of countries have recently used debt targets or ceilings as a guide to fiscal policy. Viewed from
this perspective “debt stability” can be interpreted as whether the debt process is mean reverting
(towards the target debt level) and if so how quickly it reverts. However the concept of debt
stability is an ambiguous one and also covers the notion of a government that seeks to minimise
fluctuations around a target value e.g Min Et(MVt+1 — T)2 where T is the target level for debt. It
is also possible that the government may wish to “debt smooth” by, for instance, minimising the
conditional variance of the market value of debt —Mi:nEi(MVi\[ — EtMVt+ι).
To minimise the conditional variance of debt the government should choose its debt portfolio so
that Covt(ωt+ι, Rt+ι)∕σt(Rt+1)σt(ωt+1) = —1 where σγ denotes the conditional standard deviation.
In the case of a government seeking to minimise fluctuations around a target value of debt the
optimal portfolio has to satisfy the condition4 Covt(ωt+1, Rt+1) + Vαrt(Rt+ι)MVt = — (EtRt+1 —
Etrt+1)Et(ωt+1 + Rt+ιMVt — T) where r£+1 denotes the risk free rate of return. Minimising debt
fluctuations therefore involves exploiting a negative covariance between the rates of return on debt
and the primary deficit. The precise condition to be exploited however hinges on the exact aim of
the government.
In what follows we pursue a weak implication of using debt management to stabilise debt. Be-
cause debt stability is capable of several different interpretations and because estimating conditional
variances involves considerable time series structure5 we focus instead on the unconditional variance
of debt e.g Vαr(M^V+ι) =Vαr(ω^+ι) + Vαr(R)+ιMV(*) + 2Cov(R^+ιMVt* ,ω^+ι). Our concept of
fiscal insurance is the notion that debt management can help offset the impact of the primary
deficit on the market value of debt. At a mimimum this involves creating a negative covariance
between R+1 and MVt*+1 As we have shown above specific goals of debt stability imply achieving
precise values for this covariance. However the essence of fiscal insurance is that the holding period
returns on debt offset the impact of budget shocks on the level of debt. We therefore interpret
this covariance as showing better debt management the more negative the correlation coefficient
4We are grateful to a referee for pointing out the relevance of these expressions for our analysis.
5In the expressions above, for instance, we require the conditional covariance of holding rates of return at the time
of the deficit shock.