Economic Models - Convex Optimization

The Advantages of Fiscal Leadership in an Economy 95
the government leadership with an independent central bank that directs
monetary policy exclusively towards the achievement of the inflation target
(i.e., δ = λ cb = 0). The third column gives the minimum loss associated
with a simultaneous decision-making version of the same game. In each
case, the deficit rule is soft for the Eurozone countries (λ g 2
= 0.25); medium
strength for the United States, Canada, and Switzerland (λ g 2
= 0.5); and
harder for Sweden, the United Kingdom and New Zealand (λ g 2
= 1). The
deficit ratio targets are 0% in all countries (a balanced budget in the medium
term), but the propensity to spend, s, out of any remaining deficit or any
endogenous budget improvements is one.
Evidently, complete dependence in monetary policy is extremely unfavorable,
although the magnitude of the loss varies considerably from country
to country. The losses in Column 3 (Table 3) appear to be relatively small
in comparison. However, when these figures are converted into “growth-rate
equivalents”, I find these losses to be significant. A growth-rate equivalent
is the loss in output growth that would produce the same welfare loss, if all
other variables remain fixed at their optimized values. 25
The figures in Column 4 are more interesting. They show that the losses
associated with simultaneous decision-making are equivalent to having permanent
reductions of up to 20% in the level of national income. That is,
France, Italy, and the Netherlands could have expected to have grown about
15%–20% more, had they adopted fiscal leadership with deficit targets; and
Sweden, the United Kingdom, and New Zealand around 3%–5% less, had
they not done so. Similarly, fiscal leadership with debt targeting would
be worth 10%–20% extra GDP in the United States, and Canada. These
are significant gains and significantly larger than could be expected from
international policy co-ordination itself (Currie et al., 1989).
Thus, the immediate effect of introducing a stability pact deficit rule
has been to increase the costs of an unco-ordinated (simultaneous moves)
regime dramatically. This reveals the weakness of the deficit rule as a
25 Currie et al. (1989). To obtain these figures, I compute the marginal rates of transformation
around each government’s indifference curve to find the change in output growth, dy t , that
would yield the welfare losses in Column 3. Formally,
dy t =
dEL g t
[λ g 2 {(b − θ)y t − τ t }(b − θ) − λ g 1 ]
using Eq. (9). The minimum value of dy t is, therefore, attained when tax revenues τ t grow at
the same rate as the re-payment target (b − θ)y t . These are the losses reported in Column 4.