2.3 Results
In the following we provide the estimated coefficients of the fiscal policy rule as well as the
temporal distribution of the regimes. For the estimation we use a Matlab code, which takes
30,000 draws from the corresponding posterior distribution. We allowed for two regimes to occur.
The prior probability density function (pdf) of the transition probabilities pij is assumed to follow
a β-distribution, as it is restricted to the interval [0, 1]. For the prior pdf of the coefficients we
decided to take a normal distribution with mean γ0,1 = 0 in state 1, which would depict an active
policy regime as revenues become exogenous, and γ0,2 = 1 in state 2, which would correspond to
a passive policy regime as in particular the debt/output ratio has an impact on the revenue/GDP
ratio. For the two prior pdfs we choose the same variance Σγ,0 = 1 so that they are strongly
overlapping each other6 . This prior specification implies that we initially believe that there are
no fundamental changes in policy behavior.
In case that the coefficients are not significantly different across the two regimes, i.e. the
credible intervals given by the 2.5% and 97.5% quantiles are strongly overlapping each other,
we decided to regard the corresponding coefficient as being not state-dependent. This has the
advantage that we need to estimate less coefficients, while it is easier to identify changes in the
underlying regimes. We do the same with the initially state-dependent variance of the error
terms. Finally, the error terms were checked for their properties and may be considered as white
noise.
2.3.1 Germany
Figure 1 shows the probability for each of the two potential fiscal regimes in Germany during
the period 1970-2003. We can basically see that regime 1 played no role in describing Germany’s
fiscal policy until the late 1990s. The estimated coefficients given in section 4.2 of the appendix
show that the two regimes differ only in the influence of the debt/GDP ratio and the size of
the constant. All other coefficients are not regime-dependent. The same is true for the variance
of the error terms, which turned out to be almost identical across the two regimes so that we
decided to keep the variance fixed. Starting with the regime-invariant coefficients, we may say
that Germany’s fiscal policy is countercyclical, as the revenue/GDP ratio increases with positive
output deviations. This reflects the role of automatic stabilizers7 . Furthermore, we see that
higher expenditure/GDP ratios are matched by growing revenue/GDP ratios, as the credible
interval for γG is strictly positive. More interesting insights in the fundamentals of Germany’s
fiscal policy are given by the regime-dependent parameters. In regime 2 we observe a much larger
constant combined with a less stronger reaction of the revenue/GDP ratio to increases in the
debt/output ratio. The opposite is true for regime 1. Here we find a constant which is almost
symmetrically distributed around zero, while γB(StF = 2) is substantially larger than in regime 1.
To illustrate the difference between the two regimes we reduced them to a 2-dimensional problem
6We also did the estimation with other prior specifications, which left the results basically unchanged.
7 One should note again at this point that this analysis is built on total government revenues and expenditures,
which included social security contributions.