External
Debt
Management
and the HIPCs
Thorvaldur Gylfason
Debt: Good or bad?
It depends
If foreign borrowing is used well,
to finance profitable investments, etc.,
then borrowing may be a good thing
Many countries have developed with
the aid of external loans
This is how the US built its railways and
how Korea managed to develop so
rapidly from the 1960s onwards
Both countries paid back their debts
Debt: Good or bad?
Many other countries have fared less
well with their external debt
strategies because ...
... they did not use their foreign loans well
Too often, countries have borrowed
abroad to finance consumption, not
investment
Consumption does not increase the ability
of indebted countries to service their
debts, nor does low-quality investment
But high-quality investment does
Conceptual framework
If the world interest rate is lower than
the domestic interest rate, the
country will be a borrower in world
financial markets
Domestic firms will want to borrow at
the lower world interest rate
Domestic households will reduce their
saving because the domestic interest
rate moves down to the level of the
world interest rate
Conceptual framework
Real interest rate
Saving
Domestic
equilibrium
World
equilibrium
Borrowing
0
Domestic
saving
Domestic
investment
World
interest
rate
Investment
Saving, investment
Conceptual framework
Real interest rate
Saving
A
Domestic
equilibrium
World
equilibrium
B
C
D
Borrowing
World
interest
rate
Investment
0
Saving, investment
Conceptual framework
Real interest rate
Consumer surplus
before borrowing
Saving
A
Domestic
equilibrium
World
equilibrium
0
B
C
Producer surplus
before borrowing
Investment
Saving, investment
Conceptual framework
Real interest rate
Consumer surplus
after borrowing
A
Domestic
equilibrium
World
equilibrium
B
C
D
Borrowing
Producer surplus
after borrowing
0
Saving
World
interest
rate
Investment
Saving, investment
Conceptual framework
Before trade
After trade
Change
Consumer surplus
A
A+B+D
+ (B + D)
Producer surplus
B+C
C
-B
A+B+C
A+B+C+D
+D
Total surplus
The area D shows the increase in total surplus
and represents the gains from borrowing
Gains from trade:
Three main conclusions
 Borrowers are better off and savers
are worse off
 Borrowing raises the economic wellbeing of the nation as a whole
because the gains of borrowers
exceed the losses of savers
 If world interest rate is above
domestic interest rate, savers are
better off and borrowers are worse
off, and nation as a whole still gains
External debt:
Key concepts
Debt stock
Usually measured in dollars or other
international currencies
because debt needs to be serviced in foreign
currency
Debt ratio
Ratio of external debt to GDP
Ratio of external debt to exports
More useful for some purposes, because
export earnings reflect the ability to service
the debt
External debt:
Key concepts
Debt burden
Also called debt service ratio
Equals the ratio of amortization and
interest payments to exports
A  rD
q
X
F
q = debt service ratio
A = amortization
r = interest rate
DF = foreign debt
X = exports
External debt:
Key concepts
Interest burden
Ratio of interest payments to exports
Amortization burden
Also called repayment burden
Ratio of amortization to exports
F
rD
b
X
A
a
X
q=a+b
External debt: Magnitude
and composition
Magnitude of the debt
Debt should not become too large
How large is too large?
Measurement of the debt
Gross or net?
May subtract foreign reserves in excess of
three months of imports
Composition of the debt
FDI, portfolio equity, long-term loans,
short-term loans
External debt: Magnitude
and composition
Composition of the debt
Foreign direct investment
Least likely to flee, most desirable
Portfolio equity
Long-term loans
Short-term loans
Most volatile, least desirable
As a rule, outstanding short-term debt
should not exceed foreign reserves
External debt: Numbers
How can we figure out a country’s
debt burden?
Divide through definition of q by
income
F
A
D
r
Y
Y
q
X
Y
Now we have expressed the
debt service ratio in terms
of familiar quantities: the
interest rate r, the debt ratio
DF/Y, and the export ratio
X/Y as well as the
repayment ratio A/Y
Numerical example
Suppose that
r = 0.06
DF/Y = 0.50
A/Y = 0.05
X/Y = 0.20
Here we have a country
that has to use 40% of
its export earnings to
service its external debt
F
A
D
r
Y
q Y
X
Y
0.05  0.06  0.5 0.08
q

 0.4
0.2
0.2
African countries: External debt
2001 (% of exports)
Li ber i a
M adagascar
B ur undi
Congo, Dem. Rep.
Si er r a Leone
Gui nea-B i ssau
Sao T ome and P r i nci pe
Cent r al A f r i can
Rwanda
Zambi a
M aur i t ani a
E t hi opi a
M al awi
Ni ger
Comor os
Cot e d'I voi r e
B ur ki na Faso
Chad
Gui nea
Camer oon
Zi mbabwe
Congo, Rep.
Ghana
Uganda
M al i
Senegal
K enya
Ni ger i a
B eni n
A ngol a
Gabon
Gambi a, T he
T anzani a
Cape V er de
Lesot ho
Sout h A f r i ca
E r i t r ea
M ozambi que
Swazi l and
B ot swana
E quat or i al Gui nea
0
200
400
600
800 1000 1200 1400
African countries: External debt
2001 (% of GNP)
Li ber i a
Sao T ome and P r i nci pe
Gui nea-B i ssau
Congo, Dem. Rep.
Congo, Rep.
M aur i t ani a
A ngol a
Zambi a
Si er r a Leone
Cot e d'I voi r e
B ur undi
Gabon
M al awi
Ni ger i a
Comor os
Ghana
Gambi a, T he
Camer oon
Gui nea
M al i
Cent r al A f r i can Republ i c
Ni ger
Senegal
E t hi opi a
M adagascar
E quat or i al Gui nea
Lesot ho
Rwanda
Zi mbabwe
Cape V er de
Chad
K enya
B eni n
E r i t r ea
B ur ki na Faso
M ozambi que
Swazi l and
Sout h A f r i ca
Uganda
T anzani a
B ot swana
0
50 100 150 200 250 300 350 400 450 500
African countries: External debt
service 2001 (% of exports)
Si er r a Leone
M adagascar
Gui nea-B i ssau
B ur undi
A ngol a
Sao T ome and
M aur i t ani a
E t hi opi a
K enya
Gabon
Cot e d'I voi r e
Senegal
Ghana
Camer oon
Lesot ho
Gui nea
Ni ger i a
Cent r al A f r i can
Zambi a
Sout h A f r i ca
B ur ki na Faso
Rwanda
T anzani a
M al i
Chad
B eni n
M al awi
Uganda
M aur i t i us
Zi mbabwe
Ni ger
T ogo
Cape V er de
Gambi a, T he
Congo, Rep.
Comor os
M ozambi que
Swazi l and
Seychel l es
Sudan
E r i t r ea
Congo, Dem. Rep.
B ot swana
Li ber i a
E quat or i al Gui nea
0
20
40
60
80
100
120
African countries: Exports 2001
(% of GDP)
Seychel l es
Congo, Rep.
A ngol a
Swazi l and
M aur i t i us
Gabon
Gambi a, T he
Nami bi a
Ghana
B ot swana
Ni ger i a
Gui nea-B i ssau
Cot e d'I voi r e
Sao T ome and P r i nci pe
M aur i t ani a
Lesot ho
T ogo
Camer oon
M al i
Senegal
M adagascar
Sout h A f r i ca
Gui nea
Zambi a
M al awi
K enya
Cape V er de
Zi mbabwe
M ozambi que
E r i t r ea
Congo, Dem. Rep.
Si er r a Leone
Ni ger
Comor os
T anzani a
E t hi opi a
B eni n
Chad
Sudan
Cent r al A f r i can Republ i c
Uganda
B ur ki na Faso
Rwanda
B ur undi
0
20
40
60
80
100
African countries: Current
account balance 2001 (% of GDP)
Gabon
B ot swana
M aur i t ani a
M aur i t i us
Cent r al A f r i can Republ i c
Sout h A f r i ca
M adagascar
Cot e d'I voi r e
Camer oon
Gui nea
K enya
B eni n
B ur undi
A ngol a
Swazi l and
Sudan
E t hi opi a
Ghana
Senegal
Uganda
Rwanda
T anzani a
Ni ger
Lesot ho
Gambi a, T he
B ur ki na Faso
Cape V er de
Seychel l es
E r i t r ea
M al awi
Chad
M ozambi que
Sao T ome and P r i nci pe
-50
-40
-30
-20
-10
0
10
20
African countries: Gross foreign
reserves 2001 (months of imports)
M adagascar
B ot swana
Comor os
Cent r al A f r i can Republ i c
B eni n
Gui nea-B i ssau
Uganda
Ni ger i a
T anzani a
Lesot ho
Rwanda
B ur ki na Faso
Sao T ome and P r i nci pe
M aur i t i us
Gambi a, T he
M al i
K enya
E t hi opi a
Swazi l and
Senegal
Cot e d'I voi r e
Sout h A f r i ca
Ni ger
M al awi
Gui nea
T ogo
Si er r a Leone
M ozambi que
Chad
Cape V er de
Camer oon
Nami bi a
Ghana
B ur undi
Zambi a
A ngol a
Zi mbabwe
Seychel l es
Sudan
Congo, Rep.
E quat or i al Gui nea
Gabon
0
5
10
15
20
25
30
African countries: Short-term debt
2001 (% of foreign reserves)
Congo, Rep.
Gabon
Zi mbabwe
A ngol a
B ur undi
Camer oon
Cot e d'I voi r e
Sout h A f r i ca
Zambi a
Gui nea
Ghana
K enya
M ozambi que
Sao T ome and P r i nci pe
Si er r a Leone
Senegal
Cape V er de
Swazi l and
Comor os
Ni ger
M al awi
Cent r al A f r i can Republ i c
Gambi a, T he
M al i
Ni ger i a
Gui nea-B i ssau
Chad
B ur ki na Faso
T anzani a
Rwanda
B eni n
E t hi opi a
Uganda
M adagascar
Lesot ho
B ot swana
0
500
1000
1500
2000
2500
African countries: Short-term debt
2001 (% of foreign reserves)
Zi mbabwe
A ngol a
B ur undi
Camer oon
Cot e d'I voi r e
Sout h A f r i ca
Zambi a
Gui nea
Ghana
K enya
M ozambi que
Sao T ome and P r i nci pe
Si er r a Leone
Senegal
Cape V er de
Swazi l and
Comor os
Ni ger
M al awi
Cent r al A f r i can Republ i c
Gambi a, T he
M al i
Ni ger i a
Gui nea-B i ssau
Chad
B ur ki na Faso
T anzani a
Rwanda
B eni n
E t hi opi a
Uganda
M adagascar
Lesot ho
B ot swana
0
100
200
300
400
500
External debt dynamics
Debt accumulation is, by its nature, a
dynamic phenomenon
A large stock of debt involves high
interest payments which, in turn, add to
the external deficit, which calls for
further borrowing, and so on
Debt accumulation can develop into a vicious
circle
How do we know whether a given debt
strategy will spin out of control or not?
To answer this, we need a little arithmetic
External debt dynamics
Recall balance of payments equation:
BOP = X – Z + F
where
F = capital inflow = DF
where
DF = foreign debt
Capital inflow, F, thus involves an increase
in the stock of foreign debt, DF, or a
decrease in the stock of foreign claims
(assets)
So, F is a flow and DF is a stock
External debt dynamics
Now assume
Then, it follows that
BOP = X – Z + DF = 0
so that
DF = rDF
Z = ZN + rDF
Z = total imports
ZN = non-interest imports
rDF = interest payments
Further, assume
X = ZN
BOP = 0
In other words:
ΔD
r
F
D
F
A flexible exchange rate maintains
equilibrium in the balance of payments at all
times
External debt dynamics
So, now we have:
ΔD
r
F
D
F
Now subtract growth rate of output from
both sides:
ΔD
ΔY

 r -g
F
D
Y
F
Y
g
Y
External debt dynamics
But what is
ΔD F ΔY

F
D
Y
?
This is proportional change in debt ratio:
 DF 

Δ
F
Y 
ΔD
ΔY



F
DF
D
Y
Y
This is an application of a
simple rule of arithmetic:
%(x/y) = %x - %y
Proof
z = x/y
log(z) = log(x) – log(y)
log(z) = log(x) - log(y)
But what is log(z) ?
dlog(z) dz 1 Δz
Δlog(z) 
  
dt
dt z
z
So, we obtain
Δz Δx Δy


z
x
y
Q.E.D.
Debt, interest, and growth
We have shown that

Δd
rg
d
Debt
ratio
rg
where
F
D
d
Y
r=g
rg
Time
What can we learn
from this?
It is important to keep economic growth at
home above – or at least not far below –
the world rate of interest
Otherwise, the debt ratio keeps rising over time
External deficits can be OK, even over long
periods, as long as external debt does
not increase faster than output and the
debt burden is manageable to begin with
A rising debt ratio may also be OK as long as
the borrowed funds are used efficiently
Once again, high-quality investment is key
Debt dynamics:
Another look
Let us now study the interaction
between trade deficits, debt, and
growth
Two simplifying assumptions:
Dt = aYt (omit the superscript F, so D = DF)
Y Exponential
growth
Trade deficit is constant fraction a of output
Yt = Y0egt
Output grows at constant rate g per year
t
Pictures of growth
Y
log(Y)
g
1
time
time
Exponential growth implies a linear
logarithmic growth path whose
slope equals the growth rate
Debt as the sum of
past deficits
T
DT   ΔD t dt
0
at time T
Debt as the sum of
past deficits
T
DT   ΔD t dt
at time T
0
T
T
0
0
DT   ΔD t dt   aY0egt dt
Debt as the sum of
past deficits
T
DT   ΔD t dt
at time T
0
T
T
0
0
DT   ΔD t dt   aY0egt dt
 1  gt
DT   ΔD t dt   aY0e dt  aY0  e
g
0
0
T
T
gt
Evaluate this
integral between
0 and T
Debt as the sum of
past deficits
T
DT   ΔD t dt
at time T
0
T
T
0
0
DT   ΔD t dt   aY0egt dt
So, as T goes to infinity, Dt
becomes infinitely large.
But that may be quite OK
in a growing economy!
 1  gt
DT   ΔD t dt   aY0e dt  aY0  e
g
0
0
T
T
gt
Evaluate this
integral between
0 and T


 1  gt
 1  gT
DT   ΔD t dt   aY0e dt  aY0  e  aY0   e  1
g
g
0
0
T
T
gt
Debt as the sum of
past deficits
D T  a  Y0 e gt  Y0
  
YT  g 
YT
Debt as the sum of
past deficits
D T  a  Y0 e gt  Y0
  
YT  g 
YT
DT  a  Y0egt  Y0  a  Y0 
  
  1  
YT  g 
YT
 g  YT 
Debt as the sum of
past deficits
D T  a  Y0 e gt  Y0
  
YT  g 
YT
DT  a  Y0egt  Y0  a  Y0 
  
  1  
YT  g 
YT
 g  YT 
DT  a  Y0egt  Y0  a  Y0   a 
  
  1      1  e gT
YT  g 
YT
 g  YT   g 


Debt as the sum of
past deficits
D T  a  Y0 e gt  Y0
  
YT  g 
YT
DT  a  Y0egt  Y0  a  Y0 
  
  1  
YT  g 
YT
 g  YT 
DT  a  Y0egt  Y0  a  Y0   a 
  
  1      1  e gT
YT  g 
YT
 g  YT   g 

So, as T goes to
infinity, DT/YT
approaches the
ratio a/g
lim
T 
DT a

YT g

Numerical
example
Suppose
Debt ratio
3
Trade deficit is 6% of GNP
a = 0.06
Growth rate is 2% per year
Time
g = 0.02
Then the debt ratio approaches
d = a/g = 0.06/0.02 = 3
This point will be reached regardless of
the initial position ...
... as long as a and g remain unchanged
What to conclude?
Must adjust policies
Must either
Reduce trade deficit by stimulating exports
or by reducing imports, or
Increase economic growth
Otherwise, the debt ratio will reach
unmanageable levels, automatically
No country can afford an external debt
equivalent to three times annual output
And why not?
Because the debt burden then
becomes unbearable
Recall our earlier numerical example
Where we looked at the relationship between
the debt ratio and the debt burden
Korea is a case in point
Its export-oriented growth strategy reduced the
numerator and increased the denominator of
the debt ratio, thereby quickly reducing the
country’s debt burden
An import-substitution strategy would reduce
both numerator and denominator with an
ambiguous effect on the debt burden
Numerical example, again
Here we have a
Suppose that
country whose
entire export
r = 0.06 (as before)
earnings do not
D/Y = 3 (our new number) suffice to service
its debts
A/Y = 0.05 (as before)
X/Y = 0.20 (as before)
A
DF
r
Y
q Y
X
Y
0.05  0.06  3
q
 1.15
0.2
Numerical example, again
Suppose that
r = 0.06 (as before)
D/Y = 2 (our new number)
A/Y = 0.05 (as before)
X/Y = 0.20 (as before)
A
DF
r
Y
q Y
X
Y
0.05  0.06  2
q
 0.85
0.2
Numerical example, again
Suppose that
r = 0.06 (as before)
D/Y = 1 (new number)
A/Y = 0.05 (as before)
X/Y = 0.20 (as before)
A
DF
r
Y
q Y
X
Y
0.05  0.06 1
q
 0.55
0.2
Numerical example, again
Suppose that
r = 0.06 (as before)
D/Y = 0.4 (new number)
A/Y = 0.05 (as before)
X/Y = 0.20 (as before)
A
DF
r
Y
q Y
X
Y
0.05  0.06  0.4
q
 0.37
0.2
Numerical example, again
Suppose that
r = 0.06 (as before)
D/Y = 0.4 (as before)
A/Y = 0.05 (as before)
X/Y = 0.30 (new number)
A
DF
r
Y
q Y
X
Y
0.05  0.06  0.4
q
 0.25
0.3
African countries: External debt
2001 (% of exports)
Li ber i a
M adagascar
B ur undi
Congo, Dem. Rep.
Si er r a Leone
Gui nea-B i ssau
Sao T ome and P r i nci pe
Cent r al A f r i can
Rwanda
Zambi a
M aur i t ani a
E t hi opi a
M al awi
Ni ger
Comor os
Cot e d'I voi r e
B ur ki na Faso
Chad
Gui nea
Camer oon
Zi mbabwe
Congo, Rep.
Ghana
Uganda
M al i
Senegal
K enya
Ni ger i a
B eni n
A ngol a
Gabon
Gambi a, T he
T anzani a
Cape V er de
Lesot ho
Sout h A f r i ca
E r i t r ea
M ozambi que
Swazi l and
B ot swana
E quat or i al Gui nea
0
200
400
600
800 1000 1200 1400
African countries: External debt
service 2001 (% of exports)
Si er r a Leone
M adagascar
Gui nea-B i ssau
B ur undi
A ngol a
Sao T ome and
M aur i t ani a
E t hi opi a
K enya
Gabon
Cot e d'I voi r e
Senegal
Ghana
Camer oon
Lesot ho
Gui nea
Ni ger i a
Cent r al A f r i can
Zambi a
Sout h A f r i ca
B ur ki na Faso
Rwanda
T anzani a
M al i
Chad
B eni n
M al awi
Uganda
M aur i t i us
Zi mbabwe
Ni ger
T ogo
Cape V er de
Gambi a, T he
Congo, Rep.
Comor os
M ozambi que
Swazi l and
Seychel l es
Sudan
E r i t r ea
Congo, Dem. Rep.
B ot swana
Li ber i a
E quat or i al Gui nea
0
20
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Debt relief and the HIPCs
Borrowers often renegotiate the terms
of their loans in mid-stream so as to
Delay repayments, that is, extend the
maturity of the loans, or to
Reduce interest payments by replacing
high-interest loans by loans with lower
interest
Debt rescheduling vs. debt forgiveness
Rescheduling on concessional terms
involves an element of debt forgiveness
But debt relief is not a substitute for
sound and sustainable economic policies
Debt relief and the HIPCs
HIPC initiative from 1996 and 1999
Aims to bring debt to sustainable levels,
thus eliminating the need for continued
debt relief, rescheduling, and arrears
Requires demonstrated capacity to put
debt relief provided to good use
Objective: Bring net present value of debt
down to 150% of exports, and 250% of
government revenue if
Exports exceed 30% of GDP
Revenues exceed 15% of GDP
Floating completion points
Tied to key structural reforms
In conclusion
External borrowing is a necessary and
natural part of economic development
This requires countries that borrow to invest
the funds borrowed in high-quality capital
This is necessary to be able to service the debt
If debt burden becomes too heavy, must
either reduce deficit or spur growth
It is always desirable anyway to do everything
possible to encourage economic growth
Rapid growth allows more foreign borrowing
without making the debt burden
unmanageable