Gunnar Bårdsen and Ragnar Nymoen 871condition thatδ 13 =1, homogeneity of degree one with respect to productivity,
which we have seen is implied theoretically by assuming bargaining power on
the part of unions,z(t)has a zero coefficient in the expression forrexss, which
therefore is constant in the steady state. Moreover, assumingδ 13 =1, the implied
steady-state wage share,wqss(t)−z(t)=wsss, which is also a constant in steady
state.
Withδ 13 =1, the implied steady-state inflation rate therefore follows immedi-
ately: since(pit−qt)=0 in steady state, andpt=( 1 −ζ)qt+ζpit, domestic
inflation is equal to the constant steady-state rate of imported inflation:
pt=pit=π. (17.32)The above argument implicitly assumes an exogenous and, for simplicity, constant,
nominal exchange rate. For the case of an endogenous nominal exchange rate, as
with a floating exchange rate regime, it might be noted that, since:
pit=vt+p∗t,wherevtis the nominal exchange rate and the index of import prices in foreign
currency is denotedp∗t, the stability of inflation requires stability ofvt. This con-
dition can only be verified by the use of a more complete model representation of
the economy, which is what we do when we consider the steady state of a com-
plete econometric model in section 17.3.2 below. However, to anticipate events
slightly, the complete model that we document below meets the requirement in
the sense that^2 vt→0 in the long run. But our results also indicate thatπin
(17.32) is affected by the rate of change in the nominal exchange rate, which might
be non-zero in an asymptotically stable steady state.
The supply-side determined steady state has a wider relevance as well. For exam-
ple, what does the model say about the dictum that the existence of a steady-state
inflation rate requires that the rate of unemployment follows the law of the natu-
ral rate or non-accelerating inflation rate of unemployment (NAIRU)? The version
of this natural rate/NAIRU view of the supply side that fits most easily into our
framework is the one succinctly expressed by Layard, Nickell and Jackman (1994,
p. 18; emphasis added): “Only if the real wage (W/P) desired by wage-setters is the
same as that desired by price setters will inflation be stable.And, the variable that
brings about this consistency is the level of unemployment.” Translated to our concep-
tual framework, this view corresponds to settingecmbt=ecmft=0 in (17.22) and
(17.23), withδ 13 =1, and solving for the rate of unemployment that reconciles
the two desired wage shares, call ituw:^9
uw=mw+mq
−δ 15+
1 −δ 12
−δ 15(p−q)+
1 −δ 16
−δ 15T1,which can be expressed in terms of the real exchange rate(p−pi), and the two tax
rates as:
uw=−(mw+mq)
δ 15
+1 −δ 12
δ 15 ( 1 −ζ)
ζ(p−pi)+1 −δ 12
δ 15 ( 1 −ζ)
ηT 3 +1 −δ 16
−δ 15
T1. (17.33)