-0.097
(0.010)***
0.188
(0.027)***
0.046
(0.229)
-0.004
(0.006)
Observations
Distress Events
Countries
Years (min./avg./max.)
* p < 0.1; ** p < 0.05; *** p < 0.01
Note: Bias corrected coefficients are obtained by applying the method of Fernández-Val and Vella (2011)
with the bandwidth parameter set to unity. The inverse Mills ratio λ is obtained from the Probit estimation reported in Table 8 that does not include external private NG debt as a covariate. The regressions
include country-specific fixed effects and a linear time trend. Standard errors are in parentheses.
35
Average Marginal Effect (Percentage Points)
−.07 −.06 −.05 −.04 −.03 −.02 −.01 0 .01 .02
Average Marginal Effect (Percentage Points)
−.07 −.06 −.05 −.04 −.03 −.02 −.01 0 .01 .02
0
30
60
90
Net Present Value of External PPG Debt (Percent of GDP)
estimated marginal effect
120
0
95% confidence interval
30
60
90
Net Present Value of External PPG Debt (Percent of GDP)
estimated marginal effect
95% confidence interval
Average Marginal Effect (Percentage Points)
−.07 −.06 −.05 −.04 −.03 −.02 −.01 0 .01 .02
(b) Direct Effect, Distress in t − 1
Average Marginal Effect (Percentage Points)
−.07 −.06 −.05 −.04 −.03 −.02 −.01 0 .01 .02
(a) Direct Effect, No Distress in t − 1
120
0
30
60
90
Net Present Value of External PPG Debt (Percent of GDP)
estimated marginal effect
120
0
95% confidence interval
30
60
90
Net Present Value of External PPG Debt (Percent of GDP)
estimated marginal effect
95% confidence interval
Average Marginal Effect (Percentage Points)
−.07 −.06 −.05 −.04 −.03 −.02 −.01 0 .01 .02
(d) Indirect Effect, Distress in t − 1
Average Marginal Effect (Percentage Points)
−.07 −.06 −.05 −.04 −.03 −.02 −.01 0 .01 .02
(c) Indirect Effect, No Distress in t − 1
120
0
30
60
90
Net Present Value of External PPG Debt (Percent of GDP)
estimated marginal effect
120
0
95% confidence interval
30
60
90
Net Present Value of External PPG Debt (Percent of GDP)
estimated marginal effect
(e) Total Effect, No Distress in t − 1
95% confidence interval
(f) Total Effect, Distress in t − 1
Figure 4: Marginal Effect of Debt on Output Growth
36
120
30
60
90
Net Present Value of External PPG Debt (Percent of GDP)
direct effect, CPIA = 1
direct effect, CPIA = 3
direct effect, CPIA = 5
Average Marginal Effect (Percentage Points)
−.07−.06−.05−.04−.03−.02−.01 0 .01 .02
Average Marginal Effect (Percentage Points)
−.07−.06−.05−.04−.03−.02−.01 0 .01 .02
0
120
0
direct effect, CPIA = 2
direct effect, CPIA = 4
direct effect, CPIA = 6
direct effect, CPIA = 1
direct effect, CPIA = 3
direct effect, CPIA = 5
30
60
90
Net Present Value of External PPG Debt (Percent of GDP)
indirect effect, CPIA = 1
indirect effect, CPIA = 3
indirect effect, CPIA = 5
120
0
indirect effect, CPIA = 2
indirect effect, CPIA = 4
indirect effect, CPIA = 6
total effect, CPIA = 1
total effect, CPIA = 3
total effect, CPIA = 5
120
indirect effect, CPIA = 2
indirect effect, CPIA = 4
indirect effect, CPIA = 6
(d) Indirect Effect, Distress in t − 1
Average Marginal Effect (Percentage Points)
−.07−.06−.05−.04−.03−.02−.01 0 .01 .02
Average Marginal Effect (Percentage Points)
−.07−.06−.05−.04−.03−.02−.01 0 .01 .02
30
60
90
Net Present Value of External PPG Debt (Percent of GDP)
direct effect, CPIA = 2
direct effect, CPIA = 4
direct effect, CPIA = 6
30
60
90
Net Present Value of External PPG Debt (Percent of GDP)
indirect effect, CPIA = 1
indirect effect, CPIA = 3
indirect effect, CPIA = 5
(c) Indirect Effect, No Distress in t − 1
0
120
(b) Direct Effect, Distress in t − 1
Average Marginal Effect (Percentage Points)
−.07−.06−.05−.04−.03−.02−.01 0 .01 .02
Average Marginal Effect (Percentage Points)
−.07−.06−.05−.04−.03−.02−.01 0 .01 .02
(a) Direct Effect, No Distress in t − 1
0
30
60
90
Net Present Value of External PPG Debt (Percent of GDP)
120
total effect, CPIA = 2
total effect, CPIA = 4
total effect, CPIA = 6
0
30
60
90
Net Present Value of External PPG Debt (Percent of GDP)
total effect, CPIA = 1
total effect, CPIA = 3
total effect, CPIA = 5
(e) Total Effect, No Distress in t − 1
120
total effect, CPIA = 2
total effect, CPIA = 4
total effect, CPIA = 6
(f) Total Effect, Distress in t − 1
Figure 5: Marginal Effect of Debt on Output Growth, Conditional on CPIA
37
Table 11: Switching Regression Results for the Debt Distress Effects Equation
(GDP Growth)t
NPV of External PPG Debt / GDPt−1
External Private NG Debt / GDPt−1
(NPV of External PPG Debt / GDP)t−1
× (External Private NG Debt / GDP)t−1
CPIAt
ln(GDP per Capita)t−1
(Investment / GDP)t
(Population Growth)t
λ
Distress
-0.009
(0.005)*
0.036
(0.060)
0.015
(0.004)***
-0.078
(0.011)***
0.147
(0.035)***
0.020
(0.156)
-0.006
(0.006)
Sample 1 (long)
No Distress
Distress
-0.031
-0.010
(0.017)*
(0.005)*
0.082
-0.092
(0.055)
(0.102)
0.235
(0.151)
0.010
0.015
(0.004)**
(0.004)***
-0.097
-0.076
(0.010)***
(0.011)***
0.171
0.147
(0.027)***
(0.035)***
-0.044
0.023
(0.227)
(0.156)
-0.004
-0.004
(0.006)
(0.006)
2657
1296
72
36/36.9/37
No Distress
-0.032
(0.018)*
0.064
(0.076)
0.076
(0.220)
0.010
(0.004)***
-0.097
(0.010)***
0.171
(0.027)***
-0.040
(0.227)
-0.004
(0.006)
Observations
Distress Events
Countries
Years (min./avg./max.)
* p < 0.1; ** p < 0.05; *** p < 0.01
Note: Bias corrected coefficients are obtained by applying the method of Fernández-Val and Vella (2011)
with the bandwidth parameter set to unity. The inverse Mills ratio λ is obtained from the Probit
estimation reported in Table 8 that includes external private NG debt as a covariate. The regressions
include country-specific fixed effects and a linear time trend. Standard errors are in parentheses.
38
Table 12: Switching Regression Results for the Debt Distress Effects Equation
(GDP Growth)t
NPV of External PPG Debt / GDPt−1
External Private NG Debt / GDPt−1
CPIAt
ln(GDP per Capita)t−1
(Investment / GDP)t
(Population Growth)t
λ
Sample 1 (all/L)
Distress
No Distress
-0.004
-0.018
(0.004)
(0.016)
0.113
0.063
(0.053)**
(0.059)
0.017
0.011
(0.004)***
(0.004)***
-0.075
-0.079
(0.011)***
(0.010)***
0.094
0.112
(0.036)***
(0.025)***
-0.338
-0.854
(0.103)***
(0.117)***
-0.003
-0.006
(0.007)
(0.006)
2638
1346
83
13/31.8/37
Sample 1 (all/M)
Distress
No Distress
0.001
-0.031
(0.006)
(0.020)
0.079
0.082
(0.061)
(0.047)*
0.015
0.008
(0.005)***
(0.004)*
-0.121
-0.080
(0.018)***
(0.010)***
0.240
0.179
(0.059)***
(0.032)***
-0.498
0.146
(0.402)
(0.277)
0.004
-0.031
(0.006)
(0.007)***
1891
699
62
8/30.5/37
Observations
Distress Events
Countries
Years (min./avg./max.)
* p < 0.1; ** p < 0.05; *** p < 0.01
Note: Bias corrected coefficients are obtained by applying the method of Fernández-Val and Vella (2011)
with the bandwidth parameter set to unity. The inverse Mills ratio λ is obtained from the corresponding
Probit estimation reported in Table 9. The regressions include country-specific fixed effects and a linear
time trend. Standard errors are in parentheses.
39
Table 13: Switching Regression Results for the Debt Distress Effects Equation
(GDP Growth)t
(NPV of External PPG Debt / GDP)t−1
(External Private NG Debt / GDP)t−1
(Domestic Public Debt / GDP)t−1
CPIAt
ln(GDP per Capita)t−1
(Investment / GDP)t
(Population Growth)t
λ
Sample 2 (long)
Distress
No Distress
-0.010
-0.018
(0.005)*
(0.024)
0.043
0.053
(0.076)
(0.067)
-0.008
-0.006
(0.011)
(0.028)
0.013
0.005
(0.004)***
(0.005)
-0.067
-0.093
(0.013)***
(0.014)***
0.147
0.213
(0.043)***
(0.035)***
-0.101
0.089
(0.243)
(0.264)
-0.007
-0.005
(0.007)
(0.007)
1908
970
53
36/36/36
Sample 2 (all)
Distress
No Distress
-0.005
-0.026
(0.005)
(0.016)*
0.125
0.085
(0.058)**
(0.042)**
-0.007
0.000
(0.011)
(0.020)
0.015
0.007
(0.004)***
(0.003)**
-0.076
-0.078
(0.011)***
(0.009)***
0.132
0.157
(0.033)***
(0.025)***
-0.636
-0.056
(0.099)***
(0.212)
-0.010
-0.002
(0.006)*
(0.005)
3257
1526
114
9/28.6/36
Observations
Distress Events
Countries
Years (min./avg./max.)
* p < 0.1; ** p < 0.05; *** p < 0.01
Note: Bias corrected coefficients are obtained by applying the method of Fernández-Val and Vella (2011)
with the bandwidth parameter set to unity. The inverse Mills ratio λ is obtained from the corresponding
Probit estimation reported in Tables 8 and 9. The regressions include country-specific fixed effects and
a linear time trend. Standard errors are in parentheses.
40