884 Macroeconometric Modeling for Policy
the other sub-sections, we use dynamic simulation, the main tool of model usage,
to elucidate the strength of the policy instrument, to check that the model solu-
tion generates the properties of the actual data, and whether simulation over a
long forecast horizon gives the steady state we expect from the theoretical analysis
above. We also discuss optimal policy response, forecast properties, and strategies
to reduce the damage that structural breaks have on forecasts from equilibrium
correction models. Finally in this section, we raise the more fundamental ques-
tion of testing non-nested hypotheses about the supply-side of the economy; our
example will be the New Keynesian Phillips curve against the model of wage and
price adjustment that has been presented above.
17.4.1 Tractability: stylized representations
There is a marked difference between the intricate and complex dynamics often
found in empirical models – at least if they model the data – and the very simplified
dynamics typically found in theoretical models. The purpose of this section is to
enhance the understanding of the properties of a model through the use of stylized
representations. A dynamic model, e.g.:
yt= 2 −0.4yt− 1 −0.6yt− 2
+0.2xt−0.5xt− 1 + 3 xt− 2 − 1 xt− 3 −0.5(
yt− 3 − 4 xt− 4)
+vt,can be approximated by a stylized model with simplified dynamics, in this example:
yt= 1 +0.85xt−0.25(
y− 4 x)
t− 1.This is achieved by using the mean of the dynamics of the variables.^14
In the same way as above, we let lower cases of the variables denote natural
logarithms, sozt≈ ZtZ−t−Z 1 t−^1 =gzt. If we assume that, on average, the growth
rates are constant – the variables could be “random walks with drift” – the expected
values of the growth rates are constants:
Eyt=gy∀tExt=gx∀t.If the variables also are cointegrated, the expectation of the linear combination in
the equilibrium correction term is also constant, so:
E(
yt− 3 − 4 xt− 4)
=E(
yt− 1 − 4 xt− 1)
=μ∀t.Under these assumptions, the mean dynamics of the model becomes:
Eyt= 2 −0.4Eyt− 1 −0.6Eyt− 2
+0.2Ext−0.5Ext− 1 + 3 Ext− 2 − 1 Ext− 3
−0.5E(
yt− 3 − 4 xt− 4)
+Evt
gy( 1 +0.4+0.6)= 2 +(0.2−0.5+ 3 − 1 )gx−0.5μ