and Smith (1995), the mean group estimator, is based on the separate estimation of the
coefficients for each cross-section unit, through the least squares method, and then
computing the arithmetic mean of those coefficients. Still, this alternative procedure,
does not allow for the hypothesis that some of the coefficients may indeed be the same
for several countries.
Besides the problem mentioned above, and to circumvent the potential non-stationarity
problem arising from the time-series dimension of the data, empirical models in the
literature are usually estimated with the first differences of the variables. Even so, in
most cases this procedure does not fully solve the problem.18 Also, the alternative of
using variables in first differences might not take into account the fact that there is a
levels relation between the government budget balance and the stock of outstanding
public debt, through the present value borrowing constraint.
Another version of equation (28) was therefore estimated, using the first differences of
the original variables
bit = xi + ksit , + wbit , + ®„ (29)
it i it — 1 it — 1 it ,
where xi gives now the individual effects for each country i, and bit=Bit-Bit-1 and sit=Sit-
Sit-1.
From the results results for the estimation of equation (29), presented in Table 4, one
can draw some tentative additional conclusions. With the variables in first differences,
both the pooled regression and the random effects models are chosen against the fixed
effects model, since respectively the F and Hausman test statistics are not statistically
significant. Also, the estimated coefficient k for the primary surplus maintains its
negative sign in all models. This can once more be seen as evidence against the
validation of the FTPL hypothesis for EU-15 countries.
18 Some papers dealing with the properties of estimators, and recent developments in panel unit root
tests and cointegration tests in panel data models are, for example, Alvarez and Arellano (1998),
Phillips and Moon (2000) and Arellano and Honoré (2001).
27