868 Macroeconometric Modeling for Policy
specified in terms ofwtandpt:
wt=mw+{
1 +ζδ 12
( 1 −ζ)}
pt (17.25)−
δ 12 ζ
( 1 −ζ)pit−
δ 12 η
( 1 −ζ)T (^3) t+δ 13 zt−δ 15 ut−δ 16 T (^1) t+ecmbt
pt=( 1 −ζ)mq+( 1 −ζ)
{
wt+T (^1) t−zt
}
+ζpit+ηT (^3) t−( 1 −ζ)ecmft. (17.26)
By simply viewing (17.25) and (17.26) as a pair of simultaneous equations, it is clear
that the system is unidentified in general. However, for the purpose of modeling the
aggregate economy, we choose the consumer price indexptas the representative
domestic price index by settingδ 12 =0. In this case, (17.26) is unaltered, while the
wage equation becomes:
wt=mw+pt+δ 13 zt−δ 15 ut−δ 16 T (^1) t+ecmbt. (17.27)
The long-run price equation (17.26) and the long-run wage equation (17.27) are
identified by the order condition.
17.2.6.3 VAR and identified equilibrium correction system
The third stage in the operationalization is the equilibrium-correction system,
where we follow Bårdsen and Fisher (1999). In brief, we allow wage growth
wtto interact with current and past price inflation, changes in unemployment,
changes in tax rates, and previous deviations from the desired wage level consistent
with (17.27):
wt−α12,0qt=c 1 +α 11 (L)wt+α 12 (L)qt+β 12 (L)zt
−β 14 (L)ut−β 15 (L)T (^1) t (17.28)
−γ 11 ecmbt−r+β 18 (L)pt+ (^1) t,
whereis the difference operator, and theα 1 j(L)andβ 1 j(L)are polynomials in
the lag operatorL:
α 1 j(L)=α 1 j,1L+···+α 1 j,(r− 1 )Lr−^1 ,j=1, 2,
β 1 j(L)=β 1 j,0+β 1 j,1L+···+β 1 j,(r− 1 )Lr−^1 ,j=2, 4, 5, 6.
Theβ-polynomials are defined so that they can contain contemporaneous effects.
The orderrof the lag polynomials may, of course, vary between variables and is
to be determined empirically. This specification is a generalization of the typical
European wage curve, where the American version is derived by settingγ 11 = 0
(see Blanchard and Katz, 1999).
Any increase in output above the optimal trend exerts a (lagged) positive pressure
on prices, measured by the outputgapt, as in Phillips curve inflation models (see
Clarida, Gali and Gertler, 1999). In addition, product price inflation interacts with