Robustness Checks
Taken at face value, Table 2.3 raises some doubts about the sustainability of fiscal
policies in Germany, Greece, France, Ireland, Austria, Finland, and, indeed, Japan, where
a positive and significant reaction of the primary balance to the stock of debt has not been
estimated. However, according to Section 2.2, the reaction of the primary surplus to debt
levels does not need to be positive all the time, while the descriptive analysis carried out
in Section 2.3 suggests that fiscal policy has changed over the sample period, in particular
after 1993 once the convergence criteria entered into force. Therefore, there is a case to
explore possible structural breaks, as well as non-linearity (Bohn, 2005a), in the response
of the primary balance to the stock of debt. In addition, the fact that the fiscal policy
stance may have an impact on the cycle would imply that output gaps may be partially
determined by the primary surplus, thus leading to simultaneity biases (Ballabriga and
Martinez-Mongay, 2003), which might put into question the estimation method and
advocate for instrumental variable methods. Alternatively, it might also call for the
substitution of the contemporaneous output gap by the lagged one in order to avoid
simultaneity. Finally, the parameters in specification (2.10) can be seen as a linearization
of the parameters in a partial adjustment non-linear model, in which the actual responses
of the primary balance to the debt and the output gap are the estimated in (2.10) divided
by the complement of the inertia (Ballabriga and Martinez-Mongay, 2005). This would
ask for a non-linear estimation of (2.10). Alternatively, one could consider a linear
specification in which the inertia is absent.
Table 2.4 contains the result of the analysis of robustness of the estimates of the primary
surplus reaction to debt against the above alternative specifications of the reaction
function. In all cases, the table shows the estimate of the coefficient of debt and its
heteroskedastic-consistent standard error.8 The first column reproduces the results for the
baseline model (2.10) in Table 2.3. The second column presents the baseline model
estimated by instrumental variable methods. Following Ballabriga and Martinez-Mongay
(2003), the instrument for the contemporaneous output gap for each country is a sort of
country-specific international gap estimated on the basis of the bilateral trade-weighted
average of the output gaps of the rest of the OECD countries. Overall, the potential
simultaneity bias seems to be negligible. France, where the estimate shifts from positive
to negative but remains non-significant; the Netherlands, where it decreases; and
Portugal, where it increases but remains positive and significant, are the only differences
with respect to the OLSQ estimation. Similarly, dealing with potential simultaneity bias
by substituting the contemporaneous gap with the lagged one (third column) leaves
results basically unaffected, with just a reduction in the size and significance (10%) of the
coefficient in Portugal.
The fourth column considers the effects of dropping inertia in (2.10). As a general rule,
the reaction of the primary surplus to debt becomes larger in many countries, and
significant in Greece and Austria. However, it decreases in Portugal and becomes non-
significant in Sweden and the UK. Moreover, usual tests indicate the presence of
significant misspecification errors. The estimation of the baseline model by non-linear
methods (fifth column) does not change the conclusions of the baseline model either,
since the non-linear estimates are very close to the linear ones in the first column of Table
2.4 after being divided by (1-ρ) with ρ as estimated in the fourth column of Table 2.3.
Similarly, estimation of the model by non-linear two-stage least squares (instrumental
Detailed estimates are available upon request from the authors.
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