assumption is consistent with the rationale for having a fiscal rule specifying a maximum
threshold for the deficit, suggesting the need to counteract an asymmetric deficit bias.118
Governments’ utility maximization is constrained by compliance with Maastricht’s debt
and deficit rules. The debt rule mandates that the debt-to-GDP ratio (b) must be lower
than 60 percent and, if higher than such threshold to begin with, it must be declining
towards 60 percent at a satisfactory pace. As we have noted earlier, the “satisfactory
pace” has never been defined, therefore we model this rule as requiring:
Δb = p + rb - yb - z ≤ W (6.4)
where W=0 if b>60, W=60-b if b<60
i.e. the change in the ratio of debt to GDP (Δb) - as determined by the “true deficit”
(d=p+rb where rb indicates interest payments), the reducing effect of output growth (yb),
and the debt-specific SFA (z) - must be negative if b is above 60 percent to start with.119
The change in the debt ratio can be positive if b<60 to start with, but it cannot bring b
above 60 percent of GDP.120
The deficit rule requires that reported deficits (dm) be lower than 3 percent of GDP.
Similarly to what happens for the debt ratio, if the reported deficit ratio is above 3 percent
to start with, a gradual reduction is expected. Without loss of generality, and by analogy
with the debt rule, we assume that in this case the reported deficit, as a minimum, must
not increase further. The deficit rule is therefore modelled as:
dm = p + rb - x ≤ H (6.5)
where H=3 if dm<3, H=dm if dm>3
where x denotes the deficit-specific SFA component.121
Finally, we assume that the opportunistic use of deficit and debt-specific SFA (x and z,
respectively) carries a cost C=C(x,z), with C’>0 and C,,≥0. Following Buti et al. (2007)
the costs can be thought of as deriving from the risk of being caught (higher x and z are
more visible) as well as from suboptimal allocation of resources (not all spending items
lend themselves to classification as transactions in financial items) and financial
asset/liability management.
In sum, the maximization problem facing the authorities can be described as follows:
Maxp,x,z U(p) - C(x,z) (6.6)
s.t. p + rb - yb - z ≤ W where W=0 if b>60, W=60-b, if b<60
p + rb - x ≤ H where H=3 if dm<3, H=dm if dm>3
118
119
120
121
The quadratic loss function adopted in Buti et al. (2007) is symmetric in deviations from the optimal
real output growth where real output growth depends linearly on the “true deficit”.
With respect to the analysis in Section 6.2, scaling the variables by GDP requires the consideration
of the reducing effect exerted by output growth on the debt ratio.
In this way we explicitly model the constraint also for countries where b<60 (Buti et al., 2007,
assume z=0 for b<60).
This formulation allows differentiating the constraints applying to countries with reported deficits
above and below 3 percent of GDP, rather than use dummy variables at the estimation stage.
173