Fiscal Insurance and Debt Management in OECD Economies

a shock MVj ^d∩°tt^j (b) a term reflecting how the financing costs of future deficits alter because of
^dεt+ι

the deficit shock ( ^d21i-lVl ^ωM ) and (c) a term reflecting the impact of the shock on future fiscal
^dε+ιt      ^^r*^y

.   .        , , ∂ω'' - _            _     _                         .....     .     ...

deficits Φι_t+j(L) _д^г. In the case where the return on government debt is independent of shocks to
the economy (as in the case where the government issues only one period risk free debt and shocks
are i.i.d, as in Aiyagari et al (2001))⁶, then (3) reduces to

^^MV)+j _ ʌ ,j+1-fc ^^ωt+k
≤ι = ⅛ ^ψu+j ≤1

where ф^+— is the j + 1 — Hh coefficient in the lag polynomial ≠ι_t+j (L). In other words debt would
only rise by the accumulated impact of the shock on future deficits with no offsetting effects through
changes in bond prices. Comparing (3) and (4) we have a natural measure of fiscal insurance, namely

v j++1--fe^^ωA⅛
ь ^φu+j ∂εf
k=1            ^τ

This statistic⁷ is the ratio between the estimated change in the market value of debt in response
to a deficit shock (as estimated from a VAR) and the increase in debt that would have occurred from
cumulating the total effect on current and future deficits in response to the current deficit shock. If
Φ^j = 1 then debt levels rise by exactly the amount of the primary fiscal deficits accumulated over
time in which case debt management offers no fiscal insurance. In the case where Φ^j = 0 then debt
shows no response to increases in the deficit because bond prices fall to offset the higher deficits and
debt is stabilized. Note that in the case of complete markets and persistent shocks we know that
debt levels fall on impact so that Φθ < 0 but then increases thereafter. A measure of Φj between 0
and 1 implies that the government achieves some degree of fiscal insurance - debt levels increase by
less than the accumulated impact on the fiscal deficit as changes in interest rates offset the impact
of shocks. Notice that it is also possible for Φ^j > 1. In this case the debt level rises by more than
the accumulated impact of fiscal deficits as interest rates move adversely in response to the shock.

⁶The market value of debt will vary with fiscal shocks both because the government issues explicitly state contingent
debt or fixed coupon bonds whose market price varies endogenously with the economy.

⁷Because the coefficients in the lag polynomial φ_lt+j (T) depend on the growth adjusted interest rate and are time
varying this measure of fiscal insurance is also time varying. To avoid this complication we estimate (5) evaluating
Rt+jYt/Yt+j at its sample averages and denote this measure Φ*.

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