2 A Simple Framework for Analyzing Fiscal Policy
The fundamental idea of policy rules is to evaluate and recommend certain types of policy
behavior. In a nutshell this means that we want to identify rules, which link the instrument
of policy authorities to some exogenous variables and finally turn out to be advantageous over
other rules. The question then is, what is the instrument of fiscal policy? Until now, there is no
comprehensive framework to analyze fiscal policy rules empirically. Basically fiscal policy has two
instruments, the tax rate and the benefit rate. The tax rate determines government revenues,
the benefit rate determines government spendings. We decided to follow the approach of Davig
and Leeper (2005) and use government revenues as the dependent variable for the policy rule, as
we think that it best serves for our purpose in investigating the reaction of fiscal policy to rising
debt/GDP ratios.
Our fiscal policy rule takes the following form
τt = constant + γY (StF)Yt + γG(StF)Gt + γB (StF)Bt-1 + σ(StF)εt, (2.1)
where τt denotes the ratio between government revenues and GDP in period t, Yt represents
the output gap, Gt is the expenditure/GDP ratio and Bt-1 stands for debt/GDP ratio in period
t - 1. We decided to use B in period t - 1 for two reasons. On the one hand we would run
into an endogeneity problem, when including B in period t, and other other hand it is extremely
unlikely that fiscal policy can immediately react to a change in B due to lags in the decision
process of fiscal authorities. Therefore, we think that it is plausible to include a lagged value
for the debt/GDP ratio. StF denotes the state of fiscal policy at time t. It emphasizes that the
coefficients and the variance of the error term, εt , are state dependent. We allow for regime
switches to occur in fiscal policy behavior for the reasons given in the last section. We assume
fiscal regimes to evolve according to a Markov chain with transition matrix PF . We allow for
two different states of the parameters, which should be sufficient for the purpose of the analysis2 .
In terms of the parameters in (2.1) it requires for fiscal policy to be sustainable that γB > 0
and sufficiently large such that a larger stock of public debt outstanding significantly increases
government revenues so that the path of government debt itself is stabilized.
To make inference about fiscal policy behavior, we estimate (2.1) using a Bayesian Markov
switching model. We decided to use Bayesian techniques, as the approach delivers easily inter-
pretable credible intervals3 , which are not subject to asymptotic theory. Particularly, it allows for
an evaluation of policy behavior in terms of most likely actions, as the coefficients are regarded
as being random itself.
2We also did the analysis with a higher number of regimes, which did not deliver any reasonable results.
3 Further details on credible intervals and the difference to the classical confidence interval may be found in
Koop (2003).