Gunnar Bårdsen and Ragnar Nymoen 867where we useqfas a reminder that this is a theoretical equation for firms’ price-
setting.
17.2.6.2 Cointegration and long-run identification
At this point we show how the two theoretical relationships (17.20) and (17.21) can
be transformed into hypothesized relationships between observable time series. As
explained in section 17.2.3, our maintained modeling assumption is that the real
wage and productivity areI( 1 )series. The rate of unemployment is assumed to be
I( 0 ), possibly after removal of deterministic shifts in the mean.
Using subscripttto indicate periodtvariables, equation (17.20) defineswbtas an
I( 1 )variable. Next define:
ecmbt=rwt−rwbt≡wt−wbt.Under the null hypothesis that the theory is correct, the “bargained wage”wbtco-
integrates with the actual wage, henceecmbt∼I( 0 ), which is a testable hypothesis.
We can write the long-run wage equation following from bargaining theory as:
wt=mw+qt+(
1 −δ 12)(
pt−qt)+δ 13 zt−δ 15 ut−δ 16 T (^1) t+ecmbt. (17.22)
With reference to equation (17.21), a similar argument applies to price-setting. The
“firm-side” real wage can be defined as:
rw
f
t≡wt+T^1 t−q
f
t=−mq+zt,
and the difference between the actual real wage and the real wage implied by
price-setting becomes:
ecmft=rwt−rwft=wt+T (^1) t−qt−{−mq+zt}.
Hence, the implied long-run price-setting equation becomes:
qt=mq+
(
wt+T (^1) t−zt
)
−ecm
f
t, (17.23)
where ecmft∼I( 0 ) for the equation to be consistent with the modeling
assumptions.
The two cointegrating relationships (17.22) and (17.23) are not identified in gen-
eral, but in several cases of relevance, identification is unproblematic (see Bårdsen
et al., 2005, p. 81). Here we consider a case which is relevant for an aggregate model
of the supply side in an open economy. Equations (17.22) and (17.23) can then be
combined with a definition of the consumer price indexpt,
pt=( 1 −ζ)qt+ζpit+ηT (^3) t,0<ζ <1, 0 <η≤1, (17.24)
where the import price indexpitnaturally enters. The parameterζreflects the
openness of the economy.^8 Also, the size of the parameterηwill depend on how
much of the retail price basket is covered by the indirect tax-rate indexT (^3) t.By
substitution of (17.24) in (17.22), and of (17.23) in (17.24), the system can be