Palgrave Handbook of Econometrics: Applied Econometrics

Gunnar Bårdsen and Ragnar Nymoen 885

gy=

2

2

+

1.7

2

gx−

0.5

2

μ

gy= 1 +0.85gx−0.25μ.

We can therefore write the mean-approximated, or stylized, dynamic model as:

yt= 1 +0.85xt−0.25

(

y− 4 x

)
t− 1.
To illustrate, the dynamic behavior of the model and its mean approximation
are shown in Figure 17.4. The upper panel shows the dynamic, or period, responses
inytto a unit change inxt−i. The lower panel shows the cumulative, or interim,
response. The graphs illustrate how the cyclical behavior – due to complex roots –
is averaged out in the stylized representation.

3

Dynamic multipliers

Cumulative (interim) multipliers

Full model Simplifed model

2

1

0

–1

4

0 5 10 15 20

3

2

1

0

0 5 10 15 20

Full model Simplifed model

Figure 17.4 The dynamic responses of the example model and its mean approximation

Note that all that is done is to exploit so-called growth coefficients (see Patterson
and Ryding, 1984; Patterson, 1987). The steady-state growth:

gy= 4 gx