The Global Dimension to Fiscal Sustainability

limθⁿEt(Bt+n)=0                                           (4)

n→∞

These conditions have served as the benchmark in the empirical literature on
sustainability. Hamilton and Flavin (1986), for example, examine whether the null
hypothesis of a unit root for the real stock of debt and the primary surplus can be
rejected and, hence, whether debt trends stochastically, and is hence unsustainable
(i.e. the transversality condition is satisfied). They find that the debt unit root
hypothesis can be rejected for the period 1962-1984 and that the data is consistent
with the idea that the budget is perceived by investors as being balanced in present
4
value terms.

Hakkio and Rush (1991) suggest that cointegration between real government
revenue and real government spending (inclusive of real interest rate payments) is a
necessary condition for the intertemporal budget constraint to be satisfied. They find
evidence of cointegration for the US (from 1950-1988), although evidence is less
clear cut for a later sample (1976-1988), which suggests violation of the government’s
intertemporal budget constraint.⁵ Trehan and Walsh (1991) emphasize that with
constant expected real interest rates a necessary and sufficient test of the intertemporal
budget constraint is cointegration of debt and the primary surplus and a quasi-
difference stationary primary surplus. Intuitively, if primary surplus and debt are
cointegrated the government has some concern with debt levels when deciding fiscal
policy.

Ahmed and Rogers (1995) consider the present value constraint for the US and
the UK, by examining a cointegrating vector that includes Gt and Tt. Using over a
hundred years of annual data and, taking account of breaks using dummies in the

⁴ The test statistics reject the null of unit root only very marginally and suffer from serial correlation
according to Kremers (1988).

⁵ However, Hakkio and Rush (1991) fail to find evidence of cointegration between government
spending and government revenue, when they are normalised by GDP.

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