where MV denotes the market value of government debt and ω the primary dehcit. The only
difference between these two measures is that Ψ∙2∕.∙ is normalized by the degree of persistence in
the primary deficit. The greater our estimate of Ψ⅛i = 1, 2 the worse the performance of debt
management and negative values of Φ⅛ are indicative of complete market outcomes.
2.1.2 Impact Measures
The second discriminating feature between complete and incomplete markets is that under complete
markets a persistent and unanticipated increase in the fiscal deficit leads to a fall in the market
value of debt whereas under incomplete markets the market value increases. The intuition is
straightforward. The market value of debt equals the expected present value of future primary
surpluses. Under complete markets a persistent increase in government expenditure is not matched
by an equivalent rise in taxes as debt management provides fiscal insurance. Instead bond prices
fall so that the market value of debt matches the expected present value of the now reduced level
of future fiscal surpluses. By contrast under incomplete markets governments have to raise taxes in
response to adverse expenditure shocks and so raise the NPV of future primary surpluses leading to
an increase in the level of debt. Denoting orthogonal shocks to the fiscal deficit by uf this suggests
the following measure of the impact of fiscal deficits on debt
Im =
∂MVt
dut
∂ωt
dut
i.e. the ratio of the impact of deficit shocks on the market value of debt compared to the impact
of deficit shocks on the primary deficit. If this measure is negative (or 0) then debt management
supports the complete market outcome. The more positive the number the less fiscal insurance
debt management provides. Note that Im measures how the market value of debt after the current
deficit has been financed responds to innovations in the current periods primary deficit. In other
words, we examine how end of period debt responds to the within period deficit.
2.2 Debt Stabilization Perspective
The previous section focused on the role of debt management in supporting optimal fiscal policy
as defined by tax smoothing. In this section we focus on issues of debt stability instead. A number