Delay and Haircuts in Sovereign Debt - University of St Andrews

ante payo¤s with two-period delay could be lower relative to with one-period
delay. Moreover, with an appropriate adjustment of the sovereign spread,
the ex ante creditor’s payo¤s will be una¤ected by the delay length.
Formally, let e t (respectively, K t ) denote the e¤ort choice of the debtor
(respectively, the debtor’s expected payo¤s conditional on default) with delay
length t, where t = 1; 2. As long as (1 e 1 ) K 1 ' (1 e 2 ) K 2 and
h (e 1 e 2 ) D > (e 1 ) (e 2 ), then the sovereign debtor’s payo¤s are higher
with one-period delay relative to two-period delay 16 .
By Proposition 3, relative to one-period delay, two-period delay is ine¢
cient whenever it gives the debtor lower expected payo¤ at the interim
period (conditional on default) than the one-period delay, i.e. when the direction
of the inequality in condition (3) is reversed, as in this case, both
the debtor’s and creditor’s payo¤s with two-period delay are lower than with
one-period delay. However, when the two-period delay gives the debtor lower
expected payo¤ at the interim stage (conditional on default) relative to the
one-period delay, with two-period delay, the debtor’s ex ante level of e¤ort,
e , is higher and the probability of default, (1
one-period delay.
e ) h, is lower than with
Even though, relative to one-period delay,the recovery
rate, R, is lower with two-period delay due to larger size of haircuts, the
creditor’s ex ante payo¤s will not be a¤ected as the sovereign spread will be
adjusted upwards. However, the debtor’s ex ante payo¤s could actually go
up as long as (1 e 1 ) K 1 ' (1 e 2 ) K 2 and h (e 1 e 2 ) D > (e 1 ) (e 2 ).
Therefore, the ex ante Pareto ranking of equilibria with one-period delay
and two-period delay could be di¤erent from the interim Pareto ranking of
equilibria conditional on default.
We summarize the above discussion as the following proposition:
Proposition 4 The ex ante Pareto ranking of equilibria with one-period
delay and two-period delay could be di¤erent from the interim Pareto ranking
of equilibria.
5 Policy Discussion
Drawing on the results that we have obtained so far, in what follows, we
provide a brief evaluation of a number of policy initiatives that are in relation
to the sovereign debt restructuring, abstracting away from the issue of
16 The latter condition came from he 1D (e 1) > he 2D (e 2).
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