A poor country with volatile export prices borrows in international markets. When debt is denominated in foreign currency, there is a temptation to repudiate when export prices are low. Excusable partial defaults reduce this temptation, and thus help to support lending.debt, default, terms of trade

Michael Bleaney

English

Research Papers in Economics

      
UNIVERSITY OF NOTTINGHAM 
 
 
 
Discussion Papers in Economics 
 
________________________________________________ 
Discussion Paper 
No. 08/05 
 
 
The Terms of Trade, Repudiation and Default on Sovereign 
Debt 
 
By Michael Bleaney 
June 2008 
 
 
_________________________________________________________ 
 2008    DP 08/05  
  1
  
 
 
 
The Terms of Trade, Repudiation and Default on 
Sovereign Debt 
 
 
  by 
 
 
  Michael Bleaney 
 
 School  of  Economics 
 University  of  Nottingham 
  Nottingham NG7 2RD, U.K. 
 e-mail:  michael.bleaney@nottingham.ac.uk 
  Tel. (+44) 115 951 5464 
  Fax. (+44) 115 951 4159 
 
 
 
 
 
 
Abstract 
A poor country with volatile export prices borrows in international markets.  When debt 
is denominated in foreign currency, there is a temptation to repudiate when export prices 
are low.  Excusable partial defaults reduce this temptation, and thus help to support 
lending.   
 
 
Keywords: debt, default, terms of trade 
 
JEL No:   F34 
  
  2
1.  Introduction 
 
Sovereign debt may be supported by the threat of exclusion from future borrowing or by 
other sanctions in the event of default.  Rose (2005) provides some evidence that default 
depresses international trade.  A general problem in evaluating why countries pay their 
debts is that, assuming rational expectations, countries that would not pay do not have 
any debts in the first place, because lenders would refuse to lend to them.  Arguably 
many of the poorest countries in the world are in this situation, since most of their debts 
are to official rather than private bodies, either because they have few assets to seize or 
because their time discount rate is high (so the threat of exclusion from future borrowing 
is ineffective). In practice sovereign defaults are quite frequent, and lending resumes after 
a period of negotiation over the extent of default (Manasse et al., 2003).  This has 
motivated the development of models in which excusable partial defaults occur in 
recognisably bad states of the world (Alfaro and Kanczuk, 2005; Grossman and Van 
Huyck, 1988).  The empirical evidence suggests that the risk of such defaults is priced 
relatively accurately, in the sense that in the long run risky debt yields similar returns to 
safe debt (Klingen et al., 2004; Lindert and Morton, 1989). 
 
This paper focuses on an interesting interaction between excusable partial default and the 
incentive to repudiate debt altogether.  By reducing debt repayment in bad states, it is 
possible that excusable partial default eliminates the incentive to repudiate, if the bad 
states are the critical ones in the sense that the incentive to repudiate is greatest.  This 
depends on the nature of the world (whether it is the quantity or relative price of the 
borrowing country’s output that is stochastic) and on the currency denomination of the  
  3
debt contract.  The most relevant case is where the terms of trade are volatile and debt is 
denominated in foreign currency. 
 
2.  The Model 
 
2.1. Assumptions 
 
The model is based on that of Cole and Kehoe (1995), which is attractive because of its 
simplicity.  In the original model there are two countries.  One has a risk-neutral 
government which is a monopolist of an investment project but initially has no resources 
to exploit it.  The other consists of risk-neutral bankers who compete to lend to this 
government.  All agents have a discount factor of β, and competition amongst bankers 
forces the gross interest rate down to r = 1/β.  The returns to the investment project are of 
the following pattern: in alternate periods they are zero, and in alternate periods an 
investment of one unit in the previous period produces output of a non-storable 
commodity of A > r.  There is a maximum investment of one.  The government has a 
linear per-period utility function in consumption: 
 
 U (ct) = ct  (1) 
 
 and a lifetime utility of 
  ) (
0
t
t
t c U U ∑
∞
=
= β . (2)  
  4
Thus, if t is odd, the government borrows and invests one unit and consumes nothing.  If t 
is even, the government has output of A from the previous period’s investment, repays 
debt of r, borrows and invests nothing, and consumes A–r.  Alternatively, the government 
could repudiate the debt, after which there is no further lending.  As Cole and Kehoe 
(1995) show, repudiation is always preferable if the government is able to save the 
resources obtained and earn a gross return of r on them.
1 Therefore I assume that the 
government is unable to save, and that repudiation implies immediate consumption of the 
entire output, with zero output in all future periods. 
 
This model is modified here in the following respects.  First, there are two goods, one 
produced in the borrowing country and one in the lending country.  Second, the output of 
the borrowing country is exchanged for imports from the lending country at an uncertain 
relative price (p).  The price follows a known probability distribution that is independent 
of the history of p, with a mean of one.  Finally, utility is derived from consumption of 
both home goods (x) and foreign goods (y).  Suppose that in period t the borrowing 
government has resources Wt, measured in terms of domestic output, and that its utility 
function is: 
λ λ
λ λ
⎟
⎠
⎞
⎜
⎝
⎛
⎟
⎠
⎞
⎜
⎝
⎛
−
=
−
t t
t
y x
c U
1
1
) ( .         ( 3 )  
Equation (2) is maximized subject to the constraint: 
  t
t
t
t W
p
y
x = +           ( 4 )  
                                                           
1 As Grossman and Han (1999) show, this is a consequence of the risk-neutrality of the borrower.  With 
risk-averse borrowers and state-contingent debt repayments, repudiation is not necessarily optimal when the 
borrowers can save.  
  5
which yields: 
 
 
λ
t t t p W c U = ) ( .         ( 5 )  
 
Thus utility is greater, for a given quantity of the borrower’s output, when the terms of 
trade are better and imports are cheaper. 
 
With two goods, the units in which debt is denominated need to be specified.  We 
consider three possibilities: that debt is indexed to the price of (1) the borrowing 
country’s consumption bundle; (2) its export good; and (3) its import good.  These cases 
are analogous to indexation of debt (1) to the borrowing country’s GDP deflator; (2) to 
the borrowing country’s consumer price index; and (3) to the lending country’s GDP 
deflator (i.e. in foreign currency).  The last case is particularly relevant in view of the fact 
that borrowing in foreign currency may be the only option available for many countries 
(Eichengreen and Hausmann, 1999).  When export prices are low, the borrower’s real 
exchange rate depreciates and debt denominated in foreign currency is particularly 
expensive to repay. These valuation effects may explain the severe output effects of 
currency crises in emerging markets (Frankel, 2005). 
 
2.2.  Indexation to consumer prices 
 
Debt can be supported if, whatever the realisation of the terms of trade, the benefits of 
future borrowing exceed the gains from repudiation.  If the real exchange rate at time t is  
  6
pt, and t is an even number, then repudiation of the debt at time t yields discounted utility 
of  
λ
t Ap R U = ) ( . (6) 
 
Here R denotes repudiation. The expected utility of not repudiating the debt (N) is: 
[] ] ) ( [
1
) ( 2
2
r p AE r Ap N U E t −
−
+ − =
λ λ
β
β
.      (7) 
The first two terms on the right-hand side represent utility in period t, and the last term 
represents the discounted expected utility of consumption in future even periods, when p 
is on average equal to one.  Allowing for the fact that β
 = 1/r, debt will not be repudiated 
if UI ≤  E[U(N)], i.e. if 
 
3 ) ( r p AE ≥
λ .           ( 8 )  
 
This differs only marginally from the one-good equivalent (A ≥ r
3). 
 
2.3. Debt indexed to export prices 
 
In this case U(R) is as given in (6), but E[U(N)] is  
 
[] )] ( ) [(
1
) ( ) ( 2
2
λ λ
β
β p E r A p r A N U E t −
−
+ − = .    (9)
 
  
  7
Now that the debt is not indexed to the consumption bundle, the utility cost of repaying 
the debt depends on current relative prices.  Yet the expected benefits of repayment are 
much the same, because they depend on the expected future utility cost of debt 
repayments.  A high value of pt makes present repayments particularly onerous. The 
condition for non-repudiation is that 
 
 
) 1 (
) ( ) (
2 −
−
≤
r r
p E r A
pt
λ
λ          ( 1 0 )  
 
When the terms of trade are at their most favourable, this condition may not be met.  
Thus relative price volatility makes it harder for the threat of exclusion from future 
borrowing to support debt. 
 
 
2.4. Debt indexed to import prices 
 
In this case repudiation yields the same result as before, but repayment yields an expected 
utility of: 
⎟ ⎟
⎠
⎞
⎜ ⎜
⎝
⎛
⎟ ⎟
⎠
⎞
⎜ ⎜
⎝
⎛
−
−
+ − = − − λ
λ
λ
λ
β
β
1 2
2
1
1
) (
1
)] ( [
p
rE p AE
p
r
Ap N U E
t
t      (11) 
 
and the condition that U(R) ≤  E[U(N)] is 
  
  8
  ⎟ ⎟
⎠
⎞
⎜ ⎜
⎝
⎛
⎟ ⎟
⎠
⎞
⎜ ⎜
⎝
⎛
−
−
≤ − − λ
λ
λ 1 2 1
1
) (
1
1 1
p
rE p AE
r pt
       ( 1 2 )  
 
The critical circumstances in this case are when p is exceptionally low, since this is the 
case where debt is at its most burdensome. 
 
2.5. Excusable default 
 
Now consider what happens if the lender can verify the borrower’s output and is prepared 
to accept partial default on the debt if the borrower’s current-period utility would 
otherwise fall below some threshold level, C.  When default occurs, utility is just equal to 
C, and the borrower receives the surplus output.  To compensate for this, the debt now 
bears a higher gross interest rate of R that incorporates a risk premium.  This affects the 
incentive to repudiate debt.  By making payments higher in good states and lower in bad 
states, it increases the incentive to repudiate if the critical value of p is high, and 
decreases it when the critical value of p is low.  An example of the former is indexation 
of debt to export prices.   With excusable default, the condition for non-repudiation is 
now: 
 
) 1 (
) ( ) (
2 −
−
≤
r r
p E R A
pt
λ
λ          ( 1 3 )  
 
Since R > r, this is a more stringent condition than (10). 
  
  9
When debt is indexed to import prices, we get the opposite case.  Define  p ˆ  as the 
minimum price at which there is no default;  p ˆ  is given by: 
  C
p
R
p A = − −λ
λ
1 ˆ
ˆ          ( 1 4 )  
 
Expected utility without repudiation is:  
 
⎟ ⎟
⎠
⎞
⎜ ⎜
⎝
⎛
⎟ ⎟
⎠
⎞
⎜ ⎜
⎝
⎛
−
−
+ − =
− − ]) ,
1
) ( (max[
1
) , max( )] ( [
1 2
2
1 C
p
RE p AE E C
p
R
Ap N U E
t
t λ
λ
λ
λ
β
β
 (15) 
E[U(N)] – U(R) is increasing in p for p< p ˆ  and decreasing in p for p> p ˆ , so the condition 
for lending to be supported by the threat of exclusion from future borrowing is that   
E[U(N)] ≥U(R) for p= p ˆ .  This requires that  
 
  ⎟ ⎟
⎠
⎞
⎜ ⎜
⎝
⎛
⎟ ⎟
⎠
⎞
⎜ ⎜
⎝
⎛
−
−
≤ − − ]) ,
1
) ( (max[
1
1
ˆ
1 2 1 C
p
RE p AE E
r p
R
λ
λ
λ      (16) 
 
The right-hand side of (16) cannot be less than the right-hand side of (12).  Equation (16) 
is therefore a less stringent condition than (12) if its left-hand side is smaller, i.e. if 
 
 
λ λ − − ≤ 1
min
1 ˆ p
r
p
R
          ( 1 7 )  
 
where pmin is the minimum value of p.  Suppose that pmin = (1−β) p ˆ ; that the probability 
that p < p* is α; and that the average payment in the event of default is (1−λβ)R.  Then  
  10
 
   r R R = − + − ) 1 ( ) 1 ( λβ α α        ( 1 8 )  
so 
   r R = − ) 1 ( αλβ         ( 1 9 )  
 
It follows that (19) is a less stringent condition than (12) if  
 
   αλβ β
λ − < −
− 1 ) 1 (
1         ( 2 0 )  
 
Since, for a unimodal distribution, λ ≤ ½ (i.e. at worst all degrees of default are equally 
likely), and α is likely to be a relatively small fraction, (19) is inevitably satisfied even 
for an unusually fat-tailed and truncated distribution. 
 
This result implies that, with debt indexed to import prices, there can be circumstances 
where the threat of exclusion from future borrowing can support lending only if there is 
partial default in bad states, matched by higher payments in good states. 
 
2.6. Stochastic output 
 
Consider now the case where the terms of trade are fixed (p=1) and instead the quantity 
of output At is stochastic, with a mean of A.  Without excusable defaults, we have: 
 
t A R U = ) ( . (20)  
  11
 
and: 
[] ) (
1
) ( 2
2
r A r A N U E t −
−
+ − =
β
β
       ( 2 1 )  
 
Since the utility function is now linear, expected utility is (A–r).  Non-repudiation 
requires that 
 
3 r A ≥ .          ( 2 2 )  
 
If lenders are willing to guarantee a minimum utility level for the borrower and accept 
partial defaults on occasion, then in periods where there is no default and R is repaid, the 
first r in (21) must be replaced by R, which includes a risk premium, and the condition for 
non-repudiation becomes slightly more stringent: 
 
r R r A + − ≥ ) 1 (
2 .          ( 2 3 )  
 
Thus, in the case of stochastic quantities of output as opposed to prices, excusable default 
makes it slightly harder to support lending through the threat of exclusion from future 
borrowing. 
 
3.  Conclusions 
  
  12
Fluctuations in the terms of trade can undermine the threat of exclusion from future 
borrowing as a sanction against debt repudiation when debt is not indexed to the 
consumption bundle (i.e. denominated in domestic currency), because at one end of the 
price spectrum repayment is particularly costly relative to its future benefits.  I have 
shown that a system of excusable defaults, which guarantee the borrower a minimum 
utility level in any period, help to support lending if debt is especially onerous in bad 
states, as in the case of indexation to import prices, which is analogous to the commonly 
observed case of denomination in foreign currency.  It follows that, paradoxically, the 
partial defaults on foreign debt that are commonly observed may be a condition for 
lending to occur at all.  This result applies only if it is the terms of trade rather than the 
volume of the borrower’s output that is stochastic. 
 
References 
 
Alfaro, L., and F. Kanczuk (2005) “Sovereign Debt as a Contingent Claim: A 
Quantitative Approach” Journal of International Economics 65, 297-314 
Cole, H.L., and P.J. Kehoe (1995) “The Role of Institutions in Reputation Models of 
Sovereign Debt” Journal of Monetary Economics 35, 45-64 
Eichengreen, B., and R. Hausmann (1999) “Exchange Rates and Financial Fragility” 
NBER Working Paper no. 7418 
Frankel, J.A. (2005) “Contractionary Currency Crashes in Developing Countries” IMF 
Staff Papers 52, 149-192  
  13
Grossman, H.I., and T. Han (1999) “Sovereign Debt and Consumption Smoothing” 
Journal of Monetary Economics 44, 149-158 
Grossman, H.I., and J.B. Van Huyck (1988). “Sovereign Debt as a Contingent Claim: 
Excusable Default, Repudiation, and Reputation” American Economic Review  78, 
1088-1097 
Klingen, C., B. Weder and J. Zettelmeyer (2004) “How Private Creditors Fared in 
Emerging Debt Markets, 1970-2000” IMF Working Paper no. 04/13 
Lindert, P., and P.J. Morton (1989) “How Sovereign Debt Has Worked” in Developing 
Country Debt and Economic Performance by J. Sachs, Ed., University of Chicago 
Press: Chicago, 39-106 
Manasse, P., N. Roubini and A. Schimmelpfennig (2003) “Predicting Sovereign Debt 
Crises” IMF Working Paper no. 03/221 
Rose, A.K. (2005) “One Reason Countries Pay Their Debts: Renegotiation and 
International Trade” Journal of Development Economics 77, 189-206 

Sovereign Debt as a Contingent Claim: A Quantitative Approach”

The Terms of Trade, Repudiation and Default on Sovereign Debt

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The Terms of Trade, Repudiation and Default on Sovereign Debt

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