and a full set of contingent Arrow Debren securities while in the second case markets are incomplete
with the government having access to only a one period risk free bond. The key differences induced
by these different bond market structures are :
• Under incomplete markets, the market value of government debt shows greater persistence
than other endogenous variables including taxes, government expenditure, output and the
primary fiscal deficit. Under complete markets, the market value of debt shows less persistence
than these other variables.
• Under complete markets and an optimising government the market value of government debt
declines in response to increases in the primary fiscal deficit. By contrast, under incomplete
markets, the market value of debt rises when the primary deficit increases.
Complete markets is the case where the government fully exploits the risk characteristics of
the securities available and so minimizes the distortionary costs of taxation. In assessing
the statistical performance of debt management across the OECD we will therefore interpret
better debt management as outcomes closer to the complete market case and so interpret
findings of less peristence in debt relative to deficits as better debt management3.
2.1.1 Persistence Tests
According to the above result we can use measures of the relative persistence of debt, compared to
other variables, to capture the quality of debt management.
Let
pk = Var(yt - yt-k)
y kVar(yt - yt-1)
If {yt} is stationary and ergodic then Py' → O,as k → ∞; if {yt} is i.i.d then Py' = 1/k while if
{yt} has a unit root then P^ → 1. We propose as measures of debt management the following :
Ψlk = PkMV - Pk
_________________________‰ = (pMv - Pk)∕Pk
3The Marcet-Scott result hinges on the assumption of optimal fiscal policy. It is possible that despite poor debt
management the government adjusts the fiscal deficit to reduce the persistence of debt. In this case the persistence
of debt would be uninformative regarding the quality of debt management. However, our analysis mitigates this by
examining the relative persistence of debt compared to the deficit.