Gunnar Bårdsen and Ragnar Nymoen 895(OECD panel data) demonstrated that the significance ofafcan be explained by a
linear combination of better forcing variables which reside among the overiden-
tifying instruments. Their presence is revealed by the significance of the Sargan
(1964) specification test. Importantly, the re-specified models in the two studies
lend themselves directly to interpretation either as conventional Phillips curves, or
as an equilibrium-correction price equation consistent with the theory of monop-
olistic competition in the product market and a certain element of coordination in
wage-bargaining (see Sargan, 1980; Nymoen, 1991; Bårdsenet al., 2005, Chs. 4–6).
Hence, the NKPC fails to parsimoniously encompass these models.
17.4.4.2 The equilibrium correction implications of the NKPC
The original NKPC makes no reference to open economy issues. Batini, Jackson
and Nickell (2005) have shown that the main theoretical content of the NKPC
generalizes, but that consistent estimation of the parametersaf,abandbrequires
that the model is augmented by variables which explain inflation in the open
economy case. Hence, the open economy NKPC is:
pt=af
≥ 0pet+ 1 +ab
≥ 0pt− 1 +b
≥ 0st+cxt, (17.72)wherext, in most cases a vector, contains the open-economy variables, andc
denotes the corresponding coefficient vector. The change in the real import price,
(pit−pt)in our notation, is the single most important open economy augmenta-
tion of the NKPC. The results in Batini, Jackson and Nickell are, broadly speaking,
in line with GG’s and GGL’s Results 1–3 above, but, as noted, those properties
are not robust when tested against the existing UK model in Bårdsen, Fisher and
Nymoen (1998).
We follow GG and measurestby the log of the labor share:
st=ulct−qt, (17.73)whereulcdenotes unit labor costs (in logs) andqis the log of the price level on
domestic goods and services, compare section 17.2.6. Next, define the aggregate
price level as:
pt=ζqt+( 1 −ζ)pit, (17.74)
with( 1 −ζ)as the import share. If we solve forqt, insert in (17.73) and rewrite, we
obtain the following equation for the wage share:
st=−
1
γ[
pt− 1 −γulct− 1 −( 1 −γ)pit− 1]
+ulct−
1
γpt+
1 −γ
γpit. (17.75)We can then rewrite the open economy NKPC as:
pt=af
(
1 +bγ)pet+ 1 +
ab
(
1 +γb)pt− 1 −
b
(
γ+b)
[
pt− 1 −γulct− 1 −( 1 −γ)pit− 1]+
γb
(
γ+b)ulct+
b( 1 −γ)
(
γ+b)pit+
γc
(
γ+b)xt,