the initial value, θ1 >θ1 (0), and vice versa for an expenditure instrument
( ∂θb1 < 0). . ... . . .
If there is a sustainability problem a metric of the problem is given by
lθɪ (0) - θ1∣.
An advantage of this approach is that it yields an answer to the question of
fiscal sustainability in one metric taking into account the whole future profile
of public finances and using capital markets to smooth effects across periods.
Notice that this simplicity is attained at the cost of being unable to unravel the
profile of the underlying problem from the indicator.
The sustainable value of the policy parameter can be interpreted as the
present value of the path calculated under the PAYG solution, i.e.
-~>w-
θɪ = PV (θpayg(t))
which holds exactly if initial debt is zero, as shown in the appendix.
The sustainability indicator obtained by the approach outlined above can be
interpreted as a market test of the sustainability of public finances. This is so
since the indicator is based on the intertemporal budget constraint given market
interest rates, and therefore provides an answer as to whether current policies
(policy functions f and parameters θ) are consistent with the intertemporal
budget constraint. If the answer is confirmative the conclusion is that it is
feasible to maintain current policies. However, this does not answer the question
whether it is desirable not least optimal to maintain current policies11. It
is obvious that optimal policies cannot be derived solely by considering the
budget constraint. If it is found that current policies are unsustainable it can
be concluded that an adjustment eventually would have to take place - current
policies cannot be maintained, but the analysis does not say anything about
how and when the change will take place.
The budget implications of the sustainable tax rate can be calculated by
solving for
βt xt, zt,(θeɪ, θ2.......θN)
which gives that the path the primary budget balance would have to follow in
order for policies to be sustainable. Note that this path for the primary budget
is both dependent on the particular instruments used in calculating sustainable
taxes and time dependent. This points to the fact that it is not easy to use
a budget metric as a guideline for formulating medium term objectives for
fiscal policies. However, as shown in the application below it may be useful to
consider the path for the budget balance when discussing the appropriate policy
response, cf below.
In conclusion, by calculating both the PAYG-tax and the sustainable tax
one arrives with the taxonomy that the former implies a constant level for the
public debt (and public balance) and a time varying tax rate, while the latt er
has a constant tax rate and a time dependent level for public debt and the
11 Floden(2003) shows in a model with infinitely lived household how the optimal policy
prescribes tax smoothing and a pre-funding due to demographic shifts.
10