Delay and Haircuts in Sovereign Debt - University of St Andrews

creditor is the proposer, his o¤er is ~x L = ( s)
2
. With an equal probability
that each party is the proposer, the expected payo¤s for the Cautious debtor
and the creditor at t = 2 are ;
, respectively.
+s
2
Next, we calculate the continuation values for each player as we move
to the …rst period. Let E = p L + (1
s
2
p) H denote the expected size of
. If the debtor is Optimistic, the continuation values for the Optimistic
debtor and the creditor are
, respectively. However, if the debtor
(E+s)
2
;
(E s)
2
E
2 ; E
2
is Cautious, the continuation values for the Cautious debtor and the creditor
are
, respectively.
At t = 1, the sovereign debtor is a proposer. Let Eg denote the expected
growth of the economy, where Eg = (E L)
L
and r = 1
. In what follows,
we present the condition for one-period delay when the debtor is Optimistic
and Cautious, respectively.
For the Optimistic debtor, the best o¤er that she can make is the excess
of the available bargaining surplus over his own continuation value given by
E
E
L 2
. If this o¤er falls below the creditor’s continuation value,
2 , this
o¤er will not be accepted. Formally, this condition for the …rst-period delay
for the Optimistic debtor is given by
L
E
2
< E
2
, r < Eg:
(E+s)
2
.
For the Cautious debtor, the best o¤er that she can make is L
If this o¤er falls below the creditor’s continuation value, (E s)
2
, this o¤er
will not be accepted. Formally, the condition for the …rst-period delay for
the Cautious debtor is given by
L
(E + s)
2
<
(E s)
2
, r < Eg:
Therefore, for either type of sovereign debtor, with relatively low prospect
of economic growth, there will be no delay in the …rst period and an immediate
agreement occurs. Q.E.D.
Proof of Lemma 1
We begin with the case in which the debtor is chosen to make an o¤er at
t = 2. Let (x 2 ;
x 2 ) denote the o¤er made by the debtor, where x 2 and
x 2 are payo¤ for the debtor and the creditor’s share of the bargaining
( s)
surplus, respectively. Let ~x 2 be the solution to x 2 =
2
, where
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