Economic Models - Convex Optimization

The Advantages of Fiscal Leadership in an Economy 91
Comparing these two sets of outcomes, we have five conclusions. These
conclusions signify the main results of this paper:
(a) Fiscal leadership eliminates the inflationary bias, and results in lower
inflation without any loss in output or output volatility. The proximate
cause of this surprising result is that optimization under fiscal leadership
leads to higher taxes and larger debt repayments. 22
(b) The deeper reason is that there is a self-limiting aspect to the longrun
design of fiscal policy. Unless the effect of fiscal policy on output
is so large as to generate savings/taxes that could finance both fiscal
expansions and debt re-payments (this possibility is ruled out in the
deficit rule case), each expansion designed to increase output would
simply be accompanied by a greater burden of debt. Hence, in order to
preserve the long-run sustainability of its finances, the government must
eventually raise taxes. This fact takes some inflationary pressure off the
central bank when fiscal expansions are called for. As a result, the bank
is less likely to tighten the monetary policy, and externalities are reduced
on both sides. This is what generates a better co-ordination between
the policy makers, as noted in Section 5. But, this can only happen
if the government has a genuine commitment to the long-run goals
(sustainable public finances, and a debt or deficit rule in this case), since
only then will the fiscal policy leader take into account the predictable
reactions (of the follower) to any short-run deviations by the leader.
The follower knows that the leader is not likely to sacrifice his long-run
goals by making such deviations (and anyway has the opportunity to
clear up the mess, according to the follower’s own preferences, if the
leader does so). Thus, in the short-run under simultaneous moves, each
player fails to consider the predictable response, and costs, which the
externalities he/she imposes on his/her rival would create. The ability to
co-ordinate would be lost, and the outcomes worse for both. We show
this in Section 5 (and in a more formal analysis in Hughes Hallett,
2005).
(c) These results hold independently of the commitment to the debt rule
(λ g 2
), or its target value (θ), and independently of the government’s preference
to stabilize or spend (λ g 1
,s), and of the economy’s transmission
parameters (α,β,γ)or the particular value of b as discussed above.
22 Taxes are lower under simultaneous moves because λ cb