896 Macroeconometric Modeling for Policy
or:
pt=αfpet+ 1 +αbpt− 1 +β(ulct− 1 −pt− 1 )−β( 1 −γ)(ulct− 1 −pit− 1 ) (17.76)
+βγ ulct+β( 1 −γ)pit+ψxt,where we have definedαf,αb,βandψas new coefficients for simplification.
Equation (17.76) brings out that the NKPC implies an equilibrium-correction
price equation which is very similar to the “incumbent” model in NAM (cf.
equation (17.30) in section 17.2.6). However, there are two notable differences.
First and foremost, the forward-looking termpet+ 1 with an expected high coeffi-
cientαf. The incumbent model implicitly restricts this coefficient to zero. Second,
in the NKPC, there are parameter restrictions on the coefficients of the follow-
ing variables:ulct,pit,
(
ulct− 1 −pt− 1)
and(
ulct− 1 −pit− 1)
; in fact, they are
functions of the underlying parametersβandγ.
It follows that, for the purpose of testing the NKPC, we can start with an
equilibrium correction model with a lead in the inflation term:
pt=αfpet+ 1 +αbpt− 1 +β 1 (ulct− 1 −pt− 1 )+β 2 (ulct− 1 −pit− 1 ) (17.77)
+β 3 ulct+β 4 pit+ψxt,and test the following hypotheses:H 0 a:αf=0,H 0 b:β 3 =β 1 +β 2 andH 0 c:β 4 =−β 2.
Rejection ofH 0 atogether with non-rejection ofH 0 bandH 0 cconstitute evidence that
support the NKPC, while non-rejection ofH 0 ais telling evidence against the NKPC.
As noted above, NKPC models are usually specified with the rate of change in the
real import price as one of the elements inxt. Equation (17.77) is consistent with
that interpretation, the only caveat applies toβ 4 andHb 0 , sinceβ 4 =−β 2 no longer
follows logically from the NKPC. This is becauseβ 4 is a composite parameter also
when the NKPC is the valid model.
17.4.4.3 Testing the equilibrium-correction implications of the NKPC
Consider the hybrid NKPC of the form (17.72) where we allow for two lags of
inflation as well as three deterministic seasonals. This is because NAM makes use
of seasonally unadjusted quarterly data. The wage share variablestis treated as
an endogenous variable, but we also include electricity prices(pet) and import
prices (pit)inthextvector of exogenous variables. As already noted, inflation is
measured by the consumer price index. Instrumental variable (IV) estimation gives:
pt = 0.3659
(0.107)pt+ 1 +0.04122
(0.0228)st+0.08759
(0.0772)pt− 1+0.2676
(0.0653)pt− 2 + 0.06385
(0.00597)pet+0.04024
(0.0169)pit+constant and seasonals
IV,T =111 (1979(3) - 2007(1))
χS^2 ( 9 )=11.664[0.2329].(17.78)The results shows a significant coefficient on the forward term of the same mag-
nitude as the sum of the coefficients on the two lagged inflation rates. The wage