The Global Dimension to Fiscal Sustainability

level, where a positive response parameter is seen as consistent with fiscal probity.⁷
Equation (1) can be rearranged to give the ratio of primary surplus to GDP, (Tt -
Gt)/Yt , as a function of the debt to GDP ratio, Bt/Yt.

T G=(i- g ) ^b

YY
Yt                Yt-1

Where g is the growth rate of nominal GDP. Expressing sit as the primary surplus
(i.e. taxes minus non-interest spending), bit is the debt level (both variables are ratios
of GDP) and assuming bit = bit-1 in the long run and uit is a stationary residual error,
our approach to examining fiscal probity is to estimate equation (6) in a panel time
series setting using the following regression:

sit = αi + ρbit + γZit + uit,                                          (6)

If ρ > 0, this is indicative of fiscal probity on the part of the government. Any
increase in debt is reflected in an increase in the fiscal surplus of the government.
Additionally equation (6) includes other potential determinants (Zit) of the primary
surplus, but if these are stationary while we have a cointegrating relationship between
primary surplus and debt, superconsistency would suggest we can ignore Zit.⁸
Furthermore a panel approach to estimating equation (6) assumes that the regression
error terms (uit) are cross sectionally independent. To the extent that ukt and ujt are not
independent, ∀ k ≠ j, and this correlation can be represented by a global stochastic
trend, then a Bohn reaction function which ignores a nonstationary factor may be
based on a spurious panel regression (see Bai, Kao and Ng, 2007). In the next section
we discussion how we deal with this issue.

⁷ We should also highlight that Bohn does not preclude the importance of a nonstationary debt dynamic
in finite samples, which would highlight the importance of the time series properties of the fiscal
variables. Indeed Bohn (1998) argues that for a century of US data primary surplus and debt are
stationary and that they are positively related.

⁸ For a discussion of superconsistency see Stock (1987) and the discussion in Bohn (1998) for the
stationary case.

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