We have seen that in S2 the response of GDP to government spending shocks has also
become more muted. It is then natural to ask how much, if any, of the decline in the variance of GDP can be attributed to changes in the variance of the fiscal policy shocks
and how much to changes in their transmission mechanism. Letting Δσ2y
|eg represent the
change in the variance of the 4-quarters-ahead forecast error of GDP between the two
subsamples due to eg, one can write: where Δσ2e
g is the change in the variance of the government spending shock, and the term
Ψg,J depends on the impulse response up to 1 year ahead, based on the VAR estimated
in subsample J (see Hamilton [1994] pp. 323-4). The first term of the sum on the r.h.s.
can be interpreted as the contribution of the change in the variance of the spending
shock, while the second term can be interpreted as the contribution of the change in the
impulse response to a government spending shock, or of the transmission mechanism of
government spending. An analogous formula holds for tax shocks. The sum of the r.h.s.
of (15) over all the structural shocks of the model gives the change of the 4-quarter-ahead
forecast error of GDP