We specify an empirical model of fiscal policy as a small-scale VAR in real output yt
and the expenditure gt and revenue side tt of the government budget. We can summarise
the data properties in a VAR-model (5.1), ignoring for ease of notation any deterministic
terms:
B(L)Xt =εt (5.1)
where Xt refers to the vector of variables [yt gt tt], and εt contains the reduced form
OLS-residuals. By rewriting the VAR into its Wold moving average form (5.2),
Xt = B ( L )-1 εt εtεt =Ω. (5.2)
and imposing some structure on the relation between reduced form residuals εt and
structural shocks ηt via the transformation matrix A (such that Aεt =ηt ), we can write
the model (5.2) as follows:
′
Xt=C(L)ηt=B(L)-1Aεt ηtηt =I. (5.3)
Any SVAR analysis needs to impose at least as much restrictions as contained in the
matrix A to identify the model. By imposing orthogonality of the structural shocks we
have already six (i.e. the covariance matrix of OLS residualsΩ= AA'). Hence, we need to
choose at least three more restrictions. The ones we employ are a combination of long
and short-term restrictions. The latter shape the contemporaneous relations among the
variables through a direct parameter choice onA . The former impose a long-term
neutrality constraint on the effects of a structural shock j on some variable i . That is, the
i,j-th element of the infinite horizon sum of coefficients, call it C(1)ij , is assumed to be
zero. This requires an indirect restriction in (5.3) on the product of the transformation
matrix A and the inverted long-run coefficient matrixB(1)-1. In other words,
[C(1)]ij =[B(1)-1A]ij =0. (5.4)
For the system consisting of government expenditures, revenues and output, we assume
three structural shocks to drive output and fiscal variables. The supply shock (ηq ) drives
the long-term trend rise in output and leads to the unit root behaviour of real output. This
shock is isolated by assuming there are two further shocks in the model that both have
temporary effects on output. I.e., we assume that [C(1)]12=0 and [C(1)]13=0 in (5.4).
These shocks can be interpreted respectively as a generic business cycle shock (ηc )
capturing short-term fluctuations around the moving steady state equilibrium for output,
and a fiscal shock (ηf ) with short-term ‘demand’ effects on output. In order to
distinguish the business cycle shock from that to fiscal policy, we employ the elasticity
approach advocated by Blanchard and Perotti (2002). We derive a shock to spending
and/or revenues from which the cyclical effects have been removed. In other words, the
shock with transitory effects on output - but unaffected by short-term variation in output
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