Economic Models - Convex Optimization

The Advantages of Fiscal Leadership in an Economy 81
Consequently, the United Kingdom appears to use fiscal policy for stabilization
in a minor way as claimed, while the Euro economies seem not
to use fiscal policy this way at all. Confirmation of this comes from the
responses to interest rate changes, which are positive but very small and
statistically insignificant in the United Kingdom, but negative and near significant
in Europe. This implies that the British fiscal policies are chosen
independently of the monetary policy, as suggested by our weak leadership
model. But, if there is any association at all, then both the fiscal and
monetary policies would be compliments and weakly co-ordinated.
The UK results are therefore inconclusive. They are consistent with
independent policies, or fiscal leadership — the latter, despite the insignificance
of the direct fiscal-monetary linkage, because of the significant output
gap term in the fiscal equation which, given the same effect is not found in
the monetary policy reactions, suggests fiscal leadership may in fact have
been operating. In any event, there is no suggestion of monetary leadership;
if anything happens, the results imply independence or fiscal leadership.
In the Eurozone, the results are quite different. Here, the significant
result is the conflict among instruments in monetary policy (and essentially
the same conflict in the fiscal policy reactions). Hence, the policies are
competitive, which suggests that they form a Nash equilibrium (or possibly
monetary leadership, since the coefficient on fiscal policy in the Taylor
rule is small and there is no output gap smoothing). This suggests weak
monetary leadership, or a simple non-co-operative game.
5. Theoretical Evidence: A Model of Fiscal Leadership
5.1. The Economic Model and Policy Constraints
The key question now is: would governments want to pursue fiscal precommitment?
Do they have an incentive to do so? And would there be a
clear improvement in terms of an economic performance if they did? More
important, would the fiscal leadership model be more advantageous, if fiscal
policy was limited by a deficit rule in the form of “hard” targets (as in the
original stability pact) or “soft” targets?
To answer these questions, we extend a model used in Hughes Hallett
and Weymark (2002; 2004a;b; 2005) to examine the problem of monetary
policy design when there are interactions with fiscal policy. For exposition
purposes, we suppress the spillovers among countries and focus on the
following three equations to represent the economic structure of any one