Delay and Haircuts in Sovereign Debt - University of St Andrews

If the debtor knows her own type, according to the detailed computations
in iAppendix B, the continuation value for the Optimistic debtor i is
, the continuation value for the Cautious debtor is and
h
(+s)
4
the continuation value for the creditor is
( s) s
1
(1 q 0 )
2
s
+
s
s
h
(+s)
2
(1 q 0 ) x 0 2 :
On the other hand, if the debtor does not know her own type, again following
the detailed computations in Appendix B, the debtor’s continuation
payo¤ is 2 (+s) 2 q0
2 2
, while the creditor’s continuation payo¤ is the same
as in the …rst scenario.
From these two scenarios, it follows from the detailed computations in
Appendix B that the expected payo¤ for the creditor from rejecting the
debtor’s o¤er at t = 1, ^a, is given by
(E
^a =
2
s)
(E
(1 q 0 )
s
s) (E
2
s)
E + Ex 0 2 ;
where Ex 0 2 > E (E s)
2
since x 0 2 > ( s)
2
. An alternative interpretation
for ^a could be the minimum payo¤ for the creditor to accept the
debtor’s o¤er.
For delay to occur at t = 1, when the debtor is a proposer, it should
be attractive for the the creditor to reject the debtor’s best o¤er at t = 1.
This happens when the best o¤er of the debtor falls below the creditor’s
continuation payo¤ or the expected payo¤, ^a, computed earlier.
Lemma 2 The condition for delay at t = 1 is
L
(E + s)
< ^a;
2
i.e. the excess of the available bargaining surplus over the Cautious debtor’s
own continuation value falls below the creditor’s expected payo¤ in the …rst
period.
Proof. In what follows, we derive the conditions for delay for each type
of debtor at t = 1. For the Optimistic debtor, the best o¤er that she can
make is the excess of the available bargaining surplus, L , over her own
continuation value, , i.e. L . If such o¤er falls
(E+s)
4
12
(E+s)
4