Economic Models - Convex Optimization

The Advantages of Fiscal Leadership in an Economy 85
discretionary revenues, τ t . All the other variables are as previously defined.
We may regard large values of λ g 2 , say λg 2 > max[1,λg 1
], as defining a
“hard” debt or deficit rule; and smaller values, λ g 2 < min[1,λg 1
], as a “soft”
debt or deficit rule.
The objectives of the central bank, however, may be quite different from
those of the government. We model them as follows:
L cb
t
= 1 2 (π −ˆπ)2 − (1 − δ)λ cb y t − δλ g 1 y t
+ δλg 2
2 [(b − θ)y t − τ t ] 2 (10)
where 0 ≤ δ ≤ 1, and λ cb is the weight, which the central bank assigns
to the output growth. The parameter δ measures the degree to which the
central bank is forced to take the government’s objectives into account.
The closer δ is to 0, the greater is the independence of the central bank in
making its choices. And the lower is λ cb is, the greater is the degree of its
conservatism in making these choices.
In Eq. (9), we have defined the government’s inflation target as ˆπ. The
fact that the same inflation target appears in Eq. (10) would be correct for
the cases where the bank has the instrument independence, but not target
independence. However, it is easy to relax this assumption and allow the
central bank to choose its own target, as the ECB does. But, as I show in
Hughes Hallett (2005), there is no advantage in doing so since the government
would simply adjust its parameters to compensate. Hence, only if the
bank is free to choose the value of λ cb as well, do we get an extra advantage.
Yet, even this will not be enough to outweigh the advantages to be gained
from fiscal leadership — for the reasons noted in Section 5.
A second feature is that Eqs. (9) and (10) specify symmetric inflation
targets around ˆπ. Symmetric inflation targets are particularly emphasized
as being required of both monetary policy and the fiscal authorities (HMT,
2003). We have, therefore, specified both to be features of the government
and the central bank objective functions here. However, it is not clear that
symmetry has been a feature of the European policy making in practice.
Indeed, the ECB has acquired a reputation for being more concerned to
tighten monetary policy when π> ˆπ, than it is to loosen it when π< ˆπ.
Consequently, rather than symmetry in the output-gap target, we have
asymmetric penalties, which tighten the fiscal constraints in recessions,
but weaken them in a boom when the debt and deficits would be falling
anyway. On one hand, this might not be ideal, since it introduces an element
of pro-cyclicality; on the other hand, it brings the rule closer to reality.