This approach rewrites (2.4) in the form:
∞
dt =∑(1+r)-jEt(st+j)⇔limT→∞(1+r)-TEt(dt+T)=0 (2.5)
j=1
where r is usually interpreted as the difference between the expected return on
government debt and the growth rate of GDP. Then unit roots and cointegration
conditions on fiscal debt and deficit guaranteeing that this version of the government IBC
holds are derived and tested.
But versions of (2.5) are problematic. A first problem is that (2.5) factorizes the product
of the discount rate and fiscal variables, ignoring that the discount factor may be
correlated with the primary surplus and debt, as we have just mentioned. The choice of
this discount factor is a second controversial feature of this empirical approach, since, as
we have also mentioned, the proper discount factor in an stochastic setting is the risky
rate of return (i.e. the return of state-contingent claims), not the rate of safe assets. The
arbitrariness of both the factorization and the choice of the discount factor have motivated
the distinction (Bohn, 2005a) between ad hoc sustainability, based on (2.5), and model-
based sustainability, based on (2.4).
The third characterizing feature of this approach is that it tests (2.5) by testing for unit
roots and cointegration among debt and the components of the budget deficit. However,
the order of integration of debt seems to be irrelevant, as any debt series that are
stationary after any finite number of differencing operation would satisfy (2.5) (Bohn,
2005b), rendering the order of integration of government debt uninformative for fiscal
policy sustainability.
A more recent and promising alternative empirical approach to sustainability testing is
provided by the literature on fiscal reaction functions. This literature investigates the type
of flow reaction to government debt accumulation that would guarantee that (2.4) is
satisfied. Its main result (Bohn, 1998; Canzoneri et al., 2001) is that a positive response
of the primary surplus to debt accumulation is a sufficient condition for sustainability.
More precisely, assume that the primary surplus can be written as:
st = δtdt-1 + Vt (26)
where φ is a bounded component and δt ≥ 0 ∀t with δt > 0 applying infinitely often.
Then it can be shown that fiscal policy satisfies the general condition (2.4).
The intuition of this result is that by adjusting the primary surplus in response to debt
developments the government reduces the exponential growth of debt by a factorδ
relative to the discount rate, which is sufficient to satisfy the TC in (2.4).
2.3 Government Debt Accounting
The evolution of government debt is the bottom line reference for the sustainability of
fiscal policy. In this section we take a look at debt developments in the EU 15 Member
States, excluding Luxembourg, during the sample period 1977-2005, with the US and
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