Economic Models - Convex Optimization

The Advantages of Fiscal Leadership in an Economy 83
re-distributive purposes only, but permitted discretionary expenditures for
enhancing output.We further assumed that there were two types of agents —
rich and poor — and that only the rich use their savings to buy government
bonds. Based on this view, b would be the proportion of pre-tax income
(output) going to the rich and s, the proportion of after-tax income that the
rich allocate to saving. Tax revenues, τ t , can then be used by the government
to re-distribute income from the rich to poor, either directly or via public
services. This structure, therefore, has output-enhancing expenditures g t ,
and discretionary transfers τ t . Both are financed by aggregate tax revenues;
that is, from discretionary and trend revenues. Expenditures above these
revenues must be financed by the sale of bonds.
5.2. An Alternative Interpretation
We could, however, take a completely different interpretation of Eq. (5).
We could take the term s(by t − τ t ) to be the proportion of the budget-deficit
ratio, as it currently exists, adjusted for the effect of growth on this ratio
and any discretionary taxes raised in this period, which the government
now proposes to spend in period t. The deficit ratio itself is of course
d = (G − T)/Y = (e − r), where G and T are the absolute levels of
government spending and tax revenues, and e and r are their counterparts as
a proportion of Y. If the economy grows, then d = (G−T)/Y −ẏ(e−r)
where ẏ denotes the growth rate in national income. If we wish to see what
would happen to this deficit ratio if fiscal policies were not changed, it
means new spending can only be allowed to take place out of new revenues
generated by growth: G = T = rY. Inserting this, we have d =
−(e − r)ẏ =−dẏ. Since y t is the deviation of Y from its steady-state
path, by t in Eq. (5) will equal d, the change in the existing deficit ratio
under existing expenditure plans and tax codes, if b =−(e − r)/Y 1 . The
government will spend some proportion of that, s, less new discretionary
taxes in the current period. Hence, s would typically equal 1, although it
might be less, if some parts were saved in social security funds or other
assets. This defines what would happen to the deficit ratio if there were no
change in existing fiscal policies; but the term in τ t shows that governments
may also raise additional taxes in order to reduce the current deficit ratio
to some desired target value, θ, say. This target is likely to be θ = 0, to
balance the budget over the cycle, as required by the stability pact. We give
governments such a target, in the form of either a soft or a hard rule, in the
objective functions that are discussed in Section 5.