yt = ft(xt, zt,θt) (3)
which depend on the current state, the policy form (captured by the function
f ) and the policy parameters θ. This representation allows a treatment of both
structural and parametric reforms.
Hence the public budget is for given policy functions defined by the implicit
function
βt (xt, zt,θt) ≡ b(xt, ft(xt, zt,θt), zt)
The public debt level relative to GDP evolves according to
dt+1 =(1+rt)dt + bt (4)
where r is the growth corrected effective real rate of interest on public debt.
The intertemporal budget constraint for the public sector reads6
PV(bt)-d0≥0 (5)
where PV denotes the present value operator and d0 the initial debt level.
Obviously the budget constraint - both the static and the intertemporal - are
fulfilled for a infinity of policies, and it is therefore necessary to put more struc-
ture on the analysis to arrive at usable results. The issue is to clarify policies
which are sustainable in the sense that they do not violate the intertemporal
budget constraint.
Passive policies
A frequently asked question is what the consequences would be of main-
taining unchanged policies. Specifically, how would the public sector budget
balance(b) and public debt (d) evolve in the absence of any policy initiatives?
While it may be illustrative to show a divergent path for public debt, this
approach has two major shortcomings. It is very difficult to determine critical
levels for the public budget balance and debt level beyond which the situation
is no longer tenable7 . Theoretical work teaches us that the actual path followed
by the economy depends critically on the expected future policy interventions
used to correct a crisis situation. This is well-known from e.g. the literature
on the contractionary effects of expansionary fiscal policy 8 and the so-called
"balance-of-payments-crises" literature9 . Empirical work also leaves it unclear
what the critical levels are. Moreover, the purpose of discussing sustainability
is not to clarify for how long policies can be maintained without provoking a
major crisis, but to aid in policy planning so as to avoid the possibility of such
crises.
6 Assuming the usual no-Ponzi restriction.
7cf the approach taken by e.g. IMF discussed in section 2.
8See e.g. Bertola and Drazen (1989) and Sutherland(1993).
9 The "balance of payments crises" literature shows that the crises caued by unsustainable
policies will depend on the nature of the policy intervention, which in turn critically would
affect the timing of the crises.