Ita and Itd are indicators for the cyclical developments which will be specified later on,
and αt and γt are the corresponding sensitivities/elasticities. The use of different
indicators of the cyclical development is motivated by the fact that in general policy-
makers do not necessarily respond to variables economists have in mind.
Inserting (4.2.1) and (4.2.2) in (4.1) constitutes our unobserved component model
specification, naturally cast as a state-space system. The measurement/signal equation
bt = μt + αt ■ Iat + γt ■ Id + εt (4.3.1)
links the observed balance to its components, while the state/transition equations
|
μt+1 = μt +ηt+1 |
ηt ~iid N(0,ση) |
(4.3.2) |
|
αt+1 =αt +ψt+1 |
ψt ~iid N(0,σψ ) |
(4.3.3) |
|
γt+1 = γt +ζt+1 |
ζt ~iid N(0,σζ) |
(4.3.4) |
describe the dynamics of the states. In the estimation, the log-likelihood is constructed
using the Kalman filter.56
Equation (4.3.2) specifies the core balance as a random walk, the innovations ηt
capturing fiscal shocks that have a permanent or enduring impact on the level of the
budget balance. Similarly, equations (4.3.3) and (4.3.4) set up the automatic sensitivity of
the budget balance αt and the policy response γt as random walks. While a positive
(negative) sign of γt typically indicates a counter-cyclical (pro-cyclical) reaction of
discretionary fiscal policy, the sign is interpreted just the other way round in the case of
expenditure variables. In principle, all three state equations could be generalised to
include exogenous variables. We take (4.3.1)-(4.3.4) as a transparent, easy-to-use device
to decompose budget balances.
In the general representation (4.3.2)-(4.3.4) the states - and hence budget components -
are assumed to move stochastically. If the estimation yields very small variances, this is
an indication that the corresponding component is rather deterministic. In such a case, the
model can be simplified by setting disturbances to zero (the states would then enter
(4.3.1) as recursive coefficients).
Since the focus of our interest lies primarily on the impact of the policy response to
cyclical developments (rather than on the automatic stabilisers), we can estimate a
smaller, “reduced model” for the structural balance bst consisting of the measurement
equation
bst = μt + Yt ■ It + εt (4.4)
and state equations (4.3.2) and (4.3.4).
Estimations have been carried out with RATS v6.
105