870 Macroeconometric Modeling for Policy
(17.30) is given by:
a12,0=α12,0
1 −ζ
+β18,0,a21,0=( 1 −ζ)α21,0,a 12 (L)=α 12 (L)
1 −ζ
+β 18 (L),a 21 (L)=( 1 −ζ)α 21 (L), (17.31)
b 2 j(L)=( 1 −ζ)β 2 j(L),j=1, 2, 5,d 12 =δ 12
1 −ζ
,e 1 =
1 ,
e 2 =( 1 −ζ)
2.The model (17.30) contains the different channels and sources of inflation dis-
cussed so far: imported inflationpit, and several relevant domestic variables – the
output gap, and changes in the rate of unemployment, in productivity, and in tax
rates. Finally, the model includes deviations from the two cointegration equations
associated with wage-bargaining and price-setting, which have equilibrium-
correction coefficientsγ 11 andγ 22 respectively. Consistency with assumed cointe-
gration implies that the joint hypothesis ofγ 11 =γ 22 =0 can be rejected.
17.2.6.4 Economic interpretation of the steady state
The dynamic model in (17.30) can be rewritten in terms of real wages
(
w−p)
t
and real exchange rates
(
pi−p)
t. Using a specification with first-order dynam-
ics, Bårdsenet al.(2005, Ch. 6) discuss several different aspects of this model.
Most importantly, the dynamic system is asymptotically stable under quite gen-
eral assumptions about the parameters, including, e.g., dynamic homogeneity in
the two equilibrium-correction equations. The steady state is conditional on any
given rate of unemployment, which amounts to saying that our core supply-side
model does not tie down an equilibrium rate of unemployment. Instead, there is a
stalemate in the dynamic “tug-of-war” between workers and firms that occurs for,
in principle, any given rate of unemployment (see Kolsrud and Nymoen, 1998;
Bårdsen and Nymoen, 2003, for proofs). Since there are no new unit roots implied
by the generalized dynamics in equation (17.30) above, asymptotic stability holds
also for this, extended, version of the model. We therefore have the following
important results: the dynamics of the supply side are asymptotically stable in the
usual sense that, if all stochastic shocks are switched off, then
(
pit−qt)
→rexss(t),and(wt+T (^1) t−qt)=wqss(t), whererexss(t)andwqss(t)represent deterministic
steady-state growth paths of the real exchange rate and the producer real wage.
Generally, the steady-state growth paths depend on the steady-state growth rate
of import prices, and of the mean of the logarithm of the rate of unemployment,
denoteduss, and the expected growth path of productivityz(t). However, under the